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Meantone family: Difference between revisions

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Experiment with error maps
Normalize, +missing CTE and CWE tunings, +error maps, and misc. cleanup
Line 73: Line 73:


Temperaments discussed elsewhere include
Temperaments discussed elsewhere include
* ''[[Plutus]]'' → [[Very low accuracy temperaments #Plutus|Very low accuracy temperaments]]
* ''[[Plutus]]'' (+15/14) → [[Very low accuracy temperaments #Plutus|Very low accuracy temperaments]]
* [[Godzilla]] → [[Slendro clan #Godzilla|Slendro clan]]
* [[Godzilla]] (+49/48) → [[Semaphoresmic clan #Godzilla|Semaphoresmic clan]]
* [[Mothra]] → [[Gamelismic clan #Mothra|Gamelismic clan]]
* ''[[Mothra]]'' (+1029/1024) → [[Gamelismic clan #Mothra|Gamelismic clan]]
* [[Mohaha]] → [[Rastmic clan #Mohaha|Rastmic clan]]
* ''[[Mohaha]]'' (+121/120) → [[Rastmic clan #Mohaha|Rastmic clan]]


The rest are considered below.
The rest are considered below.
Line 1,215: Line 1,215:
[[Optimal tuning]]s:  
[[Optimal tuning]]s:  
* [[CTE]]: ~2 = 1200.000, ~3/2 = 693.552
* [[CTE]]: ~2 = 1200.000, ~3/2 = 693.552
: [[error map]]: {{val| 0.000 -8.403 -12.106 -10.794 }}
* [[POTE]]: ~2 = 1200.000, ~3/2 = 693.779
* [[POTE]]: ~2 = 1200.000, ~3/2 = 693.779
: error map: {{val| 0.000 -8.176 -11.197 -12.838 }}


[[Minimax tuning]]:  
[[Minimax tuning]]:  
Line 1,287: Line 1,289:
[[Optimal tuning]]s:  
[[Optimal tuning]]s:  
* [[CTE]]: ~2 = 1200.000, ~3/2 = 692.698
* [[CTE]]: ~2 = 1200.000, ~3/2 = 692.698
* [[CWE]]: ~2 = 1200.000, ~3/2 = 692.0479
: [[error map]]: {{val| 0.000 -9.257 -15.520 +7.047 }}
* [[CWE]]: ~2 = 1200.000, ~3/2 = 692.048
: error map: {{val| 0.000 -9.907 -18.122 -4.012 }}


{{Optimal ET sequence|legend=1| 7d, 19d, 26, 59bcd, 85bccd }}
{{Optimal ET sequence|legend=1| 7d, 19d, 26, 59bcd, 85bccd }}
Line 1,308: Line 1,312:
Optimal ET sequence: {{Optimal ET sequence| 7d, 19d, 26, 59bcd, 85bccd }}
Optimal ET sequence: {{Optimal ET sequence| 7d, 19d, 26, 59bcd, 85bccd }}


'''Music'''
; Music
* [https://youtu.be/scCuGXnj5IY ''Music in 33EDO (33-Tone Equal Temperament) - Feb 2024''] - [[Budjarn Lambeth]] (2024)
* [https://youtu.be/scCuGXnj5IY ''Music in 33EDO (33-Tone Equal Temperament) - Feb 2024''] - [[Budjarn Lambeth]] (2024)


Line 1,329: Line 1,333:
[[Optimal tuning]]s:  
[[Optimal tuning]]s:  
* [[CTE]]: ~2 = 1200.000, ~3/2 = 699.622
* [[CTE]]: ~2 = 1200.000, ~3/2 = 699.622
: [[error map]]: {{val| 0.000 -2.333 +12.173 +31.931 }}
* [[POTE]]: ~2 = 1200.000, ~3/2 = 701.573
* [[POTE]]: ~2 = 1200.000, ~3/2 = 701.573
: error map: {{val| 0.000 -0.382 +19.979 +28.028 }}


[[Tuning ranges]]:  
[[Tuning ranges]]:  
Line 1,571: Line 1,577:
[[Optimal tuning]]s:  
[[Optimal tuning]]s:  
* [[CTE]]: ~2 = 1200.000, ~3/2 = 703.732
* [[CTE]]: ~2 = 1200.000, ~3/2 = 703.732
: [[error map]]: {{val| 0.000 +1.777 +28.614 -57.630 }}
* [[POTE]]: ~2 = 1200.000, ~3/2 = 700.140
* [[POTE]]: ~2 = 1200.000, ~3/2 = 700.140
: error map: {{val| 0.000 -1.815 +14.245 -68.407 }}


{{Optimal ET sequence|legend=1| 5, 7d, 12d }}
{{Optimal ET sequence|legend=1| 5, 7d, 12d }}
Line 1,601: Line 1,609:
[[Optimal tuning]]s:  
[[Optimal tuning]]s:  
* [[CTE]]: ~2 = 1200.000, ~3/2 = 703.811
* [[CTE]]: ~2 = 1200.000, ~3/2 = 703.811
: [[error map]]: {{val| 0.000 +1.856 +28.929 -11.665 }}
* [[POTE]]: ~2 = 1200.000, ~3/2 = 704.889
* [[POTE]]: ~2 = 1200.000, ~3/2 = 704.889
: error map: {{val| 0.000 +2.934 +33.242 +4.507 }}


{{Optimal ET sequence|legend=1| 5d, 12d, 17c, 29c }}
{{Optimal ET sequence|legend=1| 5d, 12d, 17c, 29c }}
Line 1,652: Line 1,662:
{{Multival|legend=1| 2 8 -11 8 -23 -48 }}
{{Multival|legend=1| 2 8 -11 8 -23 -48 }}


[[Optimal tuning]] ([[POTE]]): ~2 = 1200.000, ~128/105 = 348.415
[[Optimal tuning]]s:
* [[CTE]]: ~2 = 1200.000, ~128/105 = 348.437
: [[error map]]: {{val| 0.000 -5.080 +1.186 -1.637 }}
* [[POTE]]: ~2 = 1200.000, ~128/105 = 348.415
: error map: {{val| 0.000 -5.125 +1.005 -1.390 }}


[[Minimax tuning]]:  
[[Minimax tuning]]:  
Line 1,681: Line 1,695:
Wedgie: {{multival| 2 8 -11 5 8 -23 1 -48 -16 52 }}
Wedgie: {{multival| 2 8 -11 5 8 -23 1 -48 -16 52 }}


Optimal tuning (POTE): ~2 = 1200.000, ~11/9 = 348.477
Optimal tunings:
* CTE: ~2 = 1200.000, ~11/9 = 348.561
* POTE: ~2 = 1200.000, ~11/9 = 348.477


Minimax tuning:  
Minimax tuning:  
Line 1,705: Line 1,721:
Mapping: {{mapping| 1 1 0 6 2 4 | 0 2 8 -11 5 -1 }}
Mapping: {{mapping| 1 1 0 6 2 4 | 0 2 8 -11 5 -1 }}


