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To the gamelisma itself we need to add the comma which appears next on the modified [[Normal lists #Normal interval list|normal comma list]], which is often a 5-limit comma. The second comma on the list for mothra is 81/80, for rodan 245/243, for guiron 32805/32768, for gorgo 36/35, and for gidorah 256/245. These all use 8/7 as a generator, though in the case of gidorah that's the same as 6/5. Miracle adds 33075/32768 and uses the secor, half an 8/7, as generator. Lemba adds 525/512 to the list, and has a half-octave period. Valentine adds 6144/6125 with a generator of 21/20 and superkleismic adds 875/864 with a generator of 6/5. Unidec adds 4375/4374, and has a generator of 10/9 with a half-octave period. Hemithirds adds 65625/65536 with a generator half of a major third. Finally, tritikleismic adds 15625/15536 and has a generator of 6/5 with a 1/3 octave period.
To the gamelisma itself we need to add the comma which appears next on the modified [[Normal lists #Normal interval list|normal comma list]], which is often a 5-limit comma. The second comma on the list for mothra is 81/80, for rodan 245/243, for guiron 32805/32768, for gorgo 36/35, and for gidorah 256/245. These all use 8/7 as a generator, though in the case of gidorah that's the same as 6/5. Miracle adds 33075/32768 and uses the secor, half an 8/7, as generator. Lemba adds 525/512 to the list, and has a half-octave period. Valentine adds 6144/6125 with a generator of 21/20 and superkleismic adds 875/864 with a generator of 6/5. Unidec adds 4375/4374, and has a generator of 10/9 with a half-octave period. Hemithirds adds 65625/65536 with a generator half of a major third. Finally, tritikleismic adds 15625/15536 and has a generator of 6/5 with a 1/3 octave period.


Discussed elsewhere are [[blacksmith]], [[mothra]], [[echidnic]], [[trismegistus]], [[hemithirds]], [[gamity]], [[triwell]], [[decades]] and [[heinz]]. The rest are considered below.
Discussed elsewhere are [[blacksmith]], [[mothra]], [[echidnic]], [[valentine]], [[tritikleismic]], [[trismegistus]], [[hemithirds]], [[gamity]], [[triwell]], [[decades]] and [[heinz]]. The rest are considered below.


=== Subgroup extensions ===
=== Subgroup extensions ===
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[[Minimax tuning]]:  
[[Minimax tuning]]:  
* 7- and [[9-odd-limit]]
* [[7-odd-limit|7-]] and [[9-odd-limit]]: ~8/7 = {{monzo| 2/9 0 1/18 -1/18 }}
: [{{monzo| 1 0 0 0 }}, {{monzo| 5/3 0 1/6 -1/6 }}, {{monzo| 25/9 0 17/18 -17/18 }}, {{monzo| 25/9 0 -1/18 1/18 }}]
: [{{monzo| 1 0 0 0 }}, {{monzo| 5/3 0 1/6 -1/6 }}, {{monzo| 25/9 0 17/18 -17/18 }}, {{monzo| 25/9 0 -1/18 1/18 }}]
: [[Eigenmonzo]]s: 2, 7/5
: [[Eigenmonzo]]s: 2, 7/5
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Minimax tuning:  
Minimax tuning:  
* 11-odd-limit
* [[11-odd-limit]]: ~8/7 = {{monzo| 4/19 2/19 0 0 -1/19 }}
: [{{monzo| 1 0 0 0 0 }}, {{monzo| 31/19 6/19 0 0 -3/19 }}, {{monzo| 49/19 34/19 0 0 -17/19 }}, {{monzo| 53/19 -2/19 0 0 1/19 }}, {{monzo| 62/19 -26/19 0 0 13/19 }}]
: [{{monzo| 1 0 0 0 0 }}, {{monzo| 31/19 6/19 0 0 -3/19 }}, {{monzo| 49/19 34/19 0 0 -17/19 }}, {{monzo| 53/19 -2/19 0 0 1/19 }}, {{monzo| 62/19 -26/19 0 0 13/19 }}]
: Eigenmonzos: 2, 11/9
: Eigenmonzos: 2, 11/9
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Minimax tuning:  
Minimax tuning:  
* 13- and 15-odd-limit
* 13- and 15-odd-limit: ~8/7 = {{monzo| 3/14 1/14 0 0 0 -1/28 }}
: [{{monzo| 1 0 0 0 0 0 }}, {{monzo| 23/14 3/14 0 0 0 -3/28 }}, {{monzo| 37/14 17/14 0 0 0 -17/28 }}, {{monzo| 39/14 -1/14 0 0 0 1/28 }}, {{monzo| 45/14 -13/14 0 0 0 13/28 }}, {{monzo| 23/7 -11/7 0 0 0 11/14 }}]
: Eigenmonzos: 2, 13/9
: Eigenmonzos: 2, 13/9


