Canou scales: Difference between revisions

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This page lists scales of [[Canou family|canou temperament]], the rank-3 temperament that tempers out the [[canousma]], 4802000/4782969 = {{monzo|4 -14 3 4}}.  
This page lists scales of [[Canou family #Canou|canou temperament]], the rank-3 temperament that tempers out the [[canousma]], 4802000/4782969 = {{monzo|4 -14 3 4}}.  


== Canou[9] ==
== Canou[9] ==
A 9-note Fokker block for canou temperament.


sLsLLsLsM
sLsLLsLsM
Line 7: Line 8:
where s = 28/27, M = 10/9, L = 2187/1960~2450/2187.  
where s = 28/27, M = 10/9, L = 2187/1960~2450/2187.  


Unison vectors: 15/14, 245/243, 19683/19600.  
Unison vectors: {175/162, 245/243}.  


7-limit transversal: 28/27, 81/70, 6/5, 980/729, 3/2, 14/9, 243/140, 9/5, 2/1.  
7-limit transversal: 28/27, 81/70, 6/5, 980/729, 3/2, 14/9, 243/140, 9/5, 2/1.  


In [[80edo]] (a simple, general-purpose tuning): 4, 17, 21, 34, 47, 51, 64, 68, 80.  
Tunings in [[80edo]] (a simple, distinctive tuning) and [[410edo]] (an intricate, accurate tuning) will be presented.
 
In 80edo: 4, 17, 21, 34, 47, 51, 64, 68, 80.  


<pre>
<pre>
Line 31: Line 34:
</pre>
</pre>


In [[410edo]] (an intricate, accurate tuning): 21, 87, 108, 174, 240, 261, 327, 348, 410.  
In 410edo: 21, 87, 108, 174, 240, 261, 327, 348, 410.  


<pre>
<pre>
Line 56: Line 59:


== Semicanou[10] ==
== Semicanou[10] ==
This is rank-2; the second generator is not used. Worth documenting anyway.  
This is a rank-2 scale without the second generator being used, documented for it has some good ratios.  


LsLss-LsLss
LsLss-LsLss
Line 69: Line 72:


== Canou[14] ==
== Canou[14] ==
A 14-note Fokker block for canou temperament.


sLssLsLssLssMs
sLssLsLssLssMs
Line 74: Line 78:
where s = 28/27, M = 15/14, L = 175/162.  
where s = 28/27, M = 15/14, L = 175/162.  


Unison vectors: 25/24, 245/243, 19683/19600.  
Unison vectors: {25/24, 245/243}.  


7-limit transversal: 28/27, 2187/1960~2450/2187, 81/70, 6/5, 35/27, 980/729, 81/56, 3/2, 14/9, 1225/729, 243/140, 9/5, 27/14, 2/1.  
7-limit transversal: 28/27, 2187/1960~2450/2187, 81/70, 6/5, 35/27, 980/729, 81/56, 3/2, 14/9, 1225/729, 243/140, 9/5, 27/14, 2/1.  
Line 132: Line 136:


== Semicanou[14] ==
== Semicanou[14] ==
=== Semicanou[14-a] ===
A 14-note Fokker block for canou temperament.
LsmLsmm-LsmLsmm
where s = 28/27, m = 81/77, L = 35/33.
Unison vectors: {55/54, 121/120}
11-limit transversal:
Period 0: 35/33, 11/10, 81/70~140/121, 27/22, 14/11, 162/121~121/90, 99/70~140/99;
Period 1: 3/2, 14/9, 18/11, 243/140~210/121, 9/5, 154/81, 2/1.
13-limit transversal:
Period 0: 35/33, 11/10, 81/70~140/121, 16/13, 14/11, 162/121~121/90, 99/70~140/99;
Period 1: 3/2, 14/9, 18/11, 243/140~210/121, 9/5, 91/48, 2/1.
In 198edo: 17, 27, 42, 59, 69, 84, 99, 116, 126, 141, 158, 168, 183, 198.
=== Semicanou[14-b] ===
This is the inversion of semicanou[14-a].


LsmsLmm-LsmsLmm
sLmsLmm-sLmsLmm


where s = 28/27, m = 81/77, L = 35/33.  
where s = 28/27, m = 81/77, L = 35/33.  
Unison vectors: {55/54, 121/120}


11-limit transversal:  
11-limit transversal:  


Period 0: 35/33, 11/10, 81/70~140/121, 6/5, 14/11, 162/121~121/90, 99/70~140/99;  
Period 0: 28/27, 11/10, 81/70~140/121, 6/5, 14/11, 162/121~121/90, 99/70~140/99;  


Period 1: 3/2, 14/9, 56/33, 243/140~210/121, 9/5, 154/81, 2/1.  
Period 1: 22/15, 14/9, 18/11, 56/33, 9/5, 154/81, 2/1.  


