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= Lambda =
= Lambda =
Subgroup: 3.5.7
Subgroup: 3.5.7


Line 18: Line 17:


== Extensions ==
== Extensions ==
For full 7-limit extensions, we have sensi, bohpier, sensa/escaped, salsa, pycnic, cohemiripple, superthird, magus and leapweek discussed below, as well as [[Father family #Father|father]], [[Dicot family #Sidi|sidi]], [[Meantone family #Godzilla|godzilla]], [[Porcupine family #Hedgehog|hedgehog]], [[Archytas clan #Superpyth|superpyth]], [[Augmented family #Hemiaug|hemiaug]], [[Magic family #magic|magic]], [[Gamelismic clan#Rodan|rodan]], [[Tetracot family #Octacot|octacot]], [[Diaschismic family #Shrutar|shrutar]], and [[Kleismic family #Clyde|clyde]] discussed elsewhere.  
For full 7-limit extensions, we have sensi, bohpier, escaped, salsa, pycnic, cohemiripple, superthird, magus and leapweek discussed below, as well as [[Father family #Father|father]], [[Dicot family #Sidi|sidi]], [[Meantone family #Godzilla|godzilla]], [[Porcupine family #Hedgehog|hedgehog]], [[Archytas clan #Superpyth|superpyth]], [[Augmented family #Hemiaug|hemiaug]], [[Magic family #magic|magic]], [[Gamelismic clan#Rodan|rodan]], [[Tetracot family #Octacot|octacot]], [[Diaschismic family #Shrutar|shrutar]], [[Amity family #Bamity|bamity]], and [[Kleismic family #Clyde|clyde]] discussed elsewhere.  


Tempering out 245/243 alone in the full 7-limit leads to a [[Planar temperament|rank-3 temperament]], sensamagic, for which [[283edo]] is the [[optimal patent val]].
Tempering out 245/243 alone in the full 7-limit leads to a [[Planar temperament|rank-3 temperament]], sensamagic, for which [[283edo]] is the [[optimal patent val]].
Line 28: Line 27:
Sensi tempers out [[126/125]], [[686/675]] and [[4375/4374]] in addition to [[245/243]], and can be described as the 19&27 temperament. It has as a generator half the size of a slightly wide major sixth, which gives an interval sharp of 9/7 and flat of 13/10, both of which can be used to identify it, as 2.3.5.7.13 sensi (sensation) tempers out 91/90. 22/17, in the middle, is even closer to the generator. [[46edo]] is an excellent sensi tuning, and MOS of size 11, 19 and 27 are available. The name "sensi" is a play on the words "semi-" and "sixth."
Sensi tempers out [[126/125]], [[686/675]] and [[4375/4374]] in addition to [[245/243]], and can be described as the 19&27 temperament. It has as a generator half the size of a slightly wide major sixth, which gives an interval sharp of 9/7 and flat of 13/10, both of which can be used to identify it, as 2.3.5.7.13 sensi (sensation) tempers out 91/90. 22/17, in the middle, is even closer to the generator. [[46edo]] is an excellent sensi tuning, and MOS of size 11, 19 and 27 are available. The name "sensi" is a play on the words "semi-" and "sixth."


== 7-limit ==
== Septimal sensi ==
Subgroup: 2.3.5.7
Subgroup: 2.3.5.7


Line 308: Line 307:
{{Val list|legend=1| 17, 24, 41, 106d, 147d, 188cd, 335cd }}
{{Val list|legend=1| 17, 24, 41, 106d, 147d, 188cd, 335cd }}


[[Badness]]: 0.08015
[[Badness]]: 0.080152


== 11-limit ==
== 11-limit ==
Subgroup: 2.3.5.7.11
Subgroup: 2.3.5.7.11


Line 320: Line 318:
POTE generator: ~11/9 = 351.014
POTE generator: ~11/9 = 351.014


{{Val list|legend=1| 17, 24, 41, 106d, 147d }}
Vals: {{Val list| 17, 24, 41, 106d, 147d }}


Badness: 0.0394
Badness: 0.039444


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


Line 334: Line 331:
POTE generator: ~11/9 = 351.025
POTE generator: ~11/9 = 351.025


{{Val list|legend=1| 17, 24, 41, 106df, 147df }}
Vals: {{Val list| 17, 24, 41, 106df, 147df }}


Badness: 0.0310
Badness: 0.030793


= Pycnic =
= Pycnic =
Line 353: Line 350:
{{Val list|legend=1| 17, 19, 55c, 74cd, 93cdd }}
{{Val list|legend=1| 17, 19, 55c, 74cd, 93cdd }}


