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 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


Line 154: Line 154:
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
Line 174: Line 174:
{{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]]

Revision as of 04:00, 4 June 2021

The 5-limit parent comma for the porcupine family is 250/243, the maximal diesis or porcupine comma. Its monzo is [1 -5 3⟩, and flipping that yields ⟨⟨ 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. 3\22 is a very recommendable generator, and MOS of 7, 8 and 15 notes make for some nice scale possibilities.

Porcupine

Subgroup: 2.3.5

Comma list: 250/243

Mapping: [⟨1 2 3], ⟨0 -3 -5]]

POTE generator: ~27/25 = 163.950

Tuning ranges:

Template:Val list

Badness: 0.030778

Extensions

The second comma of the normal comma list defines which 7-limit family member we are looking at. That means

Septimal porcupine

Main article: 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.

Subgroup: 2.3.5.7

Comma list: 64/63, 250/243

Mapping: [⟨1 2 3 2], ⟨0 -3 -5 6]]

Wedgie: ⟨⟨ 3 5 -6 1 -18 -28 ]]

POTE generator: ~10/9 = 162.880

Minimax tuning:

Tuning ranges:

Template:Val list

Badness: 0.041057

11-limit

Subgroup: 2.3.5.7.11

Comma list: 55/54, 64/63, 100/99

Mapping: [⟨1 2 3 2 4], ⟨0 -3 -5 6 -4]]

POTE generator: ~11/10 = 162.747

Minimax tuning:

  • 11-odd-limit eigenmonzo: 9/7

Tuning ranges:

Vals: Template:Val list

Badness: 0.021562

13-limit

Subgroup: 2.3.5.7.11.13

Comma list: 40/39, 55/54, 64/63, 66/65

Mapping: [⟨1 2 3 2 4 4], ⟨0 -3 -5 6 -4 -2]]

POTE generator: ~11/10 = 162.708

Minimax tuning:

  • 13- and 15-odd-limit eigenmonzo: 11/8

Tuning ranges:

Vals: Template:Val list

Badness: 0.021276

Porcupinefish

See also: The Biosphere

Subgroup: 2.3.5.7.11.13

Comma list: 55/54, 64/63, 91/90, 100/99

Mapping: [⟨1 2 3 2 4 6], ⟨0 -3 -5 6 -4 -17]]

POTE generator: ~11/10 = 162.277

Minimax tuning:

  • 13- and 15-odd-limit eigenmonzo: 13/11

Tuning ranges:

Vals: Template:Val list

Badness: 0.025314

Pourcup

Subgroup: 2.3.5.7.11.13

Comma list: 55/54, 64/63, 100/99, 196/195

Mapping: [⟨1 2 3 2 4 1], ⟨0 -3 -5 6 -4 20]]

POTE generator: ~11/10 = 162.482

Minimax tuning:

  • 13- and 15-odd-limit eigenmonzo: 13/7

Vals: Template:Val list

Badness: 0.035130

Porkpie

Subgroup: 2.3.5.7.11.13

Comma list: 55/54, 64/63, 65/63, 100/99

Mapping: [⟨1 2 3 2 4 3], ⟨0 -3 -5 6 -4 5]]

POTE generator: ~11/10 = 163.688

Minimax tuning:

  • 13- and 15-odd-limit eigenmonzo: 9/7

Vals: Template:Val list

Badness: 0.026043

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.

Subgroup: 2.3.5.7

Comma list: 36/35, 160/147

Mapping: [⟨1 2 3 3], ⟨0 -3 -5 -1]]

Wedgie: ⟨⟨ 3 5 1 1 -7 -12 ]]

POTE generator: ~10/9 = 158.868

Minimax tuning:

Template:Val list

Badness: 0.044944

11-limit

Subgroup: 2.3.5.7.11

Comma list: 22/21, 36/35, 80/77

Mapping: [⟨1 2 3 3 4], ⟨0 -3 -5 -1 -4]]

POTE generator: ~11/10 = 158.750

Vals: Template:Val list

Badness: 0.026790

Porky

Subgroup: 2.3.5.7

Comma list: 225/224, 250/243

Mapping: [⟨1 2 3 5], ⟨0 -3 -5 -16]]

Wedgie: ⟨⟨ 3 5 16 1 17 23 ]]

POTE generator: ~10/9 = 164.412

Minimax tuning:

Template:Val list

Badness: 0.054389

11-limit

Subgroup: 2.3.5.7.11

Comma list: 55/54, 100/99, 225/224

Mapping: [⟨1 2 3 5 4], ⟨0 -3 -5 -16 -4]]

POTE generator: ~11/10 = 164.552

Minimax tuning:

  • 11-odd-limit eigenmonzo: 7/5

Vals: Template:Val list

Badness: 0.027268

13-limit

Subgroup: 2.3.5.7.11.13

Comma list: 55/54, 65/64, 91/90, 100/99

Mapping: [⟨1 2 3 5 4 3], ⟨0 -3 -5 -16 -4 5]]

POTE generator: ~11/10 = 164.953

Vals: Template:Val list

Badness: 0.026543

Coendou

Subgroup: 2.3.5.7

Comma list: 250/243, 525/512

Mapping: [⟨1 2 3 1], ⟨0 -3 -5 13]]

Wedgie: ⟨⟨ 3 5 -13 1 -29 -44 ]]

POTE generator: ~10/9 = 166.041

Minimax tuning:

Template:Val list

Badness: 0.118344

11-limit

Subgroup: 2.3.5.7.11

Comma list: 55/54, 100/99, 525/512

Mapping: [⟨1 2 3 1 4], ⟨0 -3 -5 13 -4]]

