Subgroup temperaments: Difference between revisions

== 4.3.5 subgroup ==

=== Tetrahanson ===

[[Subgroup]]: 4.3.5

[[Comma list]]: 15625/15552

: Mapping generators: ~4, ~5/3

[[Optimal tuning]] ([[CTE]]): ~4 = 2\1, ~5/3 = 882.941

[[Support]]ing [[ET]]s: {{EDs|19, 106, 87, 68, 11, 8, 125, 49, 30, 27, 117, 46, 41b, 79|equave=4}}

=== Tetrameantone ===

[[Subgroup]]: 4.3.5

{{Mapping|legend=2| 1 1 2 | 0 -1 -4 }}

: Mapping generators: ~4, ~4/3

[[Optimal tuning]] ([[POTE]]): 4 = 2400.0, ~4/3 = 503.761

[[Support]]ing [[ET]]s: {{EDs|5, 9, 14, 19, 24, 43, 62, 81, 100|equave=4}}

[[Subgroup]]: 4.3.5

[[Comma list]]: 3125/3072

{{Mapping|legend=2| 1 0 1 | 0 5 1 }}

[[Optimal tuning]] ([[POTE]]): 4 = 2400.0, ~5/4 = 380.059

[[Support]]ing [[ET]]s: {{EDs|6, 13, 19, 25, 38, 44, 63, 82|equave=4}}

=== Blacktetra ===

[[Subgroup]]: 4.3.5

[[Comma list]]: 256/243

{{Mapping|legend=2| 5 4 6 | 0 0 -1 }}

[[Optimal tuning]] ([[POTE]]): 1\5ed4 = 480.0, ~16/15 = 80.4062

[[Support]]ing [[ET]]s: {{EDs|5, 10, 15, 20, 25, 30, 55, 85, 115|equave=4}}

[[Subgroup]]: 4.6.5

[[Comma list]]: [[81/80]] = {{monzo| -4 4 -1 }}

{{Mapping|legend=2| 1 0 -4| 0 1 4 }}

: mapping generators: ~4, ~6

[[Optimal tuning]] (subgroup [[CTE]]): ~4 = 2\1, ~3/2 = 697.214

[[Support]]ing [[ET]]s: *7, *10, *11[-5], *13[+5], *17, *24, *27[+5], *31, *38, *41, *45, *52, *55, *69

[[Subgroup]]: 4.6.5.7

[[Comma list]]: [[36/35]] = {{monzo| 0 2 -1 -1 }}, [[64/63]] = {{monzo| 4 -2 0 -1 }}

{{Mapping|legend=2| 1 0 -4 4 | 0 1 4 -2 }}

[[Optimal tuning]] (subgroup [[CTE]]): ~4 = 2\1, ~3/2 = 699.622

[[Support]]ing [[ET]]s: *7, *10, *17, *24, *27[+5], *31, *38[+7], *41, *44[+5], *55[+7], *58[+5, +7], *65[+5, +7], *75[+5, +7]

<nowiki />* Wart for 4

=== Fourwar ===

The 23-limit version of Fourwar was created first, as an attempt to approximate subgroup 4.6.5.7.11.13.17.19.23 as accurately as possible using 25 to 35 notes per equave. Then the lower limit versions were created by simply extrapolating the temperament downwards.

{{Todo|inline=1|cleanup}}

[ ⟨ 1 0 1 ]

⟨ 0 16 2 ] ⟩

⟨2399.3973, 193.8643]

⟨25.21211, 47.81337]

⟨2399.397, 3101.829, 2787.126]

⟨-0.603, -0.126, 0.812]

[8, 1, -8⟩ (393216:390625)

</pre>

Reduced Mapping

⟨ 0 16 2 5 ] ⟩

Complexity 1.192044

Adjusted Error 0.653313 cents

[-2, -1, -2, 4⟩ (2401:2400)

[3, 0, -5, 2⟩ (3136:3125)

[8, 1, -8, 0⟩ (393216:390625)

q99, q62, q37, q161, q136, q198, q25, q124, q74, q235

</pre>

[ ⟨ 1 0 1 1 1 ]

⟨ 0 16 2 5 9 ] ⟩

TE Generator Tunings (cents)

⟨2400.1097, 193.9498]

TE Step Tunings (cents)

⟨24.18752, 48.52491]

⟨2400.110, 3103.196, 2788.009, 3369.859, 4145.658]

⟨0.110, 1.241, 1.696, 1.033, -5.660]