Optimal tuning (POTE): ~2 = 1200.000, ~11/9 = 348.558
Optimal tunings:
* CTE: ~2 = 1200.000, ~11/9 = 348.587
* POTE: ~2 = 1200.000, ~11/9 = 348.558


Optimal ET sequence: {{Optimal ET sequence| 7, 24, 31 }}
Optimal ET sequence: {{Optimal ET sequence| 7, 24, 31 }}
Line 1,720: Line 1,738:
Mapping: {{mapping| 1 1 0 6 2 4 7 | 0 2 8 -11 5 -1 -10 }}
Mapping: {{mapping| 1 1 0 6 2 4 7 | 0 2 8 -11 5 -1 -10 }}


Optimal tuning (POTE): ~2 = 1200.000, ~11/9 = 348.736
Optimal tunings:
* CTE: ~2 = 1200.000, ~11/9 = 348.735
* POTE: ~2 = 1200.000, ~11/9 = 348.736


Optimal ET sequence: {{Optimal ET sequence| 7, 24, 31, 86ef }}
Optimal ET sequence: {{Optimal ET sequence| 7, 24, 31 }}


Badness: 0.020576
Badness: 0.020576
Line 1,735: Line 1,755:
Mapping: {{mapping| 1 1 0 6 2 4 7 6 | 0 2 8 -11 5 -1 -10 -6 }}
Mapping: {{mapping| 1 1 0 6 2 4 7 6 | 0 2 8 -11 5 -1 -10 -6 }}


Optimal tuning (POTE): ~2 = 1200.000, ~11/9 = 348.810
Optimal tunings:
* CTE: ~2 = 1200.000, ~11/9 = 348.821
* POTE: ~2 = 1200.000, ~11/9 = 348.810


Optimal ET sequence: {{Optimal ET sequence| 7, 24, 31, 55, 86efh }}
Optimal ET sequence: {{Optimal ET sequence| 7, 24, 31, 55 }}


Badness: 0.017302
Badness: 0.017302
Line 1,752: Line 1,774:
: mapping generators: ~2, ~25/21
: mapping generators: ~2, ~25/21


[[Optimal tuning]] ([[POTE]]): ~2 = 1200.000, ~25/21 = 350.586
[[Optimal tuning]]s:
* [[CTE]]: ~2 = 1200.000, ~25/21 = 350.352
: [[error map]]: {{val| 0.000 -1.250 +16.505 -14.245 }}
* [[POTE]]: ~2 = 1200.000, ~25/21 = 350.586
: error map: {{val| 0.000 -0.784 +18.370 -11.214 }}


{{Optimal ET sequence|legend=1| 7d, 17c, 24, 65cc, 89ccd }}
{{Optimal ET sequence|legend=1| 7d, 17c, 24 }}


[[Badness]]: 0.077734
[[Badness]]: 0.077734
Line 1,767: Line 1,793:
Mapping: {{mapping| 1 1 0 -1 2 | 0 2 8 13 5 }}
Mapping: {{mapping| 1 1 0 -1 2 | 0 2 8 13 5 }}


Optimal tuning (POTE): ~2 = 1200.000, ~11/9 = 350.565
Optimal tunings:
* CTE: ~2 = 1200.000, ~11/9 = 350.347
* POTE: ~2 = 1200.000, ~11/9 = 350.565


Optimal ET sequence: {{Optimal ET sequence| 7d, 17c, 24, 65cc, 89ccd }}
Optimal ET sequence: {{Optimal ET sequence| 7d, 17c, 24 }}


Badness: 0.036207
Badness: 0.036207
Line 1,782: Line 1,810:
Mapping: {{mapping| 1 1 0 -1 2 4 | 0 2 8 13 5 -1 }}
Mapping: {{mapping| 1 1 0 -1 2 4 | 0 2 8 13 5 -1 }}


Optimal tuning (POTE): ~2 = 1200.000, ~11/9 = 350.745
Optimal tunings:
* CTE: ~2 = 1200.000, ~11/9 = 350.365
* POTE: ~2 = 1200.000, ~11/9 = 350.745


Optimal ET sequence: {{Optimal ET sequence| 7d, 17c, 24, 41c, 65cc }}
Optimal ET sequence: {{Optimal ET sequence| 7d, 17c, 24, 41c }}


Badness: 0.028738
Badness: 0.028738
Line 1,793: Line 1,823:
<span style="display: block; text-align: right;">[[:de:Liese|Deutsch]]</span>
<span style="display: block; text-align: right;">[[:de:Liese|Deutsch]]</span>


Liese splits the twelfth interval of 3/1 into three generators of 10/7, using the comma 1029/1000. It also tempers out 686/675, the senga. [[74edo]] makes for a good liese tuning, though [[19edo]] can be used. The tuning is well-supplied with mos scales: 7, 9, 11, 13, 15, 17, 19, 36, 55.
Liese splits the twelfth interval of 3/1 into three generators of 10/7, using the comma 1029/1000. It also tempers out 686/675, the senga. Liese is a very natural 13-limit tuning, given the generator is so near 13/9. [[74edo]] makes for a good liese tuning, though [[19edo]] can be used. The tuning is well-supplied with mos scales: 7, 9, 11, 13, 15, 17, 19, 36, 55.  


[[Subgroup]]: 2.3.5.7
[[Subgroup]]: 2.3.5.7
Line 1,805: Line 1,835:
{{Multival|legend=1| 3 12 11 12 9 -8 }}
{{Multival|legend=1| 3 12 11 12 9 -8 }}


[[Optimal tuning]] ([[POTE]]): ~2 = 1200.000, ~10/7 = 632.406
[[Optimal tuning]]s:
* [[CTE]]: ~2 = 1200.000, ~10/7 = 632.783
: [[error map]]: {{val| 0.000 -3.606 +7.084 -8.212 }}
* [[POTE]]: ~2 = 1200.000, ~10/7 = 632.406
: error map: {{val| 0.000 -4.738 +2.554 -12.363 }}


[[Minimax tuning]]:  
[[Minimax tuning]]:  
Line 1,827: Line 1,861:
Wedgie: {{multival| 3 12 11 -1 12 9 -12 -8 -44 -41 }}
Wedgie: {{multival| 3 12 11 -1 12 9 -12 -8 -44 -41 }}


Optimal tuning (POTE): ~2 = 1200.000, ~10/7 = 633.073
Optimal tunings:
* CTE: ~2 = 1200.000, ~10/7 = 632.812
* POTE: ~2 = 1200.000, ~10/7 = 633.073


Optimal ET sequence: {{Optimal ET sequence| 17c, 19, 36, 91cee }}
Optimal ET sequence: {{Optimal ET sequence| 17c, 19, 36 }}


Badness: 0.040721
Badness: 0.040721


==== 13-limit ====
==== 13-limit ====
Liesel is a very natural 13-limit tuning, given the generator is so near 13/9.
Subgroup: 2.3.5.7.11.13
Subgroup: 2.3.5.7.11.13


