Porcupine family: Difference between revisions

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<h2>IMPORTED REVISION FROM WIKISPACES</h2>
<span style="display: block; text-align: right;">[[:de:Porcupine Deutsch]]</span>
This is an imported revision from Wikispaces. The revision metadata is included below for reference:<br>
|  
: This revision was by author [[User:hearneg|hearneg]] and made on <tt>2017-05-27 13:23:04 UTC</tt>.<br>
__FORCETOC__
: The original revision id was <tt>613707509</tt>.<br>
-----
: The revision comment was: <tt></tt><br>
The 5-limit parent comma for the porcupine family is 250/243, the maximal [[diesis|diesis]] or porcupine comma. Its [[monzo|monzo]] is |1 -5 3&gt;, and flipping that yields &lt;&lt;3 5 1|| for the [[wedgie|wedgie]]. This tells us the [[generator|generator]] is a minor whole tone, the [[10/9|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.
The revision contents are below, presented both in the original Wikispaces Wikitext format, and in HTML exactly as Wikispaces rendered it.<br>
<h4>Original Wikitext content:</h4>
<div style="width:100%; max-height:400pt; overflow:auto; background-color:#f8f9fa; border: 1px solid #eaecf0; padding:0em"><pre style="margin:0px;border:none;background:none;word-wrap:break-word;white-space: pre-wrap ! important" class="old-revision-html">&lt;span style="display: block; text-align: right;"&gt;[[xenharmonie/Porcupine|Deutsch]]
&lt;/span&gt;
[[toc|flat]]
----
The 5-limit parent comma for the porcupine family is 250/243, the maximal [[diesis]] or porcupine comma. Its [[monzo]] is |1 -5 3&gt;, and flipping that yields &lt;&lt;3 5 1|| for the [[wedgie]]. This tells us the [[generator]] is a minor whole tone, the [[10_9|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.


valid range: [150.000, 171.429] (8 to 7)
valid range: [150.000, 171.429] (8 to 7)
nice range: [157.821, 166.015]
nice range: [157.821, 166.015]
strict range: [157.821, 166.015]
strict range: [157.821, 166.015]


[[POTE tuning|POTE generator]]: 163.950
[[POTE_tuning|POTE generator]]: 163.950


Map: [&lt;1 2 3|, &lt;0 -3 -5|]
Map: [&lt;1 2 3|, &lt;0 -3 -5|]


EDOs: [[15edo|15]], [[22edo|22]], [[95edo|95c]], [[117edo|117bc]], [[139edo|139bc]], [[161edo|161bc]], [[183edo|183bc]]
EDOs: [[15edo|15]], [[22edo|22]], [[95edo|95c]], [[117edo|117bc]], [[139edo|139bc]], [[161edo|161bc]], [[183edo|183bc]]
Badness: 0.0308
Badness: 0.0308


==Seven limit children==  
==Seven limit children==
The second comma of the [[Normal lists|normal comma list]] defines which [[7-limit]] family member we are looking at. That means [[64_63|64/63]], the [[64_63|Archytas comma]], for [[Porcupine family#Porcupine|porcupine]], [[36_35|36/35]], the [[septimal quarter tone]], for [[Porcupine family#Hystrix|hystrix]], [[50_49|50/49]], the [[jubilisma]], for [[Porcupine family#Hedgehog|hedgehog]], and [[49_48|49/48]], the [[slendro diesis]], for [[Porcupine family#Nautilus|nautilus]].
The second comma of the [[Normal_lists|normal comma list]] defines which [[7-limit|7-limit]] family member we are looking at. That means [[64/63|64/63]], the [[64/63|Archytas comma]], for [[Porcupine_family#Porcupine|porcupine]], [[36/35|36/35]], the [[septimal_quarter_tone|septimal quarter tone]], for [[Porcupine_family#Hystrix|hystrix]], [[50/49|50/49]], the [[jubilisma|jubilisma]], for [[Porcupine_family#Hedgehog|hedgehog]], and [[49/48|49/48]], the [[slendro_diesis|slendro diesis]], for [[Porcupine_family#Nautilus|nautilus]].


=Porcupine=  
=Porcupine=
[[Porcupine]], with wedgie &lt;&lt;3 5 -6 1 -18 -28||, uses six of its minor tone generator steps to get to [[7_4|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|Porcupine]], with wedgie &lt;&lt;3 5 -6 1 -18 -28||, uses six of its minor tone generator steps to get to [[7/4|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.


Commas: 250/243, 64/63
Commas: 250/243, 64/63


valid range: [160.000, 163.636] (15 to 22)
valid range: [160.000, 163.636] (15 to 22)
nice range: [157.821, 166.015]
nice range: [157.821, 166.015]
strict range: [160.000, 163.636]
strict range: [160.000, 163.636]


[[POTE tuning|POTE generator]]: ~10/9 = 162.880
[[POTE_tuning|POTE generator]]: ~10/9 = 162.880
 
7- and 9-limit minimax eigenmonzo: 9/7
7- and 9-limit minimax eigenmonzo: 9/7


Map: [&lt;1 2 3 2|, &lt;0 -3 -5 6|]
Map: [&lt;1 2 3 2|, &lt;0 -3 -5 6|]
EDOs: 22, [[59edo|59]], [[81edo|81bd]], [[140edo|140bd]]
EDOs: 22, [[59edo|59]], [[81edo|81bd]], [[140edo|140bd]]
Badness: 0.0411
Badness: 0.0411


==11-limit==  
==11-limit==
Commas: 55/54, 64/63, 100/99
Commas: 55/54, 64/63, 100/99


valid range: [160.000, 163.636] (15 to 22)
valid range: [160.000, 163.636] (15 to 22)
nice range: [150.637, 182.404]
nice range: [150.637, 182.404]
strict range: [160.000, 163.636]
strict range: [160.000, 163.636]


POTE generator: ~10/9 = 162.747
POTE generator: ~10/9 = 162.747
11-limit minimax eigenmonzo: 9/7
11-limit minimax eigenmonzo: 9/7


Map: [&lt;1 2 3 2 4|, &lt;0 -3 -5 6 -4|]
Map: [&lt;1 2 3 2 4|, &lt;0 -3 -5 6 -4|]
EDOs: [[7edo|7]], 15, 22, [[37edo|37]], [[59edo|59]]
EDOs: [[7edo|7]], 15, 22, [[37edo|37]], [[59edo|59]]
Badness: 0.0217
Badness: 0.0217


==13-limit==  
==13-limit==
Commas: 40/39, 55/54, 64/63, 66/65
Commas: 40/39, 55/54, 64/63, 66/65


valid range: [160.000, 163.636] (15 to 22f)
valid range: [160.000, 163.636] (15 to 22f)
nice range: [138.573, 182.404]
nice range: [138.573, 182.404]
strict range: [160.000, 163.636]
strict range: [160.000, 163.636]


POTE generator: ~10/9 = 162.708
POTE generator: ~10/9 = 162.708
13- and 15-limit minimax eigenmonzo: 11/8
13- and 15-limit minimax eigenmonzo: 11/8


Map: [&lt;1 2 3 2 4 4|, &lt;0 -3 -5 6 -4 -2|]
Map: [&lt;1 2 3 2 4 4|, &lt;0 -3 -5 6 -4 -2|]
EDOs: 7, 15, 22f, 37f
EDOs: 7, 15, 22f, 37f
Badness: 0.0213
Badness: 0.0213


==Porcupinefish==  
==Porcupinefish==
See also: [[The Biosphere]]
See also: [[The_Biosphere|The Biosphere]]
 
Commas: 55/54, 64/63, 91/90, 100/99
Commas: 55/54, 64/63, 91/90, 100/99


valid range: [160.000, 162.162] (15 to 37)
valid range: [160.000, 162.162] (15 to 37)
nice range: [150.637, 182.404]
nice range: [150.637, 182.404]
strict range: [160.000, 162.162]
strict range: [160.000, 162.162]


POTE generator: ~10/9 = 162.277
POTE generator: ~10/9 = 162.277
13- and 15-limit minimax eigenmonzo: 13/11
13- and 15-limit minimax eigenmonzo: 13/11