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POTE generator: ~8/7 = 234.524
POTE generator: ~8/7 = 234.524


Minimax tuning:  
Minimax tuning:
* 17-odd-limit eigenmonzos: 2, 18/17
* 17-odd-limit: ~8/7 = {{monzo| 3/13 1/13 0 0 0 0 -1/26 }}
: Eigenmonzos: 2, 18/17


Vals: {{Val list| 41, 46, 87, 220dg, 307dgg }}
Vals: {{Val list| 41, 46, 87, 220dg, 307dgg }}
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[[Minimax tuning]]:
[[Minimax tuning]]:
* 7- and [[9-odd-limit]]
* [[7-odd-limit|7-]] and [[9-odd-limit]]: ~8/7 = {{monzo| 7/24 0 -1/24 }}
: [{{monzo| 1 0 0 0 }}, {{monzo| 15/8 0 -1/8 0 }}, {{monzo| 0 0 1 0 }}, {{monzo| 65/24 0 1/24 0 }}]
: [{{monzo| 1 0 0 0 }}, {{monzo| 15/8 0 -1/8 0 }}, {{monzo| 0 0 1 0 }}, {{monzo| 65/24 0 1/24 0 }}]
: [[Eigenmonzo]]s: 2, 5/4
: [[Eigenmonzo]]s: 2, 5


{{Val list|legend=1| 36, 41, 77, 118, 277d }}
{{Val list|legend=1| 36, 41, 77, 118, 277d }}
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Minimax tuning:
Minimax tuning:
* 11-odd-limit
* [[11-odd-limit]]: ~8/7 = {{monzo| 7/24 0 -1/24 }}
: [{{monzo| 1 0 0 0 0 }}, {{monzo| 15/8 0 -1/8 0 0 }}, {{monzo| 0 0 1 0 0 }}, {{monzo| 65/24 0 1/24 0 0 }}, {{monzo| 37/6 0 -7/6 0 0 }}]  
: [{{monzo| 1 0 0 0 0 }}, {{monzo| 15/8 0 -1/8 0 0 }}, {{monzo| 0 0 1 0 0 }}, {{monzo| 65/24 0 1/24 0 0 }}, {{monzo| 37/6 0 -7/6 0 0 }}]  
: Eigenmonzos: 2, 5/4
: Eigenmonzos: 2, 5


Vals: {{Val list| 36e, 41, 77, 118, 159, 277d }}
Vals: {{Val list| 36e, 41, 77, 118, 159, 277d }}
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Badness: 0.047071
Badness: 0.047071


=== Music ===
; Music
* [http://clones.soonlabel.com/public/micro/gene_ward_smith/Others/Herman/gorgo-example.mp3 Gorgo Example] by [[Herman Miller]]
* [http://clones.soonlabel.com/public/micro/gene_ward_smith/Others/Herman/gorgo-example.mp3 Gorgo Example] by [[Herman Miller]]


