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__FORCETOC__
{{interwiki
| de = Sensi
| en = Sensipent family
| es =
| ja =
}}
{{Technical data page}}
Temperaments of the '''sensipent family''' temper out the [[sensipent comma]], 78732/78125, also known as medium semicomma. The head of this family is sensipent i.e. the 5-limit version of [[sensi]], generated by the naiadic interval of tempered 162/125. Two generators make 5/3, seven make harmonic 6 and nine make harmonic 10. Its [[ploidacot]] is beta-heptacot ([[pergen]] (P8, ccP5/7)) and its color name is Sepguti.


<span style="display: block; text-align: right;">[[de:Sensi]]</span>
The second comma of the comma list determines which 7-limit family member we are looking at. Sensi adds [[126/125]]. Sensei adds [[225/224]]. Warrior adds [[5120/5103]]. These are all strong extensions that use the same period and generator as sensipent.


=Sensipent=
Bison adds [[6144/6125]] with a semioctave period. Subpental adds [[3136/3125]] or [[19683/19600]] with a generator of ~56/45; two generator steps make the original. Trisensory adds [[1728/1715]] with a 1/3-octave period. Heinz adds [[1029/1024]] with a generator of ~48/35; three make the original. Catafourth adds [[2401/2400]] with a generator of ~250/189; four make the original. Finally, browser adds [[16875/16807]] with a generator of ~49/45; five make the original.
[[Comma|Comma]]: 78732/78125 = |2 9 -7&gt;


[[POTE_tuning|POTE generator]]: 162/125 = 443.058 cents
Temperaments discussed elsewhere include:
* ''[[Catafourth]]'' → [[Breedsmic temperaments #Catafourth|Breedsmic temperaments]] (+2401/2400)
* ''[[Browser]]'' → [[Mirkwai clan #Browser|Mirkwai clan]] (+16875/16807)


[[Map|Map]]: [&lt;1 6 8|, &lt;0 -7 -9|]
Considered below are sensi, sensei, warrior, bison, subpental, trisensory and heinz.


[[EDO|EDO]]s: [[8edo|8]], [[19edo|19]], [[46edo|46]], [[65edo|65]], [[539edo|539]], [[604edo|604c]], [[669edo|669c]], [[734edo|734c]], [[799edo|799c]], [[864edo|864c]], [[929edo|929c]]
== Sensipent ==
{{Main| Sensipent }}


=Sensi=
[[Subgroup]]: 2.3.5
{{main|Sensi}}
Sensi tempers out 686/675, 245/243 and 4375/4374 in addition to 126/125, and can be described as the 19&amp;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 [[13-limit|13-limit]] sensi tempers out 91/90. 22/17, in the middle, is even closer to the generator. [[46edo|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."


[[Comma|Commas]]: 126/125, 245/243
[[Comma list]]: 78732/78125


7-limit minimax
{{Mapping|legend=1| 1 -1 -1 | 0 7 9 }}


[|1 0 0 0&gt;, |1/13 0 0 7/13&gt;, |5/13 0 0 9/13&gt;, |0 0 0 1&gt;]
: mapping generators: ~2, ~162/125


[[Eigenmonzo|Eigenmonzos]]: 2, 7
[[Optimal tuning]] ([[POTE]]): ~2 = 1200.000, ~162/125 = 443.058


9-limit minimax
{{Optimal ET sequence|legend=1| 8, 19, 46, 65, 539, 604c, 669c, 734c, 799c, 864c, 929c }}


[|1 0 0 0&gt;, |2/5 14/5 -7/5 0&gt;,
[[Badness]]:
|4/5 18/5 -9/5 0&gt;, |3/5 26/5 -13/5 0&gt;<nowiki>]</nowiki>
* Smith: 0.035220
* Dirichlet: 0.826


[[Eigenmonzo|Eigenmonzos]]: 2, 9/5
=== 2.3.5.31 subgroup ===
Fascinatingly, essentially the only simple and accurate extension that preserves the occurrence of sensipent's tempered [[5-limit]] structure in such large edos as [[539edo|539]] is the one with prime 31 by interpreting the generator accurately as [[31/24]]~[[40/31]], tempering out [[961/960|S31 = 961/960]], so that the [[31-limit]] quarter-tones [[32/31]] and [[31/30]] are equated, as sensipent splits [[16/15]] into two equal parts. For a less sparse subgroup present in smaller edo tunings like [[111edo]] at the cost of slight accuracy, see the extension to the 2.3.5.11.17.31 subgroup [[#Sensible]].


