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The '''marvel family''' is the set of temperaments that temper out the [[7-limit]] ''marvel comma'' ([[225/224]] = {{monzo|-5 2 2 -1}}) which is also named ''septimal kleisma''. These temperaments hence equate [[16/15]] and [[15/14]], or equivalently they equate two [[5/4]]'s and one [[14/9]]. The marvel comma is noteworthy in that it is tempered out by many common edos and rank-2 temperaments.
The '''marvel family''' is the set of temperaments that temper out the [[7-limit]] marvel comma ([[225/224]] = {{monzo| -5 2 2 -1 }}) which is also known as ''septimal kleisma''. These temperaments hence equate [[16/15]] and [[15/14]], or equivalently they equate two [[5/4]]'s and one [[14/9]]. The marvel comma is noteworthy in that it is tempered out by many common edos and rank-2 temperaments.


The marvel comma can also be viewed as a comma of the 2.9.25.7 subgroup. Hence it is tempered out by any subset edos of marvel-supporting edos that have this subgroup, such as [[11edo]] and [[17edo]] which are subsets of [[22edo]] and [[34edo]] (when using the 34b val) which temper out the marvel comma.
The marvel comma can also be viewed as a comma of the 2.9.25.7 subgroup. Hence it is tempered out by any subset edos of marvel-supporting edos that have this subgroup, such as [[11edo]] and [[17edo]] which are subsets of [[22edo]] and [[34edo]] (when using the 34b val) which temper out the marvel comma.


== Marvel ==
== Marvel ==
{{main| Marvel }}
{{Main| Marvel }}


The head of the marvel family is marvel, which tempers out [[225/224]]. Marvel has a [[Normal lists|normal list basis]] of [2, 3, 5]; hence a [[5-limit]] scale can be converted to marvel simply by tempering it. One way to do that, and an excellent marvel tuning, is given by [[197edo]].
The head of the marvel family is marvel, which tempers out [[225/224]]. Marvel has a [[Normal lists|normal list basis]] of [2, 3, 5]; hence a [[5-limit]] scale can be converted to marvel simply by tempering it. One way to do that, and an excellent marvel tuning, is given by [[197edo]].
Line 20: Line 20:
[[Comma list]]: 225/224
[[Comma list]]: 225/224


[[Mapping]]: [{{val| 1 0 0 -5 }}, {{val| 0 1 0 2 }}, {{val| 0 0 1 2 }}]
{{Mapping|legend=1| 1 0 0 -5 | 0 1 0 2 | 0 0 1 2 }}


Mapping generators: ~2, ~3, ~5
: mapping generators: ~2, ~3, ~5


Map to lattice: [{{val| 0 0 -1 -2 }}, {{val| 0 1 -1 0 }}]
Map to lattice: [{{val| 0 0 -1 -2 }}, {{val| 0 1 -1 0 }}]
Line 30: Line 30:
: Angle (secor, 3/2) = 106.958 degrees
: Angle (secor, 3/2) = 106.958 degrees


[[Optimal tuning]] ([[POTE]]): ~3/2 = 700.4075, ~5/4 = 383.6376
[[Optimal tuning]] ([[POTE]]): ~2 = 1\1, ~3/2 = 700.4075, ~5/4 = 383.6376


[[Minimax tuning]]:  
[[Minimax tuning]]:  
* [[7-odd-limit]]: 3 and 5 1/4c flat, 7 just
* [[7-odd-limit]]: 3 and 5 1/4-comma flat, 7 just
: [{{monzo| 1 0 0 0 }}, {{monzo| 5/4 1/2 -1/2 1/4 }}, {{monzo| 5/4 -1/2 1/2 1/4 }}, {{monzo| 0 0 0 1 }}]
: {{monzo list| 1 0 0 0 | 5/4 1/2 -1/2 1/4 | 5/4 -1/2 1/2 1/4 | 0 0 0 1 }}
: [[Eigenmonzo subgroup]] ([[unchanged-interval basis]]): 2.5/3.7
: [[Eigenmonzo basis|eigenmonzo (unchanged-interval) basis]]: 2.5/3.7
* [[9-odd-limit]]: 3 1/6c flat, 5 1/3c flat, 7 just
* [[9-odd-limit]]: 3 1/6-comma flat, 5 1/3-comma flat, 7 just
: [{{monzo| 1 0 0 0 }}, {{monzo| 5/6 2/3 -1/3 1/6 }}, {{monzo| 5/3 -2/3 1/3 1/3 }}, {{monzo| 0 0 0 1 }}]
: {{monzo list| 1 0 0 0 | 5/6 2/3 -1/3 1/6 | 5/3 -2/3 1/3 1/3 | 0 0 0 1 }}
: [[Eigenmonzo subgroup]] ([[unchanged-interval basis]]): 2.9/5.7
: [[Eigenmonzo basis|eigenmonzo (unchanged-interval) basis]]: 2.9/5.7


{{Optimal ET sequence|legend=1| 9, 10, 12, 19, 31, 41, 53, 72, 197, 269c }}
{{Optimal ET sequence|legend=1| 9, 10, 12, 19, 31, 41, 53, 72, 197, 269c }}
Line 53: Line 53:


{{Databox|[[Minkowski blocks]]|
{{Databox|[[Minkowski blocks]]|
{2, 3, 5} subgroup
2.3.5 subgroup
* 8: 16/15, 250/243
* 8: 16/15, 250/243
* 9: 135/128, 128/125
* 9: 135/128, 128/125
Line 83: Line 83:
[[Comma list]]: 225/224, 385/384
[[Comma list]]: 225/224, 385/384


[[Mapping]]: [{{val| 1 0 0 -5 12 }}, {{val| 0 1 0 2 -1 }}, {{val| 0 0 1 2 -3 }}]
{{Mapping|legend=1| 1 0 0 -5 12 | 0 1 0 2 -1 | 0 0 1 2 -3 }}


Map to lattice: [{{val| 0 -1 0 -2 1 }}, {{val| 0 -1 1 0 -2 }}]
[[Map to lattice]]: [{{val| 0 -1 0 -2 1 }}, {{val| 0 -1 1 0 -2 }}]


Lattice basis:  
Lattice basis:  
Line 91: Line 91:
: Angle (secor, 5/4) = 104.028 degrees
: Angle (secor, 5/4) = 104.028 degrees