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[[Minimax tuning]]:
[[Minimax tuning]]:
* [[7-odd-limit]]
* [[7-odd-limit]]: ~15/14 = {{monzo| 2/13 1/13 -1/13 }}
: [{{monzo| 1 0 0 0 }}, {{monzo| 25/13 6/13 -6/13 0 }}, {{monzo| 25/13 -7/13 7/13 0 }}, {{monzo| 35/13 -2/13 2/13 0 }}]
: [{{monzo| 1 0 0 0 }}, {{monzo| 25/13 6/13 -6/13 0 }}, {{monzo| 25/13 -7/13 7/13 0 }}, {{monzo| 35/13 -2/13 2/13 0 }}]
: [[Eigenmonzo]]s: 2, 6/5
: [[Eigenmonzo]]s: 2, 6/5
* [[9-odd-limit]]
* [[9-odd-limit]]: ~15/14 = {{monzo| 1/19 2/19 -1/19 }}
: [{{monzo| 1 0 0 0 }}, {{monzo| 25/19 12/19 -6/19 0 }}, {{monzo| 50/19 -14/19 7/19 0 }}, {{monzo| 55/19 -4/19 2/19 0 }}]
: [{{monzo| 1 0 0 0 }}, {{monzo| 25/19 12/19 -6/19 0 }}, {{monzo| 50/19 -14/19 7/19 0 }}, {{monzo| 55/19 -4/19 2/19 0 }}]
: [[Eigenmonzo]]s: 2, 10/9
: [[Eigenmonzo]]s: 2, 10/9
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Minimax tuning:
Minimax tuning:
* 11-odd-limit
* [[11-odd-limit]]: ~15/14 = {{monzo| 1/19 2/19 -1/19 }}
: [{{monzo| 1 0 0 0 0 }}, {{monzo| 25/19 12/19 -6/19 0 0 }}, {{monzo| 50/19 -14/19 7/19 0 0 }}, {{monzo| 55/19 -4/19 2/19 0 0 }}, {{monzo| 53/19 30/19 -15/19 0 0 }}]
: [{{monzo| 1 0 0 0 0 }}, {{monzo| 25/19 12/19 -6/19 0 0 }}, {{monzo| 50/19 -14/19 7/19 0 0 }}, {{monzo| 55/19 -4/19 2/19 0 0 }}, {{monzo| 53/19 30/19 -15/19 0 0 }}]
: Eigenmonzos: 2, 10/9
: Eigenmonzos: 2, 10/9
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[[Minimax tuning]]:
[[Minimax tuning]]:
* [[7-odd-limit]]
* [[7-odd-limit]]: ~10/9 = {{monzo| 3/26 0 -1/13 1/13 }}
: [{{monzo| 1 0 0 0 }}, {{monzo| 47/26 0 6/13 -6/13 }}, {{monzo| 71/26 0 11/13 -11/13 }}, {{monzo| 71/26 0 -2/13 2/13 }}]
: [{{monzo| 1 0 0 0 }}, {{monzo| 47/26 0 6/13 -6/13 }}, {{monzo| 71/26 0 11/13 -11/13 }}, {{monzo| 71/26 0 -2/13 2/13 }}]
: [[Eigenmonzo]]s: 2, 7/5
: [[Eigenmonzo]]s: 2, 7/5
* [[9-odd-limit]]
* [[9-odd-limit]]: ~10/9 = {{monzo| 5/28 -1/7 0 1/14 }}
: [{{monzo| 1 0 0 0 }}, {{monzo| 10/7 6/7 0 -3/7 }}, {{monzo| 57/28 11/7 0 -11/14 }}, {{monzo| 20/7 -2/7 0 1/7 }}]
: [{{monzo| 1 0 0 0 }}, {{monzo| 10/7 6/7 0 -3/7 }}, {{monzo| 57/28 11/7 0 -11/14 }}, {{monzo| 20/7 -2/7 0 1/7 }}]
: [[Eigenmonzo]]s: 2, 9/7
: [[Eigenmonzo]]s: 2, 9/7
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Minimax tuning:
Minimax tuning:
* 11-odd-limit
* [[11-odd-limit]]: ~10/9 = {{monzo| 5/28 -1/7 0 1/14 }}
: [{{monzo| 1 0 0 0 0 }}, {{monzo| 10/7 6/7 0 -3/7 0 }}, {{monzo| 57/28 11/7 0 -11/14 0 }}, {{monzo| 20/7 -2/7 0 1/7 0 }}, {{monzo| 99/28 -3/7 0 3/14 0 }}]
: [{{monzo| 1 0 0 0 0 }}, {{monzo| 10/7 6/7 0 -3/7 0 }}, {{monzo| 57/28 11/7 0 -11/14 0 }}, {{monzo| 20/7 -2/7 0 1/7 0 }}, {{monzo| 99/28 -3/7 0 3/14 0 }}]
: Eigenmonzos: 2, 9/7
: Eigenmonzos: 2, 9/7
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Scales: [[Unidec26]]
Scales: [[Unidec26]]


