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The ''sensamagic clan'' tempers out the [[sensamagic family|sensamagic comma]], [[245/243]], a [[comma|triprime comma]] with no factors of 2. |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|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
Commas: 245/243, 65625/65536


POTE generator: ~28/27 = 55.122
Mapping: {{mapping| 1 0 0 0 2 | 0 13 19 23 12 }}


Map: [<1 2 2 4|, <0 -9 7 -26|]
Optimal tuning (POTE): ~2 = 1200.000, ~12/11 = 146.545


Wedgie: <<9 -7 26 -32 16 80||
Minimax tuning:  
* 11-odd-limit: ~12/11 = {{monzo| 1/7 1/7 0 0 -1/14 }}
: unchanged-interval (eigenmonzo) basis: 2.11/9


EDOs: [[22edo|22]], [[43edo|43d]], [[65edo|65]], [[87edo|87]], [[109edo|109]], [[196edo|196]], [[283edo|283]]
{{Optimal ET sequence|legend=0| 41, 90e, 131e }}


Badness: 0.0887
Badness: 0.033949


==11-limit==
==== 13-limit ====
Commas: 245/243, 385/384, 4000/3993
Subgroup: 2.3.5.7.11.13


POTE generator: ~28/27 = 55.126
Comma list: 100/99, 144/143, 196/195, 275/273


Map: [<1 2 2 4 3|, <0 -9 7 -26 10|]
Mapping: {{mapping| 1 0 0 0 2 2 | 0 13 19 23 12 14 }}


EDOs: 22, 43d, 65, 87, 109, 196, 283
Optimal tuning (POTE): ~2 = 1200.000, ~12/11 = 146.603


Badness: 0.0358
Minimax tuning:  
* 13- and 15-odd-limit: ~12/11 = {{monzo| 0 0 1/19 }}
: Unchanged-interval (eigenmonzo) basis: 2.5


==13-limit==
{{Optimal ET sequence|legend=0| 41, 90ef, 131ef, 221bdeff }}
Commas: 245/243, 352/351, 385/384, 625/624


POTE generator: ~28/27 = 55.138
Badness: 0.024864


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


EDOs: 22, 65, 87, 109, 196, 283
Subgroup: 2.3.5.7.11


Badness: 0.0317
Comma list: 245/243, 1331/1323, 3125/3087


=Salsa=
Mapping: {{mapping| 1 0 0 0 0 | 0 39 57 69 85 }}
Commas: 245/243, 32805/32768


POTE generator: ~128/105 = 351.049
Optimal tuning (POTE): ~2 = 1200.000, ~77/75 = 48.828


Map: [<1 1 7 -1|, <0 2 -16 13|]
{{Optimal ET sequence|legend=0| 49, 123ce, 172 }}


Wedgie: <<2 -16 13 -30 15 75||
Badness: 0.162592


EDOs: 17, 24, 41, 106d, 147d, 188cd, 335cd
==== 13-limit ====
Subgroup: 2.3.5.7.11.13


Badness: 0.08015
Comma list: 245/243, 275/273, 847/845, 1331/1323


==11-limit==
Mapping: {{mapping| 1 0 0 0 0 0 | 0 39 57 69 85 91 }}
Commas: 243/242, 245/242, 385/384


POTE generator: ~11/9 = 351.014
Optimal tuning (POTE): ~2 = 1200.000, ~77/75 = 48.822


Map: [<1 1 7 -1 2|, <0 2 -16 13 5|]
{{Optimal ET sequence|legend=0| 49f, 123ce, 172f, 295ce, 467bccef }}


EDOs: 17, 24, 41, 106d, 147d
Badness: 0.082158


Badness: 0.0394
== Salsa ==
{{See also| Schismatic family }}


==13-limit==
[[Subgroup]]: 2.3.5.7
Commas: 105/104, 144/143, 243/242, 245/242


POTE generator: ~11/9 = 351.025
[[Comma list]]: 245/243, 32805/32768


Map: [<1 1 7 -1 2 4|, <0 2 -16 13 5 -1|]
{{Mapping|legend=1| 1 1 7 -1 | 0 2 -16 13 }}


EDOs: 17, 24, 41, 106df, 147df
[[Optimal tuning]] ([[POTE]]): ~2 = 1200.000, ~128/105 = 351.049


Badness: 0.0310
{{Optimal ET sequence|legend=1| 17, 24, 41, 106d, 147d, 188cd, 335cd }}


=Pycnic=
[[Badness]]: 0.080152
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
=== 11-limit ===
Subgroup: 2.3.5.7.11


POTE generator: ~45/32 = 567.720
Comma list: 243/242, 245/242, 385/384


Map: [<1 3 -1 8|, <0 -3 7 -11|]
Mapping: {{mapping| 1 1 7 -1 2 | 0 2 -16 13 5 }}


Wedgie: <<3 -7 11 -18 9 45||
Optimal tuning (POTE): ~2 = 1200.000, ~11/9 = 351.014


