Talk:Semitone/Archive 2

Merge

Overall, this is an excellent article. However, I am slightly troubled by the fact that "Semitone" has been redirected to "Minor Second". (A semitone is also an Augmented Unison.) It just doesn't seem accurate to include the augmented unison under the heading, Minor Second. (It's something like include "Donkeys" under "Horses"). Prof.rick 15:59, 19 August 2006 (UTC)

I completely share Prof Rick's concerns that including 'semitone' under 'minor second' is misleading and inaccurate. A semitone in music is a very important concept, only one type of which: 'the diatonic semitone', may be considered synonymous with the minor second. It also means a whole section of the article is now irrelevent as it focuses solely on the chromatic semitone, which has nothing to do with the minor second. I suggest replacing the word 'semitone' in the opening sentence with 'diatonic semitone', and relocating the information regarding the chromatic semitone, back to its own article. It seems incredible that a musical concept as important as 'semitone' wouldn't be represented by its own article. I can't believe that if we looked up 'semitone' in The Grove Dictionary of Music and Musicians or the 'Oxford Companion to Music' they would say "see minor second". (Mark - 19 Aug 06)

There is not enough material in this article to justify a split into two articles. Semitone redirects here, which means that someone looking for information on the semitone can find it in this article. The actual article name is of much less importance than having the information a person needs grouped together into a single coherent block. Someone looking for "semitone" may be looking for the minor second, or they may be looking for other information, but why make them visit two different pages when it all fits conveniently together here? Also, what musical significance does an "augmented unison" have? The only place I can think of seeing it is maybe in works of Xenakis or Bartok where they are dealing with chromatic clusters. Other than mentioning that (which I will add to the article in a moment), who uses them? - Rainwarrior 19:35, 19 August 2006 (UTC)

Augmented unisons as harmonic intervals may be few and far between but chromatic semitones as melodic intervals are extremely common and important, and have nothing to do with minor seconds. I don't see how there's not enough material to justify their own articles. Until recently both 'semitone' and 'minor second' existed independently, each of them containing a good page worth of material. ('Chromatic semitone' then crept in independently of semitone, which I didn't agree with). Anyway, enough material or not, they are different musical concepts and we should oppose merging them on those grounds just as we both opposed merging 'fifth' with 'dominant'. C'mon Rain - You know it makes sense. (Mark 19 Aug 06)

Well Dominant (music), is a bad example, as it's also a chord function. The other semitones just don't have enough material to make them worthy of their own articles. I think "minor second" has a broader meaning than you give it credit for (it is more than just a written interval, it is also a sound, to which category all of these proposed fringe articles belong). I also amended my addition to the article a few days ago, in case that wasn't noticed, but other discussions on this page suggest that we should have an "augmented unison" heading on the page into which you could pour all sorts of information bout it into. Until such a section becomes too large, there's really no reason to give it its own page. - Rainwarrior 04:08, 1 September 2006 (UTC)

Just because two terms are contained in one article on Wikipedia doesn't mean that they are the exact same thing. If this article makes that claim it is easy enough to click "edit this page" and clarify. Is anyone claiming that the subjects are not similar? I could have proposed these two articles at Wikipedia:Proposed mergers (Wikipedia:Merging_and_moving_pages#Merging), so I imagin there is some information about how those work there. Hyacinth 20:32, 19 August 2006 (UTC)

Looking over what was at Semitone before the merge:

1. "Chromatic and diatonic semitones" is here.
2. "The size of a semitone" is covered better by "Semitones in different tunings" than it was there.
3. "Rational expressions of the equal-tempered semitone" is covered, though a little more succinctly, and the bits about 3MU and Carrillo have been removed, which I think didn't belong in the article in the first place.

So, my opinion is still that the two pages did not contain enough distinct material to justify two articles, and I agree with Hyacinth's merge. "Minor second" and "semitone" are indeed distinct, but there is nothing stopping you from writing about that distinction in this article. Just because two things are distinct doesn't mean they have to have their own page. They both cover the same topic, so we should have them together. - Rainwarrior 20:35, 19 August 2006 (UTC)

Perhaps the issue is with the title, not the merge. Would it be preferrable to have the article at Semitone? Hyacinth 20:44, 19 August 2006 (UTC)

Yes, I think I'd agree with that as a compromise, Hyacinth. A minor second is one kind of semitone, whereas a semitone isn't one kind of minor second. But then again, it would be strange to have an article for every diatonic interval, but not the minor second. I hope we can have some more opinions from others. (Mark 19 August 2006)

Validity of Augmented Unison

I agree fully with a comment made by Mark (19 Aug 06), that the Augmented Unison should NOT be dealt with under the general heading, "Minor Second". (Thanks for your support, Mark!) I also want to strongly disagree with Rainwarrior's comment of 19:35, 19 Aug 2006, which suggests that the augmented unison is not of much significance, and that it's occurence is relatively rare (such as in Bartok's chromatic tone clusters). As we know, there is more than one way to notate a chromatic scale passage! It seems that most composers prefer to use accidentals which "raise" in ascending chromatic passages, and accidentals which "lower" in descending chromatic passages (with due respect for the key signature). This practice facilitates both notation and reading. Countless examples, exist, but are probably most evident in the Romantic repertoire, when chromaticism was so prevalent. (A fine example is found in the bars 35 and 36 of Chopin's "Fantaisie-Impromptu", Op. 66...just count the Augmented Unisons!)

I would also suggest that most references to common intervals are likely to be made by students of music theory. It is decidedly misleading to such students to categorize the augmented unison under the topic, "Minor Second". Prof.rick 02:16, 31 August 2006 (UTC)

Footnote for Rainwarrior: I would LOVE to see one of your chromatic scales, notated without any augmented unisons! Prof.rick 02:54, 31 August 2006 (UTC)

I was talking about harmonic augmented unisons at the time, and had since amended my statement with an edit to the article. - Rainwarrior 06:11, 31 August 2006 (UTC)

Hi, Rainwarrior. Thanks for your speedy and effective change! (Of course the augmented unison is more frequently used melodically, but since you are providing an example of it's harmonic use, why not include more familiar and/or traditional examples? It would seem only "fair" to include examples of same by Chopin (I am thinking of Ballade No. 1, Opus 23, bar 171, where Chopin splits the note-stem to form a Y-shape in order to accomodate both A natural and A flat; also, by the same composer, the Berceuse, Op. 57, bar 18, where similar stem-splitting is employed on the final treble double grace notes of the bar.) Other examples can be found in Liszt (for instance, "Etudes d'execution transcendental", No. 2, bar 62, in which a harmonic augmented unison occurs in the bass, on the second eighth of the bar). Of course, other examples can be found, even in pre-Romantic repertoire. The point is this: IF an example is provided, it should not infer that the harmonic augmented unison is basically a "modern" phenomenon, foreign to traditional harmony. However, rather that cite numberous examples, why not simply OMIT the statement about "rarity of the harmonic augmented unison" entirely? Regards, Prof.rick 18:57, 31 August 2006 (UTC)

Very confusing re-direct!

In Google, I searched "Unison". No mention of the Augmented Unison was made by Wikipedia until I found a chart at the bottom of the page, listing all "Diatonic Intervals". I clicked on "augmented unison", and found myself at the Minor Second page!!! So I went back to Google, and searched "augmented unison". Again, I found myself on the Minor Second page of Wikipedia! At the top of the page was a tiny "note": ("redirected from Chromatic Semitone"). And what on earth, I wondered, does a Chromatic Semitone have to do with a Minor Second??? Even if I had been redirected from Diatonic Semitone, I would readily accept arriving at the Minor Second, but I would still be very disappointed, since the Diatonic Semitone has little to do with the Chromatic Semitone, or Augmented Unison, which is the topic I was seeking. (Wikipedia has led me astray!) EITHER the title "Semitone" MUST be applied to this article, OR Augmented Unisons should be discussed under the Article "Unison", or (a new article), Augmented Unison, or, Chromatic Semitone. (I am certain that even the most elementary of music students would agree.) Please, Administrators, try to make some sense of this maze! Prof.rick 04:47, 31 August 2006 (UTC)

As I argued above, all of these things have a lot to do with eachother, and furthermore don't have a great deal of content individually. We don't need five tiny articles to do what one of moderate size could do. The page right now actually isn't very big... if you've got some content to add, like a bunch of "chromatic semitone" information or whatever, add that section. When the article gets too big, then maybe we should split it, but right now it's doing quite fine.

I have now bolded chromatic and diatonic semitone in the text, as is appropriate for such a redirect. - Rainwarrior 06:15, 31 August 2006 (UTC)

These changes are effective. On most Google searches on this matter, I now arrive at "Intervals", which is far more appropriate. However, from the Unison article, if I click "augmented unison" (on the chart of Diatonic Intervals at the bottom of that page), I am led to "Minor Second". It would be more effective, I believe, if this link led instead to the Intervals article (again, an augmented unison cannot and should not be classified as a minor second!). Prof.rick 19:18, 31 August 2006 (UTC)

Sorry to be so persistent on this matter, but I just searched Diatonic Semitone on Google, and was led to this Minor Second article. Fine! Then I searched Chromatic Semitone, and again was led to this Minor Second article! (Can't "chromatic semitone" simply link to "Interval"?) This INFERS that a chromatic semitone is a form of minor second, rather than an augmented unison.

I feel quite strongly, if an encyclopedia cannot provide accurate information, properly categorized, it would be better to omit the material! (NO information is preferable to MIS-information!) I do appreciate the changes that have already been made, but maybe it's possible to clear up this issue, once and for all! Prof.rick 19:39, 31 August 2006 (UTC)

I'm still with the Prof on this. This article is a source of potential confusion and misinformation. Look at the opening sentence: "A minor second, semitone, or half step is the smallest of three commonly occurring musical intervals that span two diatonic scale degrees". This, in the language of encyclopedias, means that a semitone (or half step) is another name for a minor second. Therefore, all semitones or half steps, by definition, span two diatonic scale degrees. WRONG!

Next problem - it goes on to say that other intervals that also span two diatonic scale degrees are larger by one or two chromatic semitones - chromatic semitones?? How is the reader meant to know what they are? - No explanation has been given nor link supplied. At this point a music student could wrongly infer that they're some kind of chromatic minor second, given that semitones have been (wrongly) defined as spanning two scale degrees. Hopefully, the student will stick around long enough to find the truth when it finally appears - but that's not how encyclopedias are supposed to present information.

The next problem opens the second paragraph: "If a semitone is notated as..." Wait! Suddenly the term "semitone" is being used instead of "minor second". But why? If they're the same, then good style dictates we continue to use the term that corresponds with the article's title, i.e. "minor second". If they're NOT the same, then this is a fine time to be telling us. Anyway, go on... "If a semitone is notated as two notes based on the same scale degree, with one of the notes being inflected by an accidental (e.g., C and C#),..." The SAME scale degree? - But how is that possible?, The semitone has already been defined in the opening sentence as spanning TWO scale degrees. Now, finally, it's being admitted that only diatonic semitones are the same as minor seconds, with the sentence "A diatonic semitone can also be called a minor second".

I know someone may respond with "Well if you think you can do better, then you're free to edit" - But, I'll decline that offer because doing better in my mind would mean reverting them to their own articles, in which the above quoted definitions (many of which I wrote in the first place) made complete sense within the precise contexts of their individual articles, and were linked to each other, exactly as they should be. Merge the articles if you must, but NOT at the expense of factual accuracy - this IS an encyclopedia, after all. (Mark - 31 August 2006)

Well-stated, Mark! In the coming week or two, I will be noting many other problems with this article. I agree, our editing is pointless...the major problem is Titling and Classification. I hope you check out the many problems I will refer to, and lend your support whenever you feel it is warranted. I will do likewise. Prof.rick 21:47, 31 August 2006 (UTC)

P.S. for Mark: I am also bothered by the statement, "Augmented unisons are rarely written harmonically, but they sometimes appear as part of a chromatic tone cluster such as in works of Iannis Xanakis." This almost seems like an attempt to "sweep them under the carpet", as a curiosity of post-war avant-garde composers. Therefore I have demonstrated their rightful place in traditional European harmony, by suggesting references to their use by Chopin and Liszt. (Read above, in "Validity of Augmented Unison" section.) Prof.rick 22:43, 31 August 2006 (UTC)

If you don't like the statement edit it out, you've given your reasons. I don't consider the works of the post-war avant-garde "under the carpet" (apparently you do), but you've mentioned some good examples of their earlier appearance. I think the usage I mentioned in modern music is far more thoroughgoing, as you could find hundreds of augmented unisons in a work like Eonta or Evryali, whereas in a Liszt Etude, you'll find one, if you're lucky. That's what my statement meant, really. If you've got the examples to fill out a section called "harmonic uses of the augmented unison" or whatever, add that section to the page and put the examples in. That'd be great.