[[Optimal tuning]] ([[POTE]]): ~3/2 = 700.3887, ~5/4 = 383.5403
[[Optimal tuning]] ([[POTE]]): ~2 = 1\1, ~3/2 = 700.3887, ~5/4 = 383.5403


[[Minimax tuning]]:
[[Minimax tuning]]:
* 11-odd-limit
* [[11-odd-limit]]
: [{{monzo| 1 0 0 0 0 }}, {{monzo| 4/3 8/9 -1/3 0 -1/9 }}, {{monzo| 8/3 -2/9 1/3 0 -2/9 }}, {{monzo| 3 4/3 0 0 -2/3 }}, {{monzo| 8/3 -2/9 -2/3 0 7/9 }}]
: [{{monzo| 1 0 0 0 0 }}, {{monzo| 4/3 8/9 -1/3 0 -1/9 }}, {{monzo| 8/3 -2/9 1/3 0 -2/9 }}, {{monzo| 3 4/3 0 0 -2/3 }}, {{monzo| 8/3 -2/9 -2/3 0 7/9 }}]
: [[Eigenmonzo subgroup]] ([[unchanged-interval basis]]): 2.9/5.11/9
: [[Eigenmonzo basis|eigenmonzo (unchanged-interval) basis]]: 2.9/5.11/9


{{Optimal ET sequence|legend=1| 9, 10, 12e, 19, 22, 31, 41, 53, 72, 166, 197e, 238c, 269ce, 341ce }}
{{Optimal ET sequence|legend=1| 9, 10, 12e, 19, 22, 31, 41, 53, 72, 166, 197e, 238c, 269ce, 341ce }}
Line 111: Line 111:


{{Databox|Hobbit bases|
{{Databox|Hobbit bases|
{2, 3, 5} subgroup
2.3.5 subgroup
* 12: 128/125, 2048/2025
* 12: 128/125, 2048/2025
* 15: 128/125, 32768/30375
* 15: 128/125, 32768/30375
Line 125: Line 125:
Comma list: 225/224, 351/350, 385/384
Comma list: 225/224, 351/350, 385/384


Mapping: [{{val| 1 0 0 -5 12 -4 }}, {{val| 0 1 0 2 -1 -1 }}, {{val| 0 0 1 2 -3 4 }}]
Mapping: {{mapping| 1 0 0 -5 12 -4 | 0 1 0 2 -1 -1 | 0 0 1 2 -3 4 }}


Optimal tuning (POTE): ~3/2 = 699.7367, ~5/4 = 384.0613
Optimal tuning (POTE): ~2 = 1\1, ~3/2 = 699.7367, ~5/4 = 384.0613


Minimax tuning:  
Minimax tuning:  
* 13-odd-limit eigenmonzo subgroup (unchanged-interval basis): 2.11/9.13/9
* 13-odd-limit eigenmonzo (unchanged-interval) basis: 2.11/9.13/9
* 15-odd-limit eigenmonzo subgroup (unchanged-interval basis): 2.15/11.15/13
* 15-odd-limit eigenmonzo (unchanged-interval) basis: 2.15/11.15/13


{{Optimal ET sequence|legend=1| 19, 22, 31, 50, 53, 72, 103, 175f, 300ceff, 403bceeff, 578bbccdeeefff }}
{{Optimal ET sequence|legend=1| 19, 22, 31, 50, 53, 72, 103, 175f, 300ceff, 403bceeff, 578bbccdeeefff }}
Line 144: Line 144:
Comma list: 225/224, 325/324, 385/384
Comma list: 225/224, 325/324, 385/384


Mapping: [{{val| 1 0 0 -5 12 2 }}, {{val| 0 1 0 2 -1 4 }}, {{val| 0 0 1 2 -3 -2 }}]
Mapping: {{mapping| 1 0 0 -5 12 2 | 0 1 0 2 -1 4 | 0 0 1 2 -3 -2 }}


Optimal tuning (POTE): ~3/2 = 700.9779, ~5/4 = 383.1622
Optimal tuning (POTE): ~2 = 1\1, ~3/2 = 700.9779, ~5/4 = 383.1622


Minimax tuning:  
Minimax tuning:  
* 13-odd-limit eigenmonzo subgroup (unchanged-interval basis): 2.7.13/5
* 13-odd-limit eigenmonzo (unchanged-interval) basis: 2.7.13/5
* 15-odd-limit eigenmonzo subgroup (unchanged-interval basis): 2.7.15/13
* 15-odd-limit eigenmonzo (unchanged-interval) basis: 2.7.15/13


{{Optimal ET sequence|legend=1| 19, 22f, 31f, 41, 53, 72, 125f, 166, 238cf }}
{{Optimal ET sequence|legend=1| 19, 22f, 31f, 41, 53, 72, 125f, 166, 238cf }}
Line 165: Line 165:
Comma list: 225/224, 325/324, 385/384, 595/594
Comma list: 225/224, 325/324, 385/384, 595/594


Mapping: [{{val| 1 0 0 -5 12 2 18 }}, {{val| 0 1 0 2 -1 4 0 }}, {{val| 0 0 1 2 -3 -2 -6 }}]
Mapping: {{mapping| 1 0 0 -5 12 2 18 | 0 1 0 2 -1 4 0 | 0 0 1 2 -3 -2 -6 }}


Optimal tuning (POTE): ~3/2 = 700.9619, ~5/4 = 383.0310
Optimal tuning (POTE): ~2 = 1\1, ~3/2 = 700.9619, ~5/4 = 383.0310


{{Optimal ET sequence|legend=1| 19, 22f, 31fg, 41, 53g, 72, 166g, 238cfg, 404ccefgg }}
{{Optimal ET sequence|legend=1| 19, 22f, 31fg, 41, 53g, 72, 166g, 238cfg, 404ccefgg }}
Line 178: Line 178:
Comma list: 225/224, 325/324, 375/374, 385/384
Comma list: 225/224, 325/324, 375/374, 385/384


Mapping: [{{val| 1 0 0 -5 12 2 18 }}, {{val| 0 1 0 2 -1 4 0 }}, {{val| 0 0 1 2 -3 -2 6 }}]
Mapping: {{mapping| 1 0 0 -5 12 2 18 | 0 1 0 2 -1 4 0 | 0 0 1 2 -3 -2 6 }}


Optimal tuning (POTE): ~3/2 = 700.9658, ~5/4 = 383.3063
Optimal tuning (POTE): ~2 = 1\1, ~3/2 = 700.9658, ~5/4 = 383.3063


