Talk:List of tone rows and series

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Possible (unordered) tone rows[edit]

Klavierstück I: (second of 36 aggregates, each = two six-tone rows).
Klavierstück I: first aggregate of 36 = two six-tone rows

Should the article contain possible orderings or unordered collections, such as for Stockhausen's Klavierstück I? If so, how should they be presented? Hyacinth (talk) 03:59, 7 December 2013 (UTC)[reply]

I don't think such things should be included. The chief difficulty, as I see it, is that some "reliable source" may identify one aggregate in such a composition as "a twelve-tone row" or even the row of the composition. It is also easy to understand a statement such as "Série initiale de Kontra-Punkte" (found on p. 120 of Michel Rigoni's 1998 book on Stockhausen) as meaning "the row of the composition", whereas in fact it never recurs in the piece, and is only the first of hundreds of completely different orderings of the aggregate, created by a very arcane permutation system and then selected more or less at random from the resulting matrices. I don't see that such aggregate orderings have any place in a discussion of tone rows. Perhaps other editors would disagree with me?—Jerome Kohl (talk) 23:19, 7 December 2013 (UTC)[reply]

There could be a "List of tropes/sets used in composition" article. Hyacinth (talk) 04:52, 8 December 2013 (UTC)[reply]

There could be. Do you think this is a good idea? Without some further specification, this could mean including 3-11 for every piece using major or minor triads.—Jerome Kohl (talk) 05:04, 8 December 2013 (UTC)[reply]

I see that at some point you removed Stockhausen's Klavierstück I from this list (which of course I applaud), but left behind the first three aggregate ordering for Klavierstück IV. Do you believe there is a substantial difference in the way Stockhausen treats the pitches in these two compositions and, if so, should not the remaining 45 aggregate orderings be given as well? Klavierstücke II and III have not yet come into the discussion but could well do, since (in my opinion, at least) the pitch treatment is very similar in all of the first four Klavierstücke—that is, "unordered" collections are used in a succession of different (unsystematic) permutations.

I would like to raise another, closely related question: that of systematic permutation. Several compositions of Ernst Krenek are presently referenced to single rows, but this does not reflect the composer's practice in many of them. Sestina, for example, regularly permutes its row in six forms, like the Lamentatio Jeremiae Prophetae, and yet the former gives only one of the six forms, whereas the latter is represented in this list by all six. Circle, Chain, and Mirror is not yet present, but has 24 regular permutations of the aggregate. In Krenek's music, this permutation principle is common, and differs from Stockhausen's practice in the early Klavierstücke only in the systematic plan by which the notes are reordered. There are also intermediate cases. For example, I notice that Stockhausen's Kreuzspiel is presently listed with but a single row, as if it were a twelve-tone composition. Just which row this is meant to be I cannot say without combing through the score (it is certainly not the first one), but in fact Kreuzspiel continually permutes the members of the aggregate similar to Krenek's method, only more aggressively and not entirely systematically. The twenty-five or so rows in Kreuzspiel are all documented in reliable sources, and so would not be difficult to add, but it is not a twelve-tone composition based on a single "referential" row—is this really what this list is meant for?

The word "rotation" is sometimes used to describe Krenek's systematic permutations, but can also be used to describe the treatment of a tone row as circular, with the presentation of different rows created by starting on different order numbers. One example of this practice is Stockhausen's Zeitmaße (or at least, parts of it). Since the different rotations of the (asymmetrical) row have twelve different interval successions, how does this fit with the way this list is conceived? Another problematic case is Boulez's Marteau. The list at the moment gives two forms of "the row", taken from the composer's sketches. However, in the actual composition Boulez uses at least two different systems to derive matrices of pitch classes, each of which has twelve rows and columns, which may be read either right-to-left, left-to-right, top-down, or bottom-up, to give 48 different rows from the série droit and 48 completely different rows from the série renversée. Since there are two different permutation schemes, one for the "Bourreaux de solitude" cycle, the other for the "Artisanat furieux" cycle (there may be a third scheme for "Bel édifice", but the literature does not seem to extend to this part of the work as yet), this means Boulez had at his disposal 192 different row forms. What is worse, all of these involve clusters of simultaneous notes, which may therefore be read in multiple orderings. Although in this case one may fall back on the observation that they are all derived from a single tone row and its inversion, the situation is not really very different from the (circular) permutational schemes in Krenek and Stockhausen, where there is no clear "referential row".—Jerome Kohl (talk) 18:09, 20 December 2013 (UTC)[reply]

