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= Squares =
= Squares =
[[Comma]]s: 81/80, 2401/2400


Squares splits the interval of an eleventh, or 8/3, into four supermajor third ([[9/7]]) intervals, and uses it for a generator. [[31edo]], with a generator of 11/31, makes for a good squares tuning, with 8, 11, and 14 note MOS available. Squares tempers out 2401/2400, the breedsma, as well as 2430/2401.
Squares splits the interval of an eleventh, or 8/3, into four supermajor third ([[9/7]]) intervals, and uses it for a generator. [[31edo]], with a generator of 11/31, makes for a good squares tuning, with 8, 11, and 14 note MOS available. Squares tempers out [[2401/2400]], the breedsma, as well as [[2430/2401]].


7 and 9 limit minimax 1/4 comma
Period: 1\1


[{{Monzo| 1 0 0 0 }}, {{Monzo| 1 0 1/4 0 }}, {{Monzo| 0 0 1 0 }}, {{Monzo| 3/2 0 9/16 0 }}]
Optimal (POTE) generator: ~9/7 = 425.942


[[Eigenmonzo]]s: 2, 5
EDO generators: [[14edo|5\14]], [[17edo|6\17]], [[31edo|11\31]]


[[POTE generator]]: ~9/7 = 425.942
Scales (Scala files): [[Skwares8]], [[Skwares11]], [[Skwares14]]


Mapping generator: ~9/7
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Algebraic generator: Sceptre2, the positive root of 9''x''<sup>2</sup> + ''x'' - 16, or (sqrt (577) - 1)/18, which is 425.9311 cents.
[[Comma]] list: 81/80, 2401/2400
 
Mapping: [{{val| 1 3 8 6 }}, {{val| 0 -4 -16 -9 }}]
 
Mapping generators: ~2, ~9/7


Map: [&lt;1 3 8 6|, &lt;0 -4 -16 -9|]
Minimax tuning:
* 7- and 9-odd-limit: 1/4 comma
: [{{Monzo| 1 0 0 0 }}, {{Monzo| 1 0 1/4 0 }}, {{Monzo| 0 0 1 0 }}, {{Monzo| 3/2 0 9/16 0 }}]
: [[Eigenmonzo]]s: 2, 5


[[Generator]]s: 2, 9/7
Algebraic generator: Sceptre2, the positive root of 9''x''<sup>2</sup> + ''x'' - 16, or (sqrt (577) - 1)/18, which is 425.9311 cents.


{{Vals|legend=1| 14c, 17c, 31, 45, 76 }}
{{Vals|legend=1| 14c, 17c, 31 }}


[[Badness]]: 0.0460
[[Badness]]: 0.0460


Music:
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; Music:


By [[Chris Vaisvil]]
By [[Chris Vaisvil]]
Line 2,716: Line 2,726:


== 11-limit ==
== 11-limit ==
Commas: 81/80, 99/98, 121/120


POTE generator: ~9/7 = 425.957
Period: 1\1


Mapping generator: ~9/7
Optimal (POTE) generator: ~9/7 = 425.957


Map: [&lt;1 3 8 6 7|, &lt;0 -4 -16 -9 -10|]
EDO generators: [[14edo|5\14]], [[17edo|6\17]], [[31edo|11\31]]


{{Vals|legend=1| 14c, 17c, 31, 45e, 76e }}
Scales (Scala files): [[Skwares8]], [[Skwares11]], [[Skwares14]]
 
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Comma list: 81/80, 99/98, 121/120
 
Mapping: [{{val| 1 3 8 6 7 }}, {{val| 0 -4 -16 -9 -10 }}]
 
Mapping generators: ~2, ~9/7
 
{{Vals|legend=1| 14c, 17c, 31 }}


Badness: 0.0216
Badness: 0.0216
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=== 13-limit ===
=== 13-limit ===
Commas: 66/65, 81/80, 99/98, 121/120


POTE generator: ~9/7 = 425.550
Period: 1\1
 
Optimal (POTE) generator: ~9/7 = 425.550
 
EDO generators: [[14edo|5\14]], [[17edo|6\17]], [[31edo|11\31]]
 
Scales (Scala files): [[Skwares8]], [[Skwares11]], [[Skwares14]]
 
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Mapping generator: ~9/7
Comma list: 66/65, 81/80, 99/98, 121/120


Map: [&lt;1 3 8 6 7 3|, &lt;0 -4 -16 -9 -10 2|]
Mapping: [{{val| 1 3 8 6 7 3 }}, {{val| 0 -4 -16 -9 -10 2 }}]
 