[[POTE_tuning|POTE generator]]: ~9/7 = 443.383
[[Subgroup]]: 2.3.5.31


Algebraic generator: The [[Algebraic_number|real root]] of x^5+x^4-4x^2+x-1, at 443.3783 cents.
[[Comma list]]: 961/960, 2511/2500


[[Map|Map]]: [&lt;1 6 8 11|, &lt;0 -7 -9 -13|]
{{Mapping|legend=1| 1 -1 -1 2 | 0 7 9 8}}


Wedgie: &lt;&lt;7 9 13 -2 1 5||
: mapping generators: ~2, ~31/24


[[generator|Generators]]: 2, 14/9
{{Optimal ET sequence|legend=1| 8, 11c, 19, 46, 65, 344, 409, 474, 539, 604c }}


[[EDO|EDO]]s: [[19edo|19]], [[27edo|27]], [[46edo|46]], [[157edo|157d]], [[203edo|203cd]], [[249edo|249cdd]], [[295edo|295ccdd]]
[[Optimal tuning]] ([[CTE]]): ~2 = 1200.000, ~31/24 = 443.050


[[Badness|Badness]]: 0.0256
[[Badness]] (Sintel): 0.243


==Sensor==
=== Sendai ===
[[Comma|Comma]]s: 126/125, 245/243, 385/384
{{ See also | Sensipent#Sendai interval table }}
Sendai is an accurate extension of (2.3.5.31) [[#Sensipent|sensipent]] with primes [[23/16|23]] and [[29/16|29]] found by [[User:VIxen|VIxen]]. It is named after the body of acquis designed to prevent disaster risk and improve civil protection through international cooperation and after the city in Japan of the same name where it was signed (and where an international music competition is held).


[[POTE_tuning|POTE generator]]: ~9/7 = 443.294
[[Subgroup]]: 2.3.5.23.29.31


[[Map|Map]]: [&lt;1 6 8 11 -6|, &lt;0 -7 -9 -13 15|]
[[Comma list]]: 465/464, 576/575, 621/620, 900/899


[[EDO|EDO]]s: 19, 27, 46, 111d, 157d, 268cdd
{{Mapping|legend=1| 1 -1 -1 6 -4 2| 0 7 9 -4 24 8 }}


[[Badness|Badness]]: 0.0379
{{Optimal ET sequence|legend=1| 19, 46j, 65, 149, 363j }}


===13-limit===
[[Optimal tuning]] ([[CTE]]): ~2 = 1200.000, ~31/24 = 442.989
[[Comma|Comma]]s: 91/90, 126/125, 169/168, 385/384


[[POTE_tuning|POTE generator]]: ~9/7 = 443.321
[[Badness]] (Sintel): 0.283


[[Map|Map]]: [&lt;1 6 8 11 -6 10|, &lt;0 -7 -9 -13 15 -10|]
=== Sensible ===
{{ See also | Sensipent#Sensible interval table }}
Sensible is an extension of sensipent with prime 11 of dubious canonicity but significantly higher accuracy than [[sensi]]. It interprets the generator as [[165/128]]~[[128/99]] by tempering out [[8019/8000]] so that [[11/8]] is reached as ([[10/9]])<sup>3</sup>. This extension is very strong as supported by the [[optimal ET sequence]] going very far and as supported by another observation that it also tempers out the [[semiporwellisma]], which is equal to [[961/960|S31]] × [[1024/1023|S32]]<sup>2</sup> (thus forming the S-expression-based comma list). The vanish of the semiporwellisma, a [[lopsided comma]], implies that this temperament equates ([[33/32]])<sup>2</sup> with [[16/15]] as well as that a natural extension to prime 31 exists through {S31, S32}, which we will see is very accurate, but this itself suggests that an extension with prime 17 is reasonably accurate through tempering out [[1089/1088|S33]] so that a slightly sharp ~[[22/17]] is equated with the generator.


[[EDO|EDO]]s: [[19edo|19]], [[27edo|27]], [[46edo|46]], [[111edo|111df]], [[157edo|157df]]
The aforementioned extension with prime 17 through tempering out [[1089/1088|S33]] is equivalent to the one by tempering out [[256/255|S16]] = [[256/255]] = ([[22/17]])/([[165/128]]).


[[Badness|Badness]]: 0.0256
Sensible uses the accurate mapping of prime 31 in sensipent, so that the sensible generator serves many roles in subgroup harmony, but it is not ~[[9/7]] or ~[[13/10]] which would incur more damage. Its [[S-expression]]-based comma list is {([[256/255|S16]], [[8019/8000|S9/S10]],) [[529/528|S23]], [[576/575|S24]], [[961/960|S31]], [[1024/1023|S32]], [[1089/1088|S33]]} implying also tempering out [[496/495]] = S31 × S32 and [[528/527]] = S32 × S33 as well as [[16337/16335]] = S31/S33 = ([[17/15|34/30]])/([[33/31]])<sup>2</sup> = ([[17/15]])/([[33/31]])<sup>2</sup>. A notable [[patent val]] tuning not appearing in the optimal ET sequence is [[157edo]].


==Sensis==
[[Subgroup]]: 2.3.5.11
[[Comma|Comma]]s: 56/55, 100/99, 245/243


[[POTE_tuning|POTE generator]]: 443.962
[[Comma list]]: 8019/8000, 16384/16335


[[Map|Map]]: [&lt;1 6 8 11 6|, &lt;0 -7 -9 -13 -4|]
{{Mapping|legend=1| 1 -1 -1 9 | 0 7 9 -15 }}


[[EDO|EDO]]s: [[19edo|19]], [[27edo|27e]], [[73edo|73ee]]
: mapping generators: ~2, ~128/99


[[Badness|Badness]]: 0.0287
{{Optimal ET sequence|legend=1| 19, 46, 65, 176, 241, 306 }}


===13-limit===
[[Optimal tuning]] ([[CTE]]): ~2 = 1200.000, ~128/99 = 443.115
[[Comma|Comma]]s: 56/55, 78/77, 91/90, 100/99