Sorry, Rain...didn't mean to sweep things under the carpet. But considering the historic perspective of the entire approach to intervals, it just seemed unfair to traditional harmony! Since the frequency of use of the harmonic augmented unison is not really at issue, I think editing it out would be the best choice. Thanks Prof.rick 05:20, 1 September 2006 (UTC)

As for the complaints about the merge, I have expressed my opinion about that already. A redirect does not imply that it is a direct synonym, it only implies that it part of that subject. Interval would be a terrible place for them to redirect, as it is too broad. An augmented second, a chromatic semitone, all of these things are forms of minor seconds, not in notation, but in sound. If you think the distinction isn't clear, please make changes to the minor second article to clarify. - Rainwarrior 03:32, 1 September 2006 (UTC)

Sorry, Rainwarror, here we go again! Please consider the following:

1. Hyacinth proposed moving the article to "Semitone"

2. Mark agreed.

3. I agreed.

4. Not all intervals are identified by their "number name" in Wikipedia. I have found NO reference to the Perfect 8th, only to "Octave". Also, the "title" on augmented fourth is "Tritone", not Augmented 4th. So why MUST this article be called Minor Second, rather than Semitone?

5. Redirecting to "Interval", I agree, is terrible...but not as terrible as redirecting augmented unison / chromatic semitone to Minor Second!

6. You state that a re-direct "only implies that it is part of that subject". EXACTLY! Chromatic semitones / augmented unisons are clearly NOT part of the subject of Minor Seconds!!! (They are part of the subject of Unisons.)

7. You have stated the problem yourself: "an augmented second (?), a chromatic semitone, all of these are forms of minor seconds, not in notation, but in sound". First, I agree the chromatic and diatonic semitone sound the same (in ET), but that does NOT make them both forms of the minor second! This is what is so misleading about the title!

8. Even though two intervals may sound the same in ET, let's be careful not to underestimate the important of accurate notation! (By your reasoning, we may as well dispense with all double-sharps, double-flats, B#, Cb, E#, and Fb...and just start notating music in whatever enharmonic form seems easiest! There is an "established tradition" in musical notation. (No doubt, it is awkward at times, and we could very easily come up with a more practical system.) I may dislike it at times, but I respect it! And since this is an encyclopedia, we are here to present facts...not to change the world!

9. We can live with the merge, no prob! It's the Title which must be changed, for the sake of providing accurate information, and for the sake of students, who will no doubt be very confused by matters as they stand now. (Do I have the authority to change the Title?Prof.rick 06:11, 1 September 2006 (UTC)

PS: (Off-topic for a moment..) No, I have nothing against "avant-garde" music! In fact, I frequently compose in various electronic, microtonal idioms (which many listeners refuse to acknowledge as music!)

If the concensus is to move it to semitone, then it should be moved; but my own opinion is that this is the best place for it. If it gets moved, it's not like I'm going to move it back, but this is the talk page, and on the talk page I will leave the reasons for my own opinions. "Perfect eighth" is obscure. I don't agree that "chromatic semitones" and "augmented unisons" belong to the unison subject. (Though perhaps unison should have a little blurb about augmented unisons linking to this page.) As for the reference to ET, I wasn't saying that the minor second has only one tuning, or even only one tuning within a single tuning system. I was saying that it is an all-encompassing term that covers all of the intervals of this size. Once you get into context, into notation, into function, there are distinctions between these different types of minor seconds, but it is my opinion that they are all minor seconds. (You're point about getting rid of double sharps or whatever is not a logical consequence of my definition of minor second; it would only apply if I insisted that all of these intervals should be notated as a minor second.) I don't know if you can accomplish a page move at this point, since the Semitone article still exists. We might need an administrator to do it properly. As for avant garde music, I'm sorry I took your statement incorrectly. - Rainwarrior 17:31, 1 September 2006 (UTC)

I'm sorry, Rain but statements such as "a chromatic semitone is a form of minor second" is factually incorrect and can't be allowed to stand. They may sound the same in ET and without context, but they differ, not only in notation, but also in function and concept. Imagine telling students that a sharp in front of a note raises that note by a chromatic semitone, which is a form of minor second.

As for your statement that minor seconds have a wider meaning than I give them credit for, I can only say that they have a precisely defined meaning as any encyclopedia (apart from this one at the moment) will confirm.

Redirects, may or may not imply that two terms are synonymous, (although I think they will for many people) but, as I said earlier, opening the article with "a minor second or semitone.... spans two scale degree" most emphatically does imply they are the same thing. A minor second is a form of semitone - a semitone is NOT a form of minor second, exactly as an augmented fourth is a form of tritone, and not the other way round, a fact that has been correctly presented in that article. (Mark - 1 September 2006)

1. I don't agree that it's factually incorrect. Augmented unisons have a distinct function, but minor seconds aren't exempt from having the same function. Some composers will prefer a written minor second over an augmented unison, and the function then becomes irrelevant to the notation. Telling a student that a sharp raises a "chromatic semitone" would be strange, you would simply say "semitone". As we were discussing, "chromatic" is just a function of that semitone. The equal temperament isn't even an issue here, either, as there can be more than one type of "minor second" in a tuning system.

Whether composers call them one or the other, doesn't make them the same. Such usage masks the difference and it is the function of an encyclopedia to make clear the difference.

Yes "chromatic" is just a function of 'semitone' and the use of the word 'second' in 'minor second' indicates the diatonic function of semitone, i.e., the kind of semitone that spans TWO scale degrees. That's exactly why 'semitone' should be the article's title.

2. Cite me an encyclopedia on this, then, because I can't find the definition you're talking about.

Ok - Here is the entry for minor second from "Tonalsoft"

"Minor second - The smaller of the two diatonic intervals which encompass 2 degrees of the diatonic scale. The minor-2nd is synonymous with the diatonic semitone, and is one chromatic semitone smaller than the major-2nd. The minor-2nd always involves a change of letter-name and may or may not involve a change of accidental (as opposed to the chromatic semitone, which keeps the same letter-name but always involves a change of accidental).

3. A semitone is the same as a minor second. As I've said above, "minor second" is a broader term than how you use it.

- Rainwarrior 17:17, 1 September 2006 (UTC)

If you say that without qualification, then it means that there are minor seconds that don't span two scale degrees (despite being called seconds). If you think a minor second has a broader meaning than that already given, then that should be made clear in the definition.

On a lighter note, my search revealed a definition of minor second as "two violists playing in unison".... No I didn't find it very funny either. (Mark - September 1 2006)

I was not asserting that they are the same become some composers use them interchangeably. I am asserting that an augmented unison is often replaced with a minor second, but not the other way around. That is, the functions of a minor second encompass all functions of the augmented unison. The name "second" does indeed indicate a diatonic function, but the name "minor second" has more meaning than this, as has been my argument.

Tonalsoft is an encyclopedia of tuning. Of course from a tuning standpoint this is a good definition. My whole argument is that there are more uses of the minor second than this narrow one. I think that's the disagreement here; you can have a useful definition for minor second in terms of one thing or another (tuning, function, notation, sonic identity), but the term is used for all of them, and each category has a different scope. In terms of etymology, its name does derive from its diatonic usage, but that is only the history of the word, not its usage. In terms of function, it has all sorts of uses (which overlap use of the augmented unison). In terms of notation, there is only one thing that is a "written minor second" which is definitely not an augmented unison. In terms of the identity of the sound, a musician (unless very sensitive to the function of augmented unisons, and insistent that all possible augmented unisons be notated as such) will call either of them a minor second. It might be nice if the definition was more clear cut than this, but that is not how the word is used. The encyclopedia must cover the term as it is used, not how it should be used. - Rainwarrior 20:28, 1 September 2006 (UTC)

Well, I guess there's no more to be said then, without repeating ourselves. We seem to be coming from different perspectives. The wider meaning that you ascribe to minor seconds, I ascribe to semitones. All the various interval names that you class as types of minor second, I class as types of semitone. Maybe it's a regional thing. I'm a bit disappointed that many others didn't come in with some opinions on it, either way. Anyway, best wishes. (Mark - 02 September 2006)

Hey! You have to give people time for classes and jobs and stuff. Anyway, here's how I see it:

(Indentation reset) The major problems with the article now are the title and the lack of specific references. The title is easy to fix: in 12-equal minor second, augmented unison, semitone, and half step are all synonyms, so it doesn't matter what the title is, but in meantone and some other systems there's a big difference. Rainwarrior has given good reasons why splitting it up into two or more short articles is a bad idea, but talking about augmented unisons in an article titled minor second does seem wrong from a meantone perspective, so the best solution is to make the title something neutral like half step or semitone. Half step is already a potentially useful disambiguation page, so the logical title is Semitone.

The other issue is much more important and difficult. I totally agree with Rainwarrior's last statement that we can't just make up our own definitions for words. In order to satisfy WP:V, WP:NOR, and WP:CITE, we have to find specific sources that say which of these terms are synonyms and which refer to different intervals, and then discuss the different systems in their proper contexts. That's the only way to make this a great article. Who's with me? —Keenan Pepper 03:23, 2 September 2006 (UTC)

Thanks, Keenan! (Sorry for my little mess-up yesterday...for awhile I had better leave all matters except minor edits to more experienced uses and Administrators!)

You've raised some excellent points. We can't just make up our own definitions. You have my complete agreement on the matter. Let's define the synonyms, providing specific sources, then refer to which terms refer to different intervals, again with specific sources. I believe that once this matter is cleaned up, it could prove helpful in supplementing definitions of other intervals (e.g.: "In ET, A Perfect 5th is the sum of 7 semitones"). Then we are on our way to a great article!

I am specifically requesting support from others regarding Keenan's suggestions. Prof.rick 00:22, 6 September 2006 (UTC)

A fresh start

To: The Administrators;

This article is replete with false, misleading and irrelevant information, and requires a major overhaul. Might I suggest, the best possible place to start would be to RENAME the Article, "Semitone", as Hyancinth had suggested, 20:44, 19 August 2006, under "Merge" item. In this way, both chromatic and diatonic semitones (augmented unisons and minor seconds) could legitimately be included.

I realize that re-naming would break some links and re-directs. GREAT! Do we really want to re-direct enquiries regarding the chromatic semitone / augmented unison to "Minor second"??? (I hope not!)

Once the Article is re-named, we can argue over the details, eventually leading to an accurate and informative article, worthy of inclusion in the encyclopedia.

May I also suggest archiving sections 1 through 17, since they refer to Articles which no longer exist, and are therefore of no direct relevance. They also make the present discussion page rather awkward for editing, due to it's length.

Prof.rick 23:11, 31 August 2006 (UTC)

If you want to summon an administrator, you should use Wikipedia:Requests for administrator attention, because the only administrators who read the article talk pages are those administrators who have an interest in the particular article (Hyacinth, for instance, is an administrator.) A reason I would put forth to keep "minor second" as the article is that it is part of a series of like named articles on intervals. There should be a consistent naming for them, Unison, Minor second, Major second, Minor third, etc... You would have this sequence go Unison, Semitone, Major second? I don't think that's appropriate. - Rainwarrior 03:46, 1 September 2006 (UTC)

Thanks, Rainwarrior! As things stand now, there is an inconsistency in the naming of intervals (see my points in previous section). I sincerely appreciate the helpful leads you have provided above. I thought you were an Administrator. I am fairly new to "computerland", and a newbie at Wikipedia. Providing such help, including links, was very thoughtful of you. Prof.rick 06:47, 1 September 2006 (UTC)

Sections 1-17 contain a lot of recent posts, there's no reason to archive them just yet. Maybe when this talk page calms down a bit, but it is not a good idea to archive this thing while there's still a lot of talking going on. - Rainwarrior 03:56, 1 September 2006 (UTC)

A point well-taken! Prof.rick 06:47, 1 September 2006 (UTC)

Tip of the iceberg

The Minor second article gives us just a hint of some the glaring problems regarding Wikipedia's treatment of intervals. Here are another couple of choice examples:

1. I can find NO reference to a "Perfect eighth" (an accepted alternate name for the octave).

2. On the table of Diatonic Intervals, click "Diminished Octave". You will arrive at the Major Seventh article, which contains no reference whatsoever to the diminished 8.

Obviously, the problems we are discussing on this page, are of a nature which extends far beyond this page alone! Prof.rick 02:48, 1 September 2006 (UTC)

If Perfect eighth redirects to Octave, just edit "(also perfect eighth)" into that article's lead with "Perfect eighth redirects here" as your edit summary. Using a good edit summary or leaving an appropriate message on that article's talk page are very good ways to let the other editors know why you made the edit. Please do the same for Diminished octave and Major seventh (maybe even give a good description of the difference as well, while you're at it). - Rainwarrior 03:46, 1 September 2006 (UTC)

Apparently neither of those are redirects, if you wish to create them, create the articles containing only the text "#REDIRECT [[Article name]]". - Rainwarrior 03:58, 1 September 2006 (UTC)

Rainwarrior: Great ideas, but I think it might be worth waiting until this new Semitone page is ironed out. (Then intervals can then be defined in terms of number-of-semitones, as well as their current definitions.) Prof.rick 03:55, 6 September 2006 (UTC)

Requested move

Administrator, Hynacinth, myself (Prof.rick) and user Mark have agreed: This page should be moved/retitled Semitone(s).