Map: [&lt;1 2 3 2 4 6|, &lt;0 -3 -5 6 -4 -17|]
Map: [&lt;1 2 3 2 4 6|, &lt;0 -3 -5 6 -4 -17|]
EDOs: 15, 22, 37, 59, 96b
EDOs: 15, 22, 37, 59, 96b
&lt;span style="background-color: #ffffff;"&gt;Badness: 0.0253&lt;/span&gt;
 
<span style="background-color: #ffffff;">Badness: 0.0253</span>
 
Badness: 0.0253
Badness: 0.0253


==Pourcup==  
==Pourcup==
Commas: 55/54, 64/63, 100/99, 196/195
Commas: 55/54, 64/63, 100/99, 196/195


POTE generator: ~10/9 = 162.482
POTE generator: ~10/9 = 162.482
13- and 15-limit minimax eigenmonzo: 13/7
13- and 15-limit minimax eigenmonzo: 13/7


Map: [&lt;1 2 3 2 4 1|, &lt;0 -3 -5 6 -4 20|]
Map: [&lt;1 2 3 2 4 1|, &lt;0 -3 -5 6 -4 20|]
EDOs: 15f, 22f, 37
EDOs: 15f, 22f, 37
Badness: 0.0351
Badness: 0.0351


==Porkpie==  
==Porkpie==
Commas: 55/54, 64/63, 65/63, 100/99
Commas: 55/54, 64/63, 65/63, 100/99


POTE generator: ~10/9 = 163.688
POTE generator: ~10/9 = 163.688
13- and 15-limit minimax eigenmonzo: 9/7
13- and 15-limit minimax eigenmonzo: 9/7


Map: [&lt;1 2 3 2 4 3|, &lt;0 -3 -5 6 -4 5|]
Map: [&lt;1 2 3 2 4 3|, &lt;0 -3 -5 6 -4 5|]
EDOs: 7, 15f, 22
EDOs: 7, 15f, 22
Badness: 0.0260
Badness: 0.0260


=Hystrix=  
=Hystrix=
Hystrix, with wedgie &lt;&lt;3 5 1 1 -7 -12||, 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, with wedgie &lt;&lt;3 5 1 1 -7 -12||, 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.


Commas: 36/35, 160/147
Commas: 36/35, 160/147


[[POTE tuning|POTE generator]]: 158.868
[[POTE_tuning|POTE generator]]: 158.868
 
7- and 9-limit minimax eigenmonzo: 5/4
7- and 9-limit minimax eigenmonzo: 5/4


Line 117: Line 142:


EDOs: 10d, 12, 13d, 15
EDOs: 10d, 12, 13d, 15
Badness: 0.0449
Badness: 0.0449


=Porky=  
=Porky=
Commas: 225/224, 250/243
Commas: 225/224, 250/243


POTE generator: ~10/9 = 164.412
POTE generator: ~10/9 = 164.412
7- and 9-limit minimax eigenmonzo: 7/5
7- and 9-limit minimax eigenmonzo: 7/5


Map: [&lt;1 2 3 5|, &lt;0 -3 -5 -16|]
Map: [&lt;1 2 3 5|, &lt;0 -3 -5 -16|]
Wedgie: &lt;&lt;3 5 16 1 17 23||
Wedgie: &lt;&lt;3 5 16 1 17 23||
EDOS: 7, 8, 15, 22, 29, 51, 73
EDOS: 7, 8, 15, 22, 29, 51, 73
Badness: 0.0544
Badness: 0.0544


==11-limit==  
==11-limit==
Commas: 55/54, 100/99, 225/224
Commas: 55/54, 100/99, 225/224


POTE generator: ~10/9 = 164.552
POTE generator: ~10/9 = 164.552
11-limit minimax eigenmonzo: 7/5
11-limit minimax eigenmonzo: 7/5


Map: [&lt;1 2 3 5 4|, &lt;0 -3 -5 -16 -4|]
Map: [&lt;1 2 3 5 4|, &lt;0 -3 -5 -16 -4|]
EDOs: 7, 8, 15, 22, 29, 51, 73
EDOs: 7, 8, 15, 22, 29, 51, 73
Badness: 0.0273
Badness: 0.0273


==13-limit==  
==13-limit==
Commas: 55/54, 65/64, 91/90, 100/99
Commas: 55/54, 65/64, 91/90, 100/99


Line 146: Line 179:


Map: [&lt;1 2 3 5 4 3|, &lt;0 -3 -5 -16 -4 5|]
Map: [&lt;1 2 3 5 4 3|, &lt;0 -3 -5 -16 -4 5|]
EDOs: 22, 29, 51f, 80cdef
EDOs: 22, 29, 51f, 80cdef
Badness: 0.0265
Badness: 0.0265


=Coendou=  
=Coendou=
Commas: 250/243, 525/512
Commas: 250/243, 525/512


POTE generator: ~10/9 = 166.041
POTE generator: ~10/9 = 166.041
7- and 9-limit minimax eigenmonzo: 3/2
7- and 9-limit minimax eigenmonzo: 3/2


Map: [&lt;1 2 3 1|, &lt;0 -3 -5 13|]
Map: [&lt;1 2 3 1|, &lt;0 -3 -5 13|]
Wedgie: &lt;&lt;3 5 -13 1 -29 -44||
Wedgie: &lt;&lt;3 5 -13 1 -29 -44||
EDOs: 7, 29, 65c, 94cd
EDOs: 7, 29, 65c, 94cd
Badness: 0.1183
Badness: 0.1183


==11-limit==  
==11-limit==
Commas: 55/54, 100/99, 525/512
Commas: 55/54, 100/99, 525/512


POTE generator: ~10/9 = 165.981
POTE generator: ~10/9 = 165.981
11-limit minimax eigenmonzo: 3/2
11-limit minimax eigenmonzo: 3/2


Map: [&lt;1 2 3 1 4|, &lt;0 -3 -5 13 -4|]
Map: [&lt;1 2 3 1 4|, &lt;0 -3 -5 13 -4|]
EDOs: 7, 29, 65ce, 94cde
EDOs: 7, 29, 65ce, 94cde
Badness: 0.0497
Badness: 0.0497


==13-limit==  
==13-limit==
Commas: 55/54, 65/64, 100/99, 105/104
Commas: 55/54, 65/64, 100/99, 105/104


POTE generator: ~10/9 = 165.974
POTE generator: ~10/9 = 165.974
13- and 15-limit minimax eigenmonzo: 3/2
13- and 15-limit minimax eigenmonzo: 3/2


Map: [&lt;1 2 3 1 4 3|, &lt;0 -3 -5 13 -4 5|]
Map: [&lt;1 2 3 1 4 3|, &lt;0 -3 -5 13 -4 5|]
EDOs: 7, 29, 65cef, 94cdef
EDOs: 7, 29, 65cef, 94cdef
Badness: 0.0302
Badness: 0.0302


=Hedgehog=  
=Hedgehog=
Hedgehog, with wedgie &lt;&lt;6 10 10 2 -1 -5||, 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. 22et provides the obvious tuning, but if you are looking for an alternative, you could try the &lt;[[tel/146 232 338|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, with wedgie &lt;&lt;6 10 10 2 -1 -5||, 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. 22et provides the obvious tuning, but if you are looking for an alternative, you could try the &lt;[http://tel.wikispaces.com/146_232_338 146 232 338] 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.