Mapping generators: ~2, ~9/7


{{Vals|legend=1| 14c, 17c, 31, 45e, 79cf }}
{{Vals|legend=1| 14c, 17c, 31, 45e, 79cf }}


Badness: 0.0255
Badness: 0.0255
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=== Agora ===
=== Agora ===
Commas: 81/80, 99/98, 105/104, 121/120


POTE generator: ~9/7 = 426.276
Period: 1\1


Mapping generator: ~9/7
Optimal (POTE) generator: ~9/7 = 426.276


Map: [&lt;1 3 8 6 7 14|, &lt;0 -4 -16 -9 -10 -29|]
EDO generators: [[14edo|5\14]], [[31edo|11\31]], [[45edo|16\45]]
 
Scales (Scala files): [[Skwares8]], [[Skwares11]], [[Skwares14]]
 
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Comma list: 81/80, 99/98, 105/104, 121/120
 
Mapping: [{{val| 1 3 8 6 7 14 }}, {{val| 0 -4 -16 -9 -10 -29 }}]
 
Mapping generators: ~2, ~9/7


{{Vals|legend=1| 14cf, 31, 45ef, 76e }}
{{Vals|legend=1| 14cf, 31, 45ef, 76e }}


Badness: 0.0245
Badness: 0.0245
</div></div>


==== 17-limit ====
==== 17-limit ====
Commas: 81/80, 99/98, 105/104, 120/119, 121/119


POTE generator: ~9/7 = 426.187
Period: 1\1
 
Optimal (POTE) generator: ~9/7 = 426.187
 
EDO generators: [[14edo|5\14]], [[31edo|11\31]], [[45edo|16\45]]
 
Scales (Scala files): [[Skwares8]], [[Skwares11]], [[Skwares14]]


Mapping generator: ~9/7
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Map: [&lt;1 3 8 6 7 14 8|, &lt;0 -4 -16 -9 -10 -29 -11|]
Comma list: 81/80, 99/98, 105/104, 120/119, 121/119


{{Vals|legend=1| 14cf, 31, 45ef, 76e }}
Mapping: [{{val| 1 3 8 6 7 14 8 }}, {{val| 0 -4 -16 -9 -10 -29 -11 }}]
 
Mapping generators: ~2, ~9/7
 
{{Vals|legend=1| 14cf, 31, 76e }}
 
</div></div>


==== 19-limit ====
==== 19-limit ====
Commas: 77/76, 81/80, 99/98, 105/104, 120/119, 121/119


POTE generator: ~9/7 = 426.225
Period: 1\1


Mapping generator: ~9/7
Optimal (POTE) generator: ~9/7 = 426.225


Map: [&lt;1 3 8 6 7 14 8 11|, &lt;0 -4 -16 -9 -10 -29 -11 -19|]
EDO generators: [[14edo|5\14]], [[31edo|11\31]], [[45edo|16\45]]


{{Vals|legend=1| 14cf, 31, 45ef, 76e }}
Scales (Scala files): [[Skwares8]], [[Skwares11]], [[Skwares14]]
 
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Comma list: 77/76, 81/80, 99/98, 105/104, 120/119, 121/119
 
Mapping: [{{val| 1 3 8 6 7 14 8 11 }}, {{val| 0 -4 -16 -9 -10 -29 -11 -19 }}]
 
Mapping generators: ~2, ~9/7
 
{{Vals|legend=1| 14cf, 31, 76e }}
 
</div></div>


== Cuboctahedra ==
== Cuboctahedra ==
[[Comma]]s: 81/80, 385/384, 1375/1372


[[POTE generator]]: ~9/7 = 425.993
Period: 1\1
 
Optimal (POTE) generator: ~9/7 = 425.993
 
EDO generators: [[31edo|11\31]], [[45edo|16\45]]


Mapping generator: ~9/7
Scales (Scala files): [[Skwares8]], [[Skwares11]], [[Skwares14]]


Map: [&lt;1 3 8 6 -4|, &lt;0 -4 -16 -9 21|]
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<div style="line-height:1.6;">Technical data</div>
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{{Vals|legend=1| 14ce, 17ce, 31, 45, 76, 107b }}
[[Comma]] list: 81/80, 385/384, 1375/1372
 
Mapping: [{{val| 1 3 8 6 -4 }}, {{val| 0 -4 -16 -9 21 }}]
 
Mapping generators: ~2, ~9/7
 
{{Vals|legend=1| 14ce, 17ce, 107b }}


[[Badness]]: 0.0568
[[Badness]]: 0.0568
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= Liese =
= Liese =
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