REASON: This article includes the chromatic semitone/augmented unison. These intervals are clearly NOT forms of Seconds, but of Unisons. They are NOT discussed under Unisons, Augmented Unisons, nor under Chromatic Semitones.

The title "Semitone" would allow references to the above intervals to be more comprehensive and accurate, since the term "semitone" includes both augmented unisons and minor seconds, allowing both to be incorporated in one article.

In an encycopedia, NO information is preferable to MISinformation. The current situation presents MISinformation. I am particularly concerned about students who refer to Wikipedia on these matters: they are no doubt thoroughly confused!

Regards, Prof.rick 06:28, 2 September 2006 (UTC)06:24, 2 September 2006 (UTC)

Thanks, Rain! Your piece on the augmented unison was excellent. It was great to see an example of this interval used by Liszt, as I had pointed out, as well as your factual statement, that it occurs more frequently in 20th C. tone clusters. VERY COMPLETE! Now, just one issue remains: should this page be called "minor second" or "Semitone"? (Further arguements regarding the page, as presented by Mark, can be dealt with later.) Let's take this one step at a time! (We are progressing!) Prof.rick 05:25, 4 September 2006 (UTC)

Hi Mark! Your comment regarding a definition of a "minor second" as "two violinists playing unison" reminded of another cute one! "How do you get two guitar players to play in tune with each other?" Answer: "shoot one of them". But let's get real! Can you add your "approval" to the name-change I suggested (semitone, rather than minor second)? Your comments could be most helpful. Prof.rick 05:34, 4 September 2006 (UTC)

Well, as I said above, I prefer "minor second", but I won't stand in the way of a move to "semitone" if that's what everyone else wants. (I don't think it's that important.) - Rainwarrior 05:29, 4 September 2006 (UTC)

Yes - I definitely agree with changing the name to 'semitone' (Mark - 4 Sept 2006)

#REDIRECT Minor Second

#REDIRECT Minor Second

This move comes as a result of conscensus and considerable discussion. Since the article includes both minor seconds and augmented unisons, "Minor second" is an inappropriate title. The title "Semitone" includes both of these intervals. Prof.rick 22:33, 4 September 2006 (UTC)

I'm not sure you should put wikipedia code up on this page like that (I put nowiki tags around it to be safe). "Talk:Minor second" shouldn't redirect to "Minor second", and should never be a redirect at all really. Anyhow, you should read what it says at the top of this page. It's listed on the requests for moves, and has to wait five days (since September 2) before it will be moved by an administrator. There's really no reason for you to continue mentioning it here. Just wait. - Rainwarrior 22:41, 4 September 2006 (UTC)

I know, Rainwarrior. I've messed it up, trying to move it. Can you possibly help? Prof.rick 22:51, 4 September 2006 (UTC)

Need help moving

Hi Rainwarrior. I tried using the "move" button, because it would not work because the Semitone page already exists. I tried to find an Administrator to help...no luck. So I tried to make a "redirect", which I really messed up!!! Prof.rick 22:54, 4 September 2006 (UTC)

I'll wait!

The notice at the top of the discussion page says, "a few days". (But I did read a suggestion of waiting 5 days elsewhere). Also, I don't know how to do this myself! You've put in so much great material, I don't want to risk accidentally losing it. Prof.rick 23:17, 4 September 2006 (UTC)

Wait 5 days for an administrator to do it. You can't do it properly yourself because you're not an administrator. You can go and look at the entry for it at Wikipedia:Requested moves, and read about the process. Don't try to move it. Just relax. It'll happen in a few days. It was already requested on September 2nd, there's nothing for you to do about this at this point. - Rainwarrior 23:34, 4 September 2006 (UTC)

There have been no objections so far, so I'm going to make an administrative decision and move it now. Since Minor second and Semitone underwent parallel editing for a period of time, their histories cannot be merged, so I'll just swap them. —Keenan Pepper 14:39, 5 September 2006 (UTC)

Okay, it's done. The article that used to be Minor second is now here at Semitone, and the history of the article that used to be Semitone is now at Minor second, as a redirect. Try not to get confused. =P —Keenan Pepper 14:58, 5 September 2006 (UTC)

Proposal for re-organization

Synonyms: If we want to begin by referring to the use of the word "semitone", I suggest we start with ET, since it is most widely used today. It also lends itself neatly to the expression of synonyms. I believe this approach would be most useful to the average music student for an "opener". (Following this, could be categories of historic values of the semitone). Perhaps a "Table" would be convenient, contain such information as:

"In ET, the term Semitone refers equally to the following intervals, which are identical in sound (1 : 12th root of 2 ratio)."

1.Name: Augmented Unison OR Chromatic Semitone

Notation: The letter-name of a note is retained, but modified by an accidental (e.g. C to C#; Db to D; E to E#)

Inversion: diminished octave (dim. 8)

2.Name: Minor Second OR Diatonic Semitone

Notation: Two adjacent letter-names are used (modified by accidentals as necessary (e.g. C to Db; C# to D; E to F)

Inversion: major 7th

It could also be pointed out that 1. and 2. above are enharmonically equivalent, and examples could be provided (harmonic and melodic use of both categories).

(Following such a clarification of the obvious synonymic values, we could then proceed with a history of the semitone, again with proper references, and possibly, examples.) This is just a "rough draft" of an approach to the organization of this page. I would like to hear what others think about this... do you support this approach?

PS to Mark: Don't get discouraged about editing! Sometimes it can seem brutal, but you have much to offer. (Remember the Wikipedia advice to editors: BE BOLD!) Also, if you "sign in", you can just use 4 tildes to sign, and your message will be automatically date/time stamped. Prof.rick 01:50, 6 September 2006 (UTC)

ALL USERS: Please refer back to Keenan's piece, at the end of the "Very confusing re-direct" section. He has made some excellent points, and would appreciate our support. (So let's express it!) Prof.rick 03:37, 6 September 2006 (UTC)

Synonyms?

Perhaps we are all guilty of misusing the word "synonym" (yet it appears frequently on this talk page)regarding intervals which sound the same, but are named and notated differently. "Synonym" refers to words or phrases which are virtually interchangeable. E.g.: in 12-ET, augmented unisons and minor seconds "sound the same" and are "enharmonically equivalent". But since the naming and notation of these intervals are not interchangeable, they are not true synonyms. (Still, in 12-ET I would accept "half-step" and "semitone" as being synonymous, if the term "synonym" is necessarily involved.) Prof.rick 22:48, 7 September 2006 (UTC)

Well, the article doesn't use the word "synonym" at all at the moment. Of all of the terms given, only "half step" and "semitone" are truly synonymous (even outside of ET, any unqualified semitone is also a half step), the difference being mostly regional. While I have argued above that "minor second" that is a term that is very widely applied to the sound, and all intervals of this type in a general way, I don't think it is synonymous with the other terms. In some usage it may be interchangeable, but this is on a per-case basis and is not universal like "half step" and "semitone" are. - Rainwarrior 00:05, 8 September 2006 (UTC)

Well stated, Rain! I personally don't see any need to include the term "synonym", except if we refer to "half-step" and "semitone". In 12-ET, enharmonic is the preferred term. I do know that, during the period of mean-tone tuning, if an instrument were tuned to the key of C major, the black keys tended to wander in some "netherland", according to region, period, tuner, and personal taste. (I suppose this is why the semitone was so difficult to define, until it was generally agreed that certain black keys should be "sharps", and others "flats".) We are getting into a "cloudy" area of knowledge, since we shall never know fully how 12-tone instruments were tuned from region to region, from period to period. (One early source states, "as we know, the octave consists of 12 unequal semitones"). Of course, looking at the keyboard repertoire of the past furnishes some clues. I think the term "half-step" could be included, perhaps as a sub-title to semitone, if it needs to be included at all.

As you may have gathered, I believe the entire Article needs a re-write. I find the first paragraph or so quite confusing. Now that we are at the Semitone title, perhaps we can start re-writing the entire article. (Of course, parts of it are great, and worth saving.)Prof.rick 01:08, 8 September 2006 (UTC)

It hasn't always been 12 notes. For a long while it was less. Frequently it was more. Many Renaissance and Baroque keyboards had split keys for sharp and flat. - Rainwarrior 04:51, 8 September 2006 (UTC)

Yes, I'm aware of this. (Mercator's keyboard design was too cool!) But since the 12-note octave has dominated keyboards for so long, it seems that exceptions belong in a different article ("Keyboards"). Still, they might be worth mentioning as we approach the many historic forms of the semitone, particularly the "split" black keys. Prof.rick 00:08, 9 September 2006 (UTC)

What did Mercator's keyboard look like? (Something to do with 53-TET?) I didn't know that he built an instrument. Anyhow, what I am saying is that "12 note" systems don't really reflect the history of the intervals like the "minor second". A diatonic reference is the most relevant, I think. (After that, we can have lots of different takes on it.) - Rainwarrior 00:40, 9 September 2006 (UTC)

The design looked impossible to play! Nobody seems to know for sure if it was ever built. It was for an organ, so this would involve a ridiculous number of pipes (and space...and expense). Getting back to the split black keys! As we work ahead into historic definitions of the semitone, perhaps a picture of such a keyboard would make the page very attractive! (Also, possibly, musical examples for both diatonic and chromatic semitones, used both melodically and harmonically, such as the Liszt example we now have.) Prof.rick 00:47, 9 September 2006 (UTC)

Yes, Mercator's octave had 53 notes, but I'm not sure if it was 53-tet. I'm curious as to what you had in mind for a diatonic reference in defining the semitone. But obviously, even Pythagoras was at least theoretically familiar with the concept of a 12-note octave (derived from a circle of 12 fifths), hence the comma of Pythagoras. Why don't you give us your take on the basic definition. Prof.rick 01:04, 9 September 2006 (UTC)

"Pythagorean comma" doesn't mean that Pythagoras thought of it (it's just named for him), but there is very early work which is aware of the possibility of a 12 note scale (the Huainanzi comes to mind), but in western music the twelve note scale wasn't really part of the musical training for a good long while. There was Pythagorean tuning, yes, but that was not often extended to 12 tones in practice (I think Boethius might have mentioned it (can't remember), but the theorists who divided up the monochord didn't bother to make 12 divisions). I know there are more 12-note scale references to it in the Renaissance, Heinrich Glarean's book, for example, but I can't think of anything earlier than that offhand... Gregorian chant did quite alright with only 8 or 9 notes. My suggestion for a diatonic reference for the minor second is below. Ti-Do works, and Mi-Fa does as well. As for a definition of the semitone, I dunno. Make a bunch. - Rainwarrior 02:00, 9 September 2006 (UTC)

Wow! That's some research, Rain! Meanwhile, I found the following in Groves: 1. In about 40 B.C.E., King Fang of China (a music theorist) arrived at a "theory" of tonality, involving a spiral of 53 perfect fifths, which provided a very close approximation to 31 octaves. Although some of the fifths are named enharmonically (e.g. C# to Ab)(consider English translation) there are clearly 12 distinct notes for each "once around the spiral".

It is claimed that not only equal temperament, but Pythagorean theory, and Chinese music theory all stem from this work. (If you have Groves, check under "Temperaments".) 2. A painting by Memling in the Hospital of St. John at Bruges, dated 1479, depicts a keyboard exactly as we have today: the upper row of keys is arranged in groups of 2's and 3's. (See "Keyboard" in Groves). I think I can find earlier references, but it might take a day or so. Meanwhile, would you read my comments near the end of this page, regarding the use of the piano keyboard to help define semitones. (Who says how our hypothetical piano was tuned? 12-ET, one of the mean-tone temperaments, on of the well-temperaments? The variety of tuning systems lends itself well to the variety of definitions of the semitone.) Prof.rick 04:06, 9 September 2006 (UTC)

One more! In about 1440, Henri Arnault de Zwolle drew a diagram of a harpsichord. The layout of the keys is identical to a modern piano. The "white" keys are lettered in the German tradition: C, D, E, F, G, A, H, C, etc. The "black" keys are lettered, but it is difficult to read the letters. However, they are arranged in groups of 2's and 3's, with one letter per key. (12 notes per octave). Source: "Five Centuries of Keyboard Music" (John Gillespie, pub.Dover, 1965). Prof.rick 04:49, 9 September 2006 (UTC)

King Fang has an article (I actually wrote this one, hah!). His work was an extension of the 12-tone idea which was expressed in the Huainanzi (which was maybe 130BC? I forget). He was specifically trying to see if he could minimize the comma by going around the circle a few more times. The 12 tone system wasn't used by the chinese, though. It was only theoretical. In practice they were more or less pentatonic with a few bent pitches of indefinite tuning. I've never heard any theory that Pythagorean tuning stemmed from the chinese (especially because the idea of tuning in pure fifths is as old as mathematical descriptions of tuning), though in the Equal temperament article someone suggested that.

