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. | ||
= Porcupine = | == Porcupine == | ||
Subgroup: 2.3.5 | Subgroup: 2.3.5 | ||
| Line 25: | Line 25: | ||
[[Badness]]: 0.0308 | [[Badness]]: 0.0308 | ||
== Extensions == | === 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 | 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]], | * [[64/63]], the archytas comma, for [[#Septimal porcupine|septimal porcupine]], | ||
| Line 32: | Line 32: | ||
* [[49/48]], the slendro diesis, for [[#Nautilus|nautilus]]. | * [[49/48]], the slendro diesis, for [[#Nautilus|nautilus]]. | ||
= Septimal porcupine = | == Septimal porcupine == | ||
{{main| Porcupine }} | {{main| Porcupine }} | ||
| Line 59: | Line 59: | ||
[[Badness]]: 0.0411 | [[Badness]]: 0.0411 | ||
== 11-limit == | === 11-limit === | ||
Subgroup: 2.3.5.7.11 | Subgroup: 2.3.5.7.11 | ||
| Line 80: | Line 80: | ||
Badness: 0.0217 | Badness: 0.0217 | ||
=== 13-limit === | ==== 13-limit ==== | ||
Subgroup: 2.3.5.7.11.13 | Subgroup: 2.3.5.7.11.13 | ||
| Line 101: | Line 101: | ||
Badness: 0.0213 | Badness: 0.0213 | ||
=== Porcupinefish === | ==== Porcupinefish ==== | ||
{{see also| The Biosphere }} | {{see also| The Biosphere }} | ||
| Line 124: | Line 124: | ||
Badness: 0.0253 | Badness: 0.0253 | ||
=== Pourcup === | ==== Pourcup ==== | ||
Subgroup: 2.3.5.7.11.13 | Subgroup: 2.3.5.7.11.13 | ||
| Line 140: | Line 140: | ||
Badness: 0.0351 | Badness: 0.0351 | ||
=== Porkpie === | ==== Porkpie ==== | ||
Subgroup: 2.3.5.7.11.13 | Subgroup: 2.3.5.7.11.13 | ||
| Line 156: | Line 156: | ||
Badness: 0.0260 | Badness: 0.0260 | ||
= Hystrix = | == 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. 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. | ||
| Line 176: | Line 176: | ||
[[Badness]]: 0.0449 | [[Badness]]: 0.0449 | ||
== 11-limit == | === 11-limit === | ||
Subgroup: 2.3.5.7.11 | Subgroup: 2.3.5.7.11 | ||
| Line 189: | Line 189: | ||
Badness: 0.0268 | Badness: 0.0268 | ||
= Porky = | == Porky == | ||
Subgroup: 2.3.5.7 | Subgroup: 2.3.5.7 | ||
| Line 207: | Line 207: | ||
[[Badness]]: 0.0544 | [[Badness]]: 0.0544 | ||
== 11-limit == | === 11-limit === | ||
Subgroup: 2.3.5.7.11 | Subgroup: 2.3.5.7.11 | ||
| Line 223: | Line 223: | ||
Badness: 0.0273 | Badness: 0.0273 | ||
== 13-limit == | === 13-limit === | ||
Subgroup: 2.3.5.7.11.13 | Subgroup: 2.3.5.7.11.13 | ||
| Line 236: | Line 236: | ||
Badness: 0.0265 | Badness: 0.0265 | ||
= Coendou = | == Coendou == | ||
Subgroup: 2.3.5.7 | Subgroup: 2.3.5.7 | ||
| Line 254: | Line 254: | ||
[[Badness]]: 0.1183 | [[Badness]]: 0.1183 | ||
== 11-limit == | === 11-limit === | ||
Subgroup: 2.3.5.7.11 | Subgroup: 2.3.5.7.11 | ||
| Line 270: | Line 270: | ||
Badness: 0.0497 | Badness: 0.0497 | ||
== 13-limit == | === 13-limit === | ||
Subgroup: 2.3.5.7.11.13 | Subgroup: 2.3.5.7.11.13 | ||
| Line 286: | Line 286: | ||
Badness: 0.0302 | Badness: 0.0302 | ||
= Hedgehog = | == Hedgehog == | ||
Hedgehog has a period 1/2 octave and a generator which can be taken to be 9/7 instead of 10/9. It also tempers out [[245/243]], the sensamagic comma. 22edo provides the obvious tuning, but if you are looking for an alternative, you could try the {{val| 146 232 338 411 }} val with generator 10\73, or you could try 164 cents if you are fond of round numbers. The 14 note MOS gives scope for harmony while stopping well short of 22. | Hedgehog has a period 1/2 octave and a generator which can be taken to be 9/7 instead of 10/9. It also tempers out [[245/243]], the sensamagic comma. 22edo provides the obvious tuning, but if you are looking for an alternative, you could try the {{val| 146 232 338 411 }} val with generator 10\73, or you could try 164 cents if you are fond of round numbers. The 14 note MOS gives scope for harmony while stopping well short of 22. | ||