POTE generator: ~11/10 = 165.981

Minimax tuning:

  • 11-odd-limit eigenmonzo: 3/2

Vals: Template:Val list

Badness: 0.049669

13-limit

Subgroup: 2.3.5.7.11.13

Comma list: 55/54, 65/64, 100/99, 105/104

Mapping: [⟨1 2 3 1 4 3], ⟨0 -3 -5 13 -4 5]]

POTE generator: ~11/10 = 165.974

Minimax tuning:

  • 13- and 15-odd-limit eigenmonzo: 3/2

Vals: Template:Val list

Badness: 0.030233

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 ⟨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

Comma list: 50/49, 245/243

Mapping: [⟨2 1 1 2], ⟨0 3 5 5]]

Wedgie: ⟨⟨ 6 10 10 2 -1 -5 ]]

POTE generator: ~9/7 = 435.648

Template:Val list

Badness: 0.043983

11-limit

Subgroup: 2.3.5.7.11

Comma list: 50/49, 55/54, 99/98

Mapping: [⟨2 1 1 2 4], ⟨0 3 5 5 4]]

POTE generator: ~9/7 = 435.386

Vals: Template:Val list

Badness: 0.023095

13-limit

Subgroup: 2.3.5.7.11.13

Comma list: 50/49, 55/54, 65/63, 99/98

Mapping: [⟨2 1 1 2 4 3], ⟨0 3 5 5 4 6]]

POTE generator: ~9/7 = 435.861

Vals: Template:Val list

Badness: 0.021516

Urchin

Subgroup: 2.3.5.7.11.13

Comma list: 40/39, 50/49, 55/54, 66/65

Mapping: [⟨2 1 1 2 4 6], ⟨0 3 5 5 4 2]]

POTE generator: ~9/7 = 437.078

Vals: Template:Val list

Badness: 0.025233

Hedgepig

Subgroup: 2.3.5.7.11

Comma list: 50/49, 245/243, 385/384

Mapping: [⟨2 1 1 2 12], ⟨0 3 5 5 -7]]

POTE generator: ~9/7 = 435.425

Vals: Template:Val list

Badness: 0.068406

Music

Phobos Light by Chris Vaisvil in Hedgehog[14] tuned to 22edo.

Nautilus

Subgroup: 2.3.5.7

Comma list: 49/48, 250/243

Mapping: [⟨1 2 3 3], ⟨0 -6 -10 -3]]

Wedgie: ⟨⟨ 6 10 3 2 -12 -21 ]]

POTE generator: ~21/20 = 82.505

Template:Val list

Badness: 0.057420

11-limit

Subgroup: 2.3.5.7.11

Comma list: 49/48, 55/54, 245/242

Mapping: [⟨1 2 3 3 4], ⟨0 -6 -10 -3 -8]]

POTE generator: ~21/20 = 82.504

Vals: Template:Val list

Badness: 0.026023

13-limit

Subgroup: 2.3.5.7.11.13

Comma list: 49/48, 55/54, 91/90, 100/99

Mapping: [⟨1 2 3 3 4 5], ⟨0 -6 -10 -3 -8 -19]]

POTE generator: ~21/20 = 82.530

Vals: Template:Val list

Badness: 0.022285

Belauensis

Subgroup: 2.3.5.7.11.13

Comma list: 40/39, 49/48, 55/54, 66/65

Mapping: [⟨1 2 3 3 4 4], ⟨0 -6 -10 -3 -8 -4]]

POTE generator: ~21/20 = 81.759

Vals: Template:Val list

Badness: 0.029816

Music

Nautilus Reverie by Igliashon Calvin Jones-Coolidge

Ammonite

Subgroup: 2.3.5.7

Comma list: 250/243, 686/675

Mapping: [⟨1 5 8 10], ⟨0 -9 -15 -19]]

Wedgie: ⟨⟨ 9 15 19 3 5 2 ]]

POTE generator: ~9/7 = 454.448

Template:Val list

Badness: 0.107686

11-limit

Subgroup: 2.3.5.7.11

Comma list: 55/54, 100/99, 686/675

Mapping: [⟨1 5 8 10 8], ⟨0 -9 -15 -19 -12]]

POTE generator: ~9/7 = 454.512

Vals: Template:Val list

Badness: 0.045694

13-limit

Subgroup: 2.3.5.7.11.13

Comma list: 55/54, 91/90, 100/99, 169/168

Mapping: [⟨1 5 8 10 8 9], ⟨0 -9 -15 -19 -12 -14]]

POTE generator: ~13/10 = 454.529

Vals: Template:Val list

Badness: 0.027168

Ceratitid

Subgroup: 2.3.5.7

Comma list: 250/243, 1728/1715

Mapping: [⟨1 2 3 3], ⟨0 -9 -15 -4]]

Wedgie: ⟨⟨ 9 15 4 3 -19 -33 ]]

POTE generator: ~36/35 = 54.384

Template:Val list

Badness: 0.115304

11-limit

Subgroup: 2.3.5.7.11

Comma list: 55/54, 100/99, 5324/5145

Mapping: [⟨1 2 3 3 4], ⟨0 -9 -15 -4 -12]]

POTE generator: ~36/35 = 54.376

Vals: Template:Val list

Badness: 0.051319

13-limit

Subgroup: 2.3.5.7.11.13

Comma list: 55/54, 65/63, 100/99, 352/343

Mapping: [⟨1 2 3 3 4 4], ⟨0 -9 -15 -4 -12 -7]]

POTE generator: ~36/35 = 54.665

Vals: Template:Val list

Badness: 0.044739

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