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No-twos subgroup temperaments: Difference between revisions

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fomalhaut looks to be an extension of deneb
Lériendil (talk | contribs)
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put data in sintel-esque format rather than x31eq
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=== Fomalhaut ===
=== Fomalhaut ===
The 23-limit version of Fomalhaut was created first, as an attempt to approximate the no-2s, no-7s 23-limit as accurately as possible using 25 to 35 notes per equave. Then the lower limit versions were created by simply extrapolating the temperament downwards.
Fomalhaut is an extension of Deneb to higher limits that splits the interval of [[11/3]] in three. The 23-limit version of Fomalhaut was created first, as an attempt to approximate the no-2s, no-7s 23-limit as accurately as possible using 25 to 35 notes per equave, defined as the b28 & b33 temperament in this limit. Then the lower limit versions were created by simply extrapolating the temperament downwards.


Fomalhaut follows the convention of naming no-twos temperaments after stars.
Fomalhaut follows the convention of naming no-twos temperaments after stars.


==== 3.5.11.13 ====
[[Subgroup]]: 3.5.11.13
<pre>
 
Reduced Mapping
[[Comma list]]: 6655/6561, 274625/264627
3 5 11 13
 
[ ⟨ 1 5 1 -2 ]
[[Gencom]]: [3/1 99/65; 6655/6561 274625/264627]
⟨ 0 -9 3 11 ] ⟩
 
[[Sval]] [[mapping]]: [{{val|1 5 1 -2}}, {{val|0 -9 3 11}}]
TE Generator Tunings (cents)
 
⟨1905.7904, 749.5240]
[[POTE generator]]: ~[[99/65]] = 748.0156
 
TE Step Tunings (cents)
[[EDT]]s: {{EDs|b28, b5, b33, b23f, b61, b56f, b38c, b10cf, b66c, b51ff|equave=t}}
⟨40.98455, 22.97646]
 
TE Tuning Map (cents)
⟨1905.790, 2783.236, 4154.362, 4433.183]
TE Mistunings (cents)
⟨3.835, -3.077, 3.044, -7.345]
Complexity 1.561892
Complexity 1.561892
Adjusted Error 6.495941 cents
Adjusted Error 6.495941 cents
TE Error 1.755451 cents/octave
TE Error 1.755451 cents/octave
Unison Vectors
[-8, 1, 3, 0⟩ (6655:6561)
[1, 2, -5, 3⟩ (164775:161051)
[-7, 3, -2, 3⟩ (274625:264627)
[-15, 4, 1, 3⟩ (15104375:14348907)


Subsets
==== 3.5.11.13.17 ====
b28, b5p, b33, b23f, b61, b56f, b38c, b10cf, b66c, b51ff
[[Subgroup]]: 3.5.11.13.17
</pre>
 
[[Comma list]]: 1105/1089, 4225/4131, 6655/6561
 
[[Gencom]]: [3/1 99/65; 1105/1089 4225/4131 6655/6561]
 
[[Sval]] [[mapping]]: [{{val|1 5 1 -2 1}}, {{val|0 -9 3 11 4}}]
 
[[POTE generator]]: ~[[17/11]] = 748.0236
 
[[EDT]]s: {{EDs|b28, b5, b33, b23f, b61, b56f, b38c, b10cf, b66c, b51ffg|equave=t}}


==== 3.5.11.13.17 ====
<pre>
Reduced Mapping
3 5 11 13 17
[ ⟨ 1 5 1 -2 1 ]
⟨ 0 -9 3 11 4 ] ⟩
TE Generator Tunings (cents)
⟨1905.8711, 749.5638]
TE Step Tunings (cents)
⟨40.71768, 23.20533]
TE Tuning Map (cents)
⟨1905.871, 2783.281, 4154.563, 4433.460, 4904.126]
TE Mistunings (cents)
⟨3.916, -3.033, 3.245, -7.068, -0.829]
Complexity 1.418914
Complexity 1.418914
Adjusted Error 6.431616 cents
Adjusted Error 6.431616 cents
TE Error 1.573498 cents/octave
TE Error 1.573498 cents/octave
Unison Vectors
[-2, 1, -2, 1, 1⟩ (1105:1089)
[-5, 0, 1, -1, 2⟩ (3179:3159)
[-5, 2, 0, 2, -1⟩ (4225:4131)
[-8, 1, 3, 0, 0⟩ (6655:6561)
[-3, 1, 2, 1, -2⟩ (7865:7803)
[1, 0, -4, 0, 3⟩ (14739:14641)