Line 1,842: Line 1,876:
Mapping: {{mapping| 1 0 -4 -3 4 0 | 0 3 12 11 -1 7 }}
Mapping: {{mapping| 1 0 -4 -3 4 0 | 0 3 12 11 -1 7 }}


Optimal tuning (POTE): ~2 = 1200.000, ~10/7 = 633.042
Optimal tunings:
* CTE: ~2 = 1200.000, ~10/7 = 632.925
* POTE: ~2 = 1200.000, ~10/7 = 633.042


Optimal ET sequence: {{Optimal ET sequence| 17c, 19, 36, 91ceef }}
Optimal ET sequence: {{Optimal ET sequence| 17c, 19, 36, 91ceef }}
Line 1,857: Line 1,893:
Wedgie: {{multival| 3 12 11 16 12 9 15 -8 -4 7 }}
Wedgie: {{multival| 3 12 11 16 12 9 15 -8 -4 7 }}


Optimal tuning (POTE): ~2 = 1200.000, ~10/7 = 633.061
Optimal tunings:
* CTE: ~2 = 1200.000, ~10/7 = 633.317
* POTE: ~2 = 1200.000, ~10/7 = 633.061


Optimal ET sequence: {{Optimal ET sequence| 17c, 19e, 36e }}
Optimal ET sequence: {{Optimal ET sequence| 17c, 19e, 36e }}
Line 1,870: Line 1,908:
Mapping: {{mapping| 1 0 -4 -3 -5 0 | 0 3 12 11 16 7 }}
Mapping: {{mapping| 1 0 -4 -3 -5 0 | 0 3 12 11 16 7 }}


Optimal tuning (POTE): ~2 = 1200.000, ~10/7 = 632.991
Optimal tunings:
* CTE: ~2 = 1200.000, ~10/7 = 633.370
* POTE: ~2 = 1200.000, ~10/7 = 632.991


Optimal ET sequence: {{Optimal ET sequence| 17c, 19e, 36e }}
Optimal ET sequence: {{Optimal ET sequence| 17c, 19e, 36e }}
Line 1,883: Line 1,923:
Mapping: {{mapping| 1 0 -4 -3 -6 | 0 3 12 11 18 }}
Mapping: {{mapping| 1 0 -4 -3 -6 | 0 3 12 11 18 }}


Optimal tuning (POTE): ~2 = 1200.000, ~10/7 = 631.370
Optimal tunings:
* CTE: ~2 = 1200.000, ~10/7 = 631.981
* POTE: ~2 = 1200.000, ~10/7 = 631.370


Optimal ET sequence: {{Optimal ET sequence| 17cee, 19 }}
Optimal ET sequence: {{Optimal ET sequence| 17cee, 19 }}
Line 1,896: Line 1,938:
Mapping: {{mapping| 1 0 -4 -3 -6 0 | 0 3 12 11 18 7 }}
Mapping: {{mapping| 1 0 -4 -3 -6 0 | 0 3 12 11 18 7 }}


Optimal tuning (POTE): ~2 = 1200.000, ~10/7 = 631.221
Optimal tunings:
* CTE: ~2 = 1200.000, ~10/7 = 632.093
* POTE: ~2 = 1200.000, ~10/7 = 631.221


Optimal ET sequence: {{Optimal ET sequence| 17cee, 19 }}
Optimal ET sequence: {{Optimal ET sequence| 17cee, 19 }}
Line 1,911: Line 1,955:
{{Mapping|legend=1| 1 2 4 1 | 0 -3 -12 13 }}
{{Mapping|legend=1| 1 2 4 1 | 0 -3 -12 13 }}


[[Optimal tuning]] ([[CTE]]): ~2 = 1200.000, ~35/32 = 167.279
[[Optimal tuning]]s:
* [[CTE]]: ~2 = 1200.000, ~35/32 = 167.279
: [[error map]]: {{val| 0.000 -3.793 +6.336 +5.804 }}
* [[CWE]]: ~2 = 1200.000, ~35/32 = 167.256
: error map: {{val| 0.000 -3.723 +6.613 +5.503 }}


{{Optimal ET sequence|legend=1| 7, 36, 43, 79c }}
{{Optimal ET sequence|legend=1| 7, 36, 43, 79c }}
Line 1,924: Line 1,972:
Mapping: {{mapping| 1 2 4 1 5 | 0 -3 -12 13 -11 }}
Mapping: {{mapping| 1 2 4 1 5 | 0 -3 -12 13 -11 }}


Optimal tuning (CTE): ~2 = 1200.000, ~11/10 = 167.407
Optimal tunings:
* CTE: ~2 = 1200.000, ~11/10 = 167.407
* CWE: ~2 = 1200.000, ~11/10 = 167.338


Optimal ET sequence: {{Optimal ET sequence| 7, 36, 43 }}
Optimal ET sequence: {{Optimal ET sequence| 7, 36, 43 }}
Line 1,937: Line 1,987:
Mapping: {{mapping| 1 2 4 1 5 3 | 0 -3 -12 13 -11 5 }}
Mapping: {{mapping| 1 2 4 1 5 3 | 0 -3 -12 13 -11 5 }}


Optimal tuning (CTE): ~2 = 1200.000, ~11/10 = 167.427
Optimal tunings:
* CTE: ~2 = 1200.000, ~11/10 = 167.427
* CWE: ~2 = 1200.000, ~11/10 = 167.396


Optimal ET sequence: {{Optimal ET sequence| 7, 36, 43 }}
Optimal ET sequence: {{Optimal ET sequence| 7, 36, 43 }}
Line 1,954: Line 2,006:
: mapping generators: ~56/45, ~3
: mapping generators: ~56/45, ~3


[[Optimal tuning]] ([[CTE]]): ~56/45 = 400.000, ~3/2 = 695.827
[[Optimal tuning]]s:
* [[CTE]]: ~56/45 = 400.000, ~3/2 = 695.827 (~15/14 = 104.173)
: [[error map]]: {{val| 0.000 -6.128 -3.007 +6.135 }}
* [[CWE]]: ~56/45 = 400.000, ~3/2 = 695.141 {~15/14 = 104.859)
: error map: {{val| 0.000 -6.814 -5.748 +2.022 }}


{{Optimal ET sequence|legend=1| 12, 33cd, 45, 57 }}
{{Optimal ET sequence|legend=1| 12, 33cd, 45, 57 }}
Line 1,975: Line 2,031:
{{Multival|legend=1| 4 16 9 16 3 -24 }}
{{Multival|legend=1| 4 16 9 16 3 -24 }}


[[Optimal tuning]] ([[POTE]]): ~2 = 1200.000, ~9/7 = 425.942
[[Optimal tuning]]s:
* [[CTE]]: ~2 = 1200.000, ~9/7 = 425.695
: [[error map]]: {{val| 0.000 -4.734 +2.570 -0.079 }}
* [[POTE]]: ~2 = 1200.000, ~9/7 = 425.942
: error map: {{val| 0.000 -5.721 -1.378 -2.300 }}


[[Minimax tuning]]:  
[[Minimax tuning]]:  
Line 1,984: Line 2,044:
[[Algebraic generator]]: Sceptre2, the positive root of 9''x''<sup>2</sup> + ''x'' - 16, or (sqrt (577) - 1)/18, which is 425.9311 cents.
[[Algebraic generator]]: Sceptre2, the positive root of 9''x''<sup>2</sup> + ''x'' - 16, or (sqrt (577) - 1)/18, which is 425.9311 cents.