[[Badness]]: 0.0737
[[Badness]]: 0.073735


= Cohemiripple =
= Cohemiripple =
Line 362: Line 359:
[[Comma list]]: 245/243, 1323/1250
[[Comma list]]: 245/243, 1323/1250


[[Mapping]]: [{{val| 1 7 11 12 }}, {{val| 0 -10 -16 -17 }}]
[[Mapping]]: [{{val| 1 -3 -5 -5 }}, {{val| 0 10 16 17 }}]


{{Multival|legend=1| 10 16 17 2 -1 -5 }}
{{Multival|legend=1| 10 16 17 2 -1 -5 }}
Line 370: Line 367:
{{Val list|legend=1| 11cd, 13cd, 24 }}
{{Val list|legend=1| 11cd, 13cd, 24 }}


[[Badness]]: 0.1902
[[Badness]]: 0.190208


== 11-limit ==
== 11-limit ==
Subgroup: 2.3.5.7.11
Subgroup: 2.3.5.7.11


Comma list: 77/75, 243/242, 245/242
Comma list: 77/75, 243/242, 245/242


Mapping: [{{val| 1 7 11 12 17 }}, {{val| 0 -10 -16 -17 -25 }}]
Mapping: [{{val| 1 -3 -5 -5 -8 }}, {{val| 0 10 16 17 25 }}]


POTE generator: ~7/5 = 549.945
POTE generator: ~7/5 = 549.945


{{Val list|legend=1| 11cdee, 13cdee, 24 }}
Vals: {{Val list| 11cdee, 13cdee, 24 }}


Badness: 0.0827
Badness: 0.082716


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


Comma list: 66/65, 77/75, 147/143, 243/242
Comma list: 66/65, 77/75, 147/143, 243/242


Mapping: [{{val| 1 7 11 12 17 14 }}, {{val| 0 -10 -16 -17 -25 -19 }}]
Mapping: [{{val| 1 -3 -5 -5 -8 -5 }}, {{val| 0 -10 -16 -17 -25 -19 }}]


POTE generator: ~7/5 = 549.958
POTE generator: ~7/5 = 549.958


{{Val list|legend=1| 11cdeef, 13cdeef, 24 }}
Vals: {{Val list| 11cdeef, 13cdeef, 24 }}


Badness: 0.0499
Badness: 0.049933


= Superthird =
= Superthird =
Subgroup: 2.3.5.7
Subgroup: 2.3.5.7


[[Comma list]]: 245/243, 78125/76832
[[Comma list]]: 245/243, 78125/76832


[[Mapping]]: [{{val| 1 13 15 25 }}, {{val| 0 -18 -20 -35 }}]
[[Mapping]]: [{{val| 1 -5 -5 -10 }}, {{val| 0 18 20 35 }}]


{{Multival|legend=1| 18 20 35 -10 5 25 }}
{{Multival|legend=1| 18 20 35 -10 5 25 }}
Line 414: Line 408:
{{Val list|legend=1| 11cd, 30d, 41, 317bcc, 358bcc, 399bcc }}
{{Val list|legend=1| 11cd, 30d, 41, 317bcc, 358bcc, 399bcc }}


[[Badness]]: 0.1394
[[Badness]]: 0.139379


== 11-limit ==
== 11-limit ==
Subgroup: 2.3.5.7.11
Subgroup: 2.3.5.7.11


Comma list: 100/99, 245/243, 78125/76832
Comma list: 100/99, 245/243, 78125/76832


Mapping: [{{val| 1 13 15 25 6 }}, {{val| 0 -18 -20 -35 -4 }}]
Mapping: [{{val| 1 -5 -5 -10 2 }}, {{val| 0 18 20 35 4 }}]


POTE generator: ~9/7 = 439.152
POTE generator: ~9/7 = 439.152


{{Val list|legend=1| 11cd, 30d, 41, 153be, 194be, 235bcee }}
Vals: {{Val list| 11cd, 30d, 41, 153be, 194be, 235bcee }}


Badness: 0.0709
Badness: 0.070917


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


Comma list: 100/99, 144/143, 196/195, 1375/1352
Comma list: 100/99, 144/143, 196/195, 1375/1352


Mapping: [{{val| 1 13 15 25 6 24 }}, {{val| 0 -18 -20 -35 -4 -32 }}]
Mapping: [{{val| 1 -5 -5 -10 2 -8 }}, {{val| 0 18 20 35 4 32 }}]


POTE generator: ~9/7 = 439.119
POTE generator: ~9/7 = 439.119


{{Val list|legend=1| 11cdf, 30df, 41 }}
Vals: {{Val list| 11cdf, 30df, 41 }}


Badness: 0.0528
Badness: 0.052835


= Magus =
= Magus =
Line 449: Line 441:
[[Comma list]]: 50331648/48828125
[[Comma list]]: 50331648/48828125