Commas: 50/49, 245/243
Commas: 50/49, 245/243


[[POTE tuning|POTE generator]]: ~9/7 = 435.648
[[POTE_tuning|POTE generator]]: ~9/7 = 435.648


Map: [&lt;2 1 1 2|, &lt;0 3 5 5|]
Map: [&lt;2 1 1 2|, &lt;0 3 5 5|]
Wedgie: &lt;&lt;6 10 10 2 -1 -5||
Wedgie: &lt;&lt;6 10 10 2 -1 -5||
EDOs: 22, [[146edo|146]]
EDOs: 22, [[146edo|146]]
Badness: 0.0440
Badness: 0.0440


==11-limit==  
==11-limit==
Commas: 50/49, 55/54, 99/98
Commas: 50/49, 55/54, 99/98


Line 198: Line 246:


Map: [&lt;2 1 1 2 4|, &lt;0 3 5 5 4|]
Map: [&lt;2 1 1 2 4|, &lt;0 3 5 5 4|]
EDOs: 14c, 22, 58ce, 80ce, 102cde
EDOs: 14c, 22, 58ce, 80ce, 102cde
Badness: 0.0231
Badness: 0.0231


==13-limit==  
==13-limit==
Commas: 50/49, 55/54, 65/63, 99/98
Commas: 50/49, 55/54, 65/63, 99/98


Line 207: Line 257:


Map: [&lt;2 1 1 2 4 3|, &lt;0 3 5 5 4 6|]
Map: [&lt;2 1 1 2 4 3|, &lt;0 3 5 5 4 6|]
EDOs: 14cf, 22
EDOs: 14cf, 22
Badness: 0.0215
Badness: 0.0215


==Urchin==  
==Urchin==
Commas: 40/39, 50/49, 55/54, 66/65
Commas: 40/39, 50/49, 55/54, 66/65


Line 216: Line 268:


Map: [&lt;2 1 1 2 4 6|, &lt;0 3 5 5 4 2|]
Map: [&lt;2 1 1 2 4 6|, &lt;0 3 5 5 4 2|]
EDOs: 14c, 22f
EDOs: 14c, 22f
Badness: 0.0252
Badness: 0.0252


==Hedgepig==  
==Hedgepig==
Commas: 50/49, 245/243, 385/384
Commas: 50/49, 245/243, 385/384


Line 225: Line 279:


Map: [&lt;2 1 1 2 12|, &lt;0 3 5 5 -7|]
Map: [&lt;2 1 1 2 12|, &lt;0 3 5 5 -7|]
EDOs: 22, 80c, 102cd, 124cd
EDOs: 22, 80c, 102cd, 124cd
Badness: 0.0684
Badness: 0.0684


===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=
Commas: 49/48, 250/243
Commas: 49/48, 250/243


Line 237: Line 293:


Map: [&lt;1 2 3 3|, &lt;0 -6 -10 -3|]
Map: [&lt;1 2 3 3|, &lt;0 -6 -10 -3|]
Wedgie: &lt;&lt;6 10 3 2 -12 -21||
Wedgie: &lt;&lt;6 10 3 2 -12 -21||
EDOs: 15, [[29edo|29]], 43cd, 44d, 59d, 73cd, [[102edo|102cd]]
EDOs: 15, [[29edo|29]], 43cd, 44d, 59d, 73cd, [[102edo|102cd]]


==11-limit==  
==11-limit==
Commas: 49/48, 55/54, 245/242
Commas: 49/48, 55/54, 245/242


Line 246: Line 304:


Map: [&lt;1 2 3 3 4|, &lt;0 -6 -10 -3 -8|]
Map: [&lt;1 2 3 3 4|, &lt;0 -6 -10 -3 -8|]
EDOs: 14c, 15, 29, 43cde, 44d, 59d, 73cde, 102cde
EDOs: 14c, 15, 29, 43cde, 44d, 59d, 73cde, 102cde


==13-limit==  
==13-limit==
Commas: 49/48, 55/54, 91/90, 100/99
Commas: 49/48, 55/54, 91/90, 100/99


Line 254: Line 313:


Map: [&lt;1 2 3 3 4 5|, &lt;0 -6 -10 -3 -8 -19|]
Map: [&lt;1 2 3 3 4 5|, &lt;0 -6 -10 -3 -8 -19|]
EDOs: 15f, 29, 43cde, 44d, 59df, 73cde, 102cde
EDOs: 15f, 29, 43cde, 44d, 59df, 73cde, 102cde
Badness: 0.0223
Badness: 0.0223


==Belauensis==  
==Belauensis==
Commas: 40/39, 49/48, 55/54, 66/65
Commas: 40/39, 49/48, 55/54, 66/65


Line 263: Line 324:


Map: [&lt;1 2 3 3 4 4|, &lt;0 -6 -10 -3 -8 -4|]
Map: [&lt;1 2 3 3 4 4|, &lt;0 -6 -10 -3 -8 -4|]
EDOs: 14c, 15, 29f, 44df
EDOs: 14c, 15, 29f, 44df
Badness: 0.0298
Badness: 0.0298


[[http://micro.soonlabel.com/gene_ward_smith/Others/Igs/NautilusReverie.mp3|Nautilus Reverie]] by [[IgliashonJones|Igliashon Calvin Jones-Coolidge]]
[http://micro.soonlabel.com/gene_ward_smith/Others/Igs/NautilusReverie.mp3 Nautilus Reverie] by [[IgliashonJones|Igliashon Calvin Jones-Coolidge]]
=Ammonite=  
 
=Ammonite=
Commas: 250/243, 686/675
Commas: 250/243, 686/675


Line 273: Line 337:


Map: [&lt;1 5 8 10|, &lt;0 -9 -15 -19|]
Map: [&lt;1 5 8 10|, &lt;0 -9 -15 -19|]
Wedgie: &lt;&lt;9 15 19 3 5 2||
Wedgie: &lt;&lt;9 15 19 3 5 2||
EDOs: 29, 37, 66
EDOs: 29, 37, 66
Badness: 0.1077
Badness: 0.1077


==11-limit==  
==11-limit==
Commas: 55/54, 100/99, 686/675
Commas: 55/54, 100/99, 686/675


Line 283: Line 350:


Map: [&lt;1 5 8 10 8|, &lt;0 -9 -15 -19 -12|]
Map: [&lt;1 5 8 10 8|, &lt;0 -9 -15 -19 -12|]
EDOs: 29, 37, 66
EDOs: 29, 37, 66
Badness: 0.0457
Badness: 0.0457


==13-limit==  
==13-limit==
Commas: 55/54, 91/90, 100/99, 169/168
Commas: 55/54, 91/90, 100/99, 169/168


Line 292: Line 361:


Map: [&lt;1 5 8 10 8 9|, &lt;0 -9 -15 -19 -12 -14|]
Map: [&lt;1 5 8 10 8 9|, &lt;0 -9 -15 -19 -12 -14|]
EDOs: 29, 37, 66
EDOs: 29, 37, 66
Badness: 0.0272
Badness: 0.0272


=Ceratitid=  
=Ceratitid=
Commas: 250/243, 1728/1715
Commas: 250/243, 1728/1715


Line 301: Line 372:


Map: [&lt;1 2 3 3|, &lt;0 -9 -15 -4|]
Map: [&lt;1 2 3 3|, &lt;0 -9 -15 -4|]
Wedgie: &lt;&lt;9 15 4 3 -19 -33||
Wedgie: &lt;&lt;9 15 4 3 -19 -33||
EDOs: 22
EDOs: 22
Badness: 0.115
Badness: 0.115


==11-limit==  
==11-limit==
Commas: 55/54, 100/99, 5324/5145
Commas: 55/54, 100/99, 5324/5145


Line 311: Line 385:


Map: [&lt;1 2 3 3 4|, &lt;0 -9 -15 -4 -12|]
Map: [&lt;1 2 3 3 4|, &lt;0 -9 -15 -4 -12|]
EDOs: 22
EDOs: 22
Badness: 0.0513
Badness: 0.0513


==13-limit==  
==13-limit==
Commas: 55/54, 65/63, 100/99, 352/343
Commas: 55/54, 65/63, 100/99, 352/343


Line 320: Line 396:


Map: [&lt;1 2 3 3 4 4|, &lt;0 -9 -15 -4 -12 -7|]
Map: [&lt;1 2 3 3 4 4|, &lt;0 -9 -15 -4 -12 -7|]
EDOs: 22
EDOs: 22
Badness: 0.0447</pre></div>
 