[[POTE_tuning|POTE generator]]: 443.945
[[Badness]] (Sintel): 0.728


[[Map|Map]]: [&lt;1 6 8 11 6 10|, &lt;0 -7 -9 -13 -4 -10|]
==== 2.3.5.11.17 subgroup ====


[[EDO|EDO]]s: 19, 27e, 46e, 73ee
[[Subgroup]]: 2.3.5.11.17


[[Badness|Badness]]: 0.0200
[[Comma list]]: 256/255, 1089/1088, 1377/1375


==Sensus==
{{Mapping|legend=1| 1 -1 -1 9 10 | 0 7 9 -15 -16 }}
[[Comma|Comma]]s: 126/125, 176/175, 245/243


[[POTE_generator|POTE generator]]: ~9/7 = 443.626
: mapping generators: ~2, ~22/17


[[Map|Map]]: [&lt;1 6 8 11 23|, &lt;0 -7 -9 -13 -31|]
{{Optimal ET sequence|legend=1| 19, 46, 65, 111, 176g }}


[[EDO|EDO]]s: 19e, 27e, 46, 119c, 165c
[[Optimal tuning]] ([[CTE]]): ~2 = 1200.000, ~22/17 = 443.188


[[Badness|Badness]]: 0.0295
[[Badness]] (Sintel): 0.639


===13-limit===
==== 2.3.5.11.17.23 subgroup ====
[[Comma|Comma]]s: 91/90, 126/125, 169/168, 352/351
[[Subgroup]]: 2.3.5.11.17.23


[[POTE_generator|POTE generator]]: ~9/7 = 443.559
[[Comma list]]: 256/255, 576/575, 1089/1088, 1377/1375


[[Map|Map]]: [&lt;1 6 8 11 23 10|, &lt;0 -7 -9 -13 -31 -10|]
{{Mapping|legend=1| 1 -1 -1 9 10 6 | 0 7 9 -15 -16 -4 }}


[[EDO|EDO]]s: 19e, 27e, 46, 165cf, 211bccf, 257bccff, [[303edo|303bccdff]]
{{Optimal ET sequence|legend=1| 19, 46, 65, 111, 176g }}


[[Badness|Badness]]: 0.0208
[[Optimal tuning]] ([[CTE]]): ~2 = 1200.000, ~22/17 = 443.185


See [[Chords_of_sensus|Chords of sensus]] for a listing of chords.
[[Badness]] (Sintel): 0.555


==Sensa==
==== 2.3.5.11.17.23.31 subgroup ====
Commas: 55/54, 77/75, 99/98
[[Subgroup]]: 2.3.5.11.17.23.31


POTE generator: ~9/7 = 443.518
[[Comma list]]: 256/255, 576/575, 961/960, 1089/1088, 1377/1375


Map: [&lt;1 6 8 11 11|, &lt;0 -7 -9 -13 -12|]
{{Mapping|legend=1| 1 -1 -1 9 10 6 2 | 0 7 9 -15 -16 -4 8 }}


EDOs: 19e, 27, 46ee
{{Optimal ET sequence|legend=1| 19, 46, 65, 111, 176g }}


Badness: 0.0368
[[Optimal tuning]]s:
* [[CTE]]: 2/1 = 1\1, ~22/17 = 443.183
* [[CEE]]: 2/1 = 1\1, ~22/17 = 443.115


===13-limit===
[[Badness]] (Sintel): 0.490
Commas: 55/54, 66/65, 77/75, 143/140


POTE generator: ~9/7 = 443.506
== Sensi ==
{{Main| Sensi }}


Map: [&lt;1 6 8 11 11 10|, &lt;0 -7 -9 -13 -12 -11|]
Sensi tempers out [[245/243]], [[686/675]] and [[4375/4374]] in addition to [[126/125]], and can be described as the 19 &amp; 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 scale]]s of size 8, 11, 19 and 27 are available.


EDOs: 19e, 27, 46ee
=== Septimal sensi ===
[[Subgroup]]: 2.3.5.7


Badness: 0.0233
[[Comma list]]: 126/125, 245/243


=Hemisensi=
{{Mapping|legend=1| 1-1 -1 -2 | 0 7 9 13 }}
Commas: 126/125, 243/242, 245/242


POTE generator: ~25/22 = 221.605
: mapping generators: ~2, ~9/7


Map: [&lt;1 13 17 24 32|, &lt;0 -14 -18 -26 -35|]
[[Optimal tuning]]s:  
* [[CTE]]: ~2 = 1200.000, ~9/7 = 443.3166
* [[POTE]]: ~2 = 1200.000, ~9/7 = 443.383


EDOs: 27e, 65, 157de, 222cde
[[Minimax tuning]]:  
* [[7-odd-limit]]: ~9/7 = {{monzo| 2/13 0 0 1/13 }}
: [[Eigenmonzo basis|unchanged-interval (eigenmonzo) basis]]: 2.7
* [[9-odd-limit]]: ~9/7 = {{monzo| 1/5 2/5 -1/5 0 }}
: [[Eigenmonzo basis|unchanged-interval (eigenmonzo) basis]]: 2.9/5


