Porcupine family: Difference between revisions

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The '''porcupine family''' ~~is the~~ [[~~rank]]-2 [[Temperament families and clans~~|~~family of~~ temperaments]] ~~whose~~ [[~~5-limit~~]] ~~parent~~ [[comma]] is [[250/243]], also called the maximal diesis ~~or porcupine comma.~~

The '''porcupine family''' of [[regular temperament|temperaments]] [[tempering out|tempers out]] the [[porcupine comma]], [[250/243]], also called the maximal diesis.

The [[generator]] 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)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~~

* [[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]].

~~Temperaments discussed elsewhere include [[7th-octave temperaments #Jamesbond|jamesbond]]~~.

== 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)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.

[[Subgroup]]: 2.3.5

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[[Badness]]: 0.030778

=== Overview to extensions ===

==== 7-limit extensions ====

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]].

Temperaments discussed elsewhere include [[7th-octave temperaments #Jamesbond|jamesbond]].

==== Subgroup extensions ====

Notice {{nowrap| 250/243 {{=}} ([[55/54]])⋅([[100/99]]) }}, the temperament thus extends naturally to the 2.3.5.11 [[subgroup]], sometimes known as ''porkypine'', given right below.

=== 2.3.5.11 subgroup (porkypine) ===

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-The '''porcupine family''' is the [[rank]]-2 [[Temperament families and clans|family of temperaments]] whose [[5-limit]] parent [[comma]] is [[250/243]], also called the maximal diesis or porcupine comma.
+The '''porcupine family''' of [[regular temperament|temperaments]] [[tempering out|tempers out]] the [[porcupine comma]], [[250/243]], also called the maximal diesis.
-The [[generator]] 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.
-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
-* [[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]].
-Temperaments discussed elsewhere include [[7th-octave temperaments #Jamesbond|jamesbond]].
 == 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.
 [[Subgroup]]: 2.3.5
@@ Line 41: / Line 31: @@
 [[Badness]]: 0.030778
+=== Overview to extensions ===
+==== 7-limit extensions ====
+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]].
+Temperaments discussed elsewhere include [[7th-octave temperaments #Jamesbond|jamesbond]].
+==== Subgroup extensions ====
+Notice {{nowrap| 250/243 {{=}} ([[55/54]])⋅([[100/99]]) }}, the temperament thus extends naturally to the 2.3.5.11 [[subgroup]], sometimes known as ''porkypine'', given right below.
 === 2.3.5.11 subgroup (porkypine) ===