{{Optimal ET sequence|legend=1| 14c, 17c, 31 }}
{{Optimal ET sequence|legend=1| 14c, 17c, 31, 169b, 200b }}


[[Badness]]: 0.045993
[[Badness]]: 0.045993
Line 1,999: Line 2,059:
Wedgie: {{multival| 4 16 9 10 16 3 2 -24 -32 -3 }}
Wedgie: {{multival| 4 16 9 10 16 3 2 -24 -32 -3 }}


Optimal tuning (POTE): ~2 = 1200.000, ~9/7 = 425.957
Optimal tunings:
* CTE: ~2 = 1200.000, ~9/7 = 425.599
* POTE: ~2 = 1200.000, ~9/7 = 425.957


Optimal ET sequence: {{Optimal ET sequence| 14c, 17c, 31 }}
Optimal ET sequence: {{Optimal ET sequence| 14c, 17c, 31, 130bee, 169beee }}


Badness: 0.021636
Badness: 0.021636
Line 2,012: Line 2,074:
Mapping: {{mapping| 1 3 8 6 7 3 | 0 -4 -16 -9 -10 2 }}
Mapping: {{mapping| 1 3 8 6 7 3 | 0 -4 -16 -9 -10 2 }}


Optimal tuning (POTE): ~2 = 1200.000, ~9/7 = 425.550
Optimal tunings:
* CTE: ~2 = 1200.000, ~9/7 = 425.578
* POTE: ~2 = 1200.000, ~9/7 = 425.550


Optimal ET sequence: {{Optimal ET sequence| 14c, 17c, 31, 79cf }}
Optimal ET sequence: {{Optimal ET sequence| 14c, 17c, 31, 79cf }}
Line 2,025: Line 2,089:
Mapping: {{mapping| 1 3 8 6 7 9 | 0 -4 -16 -9 -10 -15 }}
Mapping: {{mapping| 1 3 8 6 7 9 | 0 -4 -16 -9 -10 -15 }}


Optimal tuning (POTE): ~2 = 1200.000, ~9/7 = 425.7516
Optimal tunings:
* CTE: ~2 = 1200.000, ~9/7 = 425.297
* POTE: ~2 = 1200.000, ~9/7 = 425.752


Optimal ET sequence: {{Optimal ET sequence| 14cf, 17c, 31f }}
Optimal ET sequence: {{Optimal ET sequence| 14cf, 17c, 31f }}
Line 2,038: Line 2,104:
Mapping: {{mapping| 1 3 8 6 7 14 | 0 -4 -16 -9 -10 -29 }}
Mapping: {{mapping| 1 3 8 6 7 14 | 0 -4 -16 -9 -10 -29 }}


Optimal tuning (POTE): ~2 = 1200.000, ~9/7 = 426.276
Optimal tunings:
* CTE: ~2 = 1200.000, ~9/7 = 425.870
* POTE: ~2 = 1200.000, ~9/7 = 426.276


Optimal ET sequence: {{Optimal ET sequence| 14cf, 31, 45ef, 76e }}
Optimal ET sequence: {{Optimal ET sequence| 14cf, 31, 45ef, 76e }}
Line 2,051: Line 2,119:
Mapping: {{mapping| 1 3 8 6 7 14 8 | 0 -4 -16 -9 -10 -29 -11 }}
Mapping: {{mapping| 1 3 8 6 7 14 8 | 0 -4 -16 -9 -10 -29 -11 }}


Optimal tuning (POTE): ~2 = 1200.000, ~9/7 = 426.187
Optimal tunings:
* CTE: ~2 = 1200.000, ~9/7 = 425.919
* POTE: ~2 = 1200.000, ~9/7 = 426.187


Optimal ET sequence: {{Optimal ET sequence| 14cf, 31, 76e }}
Optimal ET sequence: {{Optimal ET sequence| 14cf, 31 }}


Badness: 0.022573
Badness: 0.022573
Line 2,064: Line 2,134:
Mapping: {{mapping| 1 3 8 6 7 14 8 11 | 0 -4 -16 -9 -10 -29 -11 -19 }}
Mapping: {{mapping| 1 3 8 6 7 14 8 11 | 0 -4 -16 -9 -10 -29 -11 -19 }}


Optimal tuning (POTE): ~2 = 1200.000, ~9/7 = 426.225
Optimal tunings:
* CTE: ~2 = 1200.000, ~9/7 = 425.984
* POTE: ~2 = 1200.000, ~9/7 = 426.225


Optimal ET sequence: {{Optimal ET sequence| 14cf, 31, 76e }}
Optimal ET sequence: {{Optimal ET sequence| 14cf, 31 }}


Badness: 0.018839
Badness: 0.018839
Line 2,077: Line 2,149:
Mapping: {{mapping| 1 3 8 6 -4 | 0 -4 -16 -9 21 }}
Mapping: {{mapping| 1 3 8 6 -4 | 0 -4 -16 -9 21 }}


{{Multival|legend=1| 4 16 9 -21 16 3 -47 -24 -104 -90 }}
Wedgie: {{multival| 4 16 9 -21 16 3 -47 -24 -104 -90 }}


Optimal tuning (POTE): ~2 = 1200.000, ~9/7 = 425.993
Optimal tunings:
* CTE: ~2 = 1200.000, ~9/7 = 425.899
* POTE: ~2 = 1200.000, ~9/7 = 425.993


Optimal ET sequence: {{Optimal ET sequence| 14ce, 17ce, 31, 107b, 138b, 169be, 200be }}
Optimal ET sequence: {{Optimal ET sequence| 31, 107b, 138b, 169be, 200be }}


Badness: 0.056826
Badness: 0.056826
Line 2,098: Line 2,172:
{{Multival|legend=1| 5 20 7 20 -3 -40 }}
{{Multival|legend=1| 5 20 7 20 -3 -40 }}


[[Optimal tuning]] ([[POTE]]): ~2 = 1200.000, ~54/49 = 139.343
[[Optimal tuning]]s:
* [[CTE]]: ~2 = 1200.000, ~54/49 = 139.371
: [[error map]]: {{val| 0.000 -5.098 +1.114 +6.774 }}
* [[POTE]]: ~2 = 1200.000, ~54/49 = 139.343
: error map: {{val| 0.000 -5.238 +0.553 +6.577 }}


{{Optimal ET sequence|legend=1| 17c, 26, 43, 69, 112bd }}
{{Optimal ET sequence|legend=1| 17c, 26, 43 }}