Badness: 0.0487
[[Tuning ranges of regular temperaments|Tuning ranges]]:  
* 7-odd-limit [[diamond monotone]]: ~9/7 = [442.105, 450.000] (7\19 to 3\8)
* 9-odd-limit diamond monotone: ~9/7 = [442.105, 444.444] (7\19 to 10\27)
* 7-odd-limit [[diamond tradeoff]]: ~9/7 = [442.179, 445.628]
* 9-odd-limit diamond tradeoff: ~9/7 = [435.084, 445.628]


=Sensei=
[[Algebraic generator]]: The real root of ''x''<sup>5</sup> + ''x''<sup>4</sup> - 4''x''<sup>2</sup> + ''x'' - 1, at 443.3783 cents.
Commas: 225/224, 78732/78125


POTE generator: ~125/81 = 757.245
{{Optimal ET sequence|legend=1| 19, 27, 46 }}


Map: [&lt;1 6 8 23|, &lt;0 -7 -9 -32|]
[[Badness]]: 0.025622


Wedgie: &lt;&lt;7 9 32 -2 31 49||
==== 2.3.5.7.13 subgroup (sensation) ====
Subgroup: 2.3.5.7.13


EDOs: 19, 84, 103, 187, 290b
Comma list: 91/90, 126/125, 169/168


Badness: 0.0592
Mapping: {{mapping| 1 -1 -1 -2 0| 0 7 9 13 10 }}


=Bison=
: mapping generators: ~2, ~9/7
Commas: 6144/6125, 78732/78125


POTE generator: ~35/32 = 156.925
Optimal tuning (CTE): ~2 = 1200.000, ~9/7 = 443.4016


Map: [&lt;2 5 7 3|, &lt;0 -7 -9 10|]
{{Optimal ET sequence|legend=1| 19, 27, 46, 111df }}


Wedgie: &lt;&lt;14 18 -20 -4 -71 -97||
=== Sensor ===
Subgroup: 2.3.5.7.11


EDOs: 8, 38, 46, 84, 130
Comma list: 126/125, 245/243, 385/384


Badness: 0.0704
Mapping: {{mapping| 1 -1 -1 -2 9 | 0 7 9 13 -15 }}


==11-limit==
: mapping generators: ~2, ~9/7
Commas: 441/440, 6144/6125, 8019/8000


POTE generator: ~35/32 = 156.883
Optimal tunings:
* CTE: ~2 = 1200.000, ~9/7 = 443.2987
* POTE: ~2 = 1200.000, ~9/7 = 443.294


Map: [&lt;2 5 7 3 3|, &lt;0 -7 -9 10 15|]
{{Optimal ET sequence|legend=1| 19, 27, 46, 111d }}


EDOs: 46, 84, 130, 306, 436ce
Badness: 0.037942


Badness: 0.0371
==== 13-limit ====
Subgroup: 2.3.5.7.11.13


==13-limit==
Comma list: 91/90, 126/125, 169/168, 385/384
Commas: 351/350, 364/363, 441/440, 10985/10976


POTE generator: ~35/32 = 156.904
Mapping: {{mapping| 1 -1 -1 -2 9 0 | 0 7 9 13 -15 10 }}


Map: [&lt;2 5 7 3 3 4|, &lt;0 -7 -9 10 15 13|]
Optimal tunings:  
* CTE: ~2 = 1200.000, ~9/7 = 443.3658
* POTE: ~2 = 1200.000, ~9/7 = 443.321


EDOs: 46, 84, 130, 566ce, 596cef
{{Optimal ET sequence|legend=1| 19, 27, 46, 111df }}


Badness: 0.0235
Badness: 0.025575


=Heinz=
==== 17-limit ====
[[Comma|Comma]]s: 78732/78125, 1029/1024
Subgroup: 2.3.5.7.11.13.17


[[POTE_generator|POTE generator]]: ~48/35 = 546.815
Comma list: 91/90, 126/125, 154/153, 169/168, 256/255


[[Map|Map]]: [&lt;1 13 17 -1|, &lt;0 -21 -27 7|]
Mapping: {{mapping| 1 -1 -1 -2 9 0 10 | 0 7 9 13 -15 10 -16 }}


[[EDO|EDO]]s: [[46edo|46]], [[103edo|103]], [[149edo|149]], [[699edo|699bd]]
Optimal tunings:  
* CTE: ~2 = 1200.000, ~9/7 = 443.3775
* POTE: ~2 = 1200.000, ~9/7 = 443.365


[[Badness|Badness]]: 0.1154
{{Optimal ET sequence|legend=1| 19, 27, 46 }}


==11-limit==
Badness: 0.022908
[[Comma|Comma]]s: 385/384, 441/440, 88208/87500


[[POTE_generator|POTE generator]]: ~11/8 = 547.631
=== Sensus ===
Subgroup: 2.3.5.7.11


[[Map|Map]]: [&lt;1 13 17 -1 4|, &lt;0 -21 -27 7 -1|]
Comma list: 126/125, 176/175, 245/243


[[EDO|EDO]]s: 46, 103, 149
Mapping: {{mapping| 1 -1 -1 -2 -8| 0 7 9 13 31 }}


[[Badness|Badness]]: 0.0424
: mapping generators: ~2, ~9/7


==13-limit==
Optimal tunings:
[[Comma|Comma]]s: 351/350, 385/384, 441/440, 847/845
* CTE: ~2 = 1200.000, ~9/7 = 443.4783
* POTE: ~2 = 1200.000, ~9/7 = 443.626