{{Optimal ET sequence|legend=1| 19g, 22f, 31f, 41g, 53, 72, 166g, 238cfg, 404ccefgg }}
{{Optimal ET sequence|legend=1| 19g, 22f, 31f, 41g, 53, 72, 166g, 238cfg, 404ccefgg }}
Line 191: Line 191:
Comma list: 225/224, 385/384, 1573/1568
Comma list: 225/224, 385/384, 1573/1568


Mapping: [{{val| 1 0 0 -5 12 -29 }}, {{val| 0 1 0 2 -1 6 }}, {{val| 0 0 1 2 -3 10 }}]
Mapping: {{mapping| 1 0 0 -5 12 -29 | 0 1 0 2 -1 6 | 0 0 1 2 -3 10 }}


Optimal tuning (POTE): ~3/2 = 700.3937, ~5/4 = 383.5725
Optimal tuning (POTE): ~2 = 1\1, ~3/2 = 700.3937, ~5/4 = 383.5725


Minimax tuning:  
Minimax tuning:  
* 13-odd-limit eigenmonzo subgroup (unchanged-interval basis): 2.9/5.11/9
* 13-odd-limit eigenmonzo (unchanged-interval) basis: 2.9/5.11/9
* 15-odd-limit eigenmonzo subgroup (unchanged-interval basis): 2.7.15/13
* 15-odd-limit eigenmonzo (unchanged-interval) basis: 2.7.15/13


{{Optimal ET sequence|legend=1| 9, 22f, 31, 63, 72, 103, 166, 238cf, 269ce, 507bcceff, 610bcceeff }}
{{Optimal ET sequence|legend=1| 9, 22f, 31, 63, 72, 103, 166, 238cf, 269ce, 507bcceff, 610bcceeff }}
Line 208: Line 208:
Comma list: 225/224, 275/273, 385/384
Comma list: 225/224, 275/273, 385/384


Mapping: [{{val| 1 0 0 -5 12 17 }}, {{val| 0 1 0 2 -1 4 }}, {{val| 0 0 1 2 -3 -3 }}]
Mapping: {{mapping| 1 0 0 -5 12 17 | 0 1 0 2 -1 4 | 0 0 1 2 -3 -3 }}


Optimal tuning (POTE): ~3/2 = 701.9156, ~5/4 = 383.2445
Optimal tuning (POTE): ~2 = 1\1, ~3/2 = 701.9156, ~5/4 = 383.2445


{{Optimal ET sequence|legend=1| 10, 19f, 22, 31, 41, 53, 94 }}
{{Optimal ET sequence|legend=1| 10, 19f, 22, 31, 41, 53, 94 }}
Line 223: Line 223:
Comma list: 225/224, 364/363, 385/384
Comma list: 225/224, 364/363, 385/384


Mapping: [{{val| 1 0 0 -5 12 27 }}, {{val| 0 1 0 2 -1 -3 }}, {{val| 0 0 1 2 -3 -8 }}]
Mapping: {{mapping| 1 0 0 -5 12 27 | 0 1 0 2 -1 -3 | 0 0 1 2 -3 -8 }}


Optimal tuning (POTE): ~3/2 = 700.4560, ~5/4 = 382.8177
Optimal tuning (POTE): ~2 = 1\1, ~3/2 = 700.4560, ~5/4 = 382.8177


Minimax tuning:  
Minimax tuning:  
Line 242: Line 242:
Comma list: 105/104, 144/143, 196/195
Comma list: 105/104, 144/143, 196/195


Mapping: [{{val| 1 0 0 -5 12 -8 }}, {{val| 0 1 0 2 -1 3 }}, {{val| 0 0 1 2 -3 3 }}]
Mapping: {{mapping| 1 0 0 -5 12 -8 | 0 1 0 2 -1 3 | 0 0 1 2 -3 3 }}


Optimal tuning (POTE): ~3/2 = 699.2335, ~5/4 = 382.9775
Optimal tuning (POTE): ~2 = 1\1, ~3/2 = 699.2335, ~5/4 = 382.9775


Minimax tuning:  
Minimax tuning:  
* 13-odd-limit eigenmonzo subgroup (unchanged-interval basis): 2.9/7.13/11
* 13-odd-limit eigenmonzo (unchanged-interval) basis: 2.9/7.13/11
* 15-odd-limit eigenmonzo subgroup (unchanged-interval basis): 2.5/3.13/11
* 15-odd-limit eigenmonzo (unchanged-interval) basis: 2.5/3.13/11


{{Optimal ET sequence|legend=1| 9, 10, 19, 22f, 31, 41, 72f, 91, 122f, 163df }}
{{Optimal ET sequence|legend=1| 9, 10, 19, 22f, 31, 41, 72f, 91, 122f, 163df }}
Line 261: Line 261:
Comma list: 169/168, 225/224, 385/384
Comma list: 169/168, 225/224, 385/384


Mapping: [{{val| 1 0 0 -5 12 -1 }}, {{val| 0 2 0 4 -2 3 }}, {{val| 0 0 1 2 -3 1 }}]
Mapping: {{mapping| 1 0 0 -5 12 -1 | 0 2 0 4 -2 3 | 0 0 1 2 -3 1 }}


Mapping generators: ~2, ~26/15, ~5
: mapping generators: ~2, ~26/15, ~5


Optimal tuning (POTE): ~15/13 = 249.7138, ~5/4 = 383.5816
Optimal tuning (POTE): ~2 = 1\1, ~15/13 = 249.7138, ~5/4 = 383.5816


{{Optimal ET sequence|legend=1| 9, 10, 19, 44, 53, 72, 125f, 197ef, 269ceff }}
{{Optimal ET sequence|legend=1| 9, 10, 19, 44, 53, 72, 125f, 197ef, 269ceff }}
Line 276: Line 276:
[[Comma list]]: 99/98, 176/175
[[Comma list]]: 99/98, 176/175


[[Mapping]]: [{{val| 1 0 0 -5 -9 }}, {{val| 0 1 0 2 2 }}, {{val| 0 0 1 2 4 }}]
{{Mapping|legend=1| 1 0 0 -5 -9 | 0 1 0 2 2 | 0 0 1 2 4 }}


Map to lattice: [{{val| 0 -1 0 -2 -2 }}, {{val| 0 -1 1 0 2 }}]
Map to lattice: [{{val| 0 -1 0 -2 -2 }}, {{val| 0 -1 1 0 2 }}]
Line 284: Line 284:
: Angle (16/15, 5/4) = 98.6044 degrees
: Angle (16/15, 5/4) = 98.6044 degrees


