Porcupine family: Difference between revisions
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{{Main| Porcupine }} | {{Main| Porcupine }} | ||
The [[generator]] of porcupine is a minor whole tone, the [[10/9]] interval, and three of these add up to a perfect fourth ([[4/3]]), with two more giving the minor sixth ([[8/5]]). 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 scale]]s of 7, 8 and 15 notes make for some nice scale possibilities. | The [[generator]] of porcupine is a minor whole tone, the [[10/9]] interval, and three of these add up to a perfect fourth ([[4/3]]), with two more giving the minor sixth ([[8/5]]). In fact, {{nowrap| (10/9)<sup>3</sup> {{=}} (4/3)⋅(250/243) }}, and {{nowrap| (10/9)<sup>5</sup> {{=}} (8/5)⋅(250/243)<sup>2</sup> }}. [[22edo|3\22]] is a very recommendable generator, and [[mos scale]]s of 7, 8 and 15 notes make for some nice scale possibilities. | ||
[[Subgroup]]: 2.3.5 | [[Subgroup]]: 2.3.5 | ||
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The second comma defines which [[7-limit]] family member we are looking at. That means | The second comma defines which [[7-limit]] family member we are looking at. That means | ||
* [[64/63]], the archytas comma, for [[#Septimal porcupine|septimal porcupine]], | * [[64/63]], the archytas comma, for [[#Septimal porcupine|septimal porcupine]], | ||
* [[36/35]], the | * [[36/35]], the mint comma, for [[#Hystrix|hystrix]], | ||
* [[50/49]], the jubilisma, for [[#Hedgehog|hedgehog]], and | * [[50/49]], the jubilisma, for [[#Hedgehog|hedgehog]], and | ||
* [[49/48]], the | * [[49/48]], the semaphoresma, for [[#Nautilus|nautilus]]. | ||
Temperaments discussed elsewhere include [[7th-octave temperaments #Jamesbond|jamesbond]]. | Temperaments discussed elsewhere include [[7th-octave temperaments #Jamesbond|jamesbond]]. | ||