[[POTE_generator|POTE generator]]: ~11/8 = 547.629
{{Optimal ET sequence|legend=1| 19e, 27e, 46, 119c }}


[[Map|Map]]: [&lt;1 13 17 -1 4 -5|, &lt;0 -21 -27 7 -1 16|]
Badness: 0.029486


[[EDO|EDO]]s: 46, 57, 103, 149, 252e, 401bde
==== 13-limit ====
Subgroup: 2.3.5.7.11.13


[[Badness|Badness]]: 0.0258
Comma list: 91/90, 126/125, 169/168, 352/351


==17-limit==
Mapping: {{mapping| 1 -1 -1 -2 -8 0 | 0 7 9 13 31 10 }}
[[Comma|Comma]]s: 273/272, 351/350, 385/384, 441/440, 847/845


[[POTE_generator|POTE generator]]: ~11/8 = 547.635
Optimal tunings:
* CTE: ~2 = 1200.000, ~9/7 = 443.5075
* POTE: ~2 = 1200.000, ~9/7 = 443.559


[[Map|Map]]: [&lt;1 13 17 -1 4 -5 3|, &lt;0 -21 -27 7 -1 16 2|]
{{Optimal ET sequence|legend=1| 19e, 27e, 46 }}


[[EDO|EDO]]s: 46, 103, 149, [[252edo|252ef]], [[401edo|401bdef]]
Badness: 0.020789


[[Badness|Badness]]: 0.0185
==== 17-limit ====
Subgroup: 2.3.5.7.11.13.17


==19-limit==
Comma list: 91/90, 126/125, 136/135, 154/153, 169/168
[[Comma|Comma]]s: 171/170, 209/208, 351/350, 385/384, 441/440, 969/968


[[POTE_generator|POTE generator]]: ~11/8 = 547.614
Mapping: {{mapping| 1 -1 -1 -2 -8 0 -7 | 0 7 9 13 31 10 30 }}


[[Map|Map]]: [&lt;1 13 17 -1 4 -5 3 -5|, &lt;0 -21 -27 7 -1 16 2 17|]
Optimal tunings:  
* CTE: ~2 = 1200.000, ~9/7 = 443.5050
* POTE: ~2 = 1200.000, ~9/7 = 443.551


[[EDO|EDO]]s: 46, 103h, 149h, 252efh
{{Optimal ET sequence|legend=1| 19eg, 27eg, 46 }}


[[Badness|Badness]]: 0.0190
Badness: 0.016238
[[Category:family]]
 
[[Category:list]]
=== Sensis ===
[[Category:sensipent]]
Subgroup: 2.3.5.7.11
[[Category:theory]]
 
Comma list: 56/55, 100/99, 245/243
 
Mapping: {{mapping| 1 -1 -1 -2 2| 0 7 9 13 4 }}
 
: mapping generators: ~2, ~9/7
 
Optimal tunings:
* CTE: ~2 = 1200.000, ~9/7 = 443.1886
* POTE: ~2 = 1200.000, ~9/7 = 443.962
 
{{Optimal ET sequence|legend=1| 8d, 19, 27e }}
 
Badness: 0.028680
 
==== 13-limit ====
Subgroup: 2.3.5.7.11.13
 
Comma list: 56/55, 78/77, 91/90, 100/99
 
Mapping: {{mapping| 1 -1 -1 -2 2 0 | 0 7 9 13 4 10 }}
 
Optimal tunings:
* CTE: ~2 = 1200.000, ~9/7 = 443.2863
* POTE: ~2 = 1200.000, ~9/7 = 443.945
 
{{Optimal ET sequence|legend=1| 8d, 19, 27e }}
 
Badness: 0.020017
 
=== Sensa ===
Subgroup: 2.3.5.7.11
 
Comma list: 55/54, 77/75, 99/98
 
Mapping: {{mapping| 1 -1 -1 -2 -1| 0 7 9 13 12 }}
 
: mapping generators: ~2, ~9/7
 
Optimal tunings:
* CTE: ~2 = 1200.000, ~9/7 = 443.7814
* POTE: ~2 = 1200.000, ~9/7 = 443.518
 
{{Optimal ET sequence|legend=1| 8d, 19e, 27 }}
 
Badness: 0.036835
 
==== 13-limit ====
Subgroup: 2.3.5.7.11.13
 
Comma list: 55/54, 66/65, 77/75, 143/140
 
Mapping: {{mapping| 1 -1 -1 -2 -1 0 | 0 7 9 13 12 11}}
 
Optimal tunings:
* CTE: ~2 = 1200.000, ~9/7 = 443.7877
* POTE: ~2 = 1200.000, ~9/7 = 443.506
 
{{Optimal ET sequence|legend=1| 8d, 19e, 27 }}
 
Badness: 0.023258
 
=== Bisensi ===
Bisensi has a 1/2-octave period. Its ploidacot is diploid delta-heptacot (pergen (P8/2, ccP5/7)).
 