<h4>Original HTML content:</h4>
Badness: 0.0447
<div style="width:100%; max-height:400pt; overflow:auto; background-color:#f8f9fa; border: 1px solid #eaecf0; padding:0em"><pre style="margin:0px;border:none;background:none;word-wrap:break-word;width:200%;white-space: pre-wrap ! important" class="old-revision-html">&lt;html&gt;&lt;head&gt;&lt;title&gt;Porcupine family&lt;/title&gt;&lt;/head&gt;&lt;body&gt;&lt;span style="display: block; text-align: right;"&gt;&lt;a class="wiki_link" href="http://xenharmonie.wikispaces.com/Porcupine"&gt;Deutsch&lt;/a&gt;&lt;br /&gt;
[[Category:family]]
&lt;/span&gt;&lt;br /&gt;
[[Category:porcupine]]
&lt;!-- ws:start:WikiTextTocRule:60:&amp;lt;img id=&amp;quot;wikitext@@toc@@flat&amp;quot; class=&amp;quot;WikiMedia WikiMediaTocFlat&amp;quot; title=&amp;quot;Table of Contents&amp;quot; src=&amp;quot;/site/embedthumbnail/toc/flat?w=100&amp;amp;h=16&amp;quot;/&amp;gt; --&gt;&lt;!-- ws:end:WikiTextTocRule:60 --&gt;&lt;!-- ws:start:WikiTextTocRule:61: --&gt;&lt;!-- ws:end:WikiTextTocRule:61 --&gt;&lt;!-- ws:start:WikiTextTocRule:62: --&gt; | &lt;a href="#Porcupine"&gt;Porcupine&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:62 --&gt;&lt;!-- ws:start:WikiTextTocRule:63: --&gt;&lt;!-- ws:end:WikiTextTocRule:63 --&gt;&lt;!-- ws:start:WikiTextTocRule:64: --&gt;&lt;!-- ws:end:WikiTextTocRule:64 --&gt;&lt;!-- ws:start:WikiTextTocRule:65: --&gt;&lt;!-- ws:end:WikiTextTocRule:65 --&gt;&lt;!-- ws:start:WikiTextTocRule:66: --&gt;&lt;!-- ws:end:WikiTextTocRule:66 --&gt;&lt;!-- ws:start:WikiTextTocRule:67: --&gt;&lt;!-- ws:end:WikiTextTocRule:67 --&gt;&lt;!-- ws:start:WikiTextTocRule:68: --&gt; | &lt;a href="#Hystrix"&gt;Hystrix&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:68 --&gt;&lt;!-- ws:start:WikiTextTocRule:69: --&gt; | &lt;a href="#Porky"&gt;Porky&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:69 --&gt;&lt;!-- ws:start:WikiTextTocRule:70: --&gt;&lt;!-- ws:end:WikiTextTocRule:70 --&gt;&lt;!-- ws:start:WikiTextTocRule:71: --&gt;&lt;!-- ws:end:WikiTextTocRule:71 --&gt;&lt;!-- ws:start:WikiTextTocRule:72: --&gt; | &lt;a href="#Coendou"&gt;Coendou&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:72 --&gt;&lt;!-- ws:start:WikiTextTocRule:73: --&gt;&lt;!-- ws:end:WikiTextTocRule:73 --&gt;&lt;!-- ws:start:WikiTextTocRule:74: --&gt;&lt;!-- ws:end:WikiTextTocRule:74 --&gt;&lt;!-- ws:start:WikiTextTocRule:75: --&gt; | &lt;a href="#Hedgehog"&gt;Hedgehog&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:75 --&gt;&lt;!-- ws:start:WikiTextTocRule:76: --&gt;&lt;!-- ws:end:WikiTextTocRule:76 --&gt;&lt;!-- ws:start:WikiTextTocRule:77: --&gt;&lt;!-- ws:end:WikiTextTocRule:77 --&gt;&lt;!-- ws:start:WikiTextTocRule:78: --&gt;&lt;!-- ws:end:WikiTextTocRule:78 --&gt;&lt;!-- ws:start:WikiTextTocRule:79: --&gt;&lt;!-- ws:end:WikiTextTocRule:79 --&gt;&lt;!-- ws:start:WikiTextTocRule:80: --&gt;&lt;!-- ws:end:WikiTextTocRule:80 --&gt;&lt;!-- ws:start:WikiTextTocRule:81: --&gt; | &lt;a href="#Nautilus"&gt;Nautilus&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:81 --&gt;&lt;!-- ws:start:WikiTextTocRule:82: --&gt;&lt;!-- ws:end:WikiTextTocRule:82 --&gt;&lt;!-- ws:start:WikiTextTocRule:83: --&gt;&lt;!-- ws:end:WikiTextTocRule:83 --&gt;&lt;!-- ws:start:WikiTextTocRule:84: --&gt;&lt;!-- ws:end:WikiTextTocRule:84 --&gt;&lt;!-- ws:start:WikiTextTocRule:85: --&gt; | &lt;a href="#Ammonite"&gt;Ammonite&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:85 --&gt;&lt;!-- ws:start:WikiTextTocRule:86: --&gt;&lt;!-- ws:end:WikiTextTocRule:86 --&gt;&lt;!-- ws:start:WikiTextTocRule:87: --&gt;&lt;!-- ws:end:WikiTextTocRule:87 --&gt;&lt;!-- ws:start:WikiTextTocRule:88: --&gt; | &lt;a href="#Ceratitid"&gt;Ceratitid&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:88 --&gt;&lt;!-- ws:start:WikiTextTocRule:89: --&gt;&lt;!-- ws:end:WikiTextTocRule:89 --&gt;&lt;!-- ws:start:WikiTextTocRule:90: --&gt;&lt;!-- ws:end:WikiTextTocRule:90 --&gt;&lt;!-- ws:start:WikiTextTocRule:91: --&gt;
[[Category:theory]]
&lt;!-- ws:end:WikiTextTocRule:91 --&gt;&lt;hr /&gt;
The 5-limit parent comma for the porcupine family is 250/243, the maximal &lt;a class="wiki_link" href="/diesis"&gt;diesis&lt;/a&gt; or porcupine comma. Its &lt;a class="wiki_link" href="/monzo"&gt;monzo&lt;/a&gt; is |1 -5 3&amp;gt;, and flipping that yields &amp;lt;&amp;lt;3 5 1|| for the &lt;a class="wiki_link" href="/wedgie"&gt;wedgie&lt;/a&gt;. This tells us the &lt;a class="wiki_link" href="/generator"&gt;generator&lt;/a&gt; is a minor whole tone, the &lt;a class="wiki_link" href="/10_9"&gt;10/9&lt;/a&gt; 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.&lt;br /&gt;
&lt;br /&gt;
valid range: [150.000, 171.429] (8 to 7)&lt;br /&gt;
nice range: [157.821, 166.015]&lt;br /&gt;
strict range: [157.821, 166.015]&lt;br /&gt;
&lt;br /&gt;
&lt;a class="wiki_link" href="/POTE%20tuning"&gt;POTE generator&lt;/a&gt;: 163.950&lt;br /&gt;
&lt;br /&gt;
Map: [&amp;lt;1 2 3|, &amp;lt;0 -3 -5|]&lt;br /&gt;
&lt;br /&gt;
EDOs: &lt;a class="wiki_link" href="/15edo"&gt;15&lt;/a&gt;, &lt;a class="wiki_link" href="/22edo"&gt;22&lt;/a&gt;, &lt;a class="wiki_link" href="/95edo"&gt;95c&lt;/a&gt;, &lt;a class="wiki_link" href="/117edo"&gt;117bc&lt;/a&gt;, &lt;a class="wiki_link" href="/139edo"&gt;139bc&lt;/a&gt;, &lt;a class="wiki_link" href="/161edo"&gt;161bc&lt;/a&gt;, &lt;a class="wiki_link" href="/183edo"&gt;183bc&lt;/a&gt;&lt;br /&gt;
Badness: 0.0308&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:0:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc0"&gt;&lt;a name="x-Seven limit children"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:0 --&gt;Seven limit children&lt;/h2&gt;