Subsets
==== 3.5.11.13.17.19 ====
b28, b5p, b33, b23f, b61, b56f, b38c, b10cf, b66c, b51ffg
[[Subgroup]]: 3.5.11.13.17.19
</pre>
 
[[Comma list]]: 247/243, 325/323, 1105/1089, 4675/4617
 
[[Gencom]]: [3/1 99/65; 247/243 325/323 1105/1089 4675/4617]
 
[[Sval]] [[mapping]]: [{{val|1 5 1 -2 1 7}}, {{val|0 -9 3 11 4 -11}}]
 
[[POTE generator]]: ~[[17/11]] = 747.9960
 
[[EDT]]s: {{EDs|b28, b33, b5, b61, b56f, b23f, b38ch, b66ch, b89fgh, b10cfh|equave=t}}


==== 3.5.11.13.17.19 ====
<pre>
Reduced Mapping
3 5 11 13 17 19
[ ⟨ 1 5 1 -2 1 7 ]
⟨ 0 -9 3 11 4 -11 ] ⟩
TE Generator Tunings (cents)
⟨1905.9598, 749.5710]
TE Step Tunings (cents)
⟨41.63378, 22.43072]
TE Tuning Map (cents)
⟨1905.960, 2783.660, 4154.673, 4433.362, 4904.244, 5096.437]
TE Mistunings (cents)
⟨4.005, -2.654, 3.355, -7.166, -0.712, -1.076]
Complexity 1.449992
Complexity 1.449992
Adjusted Error 6.125446 cents
Adjusted Error 6.125446 cents
TE Error 1.441985 cents/octave
TE Error 1.441985 cents/octave
Unison Vectors
[-5, 0, 0, 1, 0, 1⟩ (247:243)
[0, 2, 0, 1, -1, -1⟩ (325:323)
[-2, 1, -2, 1, 1, 0⟩ (1105:1089)
[-3, -1, 2, 0, -1, 1⟩ (2299:2295)
[-5, 0, 1, -1, 2, 0⟩ (3179:3159)
[0, 0, -1, 2, -2, 1⟩ (3211:3179)
[-5, 2, 0, 2, -1, 0⟩ (4225:4131)
[-5, 2, 1, 0, 1, -1⟩ (4675:4617)


Subsets
==== 3.5.11.13.17.19.23 ====
b28, b33, b5p, b61, b56f, b23f, b38ch, b66ch, b89fgh, b10cfh
[[Subgroup]]: 3.5.11.13.17.19.23
</pre>
 
[[Comma list]]: 209/207, 247/243, 255/253, 325/323, 4675/4617
 
[[Gencom]]: [3/1 99/65; 209/207 247/243 255/253 325/323 4675/4617]
 
[[Sval]] [[mapping]]: [{{val|1 5 1 -2 1 7 6}}, {{val|0 -9 3 11 4 -11 -8}}]
 
[[POTE generator]]: ~[[17/11]] = 748.0874
 
[[EDT]]s: {{EDs|b28, b5, b33, b23f, b61, b56f, b38ch, b10cfhi, b66ch, b51ffg|equave=t}}


==== 3.5.11.13.17.19.23 ====
<pre>
Reduced Mapping
3 5 11 13 17 19 23
[ ⟨ 1 5 1 -2 1 7 6 ]
⟨ 0 -9 3 11 4 -11 -8 ] ⟩
TE Generator Tunings (cents)
⟨1905.4824, 749.4748]
TE Step Tunings (cents)
⟨38.60323, 24.98764]
TE Tuning Map (cents)
⟨1905.482, 2782.139, 4153.907, 4433.258, 4903.382, 5094.154, 5437.096]
TE Mistunings (cents)
⟨3.527, -4.175, 2.589, -7.270, -1.574, -3.359, 8.822]
Complexity 1.382541
Complexity 1.382541
Adjusted Error 7.087107 cents
Adjusted Error 7.087107 cents
TE Error 1.566709 cents/octave
TE Error 1.566709 cents/octave
Unison Vectors
[-2, 0, 1, 0, 0, 1, -1⟩ (209:207)
[1, 1, -1, 0, 1, 0, -1⟩ (255:253)
[-3, 0, -1, 1, 0, 0, 1⟩ (299:297)
[0, 2, 0, 1, -1, -1, 0⟩ (325:323)
[-5, 2, 1, 0, 1, -1, 0⟩ (4675:4617)
[0, -2, -1, 1, -1, 2, 0⟩ (4693:4675)
Subsets
b28, b5p, b33, b23f, b61, b56f, b38ch, b10cfhi, b66ch, b51ffg
</pre>


== Alnilam ==
== Alnilam ==
Retrieved from "https://en.xen.wiki/w/No-twos_subgroup_temperaments"