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The '''sensamagic clan''' tempers out the [[sensamagic family|sensamagic comma]], [[245/243]], a triprime [[comma]] with no factors of 2, {{val| 0 -5 1 2 }} to be exact. There are a number of [[Regular Temperaments|linear temperament]]s in the [[Regular Temperaments|clan]] (magic, father, sensi, godzilla, superpyth, octacot, rodan, hedgehog, clyde, shrutar, sidi) but they've mostly been discussed elsewhere. Tempering out 245/243 alone leads to a [[Planar temperament|rank three temperament]] for which [[283edo]] is the [[optimal patent val]].
{{Technical data page}}
The '''sensamagic clan''' tempers out the sensamagic comma, [[245/243]], a triprime [[comma]] with no factors of 2, {{val| 0 -5 1 2 }} to be exact. 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]].


= Bohpier =
== BPS ==
Comma: 1220703125/1162261467
{{Main| BPS }}


POTE generator: ~27/25 = 146.476
BPS, for ''Bohlen–Pierce–Stearns'', is the 3.5.7-subgroup temperament tempering out 245/243. This subgroup temperament was formerly called the ''lambda'' temperament, which was named after the [[4L 5s (tritave-equivalent)|lambda scale]].


Map: [<1 0 0|, <0 13 19|]
[[Subgroup]]: 3.5.7


EDOs: 8, 41, 131, 172, 213c
[[Comma list]]: 245/243


Badness: 0.8605
{{Mapping|legend=2| 1 1 2 | 0 -2 1 }}


== 7-limit ==
: sval mapping generators: ~3, ~9/7
[[Comma]]s: 245/243, 3125/3087


[[POTE_tuning|POTE generator]]: ~27/25 = 146.474
[[Optimal tuning]] ([[POTE]]): ~3 = 1901.9550, ~9/7 = 440.4881


Map: [<1 0 0 0|, <0 13 19 23|]
[[Optimal ET sequence]]: [[4edt|b4]], [[9edt|b9]], [[13edt|b13]], [[56edt|b56]], [[69edt|b69]], [[82edt|b82]], [[95edt|b95]]


[[Wedgie]]: <<13 19 23 0 0 0||
=== Overview to extensions ===
The full 7-limit extensions' relation to BPS is clearer if the mapping is normalized in terms of 3.5.7.2. In fact, the strong extensions are sensi, cohemiripple, hedgehog, and fourfives.


EDOs: [[41edo|41]], [[49edo|49]], [[90edo|90]], [[131edo|131]]
These temperaments are distributed into different family pages.
* [[Sensi]] (+126/125) → [[Sensipent family #Sensi|Sensipent family]]
* ''[[Hedgehog]]'' (+50/49) → [[Porcupine family #Hedgehog|Porcupine family]]
* ''[[Cohemiripple]]'' (+1323/1250) → [[Ripple family #Cohemiripple|Ripple family]]
* ''[[Fourfives]]'' (+235298/234375) → [[Fifive family #Fourfives|Fifive family]]


EDTs: [[13edt|13]]
The others are weak extensions. Father tempers out [[16/15]], splitting the generator in two. Godzilla tempers out [[49/48]] with a hemitwelfth period. Sidi tempers out [[25/24]], splitting the generator in two with a hemitwelfth period. Clyde tempers out [[3136/3125]] with a 1/6-twelfth period. Superpyth tempers out [[64/63]], splitting the generator in six. Magic tempers out [[225/224]] with a 1/5-twelfth period. Octacot tempers out [[2401/2400]], splitting the generator in five. Hemiaug tempers out [[128/125]]. Pentacloud tempers out [[16807/16384]]. These split the generator in seven. Bamity tempers out [[64827/64000]], splitting the generator in nine. Rodan tempers out [[1029/1024]], splitting the generator in ten. Shrutar tempers out [[2048/2025]], splitting the generator in eleven. Finally, escaped tempers out [[65625/65536]], splitting the generator in sixteen.


