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The hemimean comma, 3136/3125, is the ratio between the diesis and the tritonic diesis, or jubilisma; that is, (128/125)/(50/49).  
The hemimean comma, 3136/3125, is the ratio between the diesis and the tritonic diesis, or jubilisma; that is, (128/125)/(50/49).  


== Hemimean ==
== Hemimean ==
 
[[Subgroup]]: 2.3.5.7
Subgroup: 2.3.5.7


[[Comma list]]: 3136/3125 (hemimean)
[[Comma list]]: 3136/3125 (hemimean)
Line 22: Line 21:
* 7- and [[9-odd-limit]]
* 7- and [[9-odd-limit]]
: [{{monzo| 1 0 0 0 }}, {{monzo| 0 1 0 0 }}, {{monzo| 6/5 0 0 2/5 }}, {{monzo| 0 0 0 1 }}]
: [{{monzo| 1 0 0 0 }}, {{monzo| 0 1 0 0 }}, {{monzo| 6/5 0 0 2/5 }}, {{monzo| 0 0 0 1 }}]
: [[Eigenmonzo]]s (unchanged intervals): 2, 7/6, 4/3
: [[Eigenmonzo basis]]: 2.3.7


{{Val list|legend=1| 12, 19, 31, 68, 80, 87, 99, 217, 229, 328, 347, 446, 545c, 675c }}
{{Val list|legend=1| 12, 19, 31, 68, 80, 87, 99, 217, 229, 328, 347, 446, 545c, 675c }}
Line 32: Line 31:
[[Projection pair]]s: 5 3136/625 7 68841472/9765625 to 2.3.25/7
[[Projection pair]]s: 5 3136/625 7 68841472/9765625 to 2.3.25/7


== Belobog ==
== Belobog ==
 
[[Subgroup]]: 2.3.5.7.11
Subgroup: 2.3.5.7.11


[[Comma list]]: 441/440, 3136/3125
[[Comma list]]: 441/440, 3136/3125
Line 51: Line 49:
* [[11-odd-limit]]
* [[11-odd-limit]]
: [{{monzo| 1 0 0 0 0 }}, {{monzo| 27/22 6/11 -5/22 -3/11 5/22 }}, {{monzo| 24/11 -4/11 -2/11 2/11 2/11 }}, {{monzo| 27/11 -10/11 -5/11 5/11 5/11 }}, {{monzo| 24/11 -4/11 -13/11 2/11 13/11 }}]
: [{{monzo| 1 0 0 0 0 }}, {{monzo| 27/22 6/11 -5/22 -3/11 5/22 }}, {{monzo| 24/11 -4/11 -2/11 2/11 2/11 }}, {{monzo| 27/11 -10/11 -5/11 5/11 5/11 }}, {{monzo| 24/11 -4/11 -13/11 2/11 13/11 }}]
: [[Eigenmonzo]]s (unchanged intervals): 2, 11/10, 9/7
: [[Eigenmonzo basis]]: 2.9/7.11/5


{{Val list|legend=1| 12, 19e, 31, 87, 99e, 118, 130, 217, 248, 378, 626, 961cd }}
{{Val list|legend=1| 12, 19e, 31, 87, 99e, 118, 130, 217, 248, 378, 626, 961cd }}
Line 61: Line 59:
Scales: [[belobog31]]
Scales: [[belobog31]]


=== 13-limit ===
=== 13-limit ===
 
Subgroup: 2.3.5.7.11.13
Subgroup: 2.3.5.7.11.13


Line 69: Line 66:
Mapping: [{{val| 1 0 0 -3 -9 15 }}, {{val| 0 1 0 0 2 -2 }}, {{val| 0 0 2 5 8 -7 }}]
Mapping: [{{val| 1 0 0 -3 -9 15 }}, {{val| 0 1 0 0 2 -2 }}, {{val| 0 0 2 5 8 -7 }}]


{{Val list|legend=1| 31, 43, 56, 74, 87, 118, 130, 217, 248, 347e, 378, 465, 595e }}
Optimal GPV sequence: {{Val list| 31, 43, 56, 74, 87, 118, 130, 217, 248, 347e, 378, 465, 595e }}


