Porcupine family: Difference between revisions

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=== Overview to extensions ===

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

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.

* ~~[[64/63]], the archytas comma, for~~ [[#~~Septimal porcupine~~|~~septimal porcupine~~]],

* [[#Hystrix|Hystrix]] adds [[36/35]], the mint comma, for a tuning sharp of 8d-edo;

* [[~~225~~/~~224~~]], the ~~marvel~~ comma, for [[#~~Porky~~|~~porky~~]],

* [[#Opossum|Opossum]] adds [[28/27]], the trienstonic comma, for a tuning between 8d-edo and 15edo;

* [[~~525~~/~~512~~]], the ~~avicennma~~, for [[#~~Coendou~~|~~coendou~~]],

* [[#Septimal porcupine|Septimal porcupine]] adds [[64/63]], the archytas comma, for a tuning between 15edo and 22edo;

* [[36/35]], the ~~mint~~ comma, for [[#~~Hystrix~~|~~hystrix~~]],

* [[#Porky|Porky]] adds [[225/224]], the marvel comma, for a tuning between 22edo and 29edo;

* [[28/27]], the ~~trienstonic~~ comma, for [[#~~Opossum~~|~~opossum~~]]~~, and~~

* [[#Coendou|Coendou]] adds [[525/512]], the avicennma, for a tuning flat of 29edo.

* [[21/20]], the ~~septisemi comma~~, for ~~[[#Oxygen|oxygen]]~~.

Those all share the same generator with porcupine~~. Alternatively you could choose~~

Those all share the same generator with porcupine.

* [[49/48]], the semaphoresma, for [[#Nautilus|nautilus]],

* [[50/49]], the jubilisma, for [[#Hedgehog|hedgehog]],

* [[686/675]], the senga, for [[#Ammonite|ammonite]], and

* [[1728/1715]], the orwellisma, for [[#Ceratitid|ceratitid]].

Those split the ~~generators and/or periods~~ in ~~various ways~~.

[[#Nautilus|nautilus]] tempers out [[49/48]] and splits the generator in two. [[#Hedgehog|hedgehog]] tempers out [[50/49]] with a semi-octave period. Finally, [[#Ammonite|ammonite]] tempers out [[686/675]] and [[#Ceratitid|ceratitid]] tempers out [[1728/1715]]. Those split the generator in three.

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

Temperaments discussed elsewhere include:

* [[Oxygen]] → [[Very low accuracy temperaments #Oxygen|Very low accuracy temperaments]].

* [[Jamesbond]] → [[7th-octave temperaments #Jamesbond|7th-octave temperaments]].

==== Subgroup extensions ====

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Badness (Smith): 0.026790

~~== 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~~

~~[[Comma list]]: 21/20, 175/162~~

~~{{Mapping|legend=1| 1 2 3 3 | 0 -3 -5 -2 }}~~

~~{{Multival|legend=1| 3 5 2 1 -5 -9 }}~~

~~[[Optimal tuning]]s:~~

* [[CTE]]: ~2 = 1200.000, ~10/9 = 161.341

~~: [[error map]]: {{val| 0.000 +14.023 +6.982 -91.507 }}~~

* [[POTE]]: ~2 = 1200.000, ~10/9 = 169.112

~~: error map: {{val| 0.000 -9.291 -31.873 -107.050 }}~~

~~{{Optimal ET sequence|legend=1| 1c, …, 6bcd, 7d }}~~

~~[[Badness]] (Smith): 0.059866~~

== Hedgehog ==

@@ Line 37: / Line 37: @@
 === Overview to extensions ===
 ==== 7-limit extensions ====
-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.
-* [[64/63]], the archytas comma, for [[#Septimal porcupine|septimal porcupine]],
+* [[#Hystrix|Hystrix]] adds [[36/35]], the mint comma, for a tuning sharp of 8d-edo;
-* [[225/224]], the marvel comma, for [[#Porky|porky]],
+* [[#Opossum|Opossum]] adds [[28/27]], the trienstonic comma, for a tuning between 8d-edo and 15edo;
-* [[525/512]], the avicennma, for [[#Coendou|coendou]],
+* [[#Septimal porcupine|Septimal porcupine]] adds [[64/63]], the archytas comma, for a tuning between 15edo and 22edo;
-* [[36/35]], the mint comma, for [[#Hystrix|hystrix]],
+* [[#Porky|Porky]] adds [[225/224]], the marvel comma, for a tuning between 22edo and 29edo;
-* [[28/27]], the trienstonic comma, for [[#Opossum|opossum]], and
+* [[#Coendou|Coendou]] adds [[525/512]], the avicennma, for a tuning flat of 29edo.
-* [[21/20]], the septisemi comma, for [[#Oxygen|oxygen]].
-Those all share the same generator with porcupine. Alternatively you could choose
+Those all share the same generator with porcupine.
-* [[49/48]], the semaphoresma, for [[#Nautilus|nautilus]],
-* [[50/49]], the jubilisma, for [[#Hedgehog|hedgehog]],
-* [[686/675]], the senga, for [[#Ammonite|ammonite]], and
-* [[1728/1715]], the orwellisma, for [[#Ceratitid|ceratitid]].
-Those split the generators and/or periods in various ways.
+[[#Nautilus|nautilus]] tempers out [[49/48]] and splits the generator in two. [[#Hedgehog|hedgehog]] tempers out [[50/49]] with a semi-octave period. Finally, [[#Ammonite|ammonite]] tempers out [[686/675]] and [[#Ceratitid|ceratitid]] tempers out [[1728/1715]]. Those split the generator in three.
-Temperaments discussed elsewhere include [[7th-octave temperaments #Jamesbond|jamesbond]].
+Temperaments discussed elsewhere include:
+* [[Oxygen]] → [[Very low accuracy temperaments #Oxygen|Very low accuracy temperaments]].
+* [[Jamesbond]] → [[7th-octave temperaments #Jamesbond|7th-octave temperaments]].
 ==== Subgroup extensions ====
@@ Line 469: / Line 466: @@
 Badness (Smith): 0.026790
-== 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
-[[Comma list]]: 21/20, 175/162
-{{Mapping|legend=1| 1 2 3 3 | 0 -3 -5 -2 }}
-{{Multival|legend=1| 3 5 2 1 -5 -9 }}
-[[Optimal tuning]]s:
-* [[CTE]]: ~2 = 1200.000, ~10/9 = 161.341
-: [[error map]]: {{val| 0.000 +14.023 +6.982 -91.507 }}
-* [[POTE]]: ~2 = 1200.000, ~10/9 = 169.112
-: error map: {{val| 0.000 -9.291 -31.873 -107.050 }}
-{{Optimal ET sequence|legend=1| 1c, …, 6bcd, 7d }}
-[[Badness]] (Smith): 0.059866
 == Hedgehog ==