[[Badness]]: 0.0682
Discussed elsewhere are
* [[Father]] (+16/15 or 28/27) → [[Father family #Father|Father family]]
* [[Godzilla]] (+49/48 or 81/80) → [[Semaphoresmic clan #Godzilla|Semaphoresmic clan]]
* ''[[Sidi]]'' (+25/24) → [[Dicot family #Sidi|Dicot family]]
* ''[[Clyde]]'' (+3136/3125) → [[Kleismic family #Clyde|Kleismic family]]
* [[Superpyth]] (+64/63) → [[Archytas clan #Superpyth|Archytas clan]]
* [[Magic]] (+225/224) → [[Magic family #Septimal magic|Magic family]]
* ''[[Octacot]]'' (+2401/2400) → [[Tetracot family #Octacot|Tetracot family]]
* ''[[Hemiaug]]'' (+128/125) → [[Augmented family #Hemiaug|Augmented family]]
* ''[[Pentacloud]]'' (+16807/16384) → [[Quintile family #Pentacloud|Quintile family]]
* ''[[Bamity]]'' (+64827/64000) → [[Amity family #Bamity|Amity family]]
* [[Rodan]] (+1029/1024) → [[Gamelismic clan #Rodan|Gamelismic clan]]
* ''[[Shrutar]]'' (+2048/2025) → [[Diaschismic family #Shrutar|Diaschismic family]]
* ''[[Escaped]]'' (+65625/65536) → [[Escapade family #Escaped|Escapade family]]


== 11-limit ==
For ''no-twos'' extensions, see [[No-twos subgroup temperaments #BPS]].
Commas: 100/99, 245/243, 1344/1331


POTE generator: ~12/11 = 146.545
Considered below are bohpier, salsa, pycnic, superthird, magus and leapweek.


Map: [<1 0 0 0 2|, <0 13 19 23 12|]
== Bohpier ==
{{Main| Bohpier }}
: ''For the 5-limit version, see [[Miscellaneous 5-limit temperaments #Bohpier]].''


EDOs: 41, 90e, 131e
Bohpier is named after its interesting [[relationship between Bohlen–Pierce and octave-ful temperaments|relationship with the non-octave Bohlen–Pierce equal temperament]].


Badness: 0.0339
[[Subgroup]]: 2.3.5.7


== 13-limit ==
[[Comma list]]: 245/243, 3125/3087
Commas: 100/99, 144/143, 196/195, 275/273


POTE generator: ~12/11 = 146.603
{{Mapping|legend=1| 1 0 0 0 | 0 13 19 23 }}


Map: [<1 0 0 0 2 2|, <0 13 19 23 12 14|]
[[Optimal tuning]] ([[POTE]]): ~2 = 1200.000, ~27/25 = 146.474


EDOs: 41, 90ef, 131ef, 221bdeff
[[Minimax tuning]]:  
* [[7-odd-limit]]: ~27/25 = {{monzo| 0 0 1/19 }}
: [[eigenmonzo basis|unchanged-interval (eigenmonzo) basis]]: 2.5
* [[9-odd-limit]]: ~27/25 = {{monzo| 0 1/13 }}
: [[eigenmonzo basis|unchanged-interval (eigenmonzo) basis]]: 2.3


Badness: 0.0249
{{Optimal ET sequence|legend=1| 41, 131, 172, 213c }}


== Music ==
[[Badness]]: 0.068237


by [[Chris Vaisvil]]:
=== 11-limit ===
* [http://micro.soonlabel.com/bophier/bophier-1.mp3 bophier-1.mp3]
Subgroup: 2.3.5.7.11
* [http://micro.soonlabel.com/bophier/bophier-12equal-six-octaves.mp3 bophier-12equal-six-octaves.mp3]


= Sensa (Escaped) =
Comma list: 100/99, 245/243, 1344/1331
{{see also| Escapade family #Escaped }}


Commas: 245/243, 65625/65536
Mapping: {{mapping| 1 0 0 0 2 | 0 13 19 23 12 }}


POTE generator: ~28/27 = 55.122
Optimal tuning (POTE): ~2 = 1200.000, ~12/11 = 146.545


