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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 17: Line 17:


[[Tuning ranges]]:  
[[Tuning ranges]]:  
* [[diamond monotone]] range: [150.000, 171.429] (1\8 to 1\7)
* [[Diamond monotone]] range: [150.000, 171.429] (1\8 to 1\7)
* [[diamond tradeoff]] range: [157.821, 166.015]
* [[Diamond tradeoff]] range: [157.821, 166.015]
* diamond monotone and tradeoff range: [157.821, 166.015]
* Diamond monotone and tradeoff: [157.821, 166.015]


{{Val list|legend=1| 7, 15, 22, 95c, 117bc, 139bc, 161bc, 183bc }}
{{Val list|legend=1| 7, 15, 22, 95c, 117bc, 139bc, 161bc, 183bc }}


[[Badness]]: 0.0308
[[Badness]]: 0.030778


=== 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 }}


Porcupine uses six of its minor tone generator steps to get to [[7/4]]. For this to work you need a small minor tone such as [[22edo]] provides, and once again 3\22 is a good tuning choice, though we might pick in preference 8\59, 11\81, or 19\140 for our generator.
Porcupine uses six of its minor tone generator steps to get to [[7/4]]. For this to work you need a small minor tone such as [[22edo|22EDO]] provides, and once again 3\22 is a good tuning choice, though we might pick in preference 8\59, 11\81, or 19\140 for our generator.


Subgroup: 2.3.5.7
Subgroup: 2.3.5.7
Line 51: Line 51:


[[Tuning ranges]]:  
[[Tuning ranges]]:  
* [[diamond monotone]] range: [160.000, 163.636] (2\15 to 3\22)
* [[Diamond monotone]] range: [160.000, 163.636] (2\15 to 3\22)
* [[diamond tradeoff]] range: [157.821, 166.015]
* [[Diamond tradeoff]] range: [157.821, 166.015]
* diamond monotone and tradeoff range: [160.000, 163.636]
* Diamond monotone and tradeoff: [160.000, 163.636]


{{Val list|legend=1| 7, 15, 22, 59, 81bd, 140bbd }}
{{Val list|legend=1| 7, 15, 22, 59, 81bd, 140bbd }}


[[Badness]]: 0.0411
[[Badness]]: 0.041057


=== 11-limit ===
=== 11-limit ===
Subgroup: 2.3.5.7.11
Subgroup: 2.3.5.7.11


Line 72: Line 72:


Tuning ranges:  
Tuning ranges:  
* [[diamond monotone]] range: [160.000, 163.636] (2\15 to 3\22)
* [[Diamond monotone]] range: [160.000, 163.636] (2\15 to 3\22)
* [[diamond tradeoff]] range: [150.637, 182.404]
* [[Diamond tradeoff]] range: [150.637, 182.404]
* diamond monotone and tradeoff range: [160.000, 163.636]
* Diamond monotone and tradeoff: [160.000, 163.636]


Vals: {{val list| 7, 15, 22, 37, 59 }}
Vals: {{val list| 7, 15, 22, 37, 59 }}


Badness: 0.0217
Badness: 0.021562


==== 13-limit ====
==== 13-limit ====
Subgroup: 2.3.5.7.11.13
Subgroup: 2.3.5.7.11.13


Line 93: Line 93:


Tuning ranges:  
Tuning ranges:  
* [[diamond monotone]] range: [160.000, 163.636] (15 to 22f)
* [[Diamond monotone]] range: [160.000, 163.636] (2\15 to 3\22)
* [[diamond tradeoff]] range: [138.573, 182.404]
* [[Diamond tradeoff]] range: [138.573, 182.404]
* diamond monotone and tradeoff range: [160.000, 163.636]
* Diamond monotone and tradeoff: [160.000, 163.636]


Vals: {{val list| 7, 15, 22f, 37f }}
Vals: {{val list| 7, 15, 22f, 37f }}


Badness: 0.0213
Badness: 0.021276


==== Porcupinefish ====
==== Porcupinefish ====
{{see also| The Biosphere }}
{{see also| The Biosphere }}


Line 116: Line 116:


Tuning ranges:  
Tuning ranges:  
* [[diamond monotone]] range: [160.000, 162.162] (15 to 37)
* [[Diamond monotone]] range: [160.000, 162.162] (2\15 to 5\37)
* [[diamond tradeoff]] range: [150.637, 182.404]
* [[Diamond tradeoff]] range: [150.637, 182.404]
* diamond monotone and tradeoff range: [160.000, 162.162]
* Diamond monotone and tradeoff: [160.000, 162.162]


Vals: {{val list| 15, 22, 37, 59, 96b }}
Vals: {{val list| 15, 22, 37, 59, 96b }}


Badness: 0.0253
Badness: 0.025314


==== Pourcup ====
==== Pourcup ====
Subgroup: 2.3.5.7.11.13
Subgroup: 2.3.5.7.11.13


Line 138: Line 138:
Vals: {{val list| 15f, 22f, 37 }}
Vals: {{val list| 15f, 22f, 37 }}


Badness: 0.0351
Badness: 0.035130


==== Porkpie ====
==== Porkpie ====
Subgroup: 2.3.5.7.11.13
Subgroup: 2.3.5.7.11.13


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Vals: {{val list| 7, 15f, 22 }}
Vals: {{val list| 7, 15f, 22 }}


Badness: 0.0260
Badness: 0.026043


== 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|15EDO]]. They can try the even sharper fifth of hystrix in [[68edo|68EDO]] and see how that suits.