1479 sounds about right for having 12-tone keyboards. I don't have on-hand access to Grove so, I can't check what you're talking about at the moment, but basically it plays out in the musical practice. Until you had modulation being used as a means of expression, there was no need for 12 tones in the scale, and this didn't really start to happen until a while before the Renaissance (maybe around Dufay's time). It wasn't fully realized until the Baroque, though. The teaching was still in terms of diatonic 7 note scales, with accidental inflections (the Guidonian hexachord was a big part of the training... basically, sharps or flats indicated a transposition of the hexachord). This changed a lot through the Baroque (and use of modulation in the style is a big instigator here), and by the High Baroque, the 12 tone scale was quite fully worked out (even if the tuning wasn't) and a real part of the pedagogy. - Rainwarrior 04:57, 9 September 2006 (UTC)

You wrote it? Good stuff! (When I checked your dates I became suspicious of King Fang!) By the way, his 53-note cycle was copied by Mercator (so I don't think it could have been 53-tet tuning). Besides, an accurate tuning in 53-tet would probably be extremely difficult! Regarding the teaching of 7-note diatonic scales, isn't that the way we start, even today, albeit, we move on to modulation, other scale forms, etc. But we still start with "Doh, Re, Mi"! Prof.rick 05:13, 9 September 2006 (UTC)

This is something funny about 53-pythagorean and 53-TET. They're almost identical, numerically speaking. (They are completely identical, aurally speaking.) Mercator worked out the exact value of the 53-Pythagorean comma (Mercator's comma), which is very, very small, and was an advocate of 53-TET. (And William Holder after him.) So, I chose not to say that King Fang came up with 53-TET (which was a claim made on the 53-TET page for a long while, inciting me to look it up), but his discovery was certainly related. I guess this is all in the article. - Rainwarrior 23:39, 9 September 2006 (UTC)

Defining minor intervals

This is just a concept to toss around. Students are usually taught the major intervals, something like this: "If the interval is 2, 3, 6 or 7, and the upper note belongs to the major scale named by the lower note, the interval is major." Then minor intervals are introduced as being "one semitone smaller than major (by chromatic change)". If we continue to think in these simple terms, then defining a minor interval becomes difficult without reference to it's major counterpart. (Jumping back and forth between pages?)

Here is a suggestion...another, very simple way to define minor intervals. If major intervals are derived from the major scale (counting upwards from the tonic), then minor intervals can also be derived from a major scale, by counting downwards from the UPPER tonic. (The upper note of the interval is regarded as the upper tonic for this pupose.) E.g.: In the key of C major, upper C down to B is a MINOR second. (or vice versa, from B up to C).

In the key of C major, upper C down to A is a MINOR third (or vice versa, from A up to C).

etc., etc., true for all the minor intervals.

The problem with referring to "diatonic steps" could present a possible source of confusion to first-level theory students. (What does "diatonic" mean? Which kind of diatonic scale? Major? Natural minor? Harmonic minor? Melodic minor?) This seems to be an easier way to define a minor interval, in terms the average first-level theory student can readily grasp. (This assumes that a student who is studying intervals is at least familiar with major scales.)

Summary: To find major intervals, count UP from the tonic of a major scale. To find minor intervals, count DOWN from the tonic of a major scale. (Of course, once "semitone" is clearly defined, the number of semitones in a given interval can be used to supplement the definition.) I feel very strongly that we should keep the first section of the Article easily accessible to those with little knowledge of music theory, since it will probably be used primarily by first-level theory students. (Further items could be more technical in nature, and assume a greater theoretical vocabulary of the reader.)

YOUR THOUGHTS?

Now that an apt retitling of this article has been provided, thanks to Keenan, the realistic goal now must be to make it an article of particularly high quality. The title, "Semitone", I believe, expresses the extreme importance of this article, since the semitone is the "atom" of Western Music. This will require an ongoing effort, by all who care to contribute. Prof.rick 00:40, 8 September 2006 (UTC)

How about starting from how the semitone was originally defined before the merge? Then we can modify as necessary and also add information about augmented unisons. Minor seconds will also have to be given more prominence to reflect their importance.

"A semitone, or half step, is a musical interval. Since the introduction of the tuning system known as equal temperament, the semitone is defined as being exactly one twelfth of an octave. It is the smallest interval notated and played in diatonic music (i.e., most western music), corresponding to adjacent keys on a piano keyboard (white/black, black/white or white/white where there is no intermediate black key), or to adjacent frets on a guitar, for example.

Chromatic and diatonic semitones

If a semitone is notated as two notes based on the same scale degree, with one of the notes being inflected by an accidental (e.g., C and C#), then the semitone is said to be chromatic. If notated as two notes based on adjacent scale degrees, (e.g., C and Db), then the semitone is said to be diatonic. A diatonic semitone can also be called a minor second.

All diatonic intervals can be expressed as an equivalent number of semitones, e.g., an octave is as large as twelve semitones, and a perfect fifth equals seven semitones".

On another note, Prof, why are you considering how to define major or minor intervals? What do they have to do with this article? (Mark 08 Sept 2006)

They have to do with this article because this article includes the minor second. As the article stands, an example of a minor second is given by reference to the upper tonic ("Ti - Doh"). Prof.rick 00:16, 9 September 2006 (UTC)

Thanks, Mark. I had been sitting here, planning a possible approach, and you have summed it up very neatly. I can see where some minor editing could enhance your approach, but basically it seems sound and sensible. Although I was contemplating a re-write tonight, perhaps we should discuss it a little further, and ensure we are in agreement. I like your idea of introducing the chromatic semitone before the minor second. (It makes sense to approach intervals in order of ascending numbers...primes, seconds, thirds, etc.) I also like the references to the piano keyboard and the guitar...PRACTICAL applications are probably most useful to the average reader. Perhaps we should include the "shorthand" for these intervals, such as aug. 1 (I don't know how to type an augmented sign, but we seem to be moving away from these signs, and using abbreviations. (Obviously, minor second is now m2, rather than -2.)

Regarding your question about defining major and minor intervals, I am anticipating a revision of ALL articles on Intervals. The system I proposed avoids the ambiguity of "diatonic steps". (Readers can "picture" a minor second as the relation between upper tonic and leading note of a major scale, for a minor second, for example.) It requires knowledge of only the major scale. It makes it possible to describe minor intervals as something other than chromatically altered major intervals. I think this notion is already apparent in the article, with reference to "Ti-Doh" (or "Doh-Ti"). I am simply "thinking ahead", for example, to the Minor Sixth, as a downward "Do-Mi", etc. But I am flexible on this idea.

Suggestion: To make matters even simpler for the reader, under "Chromatic Semitone", instead of using the term "based on the same scale degree", why not, "using the same letter-name"?

I would also like to make reference to the enharmonic equivalence to the two namings of the semitone. I think inversions should also be mentioned.

Although prepared to begin a re-write (especially of that most confusing opening paragraph), perhaps I should wait a day or two, or hear what others have to say about this approach.

I like your ideas, and essentially agree with them. Thanks! Prof.rick 03:04, 8 September 2006 (UTC)

A few thoughts on Mark's suggested wording of the first section of the Article: 1. A separate opening statement (which does not refer to equal temperament) might be useful, such as

Oh no! They got him! - Rainwarrior 18:54, 8 September 2006 (UTC)

Nuts! After 2 hours work, the power went off...lost it!!! Prof.rick 19:03, 8 September 2006 (UTC)

As for your suggestion of alternative definitions for minor intervals, if you know what way students are "usually taught", we should not have our primary definition be distinctly different. We should have as many definitions as are needed to make the concept clear, but they should complement, clarify, or extend the common teaching of it. Counting steps down is quite unusual (though Harry Partch liked to speak of minor triads as an under-tonality), even if it is accurate. But... are you sure the usual definition of minor intervals is "a semitone smaller than the major"? I thought it was usually defined as the interval of a degree of the natural minor scale, (though sometimes the natural minor is defined as being the minor starting three steps down). - Rainwarrior 21:52, 8 September 2006 (UTC)

The only problem with referencing the natural minor scale is this: if we count upward from the tonic, we arrive at a major second! Also notice that in the existing article, the upper tonic is referenced (Ti to Doh). Prof.rick 23:53, 8 September 2006 (UTC)

Yes - counting steps down such as "doh - mi" seems an unusual/ upside down way to define intervals. I remember adding that "Ti - Doh" reference to the "minor second" article at the time because I knew everyone who's ever been to school would probably be familiar with that sound, not just musicians, students, etc. But doh down to mi! - I think we could even lose half the musicians with that one.

As for the definition of minor intervals, I've always held it to be the same as the Prof defines them, i.e. as one less than the major, and that the minor scale is called minor because of its characteristic minor third. I've heard that alternative theory that Rainwarrior mentioned disputed on the grounds that the minor scale's second degree is major, not minor. But it's got me thinking now - I'd like to know for sure. (Mark - 09 Sept 2006)

By reference to the upper tonic, I don't mean we necessarily "count downward". (I'm not think "Doh down to Mi", but "Mi up to Doh".Prof.rick 00:41, 9 September 2006 (UTC)

Right, it does start with a major second... hmm. This is the only exception though. Reference to the diatonic "ti-do" is a great definition for common practice music, though "mi-fa" as much more prevalent in the Renaissance and earlier (way back to Guido, probably earlier). As for U-Tonality, or ideas about the "undertone series", I haven't heard any argument about that addressing a major second in a minor scale, but the undertone series is disputed as something that is not naturally occuring (unlike the overtone series). - Rainwarrior 00:36, 9 September 2006 (UTC)

Wording of first section

I'll try again! First, I think a short, more inclusive definition should open the article, to avoid defining the interval in terms of ET. (It should apply to the entire article, and all forms of semitones.) There might also be a reference to the fact that the semitone in considered the most dissonant interval in western music. Such as:

Semitone

"A semitone, or half-step, is a musical interval. It is the smallest interval commonly used in western music, and is considered the most dissonant. In equal temperament all semitones are equal in size. However, in other tuning systems, such as Pythagorean tuning, just intonation, meantone temperament and well temperament, the term "semitone" refers to a family of intervals which may vary in both size and name.

Semitones in equal temperament

In equal temperament, a semitone is defined as exactly one twelfth of an octave, and corresponds to adjacent keys on a piano keyboard (white/black, black/white or white/white when there is no intermediate black key), or to adjacent frets on a guitar, for example. Any interval can be defined in terms of an appropriate number of semitones, e.g., an octave is as large as twelve semitones. Semitones may be named and notated as either diatonic or chromatic. In equal temperament the two forms are identical in sound (they are enharmonically equivalent), with a frequency ratio of ${\sqrt[{12}]{2}}$ (approximately 1.059463, or 196/185).

The diatonic semitone or minor second: If a semitone is notated using two adjacent letter-names (e.g., C and Db) the semitone is said to be diatonic. Diatonic semitones occur naturally in every major scale, between the third and fourth degree, (Mi and Fah), and between the seventh and eighth degree (Ti and Doh). Abbreviation: m2. Inversion: major seventh (M7).

The chromatic semitone or augmented unison: If a semitone is notated using just one letter-name, with one of the notes being inflected by an accidental (e.g., C and C#) the semitone is said to be chromatic. Abbreviation: aug 1. Inversion: diminished octave (dim 8)."

Following this, sections on other forms of the semitone would follow. Of course, I have not given any references yet.

OK, done! Ready to pull it apart now? Prof.rick 21:16, 8 September 2006 (UTC)

I don't think we need to have bold headings for them, separate paragraphs should suffice (there's no need to break flow with a heading if there's only a sentence or two in the section). Also, the minor second should come first before the chromatic semitone, as it is the much more common term. - Rainwarrior 21:42, 8 September 2006 (UTC)

I agree...the above is not a very attractive layout, and single, short lines can be changed to paragraphs, and fewer bold item titles.

I'm questioning the idea of putting the minor second first, only for the sake of keeping the names of the intervals in numerical order (aug 1, m2, etc.), but I don't think it's much of an issue. I am more interested in comparing ideas on the extent of content. Has any important information been excluded? Has any unnecessary information been included? There may also be ideas to improve wording.Prof.rick 23:20, 8 September 2006 (UTC)

That's coming along nicely, Prof. As for the order of chromatic and diatonic semitones, I see the logic of having the chromatic/aug unison first, but I agree with Rainwarrior that the diatonic/min 2nd section should come first. Not only because of its greater importance, but also because it will probably become larger than the chromatic semitone, because there's more can be said about it. (Mark - 09 Sept 2006)

Thanks, Mark! (Unfortunately I had to do it twice because the power went off here before I had saved!) "Majority rules!" If you and Rain want the minor second first, I'm agreeable. Also, regarding naming minor intervals downward from the upper tonic, you asked what minor intervals had to do with this article. You can find my answer above! Prof.rick 00:32, 9 September 2006 (UTC)

Keeping it simple

Probably the hardest part of this article will be the start...an inclusive, yet easily understood definition for an interval (the semitone) which comes in many sizes! Obviously "just" (mathematical) definitions are out...first, there are several forms of just and mean semitones. This would also exclude 12-tet semitones. Attempting to define diatonically is really the same problem in disguise. (Which form of the major scale are we referring to? Which notes of the scale, if the scale is non-ET?)