[-1, -1, -1, 0, 2⟩ (121:120)

[2, 0, -2, -1, 1⟩ (176:175)

[-3, -1, 1, 1, 1⟩ (385:384)

[-1, 0, 3, -3, 1⟩ (1375:1372)

[-2, -1, -2, 4, 0⟩ (2401:2400)

[1, 0, 1, -4, 2⟩ (2420:2401)

q37, q25, q62, q12, q74, q99, q87, q49r, q50r, q124

</pre>

==== 4.6.5.7.11.13 ====

[ ⟨ 1 0 1 1 1 0 ]

⟨ 0 16 2 5 9 23 ] ⟩

⟨2401.2305, 193.5378]

⟨42.79107, 35.98524]

⟨2401.230, 3096.606, 2788.306, 3368.920, 4143.071, 4451.371]

⟨1.230, -5.349, 1.992, 0.094, -8.247, 10.843]

Complexity 1.219191

Adjusted Error 6.699599 cents

[0, 1, -1, 0, 1, -1⟩ (66:65)

[-1, -1, -1, 0, 2, 0⟩ (121:120)

[2, 0, -2, -1, 1, 0⟩ (176:175)

[-2, 1, 1, 1, 0, -1⟩ (105:104)

[-3, -1, 1, 1, 1, 0⟩ (385:384)

[1, 3, -1, 0, 0, -2⟩ (864:845)

[-1, 0, 3, -3, 1, 0⟩ (1375:1372)

q25, q37f, q12f, q62, q50rf, q13rff, q49rff, q87, q74ff, q24rfff

</pre>

==== 4.6.5.7.11.13.17 ====

<pre>

4 6 5 7 11 13 17

[ ⟨ 1 0 1 1 1 0 1 ]

⟨ 0 16 2 5 9 23 13 ] ⟩

⟨2400.4701, 193.4599]

⟨43.39350, 35.55764]

⟨2400.470, 3095.359, 2787.390, 3367.770, 4141.609, 4449.578, 4915.449]

⟨0.470, -6.596, 1.076, -1.056, -9.709, 9.050, 10.494]

Complexity 1.129881

Adjusted Error 8.082725 cents

TE Error 1.977443 cents/octave

Unison Vectors

[0, 1, -1, 0, 1, -1, 0⟩ (66:65)

[-1, 1, 2, -2, 0, -1, 1⟩ (1275:1274)

q25, q12f, q37f, q13rffg, q50rf, q62, q49rffg, q24rfffg, q38rreffg, q74ffg

==== 4.6.5.7.11.13.17.19 ====

4 6 5 7 11 13 17 19

[ ⟨ 1 0 1 1 1 0 1 1 ]

⟨ 0 16 2 5 9 23 13 14 ] ⟩

⟨2399.9219, 193.3952]

⟨44.14256, 35.03670]

⟨2399.922, 3094.324, 2786.712, 3366.898, 4140.479, 4448.090, 4914.060, 5107.455]

⟨-0.078, -7.631, 0.399, -1.928, -10.839, 7.562, 9.104, 9.942]

Complexity 1.058472

Adjusted Error 8.712222 cents

TE Error 2.050935 cents/octave

[0, 1, -1, 0, 1, -1, 0, 0⟩ (66:65)

[-1, 0, 0, 1, 1, 0, 0, -1⟩ (77:76)

[2, 1, -1, 0, 0, 0, 0, -1⟩ (96:95)

[1, 1, 1, -1, 0, 0, -1, 0⟩ (120:119)

[0, 1, 1, 1, -1, 0, 0, -1⟩ (210:209)

[0, 0, 1, -2, 1, 0, 1, -1⟩ (935:931)

[2, 0, -3, 1, 0, 0, -1, 1⟩ (2128:2125)

q25, q12fh, q37f, q13rffgh, q50rf, q62, q49rffgh, q24rfffghh, q38rreffgh, q74ffgh

==== 4.6.5.7.11.13.17.19.23 ====

4 6 5 7 11 13 17 19 23

[ ⟨ 1 0 1 1 1 0 1 1 0 ]

⟨ 0 16 2 5 9 23 13 14 28 ] ⟩

⟨2399.3286, 193.5316]

⟨37.31613, 39.63311]

⟨2399.329, 3096.506, 2786.392, 3366.987, 4141.113, 4451.227, 4915.240, 5108.771, 5418.885]

⟨-0.671, -5.449, 0.078, -1.839, -10.205, 10.699, 10.284, 11.258, -9.389]

