Temperaments for MOS shapes: Difference between revisions

From Xenharmonic Wiki
Jump to navigation Jump to search
← Older edit
VisualWikitext
Wikispaces>FREEZE
No edit summary
BudjarnLambeth (talk | contribs)
autopatrolled, emailconfirmed
21,264 edits
Todo expand
 
(7 intermediate revisions by 3 users not shown)
Line 1: Line 1:
Below are listed temperaments of least TE complexity which result in a particular MOS shape, where "results in" is taken to mean that the POTE tuning has that shape.
Below are listed [[temperament]]s of least [[TE complexity]] which result in a particular [[mos]] shape, where "results in" is taken to mean that the [[POTE tuning]] has that shape.


=7edo=
== 7edo ==
=== 5-limit ===
{| class="wikitable center-1"
|-
! Mos !! Temperament !! Comma list
|-
| 1L 6s || [[Porcupine]] || 250/243
|-
| 2L 5s || [[Mavila]] || 135/128
|-
| 3L 4s || [[Dicot]] || 25/24
|-
| 4L 3s || [[Sixix]] || 3125/2916
|-
| 5L 2s || [[Meantone]] || 81/80
|-
| 6L 1s || [[Enipucrop]] || 1125/1024
|}


==5-limit==
=== 7-limit patent ===
1L6s <<3 5 1|| porcupine 250/243
{| class="wikitable center-1"
|-
! Mos !! Temperament !! Comma list
|-
| 1L 6s || [[Hystrix]] || 36/35, 160/147
|-
| 2L 5s || [[Medusa]] || 15/14, 64/63
|-
| 3L 4s || [[Dichotic]] || 25/24, 64/63
|-
| 4L 3s || [[Dicot]] || 15/14, 25/24
|-
| 5L 2s || [[Dominant (temperament)|Dominant]] || 36/35, 64/63
|-
| 6L 1s ||  || 15/14, 256/245
|}


2L5s <<1 -3 -7|| mavila 135/128
=== 7d ===
{| class="wikitable center-1"
|-
! Mos !! Temperament !! Comma list
|-
| 1L 6s || [[Oxygen]] || 21/20, 175/162
|-
| 2L 5s || [[Pelogic]] || 21/20, 135/128
|-
| 3L 4s || [[Sharpie]] || 25/24, 28/27
|-
| 4L 3s || [[Flattie]] || 21/20, 25/24
|-
| 5L 2s || [[Sharptone]] || 21/20, 28/27
|-
| 6L 1s ||  || 25/24, 49/45
|}


3L4s <<2 1 -3|| dicot 25/24
== 8edo ==
=== 5-limit ===
{| class="wikitable center-1"
|-
! Mos !! Temperament !! Comma list
|-
| 1L 7s || [[Progression]] || 3456/3125
|-
| 2L 6s || [[Supersharp]] || 800/729
|-
| 3L 5s || [[Sensipent]] || 78732/78125
|-
| 4L 4s || [[Diminished (temperament)|Diminished]] || 648/625
|-
| 5L 3s || [[Father]] || 16/15
|-
| 6L 2s ||  || 18432/15625
|-
| 7L 1s || [[Porcupine]] || 250/243
|}


4L3s <<5 6 -2|| sixix 3125/2916
=== 7-limit 8d ===
{| class="wikitable center-1"
|-
! Mos !! Temperament !! Comma list
|-
| 1L 7s || [[Progression]] || 36/35, 392/375
|-
| 2L 6s || [[Walid]] || 16/15, 50/49
|-
| 3L 5s || [[Pater]] || 16/15, 126/125
|-
| 4L 4s || [[Diminished (temperament)|Diminished]] || 36/35, 50/49
|-
| 5L 3s || [[Father]] || 16/15, 28/27
|-
| 6L 2s ||  || 50/49, 192/175
|-
| 7L 1s || [[Hystrix]] || 36/35, 160/147
|}


5L2s <<1 4 4|| meantone 81/80
== 9edo ==
=== 5-limit ===
{| class="wikitable center-1"
|-
! Mos !! Temperament !! Comma list
|-
| 1L 8s || [[Negri]] || 16875/16384
|-
| 2L 7s || [[Avila]] || 729/640
|-
| 3L 6s || [[Augmented (temperament)|Augmented]] || 128/125
|-
| 4L 5s ||  || 93312/78125
|-
| 5L 4s || [[Bug]] || 27/25
|-
| 6L 3s ||  || 19683/16000
|-
| 7L 2s || [[Mavila]] || 135/128
|-
| 8L 1s || [[Progression]] || 3456/3125
|}