The second comma of the &lt;a class="wiki_link" href="/Normal%20lists"&gt;normal comma list&lt;/a&gt; defines which &lt;a class="wiki_link" href="/7-limit"&gt;7-limit&lt;/a&gt; family member we are looking at. That means &lt;a class="wiki_link" href="/64_63"&gt;64/63&lt;/a&gt;, the &lt;a class="wiki_link" href="/64_63"&gt;Archytas comma&lt;/a&gt;, for &lt;a class="wiki_link" href="/Porcupine%20family#Porcupine"&gt;porcupine&lt;/a&gt;, &lt;a class="wiki_link" href="/36_35"&gt;36/35&lt;/a&gt;, the &lt;a class="wiki_link" href="/septimal%20quarter%20tone"&gt;septimal quarter tone&lt;/a&gt;, for &lt;a class="wiki_link" href="/Porcupine%20family#Hystrix"&gt;hystrix&lt;/a&gt;, &lt;a class="wiki_link" href="/50_49"&gt;50/49&lt;/a&gt;, the &lt;a class="wiki_link" href="/jubilisma"&gt;jubilisma&lt;/a&gt;, for &lt;a class="wiki_link" href="/Porcupine%20family#Hedgehog"&gt;hedgehog&lt;/a&gt;, and &lt;a class="wiki_link" href="/49_48"&gt;49/48&lt;/a&gt;, the &lt;a class="wiki_link" href="/slendro%20diesis"&gt;slendro diesis&lt;/a&gt;, for &lt;a class="wiki_link" href="/Porcupine%20family#Nautilus"&gt;nautilus&lt;/a&gt;.&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:2:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc1"&gt;&lt;a name="Porcupine"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:2 --&gt;Porcupine&lt;/h1&gt;
&lt;a class="wiki_link" href="/Porcupine"&gt;Porcupine&lt;/a&gt;, with wedgie &amp;lt;&amp;lt;3 5 -6 1 -18 -28||, uses six of its minor tone generator steps to get to &lt;a class="wiki_link" href="/7_4"&gt;7/4&lt;/a&gt;. For this to work you need a small minor tone such as &lt;a class="wiki_link" href="/22edo"&gt;22edo&lt;/a&gt; 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.&lt;br /&gt;
&lt;br /&gt;
Commas: 250/243, 64/63&lt;br /&gt;
&lt;br /&gt;
valid range: [160.000, 163.636] (15 to 22)&lt;br /&gt;
nice range: [157.821, 166.015]&lt;br /&gt;
strict range: [160.000, 163.636]&lt;br /&gt;
&lt;br /&gt;
&lt;a class="wiki_link" href="/POTE%20tuning"&gt;POTE generator&lt;/a&gt;: ~10/9 = 162.880&lt;br /&gt;
7- and 9-limit minimax eigenmonzo: 9/7&lt;br /&gt;
&lt;br /&gt;
Map: [&amp;lt;1 2 3 2|, &amp;lt;0 -3 -5 6|]&lt;br /&gt;
EDOs: 22, &lt;a class="wiki_link" href="/59edo"&gt;59&lt;/a&gt;, &lt;a class="wiki_link" href="/81edo"&gt;81bd&lt;/a&gt;, &lt;a class="wiki_link" href="/140edo"&gt;140bd&lt;/a&gt;&lt;br /&gt;
Badness: 0.0411&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:4:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc2"&gt;&lt;a name="Porcupine-11-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:4 --&gt;11-limit&lt;/h2&gt;
Commas: 55/54, 64/63, 100/99&lt;br /&gt;
&lt;br /&gt;
valid range: [160.000, 163.636] (15 to 22)&lt;br /&gt;
nice range: [150.637, 182.404]&lt;br /&gt;
strict range: [160.000, 163.636]&lt;br /&gt;
&lt;br /&gt;
POTE generator: ~10/9 = 162.747&lt;br /&gt;
11-limit minimax eigenmonzo: 9/7&lt;br /&gt;
&lt;br /&gt;
Map: [&amp;lt;1 2 3 2 4|, &amp;lt;0 -3 -5 6 -4|]&lt;br /&gt;
EDOs: &lt;a class="wiki_link" href="/7edo"&gt;7&lt;/a&gt;, 15, 22, &lt;a class="wiki_link" href="/37edo"&gt;37&lt;/a&gt;, &lt;a class="wiki_link" href="/59edo"&gt;59&lt;/a&gt;&lt;br /&gt;
Badness: 0.0217&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:6:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc3"&gt;&lt;a name="Porcupine-13-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:6 --&gt;13-limit&lt;/h2&gt;
Commas: 40/39, 55/54, 64/63, 66/65&lt;br /&gt;
&lt;br /&gt;
valid range: [160.000, 163.636] (15 to 22f)&lt;br /&gt;
nice range: [138.573, 182.404]&lt;br /&gt;
strict range: [160.000, 163.636]&lt;br /&gt;
&lt;br /&gt;
POTE generator: ~10/9 = 162.708&lt;br /&gt;
13- and 15-limit minimax eigenmonzo: 11/8&lt;br /&gt;
&lt;br /&gt;
Map: [&amp;lt;1 2 3 2 4 4|, &amp;lt;0 -3 -5 6 -4 -2|]&lt;br /&gt;
EDOs: 7, 15, 22f, 37f&lt;br /&gt;
Badness: 0.0213&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:8:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc4"&gt;&lt;a name="Porcupine-Porcupinefish"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:8 --&gt;Porcupinefish&lt;/h2&gt;
See also: &lt;a class="wiki_link" href="/The%20Biosphere"&gt;The Biosphere&lt;/a&gt;&lt;br /&gt;
Commas: 55/54, 64/63, 91/90, 100/99&lt;br /&gt;
&lt;br /&gt;
valid range: [160.000, 162.162] (15 to 37)&lt;br /&gt;
nice range: [150.637, 182.404]&lt;br /&gt;
strict range: [160.000, 162.162]&lt;br /&gt;
&lt;br /&gt;
POTE generator: ~10/9 = 162.277&lt;br /&gt;
13- and 15-limit minimax eigenmonzo: 13/11&lt;br /&gt;
&lt;br /&gt;
Map: [&amp;lt;1 2 3 2 4 6|, &amp;lt;0 -3 -5 6 -4 -17|]&lt;br /&gt;
EDOs: 15, 22, 37, 59, 96b&lt;br /&gt;
&lt;span style="background-color: #ffffff;"&gt;Badness: 0.0253&lt;/span&gt;&lt;br /&gt;
Badness: 0.0253&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:10:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc5"&gt;&lt;a name="Porcupine-Pourcup"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:10 --&gt;Pourcup&lt;/h2&gt;
Commas: 55/54, 64/63, 100/99, 196/195&lt;br /&gt;
&lt;br /&gt;
POTE generator: ~10/9 = 162.482&lt;br /&gt;
13- and 15-limit minimax eigenmonzo: 13/7&lt;br /&gt;
&lt;br /&gt;
Map: [&amp;lt;1 2 3 2 4 1|, &amp;lt;0 -3 -5 6 -4 20|]&lt;br /&gt;
EDOs: 15f, 22f, 37&lt;br /&gt;
Badness: 0.0351&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:12:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc6"&gt;&lt;a name="Porcupine-Porkpie"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:12 --&gt;Porkpie&lt;/h2&gt;
Commas: 55/54, 64/63, 65/63, 100/99&lt;br /&gt;
&lt;br /&gt;
POTE generator: ~10/9 = 163.688&lt;br /&gt;
13- and 15-limit minimax eigenmonzo: 9/7&lt;br /&gt;
&lt;br /&gt;
Map: [&amp;lt;1 2 3 2 4 3|, &amp;lt;0 -3 -5 6 -4 5|]&lt;br /&gt;
EDOs: 7, 15f, 22&lt;br /&gt;
Badness: 0.0260&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:14:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc7"&gt;&lt;a name="Hystrix"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:14 --&gt;Hystrix&lt;/h1&gt;
Hystrix, with wedgie &amp;lt;&amp;lt;3 5 1 1 -7 -12||, 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 &lt;a class="wiki_link" href="/15edo"&gt;15edo&lt;/a&gt;. They can try the even sharper fifth of hystrix in &lt;a class="wiki_link" href="/68edo"&gt;68edo&lt;/a&gt; and see how that suits.&lt;br /&gt;