Subgroup: 2.3.5.7
Subgroup: 2.3.5.7
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{{Val list|legend=1| 7, 8d, 15d }}
{{Val list|legend=1| 7, 8d, 15d }}


[[Badness]]: 0.0449
[[Badness]]: 0.044944


=== 11-limit ===
=== 11-limit ===
Subgroup: 2.3.5.7.11
Subgroup: 2.3.5.7.11


Line 187: Line 187:
Vals: {{val list| 7, 8d, 15d }}
Vals: {{val list| 7, 8d, 15d }}


Badness: 0.0268
Badness: 0.026790


== Porky ==
== Porky ==
Subgroup: 2.3.5.7
Subgroup: 2.3.5.7


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{{Val list|legend=1| 7d, 15d, 22, 29, 51, 73c }}
{{Val list|legend=1| 7d, 15d, 22, 29, 51, 73c }}


[[Badness]]: 0.0544
[[Badness]]: 0.054389


=== 11-limit ===
=== 11-limit ===
Subgroup: 2.3.5.7.11
Subgroup: 2.3.5.7.11


Line 221: Line 221:
Vals: {{val list| 7d, 15d, 22, 29, 51, 73ce }}
Vals: {{val list| 7d, 15d, 22, 29, 51, 73ce }}


Badness: 0.0273
Badness: 0.027268


=== 13-limit ===
=== 13-limit ===
Subgroup: 2.3.5.7.11.13
Subgroup: 2.3.5.7.11.13


Line 234: Line 234:
Vals: {{val list| 7d, 22, 29, 51f, 80cdeff }}
Vals: {{val list| 7d, 22, 29, 51f, 80cdeff }}


Badness: 0.0265
Badness: 0.026543


== Coendou ==
== Coendou ==
Subgroup: 2.3.5.7
Subgroup: 2.3.5.7


Line 252: Line 252:
{{Val list|legend=1| 7, 29, 65c, 94cd }}
{{Val list|legend=1| 7, 29, 65c, 94cd }}


[[Badness]]: 0.1183
[[Badness]]: 0.118344


=== 11-limit ===
=== 11-limit ===
Subgroup: 2.3.5.7.11
Subgroup: 2.3.5.7.11


Line 268: Line 268:
Vals: {{val list| 7, 29, 65ce, 94cde }}
Vals: {{val list| 7, 29, 65ce, 94cde }}


Badness: 0.0497
Badness: 0.049669


=== 13-limit ===
=== 13-limit ===
Subgroup: 2.3.5.7.11.13
Subgroup: 2.3.5.7.11.13


Line 284: Line 284:
Vals: {{val list| 7, 29, 65cef, 94cdef }}
Vals: {{val list| 7, 29, 65cef, 94cdef }}


Badness: 0.0302
Badness: 0.030233


== 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.


Subgroup: 2.3.5.7
Subgroup: 2.3.5.7
Line 301: Line 301:
{{Val list|legend=1| 8d, 14c, 22, 146bccdd }}
{{Val list|legend=1| 8d, 14c, 22, 146bccdd }}


[[Badness]]: 0.0440
[[Badness]]: 0.043983


=== 11-limit ===
=== 11-limit ===
Subgroup: 2.3.5.7.11
Subgroup: 2.3.5.7.11


Line 312: Line 312:
POTE generator: ~9/7 = 435.386
POTE generator: ~9/7 = 435.386


Vals: {{val list| 14c, 22, 58ce, 80ce, 102cde }}
Vals: {{val list| 8d, 14c, 22, 58ce, 80ce, 102cde }}


Badness: 0.0231
Badness: 0.023095


==== 13-limit ====
==== 13-limit ====
Subgroup: 2.3.5.7.11.13
Subgroup: 2.3.5.7.11.13


Line 325: Line 325:
POTE generator: ~9/7 = 435.861
POTE generator: ~9/7 = 435.861


Vals: {{val list| 14cf, 22 }}
Vals: {{val list| 8d, 14cf, 22 }}


Badness: 0.0215
Badness: 0.021516


==== Urchin ====
==== Urchin ====
Subgroup: 2.3.5.7.11.13
Subgroup: 2.3.5.7.11.13