Map: [<1 2 2 4|, <0 -9 7 -26|]
Minimax tuning:  
* 11-odd-limit: ~12/11 = {{monzo| 1/7 1/7 0 0 -1/14 }}
: unchanged-interval (eigenmonzo) basis: 2.11/9


Wedgie: <<9 -7 26 -32 16 80||
{{Optimal ET sequence|legend=0| 41, 90e, 131e }}


EDOs: [[22edo|22]], [[43edo|43d]], [[65edo|65]], [[87edo|87]], [[109edo|109]], [[196edo|196]], [[283edo|283]]
Badness: 0.033949


Badness: 0.0887
==== 13-limit ====
Subgroup: 2.3.5.7.11.13


== 11-limit ==
Comma list: 100/99, 144/143, 196/195, 275/273
Commas: 245/243, 385/384, 4000/3993


POTE generator: ~28/27 = 55.126
Mapping: {{mapping| 1 0 0 0 2 2 | 0 13 19 23 12 14 }}


Map: [<1 2 2 4 3|, <0 -9 7 -26 10|]
Optimal tuning (POTE): ~2 = 1200.000, ~12/11 = 146.603


EDOs: 22, 43d, 65, 87, 109, 196, 283
Minimax tuning:  
* 13- and 15-odd-limit: ~12/11 = {{monzo| 0 0 1/19 }}
: Unchanged-interval (eigenmonzo) basis: 2.5


Badness: 0.0358
{{Optimal ET sequence|legend=0| 41, 90ef, 131ef, 221bdeff }}


== 13-limit ==
Badness: 0.024864
Commas: 245/243, 352/351, 385/384, 625/624


POTE generator: ~28/27 = 55.138
=== Triboh ===
Triboh is named after the "[[39edt|Triple Bohlen–Pierce scale]]", which divides each step of the [[13edt|equal-tempered]] [[Bohlen–Pierce]] scale into three equal parts.  


Map: [<1 2 2 4 3 2|, <0 -9 7 -26 10 37|]
Subgroup: 2.3.5.7.11


EDOs: 22, 65, 87, 109, 196, 283
Comma list: 245/243, 1331/1323, 3125/3087


Badness: 0.0317
Mapping: {{mapping| 1 0 0 0 0 | 0 39 57 69 85 }}


= Salsa =
Optimal tuning (POTE): ~2 = 1200.000, ~77/75 = 48.828
{{see also| Schismatic family }}


Commas: 245/243, 32805/32768
{{Optimal ET sequence|legend=0| 49, 123ce, 172 }}


POTE generator: ~128/105 = 351.049
Badness: 0.162592


Map: [<1 1 7 -1|, <0 2 -16 13|]
==== 13-limit ====
Subgroup: 2.3.5.7.11.13


Wedgie: <<2 -16 13 -30 15 75||
Comma list: 245/243, 275/273, 847/845, 1331/1323


EDOs: 17, 24, 41, 106d, 147d, 188cd, 335cd
Mapping: {{mapping| 1 0 0 0 0 0 | 0 39 57 69 85 91 }}


Badness: 0.08015
Optimal tuning (POTE): ~2 = 1200.000, ~77/75 = 48.822


== 11-limit ==
{{Optimal ET sequence|legend=0| 49f, 123ce, 172f, 295ce, 467bccef }}
Commas: 243/242, 245/242, 385/384


POTE generator: ~11/9 = 351.014
Badness: 0.082158


Map: [<1 1 7 -1 2|, <0 2 -16 13 5|]
== Salsa ==
{{See also| Schismatic family }}


EDOs: 17, 24, 41, 106d, 147d
[[Subgroup]]: 2.3.5.7


Badness: 0.0394
[[Comma list]]: 245/243, 32805/32768


== 13-limit ==
{{Mapping|legend=1| 1 1 7 -1 | 0 2 -16 13 }}
Commas: 105/104, 144/143, 243/242, 245/242