Complexity 1.115920

Adjusted Error 9.502017 cents

TE Error 2.100561 cents/octave

[0, 1, -1, 0, 1, -1, 0, 0, 0⟩ (66:65)

[1, 0, 0, -1, 0, -1, 0, 0, 1⟩ (92:91)

[0, -1, 1, 0, 0, 0, 0, -1, 1⟩ (115:114)

[1, 1, 1, -1, 0, 0, -1, 0, 0⟩ (120:119)

[2, 0, -2, -1, 1, 0, 0, 0, 0⟩ (176:175)

[-3, -1, 1, 1, 1, 0, 0, 0, 0⟩ (385:384)

[1, 0, -2, 1, 0, 0, 1, -1, 0⟩ (476:475)

[1, 0, 0, -2, 1, 0, -1, 1, 0⟩ (836:833)

[0, 0, 1, -2, 1, 0, 1, -1, 0⟩ (935:931)

[1, -1, 0, 0, 0, 0, -2, 1, 1⟩ (874:867)

q25i, q12fhi, q37f, q13rffghii, q62, q50rfii, q49rffghii, q24rfffghhiii, q74ffghi, q38rreffghiii

== 4.9.25 subgroup ==

=== Meansquared ===

[[Subgroup]]: 4.9.25

 

 

{{Mapping|legend=2| 1 3 4 | 0 1 4 }}

 

 

[[Optimal tuning]] ([[CTE]]): ~4 = 2\1, ~9/4 = 1394.429

 

== 4.9.49 subgroup ==

[[Subgroup]]: 4.9.49

[[Comma list]]: 4096/3969

{{Mapping|legend=2| 1 3 0 | 0 1 -2 }}

 

Mapping generators: ~4, ~9/64

 

[[Optimal tuning]] ([[CTE]]): ~9/4 = 1419.190

 

[[Support]]ing [[ET]]s: 5, 17, 22, 12, 7, 27, 32, 8, 39[+49], 29[+49], 9[+49], 19[+49], 37, 49

 

== 8.9.7 subgroup ==

Sixscared is a tuning which still maintains some consonance, while eviscerating the rules of conventional 12-tone harmony. The familiar major, minor and perfect intervals are nowhere to be found, and octaves are far and few between, so the seventh harmonic becomes the backbone of harmony. Approximating the harmonics 7, 8, 9, Sixscared is named for the classic dad joke: "Why was six scared? Because seven ate nine."

 

[[Subgroup]]: 8.9.7

 

[[Comma list]]: 64/63

 

: [[gencom]]: [8 9/8; 64/63]

 

[[Optimal tuning]] ([[CTE]]): ~9/8 = 219.1898

 

[[Optimal ET sequence]]: {{val| 16 17 15 }}, {{val| 33 35 31 }}, {{val| 148 … }}, {{val| 181 … }}, {{val| 214 … }}, {{val| 247 … }}

 

[[Badness]]: 0.0215 × 10^-3

 

== 2.5/3.… subgroups ==

 

Magicaltet is related to [[keemic]], [[superkleismic]], and [[magic]]. The tonic and the first three generator steps make a [[magical seventh chord]], hence the name.

[[Subgroup]]: 2.5/3.7.11

[[Comma list]]: 100/99 ({{monzo| 2 2 0 -1 }}), 385/384 ({{monzo| -7 1 1 1 }})

 

{{Mapping|legend=2| 1 0 5 2 | 0 1 -3 2 }}

: mapping generators: ~2, ~5/3

 

{{Mapping|legend=3| 1 -1/2 1/2 2 4 | 0 1/2 -1/2 3 -2 }}

: [[gencom]]: [2 6/5; 100/99 385/384]

 

[[Optimal tuning]]s:

* [[Tp tuning|subgroup]] [[CTE]]: ~2 = 1200.000, ~5/3 = 877.343

* [[Tp tuning|subgroup]] [[POTE]]: ~2 = 1200.000, ~5/3 = 877.351

 

{{Optimal ET sequence|legend=1| 4, 7, 11, 15, 26, 67, 93* }}

: <nowiki/>* wart for 5/3

=== Starlingtet ===

Starlingtet, the {{nowrap| 4 & 15 }} temperament in the 2.5/3.7/3 subgroup, is related to [[starling]] as well as to [[myna]]. The tonic and the first three generator steps make a [[starling tetrad]], hence the name.