==== Ekadash ====
=== Ekadash ===
Subgroup: 2.3.5.7.11.13
Subgroup: 2.3.5.7.11.13


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Scales: [[Unidec26]]
Scales: [[Unidec26]]


==== Hendec ====
=== Hendec ===
Subgroup: 2.3.5.7.11.13
Subgroup: 2.3.5.7.11.13


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Scales: [[Unidec26]]
Scales: [[Unidec26]]


===== 17-limit =====
==== 17-limit ====
Subgroup: 2.3.5.7.11.13.17
Subgroup: 2.3.5.7.11.13.17


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Scales: [[Unidec26]]
Scales: [[Unidec26]]
== Valentine ==
{{main| Valentine }}
{{see also| Starling temperaments #Valentine }}
Subgroup: 2.3.5
[[Comma list]]: 1990656/1953125
[[Mapping]]: [{{val| 1 1 2 }}, {{val| 0 9 5 }}]
[[POTE generator]]: ~25/24 = 78.039
{{Val list|legend=1| 15, 31, 46, 77, 123 }}
[[Badness]]: 0.122765
=== 7-limit ===
Subgroup: 2.3.5.7
[[Comma list]]: 126/125, 1029/1024
[[Mapping]]: [{{val| 1 1 2 3 }}, {{val| 0 9 5 -3 }}]
Mapping generators: ~2, ~21/20
{{Multival|legend=1| 9 5 -3 -13 -30 -21 }}
[[POTE generator]]: ~21/20 = 77.864
[[Minimax tuning]]:
* [[7-odd-limit]]
: [{{monzo| 1 0 0 0 }}, {{monzo| 5/2 3/4 0 -3/4 }}, {{monzo| 17/6 5/12 0 -5/12 }}, {{monzo| 5/2 -1/4 0 1/4 }}]
: [[Eigenmonzo]]s: 2, 7/6
* [[9-odd-limit]]
: [{{monzo| 1 0 0 0 }}, {{monzo| 10/7 6/7 0 -3/7 }}, {{monzo| 47/21 10/21 0 -5/21 }}, {{monzo| 20/7 -2/7 0 1/7 }}]
: [[Eigenmonzo]]s: 2, 9/7
[[Algebraic generator]]: smaller root of ''x''<sup>2</sup> - 89''x'' + 92, or (89 - sqrt (7553))/2, at 77.8616 cents.
{{Val list|legend=1| 15, 31, 46, 77, 185, 262cd }}
[[Badness]]: 0.031056
=== 11-limit ===
Subgroup: 2.3.5.7.11
Comma list: 121/120, 126/125, 176/175
Mapping: [{{val| 1 1 2 3 3 }}, {{val| 0 9 5 -3 7 }}]
Mapping generators: ~2, ~21/20
POTE generator: ~21/20 = 77.881
Minimax tuning:
* 11-odd-limit
: [{{monzo| 1 0 0 0 0 }}, {{monzo| 1 0 0 -9/10 9/10 }}, {{monzo| 2 0 0 -1/2 1/2 }}, {{monzo| 3 0 0 3/10 -3/10 }}, {{monzo| 3 0 0 -7/10 7/10 }}]
: Eigenmonzos: 2, 11/7
Algebraic generator: positive root of 4''x''<sup>3</sup> + 15''x''<sup>2</sup> - 21, or else Gontrand2, the smallest positive root of 4''x''<sup>7</sup> - 8''x''<sup>6</sup> + 5.
Vals: {{Val list| 15, 31, 46, 77, 262cdee, 339cdeee }}
Badness: 0.016687
==== Dwynwen ====
Subgroup: 2.3.5.7.11.13
Comma list: 91/90, 121/120, 126/125, 176/175
Mapping: [{{val| 1 1 2 3 3 2 }}, {{val| 0 9 5 -3 7 26 }}]
POTE generator: ~21/20 = 78.219
Vals: {{Val list| 15, 31f, 46 }}
Badness: 0.023461
==== Lupercalia ====
Subgroup: 2.3.5.7.11.13
Comma list: 66/65, 105/104, 121/120, 126/125
Mapping: [{{val| 1 1 2 3 3 3 }}, {{val| 0 9 5 -3 7 11 }}]
POTE generator: ~21/20 = 77.709
Vals: {{Val list| 15, 31, 77ff, 108eff, 139efff }}
Badness: 0.021328
==== Valentino ====
Subgroup: 2.3.5.7.11.13
Comma list: 121/120, 126/125, 176/175, 196/195
Mapping: [{{val| 1 1 2 3 3 5 }}, {{val| 0 9 5 -3 7 -20 }}]
POTE generator: ~21/20 = 77.958
Vals: {{Val list| 15f, 31, 46, 77 }}
Badness: 0.020665
==== Semivalentine ====
Subgroup: 2.3.5.7.11.13
Comma list: 121/120, 126/125, 169/168, 176/175
Mapping: [{{val| 2 2 4 6 6 7 }}, {{val| 0 9 5 -3 7 3 }}]
POTE generator: ~21/20 = 77.839
Vals: {{Val list| 16, 30, 46, 62, 108ef }}
Badness: 0.032749