13-limit transversal:  
13-limit transversal:  


Period 0: 35/33, 11/10, 81/70~140/121, 6/5, 14/11, 162/121~121/90, 99/70~140/99;
Period 0: 28/27, 11/10, 81/70~140/121, 6/5, 14/11, 162/121~121/90, 99/70~140/99;


Period 1: 3/2, 14/9, 56/33, 243/140~210/121, 9/5, 91/48, 2/1.  
Period 1: 22/15, 14/9, 18/11, 56/33, 9/5, 91/48, 2/1.  


In 198edo: 17, 27, 42, 52, 69, 84, 99, 116, 126, 141, 151, 168, 183, 198.  
In 198edo: 10, 27, 42, 52, 69, 84, 99, 108, 126, 141, 151, 168, 183, 198.
 
== Canou[19] ==
 
mLmmmLmmLmmmLmmmsmm
 
where s = 405/392, m = 28/27, L = 25/24.
 
Unison vectors: 225/224, 245/243, 19683/19600.
 
7-limit transversal: 28/27, 175/162, 2187/1960~2450/2187, 81/70, 6/5, 5/4, 35/27, 980/729, 2187/1568~6125/4374, 81/56, 3/2, 14/9, 392/243, 1225/729, 243/140, 9/5, 729/392, 27/14, 2/1.
 
In 410edo: 21, 45, 66, 87, 108, 132, 153, 174, 198, 219, 240, 261, 285, 306, 327, 348, 368, 389, 410.  


<pre>
<pre>
! semicanou14-198.scl
! canou14-410.scl
! Created using Scale Workshop 1.0.4
! Created using Scale Workshop 1.0.4
!
!
Semicanou[14] in 198edo
Canou[19] in 410edo
  14
  19
!
!
  103.030303030
  61.4634146341
  163.636363636
  131.707317073
  254.545454545
193.170731707
  315.151515152
  254.634146341
  418.181818182
316.097560976
  509.090909091
  386.341463415
  600.
  447.804878049
  703.030303030
  509.268292683
  763.636363636
  579.512195122
  854.545454545
  640.975609756
  915.151515152
702.439024390
  1018.181818182
  763.902439024
  1109.090909091
834.146341463
  895.609756098
  957.073170732
  1018.53658537
1077.07317073
  1138.53658537
  1200.
  1200.
</pre>
</pre>


Notable modes:  
[[Category:9-tone scales]]
* LmmLsms-LmmLsms (major-ish 5th mode)
[[Category:10-tone scales]]
* mLsmsLm-mLsmsLm (symmetric 7th mode)
[[Category:14-tone scales]]
 
[[Category:19-tone scales]]
[[Category:Scale]]
[[Category:Tempered scales]]
[[Category:Pages with mostly numerical content]]
[[Category:Canou]]
[[Category:Canou]]
[[Category:Pages with Scala files]]

Latest revision as of 02:54, 24 June 2025

This page lists scales of canou temperament, the rank-3 temperament that tempers out the canousma, 4802000/4782969 = [4 -14 3 4⟩.

Canou[9]

A 9-note Fokker block for canou temperament.

sLsLLsLsM

where s = 28/27, M = 10/9, L = 2187/1960~2450/2187.

Unison vectors: {175/162, 245/243}.

7-limit transversal: 28/27, 81/70, 6/5, 980/729, 3/2, 14/9, 243/140, 9/5, 2/1.

Tunings in 80edo (a simple, distinctive tuning) and 410edo (an intricate, accurate tuning) will be presented.

In 80edo: 4, 17, 21, 34, 47, 51, 64, 68, 80. 

! canou9-80.scl
! Created using Scale Workshop 1.0.4
!
Canou[9] in 80edo
 9
!
 60.
 255.
 315.
 510.
 705.
 765.
 960.
 1020.
 1200.

In 410edo: 21, 87, 108, 174, 240, 261, 327, 348, 410. 

! canou9-410.scl
! Created using Scale Workshop 1.0.4
!
Canou[9] in 410edo
 9
!
 61.4634146341
 254.634146341
 316.097560976
 509.268292683
 702.439024390
 763.902439024
 957.073170732
 1018.53658537
 1200.

Notable modes:

  • LLsLsMsLs (major-ish 4th mode)
  • LsLsMsLsL (symmetric 5th mode)

Semicanou[10]

This is a rank-2 scale without the second generator being used, documented for it has some good ratios.

