[lilly]

I'm looking for some music examples of compositions written in 53 part equal temperment. Someone have something to suggest?

[experimentalangel]

I don't have any music songs to suggest, but apparently the 53 note equal temperment system is a more "pure" system thatn the 12 note one....

Let's compare the twelve-tone equal-tempered scale to some other scales.

All equal-tempered scales with 14 notes or fewer (except the twelve-tone equal-tempered scale) contain at most only two of the six basic intervals within one percent.
Several equal-tempered scales with between 15 and 30 notes (notably the 19-tone and 24-tone scales) contain all six basic intervals, but in none of these scales are the intervals more nearly pure than in the twelve-tone equal-tempered scale.
The 31-tone equal-tempered scale has all six basic intervals to a good approximation, some with better accuracy than the twelve-tone scale, but the most important fifth (3/2) interval is less accurate than in the twelve-tone scale (218/31=1.495). Some Indonesian music actually uses a 31-tone equal-tempered scale.
The 41-tone equal-tempered scale is the first with a better fifth (3/2) interval than the twelve-tone scale (224/41=1.5004).
The 53-tone equal-tempered scale has all six basic intervals with a better accuracy than the twelve-tone scale (231/53=1.49994).

[broken]

Yeah, the 53 tone temperment is pretty much the theorists wet dream. Too bad its too impractical for any real instruments to be based upon.

[Experimental music fan]

on a historical note..............

In music, 53 equal temperament, called 53-tet, 53-edo, or 53-et, is the scale derived by dividing the octave into fifty-three equally large steps. Each step represents a frequency ratio of 21/53, or 22.6415 cents, an interval sometimes called the Holdrian comma.

Theoretical interest in this division goes back to antiquity. Jing Fang (also spelled Ching Fang and King Fang), a Chinese music theorist, observed around 40 BC that the fifths very nearly close into a circle of 53 fifths, making up 31 octaves. The same obsevation was eventually made in the west by the mathematician and music theorist Nicholas Mercator. This is due to one of the most salient features of this temperament, which is that the fifths are very nearly the pure 3/2 ratio of just intonation, being a mere 0.07 cents flat. While it does not represent major thirds to anything like this degree of accuracy, major thirds are still only 1.4 cents flat; consequently, 53 equal temperament represents the intervals of 5-limit just intonation with great accuracy. This fact seems to have first been published by the seventeenth century music theorist William Holder, though Isaac Newton's unpublished manuscripts show he was aware of it also.

[random generator]

An interesting side not of this temperment is that standard musical notation can be used to denote 53 equal temperament; however, since it is a Pythagorean system, with nearly pure fifths, major and minor triads cannot be spelled in the same manner as in a meantone tuning. Instead, the major triads are chords like C-Fb-G, where the major third is a diminished fourth; this is the defining characteristic of schismatic temperament. Likewise, the minor triads are chords like C-D#-G. In 53-et the dominant seventh chord would be spelled C-Fb-G-Bb, but the otonal tetrad is C-Fb-G-Cbb, and C-Fb-G-A# is still another seventh chord. The utonal tetrad, the inversion of the otonal tetrad, is spelled C-D#-G-Gx.

Further septimal chords are the diminished triad, having the two forms C-D#-Gb and C-Fbb-Gb, the subminor triad, C-Fbb-G, the supermajor triad C-Dx-G, and corresponding tetrads C-Fbb-G-Bbb and C-Dx-G-A#. Since 53-et tempers out the septimal kleisma, the septimal kleisma augmented triad C-Fb-Bbb in its various inversions is also a chord of the system. So is the orwell tetrad, C-Fb-Dxx-Gx in its various inversions.