[[Subgroup]]: 2.5/3.7/3

[[Comma list]]: [[126/125]] ({{monzo| 1 -3 1 }})

{{Mapping|legend=2| 1 0 -1 | 0 1 3 }}

: mapping generators: ~2, ~5/3

{{Mapping|legend=3| 1 -1 0 1 | 0 4/3 1/3 -5/3 }}

: [[gencom]]: [2 6/5; 126/125]

[[Optimal tuning]]s:  

* [[Tp tuning|subgroup]] [[POTE]]: ~2 = 1200.000, ~5/3 = 888.846

{{Optimal ET sequence|legend=1| 4, 15, 19, 23, 27 }}

[[Tp tuning #T2 tuning|RMS error]]: 0.8398 cents

==== Greeley ====

Greeley is related to [[opossum]] as well as to [[nusecond]].

[[Subgroup]]: 2.5/3.7/3.11/3

[[Comma list]]: 121/120 ({{monzo| -3 -1 0 2 }}), 126/125 ({{monzo| 1 -3 1 }})

{{Mapping|legend=3| 1 -5/4 -1/4 3/4 3/4 | 0 9/4 1/4 -15/4 5/4 }}

[[Optimal tuning]]s:  

* [[Tp tuning|subgroup]] [[CTE]]: ~2 = 1200.000, ~11/10 = 155.696

: <nowiki/>* wart for 11/3

[[Tp tuning #T2 tuning|RMS error]]: 1.034 cents

{{See also| Chromatic pairs #Skateboard }}

Skateboard is related to [[thrasher]].  

[[Subgroup]]: 2.5/3.7/3.11.13/9

[[Comma list]]: 56/55 ({{monzo| 3 -1 1 -1 }}), 91/90 ({{monzo| -1 -1 1 0 1 }}), 100/99 ({{monzo| 2 2 0 -1 }})

{{Mapping|legend=2| 1 0 -1 2 2 | 0 1 3 2 -2 }}

{{Mapping|legend=3| 1 -3/7 4/7 11/7 4 -6/7 | 0 0 -1 -3 -2 2 }}

* [[Tp tuning|subgroup]] [[CTE]]: ~2 = 1200.000, ~5/3 = 886.158

* [[Tp tuning|subgroup]] [[POTE]]: ~2 = 1200.000, ~5/3 = 886.158

{{Optimal ET sequence|legend=1| 11, 15, 19, 23, 42d, 65d }}

[[Tp tuning #T2 tuning|RMS error]]: 2.396 cents

=== Gariberttet ===

Gariberttet is the 2.5/3.7/3 [[Subgroup temperament families, relationships, and genes|altergene]] of [[sirius]].

{{See also | Chromatic pairs #Gariberttet }}

Gariberttet can be described as the {{nowrap| 4 & 29 }} temperament in the 2.5/3.7/3.13/11 subgroup. Extensions to the full 7-, 11-, and 13-limits include [[quasitemp]].

[[Subgroup]]: 2.5/3.7/3.13/11

[[Comma list]]: [[275/273]] ({{monzo| 0 2 -1 -1 }}), [[847/845]] ({{monzo| 0 -1 1 -2 }})

{{Mapping|legend=2| 1 0 0 0 | 0 3 5 1 }}

{{Mapping|legend=3| 1 0 0 0 0 0 | 0 -8/3 1/3 7/3 -1/2 1/2 }}

[[Optimal tuning]]s:  

* [[Tp tuning|subgroup]] [[CTE]] and [[POTE]]: ~2 = 1200.000, ~13/11 = 293.679

{{Optimal ET sequence|legend=1| 29, 33, 37, 41, 45, 49, 78, 94, 143* }}

: <nowiki/>* wart for 13/11

[[Tp tuning #T2 tuning|RMS error]]: 0.6914 cents

{{See also | Chromatic pairs #Indium }}

Indium can be described as the {{nowrap| 8 & 33 }} temperament in the 2.5/3.7/3.11/3 subgroup.  