6L1s <<3 -2 -10|| enipucrop 1125/1024
=== 7-limit ===
{| class="wikitable center-1"
|-
! Mos !! Temperament !! Comma list
|-
| 1L 8s || [[Negri]] || 49/48, 225/224
|-
| 2L 7s ||  || 21/20, 243/224
|-
| 3L 6s || [[August]] || 36/35, 128/125
|-
| 4L 5s ||  || 36/35, 686/625
|-
| 5L 4s || [[Beep]] || 21/20, 27/25
|-
| 6L 3s ||  || 21/20, 729/686
|-
| 7L 2s || [[Pelogic]] || 21/20, 135/128
|-
| 8L 1s || [[Progression]] || 36/35, 392/375
|}


==7-limit patent==
== 10edo ==
1L6s <<3 5 1 1 -7 -12|| hystrix {36/35, 160/147}
=== 5-limit ===
{| class="wikitable center-1"
|-
! Mos !! Temperament !! Comma list
|-
| 1L 9s ||  || 2500/2187
|-
| 2L 8s || [[Diaschismic]] || 2048/2025
|-
| 3L 7s ||  || 204800/177147
|-
| 4L 6s ||  || 6103515625/4353564672
|-
| 5L 5s || [[Blackwood]] || 256/243
|-
| 6L 4s ||  || 15625/13122
|-
| 7L 3s || [[Dicot]] || 25/24
|-
| 8L 2s || [[Supersharp]] || 800/729
|-
| 9L 1s || [[Negri]] || 16875/16384
|}


2L5s <<1 -3 -2 -7 -6 4|| {15/14, 64/63}
=== 7-limit ===
{| class="wikitable center-1"
|-
! Mos !! Temperament !! Comma list
|-
| 1L 9s ||  || 49/48, 175/162
|-
| 2L 8s || [[Pajara]] || 50/49, 64/63
|-
| 3L 7s ||  || 28/27, 2401/2400
|-
| 4L 6s || [[Decimal]] || 25/24, 49/48
|-
| 5L 5s || [[Blackwood]] || 28/27, 49/48
|-
| 6L 4s ||  || 50/49, 175/162
|-
| 7L 3s || [[Sharpie]] || 25/24, 28/27
|-
| 8L 2s || [[Octokaidecal]] || 28/27, 50/49
|-
| 9L 1s || [[Negri]] || 49/48, 225/224
|}


3L4s <<2 1 -4 -3 -12 -12|| dichotic {25/24, 64/63}
=== 11-limit ===
{| class="wikitable center-1"
|-
! Mos !! Temperament !! Comma list
|-
| 1L 9s ||  || 35/33, 49/48, 55/54
|-
| 2L 8s ||  || 28/27, 35/33, 128/121
|-
| 3L 7s || [[Dichosis]] || 25/24, 35/33, 64/63
|-
| 4L 6s || [[Decibel]] || 25/24, 35/33, 49/48
|-
| 5L 5s || [[Ferrum]] || 28/27, 35/33, 49/48
|-
| 6L 4s ||  || 35/33, 50/49, 55/54
|-
| 7L 3s || [[Sharpie]] || 25/24, 28/27, 35/33
|-
| 8L 2s ||  || 28/27, 35/33, 50/49
|-
| 9L 1s || [[Negri]] || 45/44, 49/48, 56/55
|}


4L3s <<2 1 3 -3 -1 4|| dicot {15/14, 25/24}
== 11edo ==
=== 5-limit 11b ===
{| class="wikitable center-1"
|-
! Mos !! Temperament !! Comma list
|-
| 1L 10s ||  || 82944/78125
|-
| 2L 9s ||  || 8000/6561
|-
| 3L 8s ||  || 12582912/9765625
|-
| 4L 7s || [[Hanson]] || 15625/15552
|-
| 5L 6s ||  || 25600/19683
|-
| 6L 5s ||  || 2359296/1953125
|-
| 7L 4s || [[Sixix]] || 3125/2916
|-
| 8L 3s ||  || 81920/59049
|-
| 9L 2s ||  || 442368/390625
|-
| 10L 1s ||  || 2500/2187
|}