Line 340: Line 340:
Vals: {{val list| 14c, 22f }}
Vals: {{val list| 14c, 22f }}


Badness: 0.0252
Badness: 0.025233


=== Hedgepig ===
=== Hedgepig ===
Subgroup: 2.3.5.7.11
Subgroup: 2.3.5.7.11


Line 353: Line 353:
Vals: {{val list| 22, 80c, 102cd, 124cd }}
Vals: {{val list| 22, 80c, 102cd, 124cd }}


Badness: 0.0684
Badness: 0.068406


; Music
; Music
[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 369: Line 369:
[[POTE generator]]: ~21/20 = 82.505
[[POTE generator]]: ~21/20 = 82.505


{{Val list|legend=1| 15, 29, 43cd, 44d, 59d, 73cd, 102cd }}
{{Val list|legend=1| 15, 29, 44d, 59d, 73cd, 102cd }}


=== 11-limit ===
[[Badness]]: 0.057420
 
=== 11-limit ===
Subgroup: 2.3.5.7.11
Subgroup: 2.3.5.7.11


Line 380: Line 382:
POTE generator: ~21/20 = 82.504
POTE generator: ~21/20 = 82.504


Vals: {{val list| 14c, 15, 29, 43cde, 44d, 59d, 73cde, 102cde }}
Vals: {{val list| 14c, 15, 29, 44d, 59d, 73cde, 102cde }}
 
Badness: 0.026023


==== 13-limit ====
==== 13-limit ====
Subgroup: 2.3.5.7.11.13
Subgroup: 2.3.5.7.11.13


Line 389: Line 393:
Mapping: [{{val| 1 2 3 3 4 5 }}, {{val| 0 -6 -10 -3 -8 -19 }}]
Mapping: [{{val| 1 2 3 3 4 5 }}, {{val| 0 -6 -10 -3 -8 -19 }}]


POTE generator: ~21/20 = 62.530
POTE generator: ~21/20 = 82.530


Vals: {{val list| 15f, 29, 43cde, 44d, 59df, 73cde, 102cde }}
Vals: {{val list| 15, 29, 44d, 59df, 73cde, 102cde }}


Badness: 0.0223
Badness: 0.022285


==== Belauensis ====
==== Belauensis ====
Subgroup: 2.3.5.7.11.13
Subgroup: 2.3.5.7.11.13


Line 406: Line 410:
Vals: {{val list| 14c, 15, 29f, 44df }}
Vals: {{val list| 14c, 15, 29f, 44df }}


Badness: 0.0298
Badness: 0.029816


; Music
; Music
[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 424: Line 428:
{{Val list|legend=1| 29, 37, 66 }}
{{Val list|legend=1| 29, 37, 66 }}


[[Badness]]: 0.1077
[[Badness]]: 0.107686


=== 11-limit ===
=== 11-limit ===
Subgroup: 2.3.5.7.11
Subgroup: 2.3.5.7.11


Line 437: Line 441:
Vals: {{val list| 29, 37, 66 }}
Vals: {{val list| 29, 37, 66 }}


Badness: 0.0457
Badness: 0.045694


=== 13-limit ===
=== 13-limit ===
Subgroup: 2.3.5.7.11.13
Subgroup: 2.3.5.7.11.13


Line 446: Line 450:
Mapping: [{{val| 1 5 8 10 8 9 }}, {{val| 0 -9 -15 -19 -12 -14 }}]
Mapping: [{{val| 1 5 8 10 8 9 }}, {{val| 0 -9 -15 -19 -12 -14 }}]


POTE generator: ~13/10 = 454.429
POTE generator: ~13/10 = 454.529


Vals: {{val list| 29, 37, 66 }}
Vals: {{val list| 29, 37, 66 }}


Badness: 0.0272
Badness: 0.027168


== Ceratitid ==
== Ceratitid ==
Subgroup: 2.3.5.7
Subgroup: 2.3.5.7


Line 465: Line 469:
{{Val list|legend=1| 22 }}
{{Val list|legend=1| 22 }}


[[Badness]]: 0.115
[[Badness]]: 0.115304


=== 11-limit ===
=== 11-limit ===
Subgroup: 2.3.5.7.11
Subgroup: 2.3.5.7.11


Line 478: Line 482:
Vals: {{val list| 22 }}
Vals: {{val list| 22 }}


Badness: 0.0513
Badness: 0.051319


=== 13-limit ===
=== 13-limit ===
Subgroup: 2.3.5.7.11.13
Subgroup: 2.3.5.7.11.13


Line 491: Line 495:
Vals: {{val list| 22 }}
Vals: {{val list| 22 }}


Badness: 0.0447
Badness: 0.044739


[[Category:Regular temperament theory]]
[[Category:Regular temperament theory]]
Retrieved from "https://en.xen.wiki/w/Porcupine_family"