[[Optimal tuning]] ([[POTE]]): ~3/2 = 700.2593, ~5/4 = 386.5581
[[Optimal tuning]] ([[POTE]]): ~2 = 1\1, ~3/2 = 700.2593, ~5/4 = 386.5581


[[Minimax tuning]]: [[11-odd-limit]] [[Eigenmonzo subgroup]] ([[unchanged-interval basis]]): 2.7/5.11/9
[[Minimax tuning]]: [[11-odd-limit]] [[Eigenmonzo subgroup]] ([[unchanged-interval basis]]): 2.7/5.11/9
Line 294: Line 294:
[[Projection pair]]s: 7 225/32 11 5625/512
[[Projection pair]]s: 7 225/32 11 5625/512


Scales (Scala files): [[minerva12]], [[minerva22x]]
Scales: [[minerva12]], [[minerva22x]]


[[Associated temperament]]: [[Würschmidt family #Würschmidt|würschmidt]]
[[Associated temperament]]: [[Würschmidt family #Würschmidt|würschmidt]]
Line 303: Line 303:
Comma list: 99/98, 176/175, 275/273
Comma list: 99/98, 176/175, 275/273


Mapping: [{{val| 1 0 0 -5 -9 -4 }}, {{val| 0 1 0 2 2 -1 }}, {{val| 0 0 1 2 4 4 }}]
Mapping: {{mapping| 1 0 0 -5 -9 -4 | 0 1 0 2 2 -1 | 0 0 1 2 4 4 }}


Optimal tuning (POTE): ~3/2 = 701.2342, ~5/4 = 385.9594
Optimal tuning (POTE): ~2 = 1\1, ~3/2 = 701.2342, ~5/4 = 385.9594


Minimax tuning:  
Minimax tuning:  
* 13-odd-limit eigenmonzo subgroup (unchanged-interval basis): 2.11/9.13/7
* 13-odd-limit eigenmonzo (unchanged-interval) basis: 2.11/9.13/7
* 15-odd-limit eigenmonzo subgroup (unchanged-interval basis): 2.11/9.13/7
* 15-odd-limit eigenmonzo (unchanged-interval) basis: 2.11/9.13/7


{{Optimal ET sequence|legend=1| 12f, 19e, 22, 31, 53, 84e, 118d, 171de, 202def }}
{{Optimal ET sequence|legend=1| 12f, 19e, 22, 31, 53, 84e, 118d, 171de, 202def }}
Line 322: Line 322:
[[Comma list]]: 100/99, 225/224
[[Comma list]]: 100/99, 225/224


[[Mapping]]: [{{val| 1 0 0 -5 2 }}, {{val| 0 1 0 2 -2 }}, {{val| 0 0 1 2 2 }}]
{{Mapping|legend=1| 1 0 0 -5 2 | 0 1 0 2 -2 | 0 0 1 2 2 }}


[[Optimal tuning]] ([[POTE]]): ~3/2 = 703.4846, ~5/4 = 381.6033
[[Optimal tuning]] ([[POTE]]): ~2 = 1\1, ~3/2 = 703.4846, ~5/4 = 381.6033


[[Minimax tuning]]: [[11-odd-limit]] [[Eigenmonzo subgroup]] ([[unchanged-interval basis]]): 2.7/5.11/9
[[Minimax tuning]]: [[11-odd-limit]] [[Eigenmonzo basis|eigenmonzo (unchanged-interval) basis]]: 2.7/5.11/9


{{Optimal ET sequence|legend=1| 12, 19, 22, 34d, 41, 104, 157ce, 198ce, 220ce, 261ce }}
{{Optimal ET sequence|legend=1| 12, 19, 22, 34d, 41, 104, 157ce, 198ce, 220ce, 261ce }}
Line 332: Line 332:
[[Projection pair]]s: 7 225/32 11 100/9
[[Projection pair]]s: 7 225/32 11 100/9


[[Associated temperament]]: [[Magic family #magic|magic]]
[[Associated temperament]]: [[magic]]


=== 13-limit ===
=== 13-limit ===
Line 339: Line 339:
Comma list: 100/99, 225/224, 275/273
Comma list: 100/99, 225/224, 275/273


Mapping: [{{val| 1 0 0 -5 2 7 }}, {{val| 0 1 0 2 -2 -5 }}, {{val| 0 0 1 2 2 2 }}]
Mapping: {{mapping| 1 0 0 -5 2 7 | 0 1 0 2 -2 -5 | 0 0 1 2 2 2 }}


Optimal tuning (POTE): ~3/2 = 703.9984, ~5/4 = 381.5352
Optimal tuning (POTE): ~2 = 1\1, ~3/2 = 703.9984, ~5/4 = 381.5352


Minimax tuning: 13-odd-limit eigenmonzo subgroup (unchanged-interval basis): 2.11/9.13/9
Minimax tuning: 13-odd-limit eigenmonzo (unchanged-interval) basis: 2.11/9.13/9


{{Optimal ET sequence|legend=1| 12f, 19f, 22, 29, 34d, 41, 63, 104, 179cef, 242cde, 283def, 346bcdef }}
{{Optimal ET sequence|legend=1| 12f, 19f, 22, 29, 34d, 41, 63, 104, 179cef, 242cde, 283def, 346bcdef }}
Line 354: Line 354:
[[Comma list]]: 45/44, 56/55
[[Comma list]]: 45/44, 56/55


[[Mapping]]: [{{val| 1 0 0 -5 -2 }}, {{val| 0 1 0 2 2 }}, {{val| 0 0 1 2 1 }}]
{{Mapping|legend=1| 1 0 0 -5 -2 | 0 1 0 2 2 | 0 0 1 2 1 }}


[[Optimal tuning]] ([[POTE]]): ~3/2 = 696.1714, ~5/4 = 385.0500
[[Optimal tuning]] ([[POTE]]): ~2 = 1\1, ~3/2 = 696.1714, ~5/4 = 385.0500


[[Minimax tuning]]: [[11-odd-limit]] [[Eigenmonzo subgroup]] ([[unchanged-interval basis]]): 2.9/7.11
[[Minimax tuning]]: [[11-odd-limit]] [[Eigenmonzo basis|eigenmonzo (unchanged-interval) basis]]: 2.9/7.11


