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Cathartic scales: Difference between revisions

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Created page with "This page lists scales of canou temperament, the rank-3 temperament that tempers out the canousma, 4802000/4782969 = {{monzo|4 -14 3 4}}. == Canou[9] ==..."
 
m FloraC moved page Canou scales to Cathartic scales: Rename (see talk at Cathartic family)
 
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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 the [[cathartic]] temperament, the rank-3 temperament that tempers out the [[cathartic comma]], 4802000/4782969 = {{monzo|4 -14 3 4}}.  


== Canou[9] ==
== Cathartic[9] ==
A 9-note Fokker block for cathartic 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>
! canou9-80.scl
! cathartic9-80.scl
! Created using Scale Workshop 1.0.4
! Created using Scale Workshop 1.0.4
!
!
Canou[9] in 80edo
Cathartic[9] in 80edo
  9
  9
!
!
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>
! canou9-410.scl
! cathartic9-410.scl
! Created using Scale Workshop 1.0.4
! Created using Scale Workshop 1.0.4
!
!
Canou[9] in 410edo
Cathartic[9] in 410edo
  9
  9
!
!
Line 55: Line 58:
* LsLsMsLsL (symmetric 5th mode)
* LsLsMsLsL (symmetric 5th mode)


== Canou[14] ==
== Semicathart[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.
 
== Cathartic[14] ==
A 14-note Fokker block for the cathartic temperament.


sLssLsLssLssMs
sLssLsLssLssMs
Line 61: 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 68: Line 85:


<pre>
<pre>
! canou14-80.scl
! cathartic14-80.scl
! Created using Scale Workshop 1.0.4
! Created using Scale Workshop 1.0.4
!
!
Canou[14] in 80edo
Cathartic[14] in 80edo
  14
  14
!
!
Line 93: Line 110:


<pre>
<pre>
! canou14-410.scl
! cathartic14-410.scl
! Created using Scale Workshop 1.0.4
! Created using Scale Workshop 1.0.4
!
!
Canou[14] in 410edo
Cathartic[14] in 410edo
  14
  14
!
!
Line 118: Line 135:
* LsLssLssMssLss (major-ish 5th mode)
* LsLssLssMssLss (major-ish 5th mode)


== Semicathart[14] ==
=== Semicathart[14-a] ===
A 14-note Fokker block for the semicathart 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.
=== Semicathart[14-b] ===
This is the inversion of Semicathart[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.
== Cathartic[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>
! cathartic19-410.scl
! Created using Scale Workshop 1.0.4
!
Cathartic[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.
</pre>


[[Category:Scale]]
[[Category:9-tone scales]]
[[Category:Canou]]
[[Category:10-tone scales]]
[[Category:14-tone scales]]
[[Category:19-tone scales]]
[[Category:Tempered scales]]
[[Category:Pages with mostly numerical content]]
[[Category:Cathartic]]
[[Category:Pages with Scala files]]
Retrieved from "https://en.xen.wiki/w/Cathartic_scales"