Features vs. simplicity[edit]

A sample as the article was formatted is 2,465 bytes.

A version with numbered lists instead of separate cells for items such as composers is 2,393 bytes (72 byte reduction).

A version with row forms in one cell rather than four is 2230 bytes (235 byte reduction).

A version with row forms written out rather than displayed with Template:Tone row is 2,412 bytes (53 byte reduction).

Thus I have begun consolidate the row forms into one cell in order to reduce the article size, as even a small reduction of dozens or hundreds of items would add up. Hyacinth (talk) 04:11, 7 December 2013 (UTC)[reply]

The big jump in the size of the article was when the cells for row forms was added. The biggest reduction in size would be accomplished by removing the non-prime row forms. The inverse forms are the most useful for comparison (starting with zero). Hyacinth (talk) 05:05, 7 December 2013 (UTC)[reply]

Is the size of the article [recte: list] actually the (a) problem?—Jerome Kohl (talk) 09:53, 7 December 2013 (UTC)[reply]

I have split Template:Tone row into separate templates (P, R, I, RI), making it more managable, such as removing the "row form" parameter. Hyacinth (talk) 17:46, 7 December 2013 (UTC)[reply]

OK, this should help. I don't know where my long comment disappeared to, but there is still the question of how to define the Prime form. Compositionally, this usually means a particular transposition level, and some scholars attempt to reflect this when using numerical notation by fixing zero to C (an example is David Smyth's article on Stravinsky's Second Crisis, where a prime form beginning on D, for example, begins in numerical notation with 2). This list currently follows the more frequent practice of always starting from zero, which has the advantage of making it easier to compare different rows. However, it is entirely possible that composer A may use a particular row form as prime, whereas composer B treats it as the inversion, composer C as the retrograde, and so on. For this reason, many scholars treat the "most normal" form of any row as prime. Following this practice would simplify this list, to the extent that row forms would be consolidated into the range from rows beginning 0 1 2 3 … to those beginning 0 6 e … (or thereabouts). The advantage would again be ease of comparison of different rows: the "wedge" row used by Nono in Il canto sospeso, for example (0 1 e 2 t etc.), is the inversion of the "wedge" row used by Stockhausen in Carré and parts of Zeitmaße (0 e 1 t 2 etc.); the disadvantage is that it creates more distance between the model and what the composer used in the score. (The cryptogram of the SACHER hexachord, for example, is hard enough to see when all you have are numbers starting on zero, but the "most normal" form of the ordered hexachord is actually 0 2 9 t 7 1, which is the retrograde of E♭ A C B E D, used to spell Paul Sacher's surname.)—Jerome Kohl (talk) 23:08, 7 December 2013 (UTC)[reply]

It appears that above you argue that order is essential and that unordered sets should be ignored, and then you propose that order could be ignored and series given in their normal or prime form. Hyacinth (talk) 02:43, 8 December 2013 (UTC)[reply]

Then I had better clarify: I intend the expression "most normal form" to refer only to ordered sets. It is distinct in this way from the usual use of "normal form", which is used in connection with unordered sets. The question of "prime form" is a problem of several different conflicting definitions (the version a composer names as prime, the first occurrence of the row in a composition, the numerical representation of either of the former normalized to begin with zero, the "intervalically most compact" canonic form of the row, etc.). I do not particularly care which of these definitions is used, since I think each has its advantages for different purposes. The best choice here depends on what the main purpose of this list is.—Jerome Kohl (talk) 04:49, 8 December 2013 (UTC)[reply]