{{Optimal ET sequence|legend=1| 7d, 9, 10, 12, 19, 31e, 50e }}
{{Optimal ET sequence|legend=1| 7d, 9, 10, 12, 19, 31e, 50e }}
Line 371: Line 371:
Comma list: 45/44, 56/55, 78/77
Comma list: 45/44, 56/55, 78/77


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


Optimal tuning (POTE): ~3/2 = 696.0103, ~5/4 = 384.6785
Optimal tuning (POTE): ~2 = 1\1, ~3/2 = 696.0103, ~5/4 = 384.6785


Minimax tuning:  
Minimax tuning:  
* 13-odd-limit eigenmonzo subgroup (unchanged-interval basis): 2.9/7.13/9
* 13-odd-limit eigenmonzo (unchanged-interval) basis: 2.9/7.13/9
* 15-odd-limit eigenmonzo subgroup (unchanged-interval basis): 2.9/7.13/9
* 15-odd-limit eigenmonzo (unchanged-interval) basis: 2.9/7.13/9


{{Optimal ET sequence|legend=1| 9, 10, 12f, 19, 31e, 50e }}
{{Optimal ET sequence|legend=1| 9, 10, 12f, 19, 31e, 50e }}
Line 390: Line 390:
[[Comma list]]: 225/224, 2200/2187
[[Comma list]]: 225/224, 2200/2187


[[Mapping]]: [{{val| 1 0 0 -5 -3 }}, {{val| 0 1 0 2 7 }}, {{val| 0 0 1 2 -2 }}]
{{Mapping|legend=1| 1 0 0 -5 -3 | 0 1 0 2 7 | 0 0 1 2 -2 }}


[[Optimal tuning]] ([[POTE]]): ~3/2 = 701.8913, ~5/4 = 382.4083
[[Optimal tuning]] ([[POTE]]): ~2 = 1\1, ~3/2 = 701.8913, ~5/4 = 382.4083


{{Optimal ET sequence|legend=1| 12e, 19e, 34d, 41, 53, 60e, 94, 229c, 248ce, 289cce, 342ccee, 383cce }}
{{Optimal ET sequence|legend=1| 12e, 19e, 34d, 41, 53, 60e, 94, 229c, 248ce, 289cce, 342ccee, 383cce }}
Line 403: Line 403:
Comma list: 225/224, 275/273, 325/324
Comma list: 225/224, 275/273, 325/324


Mapping: [{{val| 1 0 0 -5 -3 2 }}, {{val| 0 1 0 2 7 4 }}, {{val| 0 0 1 2 -2 -2 }}]
Mapping: {{mapping| 1 0 0 -5 -3 2 | 0 1 0 2 7 4 | 0 0 1 2 -2 -2 }}


Optimal tuning (POTE): ~3/2 = 701.8913, ~5/4 = 382.4083
Optimal tuning (POTE): ~2 = 1\1, ~3/2 = 701.8913, ~5/4 = 382.4083


{{Optimal ET sequence|legend=1| 12e, 19e, 34d, 41, 53, 94, 429ccdeef, 523ccdeef }}
{{Optimal ET sequence|legend=1| 12e, 19e, 34d, 41, 53, 94, 429ccdeef, 523ccdeef }}
Line 412: Line 412:


== Prodigy ==
== Prodigy ==
Prodigy shrinks 1024/1029, 243/242, 384/385 and 2400/2401 down to the same tiny interval. Hence in practice it probably makes the most sense to temper this out as well, leading to [[miracle temperament]]. This, however, does not render it pointless to consider prodigy; for one thing, scales in prodigy such as hobbit scales translate into interesting scales for miracle.
Prodigy shrinks 1024/1029, 243/242, 384/385 and 2400/2401 down to the same tiny interval. Hence in practice it probably makes the most sense to temper this out as well, leading to [[miracle]]. This, however, does not render it pointless to consider prodigy; for one thing, scales in prodigy such as hobbit scales translate into interesting scales for miracle.


[[Subgroup]]: 2.3.5.7.11
[[Subgroup]]: 2.3.5.7.11
Line 418: Line 418:
[[Comma list]]: 225/224, 441/440
[[Comma list]]: 225/224, 441/440


[[Mapping]]: [{{val| 1 0 0 -5 -13 }}, {{val| 0 1 0 2 6 }}, {{val| 0 0 1 2 3 }}]
{{Mapping|legend=1| 1 0 0 -5 -13 | 0 1 0 2 6 | 0 0 1 2 3 }}


Map to lattice: [{{val| 0 0 -1 -2 -3 }}, {{val| 0 1 -1 0 3 }}]
Map to lattice: [{{val| 0 0 -1 -2 -3 }}, {{val| 0 1 -1 0 3 }}]
Line 426: Line 426:
: Angle (secor, 3/2) = 65.933
: Angle (secor, 3/2) = 65.933


[[Optimal tuning]] ([[POTE]]): ~3/2 = 699.7981, ~5/4 = 383.5114
[[Optimal tuning]] ([[POTE]]): ~2 = 1\1, ~3/2 = 699.7981, ~5/4 = 383.5114


[[Minimax tuning]]:
[[Minimax tuning]]:
* [[11-odd-limit]]
* [[11-odd-limit]]
: [{{monzo| 1 0 0 0 0 }}, {{monzo| 13/12 1/2 -1/4 0 1/12 }}, {{monzo| 13/6 -1 1/2 0 1/6 }}, {{monzo| 3/2 -1 1/2 0 1/2 }}, {{monzo| 0 0 0 0 1 }}]
: [{{monzo| 1 0 0 0 0 }}, {{monzo| 13/12 1/2 -1/4 0 1/12 }}, {{monzo| 13/6 -1 1/2 0 1/6 }}, {{monzo| 3/2 -1 1/2 0 1/2 }}, {{monzo| 0 0 0 0 1 }}]
: [[Eigenmonzo subgroup]] ([[unchanged-interval basis]]): 2.9/5.11
: [[Eigenmonzo basis|eigenmonzo (unchanged-interval) basis]]: 2.9/5.11


{{Optimal ET sequence|legend=1| 10, 12, 19e, 29, 31, 41, 60e, 72, 247c, 319bcde, 391bcde, 463bccde }}
{{Optimal ET sequence|legend=1| 10, 12, 19e, 29, 31, 41, 60e, 72, 247c, 319bcde, 391bcde, 463bccde }}
Line 441: Line 441:
Scales: [[prodigy11]], [[prodigy12]], [[prodigy29]]
Scales: [[prodigy11]], [[prodigy12]], [[prodigy29]]