POTE generator: ~11/9 = 351.025
[[Optimal tuning]] ([[POTE]]): ~2 = 1200.000, ~128/105 = 351.049


Map: [<1 1 7 -1 2 4|, <0 2 -16 13 5 -1|]
{{Optimal ET sequence|legend=1| 17, 24, 41, 106d, 147d, 188cd, 335cd }}


EDOs: 17, 24, 41, 106df, 147df
[[Badness]]: 0.080152


Badness: 0.0310
=== 11-limit ===
Subgroup: 2.3.5.7.11


= Pycnic =
Comma list: 243/242, 245/242, 385/384
The fifth of pycnic in size is a meantone fifth, but four of them are not used to reach 5. This has the effect of making the Pythagorean major third, nominally 81/64, very close to 5/4 in tuning, being a cent sharp of it in the POTE tuning for instance. Pycnic has MOS of size 9, 11, 13, 15, 17... which contain these alternative thirds, leading to two kinds of major triads, an official one and a nominally Pythagorean one which is actually in better tune.


Commas: 245/243, 525/512
Mapping: {{mapping| 1 1 7 -1 2 | 0 2 -16 13 5 }}


POTE generator: ~45/32 = 567.720
Optimal tuning (POTE): ~2 = 1200.000, ~11/9 = 351.014


Map: [<1 3 -1 8|, <0 -3 7 -11|]
{{Optimal ET sequence|legend=0| 17, 24, 41, 106d, 147d }}


Wedgie: <<3 -7 11 -18 9 45||
Badness: 0.039444


EDOs: 17, 19, 36c, 55c, 74cd, 93cdd
=== 13-limit ===
Subgroup: 2.3.5.7.11.13


Badness: 0.0737
Comma list: 105/104, 144/143, 243/242, 245/242


= Cohemiripple =
Mapping: {{mapping| 1 1 7 -1 2 4 | 0 2 -16 13 5 -1 }}
{{see also| Ripple family }}


Commas: 245/243, 1323/1250
Optimal tuning (POTE): ~2 = 1200.000, ~11/9 = 351.025


POTE generator: ~7/5 = 549.944
{{Optimal ET sequence|legend=0| 17, 24, 41, 106df, 147df }}


Map: [<1 7 11 12|, <0 -10 -16 -17|]
Badness: 0.030793


Wedgie: <<10 16 17 2 -1 -5||
== Pycnic ==
: ''For the 5-limit version, see [[Miscellaneous 5-limit temperaments #Stump]].''


EDOs: 11cd, 13cd, 24
The fifth of pycnic in size is a meantone fifth, but four of them are not used to reach 5. This has the effect of making the Pythagorean major third, nominally 81/64, very close to 5/4 in tuning, being a cent sharp of it in the POTE tuning for instance. Pycnic has [[mos]] of size 9, 11, 13, 15, 17… which contain these alternative thirds, leading to two kinds of major triads, an official one and a nominally Pythagorean one which is actually in better tune.


Badness: 0.1902
[[Subgroup]]: 2.3.5.7


== 11-limit ==
[[Comma list]]: 245/243, 525/512
Commas: 77/75, 243/242, 245/242


POTE generator: ~7/5 = 549.945
{{Mapping|legend=1| 1 3 -1 8 | 0 -3 7 -11 }}


Map: [<1 7 11 12 17|, <0 -10 -16 -17 -25|]
[[Optimal tuning]] ([[POTE]]): ~2 = 1200.000, ~45/32 = 567.720


EDOs: 11cdee, 13cdee, 24
{{Optimal ET sequence|legend=1| 17, 19, 55c, 74cd, 93cdd }}


Badness: 0.0827
[[Badness]]: 0.073735


== 13-limit ==
== Superthird ==
Commas: 66/65, 77/75, 147/143, 243/242
: ''For the 5-limit version, see [[Miscellaneous 5-limit temperaments #Shibboleth]].''