&lt;br /&gt;
Commas: 36/35, 160/147&lt;br /&gt;
&lt;br /&gt;
&lt;a class="wiki_link" href="/POTE%20tuning"&gt;POTE generator&lt;/a&gt;: 158.868&lt;br /&gt;
7- and 9-limit minimax eigenmonzo: 5/4&lt;br /&gt;
&lt;br /&gt;
Map: [&amp;lt;1 2 3 3|, &amp;lt;0 -3 -5 -1|]&lt;br /&gt;
&lt;br /&gt;
EDOs: 10d, 12, 13d, 15&lt;br /&gt;
Badness: 0.0449&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:16:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc8"&gt;&lt;a name="Porky"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:16 --&gt;Porky&lt;/h1&gt;
Commas: 225/224, 250/243&lt;br /&gt;
&lt;br /&gt;
POTE generator: ~10/9 = 164.412&lt;br /&gt;
7- and 9-limit minimax eigenmonzo: 7/5&lt;br /&gt;
&lt;br /&gt;
Map: [&amp;lt;1 2 3 5|, &amp;lt;0 -3 -5 -16|]&lt;br /&gt;
Wedgie: &amp;lt;&amp;lt;3 5 16 1 17 23||&lt;br /&gt;
EDOS: 7, 8, 15, 22, 29, 51, 73&lt;br /&gt;
Badness: 0.0544&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:18:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc9"&gt;&lt;a name="Porky-11-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:18 --&gt;11-limit&lt;/h2&gt;
Commas: 55/54, 100/99, 225/224&lt;br /&gt;
&lt;br /&gt;
POTE generator: ~10/9 = 164.552&lt;br /&gt;
11-limit minimax eigenmonzo: 7/5&lt;br /&gt;
&lt;br /&gt;
Map: [&amp;lt;1 2 3 5 4|, &amp;lt;0 -3 -5 -16 -4|]&lt;br /&gt;
EDOs: 7, 8, 15, 22, 29, 51, 73&lt;br /&gt;
Badness: 0.0273&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:20:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc10"&gt;&lt;a name="Porky-13-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:20 --&gt;13-limit&lt;/h2&gt;
Commas: 55/54, 65/64, 91/90, 100/99&lt;br /&gt;
&lt;br /&gt;
POTE generator: ~10/9 = 164.953&lt;br /&gt;
&lt;br /&gt;
Map: [&amp;lt;1 2 3 5 4 3|, &amp;lt;0 -3 -5 -16 -4 5|]&lt;br /&gt;
EDOs: 22, 29, 51f, 80cdef&lt;br /&gt;
Badness: 0.0265&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:22:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc11"&gt;&lt;a name="Coendou"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:22 --&gt;Coendou&lt;/h1&gt;
Commas: 250/243, 525/512&lt;br /&gt;
&lt;br /&gt;
POTE generator: ~10/9 = 166.041&lt;br /&gt;
7- and 9-limit minimax eigenmonzo: 3/2&lt;br /&gt;
&lt;br /&gt;
Map: [&amp;lt;1 2 3 1|, &amp;lt;0 -3 -5 13|]&lt;br /&gt;
Wedgie: &amp;lt;&amp;lt;3 5 -13 1 -29 -44||&lt;br /&gt;
EDOs: 7, 29, 65c, 94cd&lt;br /&gt;
Badness: 0.1183&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:24:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc12"&gt;&lt;a name="Coendou-11-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:24 --&gt;11-limit&lt;/h2&gt;
Commas: 55/54, 100/99, 525/512&lt;br /&gt;
&lt;br /&gt;
POTE generator: ~10/9 = 165.981&lt;br /&gt;
11-limit minimax eigenmonzo: 3/2&lt;br /&gt;
&lt;br /&gt;
Map: [&amp;lt;1 2 3 1 4|, &amp;lt;0 -3 -5 13 -4|]&lt;br /&gt;
EDOs: 7, 29, 65ce, 94cde&lt;br /&gt;
Badness: 0.0497&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:26:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc13"&gt;&lt;a name="Coendou-13-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:26 --&gt;13-limit&lt;/h2&gt;
Commas: 55/54, 65/64, 100/99, 105/104&lt;br /&gt;
&lt;br /&gt;
POTE generator: ~10/9 = 165.974&lt;br /&gt;
13- and 15-limit minimax eigenmonzo: 3/2&lt;br /&gt;
&lt;br /&gt;
Map: [&amp;lt;1 2 3 1 4 3|, &amp;lt;0 -3 -5 13 -4 5|]&lt;br /&gt;
EDOs: 7, 29, 65cef, 94cdef&lt;br /&gt;
Badness: 0.0302&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:28:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc14"&gt;&lt;a name="Hedgehog"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:28 --&gt;Hedgehog&lt;/h1&gt;
Hedgehog, with wedgie &amp;lt;&amp;lt;6 10 10 2 -1 -5||, 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. 22et provides the obvious tuning, but if you are looking for an alternative, you could try the &amp;lt;&lt;a class="wiki_link" href="http://tel.wikispaces.com/146%20232%20338"&gt;146 232 338&lt;/a&gt; 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.&lt;br /&gt;
&lt;br /&gt;
Commas: 50/49, 245/243&lt;br /&gt;
&lt;br /&gt;
&lt;a class="wiki_link" href="/POTE%20tuning"&gt;POTE generator&lt;/a&gt;: ~9/7 = 435.648&lt;br /&gt;
&lt;br /&gt;
Map: [&amp;lt;2 1 1 2|, &amp;lt;0 3 5 5|]&lt;br /&gt;
Wedgie: &amp;lt;&amp;lt;6 10 10 2 -1 -5||&lt;br /&gt;
EDOs: 22, &lt;a class="wiki_link" href="/146edo"&gt;146&lt;/a&gt;&lt;br /&gt;
Badness: 0.0440&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:30:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc15"&gt;&lt;a name="Hedgehog-11-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:30 --&gt;11-limit&lt;/h2&gt;
Commas: 50/49, 55/54, 99/98&lt;br /&gt;
&lt;br /&gt;
POTE generator: ~9/7 = 435.386&lt;br /&gt;
&lt;br /&gt;
Map: [&amp;lt;2 1 1 2 4|, &amp;lt;0 3 5 5 4|]&lt;br /&gt;
EDOs: 14c, 22, 58ce, 80ce, 102cde&lt;br /&gt;
Badness: 0.0231&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:32:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc16"&gt;&lt;a name="Hedgehog-13-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:32 --&gt;13-limit&lt;/h2&gt;
Commas: 50/49, 55/54, 65/63, 99/98&lt;br /&gt;
&lt;br /&gt;
POTE generator: ~9/7 = 435.861&lt;br /&gt;
&lt;br /&gt;
Map: [&amp;lt;2 1 1 2 4 3|, &amp;lt;0 3 5 5 4 6|]&lt;br /&gt;
EDOs: 14cf, 22&lt;br /&gt;
Badness: 0.0215&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:34:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc17"&gt;&lt;a name="Hedgehog-Urchin"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:34 --&gt;Urchin&lt;/h2&gt;
Commas: 40/39, 50/49, 55/54, 66/65&lt;br /&gt;
&lt;br /&gt;
POTE generator: ~9/7 = 437.078&lt;br /&gt;
&lt;br /&gt;
Map: [&amp;lt;2 1 1 2 4 6|, &amp;lt;0 3 5 5 4 2|]&lt;br /&gt;
EDOs: 14c, 22f&lt;br /&gt;