Another major challenge is the "KISS" principle ("Keep It Simple, Stupid"). The earlier sections of the article must be readily understood by the average first-level theory student, who will probably make the most use of the article. We should probably avoid technical jargon, or even the use of many terms which might require very much page-jumping. (The earlier sections cannot possibly be geared towards the student who is preparing his Ph.D. thesis! However, as the article progresses into the more subtle and complex aspects of the semitone, we are probably aiming at more knowledgeable readers, and can allow ourselves a more technical vocabulary.)

In a way I'd like to see an avoidance of reference to Solfege. Many students learn the sounds of intervals by reference to specific songs (in effect, to specific scale degrees). For example, for a major second, the tune "Frere Jacques" might be used (Doh - Re). But this can easily lead to a failure to recognize the same interval occurring on other notes of the scale (such as "London Bridge", which uses Soh - La).

I don't mean to complicate matters, but the initial definition of the semitone is going to be extremely important...very challenging for us, but I hope, clear as a bell to the reader. Prof.rick 01:41, 9 September 2006 (UTC)

One more idea! I see NO problem with reference to the piano keyboard in defining the semitone! Nobody has said what system was used to tune our hypothetical piano...it could be 12-ET, it could be one of the mean temperaments, it could also be a well-temperament!! The variety of tuning systems seems to coincide with the variety of sizes of semitones. (Sorry if anyone feels overloaded...I'm burnt out!) Prof.rick 02:14, 9 September 2006 (UTC)

I wouldn't use it as a primary definition, but what are you going to say about it? That every interval between adjacent piano keys is a semitone? I don't really have suggestions about definiting the semitone, except that we should probably have several, but the minor second should be primarily defined in terms of diatonic steps. The lead of the article should clarify the distinctions between terms and generally define them in a very quick and efficient manner, and better descriptions should be left to individual sections. This way the reader can figure out what they want to read and get to it without unnecessary delay. Anyhow, make edits to the page. I'll comment on or amend when I think it's appropriate. - Rainwarrior 05:11, 9 September 2006 (UTC)

Yes, I guess I am saying that every pair of adjacent piano keys is a semitone. (I am going to guess that Mark would agree.) (That does NOT mean it is necessarily a minor second or an augmented unison.) I really can't think of anything else to add to the introductory definition. Does anyone else have ideas? Meanwhile, I will try to add a diatonic reference to the minor second, but I want to know, which scale notes did you have in mind? (Maybe both Mi to Fa, AND Ti to Doh.)

For that matter, it might even be possible to use Solfege in describing the chromatic scale. For example, Doh to Di is a chromatic semitone, while Doh to Ra is a diatonic semitone. (Or is that pushing it, making it more confusing?) Prof.rick 05:27, 9 September 2006 (UTC)

Adjacent piano keys. (We don't mean white/white when there IS an intermediate black key.) To "get the picture", cover the front half of a section of keyboard with a book. Look at the back...see the pattern: white, black, white, black, white, white, black, white, black, white, black, white, white. At the back, the black and white keys are about the same width. Their "sound widths" are identical (the twelve semitones of one octave in 12-ET). Prof.rick 05:49, 9 September 2006 (UTC)

Check it over

I've done some editing to the draft, according to suggestions made by Rain and Mark. Check it over, pull it apart! (Or edit if you see fit.) Prof.rick 07:16, 9 September 2006 (UTC)

Great work Prof. I'd just like to add some points, namely:

I think instead of just solfege we should use scale degrees first as it sounds more encyclopedic and then solfege to illustrate it, such as

"Diatonic semitones occur naturally in major scales, between the third and fourth, and between the seventh and eighth degrees of the major scale, or between, mi - Fah, and ti - doh in solfege."

I think we need both because there are significant numbers of people who are familiar with one system but not the other.

I don't think we should use "Doh-Di" to illustrate chromatic semitones. It's too obscure,

Overall, I'm very impressed. (Mark - 09 September 2006)

What draft? Why is there a draft? Why don't you just edit the article? —Keenan Pepper 18:45, 9 September 2006 (UTC)

Mark, you have expressed my exact thoughts since I re-wrote the draft. It is not adequate to refer to "Mi to Fah", but first to name the third and fourth degrees of the scale. (Are you a mind-reader?) My only doubt is about the term "Solfege", which I'm afraid most readers may not understand...let me expand: they understand "Doh-Re-Mi" but are probably not aquainted with the NAME of the system! I also agree, using chromatic Solfege can be very confusing! (I'd rather avoid it.) Thanks for both your support and helpful suggestions. Prof.rick 02:59, 10 September 2006 (UTC)

Thanks, Keenan! I interpret this is as an encouragement. Hope you noticed I excluded reference to the 1/8 semitone, which could possibly tie in with "Micotonal Music", but in retrospect, is rather silly in relation to the semitone! Prof.rick 02:40, 10 September 2006 (UTC) PS: I won't just edit an article! I realize that the public leans on us as a source of factual information. I therefore consider drafts, along with highly valued talk, a prerequisite of "decent" articles!

Whoever edited, adding "between the 3rd and 4th degree" and "between the 7th and 8th degree", THANK YOU! (Was it you, Mark?)Prof.rick 03:47, 10 September 2006 (UTC)

Done?

OK, friends, I've done it! I took Keenan's advice and moved the draft to the actual article. (Lead and Equal Temperament). If you have any comments, I'd like to hear! I made another couple of edits, to clarify. I am sure Rain can make the article appear tidier; also thanks to Mark for the basic draft. (Of course, you can edit the article without saying a word, but if you do, I'd really like to know your reasons. Chances are, I'd agree.)

So we have dealt with the first part of the article. (The hardest!) Rain could add so much, not only by making it page-tidier, but by adding musical examples (like the Liszt), not to mention suggested revisions. And Mark can state things so precisely and intelligently! Let's make this the BEST article Wikipedia has ever seen!

As we move into the various forms of semitones, some pictures could also be very useful. (I will send my picture of a 1440 conventional 12-tone keyboard, if the copying is up to par; also a diagram of Mercator's proposed 53-note keyboard!) I really think some pictures and musical examples could "brighten up" this page! So far, Kennan seems to support our efforts, but Hyacinth has yet to comment! Let's make this Article a WINNER!!!Prof.rick 06:54, 10 September 2006 (UTC

The lead (the part of the article before any headings) needs to reflect the fact that half step, chromatic semitone, diatonic semitone, augmented unison, and minor second all redirect to this page. This means that each of these terms should appear in bold and be defined as briefly as possible (and then the reader should be able to find to the relevant section as quickly as possible through the table of contents). I will fix this later when I have time.

All of the links to popular tuning systems (Pythagorean, Meantone, etc.) are unnecessary. Keyboard pictures aren't really relevant to the article. We shouldn't just add pictures for the sake of having pictures. - Rainwarrior 09:28, 10 September 2006 (UTC)

Also, it is not appropriate to define diatonic and chromatic semitones in the "equal tempered" section, because they apply to all temperaments. - Rainwarrior 09:32, 10 September 2006 (UTC)

Some very good points. First I will remove the links for the various tuning systems. I agree...a picture of a keyboard is really pushing it! I'm not sure how we can define all the terms you referred to, within the lead. If we define them, then shouldn't we include inversions and abbreviations as well? If we do, it might get a little lengthy for a lead. What do think of just naming them, in bold, then create a section "Diatonic and chromatic semitones",or "Kinds of semitones" in which they are defined, and abbreviations and inversions are included? They could be named, "something like" synonyms in the lead, or else just a simple statement, "Half-tone, diatonic semitone, chromatic semitone, minor second and augmented unison redirect to this page." (If I have time today, I'll try doing one of these possibilities, understanding that it is "subject to change".

I like your table for the minor second. But I feel it would only be fair to provide one for the augmented unison as well. Also some later items can be removed...we don't need two section on semitones in equal temperament. Prof.rick 17:47, 10 September 2006 (UTC)

Hold on! IF a table is also provided for the chromatic semitone (augmented unison), then the only definitions required in the lead would pertain to the naming (note-spelling), which could be quite brief. If we approach it this way, the section to define diatonic and chromatic semitones can be brief. (The tables provide most of the pertinent information, such as alternate names, inversions, abbreviation, "just" size, etc.) I'd like to know what you think of this idea before I move the definitions out of the equal temperament section. The definitions should come before the ET section, so ET section can refer to them.Prof.rick 18:11, 10 September 2006 (UTC)

OK, Rain. I tried adding all the terms to mention in bold in the lead, with very brief definitions. I also took the liberty of changing one term in the table: under "other names" I changed semitone to "diatonic semitone". (Otherwise it seems to imly that "semitone" and "minor second" are synonymous.)Prof.rick 19:07, 10 September 2006 (UTC)

I've massaged the article a bit, moving sections around and dispersing that "in equal temperament" section throughout the other parts (the tuning, for instance, had already been covered lower down). (Cosmetic changes too, like unicode sharps and flats instead of b and #.) At present I think the history needs expansion... probably a discussion of different types of cadential chord progressions, from the occursus to the authentic to the augmented sixth. Possibly the chromaticisim of the mid-Renaissance (Gesualdo comes to mind, or maybe Lasso's experiments). This can have examples, etc. Right now, though, I'm disappointed that the "minor second" and "augmented unison" definitions repeat what's in the lead more or less word for word. There must be a more elegant way to do this. - Rainwarrior 20:13, 10 September 2006 (UTC)

There WAS a more elegant way! But we had an editing conflict and mine was lost! The lead was quite brief, and the first "Section" was about diatonic and chromatic semitones. IF there was a Table for the augmented unison, between the lead and the tables, very little would have to be said in this section. It would be followed by a section on semitones in equal temperament, then other temperaments. The layout avoided all redundancy. But, UGHHH!!! You got me again!!! Prof.rick 20:35, 10 September 2006 (UTC)

Well, the best way to make edit conflicts as painless as possible is to get the sections of the article well defined as quickly as we can (that way edits can be made to an individual section, rather than the whole article, and to not cause as much merging problems). My edits a few hours ago were intended to that effect. I don't forsee the need to add new sections to the article at this point, but each of them needs an individual cleanup. I think the lead as it is right now is okay (but am not adverse to further modification), but every other part of the article needs work. What do you think? How is the structure at the moment? I think there is right now a place for all of the topics we need to discuss, and future edits can be compartmentalized. - Rainwarrior 21:10, 10 September 2006 (UTC)

Overall, I like what you've done,very much! However, I don't think we need to mention equal temperament in much detail in the lead, but a reference to the "spelling" of diatonic and chromatic semitones would be good. As I said, if we had a table for the augmented unison, then the lead and tables covers most of what we want to say in basic definitions. It would then be possible to include both kinds of semitones in on Section, keeping it brief. (The only new material for the diatonic semitone would be references to it's occurrence in major scale; and for the chromatic scale, show only it's melodic use, with the two examples of note-spelling you have. I don't mind if the harmonic use of the chromatic semitones is dropped.) At this point we would have pretty complete definitions. Following this, the "History" section, then "Semitones is various tuning systems" (starting with 12-ET, which would be best place to mention enharmonicity, and to use the keyboard and guitar frets to enhance the definitions).

Your table on meantone semitones is excellent!

Regarding editing, I had to open the whole page, since I was copying some of the definitions material from one section to another...so that definitions is one, general section,(the first) appearing before specific tuning systems. But thanks for the tip.

Again, I want to push the idea of a table for the augmented unison. (Otherwise, the "definition" section for chromatic semitones would be rather lengthy and redundant of the table, or very short.) Otherwise, the chromatic semitone definition section could be too lengthy, when we include, size, alternate name, inversion, abbreviation, etc., but the diatonic section would be short, unless we repeat information already in the table. (This could possibly give the impression that the chromatic semitone is more important.) I think we could swallow our pride, and forego references to harmonic use of the chromatic semitone, including the Liszt excerpt. This would also justify a table for the augmented unison.

Is it possible to combine two tables into one, double table, which includes both the diatonic and chromatic semitone? I think we should try to be "fair" to both intervals, but by placing the minor second first, we have announced it's importance.

If we can finish any possible revisions of the lead, the table(s), and a "Definitions of diatonic and chromatic semitones" section (very brief), then we are really ready to look ahead at the rest of the article. Right now, the lead seems too long, we have redundant definitions, and the "augmented unison" section looks too long, if we don't want it to "steal the page".