5L2s <<1 4 -2 4 -6 -16|| dominant {36/35, 64/63}
=== 5-limit 11c ===
{| class="wikitable center-1"
|-
! Mos !! Temperament !! Comma list
|-
| 1L 10s || [[Ripple]] || 6561/6250
|-
| 2L 9s ||  || 1215/1024
|-
| 3L 8s ||  || 1594323/1280000
|-
| 4L 7s ||  || 1953125/1889568
|-
| 5L 6s || [[Laconic]] || 2187/2000
|-
| 6L 5s ||  || 14348907/12500000
|-
| 7L 4s ||  || 1220703125/1088391168
|-
| 8L 3s || [[Sensipent]] || 78732/78125
|-
| 9L 2s || [[Avila]] || 729/640
|-
| 10L 1s ||  || 14946778125/8589934592
|}


6L1s <<3 -2 1 -10 -7 8|| {15/14, 256/245}
[[Category:Lists of temperaments]]
 
[[Category:MOS scale]]
==7d==
{{todo|expand}}
1L6s <<3 5 2 1 -5 -9|| oxygen {21/20, 175/162}
 
2L5s <<1 -3 -4 -7 -9 -1|| pelogic {21/20, 135/128}
 
3L4s <<2 1 6 -3 4 11|| sharp {25/24, 28/27}
 
4L3s <<2 1 -1 -3 -7 -5|| flat {21/20, 25/24}
 
5L2s <<1 4 3 4 2 -4|| sharptone {21/20, 28/27}
 
6L1s <<4 2 5 -6 -3 6|| {25/24, 49/45}
 
=8edo=
 
==5-limit==
1L7s <<5 3 -7|| progression 3456/3125
 
2L6s <<2 6 5|| supersharp 800/729
 
3L5s <<7 9 -2|| sensi 78732/78125
 
4L4s <<4 4 -3|| diminished 648/625
 
5L3s <<1 -1 -4|| father 16/15
 
6L2s <<6 2 -11|| 18432/15625
 
7L1s <<3 5 1|| porcupine 250/243
 
==7-limit 8d==
1L7s <<5 3 7 -7 -3 8|| progression {36/35, 392/375}
 
2L6s <<2 -2 -2 -8 -9 1|| walid {16/15, 50/49}
 
3L5s <<1 -1 -5 -4 -11 -9|| pater {16/15, 126/125}
 
4L4s <<4 4 4 -3 -5 -2|| diminished {36/35, 50/49}
 
5L3s <<1 -1 3 -4 2 10|| father {16/15, 28/27}
 
6L2s <<6 2 2 -11 -14 -1|| {50/49, 192/175}
 
7L1s <<3 5 1 1 -7 -12|| hystrix {36/35, 160/147}
 
=9edo=
 
==5-limit==
1L8s <<4 -3 -14|| negri 16875/16384
 
2L7s <<1 6 -7|| avila 729/640
 
3L6s <<3 0 -7|| augmented 128/125
 
4L5s <<7 6 -7|| 93312/78125
 
5L4s <<2 3 0|| bug 27/25
 
6L3s <<3 9 7|| 19683/16000
 
7L2s <<1 -3 -7|| mavila 135/128
 
8L1s <<5 3 -7|| progression 3456/3125
 
==7-limit==
1L8s <<4 -3 2 -14 -8 13|| negri {49/48, 225/224}
 
2L7s <<1 6 5 7 5 -5|| {21/20, 243/224}
 
3L6s <<3 0 6 -7 1 14|| august {36/35, 128/125}
 
4L5s <<7 6 8 -7 -7 2|| {36/35, 686/625}
 
5L4s <<2 3 1 0 -4 -6|| beep {21/20, 27/25}
 
6L3s <<3 9 6 7 1 -11|| {21/20, 729/686}
 
7L2s <<1 -3 -4 -7 -9 -1|| pelogic {21/20, 135/128}
 
8L1s <<5 3 7 -7 -3 8|| progression {36/35, 392/375}  
 
=10edo=
 
==5-limit==
1L9s <<4 7 2|| 2500/2187
 