[[Associated temperament]]: [[Gamelismic clan #Miracle|miracle]]
[[Associated temperament]]: [[miracle]]


{{Databox|Hobbit bases|
{{Databox|Hobbit bases|
{2, 3, 5} subgroup
2.3.5 subgroup
* 31: 81/80, 34171875/33554432
* 31: 81/80, 34171875/33554432
* 41: 34171875/33554432, 32805/32768
* 41: 34171875/33554432, 32805/32768
Line 454: Line 454:
Comma list: 105/104, 196/195, 352/351
Comma list: 105/104, 196/195, 352/351


Mapping: [{{val| 1 0 0 -5 -13 -8 }}, {{val| 0 1 0 2 6 3 }}, {{val| 0 0 1 2 3 3 }}]
Mapping: {{mapping| 1 0 0 -5 -13 -8 | 0 1 0 2 6 3 | 0 0 1 2 3 3 }}


Optimal tuning (POTE): ~3/2 = 700.4006, ~5/4 = 381.4025
Optimal tuning (POTE): ~2 = 1\1, ~3/2 = 700.4006, ~5/4 = 381.4025


{{Optimal ET sequence|legend=1| 10, 12f, 19e, 29, 31, 41, 60e, 72f, 91e, 101cd, 132def, 233ccddeef, 274ccddeff, 305ccddeeff }}
{{Optimal ET sequence|legend=1| 10, 12f, 19e, 29, 31, 41, 60e, 72f, 91e, 101cd, 132def, 233ccddeef, 274ccddeff, 305ccddeeff }}
Line 467: Line 467:
Comma list: 225/224, 364/363, 441/440
Comma list: 225/224, 364/363, 441/440


Mapping: [{{val| 1 0 0 -5 -13 -23 }}, {{val| 0 1 0 2 6 11 }}, {{val| 0 0 1 2 3 4 }}]
Mapping: {{mapping| 1 0 0 -5 -13 -23 | 0 1 0 2 6 11 | 0 0 1 2 3 4 }}


Optimal tuning (POTE): ~3/2 = 700.3407, ~5/4 = 383.2592
Optimal tuning (POTE): ~2 = 1\1, ~3/2 = 700.3407, ~5/4 = 383.2592


{{Optimal ET sequence|legend=1| 12f, 29, 31f, 41, 72, 185cf, 341cf, 413bcff, 526bccdff }}
{{Optimal ET sequence|legend=1| 12f, 29, 31f, 41, 72, 185cf, 341cf, 413bcff, 526bccdff }}
Line 480: Line 480:
Comma list: 225/224, 351/350, 441/440
Comma list: 225/224, 351/350, 441/440


Mapping: [{{val| 1 0 0 -5 -13 -4 }}, {{val| 0 1 0 2 6 -1 }}, {{val| 0 0 1 2 3 4 }}]
Mapping: {{mapping| 1 0 0 -5 -13 -4 | 0 1 0 2 6 -1 | 0 0 1 2 3 4 }}


Optimal tuning (POTE): ~3/2 = 699.4864, ~5/4 = 384.0998
Optimal tuning (POTE): ~2 = 1\1, ~3/2 = 699.4864, ~5/4 = 384.0998


{{Optimal ET sequence|legend=1| 12f, 19e, 31, 53e, 60eff, 72, 103, 175f }}
{{Optimal ET sequence|legend=1| 12f, 19e, 31, 53e, 60eff, 72, 103, 175f }}
Line 493: Line 493:
Comma list: 225/224, 441/440, 1001/1000
Comma list: 225/224, 441/440, 1001/1000


Mapping: [{{val| 1 0 0 -5 -13 21 }}, {{val| 0 1 0 2 6 -8 }}, {{val| 0 0 1 2 3 -2 }}]
Mapping: {{mapping| 1 0 0 -5 -13 21 | 0 1 0 2 6 -8 | 0 0 1 2 3 -2 }}


Optimal tuning (POTE): ~3/2 = 699.5536, ~5/4 = 383.5696
Optimal tuning (POTE): ~2 = 1\1, ~3/2 = 699.5536, ~5/4 = 383.5696


{{Optimal ET sequence|legend=1| 29, 31, 43, 60e, 72, 103, 175f, 482bccddeefff, 554bbccddeeeffff }}
{{Optimal ET sequence|legend=1| 29, 31, 43, 60e, 72, 103, 175f, 482bccddeefff, 554bbccddeeeffff }}
Line 506: Line 506:
Comma list: 225/224, 273/272, 375/374, 441/440
Comma list: 225/224, 273/272, 375/374, 441/440


Mapping: [{{val| 1 0 0 -5 -13 21 12 }}, {{val| 0 1 0 2 6 -8 -5 }}, {{val| 0 0 1 2 3 -2 0 }}]
Mapping: {{mapping| 1 0 0 -5 -13 21 12 | 0 1 0 2 6 -8 -5 | 0 0 1 2 3 -2 0 }}


Optimal tuning (POTE): ~3/2 = 699.6262, ~5/4 = 383.4458
Optimal tuning (POTE): ~2 = 1\1, ~3/2 = 699.6262, ~5/4 = 383.4458


{{Optimal ET sequence|legend=1| 29g, 31, 43, 60e, 72, 103, 175f, 307bcdeeffg, 379bccdeeffgg, 482bccddeefffgg, 554bbccddeeeffffgg }}
{{Optimal ET sequence|legend=1| 29g, 31, 43, 60e, 72, 103, 175f, 307bcdeeffg, 379bccdeeffgg, 482bccddeefffgg, 554bbccddeeeffffgg }}
Line 519: Line 519:
[[Comma list]]: 225/224, 4375/4356
[[Comma list]]: 225/224, 4375/4356


[[Mapping]]: [{{val| 2 0 0 -10 -7 }}, {{val| 0 1 0 2 0 }}, {{val| 0 0 1 2 3 }}]
{{Mapping|legend=1| 2 0 0 -10 -7 | 0 1 0 2 0 | 0 0 1 2 3 }}


Mapping generators: ~99/70, ~3, ~5
: mapping generators: ~99/70, ~3, ~5


[[Optimal tuning]] ([[POTE]]): ~3/2 = 700.6242, ~5/4 = 383.2978
[[Optimal tuning]] ([[POTE]]): ~99/70 = 1\2, ~3/2 = 700.6242, ~5/4 = 383.2978


