User:FloraC/Flora's 12-note well temperament: Difference between revisions
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The '''Canou | The '''Canou I''' is a twelve-tone well temperament based on [[12edo|12et]]. In summary, it is [[1/5 syntonic comma meantone|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 [https://youtu.be/F9Zv6MGdh7Y shades of gray] without messing things up. | ||
== Definition == | == Definition == | ||
| Line 5: | Line 5: | ||
The commas in consideration are the [[Pythagorean comma]] ~ 23.4600¢, denoted ''p'', and the [[syntonic comma]] ~ 21.5063¢, denoted ''c''. | 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 | 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, | ||
* '' | * ''g''<sub>1</sub> = P5 - ''c''/5 ~ 697.6537¢ | ||
: at C–G, G–D, D–A, A–E. | : at C–G, G–D, D–A, A–E. | ||
* '' | * ''g''<sub>2</sub> = P5 - ''p''/12 = 700¢ = 7\12 | ||
: at Bb–F, F–C, E–B, B–F#. | : at Bb–F, F–C, E–B, B–F#. | ||
* '' | * ''g''<sub>3</sub> = P5 - ''p''/6 + ''c''/5 ~ 702.3463¢ | ||
: at F#–C#, C#–G#/Ab, G#/Ab–Eb, Eb–Bb. | : at F#–C#, C#–G#/Ab, G#/Ab–Eb, Eb–Bb. | ||
=== As Scala file === | === As Scala file === | ||
<pre> | <pre> | ||
! | ! canou1d.scl | ||
! | ! | ||
Canou | Canou I, Flora Canou's first well temperament, D = 0, single circle edition | ||
12 | 12 | ||
! | ! | ||
| Line 88: | Line 88: | ||
{| class="wikitable center-all left-4" | {| class="wikitable center-all left-4" | ||
|+ Sizes and occurrences of | |+ Sizes and occurrences of minor third | ||
! rowspan="2" | Cents | ! rowspan="2" | Cents | ||
! colspan="2" | Error | ! colspan="2" | Error | ||
| Line 126: | Line 126: | ||
| Bb–Db, D#–F# | | Bb–Db, D#–F# | ||
|} | |} | ||
[[Category:Pages with Scala files]] | |||
[[Category:12-tone scales]] | |||
[[Category:Tempered scales]] | |||
Latest revision as of 12:26, 2 January 2024
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.
| 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.
| 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# |