Badness: 0.0252&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:36:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc18"&gt;&lt;a name="Hedgehog-Hedgepig"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:36 --&gt;Hedgepig&lt;/h2&gt;
Commas: 50/49, 245/243, 385/384&lt;br /&gt;
&lt;br /&gt;
POTE generator: ~9/7 = 435.425&lt;br /&gt;
&lt;br /&gt;
Map: [&amp;lt;2 1 1 2 12|, &amp;lt;0 3 5 5 -7|]&lt;br /&gt;
EDOs: 22, 80c, 102cd, 124cd&lt;br /&gt;
Badness: 0.0684&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:38:&amp;lt;h3&amp;gt; --&gt;&lt;h3 id="toc19"&gt;&lt;a name="Hedgehog-Hedgepig-Music"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:38 --&gt;Music&lt;/h3&gt;
&lt;a class="wiki_link_ext" href="http://micro.soonlabel.com/22-ET/20120207-phobos-light-hedgehog14.mp3" rel="nofollow"&gt;Phobos Light&lt;/a&gt; by Chris Vaisvil in Hedgehog[14] &lt;a class="wiki_link" href="/hedgehog14"&gt;tuned&lt;/a&gt; to 22edo.&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:40:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc20"&gt;&lt;a name="Nautilus"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:40 --&gt;Nautilus&lt;/h1&gt;
Commas: 49/48, 250/243&lt;br /&gt;
&lt;br /&gt;
POTE generator: ~21/20 = 82.505&lt;br /&gt;
&lt;br /&gt;
Map: [&amp;lt;1 2 3 3|, &amp;lt;0 -6 -10 -3|]&lt;br /&gt;
Wedgie: &amp;lt;&amp;lt;6 10 3 2 -12 -21||&lt;br /&gt;
EDOs: 15, &lt;a class="wiki_link" href="/29edo"&gt;29&lt;/a&gt;, 43cd, 44d, 59d, 73cd, &lt;a class="wiki_link" href="/102edo"&gt;102cd&lt;/a&gt;&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:42:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc21"&gt;&lt;a name="Nautilus-11-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:42 --&gt;11-limit&lt;/h2&gt;
Commas: 49/48, 55/54, 245/242&lt;br /&gt;
&lt;br /&gt;
POTE generator: ~21/20 = 82.504&lt;br /&gt;
&lt;br /&gt;
Map: [&amp;lt;1 2 3 3 4|, &amp;lt;0 -6 -10 -3 -8|]&lt;br /&gt;
EDOs: 14c, 15, 29, 43cde, 44d, 59d, 73cde, 102cde&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:44:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc22"&gt;&lt;a name="Nautilus-13-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:44 --&gt;13-limit&lt;/h2&gt;
Commas: 49/48, 55/54, 91/90, 100/99&lt;br /&gt;
&lt;br /&gt;
POTE generator: ~21/20 = 62.530&lt;br /&gt;
&lt;br /&gt;
Map: [&amp;lt;1 2 3 3 4 5|, &amp;lt;0 -6 -10 -3 -8 -19|]&lt;br /&gt;
EDOs: 15f, 29, 43cde, 44d, 59df, 73cde, 102cde&lt;br /&gt;
Badness: 0.0223&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:46:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc23"&gt;&lt;a name="Nautilus-Belauensis"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:46 --&gt;Belauensis&lt;/h2&gt;
Commas: 40/39, 49/48, 55/54, 66/65&lt;br /&gt;
&lt;br /&gt;
POTE generator: ~21/20 = ~14/13 = 81.759&lt;br /&gt;
&lt;br /&gt;
Map: [&amp;lt;1 2 3 3 4 4|, &amp;lt;0 -6 -10 -3 -8 -4|]&lt;br /&gt;
EDOs: 14c, 15, 29f, 44df&lt;br /&gt;
Badness: 0.0298&lt;br /&gt;
&lt;br /&gt;
&lt;a class="wiki_link_ext" href="http://micro.soonlabel.com/gene_ward_smith/Others/Igs/NautilusReverie.mp3" rel="nofollow"&gt;Nautilus Reverie&lt;/a&gt; by &lt;a class="wiki_link" href="/IgliashonJones"&gt;Igliashon Calvin Jones-Coolidge&lt;/a&gt;&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:48:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc24"&gt;&lt;a name="Ammonite"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:48 --&gt;Ammonite&lt;/h1&gt;
Commas: 250/243, 686/675&lt;br /&gt;
&lt;br /&gt;
POTE generator: ~9/7 = 454.448&lt;br /&gt;
&lt;br /&gt;
Map: [&amp;lt;1 5 8 10|, &amp;lt;0 -9 -15 -19|]&lt;br /&gt;
Wedgie: &amp;lt;&amp;lt;9 15 19 3 5 2||&lt;br /&gt;
EDOs: 29, 37, 66&lt;br /&gt;
Badness: 0.1077&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:50:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc25"&gt;&lt;a name="Ammonite-11-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:50 --&gt;11-limit&lt;/h2&gt;
Commas: 55/54, 100/99, 686/675&lt;br /&gt;
&lt;br /&gt;
POTE generator: ~9/7 = 454.512&lt;br /&gt;
&lt;br /&gt;
Map: [&amp;lt;1 5 8 10 8|, &amp;lt;0 -9 -15 -19 -12|]&lt;br /&gt;
EDOs: 29, 37, 66&lt;br /&gt;
Badness: 0.0457&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:52:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc26"&gt;&lt;a name="Ammonite-13-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:52 --&gt;13-limit&lt;/h2&gt;
Commas: 55/54, 91/90, 100/99, 169/168&lt;br /&gt;
&lt;br /&gt;
POTE generator: ~13/10 = 454.429&lt;br /&gt;
&lt;br /&gt;
Map: [&amp;lt;1 5 8 10 8 9|, &amp;lt;0 -9 -15 -19 -12 -14|]&lt;br /&gt;
EDOs: 29, 37, 66&lt;br /&gt;
Badness: 0.0272&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:54:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc27"&gt;&lt;a name="Ceratitid"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:54 --&gt;Ceratitid&lt;/h1&gt;
Commas: 250/243, 1728/1715&lt;br /&gt;
&lt;br /&gt;
POTE generator: ~36/35 = 54.384&lt;br /&gt;
&lt;br /&gt;
Map: [&amp;lt;1 2 3 3|, &amp;lt;0 -9 -15 -4|]&lt;br /&gt;
Wedgie: &amp;lt;&amp;lt;9 15 4 3 -19 -33||&lt;br /&gt;
EDOs: 22&lt;br /&gt;
Badness: 0.115&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:56:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc28"&gt;&lt;a name="Ceratitid-11-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:56 --&gt;11-limit&lt;/h2&gt;
Commas: 55/54, 100/99, 5324/5145&lt;br /&gt;
&lt;br /&gt;
POTE generator: ~36/35 = 54.376&lt;br /&gt;
&lt;br /&gt;
Map: [&amp;lt;1 2 3 3 4|, &amp;lt;0 -9 -15 -4 -12|]&lt;br /&gt;
EDOs: 22&lt;br /&gt;
Badness: 0.0513&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:58:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc29"&gt;&lt;a name="Ceratitid-13-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:58 --&gt;13-limit&lt;/h2&gt;
Commas: 55/54, 65/63, 100/99, 352/343&lt;br /&gt;
&lt;br /&gt;
POTE generator: ~36/35 = 54.665&lt;br /&gt;
&lt;br /&gt;
Map: [&amp;lt;1 2 3 3 4 4|, &amp;lt;0 -9 -15 -4 -12 -7|]&lt;br /&gt;
EDOs: 22&lt;br /&gt;
Badness: 0.0447&lt;/body&gt;&lt;/html&gt;</pre></div>

