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The '''Canou XII''' is a twelve-note well temperament based on [[12edo|12-et]]. 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.  
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 ==
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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 tempered to three sizes: ''G''<sub>1</sub>, ''G''<sub>2</sub>, and ''G''<sub>3</sub>. Their sizes and places are shown below.  
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¢
* ''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
* ''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¢
* ''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>
! canou12d.scl
! canou1d.scl
!
!
Canou XII, Flora Canou's well temperament based on 12-et, starting with D = 0
Canou I, Flora Canou's first well temperament, D = 0, single circle edition
  12
  12
!
!
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{| class="wikitable center-all left-4"
{| class="wikitable center-all left-4"
|+ Sizes and occurrences of major third
|+ Sizes and occurrences of minor third
! rowspan="2" | Cents
! rowspan="2" | Cents
! colspan="2" | Error
! colspan="2" | Error
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| Bb–Db, D#–F#
| Bb–Db, D#–F#
|}
|}
[[Category:Pages with Scala files]]
[[Category:12-tone scales]]
[[Category:Tempered scales]]
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