[[Badness]]: 0.108656
[[Badness]]: 0.108656
Line 2,113: Line 2,191:
Wedgie: {{multival| 5 20 7 4 20 -3 -11 -40 -60 -13 }}
Wedgie: {{multival| 5 20 7 4 20 -3 -11 -40 -60 -13 }}


Optimal tuning (POTE): ~2 = 1200.000, ~12/11 = 139.428
Optimal tunings:
* CTE: ~2 = 1200.000, ~12/11 = 139.349
* POTE: ~2 = 1200.000, ~12/11 = 139.428


Optimal ET sequence: {{Optimal ET sequence| 17c, 26, 43, 69 }}
Optimal ET sequence: {{Optimal ET sequence| 17c, 26, 43 }}


Badness: 0.047914
Badness: 0.047914
Line 2,126: Line 2,206:
Mapping: {{mapping| 1 1 0 2 3 3 | 0 5 20 7 4 6 }}
Mapping: {{mapping| 1 1 0 2 3 3 | 0 5 20 7 4 6 }}


Optimal tuning (POTE): ~2 = 1200.000, ~12/11 = 139.387
Optimal tunings:
* CTE: ~2 = 1200.000, ~13/12 = 139.369
* POTE: ~2 = 1200.000, ~13/12 = 139.387


Optimal ET sequence: {{Optimal ET sequence| 17c, 26, 43, 69 }}
Optimal ET sequence: {{Optimal ET sequence| 17c, 26, 43 }}


Badness: 0.029285
Badness: 0.029285
Line 2,139: Line 2,221:
Mapping: {{mapping| 1 1 0 2 3 3 2 | 0 5 20 7 4 6 18 }}
Mapping: {{mapping| 1 1 0 2 3 3 2 | 0 5 20 7 4 6 18 }}


Optimal tuning (POTE): ~2 = 1200.000, ~12/11 = 139.362
Optimal tunings:
* CTE: ~2 = 1200.000, ~13/12 = 139.334
* POTE: ~2 = 1200.000, ~13/12 = 139.362


Optimal ET sequence: {{Optimal ET sequence| 17cg, 26, 43, 69 }}
Optimal ET sequence: {{Optimal ET sequence| 17cg, 26, 43 }}


Badness: 0.020878
Badness: 0.020878
Line 2,152: Line 2,236:
Mapping: {{mapping| 1 1 0 2 3 3 2 1 | 0 5 20 7 4 6 18 28 }}
Mapping: {{mapping| 1 1 0 2 3 3 2 1 | 0 5 20 7 4 6 18 28 }}


Optimal tuning (POTE): ~2 = 1200.000, ~12/11 = 139.313
Optimal tunings:
* CTE: ~2 = 1200.000, ~13/12 = 139.296
* POTE: ~2 = 1200.000, ~13/12 = 139.313


Optimal ET sequence: {{Optimal ET sequence| 17cgh, 26, 43, 69 }}
Optimal ET sequence: {{Optimal ET sequence| 17cgh, 26, 43, 69 }}
Line 2,169: Line 2,255:
{{Multival|legend=1| 5 20 19 20 16 -12 }}
{{Multival|legend=1| 5 20 19 20 16 -12 }}


[[Optimal tuning]] ([[POTE]]): ~2 = 1200.000, ~7/5 = 580.766
[[Optimal tuning]]s:
* [[CTE]]: ~2 = 1200.000, ~7/5 = 580.568
: [[error map]]: {{val| 0.000 -4.795 +2.325 +0.381 }}
* [[POTE]]: ~2 = 1200.000, ~7/5 = 580.766
: error map: {{val| 0.000 -5.785 -1.634 -3.380 }}


{{Optimal ET sequence|legend=1| 2cd, 29cd, 31 }}
{{Optimal ET sequence|legend=1| 29cd, 31, 188bcd, 219bbcd }}


[[Badness]]: 0.082239
[[Badness]]: 0.082239
Line 2,182: Line 2,272:
Mapping: {{mapping| 1 4 12 12 17 | 0 -5 -20 -19 -28 }}
Mapping: {{mapping| 1 4 12 12 17 | 0 -5 -20 -19 -28 }}


Optimal tuning (POTE): ~2 = 1200.000, ~7/5 = 580.647
Optimal tunings:
* CTE: ~2 = 1200.000, ~7/5 = 580.482
* POTE: ~2 = 1200.000, ~7/5 = 580.647


Optimal ET sequence: {{Optimal ET sequence| 2cde, 29cde, 31 }}
Optimal ET sequence: {{Optimal ET sequence| 29cde, 31 }}


Badness: 0.042869
Badness: 0.042869
Line 2,203: Line 2,295:
{{Multival|legend=1| 2 8 8 8 7 -4 }}
{{Multival|legend=1| 2 8 8 8 7 -4 }}


[[Optimal tuning]] ([[POTE]]): ~7/5 = 600.000, ~3/2 = 694.375
[[Optimal tuning]]s:
* [[CTE]]: ~7/5 = 600.000, ~3/2 = 695.330 (~21/20 = 95.330)
: [[error map]]: {{val| 0.000 -6.625 -4.993 +12.495 }}
* [[POTE]]: ~7/5 = 600.000, ~3/2 = 694.375 (~21/20 = 94.375)
: error map: {{val| 0.000 -7.580 -8.813 +8.675 }}


[[Tuning ranges]]:  
[[Tuning ranges]]:  
Line 2,210: Line 2,306:
* 9-odd-limit diamond tradeoff: ~3/2 = [682.458, 701.955]
* 9-odd-limit diamond tradeoff: ~3/2 = [682.458, 701.955]


{{Optimal ET sequence|legend=1| 12, 26, 38, 102bcd, 140bccd, 178bbccdd }}
{{Optimal ET sequence|legend=1| 12, 26, 38 }}


[[Badness]]: 0.031130
[[Badness]]: 0.031130
Line 2,224: Line 2,320:
Mapping: {{mapping| 2 0 -8 -7 -12 | 0 1 4 4 6 }}
Mapping: {{mapping| 2 0 -8 -7 -12 | 0 1 4 4 6 }}


{{Multival|legend=1| 2 8 8 12 8 7 12 -4 0 6 }}
Wedgie: {{Multival| 2 8 8 12 8 7 12 -4 0 6 }}


Optimal tuning (POTE): ~7/5 = 600.000, ~3/2 = 692.840
Optimal tunings:
* CTE: ~7/5 = 600.000, ~3/2 = 694.098 (~21/20 = 94.098)
* POTE: ~7/5 = 600.000, ~3/2 = 692.840 (~21/20 = 92.840)


Tuning ranges:  
Tuning ranges:  
Line 2,232: Line 2,330:
* 11-odd-limit diamond tradeoff: ~3/2 = [682.458, 701.955]
* 11-odd-limit diamond tradeoff: ~3/2 = [682.458, 701.955]


Optimal ET sequence: {{Optimal ET sequence| 12, 14c, 26, 90bce, 116bcce }}
Optimal ET sequence: {{Optimal ET sequence| 12, 26 }}