== Superkleismic ==
== Superkleismic ==
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Badness: 0.021478
Badness: 0.021478
== Tritikleismic ==
{{see also| Kleismic family #Tritikleismic }}
Subgroup: 2.3.5.7
[[Comma list]]: 1029/1024, 15625/15552
[[Mapping]]: [{{val| 3 0 3 10 }}, {{val| 0 6 5 -2 }}]
Mapping generators: ~63/50, ~6/5
{{Multival|legend=1| 18 15 -6 -18 -60 -56 }}
[[POTE generator]]: ~6/5 = 316.872
[[Minimax tuning]]:
* [[7-odd-limit]]
: [{{monzo| 1 0 0 0 }}, {{monzo| 2 0 6/7 -6/7 }}, {{monzo| 8/3 0 5/7 -5/7 }}, {{monzo| 8/3 0 -2/7 2/7 }}]
: [[Eigenmonzo]]s: 2, 7/5
* [[9-odd-limit]]
: [{{monzo| 1 0 0 0 }}, {{monzo| 10/7 6/7 0 -3/7 }}, {{monzo| 46/21 5/7 0 -5/14 }}, {{monzo| 20/7 -2/7 0 1/7 }}]
: [[Eigenmonzo]]s: 2, 9/7
{{Val list|legend=1| 15, 42bc, 57, 72, 159, 231 }}
[[Badness]]: 0.056337
=== 11-limit ===
Subgroup: 2.3.5.7.11
Comma list: 385/384, 441/440, 4000/3993
Mapping: [{{val| 3 0 3 10 8 }}, {{val| 0 6 5 -2 3 }}]
Mapping generators: ~44/35, ~6/5
POTE generator: ~6/5 = 316.881
Minimax tuning:
* 11-odd-limit
: [{{monzo| 1 0 0 0 0 }}, {{monzo| 10/7 6/7 0 -3/7 0 }}, {{monzo| 46/21 5/7 0 -5/14 0 }}, {{monzo| 20/7 -2/7 0 1/7 0 }}, {{monzo| 71/21 3/7 0 -3/14 0 }}]
: Eigenmonzos: 2, 9/7
Vals: {{Val list| 15, 42bc, 57, 72, 159, 231 }}
Badness: 0.019333
=== 13-limit ===
Subgroup: 2.3.5.7.11.13
Comma list: 325/324, 364/363, 385/384, 625/624
Mapping: [{{val| 3 0 3 10 8 0 }}, {{val| 0 6 5 -2 3 14 }}]
Mapping generators: ~44/35, ~6/5
POTE generator: ~6/5 = 316.9585
Vals: {{Val list| 72, 87, 159 }}
Badness: 0.015652
=== 17-limit ===
Subgroup: 2.3.5.7.11.13.17
Comma list: 273/272, 325/324, 364/363, 375/374, 385/384
Mapping: [{{val| 3 0 3 10 8 0 -2 }}, {{val| 0 6 5 -2 3 14 18 }}]
Mapping generators: ~34/27, ~6/5
POTE generator: ~6/5 = 316.9082
Vals: {{Val list| 72, 159, 231f }}
Badness: 0.013551


== Necromanteion ==
== Necromanteion ==
Retrieved from "https://en.xen.wiki/w/Gamelismic_clan"