User:FloraC/Flora's 12-note well temperament

The Canou I is a twelve-tone well temperament based on 12et. In summary, it is 1/5-comma meantone in the natural keys and close to Pythagorean tuning in the remote keys. The goal of this temperament is to add a little bit spice to the equal shades of gray without messing things up.

Definition

The commas in consideration are the Pythagorean comma ~ 23.4600¢, denoted p, and the syntonic comma ~ 21.5063¢, denoted c.

The generator is a perfect fifth, which comes in three sizes, with four 1/5-comma meantone fifths, four 12edo fifths, and four counterpyth fifths. Specifically,

• g₁ = P5 - c/5 ~ 697.6537¢

at C–G, G–D, D–A, A–E.

• g₂ = P5 - p/12 = 700¢ = 7\12

at Bb–F, F–C, E–B, B–F#.

• g₃ = P5 - p/6 + c/5 ~ 702.3463¢

at F#–C#, C#–G#/Ab, G#/Ab–Eb, Eb–Bb.

As Scala file

! canou1d.scl
!
Canou I, Flora Canou's first well temperament, D = 0, single circle edition
 12
!
 102.346257054
 195.307485892
 304.692514108
 395.307485892
 502.346257054
 600.
 697.653742946
 804.692514108
 895.307485892
 1004.692514108
 1097.653742956
 1200.

Intervals

The major third gradually shifts between 5/4 in the natural keys and 81/64 in the remote keys.

Sizes and occurrences of major third

Cents	Error		Occurrences
	from 5/4	from 81/64
390.615	+4.301	-17.205	C–E
392.961	+6.648	-14.859	F–A, G–B
395.307	+8.994	-12.513	Bb–D, D–F#
400.000	+13.686	-7.820	Eb–G, A–C#
404.693	+18.379	-3.127	Ab–C, E–G#
407.039	+20.725	-0.781	Db–F, B–D#
409.385	+23.071	+1.565	F#/Gb–A#/Bb

The minor third gradually shifts between 6/5 in the natural keys and 32/27 in the remote keys.

Sizes and occurrences of minor third

Cents	Error		Occurrences
	from 6/5	from 32/27
307.039	-8.603	+12.904	A–C, E–G
304.693	-10.949	+10.558	D–F, B–D
302.346	-13.295	+8.211	G–Bb, F#–A
297.654	-17.988	+3.519	C–Eb, C#–E
295.307	-20.334	+1.172	F–Ab, G#–B
292.961	-22.680	-1.174	Bb–Db, D#–F#