If you let me know what you think. If you agree to to another table, I don't mind rewriting the lead, and the "definitions" section. Also, I could re-write the "equal temperment" sub-section...a good place to define semitones in terms of black/white key juxtapositions. Prof.rick 03:26, 11 September 2006 (UTC)

What are you calling a table? The infobox in the top right? I don't think we should have a second one. No other interval page has two infoboxes, and what information would be different in it? In the infobox we have now, I think it would be better to say "semitone, augmented unison" under other names, and more or less leave it at that (but if you can't stand to see them together like that, what we have now is fine). We don't really need a quick reference card for the augmented unison; none of the other augmented or diminished intervals have one (but I think it's a good thing to have one such card on each diatonic interval page). As for "stealing the page", the solution is to fill out the minor second part of the article. - Rainwarrior 15:02, 11 September 2006 (UTC)

I can't see putting the augmented unison/chromatic semitone under "other names" within the info box...they are NOT other names for the minor second. I don't you weren't too happy to see the move of minor seconds to "semitones", but it seems like the name-change hasn't achieved it's purpose if we have an info box for just the minor second. This page is unique, in that it discusses TWO intervals...therefore two info box would be well-justified. Maybe we need a consensus on this one. What about a horizontal box, with the top line for minor seconds and the second line for augmented unisons (something like that nice box for meantone semitones. Prof.rick 16:22, 11 September 2006 (UTC)

Why not put the infobox in the minor second section? Another option is to copy the tritone infobox. That box is titled 'tritone' and contains both the aug4 AND dim5. We could call our box 'semitone' and include the min2 AND aug1 (Mark - 11 September 2006)

I like this second suggestion. Call it tritone, and address both intervals in the box. - Rainwarrior 00:24, 12 September 2006 (UTC)

I like Mark's second suggestion, too. By calling the box "semitone" (I think that's what you meant, Rain, when you said "call it tritone"), and including the information for both intervals, we are conveying the importance of both. And as I said earlier, this means we can greatly reduce the section on the augmented unison. In fact, I think we would require only one section to cover both: "Diatonic and chromatic semitones", since about the only information not covered by the lead and info box will probably be the diatonic (scale) references for the diatonic semitone, and a referral to the "primarily melodic" use of the chromatic semitone. Prof.rick 01:26, 12 September 2006 (UTC)

If the new box ("Semitone") is to include complete information on both intervals, it could be a little large, and might be divided into two columns...that's why I suggested a horizontal box. Mark, the idea of ONE box, for SEMITONE also occurred to me earlier today. It seems to make the most sense, since we are dealing with 2 intervals, each with 2 names, and a variety of sizes. This makes it probably the hardest interval to deal with, but it is so important...the "atom" of western music.

I have a few ideas for condensing the lead. It would still include all the same terms in bold, but less could be said about semitones in equal temperament. Such information could be placed in the "equal temperament" or "semitones in various tuning systems" section...such matters as enharmonic equivalence, defining ET intervals in terms of number of semitones, and hopefully, referring to adjacent keys of a piano keyboard...I think that was an important reference, enhancing the definition in terms almost anyone could understand. Mark had also rephrased the reference from the original very effectively. Since I contributed both to the present writing on E.T. semitones (and now find that some of the information doesn't belong there, such as non-ET ratios) and to the the re-write (of which I made a further revision which never made it to the screen), I have to say the latter better "fits the niche" in the article.

It seems historically appropriate that we do not overemphasize equal temperament in the lead; enough to say that chromatic semitones and diatonic semitones are equal in size in 12-ET. The lead also has a little redundance of the interval names, which could be avoided. Here is a summary of what I had in mind for the total picture:

1. Lead and complete info box (can be condensed)

2. Diatonic and chromatic semitones (one section...pretty short)

3. History

4. Semitones in various tuning systems (the heart of the article,starting, of course, with 12-ET.)

5. See also

6. Sources

7. External links

Prof.rick 02:43, 12 September 2006 (UTC)

I don't think it's inappropriate to discuss its use in equal temperament in the lead. Under equal temperament, which is by far the most commonly used tuning in western music, there is no distinction between a diatonic and chromatic semitone. If we are to define them in the lead, it bears mention that they have no relevance outside of ET. - Rainwarrior 23:17, 12 September 2006 (UTC)

Bold in brackets?

For Rain, or anyone who can answer: When we use bold in the lead to establish links/re-directs, will they still work if in brackets? (Non-bold brackets, of course.) Prof.rick 03:10, 12 September 2006 (UTC)

They don't establish redirects, the redirects are established by actually creating the redirect pages themselves (see Wikipedia:Redirect). The bold link is strongly reccomended for the first use of terms that belong to the article (redirects tend to fit), and in a redirect situtation it is usually important to put the term in the lead so that someone who is redirected can quickly find what they are looking for (the eye is drawn to bold text quickly). - Rainwarrior 03:18, 12 September 2006 (UTC)

And, to answer your question, brackets don't have any functional effect, no. When I adjusted your edits to the lead, I moved "minor second" and "augmented unison" out of brackets because I think the terms belong grouped together, but also because these terms are much more common than "diatonic semitone" and "chromatic semitone". - Rainwarrior 03:22, 12 September 2006 (UTC)

Thanks, Rainwarrior. Are you going to do the new info box? Prof.rick 03:29, 12 September 2006 (UTC)

Info box

Nice work, Rain. But the inverse must be defined in both contexts (M7, dim8). Also, the terms "chromatic semitone" and "diatonic semitone" should be included. Regarding "just" intervals, again, both intervals should be included. I hate to sound petty, but this IS an article about TWO intervals, and we cannot in any sense appear to exclude one of them. (The size of the box cannot be our primary concern; we are interested in the completeness of the article.) Prof.rick 05:48, 13 September 2006 (UTC)

When I altered it, I was modelling it after the other interval boxes on the other interval pages, none of which mention enharmonic spellings of the interval. I'm not partial to either way though, it's fine as it is.

Anyhow, just intonation doesn't really have a chromatic semitone. It may have unevenly sized semitones, but their each going to be different, there's not just two of them. The "chromatic" and "diatonic" ones only come about as a result of a broken circle of fifths, as in any meantone temperament (including Pythagorean). Just intonation doesn't have that. - Rainwarrior 07:00, 13 September 2006 (UTC)

The Pythagorean example seems to be incomplete as well. (I haven't really done any work on the tuning section, other than the meantone table.) - Rainwarrior 07:02, 13 September 2006 (UTC)

As for the "Just interval" in the info box, I think only 16/15 is appropriate. That is the only one consistently present in just intonation systems. The others are just rational approximations of the ET semitone, which aren't really applicable to just intonation (I'd like to see someone tune a 17:16 by ear). - Rainwarrior 07:21, 13 September 2006 (UTC)

Rain, I have made a few changes to in the info box. My major "beef" was that the only inversion mentioned was the major seventh. So while at it, I included more alternate names, and various sizes of just semitones. The main point is, this article (and info box) has to be "fair" to BOTH intervals we call "semitone". Keep in mind, "just" is not a scale system, but an intervallic system.

But the 17:16, 18:17, and 25:24 were also used in Just. (Actually, I'd like to see anyone tune a 16:15 by ear!) I think it's important that we cover the semitone in agreement with all conventions, not just the most prominent one. I hope we all want this article to reach a happy medium of "most common" and "most complete".

I agree, the Phythagorean section is incomplete. But for that matter, we have zeroed in on just ONE of the many meantone temperaments. Also, I like your example of the Bach Prelude. (Man, this is a "touchy" page! I think, historically, tuning systems tended to allow more flexibility with the semitone than with other, more consonant intervals, since any "wolfs" would be least noticed upon the most dissonant interval!) Prof.rick 07:33, 13 September 2006 (UTC)

Regarding the fact that other info boxes don't contain information on enharmonic forms of the interval, please remember, this is a merge. We are trying to cover two distinct intervals. They are only enharmonically equivalent in ET. (Otherwise, why have "split" black keys on old keyboards?) Imagine tuners of the past: "And how would you like this note tuned today...as D# or Eb? And what about the A...would you like it in tune with the D or the E?" It's ALL crazy! Prof.rick 07:52, 13 September 2006 (UTC)

Rain, I'm begging...PLEASE leave the info box as I have left it for a day or two, 'til wel get some feedback (especially from Mark). I feel quite sure most users would prefer this "fairer" version, rather the one in which you declared the inversion of a semitone to be minor seventh. Period. (Same old problem...we are covering TWO intervals.) So please, give this one a chance. I assure, Wikipedia won't collapse! Prof.rick 09:01, 13 September 2006 (UTC)

Great work guys. A lot of good, concise information is being produced as a result of your latest intelligent debates that have ranged from lively to fiery, but never boring.

I want to comment on the point regarding the inversion of the semitone. First, I agree that we can't have just the major seventh, for reasons given by Prof Rick.

But on the other hand, including both doesn't seem any better. It seems wrong to say that the inversion of a semitone is a maj7 or dim8. They come from different 'measuring systems' for want of a better term. The true inversion of a semitone (if such a thing exists) would be 11 semitones - for which there is no term. The 'tritone' article names its inversion as a 'tritone', which is a stroke of luck for those authors. We don't have a word for 11 semitones but we shouldn't mix up the different systems. Major sevenths and diminished octaves are scale derived names and should only be referred to as inversions of other scale derived names, namely: min2 and aug1, but not 'semitone'. If nothing else it seems like bad style. I propose modifying the box and naming the inversions individually after each of the scale derived names: min2 and aug1. (Mark - 13 September 2006)

15:16 is a natural result of 5-limit just intonation (the next step after Pythagorean tuning). (4/3)/(5/4) = 16/15 (this is mi-fa), and also 15/8 (ti) is easily acquired by: (5/4) * (3/2). All of these basica intervals (3/2, 4/3, and 5/4) are tuneable by ear. 7 limit isn't that much harder to tune, but I find 11 limit takes a bit of care. 13 is a hard challenge. 17? I don't think I can do it. No just intonation system is going to use 17:16, or 18:17. As for 25:24 and 27:25, they are rather obscure 5-limit intervals. The reason I think you want them included is that they are approximations of the ET semitone. The box doesn't say "Rationalization of ET" though, it says "Just intonation". These intervals are not practical in just intonation. - Rainwarrior 16:30, 13 September 2006 (UTC)

(The rest of the infobox I said was fine.) - Rainwarrior 16:33, 13 September 2006 (UTC)

As for meantone, we have covered the three most common meantone tunings (1/4 comma, ET, and Pythagorean). Extended meantone (giving rise to split keys) does not change the size of the semitones present. There are still only two in a meantone system. I don't think we need to discuss any more meantone systems, we've got the most common ones. In well temperaments, there isn't a consistent semitone at all, and because under these temperaments all of these various semitones became enharmonic (in function if not in tuning) there really isn't a distinction made between them in theory. - Rainwarrior 17:26, 13 September 2006 (UTC)

Corrected my mistake on size of just semitone in info box. Tried to make info box more complete. Prof.rick Sept. 13, 2006

More points

Hats off, Rain! You have done a SPECTACULAR job! There are just a few very minor points I think could use a little polish. First, the musical example of chromatic semitones seems to imply that they are used chiefly to avoid triple-flats and such. But they occur very often in situations where a melody or voice) of, say 3 notes (sometimes 2)rises by semitones, and each note is harmonized. Example, in key of C: in any of the upper voices: C - C# - D; accompanying harmony: C - A7 - D (or Dm). Other examples: in any upper voice: F, F#, G; accompanying harmony: F/A - German, French or Italian sixth on Ab - G (or C/G). I realize they are being used melodically, but they correct note-spellings, and occur quite frequently. Perhaps we could have an example of one of these...they form "ideal" approached to secondary dominant sevenths, leading to the third of the V7. They are also useful in descending to the seventh. E.g., key of C: in any of the upper voices: C - B - Bb; accompanying chords: C - G - C7. In other words, chromatic semitones are used frequently in common repertoire.

When "approximations of 12-ET semitones" was originally written, Keenan provided purely mathematical examples, and I provided those based on actual musical usage. My source was Groves, so I think we have to recognize 17/16, 18/17, 25/24, 27/25 and 256/243 as something more than approximations of equal temperament.

Also, the two common just semitones should be recognized in the table.

(Picky, picky, picky, I know!!!) Please, don't regard any of this entry as a criticism of your very excellent and pains-taking work, which is "totally awesome"! Prof.rick 02:21, 14 September 2006 (UTC)

Well, secondary dominants (or augmented sixth chords) are a prime place for chromatic semitones to appear (followed by a melodic semitone). I was just trying to explain the phenomenon purely melodically. (I think even your C-B-Bflat example is also a secondary dominant, you just haven't written the next chord.) That's a good point. I'll put a sentence in there to that effect.

