History
Theoretical interest in this division goes back to antiquity. Ching Fang (78–37 BC), a Chinese music theorist, observed that a series of 53 just fifths is very nearly equal to 31 octaves . He calculated this difference with six-digit accuracy to be . Later the same observation was made by the mathematician and music theorist Nicholas Mercator (c. 1620–1687), who calculated this value precisely as, which is known as Mercator's comma. Mercator's comma is of such small value to begin with (≈ 3.615 cents), but 53 equal temperament flattens each fifth by only 1/53 of that comma (≈ 0.0682 cent ≈ 1/315 syntonic comma). Thus, 53 equal temperament is for all practical purposes equivalent to an extended Pythagorean tuning.
After Mercator, William Holder published a treatise in 1694 which pointed out that 53 equal temperament also very closely approximates the just major third (to within 1.4 cents), and consequently 53 equal temperament accommodates the intervals of 5-limit just intonation very well. This property of 53-TET may have been known earlier; Isaac Newton's unpublished manuscripts suggest that he had been aware of it as early as 1664–65.
Read more about this topic: 53 Equal Temperament
Famous quotes containing the word history:
“No one is ahead of his time, it is only that the particular variety of creating his time is the one that his contemporaries who are also creating their own time refuse to accept.... For a very long time everybody refuses and then almost without a pause almost everybody accepts. In the history of the refused in the arts and literature the rapidity of the change is always startling.”
—Gertrude Stein (18741946)
“If usually the present age is no very long time, still, at our pleasure, or in the service of some such unity of meaning as the history of civilization, or the study of geology, may suggest, we may conceive the present as extending over many centuries, or over a hundred thousand years.”
—Josiah Royce (18551916)
“America is, therefore the land of the future, where, in the ages that lie before us, the burden of the Worlds history shall reveal itself. It is a land of desire for all those who are weary of the historical lumber-room of Old Europe.”
—Georg Wilhelm Friedrich Hegel (17701831)