User:Annielogue/Sandbox3

Venez à la leçon , jeunesse vive et folle ,

Esope vous appelle à sa riante école ;

Les bétes autrefois parlaient mieux que les gens,

Et le siècle n'a point de si doctes régens.

Come to the lesson, youth lively and wild,

Aesop calls you to his cheerful school

The beasts once spoke better than people,

Our time lacks such learned teachers.

Plato fables: The Fox and the Sick Lion in First Alcibiades , Pleasure and Pain (Perry 445) in Phaedo.

Aesop in Bayeux

Aristotle fables: "The Horse and the Stag" and "The Fox and the Hedgehog" in the Rhetoric, "Aesop at the Shipyard" in the Meteorology , "Lions and Hares" in Politics III

So the tales were told ages before Aesop; and asses under lions' manes roared in Hebrew; and sly foxes flattered in Etruscan; and wolves in sheep's clothing gnashed their teeth in Sanskrit no doubt.

Thackeray, The Newcomes.

Aesop Fables. The animals on the borders of the Bayeux Tapestry have been identified as:

• The fox and the crow
• The wolf and the lamb
• The wolf and the crane
• The wolf and the kid

Nichomachus

While thus engaged, he walked by a smithy, and by Providence, heard the hammers beating out iron on the anvil and giving off in combination, sounds which were most harmonious with one another, except for one combination.

He recognized in these sounds the consonance of the octave, the fifth and the fourth. But he perceived that the interval between the fourth and the fifth was dissonant in itself but was otherwise complementary to the greater of these two consonances.

Elated, therefore, since it was as if his purpose was being divinely accomplished, he ran into the smithy and found by various experiments that the difference of sound arose from the weight of the hammers, but not from the force of the blows, nor from the shape of the hammers, nor from the alteration of the iron being forged. After carefully examining the weights of the hammers and their impacts, which were identical, he went home .

He planted a single stake diagonally in the walls, in order that no difference might arise in this procedure, in short, that no variation might be detected from the use of several stakes, each with its own peculiar properties. From this stake, he suspended four strings of the same material and made of an equal number of strands, equal in thickness and of equal torsion. He then attached a weight to the bottom of each string, having suspended each by each in succession. When he arranged that the lengths of the strings should be exactly equal, he alternately struck two strings simultaneously and found the aforementioned consonances, a different consonance being produced by a different pair of strings .

Other instruments

Four chisels with different lengths (12, 9, 8, and 6 units) and the same cross-sectional area.
Soundfiles of chisels with pitches that are in integer ratios to one another:

Tone (12 units long)

Fourth (9 units long)

Fifth (8 units long)

Octave (6 units long)

Chisel with non-integer ratio to the root note (tritone = ½ octave):

Tritone (8,485 units long)

The most detailed classical account is given by Boethus:

"For some time Pythagoras was seeking a way to acquire, through reason, full and accurate knowledge of the criteria for consonances. In the meantime, by a kind of divine will, while passing the workshop of blacksmiths, he overheard the beating of hammers somehow emit a single consonance from differing sounds. Thus in the presence of what he had long sought, he approached the activity spellbound. Reflecting for a time, he decided that the strength of the men hammering caused the diversity of sounds, and in order to prove this more clearly, he commanded them to exchange hammers among themselves. But the property of sounds did not rest in the muscles of the men; rather, it followed the exchanged hammers. When he observed this, he examined the weight of the hammers. There happened to be five hammers, and those that sounded together the consonance of the octave were found to be double in weight. Pythagoras determined further that the one which weighed twice the second was in the ratio 4:3 with another, with which it sounded a fourth. Then he found that the same double of the second formed the ratio 3:2 with still another, and that it joined with it in the consonance of the fifth."

Boethus has Pythagoras return home to recreate what he has observed in the forge using a number of different set-ups, such as water-filled glasses, pipes and vases:

Upon returning home, Pythagoras weighed carefully by means of different observations whether the complete theory of consonances might consist of these ratios. First, he attached corresponding weights to strings and discerned by ear their consonances; then, he applied the double and mean and fitted other ratios to lengths of pipes. He came to enjoy a most complete assurance through the various experiments. By way of measurement, he poured ladles of corresponding weights into glasses, and he struck these glasses - set in order according to various weights - with a rod of copper or iron, and he was glad to have found nothing at variance. Thus led, he turned to length and thickness of strings, that he might test further.

Metal rod of length l and the cross-sectional area A

Metal rods such as the chisels of stone masons or metal wedges used to break stone could have produced harmonies such as Pythagoras attributed to the hammers, namely that the pitch of the tools would be in proportion to their weight. If the metal tools, ignoring their tapered cutting edges, all have the same uniform cross-sectional area A , but different lengths l their weight would be proportional to the length and thus also to the pitch when struck (sound examples, see in the box on the right).