18/17 was used as an approximation of ET by luthiers in the Renaissance. I don't think it has any musical usage as "more than" that. 17/16 and 27/25 I haven't heard of, and their high prime numbers make them unsuitable for just intonation. 25/24 occurs between 5-limit major and minor thirds (maybe we should say that instead of two thirds and a fifth in the article?). There's a neat (irrational) approximation of the ET semitone over at Marin Mersenne. Does the Grove encyclopedia actually give an information about any of them, or does it just list them? (Tell me what article it's in, and I'll look it up next time I'm at the library.)

If you really want to say that 25/24 is Just Intonation's chromatic semitone, I won't stop you, but I don't think it's very definitive. It's very context sensitive, depending on how many notes you want in your scale, what kind of limit you want, and what kind of intervals you want to allow. In a great deal of JI music, there just isn't such thing as a "chromatic" semitone. - Rainwarrior 02:53, 14 September 2006 (UTC)

I see your point. However, because all intervals were "flexible" in Just Intonation, I think we should include more than one example, which implies the semitone was a "fixed" interval. (Obviously, with voices and strings, one can slightly inflect.) I'm not saying we need a long list, but the two examples are enough to convey the concept that the just intervals are flexible.

I'm interested in your response to my last comments regarding the used of chromatic semitones in 3-note chromatic groups, each note with a different harmony. It is extremely common, and it seems odd that we have just one example of the use of chromatic semitones, but 3 of diatonic semitones. I can give you countless examples, but for starters, look at Chopin's 3rd Ballade (Opus 47). Look at bars 11, 12, 15, 16 in the bass staff chords, for example.

Like I said, these are picky little points, and again I want to comment on your great work on the whole article. Prof.rick 03:34, 14 September 2006 (UTC)

Thanks for your reference to Mersenne. I will check it out. (I "knew" him only as a mathematician, and particularly for the "Mersenne primes".) I will have to check later tonight for the name of the Grove's article to which I referred. Prof.rick 03:43, 14 September 2006 (UTC)

Ha! First you complain that the article is unbalanced in favour of the augmented unison, now it's unbalanced in favour of the minor second! Anyhow, an applied dominants example might be nice. I don't think the Ballade example is very clear though, and besides: I've already used Chopin once. If I have time I'll find a good one and make an example tonight, but if I don't get to it, I won't be doing it for a few days (I'm going on a trip). - Rainwarrior 04:03, 14 September 2006 (UTC)

Ha, ha! You caught me! (Obviously there can be an imbalance either way!) But I'm really, really, glad you'll look for some examples tonight! (I agree, the Chopin Ballade is a weak example, and we've already used him once.) If you don't get it done tonight, it can certainly wait a few days. Have a good trip. (By the way, remind me to tell you about "Prof.rick's temperament", which deviates slightly from 12-ET, with the primary triads of the "flat" keys being somewhat smoother and mellower, and the "sharp" keys brighter and more vibrant.)

Also some "fun" experiments with 5-tet, 7-tet, 8-tet, 9-tet, and 10 tet, as well as tunings based on ratios of orbital periods of planets and their satellites!!!) I think this one addition, whoever the composer will make a nice balance between the two semitones! Thanks! Prof.rick 04:24, 14 September 2006 (UTC)

I do recall, most of the information I took from Groves was under articles on Intervals, Tuning,and Temperaments. Prof.rick 03:59, 14 September 2006 (UTC)

Excellent example, Rain!!! (I don't care for the piece itself, but it is an ideal example.) I took the liberty of reversing two sentences in this section, referring to the interval's use in chord progressions before the "chromatic scale" information, and also adding the dim.7. OK with you? Prof.rick 05:29, 14 September 2006 (UTC)

It was really hard to find a clean one. In the harmonic context usually there are just chromatic chord alterations in general, not often a clear chromatic semitone. I found a few good Aug6 examples before I managed to spot this Mendelssohn one with real dominants. There are really a lot of chromatic scales just scattered about the classical repertoire with no harmonic underpinning (in everything by Mozart or Beethoven), so I think it's good to mention the purely melodic case as well. - Rainwarrior 05:52, 14 September 2006 (UTC)

I noticed you highlighted (in red) specific notes in some of the examples. Could the same be done for the Chopin Etude, the Liszt Etude, and the Mendelssohn?Prof.rick 05:38, 14 September 2006 (UTC)

I'm not up to that at the moment. If you think it's important, you can click on the images, save them, edit them yourself, and upload the new versions over top of mine at the wikimedia commons. - Rainwarrior 05:43, 14 September 2006 (UTC)

I have added a reference to chromatic melodic passages without a harmonic underpinning. I don't want to try the highlighting myself, fearing I'll mess it up! I'll wait, if you will consider doing it, perhaps after your trip. This would add a unity to the way all of our musical examples are treated. Prof.rick 06:35, 14 September 2006 (UTC)

I have removed "other approximations" of the 12-ET semitone, for two reasons: First, we already have exact figures, as well as two excellent approximations. (Surely that's enough.) Second, most of the mentioned ratios were, in fact, not approximations of the 12-ET semitone, but expressions of semitones from other tuning systems, and therefore, if mentioned at all, don"t really belong in the ET section. (They were originally listed as "historic" semitones.)

If anyone really wants them there, it's easy enough to add them back. Prof.rick 20:18, 14 September 2006 (UTC)

In the info box, I have added "and others", on the basis that under the section, Just Intonation, it is stated, "in just intonation there are infinite possibilities for intervals than fall within the range of the semitone". Prof.rick 04:27, 16 September 2006 (UTC)

Comments to Mark

Hello Mark, and thank you for your kind comments regarding the work Rain and I have done on the Semitone. However, I feel your contributions were absolutely essential. I am sorry to see that your rewrite of the original "semitone" lead was not fully retained, and that your well-phrased references to the piano keyboard (and guitar frets) were removed from the page (apparently due to an administrator's objection.) But more importantly, you defended the augmented unison (chromatic semitone) as a distinct interval! If it hadn't been for your imput, this might have remained nothing more than a renamed article on the minor second. You have raised other points which must still be addressed, e.g., how can we really name an inversion of the semitone? (there is no name for 11 semitones). I hope you will continue to express whatever concerns you may have, regarding ANY content of the article, and feel free to edit. (Sure, someone may remove or change it...that's the cruel side of Wikipedia!) We "live with it". But you have much to contribute.) Incidentally, Rain has proven to be highly knowledgeable, extremely dedicated, very helful in Wiki technical matters, and surprisingly open to compromise (despite our many little disputes!) Although the article has progressed considerably, it is by no means finished! I have done considerable editing tonight, clarifying some technical data, technical matters, as well as minor improvements in grammar, spelling, and punctuation. But we need your imput, too! Thank you! Prof.rick 02:03, 16 September 2006 (UTC)Prof.rick 07:26, 16 September 2006 (UTC)

Minor Second: Cadences

I have expanded this section, since it previously referred to the resolution of the leading-tone in "all the important cadences", without qualification. I qualified this, explaining the use of the minor second in the plagal cadence, and in many forms of the imperfect cadence. Prof.rick 05:40, 16 September 2006 (UTC)

well temperaments

I changed "character" to "color or character", to try to better convey the concept of subtle differences in musical nuance, which are so difficult to express in words. Prof.rick 06:34, 16 September 2006 (UTC)

Changed last phrase to "beyond the capabilities of conventional notation." (rather than "beyond notation"). Prof.rick 06:49, 16 September 2006 (UTC)

The golden ratio

Rain, I find it a fascinating fact that, because meantone temperament maintains a Just major third between tonic and mediant, when the supertonic is exactly halfway between tonic and mediant, and if the M3's ratio to the tonic is 5/4, or 1.25, then the supertonic would have a value (ratio to 1) of "square root of 1.25", or app. 1.118033989. Now play the supertonic along with the tonic of the lower octave. (It will have a 0.5 value, if the original tonic is assigned a value of 1). The summation tone (Helmholtz) of the values 0.5 and 1.118033989 is 1.618033989, or the Golden Ratio, and would occur 8.33 semitones above the original tonic. (3 such intervals total almost exactly 25 semitones (almost exactly two octaves plus one semitone) each "golden" semitone having a value of 1.059445247, or approximately 99.970836 cents. [Math: 25th root of Phi cubed.] Prof.rick 04:42, 18 September 2006 (UTC)

(This was a response I'd written before you copyedited your talk page comments. I don't think there's any change of meaning though.) Well, anything with the square root of 5 should have some sort of relationship to the golden mean. In this case you're mixing meantone intervals (sqrt 5) with just ones (0.5). I suppose you're also suggesting that 36-TET would have that interval (8 1/3 semitones) pretty close. The extended meanton 31-TET completely misses it (it's tones straddle the golden interval). I've heard of a "golden meantone tuning", adjusting meantone to actually have that golden ratio. How useful is this ratio, musically speakin, though? (I've heard stories that Bartok was obsessed with it in terms of the structure of his pieces.) - Rainwarrior 06:32, 18 September 2006 (UTC)

Yes, several composers have used the golden ratio in various ways, particularly in rhythm and structure, Elliot Sharp's String Quartets being an extreme example. I don't think I "forced" any facts...first, according to your own meantone temperament chart in the article, the C to E major third is 386 cents, which is just! Also, the interval from C to D is 193 cents, and from D to E, 193 cents. (And this is something I've always understood to be true.) This being the case, my arguement holds. It has NOTHING to do with 31-TET, but would with 36 TET. I just find it interesting that the golden ratio would be produced as a summation tone in meantone temperament, and that such a close approximation of the ET semitone is achieved, as 25th root of (Phi^3). I don't suggest we include it in the article, though. It might have a place in the "Golden Ratio" article. (Yes, I had to go back and change my figures due to a miscalculation on the first run. The corrections are completed.)

The "golden semitone" is so close to the ET semitone, only a few cents difference would accumulate over the entire range of a piano keyboard...a piano could probably be tuned in "golden ET" and nobody would notice the difference. (Perhaps this is an attempt to justify equal temperament as somehow "natural", not "contrived".) I just thought it was interesting. By the way, welcome back from your trip. Prof.rick 07:18, 18 September 2006 (UTC)

I am not confusing the square root of 5 with 0.5 (I am using 0.5 strictly as a frequency ratio with 1.0.)Prof.rick 07:24, 18 September 2006 (UTC)

Accumulated difference between ET semitones and "golden semitones" would be about 2 1/2 cents over the range of a piano. Prof.rick 07:32, 18 September 2006 (UTC)

Sorry, I read "31-tet", and missed "36-tet". Of course, 36 tet would involve the golden ratio, since the latter results in 1/3 semitones. Prof.rick 07:44, 18 September 2006 (UTC)

I didn't say "confusing", I just said "mixing". You can't get this ratio (as a fundamental) by meantone alone, is all I was saying. (In terms of acoustics, every tuning system is mixed with just intonation in some way, sort of... inharmonic instruments like the gamelan or piano aside). - Rainwarrior 08:26, 18 September 2006 (UTC)

OK. I had no intention of mixing them. That was coincidence. But yes, you can get these ratios in meantone. In key of C, C to E = 5/4, or 1.25. D= sqrt 1.25. If C is 1, then one octave lower is 0.5 Also, I was referring not to a fundamental, but a summation tone. Prof.rick 11:45, 18 September 2006 (UTC)

Or maybe I should have used a different word than "just intonation"... addition is a harmonic effect, of which Just intonation can play a part... I'm thinking you could actually make this interval heard by ring modulation of a (dull timbred) meantone instrument. - Rainwarrior 08:46, 18 September 2006 (UTC)

But, as for "use"... I don't really see it as more or less significant than any other irrational number one might use in composition. Things can be based on phi, pi, the mandelbrot set, star charts, ingredients based on a soup packet, but do any of these things have any interesting and unique properties? Like as I suggested, if you used ring modulation on a meantone instrument, could you exploit this tone to do something that would be impossible with a non-golden system? - Rainwarrior 08:49, 18 September 2006 (UTC)

I see a big difference! Soup packets do not provide natural data (and Phi IS natural, although there's been too much hype about it). Phi provides an almost exact 12-ET semitone. Also, by "summation tone" I did not have "ring modulation" in mind, but summation tones. ("When two frequencies are sounded together they produce two additional frequencies, one being the difference of their frequencies, and one being the simple addition of their frequencies.") (Helmholtz)

Unfortunately, we had another "edit conflict". I had written two lengthy paragraphs, clarifying my statements. I'm not as interested in the fact that the "Golden Ratio Tone" could be produced as a summation tone, but in the possiblity of a "golden semitone". (5^2 root of Phi^3, or [Phi^3]^1/(5^2), which leads to a a semitone of 0.99970836 cents (that accumulates to about 2 1/2 cents discrepancy from 12-ET over the entire range of a piano). Could this be purely coincidence? Calculate the odds. I am suggesting that because Phi occurs so often in nature (despite the hype and misrepresentations) that this may be another "natural" system of tuning, which overcomes the conflicts of ratio-based tuning.