Badness: 0.023124
Badness: 0.023124
Line 2,243: Line 2,341:
Mapping: {{mapping| 2 0 -8 -7 -12 -21 | 0 1 4 4 6 9 }}
Mapping: {{mapping| 2 0 -8 -7 -12 -21 | 0 1 4 4 6 9 }}


Optimal tuning (POTE): ~7/5 = 600.000, ~3/2 = 692.673
Optimal tunings:
* CTE: ~7/5 = 600.000, ~3/2 = 693.806 (~21/20 = 93.806)
* POTE: ~7/5 = 600.000, ~3/2 = 692.673 (~21/20 = 92.673)


Tuning ranges:  
Tuning ranges:  
Line 2,249: Line 2,349:
* 13- and 15-odd-limit diamond tradeoff: ~3/2 = [682.458, 701.955]
* 13- and 15-odd-limit diamond tradeoff: ~3/2 = [682.458, 701.955]


Optimal ET sequence: {{Optimal ET sequence| 12f, 14cf, 26, 38e }}
Optimal ET sequence: {{Optimal ET sequence| 12f, 14cf, 26 }}


Badness: 0.021565
Badness: 0.021565
Line 2,260: Line 2,360:
Mapping: {{mapping| 2 0 -8 -7 -12 -21 5 | 0 1 4 4 6 9 1 }}
Mapping: {{mapping| 2 0 -8 -7 -12 -21 5 | 0 1 4 4 6 9 1 }}


Optimal tuning (POTE): ~7/5 = 600.000, ~3/2 = 692.487
Optimal tunings:
* CTE: ~7/5 = 600.000, ~3/2 = 693.852 (~21/20 = 93.852)
* POTE: ~7/5 = 600.000, ~3/2 = 692.487 (~21/20 = 92.487)


Optimal ET sequence: {{Optimal ET sequence| 12f, 14cf, 26 }}
Optimal ET sequence: {{Optimal ET sequence| 12f, 14cf, 26 }}
Line 2,273: Line 2,375:
Mapping: {{mapping| 2 0 -8 -7 -12 -21 5 -1 | 0 1 4 4 6 9 1 3 }}
Mapping: {{mapping| 2 0 -8 -7 -12 -21 5 -1 | 0 1 4 4 6 9 1 3 }}


Optimal tuning (POTE): ~7/5 = 600.000, ~3/2 = 692.299
Optimal tunings:
* CTE: ~7/5 = 600.000, ~3/2 = 694.031 (~21/20 = 94.031)
* POTE: ~7/5 = 600.000, ~3/2 = 692.299 (~21/20 = 92.299)


Optimal ET sequence: {{Optimal ET sequence| 12f, 14cf, 26 }}
Optimal ET sequence: {{Optimal ET sequence| 12f, 14cf, 26 }}
Line 2,286: Line 2,390:
Mapping: {{mapping| 2 0 -8 -7 -12 -2 | 0 1 4 4 6 3 }}
Mapping: {{mapping| 2 0 -8 -7 -12 -2 | 0 1 4 4 6 3 }}


Optimal tuning (POTE): ~7/5 = 600.000, ~3/2 = 694.121
Optimal tunings:
* CTE: ~7/5 = 600.000, ~3/2 = 693.088 (~21/20 = 93.088)
* POTE: ~7/5 = 600.000, ~3/2 = 694.121 (~21/20 = 94.121)


Optimal ET sequence: {{Optimal ET sequence| 12f, 14c, 26f, 38eff }}
Optimal ET sequence: {{Optimal ET sequence| 10cdeef, 12f }}


Badness: 0.026542
Badness: 0.026542
Line 2,299: Line 2,405:
Mapping: {{mapping| 2 0 -8 -7 10 | 0 1 4 4 -1 }}
Mapping: {{mapping| 2 0 -8 -7 10 | 0 1 4 4 -1 }}


Optimal tuning (POTE): ~7/5 = 600.000, ~3/2 = 690.548
Optimal tunings:
* CTE: ~7/5 = 600.000, ~3/2 = 694.619 (~21/20 = 94.619)
* POTE: ~7/5 = 600.000, ~3/2 = 690.548 (~21/20 = 90.548)


Optimal ET sequence: {{Optimal ET sequence| 12e, 14c, 26e, 40cee }}
Optimal ET sequence: {{Optimal ET sequence| 12e, 14c, 26e, 40cee }}
Line 2,312: Line 2,420:
Mapping: {{mapping| 2 0 -8 -7 7 | 0 1 4 4 0 }}
Mapping: {{mapping| 2 0 -8 -7 7 | 0 1 4 4 0 }}


Optimal tuning (POTE): ~7/5 = 600.000, ~3/2 = 699.001
Optimal tunings:
* CTE: ~7/5 = 600.000, ~3/2 = 695.330 (~21/20 = 95.330)
* POTE: ~7/5 = 600.000, ~3/2 = 699.001 (~21/20 = 99.001)


Optimal ET sequence: {{Optimal ET sequence| 2cd, 10cd, 12 }}
Optimal ET sequence: {{Optimal ET sequence| 10cd, 12 }}


Badness: 0.043062
Badness: 0.043062
Line 2,331: Line 2,441:
: mapping generators: ~7/5, ~16/11
: mapping generators: ~7/5, ~16/11


Optimal tuning (POTE): ~7/5 = 600.000, ~11/8 = 552.5303
Optimal tunings:
* CTE: ~7/5 = 600.000, ~11/8 = 552.331 (~33/32 = 47.669)
* POTE: ~7/5 = 600.000, ~11/8 = 552.530 (~33/32 = 47.470)


Optimal ET sequence: {{Optimal ET sequence| 24d, 26, 50d }}
Optimal ET sequence: {{Optimal ET sequence| 24d, 26, 50d }}
Line 2,344: Line 2,456:
Mapping: {{mapping| 2 1 -4 -3 8 2 | 0 2 8 8 -1 5 }}
Mapping: {{mapping| 2 1 -4 -3 8 2 | 0 2 8 8 -1 5 }}


Optimal tuning (POTE): ~7/5 = 600.000, ~11/8 = 552.5324
Optimal tunings:
* CTE: ~7/5 = 600.000, ~11/8 = 552.297 (~33/32 = 47.703)
* POTE: ~7/5 = 600.000, ~11/8 = 552.532 (~33/32 = 47.468)


Optimal ET sequence: {{Optimal ET sequence| 24d, 26, 50d }}
Optimal ET sequence: {{Optimal ET sequence| 24d, 26, 50d }}
Line 2,357: Line 2,471:
Mapping: {{mapping| 2 1 -4 -3 8 2 6 | 0 2 8 8 -1 5 2 }}
Mapping: {{mapping| 2 1 -4 -3 8 2 6 | 0 2 8 8 -1 5 2 }}