Subgroup: 2.3.5.7.11
 
Comma list: 121/120, 126/125, 245/243
 
Mapping:
* common form: {{mapping| 2 -2 -2 -4 1 | 0 7 9 13 8 }}
:: mapping generators: ~99/70, ~9/7
* mingen form: {{mapping| 2 5 7 9 9 | 0 -7 -9 -13 -8 }}
:: mapping generators: ~99/70, ~11/10
 
Optimal tunings:
* CTE: ~99/70 = 600.000, ~9/7 = 443.3688 (~11/10 = 156.6312)
* POTE: ~99/70 = 600.000, ~9/7 = 443.308 (~11/10 = 156.692)
 
{{Optimal ET sequence|legend=1| 8d, …, 38d, 46 }}
 
Badness: 0.041723
 
==== 13-limit ====
Subgroup: 2.3.5.7.11.13
 
Comma list: 91/90, 121/120, 126/125, 169/168
 
Mapping:
* common form: {{mapping| 2 -2 -2 -4 1 0 | 0 7 9 13 8 10}}
:: mapping generators: ~99/70, ~9/7
* mingen form: {{mapping| 2 5 7 9 9 10 | 0 -7 -9 -13 -8 -10 }}
:: mapping generators: ~99/70, ~11/10
 
Optimal tunings:
* CTE: ~55/39 = 600.000, ~9/7 = 443.4416, ~11/10 = 156.5584
* POTE: ~55/39 = 600.000, ~9/7 = 443.275, ~11/10 = 156.725
 
{{Optimal ET sequence|legend=1| 8d, …, 38df, 46 }}
 
Badness: 0.026339
 
==== 17-limit ====
Subgroup: 2.3.5.7.11.13.17
 
Comma list: 91/90, 121/120, 126/125, 154/153, 169/168
 
Mapping:
* common form: {{mapping| 2 -2 -2 -4 1 0 3 | 0 7 9 13 8 10 7}}
:: mapping generators: ~99/70, ~9/7
* mingen form: {{mapping| 2 5 7 9 9 10 10 | 0 -7 -9 -13 -8 -10 -7 }}
:: mapping generators: ~99/70, ~11/10
 
Optimal tunings:
* CTE: ~17/12 = 600.000, ~9/7 = 443.4466 (~11/10 = 156.5534)
 
{{Optimal ET sequence|legend=1| 8d, …, 38df, 46 }}
 
Badness: 0.0188
 
=== Hemisensi ===
Hemisensi splits the ~9/7 generator in two, each for ~25/22. Its ploidacot is beta-tetradecacot (pergen (P8, ccP5/14)).
 
Subgroup: 2.3.5.7.11
 
Comma list: 126/125, 243/242, 245/242
 
Mapping: {{mapping| 1 -1 -1 -2 -3 | 0 14 18 26 35 }}
 
: mapping generators: ~2, ~25/22
 
Optimal tunings:
* CTE: ~2 = 1200.000, ~25/22 = 221.5981
* POTE: ~2 = 1200.000, ~25/22 = 221.605
 
{{Optimal ET sequence|legend=1| 27e, 38d, 65 }}
 
Badness: 0.048714
 
==== 13-limit ====
Subgroup: 2.3.5.7.11.13
 
Comma list: 91/90, 126/125, 169/168, 243/242
 
Mapping: {{mapping| 1 -1 -1 -2 -3 0 | 0 14 18 26 35 20 }}
 
Optimal tunings:
* CTE: ~2 = 1200.000, ~25/22 = 221.6333
* POTE: ~2 = 1200.000, ~25/22 = 221.556
 