{{Optimal ET sequence|legend=1| 12, 22, 34d, 50, 60e, 72, 166, 238c, 310c }}
{{Optimal ET sequence|legend=1| 12, 22, 34d, 50, 60e, 72, 166, 238c, 310c }}
Line 534: Line 534:
[[Comma list]]: 225/224, 243/242
[[Comma list]]: 225/224, 243/242


[[Mapping]]: [{{val| 1 1 0 -3 2 }}, {{val| 0 2 0 4 5 }}, {{val| 0 0 1 2 0 }}]
{{Mapping|legend=1| 1 1 0 -3 2 | 0 2 0 4 5 | 0 0 1 2 0 }}


Mapping generators: ~2, ~11/9, ~5
: mapping generators: ~2, ~11/9, ~5


[[Optimal tuning]] ([[POTE]]): ~11/9 = 350.0570, ~5/4 = 383.9323
[[Optimal tuning]] ([[POTE]]): ~2 = 1\1, ~11/9 = 350.0570, ~5/4 = 383.9323


[[Minimax tuning]]:
[[Minimax tuning]]:
* [[11-odd-limit]]
* [[11-odd-limit]]
: [{{monzo| 1 0 0 0 0 }}, {{monzo| 1/5 0 0 0 2/5 }}, {{monzo| 2/5 -2 1 0 4/5 }}, {{monzo| -19/5 -4 2 0 12/5 }}, {{monzo| 0 0 0 0 1 }}]
: [{{monzo| 1 0 0 0 0 }}, {{monzo| 1/5 0 0 0 2/5 }}, {{monzo| 2/5 -2 1 0 4/5 }}, {{monzo| -19/5 -4 2 0 12/5 }}, {{monzo| 0 0 0 0 1 }}]
: [[Eigenmonzo subgroup]] ([[unchanged-interval basis]]): 2.9/5.11
: [[Eigenmonzo basis|eigenmonzo (unchanged-interval) basis]]: 2.9/5.11


{{Optimal ET sequence|legend=1| 31, 41, 72, 247c, 281, 353c, 425bc, 497bc }}
{{Optimal ET sequence|legend=1| 31, 41, 72, 247c, 281, 353c, 425bc, 497bc }}
Line 551: Line 551:
[[Projection pair]]s: 3 242/81 7 366025/52488 11 644204/59049 to 2.5.11/9
[[Projection pair]]s: 3 242/81 7 366025/52488 11 644204/59049 to 2.5.11/9


Scales (Scala files): [[spectacle31]]
Scales: [[spectacle31]]


[[Associated temperament]]: [[Marvel temperaments #Marvo|marvo]]
[[Associated temperament]]: [[marvo]]


=== 13-limit ===
=== 13-limit ===
Line 560: Line 560:
Comma list: 225/224, 243/242, 351/350
Comma list: 225/224, 243/242, 351/350


Mapping: [{{val| 1 1 0 -3 2 -5 }}, {{val| 0 2 0 4 5 -2 }}, {{val| 0 0 1 2 0 4 }}]
Mapping: {{mapping| 1 1 0 -3 2 -5 | 0 2 0 4 5 -2 | 0 0 1 2 0 4 }}
 
Mapping generators: ~2, ~11/9, ~5


Optimal tuning (POTE): ~11/9 = 349.9247, ~5/4 = 384.3505
Optimal tuning (POTE): ~2 = 1\1, ~11/9 = 349.9247, ~5/4 = 384.3505


{{Optimal ET sequence|legend=1| 31, 72, 103, 175f }} <nowiki>*</nowiki>
{{Optimal ET sequence|legend=1| 31, 72, 103, 175f }} <nowiki>*</nowiki>
Line 577: Line 575:
[[Comma list]]: 225/224, 125000/124509
[[Comma list]]: 225/224, 125000/124509


[[Mapping]]: [{{val| 1 0 0 -5 9 }}, {{val| 0 2 0 4 -7 }}, {{val| 0 0 1 2 0 }}]
{{Mapping|legend=1| 1 0 0 -5 9 | 0 2 0 4 -7 | 0 0 1 2 0 }}


Mapping generators: ~2, ~400/231, ~5
: mapping generators: ~2, ~400/231, ~5


[[Optimal tuning]] ([[POTE]]): ~400/231 = 950.1474, ~5/4 = 383.6467
[[Optimal tuning]] ([[POTE]]): ~2 = 1\1, ~400/231 = 950.1474, ~5/4 = 383.6467


{{Optimal ET sequence|legend=1| 19, 29, 43, 53, 72, 197e, 269ce, 341ce, 610bce }}
{{Optimal ET sequence|legend=1| 19, 29, 43, 53, 72, 197e, 269ce, 341ce, 610bce }}
Line 592: Line 590:
Comma list: 169/168, 225/224, 1001/1000
Comma list: 169/168, 225/224, 1001/1000


Mapping: [{{val| 1 0 0 -5 9 -1 }}, {{val| 0 2 0 4 -7 3 }}, {{val| 0 0 1 2 0 1 }}]
Mapping: {{mapping| 1 0 0 -5 9 -1 | 0 2 0 4 -7 3 | 0 0 1 2 0 1 }}


Optimal tuning (POTE): ~26/15 = 950.2349, ~5/4 = 383.5558
Optimal tuning (POTE): ~2 = 1\1, ~26/15 = 950.2349, ~5/4 = 383.5558


{{Optimal ET sequence|legend=1| 19, 29, 43, 53, 72, 125f, 197ef, 269cef }}
{{Optimal ET sequence|legend=1| 19, 29, 43, 53, 72, 125f, 197ef, 269cef }}
Line 605: Line 603:
[[Comma list]]: 121/120, 225/224
[[Comma list]]: 121/120, 225/224


[[Mapping]]: [{{val| 1 0 1 -3 2 }}, {{val| 0 1 1 4 1 }}, {{val| 0 0 -2 -4 -1 }}]
{{Mapping|legend=1| 1 0 1 -3 2 | 0 1 1 4 1 | 0 0 -2 -4 -1 }}


Mapping generators: ~2, ~3, ~11/10
: mapping generators: ~2, ~3, ~11/10


[[Optimal tuning]] ([[POTE]]): ~3/2 = 699.8719, ~11/10 = 158.3232
[[Optimal tuning]] ([[POTE]]): ~2 = 1\1, ~3/2 = 699.8719, ~11/10 = 158.3232