Optimal tuning (POTE): ~7/5 = 600.000, ~11/8 = 552.6558
Optimal tunings:
* CTE: ~7/5 = 600.000, ~11/8 = 552.249 (~34/33 = 47.751)
* POTE: ~7/5 = 600.000, ~11/8 = 552.656 (~34/33 = 47.344)


Optimal ET sequence: {{Optimal ET sequence| 24d, 26 }}
Optimal ET sequence: {{Optimal ET sequence| 24d, 26 }}
Line 2,370: Line 2,486:
Mapping: {{mapping| 2 1 -4 -3 8 2 6 2 | 0 2 8 8 -1 5 2 6 }}
Mapping: {{mapping| 2 1 -4 -3 8 2 6 2 | 0 2 8 8 -1 5 2 6 }}


Optimal tuning (POTE): ~7/5 = 600.000, ~11/8 = 552.6382
Optimal tunings:
* CTE: ~7/5 = 600.000, ~11/8 = 552.107 (~34/33 = 47.893)
* POTE: ~7/5 = 600.000, ~11/8 = 552.638 (~34/33 = 47.362)


Optimal ET sequence: {{Optimal ET sequence| 24d, 26 }}
Optimal ET sequence: {{Optimal ET sequence| 24d, 26 }}
Line 2,389: Line 2,507:
{{Multival|legend=1| 4 16 -10 16 -27 -68 }}
{{Multival|legend=1| 4 16 -10 16 -27 -68 }}


[[Optimal tuning]] ([[POTE]]): ~735/512 = 600.000, ~48/35 = 552.2206
[[Optimal tuning]]s:
* [[CTE]]: ~735/512 = 600.000, ~48/35 = 551.845 (~36/35 = 48.155)
: [[error map]]: {{val| 0.000 -5.645 -1.075 -9.600 }}
* [[POTE]]: ~735/512 = 600.000, ~48/35 = 552.221 (~36/35 = 48.779)
: error map: {{val| 0.000 -6.229 -3.411 -8.140 }}


{{Optimal ET sequence|legend=1| 24, 26, 50, 126bcd, 176bcdd, 226bbcdd }}
{{Optimal ET sequence|legend=1| 24, 26, 50, 126bcd, 176bcdd, 226bbcdd }}
Line 2,402: Line 2,524:
Mapping: {{mapping| 2 1 -4 11 8 | 0 2 8 -5 -1 }}
Mapping: {{mapping| 2 1 -4 11 8 | 0 2 8 -5 -1 }}


Optimal tuning (POTE): ~99/70 = 600.000, ~11/8 = 552.0929
Optimal tunings:
* CTE: ~99/70 = 600.000, ~11/8 = 551.843 (~36/35 = 48.157)
* POTE: ~99/70 = 600.000, ~11/8 = 552.093 (~36/35 = 47.907)


Optimal ET sequence: {{Optimal ET sequence| 24, 26, 50 }}
Optimal ET sequence: {{Optimal ET sequence| 24, 26, 50 }}
Line 2,415: Line 2,539:
Mapping: {{mapping| 2 1 -4 11 8 2 | 0 2 8 -5 -1 5 }}
Mapping: {{mapping| 2 1 -4 11 8 2 | 0 2 8 -5 -1 5 }}


Optimal tuning (POTE): ~99/70 = 600.000, ~11/8 = 552.1498
Optimal tunings:
* CTE: ~99/70 = 600.000, ~11/8 = 551.848 (~36/35 = 48.152)
* POTE: ~99/70 = 600.000, ~11/8 = 552.150 (~36/35 = 47.850)


Optimal ET sequence: {{Optimal ET sequence| 24, 26, 50 }}
Optimal ET sequence: {{Optimal ET sequence| 24, 26, 50 }}
Line 2,428: Line 2,554:
Mapping: {{mapping| 2 1 -4 11 8 2 6 | 0 2 8 -5 -1 5 2 }}
Mapping: {{mapping| 2 1 -4 11 8 2 6 | 0 2 8 -5 -1 5 2 }}


Optimal tuning (POTE): ~17/12 = 600.000, ~11/8 = 552.1579
Optimal tunings:
* CTE: ~17/12 = 600.000, ~11/8 = 551.793 (~36/35 = 48.207)
* POTE: ~17/12 = 600.000, ~11/8 = 552.158 (~36/35 = 47.842)


Optimal ET sequence: {{Optimal ET sequence| 24, 26, 50 }}
Optimal ET sequence: {{Optimal ET sequence| 24, 26, 50 }}
Line 2,441: Line 2,569:
Mapping: {{mapping| 2 1 -4 11 8 2 6 2 | 0 2 8 -5 -1 5 2 6 }}
Mapping: {{mapping| 2 1 -4 11 8 2 6 2 | 0 2 8 -5 -1 5 2 6 }}


Optimal tuning (POTE): ~17/12 = 600.000, ~11/8 = 552.1196
Optimal tunings:
* CTE: ~17/12 = 600.000, ~11/8 = 551.660 (~36/35 = 48.340)
* POTE: ~17/12 = 600.000, ~11/8 = 552.120 (~36/35 = 47.880)


Optimal ET sequence: {{Optimal ET sequence| 24, 26, 50 }}
Optimal ET sequence: {{Optimal ET sequence| 24, 26, 50 }}
Line 2,452: Line 2,582:
[[Comma list]]: 81/80, 5898240/5764801
[[Comma list]]: 81/80, 5898240/5764801


{{Mapping|legend=1| 2 5 12 7 | 0 -4 -16 -3 }}
{{Mapping|legend=1| 2 1 -4 4 | 0 4 16 3 }}


: mapping generators: ~2401/1728, ~7/6
: mapping generators: ~2401/1728, ~343/288


{{Multival|legend=1| 8 32 6 32 -13 -76 }}
{{Multival|legend=1| 8 32 6 32 -13 -76 }}


[[Optimal tuning]] ([[POTE]]): ~2401/1728 = 600.000, ~7/6 = 275.794
[[Optimal tuning]]s:
* [[CTE]]: ~2401/1728 = 600.000, ~343/288 = 324.275 (~7/6 = 275.725)
: [[error map]]: {{val| 0.000 -4.854 +2.091 +4.000 }}
* [[POTE]]: ~2401/1728 = 600.000, ~343/288 = 324.206 (~7/6 = 275.794)
: error map: {{val| 0.000 -5.131 +0.983 +3.792 }}


{{Optimal ET sequence|legend=1| 26, 48c, 74, 174bd, 248bbd }}
{{Optimal ET sequence|legend=1| 26, 48c, 74 }}


[[Badness]]: 0.258825
[[Badness]]: 0.258825
Line 2,469: Line 2,603:
Comma list: 81/80, 99/98, 73728/73205
Comma list: 81/80, 99/98, 73728/73205


Mapping: {{mapping| 2 5 12 7 6 | 0 -4 -16 -3 2 }}
Mapping: {{mapping| 2 1 -4 4 8 | 0 -4 -16 -3 2 }}