POTE generator: ~7/5 = 549.958
[[Subgroup]]: 2.3.5.7


Map: [<1 7 11 12 17 14|, <0 -10 -16 -17 -25 -19|]
[[Comma list]]: 245/243, 78125/76832


EDOs: 11cdeef, 13cdeef, 24
{{Mapping|legend=1| 1 -5 -5 -10 | 0 18 20 35 }}


Badness: 0.0499
[[Optimal tuning]] ([[POTE]]): ~2 = 1200.000, ~9/7 = 439.076


= Superthird =
{{Optimal ET sequence|legend=1| 11cd, 30d, 41, 317bcc, 358bcc, 399bcc }}
Commas: 245/243, 78125/76832


POTE generator: ~9/7 = 439.076
[[Badness]]: 0.139379


Map: [<1 13 15 25|, <0 -18 -20 -35|]
=== 11-limit ===
Subgroup: 2.3.5.7.11


Wedgie: <<18 20 35 -10 5 25||
Comma list: 100/99, 245/243, 78125/76832


EDOs: 41, 317bc, 358bc, 399bc
Mapping: {{mapping| 1 -5 -5 -10 2 | 0 18 20 35 4 }}


Badness: 0.1394
Optimal tuning (POTE): ~2 = 1200.000, ~9/7 = 439.152


== 11-limit ==
{{Optimal ET sequence|legend=0| 11cd, 30d, 41, 153be, 194be, 235bcee }}
Commas: 100/99, 245/243, 78125/76832


POTE generator: ~9/7 = 439.152
Badness: 0.070917


Map: [<1 13 15 25 6|, <0 -18 -20 -35 -4|]
=== 13-limit ===
Subgroup: 2.3.5.7.11.13


EDOs: 41, 153be, 194be, 235bce
Comma list: 100/99, 144/143, 196/195, 1375/1352


Badness: 0.0709
Mapping: {{mapping| 1 -5 -5 -10 2 -8 | 0 18 20 35 4 32 }}


== 13-limit ==
Optimal tuning (POTE): ~2 = 1200.000, ~9/7 = 439.119
Commas: 100/99, 144/143, 196/195, 1375/1352


POTE generator: ~9/7 = 439.119
{{Optimal ET sequence|legend=0| 11cdf, 30df, 41 }}


Map: [<1 13 15 25 6 24|, <0 -18 -20 -35 -4 -32|]
Badness: 0.052835


EDOs: 41
== Superenneadecal ==
Superenneadecal is a cousin of [[enneadecal]] but sharper fifth is used to temper 245/243.


Badness: 0.0528
[[Subgroup]]: 2.3.5.7


= Magus =
[[Comma list]]: 245/243, 395136/390625
Commas: 50331648/48828125


POTE generator: ~5/4 = 391.225
{{Mapping|legend=1| 19 0 14 -7 | 0 1 1 2 }}


Map: [<1 9 3|, <0 -11 -1|]
[[Optimal tuning]] ([[POTE]]): ~392/375 = 63.158, ~3/2 = 704.166


EDOs: 40, 43, 46, 181c, 227c, 273c, 319c
{{Optimal ET sequence|legend=1| 19, 76bcd, 95, 114, 133, 247b, 380bcd }}


Badness: 0.3602
[[Badness]]: 0.132311


== 7-limit ==
=== 11-limit ===
Commas: 245/243, 28672/28125
Subgroup: 2.3.5.7.11


POTE generator: ~5/4 = 391.465
Comma list: 245/243, 2560/2541, 3773/3750


Map: [<1 9 3 21|, <0 -11 -1 -27|]
Mapping: {{mapping| 19 0 14 -7 96 | 0 1 1 2 -1 }}


Wedgie: <<11 1 27 -24 12 60||
Optimal tuning (POTE): ~33/32 = 63.158, ~3/2 = 705.667


EDOs: 46, 95, 141bc, 187bc, 328bc
{{Optimal ET sequence|legend=0| 19, 76bcd, 95, 114e }}