{{Optimal ET sequence|legend=1| 27e, 38df, 65f }}
 
Badness: 0.033016
 
== Sensei ==
[[Subgroup]]: 2.3.5.7
 
[[Comma list]]: 225/224, 78732/78125
 
{{Mapping|legend=1| 1 -1 -1 -9 | 0 7 9 32 }}
 
: mapping generators: ~2, ~162/125
 
[[Optimal tuning]] ([[POTE]]): ~2 = 1200.000, ~162/125 = 442.755
 
{{Optimal ET sequence|legend=1| 19, 65d, 84, 103, 187, 290b }}
 
[[Badness]]: 0.059218
 
== Warrior ==
[[Subgroup]]: 2.3.5.7
 
[[Comma list]]: 5120/5103, 78732/78125
 
{{Mapping|legend=1| 1 -1 -1 15 | 0 7 9 -33 }}
 
: mapping generators: ~2, ~162/125
 
[[Optimal tuning]] ([[POTE]]): ~2 = 1200.000, ~162/125 = 443.289
 
{{Optimal ET sequence|legend=1| 46, 111, 157, 268cd }}
 
[[Badness]]: 0.118239
 
=== 11-limit ===
Subgroup: 2.3.5.7.11
 
Comma list: 176/175, 1331/1323, 5120/5103
 
Mapping: {{mapping| 1 -1 -1 15 9 | 0 7 9 -33 -15}}
 
: mapping generators: ~2, ~128/99
 
Optimal tuning (POTE): ~2 = 1200.000, ~128/99 = 443.274
 
{{Optimal ET sequence|legend=1| 46, 65d, 111, 268cd, 379cdd}}
 
Badness: 0.046383
 
=== 13-limit ===
Subgroup: 2.3.5.7.11.13
 
Comma list: 176/175, 351/350, 847/845, 1331/1323
 
Mapping: {{mapping| 1 -1 -1 15 9 17| 0 7 9 -33 -15 -36}}
 
: mapping generators: ~2, ~84/65
 
Optimal tuning (POTE): ~2 = 1200.000, ~84/65 = 443.270
 
{{Optimal ET sequence|legend=1| 46, 65d, 111, 268cd, 379cddf}}
 
Badness: 0.028735
 
=== 17-limit ===
Subgroup: 2.3.5.7.11.13.17
 
Comma list: 176/175, 256/255, 351/350, 442/441, 715/714
 
Mapping: {{mapping| 1 -1 -1 15 9 17 10| 0 7 9 -33 -15 -36 -16}}
 
: mapping generators: ~2, ~22/17
 
Optimal tuning (POTE): ~2 = 1200.000, ~22/17 = 443.270
 
{{Optimal ET sequence|legend=1| 46, 65d, 111, 268cdg, 379cddfg }}
 
Badness: 0.018105
 
== Bison ==
Bison has a 1/2-octave period. Its ploidacot is diploid delta-heptacot (pergen (P8/2, ccP5/7)). Related page: [[Bison/Eliora's Approach]].
 
[[Subgroup]]: 2.3.5.7
 
[[Comma list]]: 6144/6125, 78732/78125
 
[[Mapping]]:
* common form: {{mapping| 2 -2 -2 13 | 0 7 9 -10}}
:: mapping generators: ~567/400, ~162/125
* mingen form: {{mapping| 2 5 7 3 | 0 -7 -9 10 }}
:: mapping generators: ~567/400, ~35/32
 
[[Optimal tuning]] ([[POTE]]): ~567/400 = 600.000, ~162/125 = 443.075 (~35/32 = 156.925)
 
{{Optimal ET sequence|legend=1| 8, 38, 46, 84, 130 }}
 
[[Badness]]: 0.070375
 
=== 11-limit ===
Subgroup: 2.3.5.7.11
 
Comma list: 441/440, 6144/6125, 8019/8000
 
Mapping:
* common form: {{mapping| 2 -2 -2 13 18 | 0 7 9 -10 -15}}
:: mapping generators: ~567/400, ~162/125
* mingen form: {{mapping| 2 5 7 3 3 | 0 -7 -9 10 15 }}
:: mapping generators: ~567/400, ~35/32
 
Optimal tuning (POTE): ~99/70 = 600.000, ~162/125 = 443.117 (~35/32 = 156.883)
 
{{Optimal ET sequence|legend=1| 46, 84, 130, 306, 436ce }}
 
Badness: 0.037132
 
=== 13-limit ===
Subgroup: 2.3.5.7.11.13
 
Comma list: 351/350, 364/363, 441/440, 10985/10976
 
Mapping:
* common form: {{mapping| 2 -2 -2 13 18 17 | 0 7 9 -10 -15 -13 }}
:: mapping generators: ~55/39, ~162/125
* mingen form: {{mapping| 2 5 7 3 3 4 | 0 -7 -9 10 15 13 }}
:: mapping generators: ~55/39, ~35/32
 
Optimal tuning (POTE): ~55/39 = 600.000, ~162/125 = 443.096 (~35/32 = 156.904)
 
{{Optimal ET sequence|legend=1| 46, 84, 130, 566ce, 596cef }}
 
Badness: 0.023504
 
== Subpental ==
Subpental splits the generator ~14/9 in two. Its ploidacot is theta-tetradecacot (pergen (P8, c<sup>4</sup>P4/14)).
 
[[Subgroup]]: 2.3.5.7
 
[[Comma list]]: 3136/3125, 19683/19600
 
{{Mapping|legend=1| 1 6 8 17 | 0 -14 -18 -45 }}
 
: mapping generators: ~2, ~56/45
 
[[Optimal tuning]] ([[POTE]]): ~2 = 1200.000, ~56/45 = 378.467
 
{{Optimal ET sequence|legend=1| 19, 111, 130, 929c, 1059c, 1189bc, 1319bc }}
 
[[Badness]]: 0.054303
 
=== 11-limit ===
Subgroup: 2.3.5.7.11
 
Comma list: 540/539, 3136/3125, 8019/8000
 
Mapping: {{mapping| 1 6 8 17 -6 | 0 -14 -18 -45 30 }}
 
Optimal tuning (POTE): ~2 = 1200.000, ~56/45 = 378.440
 
{{Optimal ET sequence|legend=1| 19, 111, 130, 241, 371ce, 501cde, 872cde }}
 
Badness: 0.045352
 
=== 13-limit ===
Subgroup: 2.3.5.7.11.13
 
Comma list: 351/350, 540/539, 676/675, 3136/3125
 
Mapping: {{mapping| 1 6 8 17 -6 16 | 0 -14 -18 -45 30 -39 }}
 
Optimal tuning (POTE): ~2 = 1200.000, ~56/45 = 378.437
 
{{Optimal ET sequence|legend=1| 19, 111, 130, 241, 371ce }}
 
Badness: 0.023940
 
== Heinz ==
Heinz splits the generator ~18/7 in three. Its ploidacot is theta-21-cot (pergen (P8, c<sup>9</sup>P5/21)). A notable tuning of heinz not shown below for those who like [[19edo]]'s representation of the [[5-limit]] is [[57edo]] (57 = 103 - 46).
 