Optimal tuning (POTE): ~363/256 = 600.000, ~7/6 = 275.762
Optimal tunings:
* CTE: ~363/256 = 600.000, ~77/64 = 324.276 (~7/6 = 275.724)
* POTE: ~363/256 = 600.000, ~77/64 = 324.238 (~7/6 = 275.762)


Optimal ET sequence: {{Optimal ET sequence| 26, 48c, 74, 248bbd, 322bbdd }}
Optimal ET sequence: {{Optimal ET sequence| 26, 48c, 74 }}


Badness: 0.101499
Badness: 0.101499
Line 2,482: Line 2,618:
Comma list: 81/80, 99/98, 144/143, 2200/2197
Comma list: 81/80, 99/98, 144/143, 2200/2197


Mapping: {{mapping| 2 5 12 7 6 12 | 0 -4 -16 -3 2 -10 }}
Mapping: {{mapping| 2 1 -4 4 8 2 | 0 -4 -16 -3 2 -10 }}


Optimal tuning (POTE): ~55/39 = 600.000, ~7/6 = 275.774
Optimal tunings:
* CTE: ~55/39 = 600.000, ~77/64 = 324.250 (~7/6 = 275.750)
* POTE: ~55/39 = 600.000, ~77/64 = 324.226 (~7/6 = 275.774)


Optimal ET sequence: {{Optimal ET sequence| 26, 48c, 74, 174bd, 248bbd, 322bbdd }}
Optimal ET sequence: {{Optimal ET sequence| 26, 48c, 74 }}


Badness: 0.053482
Badness: 0.053482
Line 2,503: Line 2,641:
{{Multival|legend=1| 5 20 0 20 -14 -56 }}
{{Multival|legend=1| 5 20 0 20 -14 -56 }}


[[Optimal tuning]] ([[POTE]]): ~8/7 = 240.000, ~3/2 = 695.720
[[Optimal tuning]]s:
* [[CTE]]: ~8/7 = 240.000, ~3/2 = 697.214 (~49/48 = 22.786)
: [[error map]]: {{val| 0.000 -4.741 +2.544 -8.826 }}
* [[POTE]]: ~8/7 = 240.000, ~3/2 = 695.720 (~49/48 = 24.280)
: error map: {{val| 0.000 -6.235 -3.435 -8.826 }}


{{Optimal ET sequence|legend=1| 5, 45, 50 }}
{{Optimal ET sequence|legend=1| 5, 40c, 45, 50 }}


[[Badness]]: 0.102256
[[Badness]]: 0.102256
Line 2,516: Line 2,658:
Mapping: {{mapping| 5 0 -20 14 41 | 0 1 4 0 -3 }}
Mapping: {{mapping| 5 0 -20 14 41 | 0 1 4 0 -3 }}


Optimal tuning (POTE): ~8/7 = 240.000, ~3/2 = 696.536
Optimal tunings:
* CTE: ~8/7 = 240.000, ~3/2 = 697.034 (~56/55 = 22.966)
* POTE: ~8/7 = 240.000, ~3/2 = 696.536 (~56/55 = 23.464)


Optimal ET sequence: {{Optimal ET sequence| 5, 45, 50, 155bdd, 205bddd }}
Optimal ET sequence: {{Optimal ET sequence| 5, 45, 50 }}


Badness: 0.070378
Badness: 0.070378
Line 2,529: Line 2,673:
Mapping: {{mapping| 5 0 -20 14 41 -21 | 0 1 4 0 -3 5 }}
Mapping: {{mapping| 5 0 -20 14 41 -21 | 0 1 4 0 -3 5 }}


Optimal tuning (POTE): ~8/7 = 240.000, ~3/2 = 696.162
Optimal tunings:
* CTE: ~8/7 = 240.000, ~3/2 = 696.749 (~91/90 = 23.251)
* POTE: ~8/7 = 240.000, ~3/2 = 696.162 (~91/90 = 23.838)


Optimal ET sequence: {{Optimal ET sequence| 5, 45f, 50 }}
Optimal ET sequence: {{Optimal ET sequence| 5, 45f, 50 }}
Line 2,549: Line 2,695:
: [[gencom]]: [2 3; 81/80 96/95]
: [[gencom]]: [2 3; 81/80 96/95]


[[Optimal tuning]] ([[POTE]]): ~2 = 1200.000, ~3/2 = 697.867
[[Optimal tuning]]s:
* [[CTE]]: ~2 = 1200.000, ~3/2 = 697.681
* [[POTE]]: ~2 = 1200.000, ~3/2 = 697.867


{{Optimal ET sequence|legend=1| 5, 7, 12, 31, 43 }}
{{Optimal ET sequence|legend=1| 5, 7, 12, 31, 43 }}
Line 2,564: Line 2,712:
: sval mapping generators: ~2, ~3
: sval mapping generators: ~2, ~3


[[Optimal tuning]] ([[CTE]]): ~2 = 1200.000, ~3/2 = 694.700
[[Optimal tuning]]s:
* [[CTE]]: ~2 = 1200.000, ~3/2 = 694.700
* [[CWE]]: ~2 = 1200.000, ~3/2 = 693.908


{{Optimal ET sequence|legend=1| 7, 12, 19, 26, 45 }}
{{Optimal ET sequence|legend=1| 7, 12, 19, 26, 45 }}
Line 2,579: Line 2,729:
: sval mapping generators: ~2, ~3
: sval mapping generators: ~2, ~3


Optimal tuning (CTE): ~2/1 = 1\1, ~3/2 = 693.951
Optimal tunings:
* CTE: ~2 = 1200.000, ~3/2 = 693.951
* CTE: ~2 = 1200.000, ~3/2 = 693.087


Optimal ET sequence: {{Optimal ET sequence| 7, 12, 19, 26, 45f }}
Optimal ET sequence: {{Optimal ET sequence| 7, 12, 19, 26, 45f }}
Line 2,594: Line 2,746:
: sval mapping generators: ~2, ~3
: sval mapping generators: ~2, ~3


[[Optimal tuning]] ([[CTE]]): ~2 = 1200.000, ~3/2 = 696.0387
[[Optimal tuning]]s:
* [[CTE]]: ~2 = 1200.000, ~3/2 = 696.039
* [[CWE]]: ~2 = 1200.000, ~3/2 = 693.121


{{Optimal ET sequence|legend=1| 5, 7, 19e, 26e }}
{{Optimal ET sequence|legend=1| 5, 7, 19e, 26e }}
Line 2,609: Line 2,763:
: sval mapping generators: ~2, ~3
: sval mapping generators: ~2, ~3


Optimal tuning (CTE): ~2 = 1200.000, ~3/2 = 689.6993
Optimal tunings:
* CTE: ~2 = 1200.000, ~3/2 = 689.699
* CWE: ~2 = 1200.000, ~3/2 = 690.183


Optimal ET sequence: {{Optimal ET sequence| 7, 19eff, 26eff, 33ceeff, 40ceeff }}
Optimal ET sequence: {{Optimal ET sequence| 7, 19eff, 26eff, 33ceeff, 40ceeff }}
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