Porcupine family: Difference between revisions
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The 5-limit parent comma for the '''porcupine family''' is [[250/243]], the maximal diesis or porcupine comma. Its [[monzo]] is {{monzo| 1 -5 3 }}, and flipping that yields {{multival| 3 5 1 }} for the [[wedgie]]. This tells us the [[generator]] is a minor whole tone, the [[10/9]] interval, and that three of these add up to a fourth, with two more giving the minor sixth. In fact, (10/9)<sup>3</sup> = 4/3 × 250/243, and (10/9)<sup>5</sup> = 8/5 × (250/243)<sup>2</sup>. [[22edo|3\22]] is a very recommendable generator, and MOS of 7, 8 and 15 notes make for some nice scale possibilities. | The 5-limit parent comma for the '''porcupine family''' is [[250/243]], the maximal diesis or porcupine comma. Its [[monzo]] is {{monzo| 1 -5 3 }}, and flipping that yields {{multival| 3 5 1 }} for the [[wedgie]]. This tells us the [[generator]] is a minor whole tone, the [[10/9]] interval, and that three of these add up to a fourth, with two more giving the minor sixth. In fact, (10/9)<sup>3</sup> = 4/3 × 250/243, and (10/9)<sup>5</sup> = 8/5 × (250/243)<sup>2</sup>. [[22edo|3\22]] is a very recommendable generator, and MOS of 7, 8 and 15 notes make for some nice scale possibilities. | ||
The second comma of the [[Normal lists #Normal interval list|normal comma list]] defines which [[7-limit]] family member we are looking at. That means | |||
* [[64/63]], the archytas comma, for [[#Septimal porcupine|septimal porcupine]], | |||
* [[36/35]], the septimal quarter tone, for [[#Hystrix|hystrix]], | |||
* [[50/49]], the jubilisma, for [[#Hedgehog|hedgehog]], and | |||
* [[49/48]], the slendro diesis, for [[#Nautilus|nautilus]]. | |||
All these 7-limit extensions notably share the same 2.3.5.11 subgroup, ''porkypine''. | |||
Temperaments discussed elsewhere include [[opossum]] and [[Dicot family #Jamesbond|jamesbond]]. | |||
== Porcupine == | == Porcupine == | ||
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* 5-odd-limit diamond monotone and tradeoff: ~10/9 = [157.821, 166.015] | * 5-odd-limit diamond monotone and tradeoff: ~10/9 = [157.821, 166.015] | ||
{{Val list|legend=1| 7, 15, 22, 95c | {{Val list|legend=1| 7, 15, 22, 95c }} | ||
[[Badness]]: 0.030778 | [[Badness]]: 0.030778 | ||
=== | === Porkypine === | ||
Subgroup: 2.3.5.11 | |||
Comma list: 55/54, 100/99 | |||
Sval mapping: [{{val| 1 2 3 4 }}, {{val| 0 -3 -5 -4 }}] | |||
Gencom mapping: [{{val| 1 2 3 0 4 }}, {{val| 0 -3 -5 0 -4 }}] | |||
Gencom: [2 10/9; 55/54, 100/99] | |||
POTE generator: ~11/10 = 164.0777 | |||
Vals: {{val list| 7, 15, 22, 37, 73ce, 95ce }} | |||
== Septimal porcupine == | == Septimal porcupine == | ||
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* 7- and 9-odd-limit diamond monotone and tradeoff: ~10/9 = [160.000, 163.636] | * 7- and 9-odd-limit diamond monotone and tradeoff: ~10/9 = [160.000, 163.636] | ||
{{Val list|legend=1| 7, 15, 22, 59, 81bd | {{Val list|legend=1| 7, 15, 22, 59, 81bd }} | ||
[[Badness]]: 0.041057 | [[Badness]]: 0.041057 | ||
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[[POTE generator]]: ~21/20 = 82.505 | [[POTE generator]]: ~21/20 = 82.505 | ||
{{Val list|legend=1| 15, 29, 44d, 59d, 73cd, 102cd }} | {{Val list|legend=1| 14c, 15, 29, 44d, 59d, 73cd, 102cd }} | ||
[[Badness]]: 0.057420 | [[Badness]]: 0.057420 | ||
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POTE generator: ~21/20 = 82.530 | POTE generator: ~21/20 = 82.530 | ||
Vals: {{val list| 15, 29, 44d, 59df, 73cde, 102cde }} | Vals: {{val list| 14cf, 15, 29, 44d, 59df, 73cde, 102cde }} | ||
Badness: 0.022285 | Badness: 0.022285 | ||