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

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The Canou XII is a twelve-note well temperament based on 12-et. 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 tempered to three sizes: G1, G2, and G3. Their sizes and places are shown below.

  • 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

! canou12d.scl
!
Canou XII, Flora Canou's well temperament based on 12-et, starting with D = 0
 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 major 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#