The method where rows begin with zero seems preferable here in that it makes rows comparable to one another without having to devote space to both the tone row's members and the distance between them. Hyacinth (talk) 05:04, 8 December 2013 (UTC)[reply]

If one purpose of this list is to compare one row form with another, then I certainly agree that setting all forms to begin with zero is the preferable method.—Jerome Kohl (talk) 08:33, 14 December 2013 (UTC)[reply]

The practice of always beginning with zero would presumably not preclude the use of the "most normal form" for ordered sets, though that seems like it would produce a lot of work. Hyacinth (talk) 03:18, 15 December 2013 (UTC)[reply]

Always beginning with zero would actually make determining "most normal form" for ordered sets a lot easier. I don't understand how this would produce more work. Cannot the templates be tweaked to automatically transpose the retrograde and retrograde-inverse forms to begin with zero? I should think this would save work, not produce more.—Jerome Kohl (talk) 04:16, 15 December 2013 (UTC)[reply]

Modifying a template would itself be work. However, if we suspect that this template is causing trouble, making it larger and more complicated probably won't help.

Presumably, article space devoted to "most normal form" should precede its use in a list. Hyacinth (talk) 00:49, 16 December 2013 (UTC)[reply]

As I said previously, I know next to nothing about templates. From (now long-out-of-date) programming experience, however, it seemed to me that it should make little difference whether the calculations for R and RI return a string beginning with zero or with the last numeral of the P form of the row. I bow to your superior knowledge in this area. Where I think work might be saved is in sorting out the various row forms, in order to determine which ones are really just canonical transformations of others.

You are correct about article space devoted to the expression "most normal form". There may be other phrases used for exactly the same thing, which would work just as well. Let me see what I can discover about this terminological question. You have already adopted one aspect of this in the way you have ordered the P forms of the rows (nominally from 0 1 2 3 4 5 etc. to 0 e t 9 8 etc.). The only remaining differences would be to regard row forms beginning with ics larger than 6 as inversions of the actual prime form, and similarly examine the retrogrades to determine whether they might begin with a smaller interval or interval sequence. Whether or not this is a desirable thing to do is another question, since it may diminish the ease of finding rows regarded by composers as the prime form in their compositions, and published that way in the literature.—Jerome Kohl (talk) 01:17, 16 December 2013 (UTC)[reply]

Tone row definition[edit]

I have split the rows into two sections, split {{Tone row}} into {{Tone row P}} (etc.), and removed all instances of {{Cite book}} (etc.). I can now edit the article without getting a timeout message. Hyacinth (talk) 04:49, 16 December 2013 (UTC)[reply]

I shall have to look at the list to see what "splitting the rows into sections" means, but I gather from the rest of what you say that it must have been an overload of {{Cite book}} and similar templates that was causing the blockage. I've always suspected that those templates were bad news (quite apart from their inability to deal with many standard bibliography elements). Now it sounds like the evidence is in. Shall I begin loading in the 3,000 or so tone rows found in Kontra-Punkte, or do we need still to discuss what actually counts as a tone row?—Jerome Kohl (talk) 06:03, 16 December 2013 (UTC)[reply]

It still takes a while for the article to accept my edits. I put the rows into one group with twelve tones and another with those of all other lengths. Hyacinth (talk) 09:30, 16 December 2013 (UTC)[reply]

Ah! I understand now. In my opinion, that is a good move, and suggests that, if the "other-than-twelve" series mount up to a sufficient number, they might be split off into their own list. That ought to help with the slow-editing problem.—Jerome Kohl (talk) 17:00, 16 December 2013 (UTC)[reply]

Normal form (music) [currently] redirects to Set (music)#Non-serial. I rewrote the tone row templates (in an effort to lower the preprocessor node count) and may now both display 10 and 11 as t and e and view the page. Hyacinth (talk) 13:01, 21 December 2013 (UTC)[reply]

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