| Line 303: | Line 303: | ||
[[Badness]]: 0.0440 | [[Badness]]: 0.0440 | ||
== 11-limit == | === 11-limit === | ||
Subgroup: 2.3.5.7.11 | Subgroup: 2.3.5.7.11 | ||
| Line 316: | Line 316: | ||
Badness: 0.0231 | Badness: 0.0231 | ||
=== 13-limit === | ==== 13-limit ==== | ||
Subgroup: 2.3.5.7.11.13 | Subgroup: 2.3.5.7.11.13 | ||
| Line 329: | Line 329: | ||
Badness: 0.0215 | Badness: 0.0215 | ||
=== Urchin === | ==== Urchin ==== | ||
Subgroup: 2.3.5.7.11.13 | Subgroup: 2.3.5.7.11.13 | ||
| Line 342: | Line 342: | ||
Badness: 0.0252 | Badness: 0.0252 | ||
== Hedgepig == | === Hedgepig === | ||
Subgroup: 2.3.5.7.11 | Subgroup: 2.3.5.7.11 | ||
| Line 358: | Line 358: | ||
[http://micro.soonlabel.com/22-ET/20120207-phobos-light-hedgehog14.mp3 Phobos Light] by [[Chris Vaisvil]] in Hedgehog[14] [[hedgehog14|tuned]] to 22edo. | [http://micro.soonlabel.com/22-ET/20120207-phobos-light-hedgehog14.mp3 Phobos Light] by [[Chris Vaisvil]] in Hedgehog[14] [[hedgehog14|tuned]] to 22edo. | ||
= Nautilus = | == Nautilus == | ||
Subgroup: 2.3.5.7 | Subgroup: 2.3.5.7 | ||
| Line 371: | Line 371: | ||
{{Val list|legend=1| 15, 29, 43cd, 44d, 59d, 73cd, 102cd }} | {{Val list|legend=1| 15, 29, 43cd, 44d, 59d, 73cd, 102cd }} | ||
== 11-limit == | === 11-limit === | ||
Subgroup: 2.3.5.7.11 | Subgroup: 2.3.5.7.11 | ||
| Line 382: | Line 382: | ||
Vals: {{val list| 14c, 15, 29, 43cde, 44d, 59d, 73cde, 102cde }} | Vals: {{val list| 14c, 15, 29, 43cde, 44d, 59d, 73cde, 102cde }} | ||
=== 13-limit === | ==== 13-limit ==== | ||
Subgroup: 2.3.5.7.11.13 | Subgroup: 2.3.5.7.11.13 | ||
| Line 395: | Line 395: | ||
Badness: 0.0223 | Badness: 0.0223 | ||
=== Belauensis === | ==== Belauensis ==== | ||
Subgroup: 2.3.5.7.11.13 | Subgroup: 2.3.5.7.11.13 | ||
| Line 411: | Line 411: | ||
[http://micro.soonlabel.com/gene_ward_smith/Others/Igs/NautilusReverie.mp3 Nautilus Reverie] by [[Igliashon Jones|Igliashon Calvin Jones-Coolidge]] | [http://micro.soonlabel.com/gene_ward_smith/Others/Igs/NautilusReverie.mp3 Nautilus Reverie] by [[Igliashon Jones|Igliashon Calvin Jones-Coolidge]] | ||
= Ammonite = | == Ammonite == | ||
Subgroup: 2.3.5.7 | Subgroup: 2.3.5.7 | ||
| Line 426: | Line 426: | ||
[[Badness]]: 0.1077 | [[Badness]]: 0.1077 | ||
== 11-limit == | === 11-limit === | ||
Subgroup: 2.3.5.7.11 | Subgroup: 2.3.5.7.11 | ||
| Line 439: | Line 439: | ||
Badness: 0.0457 | Badness: 0.0457 | ||
== 13-limit == | === 13-limit === | ||
Subgroup: 2.3.5.7.11.13 | Subgroup: 2.3.5.7.11.13 | ||
| Line 452: | Line 452: | ||
Badness: 0.0272 | Badness: 0.0272 | ||
= Ceratitid = | == Ceratitid == | ||
Subgroup: 2.3.5.7 | Subgroup: 2.3.5.7 | ||
| Line 467: | Line 467: | ||
[[Badness]]: 0.115 | [[Badness]]: 0.115 | ||
== 11-limit == | === 11-limit === | ||
Subgroup: 2.3.5.7.11 | Subgroup: 2.3.5.7.11 | ||
| Line 480: | Line 480: | ||
Badness: 0.0513 | Badness: 0.0513 | ||
== 13-limit == | === 13-limit === | ||
Subgroup: 2.3.5.7.11.13 | Subgroup: 2.3.5.7.11.13 | ||