Revision as of 00:00, 17 July 2018

de:Porcupine Deutsch |

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.

valid range: [150.000, 171.429] (8 to 7)

nice range: [157.821, 166.015]

strict range: [157.821, 166.015]

POTE generator: 163.950

Map: [<1 2 3|, <0 -3 -5|]

EDOs: 15, 22, 95c, 117bc, 139bc, 161bc, 183bc

Badness: 0.0308

Seven limit children

The second comma of the normal comma list defines which 7-limit family member we are looking at. That means 64/63, the Archytas comma, for porcupine, 36/35, the septimal quarter tone, for hystrix, 50/49, the jubilisma, for hedgehog, and 49/48, the slendro diesis, for nautilus.

Porcupine

Porcupine, with wedgie <<3 5 -6 1 -18 -28||, 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.

Commas: 250/243, 64/63

valid range: [160.000, 163.636] (15 to 22)

nice range: [157.821, 166.015]

strict range: [160.000, 163.636]

POTE generator: ~10/9 = 162.880

7- and 9-limit minimax eigenmonzo: 9/7

Map: [<1 2 3 2|, <0 -3 -5 6|]

EDOs: 22, 59, 81bd, 140bd

Badness: 0.0411

11-limit

Commas: 55/54, 64/63, 100/99

valid range: [160.000, 163.636] (15 to 22)

nice range: [150.637, 182.404]

strict range: [160.000, 163.636]

POTE generator: ~10/9 = 162.747

11-limit minimax eigenmonzo: 9/7

Map: [<1 2 3 2 4|, <0 -3 -5 6 -4|]

EDOs: 7, 15, 22, 37, 59

Badness: 0.0217

13-limit

Commas: 40/39, 55/54, 64/63, 66/65

valid range: [160.000, 163.636] (15 to 22f)

nice range: [138.573, 182.404]

strict range: [160.000, 163.636]

POTE generator: ~10/9 = 162.708

13- and 15-limit minimax eigenmonzo: 11/8

Map: [<1 2 3 2 4 4|, <0 -3 -5 6 -4 -2|]

EDOs: 7, 15, 22f, 37f

Badness: 0.0213

Porcupinefish

See also: The Biosphere

Commas: 55/54, 64/63, 91/90, 100/99

valid range: [160.000, 162.162] (15 to 37)

nice range: [150.637, 182.404]

strict range: [160.000, 162.162]

POTE generator: ~10/9 = 162.277

13- and 15-limit minimax eigenmonzo: 13/11

Map: [<1 2 3 2 4 6|, <0 -3 -5 6 -4 -17|]

EDOs: 15, 22, 37, 59, 96b

Badness: 0.0253

Badness: 0.0253

Pourcup

Commas: 55/54, 64/63, 100/99, 196/195

POTE generator: ~10/9 = 162.482

13- and 15-limit minimax eigenmonzo: 13/7

Map: [<1 2 3 2 4 1|, <0 -3 -5 6 -4 20|]

EDOs: 15f, 22f, 37

Badness: 0.0351

Porkpie

Commas: 55/54, 64/63, 65/63, 100/99

POTE generator: ~10/9 = 163.688

13- and 15-limit minimax eigenmonzo: 9/7

Map: [<1 2 3 2 4 3|, <0 -3 -5 6 -4 5|]

EDOs: 7, 15f, 22

Badness: 0.0260

Hystrix

Hystrix, with wedgie <<3 5 1 1 -7 -12||, 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.

Commas: 36/35, 160/147

POTE generator: 158.868

7- and 9-limit minimax eigenmonzo: 5/4

Map: [<1 2 3 3|, <0 -3 -5 -1|]

EDOs: 10d, 12, 13d, 15

Badness: 0.0449

Porky

Commas: 225/224, 250/243

POTE generator: ~10/9 = 164.412

7- and 9-limit minimax eigenmonzo: 7/5

Map: [<1 2 3 5|, <0 -3 -5 -16|]

Wedgie: <<3 5 16 1 17 23||

EDOS: 7, 8, 15, 22, 29, 51, 73

Badness: 0.0544

11-limit

Commas: 55/54, 100/99, 225/224

POTE generator: ~10/9 = 164.552

11-limit minimax eigenmonzo: 7/5

Map: [<1 2 3 5 4|, <0 -3 -5 -16 -4|]

EDOs: 7, 8, 15, 22, 29, 51, 73

Badness: 0.0273

13-limit

Commas: 55/54, 65/64, 91/90, 100/99

POTE generator: ~10/9 = 164.953

Map: [<1 2 3 5 4 3|, <0 -3 -5 -16 -4 5|]

EDOs: 22, 29, 51f, 80cdef

Badness: 0.0265

Coendou

Commas: 250/243, 525/512

POTE generator: ~10/9 = 166.041

7- and 9-limit minimax eigenmonzo: 3/2

Map: [<1 2 3 1|, <0 -3 -5 13|]

Wedgie: <<3 5 -13 1 -29 -44||

EDOs: 7, 29, 65c, 94cd

Badness: 0.1183

11-limit

Commas: 55/54, 100/99, 525/512

POTE generator: ~10/9 = 165.981

11-limit minimax eigenmonzo: 3/2

Map: [<1 2 3 1 4|, <0 -3 -5 13 -4|]

EDOs: 7, 29, 65ce, 94cde

Badness: 0.0497

13-limit

Commas: 55/54, 65/64, 100/99, 105/104

POTE generator: ~10/9 = 165.974

13- and 15-limit minimax eigenmonzo: 3/2

Map: [<1 2 3 1 4 3|, <0 -3 -5 13 -4 5|]

EDOs: 7, 29, 65cef, 94cdef

Badness: 0.0302

Hedgehog

Hedgehog, with wedgie <<6 10 10 2 -1 -5||, 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. 22et 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.

Commas: 50/49, 245/243

POTE generator: ~9/7 = 435.648

Map: [<2 1 1 2|, <0 3 5 5|]

Wedgie: <<6 10 10 2 -1 -5||

EDOs: 22, 146

Badness: 0.0440

11-limit

Commas: 50/49, 55/54, 99/98

POTE generator: ~9/7 = 435.386

Map: [<2 1 1 2 4|, <0 3 5 5 4|]

EDOs: 14c, 22, 58ce, 80ce, 102cde

Badness: 0.0231

13-limit

Commas: 50/49, 55/54, 65/63, 99/98

POTE generator: ~9/7 = 435.861

Map: [<2 1 1 2 4 3|, <0 3 5 5 4 6|]

EDOs: 14cf, 22

Badness: 0.0215

Urchin

Commas: 40/39, 50/49, 55/54, 66/65

POTE generator: ~9/7 = 437.078

Map: [<2 1 1 2 4 6|, <0 3 5 5 4 2|]

EDOs: 14c, 22f

Badness: 0.0252

Hedgepig

Commas: 50/49, 245/243, 385/384

POTE generator: ~9/7 = 435.425

Map: [<2 1 1 2 12|, <0 3 5 5 -7|]

EDOs: 22, 80c, 102cd, 124cd

Badness: 0.0684

Music

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

Nautilus

Commas: 49/48, 250/243

POTE generator: ~21/20 = 82.505

Map: [<1 2 3 3|, <0 -6 -10 -3|]

Wedgie: <<6 10 3 2 -12 -21||

EDOs: 15, 29, 43cd, 44d, 59d, 73cd, 102cd

11-limit

Commas: 49/48, 55/54, 245/242

POTE generator: ~21/20 = 82.504

Map: [<1 2 3 3 4|, <0 -6 -10 -3 -8|]

EDOs: 14c, 15, 29, 43cde, 44d, 59d, 73cde, 102cde

13-limit

Commas: 49/48, 55/54, 91/90, 100/99

POTE generator: ~21/20 = 62.530

Map: [<1 2 3 3 4 5|, <0 -6 -10 -3 -8 -19|]

EDOs: 15f, 29, 43cde, 44d, 59df, 73cde, 102cde

Badness: 0.0223

Belauensis

Commas: 40/39, 49/48, 55/54, 66/65

POTE generator: ~21/20 = ~14/13 = 81.759

Map: [<1 2 3 3 4 4|, <0 -6 -10 -3 -8 -4|]

EDOs: 14c, 15, 29f, 44df

Badness: 0.0298

Nautilus Reverie by Igliashon Calvin Jones-Coolidge

Ammonite

Commas: 250/243, 686/675

POTE generator: ~9/7 = 454.448

Map: [<1 5 8 10|, <0 -9 -15 -19|]

Wedgie: <<9 15 19 3 5 2||

EDOs: 29, 37, 66

Badness: 0.1077

11-limit

Commas: 55/54, 100/99, 686/675

POTE generator: ~9/7 = 454.512

Map: [<1 5 8 10 8|, <0 -9 -15 -19 -12|]

EDOs: 29, 37, 66

Badness: 0.0457

13-limit

Commas: 55/54, 91/90, 100/99, 169/168

POTE generator: ~13/10 = 454.429

Map: [<1 5 8 10 8 9|, <0 -9 -15 -19 -12 -14|]

EDOs: 29, 37, 66

Badness: 0.0272

Ceratitid

Commas: 250/243, 1728/1715

POTE generator: ~36/35 = 54.384

Map: [<1 2 3 3|, <0 -9 -15 -4|]

Wedgie: <<9 15 4 3 -19 -33||

EDOs: 22

Badness: 0.115

11-limit

Commas: 55/54, 100/99, 5324/5145

POTE generator: ~36/35 = 54.376

Map: [<1 2 3 3 4|, <0 -9 -15 -4 -12|]

EDOs: 22

Badness: 0.0513

13-limit

Commas: 55/54, 65/63, 100/99, 352/343

POTE generator: ~36/35 = 54.665

Map: [<1 2 3 3 4 4|, <0 -9 -15 -4 -12 -7|]

EDOs: 22

Badness: 0.0447

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