[[Comma list]]: [[3025/3024]] ({{monzo| -4 2 -1 2 }}), [[3125/3087]] ({{monzo| 0 5 -3 }})

{{Mapping|legend=2| 1 0 0 2 | 0 6 10 -1 }}

{{Mapping|legend=3| 1 -1/2 -1/2 -1/2 3/2 | 0 -15/4 9/4 25/4 -19/4 }}

: [[gencom]]: [2 12/11; 3025/3024 3125/3087]

* [[Tp tuning|subgroup]] [[CTE]]: ~2 = 1200.000, ~12/11 = 146.978

* [[Tp tuning|subgroup]] [[POTE]]: ~2 = 1200.000, ~12/11 = 147.010

{{Optimal ET sequence|legend=1| 8, 33, 41, 49, 204*^† }}

: <nowiki/>* wart for 7/3

: ^† wart for 11/3

[[Tp tuning #T2 tuning|RMS error]]: 0.7788 cents

==== Ammon ====

{{See also| Chromatic pairs #Ammon }}

Ammon can be described as the {{nowrap| 8 & 29 }} temperament in the 2.5/3.7/3.11/3.13/3 subgroup. It extends [[tridec]], and is related to [[ammonite]]. It is generated by a semidiminished fourth, hence the old name ''semidim'', which has been rejected since 2025 to avoid confusion with another temperament of the same name.

[[Subgroup]]: 2.5/3.7/3.11/3.13/3

[[Comma list]]: [[121/120]] ({{monzo| -3 -1 0 2 }}), [[169/168]] ({{monzo| -3 0 -1 0 2 }}), [[275/273]] ({{monzo| 0 2 -1 1 -1 }})

{{Mapping|legend=2| 1 3 5 3 4 | 0 -6 -10 -3 -5 }}

{{Mapping|legend=3| 1 -3 0 2 0 1 | 0 24/5 -6/5 -26/5 9/5 -1/5 }}

: [[gencom]]: [2 13/10; 121/120 169/168 275/273]

* [[Tp tuning|subgroup]] [[CTE]]: ~2 = 1200.000, ~13/10 = 453.121

* [[Tp tuning|subgroup]] [[POTE]]: ~2 = 1200.000, ~13/10 = 453.242

{{Optimal ET sequence|legend=1| 8, 29, 37, 45 }}

[[Tp tuning #T2 tuning|RMS error]]: 1.052 cents

=== Sentry ===

{{See also | Chromatic pairs #Sentry }}

Sentry, the {{nowrap| 3 & 5 }} temperament in the 2.5/3.9/7 subgroup, is related to [[sensi]].  

[[Subgroup]]: 2.5/3.9/7

[[Comma list]]: [[245/243]] ({{monzo| 0 1 -2 }})

{{Mapping|legend=2| 1 0 0 | 0 2 1 }}

{{Mapping|legend=3| 1 0 0 0 | 0 0 2 -1 }}

: [[gencom]]: [2 9/7; 245/243]

* [[Tp tuning|subgroup]] [[CTE]] and [[POTE]]: ~2 = 1200.000, ~9/7 = 440.902

{{Optimal ET sequence|legend=1| 8, 11, 19, 30, 41, 49, 52, 145*, 166^†, 197*^†, 215^†, 264*^† }}

: <nowiki/>* wart for 5/3

[[Tp tuning #T2 tuning|RMS error]]: 0.7105 cents

=== Marveltwintri ===

{{See also| Chromatic pairs #Marveltwintri }}

Marveltwintri can be described as the {{nowrap| 3 & 4 }} temperament in the 2.5/3.13/9 subgroup. The tonic and the first two generator steps make a [[marveltwin triad]], hence the name. [[Cata]] is a very natural extension of this temperament to the [[2.3.5.13 subgroup|2.3.5.13-subgroup]].

[[Subgroup]]: 2.5/3.13/9

[[Comma list]]: [[325/324]] ({{monzo| -2 2 1 }})

{{Mapping|legend=2| 1 0 2 | 0 1 -2 }}

{{Mapping|legend=3| 1 -1/6 5/6 0 0 -1/3 | 0 -1/2 -3/2 0 0 1 }}

: [[gencom]]: [2 6/5; 325/324]

* [[Tp tuning|subgroup]] [[CTE]]: ~2 = 1200.000, ~5/3 = 882.886

* [[Tp tuning|subgroup]] [[POTE]]: ~2 = 1200.000, ~5/3 = 882.861

{{Optimal ET sequence|legend=1| 3, 4, 11, 15, 19, 34, 53, 87, 140 }}

[[Tp tuning #T2 tuning|RMS error]]: 0.2444 cents

== 2.….7/3.… subgroups ==

=== Guanyintet ===

{{See also | Chromatic pairs #Guanyintet }}

Guanyintet, the {{nowrap| 4 & 9 }} temperament in the 2.5.7/3.11/3 subgroup, is the main rank-2 chain of [[guanyin]] and a restriction of [[orwell]]. It is defined by tempering out [[1728/1715]] ({{S|6/S7}}) and [[540/539]] (S12/S14), which imply [[176/175]] (S8/S10) as well as S11/S15 being tempered out. The tonic and the first three generator steps make a [[guanyin tetrad]], hence the name.  