LsLss-LsLss

where s = 81/77, L = 11/10.

11-limit transversal:

Period 0: 11/10, 81/70~140/121, 14/11, 162/121~121/90, 99/70~140/99;

Period 1: 14/9, 18/11, 9/5, 154/81, 2/1.

Canou[14]

A 14-note Fokker block for canou temperament.

sLssLsLssLssMs

where s = 28/27, M = 15/14, L = 175/162.

Unison vectors: {25/24, 245/243}.

7-limit transversal: 28/27, 2187/1960~2450/2187, 81/70, 6/5, 35/27, 980/729, 81/56, 3/2, 14/9, 1225/729, 243/140, 9/5, 27/14, 2/1.

In 80edo: 4, 13, 17, 21, 30, 34, 43, 47, 51, 60, 64, 68, 76, 80. 

! canou14-80.scl
! Created using Scale Workshop 1.0.4
!
Canou[14] in 80edo
 14
!
 60.
 195.
 255.
 315.
 450.
 510.
 645.
 705.
 765.
 900.
 960.
 1020.
 1140.
 1200.

In 410edo: 21, 66, 87, 108, 153, 174, 219, 240, 261, 306, 327, 348, 389, 410. 

! canou14-410.scl
! Created using Scale Workshop 1.0.4
!
Canou[14] in 410edo
 14
!
 61.4634146341
 193.170731707
 254.634146341
 316.097560976
 447.804878049
 509.268292683
 640.975609756
 702.439024390
 763.902439024
 895.609756098
 957.073170732
 1018.53658537
 1138.53658537
 1200.

Notable modes:

  • LsLssLssMssLss (major-ish 5th mode)

Semicanou[14]

Semicanou[14-a]

A 14-note Fokker block for canou temperament.

LsmLsmm-LsmLsmm

where s = 28/27, m = 81/77, L = 35/33.

Unison vectors: {55/54, 121/120}

11-limit transversal:

Period 0: 35/33, 11/10, 81/70~140/121, 27/22, 14/11, 162/121~121/90, 99/70~140/99;

Period 1: 3/2, 14/9, 18/11, 243/140~210/121, 9/5, 154/81, 2/1.

13-limit transversal:

Period 0: 35/33, 11/10, 81/70~140/121, 16/13, 14/11, 162/121~121/90, 99/70~140/99;

Period 1: 3/2, 14/9, 18/11, 243/140~210/121, 9/5, 91/48, 2/1.

In 198edo: 17, 27, 42, 59, 69, 84, 99, 116, 126, 141, 158, 168, 183, 198.

Semicanou[14-b]

This is the inversion of semicanou[14-a].

sLmsLmm-sLmsLmm

where s = 28/27, m = 81/77, L = 35/33.

Unison vectors: {55/54, 121/120}

11-limit transversal:

Period 0: 28/27, 11/10, 81/70~140/121, 6/5, 14/11, 162/121~121/90, 99/70~140/99;

Period 1: 22/15, 14/9, 18/11, 56/33, 9/5, 154/81, 2/1.

13-limit transversal:

Period 0: 28/27, 11/10, 81/70~140/121, 6/5, 14/11, 162/121~121/90, 99/70~140/99;

Period 1: 22/15, 14/9, 18/11, 56/33, 9/5, 91/48, 2/1.

In 198edo: 10, 27, 42, 52, 69, 84, 99, 108, 126, 141, 151, 168, 183, 198.

Canou[19]

mLmmmLmmLmmmLmmmsmm

where s = 405/392, m = 28/27, L = 25/24.

Unison vectors: 225/224, 245/243, 19683/19600.

7-limit transversal: 28/27, 175/162, 2187/1960~2450/2187, 81/70, 6/5, 5/4, 35/27, 980/729, 2187/1568~6125/4374, 81/56, 3/2, 14/9, 392/243, 1225/729, 243/140, 9/5, 729/392, 27/14, 2/1.

In 410edo: 21, 45, 66, 87, 108, 132, 153, 174, 198, 219, 240, 261, 285, 306, 327, 348, 368, 389, 410. 

! canou14-410.scl
! Created using Scale Workshop 1.0.4
!
Canou[19] in 410edo
 19
!
 61.4634146341
 131.707317073
 193.170731707
 254.634146341
 316.097560976
 386.341463415
 447.804878049
 509.268292683
 579.512195122
 640.975609756
 702.439024390
 763.902439024
 834.146341463
 895.609756098
 957.073170732
 1018.53658537
 1077.07317073
 1138.53658537
 1200.
Retrieved from "https://en.xen.wiki/index.php?title=Canou_scales&oldid=202836"