[[Mapping]]: [{{val| 1 9 3 }}, {{val| 0 -11 -1 }}]
[[Mapping]]: [{{val| 1 -2 2 }}, {{val| 0 11 1 }}]


[[POTE generator]]: ~5/4 = 391.225
[[POTE generator]]: ~5/4 = 391.225
Line 455: Line 447:
{{Val list|legend=1| 46, 181c, 227c, 273c, 319c }}
{{Val list|legend=1| 46, 181c, 227c, 273c, 319c }}


[[Badness]]: 0.3602
[[Badness]]: 0.360162


== 7-limit ==
== 7-limit ==
Line 462: Line 454:
[[Comma list]]: 245/243, 28672/28125
[[Comma list]]: 245/243, 28672/28125


[[Mapping]]: [{{val| 1 9 3 21 }}, {{val| 0 -11 -1 -27 }}]
[[Mapping]]: [{{val| 1 -2 2 -6 }}, {{val| 0 11 1 27 }}]


{{Multival|legend=1| 11 1 27 -24 12 60 }}
{{Multival|legend=1| 11 1 27 -24 12 60 }}
Line 477: Line 469:
Comma list: 176/175, 245/243, 1331/1323
Comma list: 176/175, 245/243, 1331/1323


Mapping: [{{val| 1 9 3 21 23 }}, {{val| 0 -11 -1 -27 -29 }}]
Mapping: [{{val| 1 -2 2 -6 -6 }}, {{val| 0 11 1 27 29 }}]


POTE generator: ~5/4 = 391.503
POTE generator: ~5/4 = 391.503


{{Val list|legend=1| 46, 95, 141bc }}
Vals: {{Val list| 46, 95, 141bc }}


Badness: 0.0451
Badness: 0.045108


== 13-limit ==
== 13-limit ==
Line 490: Line 482:
Comma list: 91/90, 176/175, 245/243, 1331/1323
Comma list: 91/90, 176/175, 245/243, 1331/1323


Mapping: [{{val| 1 9 3 21 23 1 }}, {{val| 0 -11 -1 -27 -29 4 }}]
Mapping: [{{val| 1 -2 2 -6 -6 5 }}, {{val| 0 11 1 27 29 -4 }}]


POTE generator: ~5/4 = 391.366
POTE generator: ~5/4 = 391.366


{{Val list|legend=1| 46, 233bcff, 279bccff }}
Vals: {{Val list| 46, 233bcff, 279bccff }}


Badness: 0.0430
Badness: 0.043024


= Leapweek =
= Leapweek =
Line 509: Line 501:
{{Val list|legend=1| 17, 29c, 46, 109, 155, 264b, 419b }}
{{Val list|legend=1| 17, 29c, 46, 109, 155, 264b, 419b }}


[[Badness]]: 0.14058
[[Badness]]: 0.140577


== 11-limit ==
== 11-limit ==
Line 520: Line 512:
POTE generator: ~3/2 = 704.554
POTE generator: ~3/2 = 704.554


{{Val list|legend=1| 17, 29c, 46, 109, 264b, 373b, 637be }}
Vals: {{Val list| 17, 29c, 46, 109, 264b, 373b, 637be }}


Badness: 0.0507
Badness: 0.050679


== 13-limit ==
== 13-limit ==
Line 533: Line 525:
POTE generator: ~3/2 = 704.571
POTE generator: ~3/2 = 704.571


{{Val list|legend=1| 17, 29c, 46, 63, 109, 218f, 373bf }}
Vals: {{Val list| 17, 29c, 46, 63, 109, 218f, 373bf }}


Badness: 0.0327
Badness: 0.032727


=Semiwolf=
= Semiwolf =
[[Subgroup]]: 3/2.7/4.5/2
[[Subgroup]]: 3/2.7/4.5/2


Line 548: Line 540:
[[Vals]]: {{val list|8edf, 11edf, 13edf}}
[[Vals]]: {{val list|8edf, 11edf, 13edf}}


==Semilupine==
== Semilupine ==
[[Subgroup]]: 3/2.7/4.5/2.11/4
[[Subgroup]]: 3/2.7/4.5/2.11/4


Line 559: Line 551:
[[Vals]]: {{val list|8edf, 13edf}}
[[Vals]]: {{val list|8edf, 13edf}}


==Hemilycan==
== Hemilycan ==
[[Subgroup]]: 3/2.7/4.5/2.11/4
[[Subgroup]]: 3/2.7/4.5/2.11/4


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