Badness: 0.1084
Badness: 0.101496


== 11-limit ==
=== 13-limit ===
Commas: 176/175, 245/243, 1331/1323
Subgroup: 2.3.5.7.11.13


POTE generator: ~5/4 = 391.503
Comma list: 196/195, 245/243, 832/825, 1001/1000


Map: [<1 9 3 21 23|, <0 -11 -1 -27 -29|]
Mapping: {{mapping| 19 0 14 -7 96 10 | 0 1 1 2 -1 2 }}


EDOs: 46, 95, 141bc
Optimal tuning (POTE): ~33/32 = 63.158, ~3/2 = 705.801


Badness: 0.0451
{{Optimal ET sequence|legend=0| 19, 76bcdf, 95, 114e }}


== 13-limit ==
Badness: 0.053197
Commas: 91/90, 176/175, 245/243, 1331/1323


POTE generator: ~5/4 = 391.366
== Magus ==
: ''For the 5-limit version, see [[Miscellaneous 5-limit temperaments #Magus]].''


Map: [<1 9 3 21 23 1|, <0 -11 -1 -27 -29 4|]
Magus temperament tempers out [[50331648/48828125]] (salegu) in the 5-limit. This temperament can be described as {{nowrap| 46 & 49 }} temperament, which tempers out the sensamagic and 28672/28125 (sazoquingu). The alternative extension [[starling temperaments #Amigo|amigo]] ({{nowrap|43 & 46}}) tempers out the same 5-limit comma as the magus, but with the [[126/125|starling comma]] (126/125) rather than the sensamagic tempered out.


EDOs: 46, 233bcf, 279bcf
Magus has a generator of a sharp ~5/4 (so that ~[[25/16]] is twice as sharp so that it makes sense to equate with [[11/7]] by tempering [[176/175]]), so that three reaches [[128/125]] short of the octave (where 128/125 is tuned narrow); this is significant because magus reaches [[3/2]] as ([[25/16]])/([[128/125]])<sup>3</sup>, that is, {{nowrap|2 + 3 × 3 {{=}} 11}} generators. Therefore, it implies that [[25/24]] is split into three [[128/125]]'s. Therefore, in the 5-limit, magus can be thought of as a higher-complexity and sharper analogue of [[würschmidt]] (which reaches [[3/2]] as (25/16)/(128/125)<sup>2</sup> implying 25/24 is split into two 128/125's thus having a guaranteed neutral third), which itself is a higher-complexity and sharper analogue of [[magic]] (which equates 25/24 with 128/125 by flattening 5). For more details on these connections see [[Würschmidt comma]].


Badness: 0.0430
[[Subgroup]]: 2.3.5.7


= Leapweek =
[[Comma list]]: 245/243, 28672/28125
Commas: 245/243, 2097152/2066715


POTE generator: ~3/2 = 704.536
{{Mapping|legend=1| 1 -2 2 -6 | 0 11 1 27 }}


Map: [&lt;1 1 17 -6|, &lt;0 1 -25 15|]
[[Optimal tuning]] ([[POTE]]): ~2 = 1200.000, ~5/4 = 391.465


EDOs: 17, 46, 109, 155, 264b, 419b
{{Optimal ET sequence|legend=1| 46, 95, 141bc, 187bc, 328bbcc }}


Badness: 0.14058
[[Badness]]: 0.108417


== 11-limit ==
=== 11-limit ===
Commas: 245/243, 385/384, 1331/1323
Subgroup: 2.3.5.7.11


POTE generator: ~3/2 = 704.554
Comma list: 176/175, 245/243, 1331/1323


Map: [&lt;1 1 17 -6 -3|, &lt;0 1 -25 15 11|]
Mapping: {{mapping| 1 -2 2 -6 -6 | 0 11 1 27 29 }}


EDOs: 17, 46, 109, 264b, 373b, 637be
Optimal tuning (POTE): ~2 = 1200.000, ~5/4 = 391.503