Badness: 1.11 × 10<sup>-3</sup>
Badness: 1.11 × 10<sup>-3</sup>


=== Bellowblog ===
=== Bellowblog ===
 
Subgroup: 2.3.5.7.11.13
Subgroup: 2.3.5.7.11.13


Line 81: Line 77:
Mapping: [{{val| 0 0 -3 -9 -4 }}, {{val| 0 1 0 0 2 -1 }}, {{val| 0 0 2 5 8 8 }}]
Mapping: [{{val| 0 0 -3 -9 -4 }}, {{val| 0 1 0 0 2 -1 }}, {{val| 0 0 2 5 8 8 }}]


{{Val list|legend=1| 12f, 19e, 31, 56, 68e, 87, 118, 205d, 263f, 304f, 391df, 509df }}
Optimal GPV sequence: {{Val list| 12f, 19e, 31, 56, 68e, 87, 118, 205d, 263f, 304f, 391df, 509df }}


Badness: 1.26 × 10<sup>-3</sup>
Badness: 1.26 × 10<sup>-3</sup>


== Siebog ==
== Siebog ==
[[Subgroup]]: 2.3.5.7.11
 
[[Comma list]]: 540/539, 3136/3125


Subgroup: 2.3.5.7.11
[[Mapping]]: [{{val| 1 0 0 -3 8 }}, {{val| 0 1 0 0 3 }}, {{val| 0 0 2 5 -8 }}]


[[Comma list]]: 540/539, 3136/3125
Mapping generators: ~2, ~3, ~768/343


[[Minimax tuning]]:  
[[Minimax tuning]]:  
* [[11-odd-limit]]
* [[11-odd-limit]]
: [{{monzo| 1 0 0 0 0 }}, {{monzo| 0 1 0 0 0 }}, {{monzo| 8/5 3/5 1/5 0 -1/5 }}, {{monzo| 1 3/2 1/2 0 -1/2 }}, {{monzo| 8/5 3/5 -4/5 0 4/5 }}]
: [{{monzo| 1 0 0 0 0 }}, {{monzo| 0 1 0 0 0 }}, {{monzo| 8/5 3/5 1/5 0 -1/5 }}, {{monzo| 1 3/2 1/2 0 -1/2 }}, {{monzo| 8/5 3/5 -4/5 0 4/5 }}]
: [[Eigenmonzo]]s (unchanged intervals): 2, 11/10, 4/3
: [[Eigenmonzo basis]]: 2.3.11/10
 
[[Mapping]]: [{{val| 1 0 0 -3 8 }}, {{val| 0 1 0 0 3 }}, {{val| 0 0 2 5 -8 }}]
 
Mapping generators: ~2, ~3, ~768/343


{{Val list|legend=1| 12e, 19, 31, 68e, 80, 99e, 130, 241, 340ce, 371ce, 470cde, 711cde }}
{{Val list|legend=1| 12e, 19, 31, 68e, 80, 99e, 130, 241, 340ce, 371ce, 470cde, 711cde }}
Line 104: Line 99:
[[Badness]]: 0.870 × 10<sup>-3</sup>
[[Badness]]: 0.870 × 10<sup>-3</sup>


== Triglav ==
== Triglav ==
 
[[Subgroup]]: 2.3.5.7.11
Subgroup: 2.3.5.7.11


[[Comma list]]: 3025/3024, 3136/3125
[[Comma list]]: 3025/3024, 3136/3125


[[Mapping]]: [{{val| 1 0 2 2 1 }}, {{val| 0 1 2 5 2 }}, {{val| 0 0 -4 -10 -1 }}]
[[Mapping]]: [{{val| 1 0 2 2 1 }}, {{val| 0 1 2 5 2 }}, {{val| 0 0 -4 -10 -1 }}]
Mapping generators: ~2, ~3, ~18/11


{{Val list|legend=1| 31, 80, 87, 111, 118, 198, 316, 545c, 861ce }}
{{Val list|legend=1| 31, 80, 87, 111, 118, 198, 316, 545c, 861ce }}
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