EDOs: 17, 19, 36c, 55c, 74cd, 93cdd
{{Optimal ET sequence|legend=0| 17, 24, 41, 106d, 147d }}


Badness: 0.0737
Badness: 0.039444


=Cohemiripple=
=== 13-limit ===
Commas: 245/243, 1323/1250
Subgroup: 2.3.5.7.11.13


POTE generator: ~7/5 = 549.944
Comma list: 105/104, 144/143, 243/242, 245/242


Map: [<1 7 11 12|, <0 -10 -16 -17|]
Mapping: {{mapping| 1 1 7 -1 2 4 | 0 2 -16 13 5 -1 }}


Wedgie: <<10 16 17 2 -1 -5||
Optimal tuning (POTE): ~2 = 1200.000, ~11/9 = 351.025


EDOs: 11cd, 13cd, 24
{{Optimal ET sequence|legend=0| 17, 24, 41, 106df, 147df }}


Badness: 0.1902
Badness: 0.030793


==11-limit==
== Pycnic ==
Commas: 77/75, 243/242, 245/242
: ''For the 5-limit version, see [[Miscellaneous 5-limit temperaments #Stump]].''


POTE generator: ~7/5 = 549.945
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.


Map: [<1 7 11 12 17|, <0 -10 -16 -17 -25|]
[[Subgroup]]: 2.3.5.7


EDOs: 11cdee, 13cdee, 24
[[Comma list]]: 245/243, 525/512


Badness: 0.0827
{{Mapping|legend=1| 1 3 -1 8 | 0 -3 7 -11 }}


==13-limit==
[[Optimal tuning]] ([[POTE]]): ~2 = 1200.000, ~45/32 = 567.720
Commas: 66/65, 77/75, 147/143, 243/242


POTE generator: ~7/5 = 549.958
{{Optimal ET sequence|legend=1| 17, 19, 55c, 74cd, 93cdd }}


Map: [<1 7 11 12 17 14|, <0 -10 -16 -17 -25 -19|]
[[Badness]]: 0.073735


EDOs: 11cdeef, 13cdeef, 24
== Superthird ==
: ''For the 5-limit version, see [[Miscellaneous 5-limit temperaments #Shibboleth]].''


Badness: 0.0499
[[Subgroup]]: 2.3.5.7


=Superthird=
[[Comma list]]: 245/243, 78125/76832
Commas: 245/243, 78125/76832


POTE generator: ~9/7 = 439.076
{{Mapping|legend=1| 1 -5 -5 -10 | 0 18 20 35 }}


Map: [<1 13 15 25|, <0 -18 -20 -35|]
[[Optimal tuning]] ([[POTE]]): ~2 = 1200.000, ~9/7 = 439.076


Wedgie: <<18 20 35 -10 5 25||
{{Optimal ET sequence|legend=1| 11cd, 30d, 41, 317bcc, 358bcc, 399bcc }}


EDOs: 41, 317bc, 358bc, 399bc
[[Badness]]: 0.139379


Badness: 0.1394
=== 11-limit ===
Subgroup: 2.3.5.7.11


==11-limit==
Comma list: 100/99, 245/243, 78125/76832
Commas: 100/99, 245/243, 78125/76832


POTE generator: ~9/7 = 439.152
Mapping: {{mapping| 1 -5 -5 -10 2 | 0 18 20 35 4 }}


Map: [<1 13 15 25 6|, <0 -18 -20 -35 -4|]
Optimal tuning (POTE): ~2 = 1200.000, ~9/7 = 439.152


EDOs: 41, 153be, 194be, 235bce
{{Optimal ET sequence|legend=0| 11cd, 30d, 41, 153be, 194be, 235bcee }}


Badness: 0.0709
Badness: 0.070917


==13-limit==
=== 13-limit ===
Commas: 100/99, 144/143, 196/195, 1375/1352
Subgroup: 2.3.5.7.11.13


POTE generator: ~9/7 = 439.119
Comma list: 100/99, 144/143, 196/195, 1375/1352


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


EDOs: 41
Optimal tuning (POTE): ~2 = 1200.000, ~9/7 = 439.119


Badness: 0.0528
{{Optimal ET sequence|legend=0| 11cdf, 30df, 41 }}


=Magus=
Badness: 0.052835
Commas: 50331648/48828125


POTE generator: ~5/4 = 391.225
== Superenneadecal ==
Superenneadecal is a cousin of [[enneadecal]] but sharper fifth is used to temper 245/243.