Badness: 0.0507
{{Optimal ET sequence|legend=0| 46, 95, 141bc }}


== 13-limit ==
Badness: 0.045108
Commas: 169/168, 245/243, 352/351, 364/363


POTE generator: ~3/2 = 704.571
=== 13-limit ===
Subgroup: 2.3.5.7.11.13


Map: [&lt;1 1 17 -6 -3 -1|, &lt;0 1 -25 15 11 8|]
Comma list: 91/90, 176/175, 245/243, 1331/1323


EDOs: 17, 46, 63, 109, 218f, 373bf
Mapping: {{mapping| 1 -2 2 -6 -6 5 | 0 11 1 27 29 -4 }}


Badness: 0.0327
Optimal tuning (POTE): ~2 = 1200.000, ~5/4 = 391.366


[[Category:Theory]]
{{Optimal ET sequence|legend=0| 46, 233bcff, 279bccff }}
[[Category:Temperament clan]]
 
[[Category:Sensamagic]]
Badness: 0.043024
 
== Leapweek ==
: ''Not to be confused with scales produced by leap week calendars such as [[Symmetry454]].''
 
[[Subgroup]]: 2.3.5.7
 
[[Comma list]]: 245/243, 2097152/2066715
 
{{Mapping|legend=1| 1 0 42 -21 | 0 1 -25 15 }}
 
: mapping generators: ~2, ~3
 
[[Optimal tuning]] ([[POTE]]): ~2 = 1200.000, ~3/2 = 704.536
 
{{Optimal ET sequence|legend=1| 17, 29c, 46, 109, 155, 264b, 419b }}
 
[[Badness]]: 0.140577
 
=== 11-limit ===
Subgroup: 2.3.5.7.11
 
Comma list: 245/243, 385/384, 1331/1323
 
Mapping: {{mapping| 1 0 42 -21 -14 | 0 1 -25 15 11 }}
 
Optimal tuning (POTE): ~2 = 1200.000, ~3/2 = 704.554
 
{{Optimal ET sequence|legend=0| 17, 29c, 46, 109, 264b, 373b, 637bbe }}
 
Badness: 0.050679
 
=== 13-limit ===
Subgroup: 2.3.5.7.11.13
 
Comma list: 169/168, 245/243, 352/351, 364/363
 
Mapping: {{mapping| 1 0 42 -21 -14 -9 | 0 1 -25 15 11 8 }}
 
Optimal tuning (POTE): ~2 = 1200.000, ~3/2 = 704.571
 
{{Optimal ET sequence|legend=0| 17, 29c, 46, 63, 109 }}
 
Badness: 0.032727
 
==== 17-limit ====
Subgroup: 2.3.5.7.11.13.17
 
Comma list: 154/153, 169/168, 245/243, 256/255, 273/272
 
Mapping: {{mapping| 1 0 42 -21 -14 -9 -34 | 0 1 -25 15 11 8 24 }}
 
Optimal tuning (POTE): ~2 = 1200.000, ~3/2 = 704.540
 
{{Optimal ET sequence|legend=0| 17g, 29cg, 46, 109, 155f, 264bfg }}
 
Badness: 0.026243
 
==== Leapweeker ====
Subgroup: 2.3.5.7.11.13.17
 
Comma list: 136/135, 169/168, 221/220, 245/243, 364/363
 
Mapping: {{mapping| 1 0 42 -21 -14 -9 39 | 0 1 -25 15 11 8 -22 }}
 
Optimal tuning (POTE): ~2 = 1200.000, ~3/2 = 704.537
 
{{Optimal ET sequence|legend=0| 17, 29c, 46, 109g, 155fg, 264bfgg }}
 
Badness: 0.026774
 
[[Category:Temperament clans]]
[[Category:Pages with mostly numerical content]]
[[Category:Sensamagic clan| ]] <!-- main article -->
[[Category:Rank 2]]
[[Category:Rank 2]]
[[Category:Listen]]
[[Category:Listen]]
Retrieved from "https://en.xen.wiki/w/Sensamagic_clan"