[[Subgroup]]: 2.3.5.7
 
[[Comma list]]: 1029/1024, 78732/78125
 
{{Mapping|legend=1| 1 -8 -10 6| 0 21 27 -7 }}
 
: mapping generators: ~2, ~48/35
 
[[Optimal tuning]] ([[POTE]]): ~2 = 1200.000, ~48/35 = 546.815
 
{{Optimal ET sequence|legend=1| 46, 103, 149, 699bdd }}
 
[[Badness]]: 0.115385
 
=== 11-limit ===
Subgroup: 2.3.5.7.11
 
Comma list: 385/384, 441/440, 78732/78125
 
{{Mapping|legend=1| 1 -8 -10 6 3 | 0 21 27 -7 1}}
 
: mapping generators: ~2, ~11/8
 
Optimal tuning (POTE): ~2 = 1200.000, ~11/8 = 547.631
 
{{Optimal ET sequence|legend=1| 46, 103, 149, 252e, 401bdee }}
 
Badness: 0.042412
 
=== 13-limit ===
Subgroup: 2.3.5.7.11.13
 
Comma list: 351/350, 385/384, 441/440, 847/845
 
{{Mapping|legend=1| 1 -8 -10 6 3 11 | 0 21 27 -7 1 -16}}
 
Optimal tuning (POTE): ~2 = 1200.000, ~11/8 = 547.629
 
{{Optimal ET sequence|legend=1| 46, 103, 149, 252ef, 401bdeef }}
 
Badness: 0.025779
 
=== 17-limit ===
Subgroup: 2.3.5.7.11.13.17
 
Comma list: 273/272, 351/350, 385/384, 441/440, 847/845
 
{{Mapping|legend=1| 1 -8 -10 6 3 11 5 | 0 21 27 -7 1 -16 -2}}
 
Optimal tuning (POTE): ~2 = 1200.000, ~11/8 = 547.635
 
{{Optimal ET sequence|legend=1| 46, 103, 149, 252ef, 401bdeef }}
 
Badness: 0.018479
 
=== 19-limit ===
Subgroup: 2.3.5.7.11.13.17.19
 
Comma list: 171/170, 209/208, 351/350, 385/384, 441/440, 969/968
 
{{Mapping|legend=1| 1 -8 -10 6 3 11 5 12 | 0 21 27 -7 1 -16 -2 -17}}
 
Optimal tuning (POTE): ~2 = 1200.000, ~11/8 = 547.614
 
{{Optimal ET sequence|legend=1| 46, 103h, 149h, 252efhh }}
 
Badness: 0.019005
 
== Trisensory ==
Trisensory has 1/3-octave period. Its ploidacot is triploid digamma-heptacot (pergen (P8/3, M6/21)).
 
[[Subgroup]]: 2.3.5.7
 
[[Comma list]]: 1728/1715, 78732/78125
 
{{Mapping|legend=1| 3 4 6 8 | 0 7 9 4 }}
 
: mapping generators: ~63/50, ~36/35
 
[[Optimal tuning]] ([[POTE]]): ~63/50 = 400.000, ~36/35 = 43.147
 
{{Optimal ET sequence|legend=1| 27, 57, 84, 111, 195d, 306d }}
 
[[Badness]]: 0.089740
 
=== 11-limit ===
Subgroup: 2.3.5.7.11
 
Comma list: 176/175, 540/539, 78732/78125
 
Mapping: {{mapping| 3 4 6 8 8 | 0 7 9 4 22 }}
 
Optimal tuning (POTE): ~63/50 = 400.000, ~36/35 = 43.292
 
{{Optimal ET sequence|legend=1| 27e, 84e, 111 }}
 
Badness: 0.058413
 
=== 13-limit ===
Subgroup: 2.3.5.7.11.13
 
Comma list: 176/175, 351/350, 540/539, 9295/9261
 
Mapping: {{mapping| 3 4 6 8 8 11 | 0 7 9 4 22 1 }}
 
: mapping generators: ~49/39, ~36/35
 
Optimal tuning (POTE): ~49/39 = 400.000, ~36/35 = 43.288
 
{{Optimal ET sequence|legend=1| 27e, 84e, 111 }}
 
Badness: 0.034829
 
=== 17-limit ===
Subgroup: 2.3.5.7.11.13.17
 
Comma list: 176/175, 351/350, 442/441, 540/539, 715/714
 
Mapping: {{mapping| 3 4 6 8 8 11 10 | 0 7 9 4 22 1 21 }}
 
Optimal tuning (POTE): ~49/39 = 400.000, ~36/35 = 43.276
 
{{Optimal ET sequence|legend=1| 27eg, 84e, 111 }}
 
Badness: 0.024120
 
=== 19-limit ===
Subgroup: 2.3.5.7.11.13.17.19
 
Comma list: 176/175, 286/285, 324/323, 351/350, 400/399, 476/475
 
Mapping: {{mapping| 3 4 6 8 8 11 10 12 | 0 7 9 4 22 1 21 7 }}
 
Optimal tuning (POTE): ~49/39 = 400.000, ~36/35 = 43.292
 
{{Optimal ET sequence|legend=1| 27eg, 84e, 111 }}
 
Badness: 0.018466
 
[[Category:Temperament families]]
[[Category:Pages with mostly numerical content]]
[[Category:Sensipent family| ]] <!-- main article -->
[[Category:Rank 2]]
Retrieved from "https://en.xen.wiki/w/Sensipent_family"