2L8s <<2 -4 -11|| srutal 2048/2025
 
3L7s <<2 11 13|| 204800/177147
 
4L6s <<14 12 -13|| 6103515625/4353564672
 
5L5s <<0 5 8|| blackwood 256/243
 
6L4s <<6 8 -1|| 15625/13122
 
7L3s <<2 1 -3|| dicot 25/24
 
8L2s <<2 6 5|| supersharp 800/729
 
9L1s <<4 -3 -14|| negri 16875/16384
 
==7-limit==
1L9s <<4 7 2 2 -8 -15|| {49/48, 175/162}
 
2L8s <<2 -4 -4 -11 -12 2|| pajara {50/49, 64/63}
 
3L7s <<2 11 6 13 4 -17|| {28/27, 2401/2400}
 
4L6s <<4 2 2 -6 -8 -1|| decimal {25/24, 49/48}
 
5L5s  <<0 5 0 8 0 -14|| blacksmith {28/27, 49/48}
 
6L4s <<6 8 8 -1 -4 -4|| {50/49, 175/162}
 
7L3s <<2 1 6 -3 4 11|| sharp {25/24, 28/27}
 
8L2s <<2 6 6 5 4 -3|| octokaidecal {28/27, 50/49}
 
9L1s <<4 -3 2 -14 -8 13|| negri {49/48, 225/224}
 
==11-limit==
1L9s <<4 7 2 5 2 -8 -6 -15 -13 7|| {35/33, 49/48, 55/54}
 
2L8s <<2 -4 6 0 -11 4 -7 25 14 -21|| {28/27, 35/33, 128/121}
 
3L7s <<2 1 -4 -5 -3 -12 -15 -12 -15 0|| dichosis {25/24, 35/33, 64/63}
 
4l6s <<4 2 2 0 -6 -8 -14 -1 -7 -7|| decibel {25/24, 35/33, 49/48}
 
5L5s <<0 5 0 5 8 0 8 -14 -6 14|| ferrum {28/27, 35/33, 49/48}
 
6L4s <<6 8 8 10 -1 -4 -5 -4 -5 0|| {35/33, 50/49, 55/54}
 
7L3s <<2 1 6 5 -3 4 1 11 8 -7|| sharp {25/24, 28/27, 35/33}
 
8L2s  <<2 6 6 10 5 4 9 -3 2 7|| {28/27, 35/33, 50/49}
 
9L1s <<4 -3 2 5 -14 -8 -6 13 22 7|| negri {45/44, 49/48, 56/55}
 
=11edo=
 
==5-limit 11b==
1L10s <<7 4 -10|| 82944/78125
 
2L9s <<3 8 6|| 8000/6561
 
3L8s <<10 1 -22|| 12582912/9765625
 
4L7s <<6 5 -6|| hanson 15625/15552
 
5L6s <<2 9 10|| 25600/19683
 
6L5s <<9 2 -18|| 2359296/1953125
 
7L4s <<5 6 -2|| sixix 3125/2916
 
8L3s <<1 10 14|| 81920/59049
 
9L2s <<8 3 -14|| 442368/390625
 
10L1s <<4 7 2|| 2500/2187
 
==5-limit 11c==
1L10s <<5 8 1|| ripple 6561/6250
 
2L9s <<1 -5 -10|| 1215/1024
 
3L8s <<4 13 11|| 1594323/1280000
 
4L7s <<9 10 -5|| 1953125/1889568
 
5L6s <<3 7 4|| laconic 2187/2000
 
6L5s <<8 15 5|| 14348907/12500000
 
7L4s <<13 12 -11|| 1220703125/1088391168
 
8L3s <<7 9 -2|| sensi 78732/78125
 
9L2s <<1 6 7|| avila 729/640
 
10L1s <<5 -14 -33|| 14946778125/8589934592
[[Category:todo:link]]

Latest revision as of 23:34, 8 April 2026

Below are listed temperaments of least TE complexity which result in a particular mos shape, where "results in" is taken to mean that the POTE tuning has that shape.