My understanding, and backed by Wikipedia's articles, and your meantone chart, is that the major third is true (5/4, or 1.25). The major second is exactly halfway between the first and third (C and E in the key of C). To find it take the square root of 1.25, and multiply by the frequency of the lower number, say, 1. In JI, the D would not be centered; C - D would be a major tone (9/8) and D - E a minor tone (10/9). Think of it...99.970836 cents is very close to an ET semitone!Prof.rick 11:34, 18 September 2006 (UTC)

I don't expect this little Phi formula to make it into the article...it is the result of independent research. But I would challenge you to distinguish between two tunings: one, 12-ET, the other "golden semitone" ET! But I am hoping there is some place in Wikipedia for this concept...perhaps in Golden Ratio. Prof.rick 12:00, 18 September 2006 (UTC)

Is it useful? We know about 1/4 tones, 1/8 tones, and even 1/16 tones Carrillo. But dividing a semitone in three can produce some very interesting sounds! (36-TET). EVERY audible frequency is useful in music. Prof.rick 12:05, 18 September 2006 (UTC)

Final words before sleep: You section on "History" was ideal! Plenty of useful information, but not at all excessive. You hit a nice balance, and included the most relevant material. Great stuff! Prof.rick 12:11, 18 September 2006 (UTC)

A definition for quarter-comma meantone is to tune a cycle of fifths, replacing ${\sqrt[{4}]{5}}$ for ${\frac {3}{2}}$. So, yes, the tone (two fifths) is going to be ${\frac {\sqrt {5}}{2}}$. (31-TET is a really close cyclical approximation of it as well.)

The reason I suggested ring modulation is that it makes sum and difference tones extremely audible (the original tones are actually removed). (There are ways to accomplish this without electronics, but they are difficult.) Otherwise, summation tones are, well, very subtle. It's difficult to actually produce a "+ 0.5" interval that is not already part of a harmonic series integral to that interval. In this case we want ${\frac {\sqrt {5}}{2}}+{\frac {1}{2}}$. How do you tune that audibly? With ring modulation you could actually do this fairly reliably by ear. Otherwise... you're going to have to go by beat frequencies, which you could use to tune any interval.

As far as "natural"... phi is as natural as most numbers (well, except it doesn't actually belong to the set of "natural numbers", :P), but it is not a naturally occuring acoustic phenomenon. It's application to musical tuning is arbitrary. It's interesting that ${\sqrt[{12}]{2}}\approx \left({\frac {1+{\sqrt {5}}}{2}}\right)^{\frac {3}{25}}$, sure, but I don't really see what's natural or useful about this coincidence, aurally speaking. The golden interval sounds just as out of tune as the ET minor sixth. My question is are there any practical properties which make it specifically worthwhile? ET is a a worthwhile compromise of JI because it enables enharmonic modulation to a degree that no other equal temperament can do (compare 11-TET or 13-TET). Wendy Carlos's Alpha and Beta tunings compromise the octave to approximate JI. What does a tuning related to phi do that no other tuning can do (other than produce phi)? I'm not saying it's a worthless interval, but I'm saying that it's not really any more interesting than any other number that could be arbitrarily chosen as a basis for tuning. (I'd love to be surprised with a counterargument though. It would be really interesting if there were real possibilities here.)

If you have an edit conflict, all of your stuff is still there. There are two edit windows on the page when it says "edit conflict", and the one below has everything you had just typed (from which you can copy and paste). There is no reason for you to "lose" an edit, especially on a talk page. - Rainwarrior 15:28, 18 September 2006 (UTC)

A more direct question than my challenge above might be: what advantage is there in compromising the octave (by narrowing your ET semitone) to achieve ${\varphi }^{3}$? (other than a love of phi?) - Rainwarrior 15:43, 18 September 2006 (UTC)

I see your point on regarding ring modulation...good point. The only value in the very slight compromise of the octave is that M3's and M6's would be slightly less stretched. (I have no stats on this, but I believe the stretching of M3 and M6 is more objectionable than the contracting of the m3 and m6, for most musicians. But I doubt if such a slight difference would ever be noticed. (I don't think I'd even attempt a "golden ratio" tuning by ear, but rely on a very accurate electronic tuner, the difference being so little.) Anyway, it's all just speculation, and as you stated, has no acoustic basis...and it's only natural because Phi occurs in nature so often (I didn't really mean a "natural number" in the common sense.) There is something aesthetically satisfying about the idea, but I will be the first to admit, there has been just too much "hype" and misinformation about Phi lately.

Thanks for the tips on handling an edit conflict. I'll remember that one! Prof.rick Sept 18, 2006

Again, clarifying 0.5: Alright, call your orginal C 2 instead of 1. Then the octave above it is 4, and the octave below it is 1. Therefore if the orginical C is 1, the octave above is 2, and the octave below is 0.5 (a simple 2:1 ratio). Prof.rick Sept. 18, 2006

changes to equal temperament

Rain, I assume you did the re-write of the E.T. section. I think, overall, it's great! BUT the reference to Hammond organs does not seem to be justified by the link. (The Hammond tuning is accurate within 1 cent, not 1/100 cent, and I can't find any reference to the given ratio on the link. Please, check it out.) Do you think the Phi semitone, of 0.99970836 cents is worth mentioning? Really, at an accumulated discrepancy over an 88-note piano in 12-ET of less that 2.5 cents, it's pretty accurate! It is certainly not essential..use your own judgement...I'm agreeable. I'm glad you moved the other approximations (which I had removed from ET, since they were used as semitones in the practice of other tuning systems).

Do you think you could highlight the semitones in red in ALL the musical examples of Minor Second and Augmented Unison? (I would do it myself, were I not so computer-illiterate. I'm an "old man" who has been using computers for less than 2 years. I'm also a slow learner.)

Nice work! Prof.rick 08:25, 19 September 2006 (UTC)

The "Mersenne suggestion" is more complex, and less accurate than the Golden Ratio semitone I proposed. Let's debate it! I suggest, either include the Golden Ratio semitone, or eliminate the Mersenne suggestion! My proposal, 25th root of Phi^3, seems "natural" because the Fibonacci Series converges to the Golden Ratio, and each third number of the Fib. Series is even (EVEN, odd, odd, EVEN, odd, odd) etc. So to move from one even Fib. number to the next, say from 10,946, multiply by Phi cubed (rounded) = 46,368, the next even Fib. number. (Phi cubed = (roughly) 8.33 + 8.33 + 8.33 semitones, almost exactly 25 ET semitones. Also the 25th root is so typical of Phi, being 5^2. I don't know...the Phi formula is a much closer approximation to the ET semitone than the Mersenne suggestion. As far as I know, neither has ever had a practical application. I think we need more imput on this one! (This is all "minor stuff", the biggest problem being that the Hammond link does NOT support the 196/185 ratio, unless I am blind!)

At last we are into the "finer points". This article is looking GREAT, and I can't wait to move on...say some work on Musical Notation: Ethnic (which I started to edit, but have not yet substantiated by actual notation or references...I've pretty much given up on it.) But I just couldn't tolerate the subtle anti-African bias which seemed to be there, along with many misspellings and poor grammar, and the fact that other musics of the world were not even mentioned. More successfully, I also edited "Octatonic Scale" with a much earlier example than had been quoted (it's in Liszt's Transendental Etude, Feux Follets). Also some of the wording on other INTERVALS could use a little clean-up. We should also do something about the Tristan chord, which had been used by Liszt 10 years before Wagner used it! Summary of Semitone: Bravo, Rain! Prof.rick 10:03, 19 September 2006 (UT)

My criteria for inclusion of approximations of the ET semitone had nothing to do with their accuracy. I wanted to include any that were actually used historically. 18/17 was indeed well used. Mersenne's, according to Marin Mersenne) was useful because it was constructible. (Mersenne also knew how to calculate the actual ET value with arbitrary precision using logarithms.) The Hammond Organ one is listed on the linked page, though there seem to be others (some accurate to 1 cent, some more, like this one... maybe this one was the most accurate? who added it initially?). I picked it up because it had been on the page before the merge. If you really think it doesn't belong, I could understand its removal, but I'd like to hear from whomever added it to the page initially if possible.

The 25th root of Phi cubed doesn't seem to have any historical significance. It is not rational, it is not constructible (phi is, but not its 25th root), and its calculation is no simpler. Frankly I don't think it's even much of a coincidence. If you try enough exponential combinations of any of the irrational numbers, eventually you'll get one that's close to whatever value you need. How about the 59th root of Pi cubed, or the 69th root of e₄ instead?

As for red notes, I don't think the other examples can actually be done with just red notes, and some of them I don't want to. The Chopin might have use elsewhere (like on the Chopin Etudes page). The Mendelssohn one can't have the augmented unisons indicated by just red notes because they would overlap (and the description describes it clearly). I don't think these examples really need red notes, as the description I think is quite clear. With the bach one I added red notes because it would have taken more words to describe exactly where the minor second was. Same with the cadence example. Anyhow, if you think it's important, click on the image, go to the high resolution verison of it, save it, edit it, then upload it (with a new filename, like Mendelssohn_dominants_version_2.png) and replace the name on this page. I don't want to do it though because it is not my opinion that it will help the other examples. - Rainwarrior 15:47, 19 September 2006 (UTC)

I accept your reasoning regarding inclusion of the Mersenne semitone. I thought the phi approach was interesting, but I'm not offended if it's not included. (I agree, we could manipulate pi or e to arrive at some sort of approximation of "what you need".) Too bad about the red notes, but now that you've explained the situation, I'm satisfied as it stands.

It was Keenan Pepper who introduced the 196/185 ratio, and the link to Hammond organ stats. At the link, look at the table, "Relative ratios for each note..."; look at the right-hand column for C, "cents error from 12-edo". First, you notice the fractions vary from note to note. Keep in mind, the 196/185 ratio is accurate within less than 1/100 of one cent. Also, to view this table correctly, we must consider that it takes 2 notes to make a semitone! For example, while C# is 1/9 cents flat of the ET semitone, D is 7/9 cents sharp. Therefore the actual semitone, C# to D, turns out to be 8/9 of one cent sharp. I checked the B and C, given as "0 cents error", and took the given fraction 2975/2808, and it turns out to be 1.05472934 (slightly sharp of the ET semitone). The 196/185 ratio turns out to be 1.059459459 (slightly flat of the ET semitone). (I still can't find the 196/185 ratio anywhere in the link, although it is an excellent approximation in itself.) I objected, because it seemed to me to imply that this was a "standard" in Hammond tuning. I also objected to the link because the discrepancies of Hammond tone-wheel semitones from those of 12-ET are not the result of musical intention, but of the mechanical limitations of the tone-wheel system. (If you can find the 196/185 ratio in the table, please tell me where!) Prof.rick Sept. 19, 2006.

Sorry, Rain! I found the 196/185 on the Hammond link, but only between F# and G. If we include it, I feel strongly that we should indicate it occurs ONLY between F# and G, both of which are about 3/5 of one cent sharp of true 12-ET values in relation to C, and that most of Hammond semitones are far less accurate. (Also, you stated you were not interested in degree of accuracy but in actual usage. Then WHY make reference to only one of the various Hammond semitones? Were the F#'s and G's used more often than the other notes? Prof.rick 03:58, 20 September 2006 (UTC)

I don't really want to defend the hammond organ tuning, as I myself don't see any reason why it's particularly notable. I merely restored it because it had been on the page before, and assumed there was good reason for that. - Rainwarrior 04:33, 20 September 2006 (UTC)

You stated, "My criteria for inclusion of approximations of the ET semitone had nothing to do with their accuracy. I wanted to include any that were actually used historically." Then shouldn't we include all the Hammond tone-wheel semitones? Prof.rick 04:30, 20 September 2006 (UTC)

Good! I'll be HAPPY to see the Hammond reference go, but must we throw out the baby with the bathwater? Why not change the criteria to include this very accurate approximation of 196/185, without reference to use? Or would you prefer to avoid such an inconsistency in the section? I dunno. Prof.rick 04:44, 20 September 2006 (UTC)

The Mersenne semitone existed in theory. Do you know if was actually ever used (not just constructable)? Prof.rick 04:50, 20 September 2006 (UTC)

I don't see any point to including random "good" approximations of the ET semitone, as they are in infinite supply. I could write a computer program to generate a comprehensive list if you like, but there will be a lot of them.

Mersenne's writings on harmony were quite widely known (William Holder, for instance, makes mention of him in his treatise on harmony). I expect his suggestion would have been used; I have seen historical lute fretting diagrams with complicated compass-and-straightedge diagrams on them, so it doesn't seem like it would be out of place... but if we're going to be discussing distinctions between 1.1 and 0.4 cents, I think it's acceptable even if it was only a "theoretical" construction. At any rate, the influence of Mersenne on tuning theory was great. - Rainwarrior 05:17, 20 September 2006 (UTC)

Very useful information. I was unaware of the lute diagram. Mersenne stays! You are right...there is an endless supply of purely mathematical approximations. So it seems the "right move" is to "remove" both 196/185 along with the hammond reference. Agree?Prof.rick 05:34, 20 September 2006 (UTC)