{{Optimal ET sequence|legend=1| 9, 15d, 16d, 20, 22, 31, 53, 82e, 84e, 113e, 144ee }}
{{Optimal ET sequence|legend=1| 9, 15d, 16d, 20, 22, 31, 53, 82e, 84e, 113e, 144ee }}
Line 618: Line 616:
Comma list: 105/104, 121/120, 196/195
Comma list: 105/104, 121/120, 196/195


Mapping: [{{val| 1 0 1 -3 2 -5 }}, {{val| 0 1 1 4 1 6 }}, {{val| 0 0 -2 -4 -1 -6 }}]
Mapping: {{mapping| 1 0 1 -3 2 -5 | 0 1 1 4 1 6 | 0 0 -2 -4 -1 -6 }}
 
Mapping generators: ~2, ~3, ~11/10


Optimal tuning (POTE): ~3/2 = 698.7090, ~11/10 = 158.7117
Optimal tuning (POTE): ~2 = 1\1, ~3/2 = 698.7090, ~11/10 = 158.7117


{{Optimal ET sequence|legend=1| 9, 20, 22f, 29, 31 }}
{{Optimal ET sequence|legend=1| 9, 20, 22f, 29, 31 }}
Line 631: Line 627:
Comma list: 121/120, 225/224, 275/273
Comma list: 121/120, 225/224, 275/273


Mapping: [{{val| 1 0 1 -3 2 7 }}, {{val| 0 1 1 4 1 -2 }}, {{val| 0 0 -2 -4 -1 -1 }}]
Mapping: {{mapping| 1 0 1 -3 2 7 | 0 1 1 4 1 -2 | 0 0 -2 -4 -1 -1 }}


Mapping generators: ~2, ~3, ~11/10
Optimal tuning (POTE): ~2 = 1\1, ~3/2 = 700.9789, ~11/10 = 159.0048
 
Optimal tuning (POTE): ~3/2 = 700.9789, ~11/10 = 159.0048


{{Optimal ET sequence|legend=1| 22, 29, 31, 53, 82e, 84e, 113e, 166ee }}
{{Optimal ET sequence|legend=1| 22, 29, 31, 53, 82e, 84e, 113e, 166ee }}
Line 644: Line 638:
[[Comma list]]: 225/224, 1331/1323
[[Comma list]]: 225/224, 1331/1323


[[Mapping]]: [{{val| 1 0 1 -3 -2 }}, {{val| 0 1 2 6 5 }}, {{val| 0 0 -3 -6 -4 }}]
{{Mapping|legend=1| 1 0 1 -3 -2 | 0 1 2 6 5 | 0 0 -3 -6 -4 }}


Mapping generators: ~2, ~3, ~84/55
: mapping generators: ~2, ~3, ~84/55


[[Optimal tuning]] ([[POTE]]): ~3/2 = 700.8983, ~84/55 = 739.3812
[[Optimal tuning]] ([[POTE]]): ~2 = 1\1, ~3/2 = 700.8983, ~84/55 = 739.3812


{{Optimal ET sequence|legend=1| 29, 31, 60e, 91e, 94, 125 }}
{{Optimal ET sequence|legend=1| 29, 31, 60e, 91e, 94, 125 }}
Line 659: Line 653:
[[Comma list]]: 225/224, 4375/4374
[[Comma list]]: 225/224, 4375/4374


[[Mapping]]: [{{val| 1 0 1 -3 0 }}, {{val| 0 6 5 22 0 }}, {{val| 0 0 0 0 1 }}]
{{Mapping|legend=1| 1 0 1 -3 0 | 0 6 5 22 0 | 0 0 0 0 1 }}


Mapping generators: ~2, ~6/5, ~11
: mapping generators: ~2, ~6/5, ~11


[[Optimal tuning]] ([[POTE]]): ~6/5 = 316.7318, ~11/8 = 549.2528
[[Optimal tuning]] ([[POTE]]): ~2 = 1\1, ~6/5 = 316.7318, ~11/8 = 549.2528


{{Optimal ET sequence|legend=1| 19, 34d, 53, 72, 197e, 269ce }}
{{Optimal ET sequence|legend=1| 19, 34d, 53, 72, 197e, 269ce }}
Line 674: Line 668:
Comma list: 169/168, 225/224, 325/324
Comma list: 169/168, 225/224, 325/324


Mapping: [{{val| 1 0 1 -3 0 0 }}, {{val| 0 6 5 22 0 14 }}, {{val| 0 0 0 0 1 0 }}]
Mapping: {{mapping| 1 0 1 -3 0 0 | 0 6 5 22 0 14 | 0 0 0 0 1 0 }}
 
Mapping generators: ~2, ~6/5, ~11


Optimal tuning (POTE): ~6/5 = 316.7410, ~11/8 = 548.6028
Optimal tuning (POTE): ~2 = 1\1, ~6/5 = 316.7410, ~11/8 = 548.6028


{{Optimal ET sequence|legend=1| 19, 34d, 53, 72, 125f, 197ef, 269cef }}
{{Optimal ET sequence|legend=1| 19, 34d, 53, 72, 125f, 197ef, 269cef }}
Line 689: Line 681:
Comma list: 225/224, 243/242, 385/384
Comma list: 225/224, 243/242, 385/384


Mapping: [{{val| 1 1 3 3 2 0 }}, {{val| 0 6 -7 -2 15 0 }}, {{val| 0 0 0 0 0 1 }}]
Mapping: {{mapping| 1 1 3 3 2 0 | 0 6 -7 -2 15 0 | 0 0 0 0 0 1 }}


Mapping generators: ~2, ~15/14, ~13
: mapping generators: ~2, ~15/14, ~13


Optimal tuning (POTE): ~15/14 = 116.6327, ~13/8 = 837.7040
Optimal tuning (POTE): ~2 = 1\1, ~15/14 = 116.6327, ~13/8 = 837.7040


{{Optimal ET sequence|legend=1| 10, 31, 41, 62, 72, 103, 175f, 216c, 288cdf, 391bcdef }}
{{Optimal ET sequence|legend=1| 10, 31, 41, 62, 72, 103, 175f, 216c, 288cdf, 391bcdef }}
Line 701: Line 693:
[[Category:Temperament families]]
[[Category:Temperament families]]
[[Category:Marvel family| ]] <!-- main article -->
[[Category:Marvel family| ]] <!-- main article -->
[[Category:Marvel]]
[[Category:Marvel| ]] <!-- key article -->
[[Category:Rank 3]]
[[Category:Rank 3]]
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