[[Subgroup]]: 2.5.7/3.11/3

[[Comma list]]: [[176/175]] ({{monzo| 4 -2 -1 1 }}), [[540/539]] ({{monzo| 2 1 -2 -1 }})

{{Mapping|legend=2| 1 0 1 3 | 0 -3 1 -5 }}

{{Mapping|legend=3| 1 -4/3 3 -1/3 5/3 | 0 4/3 -3 7/3 -11/3 }}

: [[gencom]]: [2 7/6; 176/175 540/539]

* ([[Tp tuning|subgroup]] [[CTE]]): ~2 = 1200.000, ~7/6 = 270.455

* ([[Tp tuning|subgroup]] [[POTE]]): ~2 = 1200.000, ~7/6 = 270.093

{{Optimal ET sequence|legend=1| 9, 22, 31, 40, 191c*, 231c*, 271c*, 311c* }}

[[Tp tuning #T2 tuning|RMS error]]: 0.6028 cents

==== Tridecimal guanyintet ====

Guanyintet can extend to the 13th harmonic by the equivalences ([[12/11]])³ = [[13/10]] and ([[15/14]])³ = [[16/13]], therefore tempering out {S11/S12/S14/S15}. However, note that it is not supported by the 31 & 53 orwell extension dubbed "tridecimal orwell", but instead the less accurate [[winston]] (22f & 31), as orwell prefers slightly sharper tunings than guanyintet. [[40edo]] remains an excellent tuning.

[[Subgroup]]: 2.5.7/3.11/3.13

[[Comma list]]: [[176/175]] ({{monzo| 4 -2 -1 1 0 }}), [[540/539]] ({{monzo| 2 1 -2 -1 0 }}), [[1573/1568]] ({{monzo| -5 0 -2 2 1 }})

{{Mapping|legend=2| 1 0 1 3 1 | 0 -3 1 -5 12 }}

* ([[Tp tuning|subgroup]] [[CTE]]): ~2 = 1200.000, ~7/6 = 270.152

* ([[Tp tuning|subgroup]] [[POTE]]): ~2 = 1200.000, ~7/6 = 270.218

{{Optimal ET sequence|legend=1| 9, 22, 31, 40, 71, 111, 151, 262c*}} <small> using subgroup TE </small>

: <nowiki/>* wart for 7/3

Badness (Sintel): 0.329

{{See also | Chromatic pairs #Laz }}

Laz is related to [[avalokita]] as well as to [[winston]].  

[[Comma list]]: [[144/143]] ({{monzo| 4 0 0 -1 -1 }}), [[176/175]] ({{monzo| 4 -2 -1 1 }}), [[196/195]] ({{monzo| 2 -1 2 0 -1 }}

{{Mapping|legend=2| 1 0 2 -2 6 | 0 3 -1 5 -5 }}

: [[gencom]]: [2 7/6; 144/143 176/175 196/195]

* [[Tp tuning|subgroup]] [[CTE]]: ~2 = 1200.000, ~12/7 = 930.598

* [[Tp tuning|subgroup]] [[POTE]]: ~2 = 1200.000, ~12/7 = 930.700

{{Optimal ET sequence|legend=1| 9, 31, 40, 49, 156c*†, 205c*† }}

: <nowiki/>* wart for 7/3

: † wart for 11/3

[[Tp tuning #T2 tuning|RMS error]]: 0.8790 cents

{{See also| Chromatic pairs #Kryptonite }}

Kryptonite is related to [[krypton]].  

[[Subgroup]]: 2.5.7/3.11/3.13/3

[[Comma list]]: 56/55 ({{monzo| 3 -1 1 -1 }}), 78/77 ({{monzo| 1 0 -1 -1 1 }}), 91/90 ({{monzo| -1 -2 1 0 1 }})

: mapping generators: ~2, ~13/12

{{Mapping|legend=3| 1 -5/4 2 -1/4 3/4 3/4 | 0 -1/2 3 3/2 -3/2 1/2 }}

: [[gencom]]: [2 13/12; 56/55 78/77 91/90]

* [[Tp tuning|subgroup]] [[CTE]]: ~2 = 1200.000, ~13/12 = 130.945

* [[Tp tuning|subgroup]] [[POTE]]: ~2 = 1200.000, ~13/12 = 132.428

{{Optimal ET sequence|legend=1| 1, …, 8, 9 }}