7edo

5-limit

Mos Temperament Comma list
1L 6s Porcupine 250/243
2L 5s Mavila 135/128
3L 4s Dicot 25/24
4L 3s Sixix 3125/2916
5L 2s Meantone 81/80
6L 1s Enipucrop 1125/1024

7-limit patent

Mos Temperament Comma list
1L 6s Hystrix 36/35, 160/147
2L 5s Medusa 15/14, 64/63
3L 4s Dichotic 25/24, 64/63
4L 3s Dicot 15/14, 25/24
5L 2s Dominant 36/35, 64/63
6L 1s 15/14, 256/245

7d

Mos Temperament Comma list
1L 6s Oxygen 21/20, 175/162
2L 5s Pelogic 21/20, 135/128
3L 4s Sharpie 25/24, 28/27
4L 3s Flattie 21/20, 25/24
5L 2s Sharptone 21/20, 28/27
6L 1s 25/24, 49/45

8edo

5-limit

Mos Temperament Comma list
1L 7s Progression 3456/3125
2L 6s Supersharp 800/729
3L 5s Sensipent 78732/78125
4L 4s Diminished 648/625
5L 3s Father 16/15
6L 2s 18432/15625
7L 1s Porcupine 250/243

7-limit 8d

Mos Temperament Comma list
1L 7s Progression 36/35, 392/375
2L 6s Walid 16/15, 50/49
3L 5s Pater 16/15, 126/125
4L 4s Diminished 36/35, 50/49
5L 3s Father 16/15, 28/27
6L 2s 50/49, 192/175
7L 1s Hystrix 36/35, 160/147

9edo

5-limit

Mos Temperament Comma list
1L 8s Negri 16875/16384
2L 7s Avila 729/640
3L 6s Augmented 128/125
4L 5s 93312/78125
5L 4s Bug 27/25
6L 3s 19683/16000
7L 2s Mavila 135/128
8L 1s Progression 3456/3125

7-limit

Mos Temperament Comma list
1L 8s Negri 49/48, 225/224
2L 7s 21/20, 243/224
3L 6s August 36/35, 128/125
4L 5s 36/35, 686/625
5L 4s Beep 21/20, 27/25
6L 3s 21/20, 729/686
7L 2s Pelogic 21/20, 135/128
8L 1s Progression 36/35, 392/375

10edo

5-limit

Mos Temperament Comma list
1L 9s 2500/2187
2L 8s Diaschismic 2048/2025
3L 7s 204800/177147
4L 6s 6103515625/4353564672
5L 5s Blackwood 256/243
6L 4s 15625/13122
7L 3s Dicot 25/24
8L 2s Supersharp 800/729
9L 1s Negri 16875/16384

7-limit

Mos Temperament Comma list
1L 9s 49/48, 175/162
2L 8s Pajara 50/49, 64/63
3L 7s 28/27, 2401/2400
4L 6s Decimal 25/24, 49/48
5L 5s Blackwood 28/27, 49/48
6L 4s 50/49, 175/162
7L 3s Sharpie 25/24, 28/27
8L 2s Octokaidecal 28/27, 50/49
9L 1s Negri 49/48, 225/224

11-limit

Mos Temperament Comma list
1L 9s 35/33, 49/48, 55/54
2L 8s 28/27, 35/33, 128/121
3L 7s Dichosis 25/24, 35/33, 64/63
4L 6s Decibel 25/24, 35/33, 49/48
5L 5s Ferrum 28/27, 35/33, 49/48
6L 4s 35/33, 50/49, 55/54
7L 3s Sharpie 25/24, 28/27, 35/33
8L 2s 28/27, 35/33, 50/49
9L 1s Negri 45/44, 49/48, 56/55

11edo

5-limit 11b

Mos Temperament Comma list
1L 10s 82944/78125
2L 9s 8000/6561
3L 8s 12582912/9765625
4L 7s Hanson 15625/15552
5L 6s 25600/19683
6L 5s 2359296/1953125
7L 4s Sixix 3125/2916
8L 3s 81920/59049
9L 2s 442368/390625
10L 1s 2500/2187

5-limit 11c

Mos Temperament Comma list
1L 10s Ripple 6561/6250
2L 9s 1215/1024
3L 8s 1594323/1280000
4L 7s 1953125/1889568
5L 6s Laconic 2187/2000
6L 5s 14348907/12500000
7L 4s 1220703125/1088391168
8L 3s Sensipent 78732/78125
9L 2s Avila 729/640
10L 1s 14946778125/8589934592
Retrieved from "https://en.xen.wiki/index.php?title=Temperaments_for_MOS_shapes&oldid=227479"