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)3 = 4/3 × 250/243, and (10/9)5 = 8/5 × (250/243)2. [[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 perfect fourth ([[4/3]]), with two more giving the minor sixth ([[8/5]]). In fact, (10/9)3 = 4/3 × 250/243, and (10/9)5 = 8/5 × (250/243)2. [[22edo|3\22]] is a very recommendable generator, and [[mos scale]]s of 7, 8 and 15 notes make for some nice scale possibilities.

Notice 250/243 = ([[55/54]])([[100/99]]), the temperament thus extends naturally to the 2.3.5.11 [[subgroup]], sometimes known as ''porkypine''.

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

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* [[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, known as ''porkypine''.~~

Temperaments discussed elsewhere include [[Dicot family #Jamesbond|jamesbond]].

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== Opossum ==

Opossum can be described as 7d & 8d. Tempering out [[28/27]], the perfect fifth of three generator steps is conflated with not [[32/21]] as in porcupine but [[14/9]]. Three such fifths or nine generator steps octave reduced give a flat 7/4. 2\15 is a good generator.

[[Subgroup]]: 2.3.5.7

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Badness: 0.022325

=== 13-limit ===

Subgroup: 2.3.5.7.11.13

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== Porky ==

Porky can be described as 7d & 22, suggesting a less sharp perfect fifth. 7\51 is a good generator.

[[Subgroup]]: 2.3.5.7

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== Coendou ==

Coendou can be described as 7 & 29, suggesting an even less sharp or near-just perfect fifth. 9\65 is a good generator.

[[Subgroup]]: 2.3.5.7

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== Hystrix ==

Hystrix provides a less complex avenue to the 7-limit. Unfortunately in temperaments as in life you get what you pay for, and hystrix, for which a generator of 2\15 or 9\68 can be used, is a temperament for the adventurous souls who have probably already tried [[15edo]]. They can try the even sharper fifth of hystrix in [[68edo]] and see how that suits.

Hystrix provides a less complex avenue to the 7-limit, with the generator taking on the role of approximating 8/7. Unfortunately in temperaments as in life you get what you pay for, and hystrix, for which a generator of 2\15 or 9\68 can be used, is a temperament for the adventurous souls who have probably already tried [[15edo]]. They can try the even sharper fifth of hystrix in [[68edo]] and see how that suits.

[[Subgroup]]: 2.3.5.7

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== Oxygen ==

Oxygen is perhaps not meant to be used as a serious temperament of harmony. Its comma basis suggests potential utility to construct [[Fokker block]]s.

[[Subgroup]]: 2.3.5.7

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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 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.
+Notice 250/243 = ([[55/54]])([[100/99]]), the temperament thus extends naturally to the 2.3.5.11 [[subgroup]], sometimes known as ''porkypine''.
 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
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 * [[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, known as ''porkypine''.
 Temperaments discussed elsewhere include [[Dicot family #Jamesbond|jamesbond]].
@@ Line 209: / Line 209: @@
 == Opossum ==
+Opossum can be described as 7d & 8d. Tempering out [[28/27]], the perfect fifth of three generator steps is conflated with not [[32/21]] as in porcupine but [[14/9]]. Three such fifths or nine generator steps octave reduced give a flat 7/4. 2\15 is a good generator.
 [[Subgroup]]: 2.3.5.7
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 Badness: 0.022325
-=== 13-limit  ===
+=== 13-limit ===
 Subgroup: 2.3.5.7.11.13
@@ Line 259: / Line 261: @@
 == Porky ==
+Porky can be described as 7d & 22, suggesting a less sharp perfect fifth. 7\51 is a good generator.
 [[Subgroup]]: 2.3.5.7
@@ Line 308: / Line 312: @@
 == Coendou ==
+Coendou can be described as 7 & 29, suggesting an even less sharp or near-just perfect fifth. 9\65 is a good generator.
 [[Subgroup]]: 2.3.5.7
@@ Line 361: / Line 367: @@
 == Hystrix ==
-Hystrix provides a less complex avenue to the 7-limit. Unfortunately in temperaments as in life you get what you pay for, and hystrix, for which a generator of 2\15 or 9\68 can be used, is a temperament for the adventurous souls who have probably already tried [[15edo]]. They can try the even sharper fifth of hystrix in [[68edo]] and see how that suits.
+Hystrix provides a less complex avenue to the 7-limit, with the generator taking on the role of approximating 8/7. Unfortunately in temperaments as in life you get what you pay for, and hystrix, for which a generator of 2\15 or 9\68 can be used, is a temperament for the adventurous souls who have probably already tried [[15edo]]. They can try the even sharper fifth of hystrix in [[68edo]] and see how that suits.
 [[Subgroup]]: 2.3.5.7
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 == Oxygen ==
+Oxygen is perhaps not meant to be used as a serious temperament of harmony. Its comma basis suggests potential utility to construct [[Fokker block]]s.
 [[Subgroup]]: 2.3.5.7