Map: [<1 9 3|, <0 -11 -1|]
[[Subgroup]]: 2.3.5.7


EDOs: 40, 43, 46, 181c, 227c, 273c, 319c
[[Comma list]]: 245/243, 395136/390625


Badness: 0.3602
{{Mapping|legend=1| 19 0 14 -7 | 0 1 1 2 }}


==7-limit==
[[Optimal tuning]] ([[POTE]]): ~392/375 = 63.158, ~3/2 = 704.166
Commas: 245/243, 28672/28125


POTE generator: ~5/4 = 391.465
{{Optimal ET sequence|legend=1| 19, 76bcd, 95, 114, 133, 247b, 380bcd }}


Map: [<1 9 3 21|, <0 -11 -1 -27|]
[[Badness]]: 0.132311


Wedgie: <<11 1 27 -24 12 60||
=== 11-limit ===
Subgroup: 2.3.5.7.11


EDOs: 46, 95, 141bc, 187bc, 328bc
Comma list: 245/243, 2560/2541, 3773/3750


Badness: 0.1084
Mapping: {{mapping| 19 0 14 -7 96 | 0 1 1 2 -1 }}


==11-limit==
Optimal tuning (POTE): ~33/32 = 63.158, ~3/2 = 705.667
Commas: 176/175, 245/243, 1331/1323


POTE generator: ~5/4 = 391.503
{{Optimal ET sequence|legend=0| 19, 76bcd, 95, 114e }}


Map: [<1 9 3 21 23|, <0 -11 -1 -27 -29|]
Badness: 0.101496


EDOs: 46, 95, 141bc
=== 13-limit ===
Subgroup: 2.3.5.7.11.13


Badness: 0.0451
Comma list: 196/195, 245/243, 832/825, 1001/1000


==13-limit==
Mapping: {{mapping| 19 0 14 -7 96 10 | 0 1 1 2 -1 2 }}
Commas: 91/90, 176/175, 245/243, 1331/1323


POTE generator: ~5/4 = 391.366
Optimal tuning (POTE): ~33/32 = 63.158, ~3/2 = 705.801


Map: [<1 9 3 21 23 1|, <0 -11 -1 -27 -29 4|]
{{Optimal ET sequence|legend=0| 19, 76bcdf, 95, 114e }}


EDOs: 46, 233bcf, 279bcf
Badness: 0.053197


Badness: 0.0430
== Magus ==
: ''For the 5-limit version, see [[Miscellaneous 5-limit temperaments #Magus]].''


=Leapweek=
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.
Commas: 245/243, 2097152/2066715


POTE generator: ~3/2 = 704.536
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]].


Map: [&lt;1 1 17 -6|, &lt;0 1 -25 15|]
[[Subgroup]]: 2.3.5.7


EDOs: 17, 46, 109, 155, 264b, 419b
[[Comma list]]: 245/243, 28672/28125


Badness: 0.14058
{{Mapping|legend=1| 1 -2 2 -6 | 0 11 1 27 }}


==11-limit==
[[Optimal tuning]] ([[POTE]]): ~2 = 1200.000, ~5/4 = 391.465
Commas: 245/243, 385/384, 1331/1323


POTE generator: ~3/2 = 704.554
{{Optimal ET sequence|legend=1| 46, 95, 141bc, 187bc, 328bbcc }}


Map: [&lt;1 1 17 -6 -3|, &lt;0 1 -25 15 11|]
[[Badness]]: 0.108417


EDOs: 17, 46, 109, 264b, 373b, 637be
=== 11-limit ===
Subgroup: 2.3.5.7.11


Badness: 0.0507
Comma list: 176/175, 245/243, 1331/1323


==13-limit==
Mapping: {{mapping| 1 -2 2 -6 -6 | 0 11 1 27 29 }}
Commas: 169/168, 245/243, 352/351, 364/363


POTE generator: ~3/2 = 704.571
Optimal tuning (POTE): ~2 = 1200.000, ~5/4 = 391.503


Map: [&lt;1 1 17 -6 -3 -1|, &lt;0 1 -25 15 11 8|]
{{Optimal ET sequence|legend=0| 46, 95, 141bc }}


EDOs: 17, 46, 63, 109, 218f, 373bf
Badness: 0.045108


Badness: 0.0327
=== 13-limit ===
Subgroup: 2.3.5.7.11.13


[[Category:Theory]]
Comma list: 91/90, 176/175, 245/243, 1331/1323
[[Category:Sensamagic]]
 
[[Category:Temperament clan]]
Mapping: {{mapping| 1 -2 2 -6 -6 5 | 0 11 1 27 29 -4 }}
 
Optimal tuning (POTE): ~2 = 1200.000, ~5/4 = 391.366
 
{{Optimal ET sequence|legend=0| 46, 233bcff, 279bccff }}
 
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:Listen]]
[[Category:Listen]]
Retrieved from "https://en.xen.wiki/w/Sensamagic_clan"