Xenharmonic Wiki

Porcupine family: Difference between revisions

← Older editNewer edit →
VisualWikitext
Xenwolf (talk | contribs)
autopatrolled, Bureaucrats, confirmaccount-notify, Interface administrators, Sysops
8,705 edits
m recat
m Cleanup
Line 1: Line 1:
<span style="display: block; text-align: right;">[[de:Porcupine]]</span>
<span style="display: block; text-align: right;">[[de:Porcupine]]</span>
-----
-----
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]] 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 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 &lt;&lt;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>. 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)
Line 13: Line 13:
Map: [&lt;1 2 3|, &lt;0 -3 -5|]
Map: [&lt;1 2 3|, &lt;0 -3 -5|]


EDOs: [[7edo|7]], [[15edo|15]], [[22edo|22]], [[95edo|95c]], [[117edo|117bc]], [[139edo|139bc]], [[161edo|161bc]], [[183edo|183bc]]
EDOs: {{EDOs| 7, 15, 22, 95c, 117bc, 139bc, 161bc, 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|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]].
The second comma of the [[Normal lists|normal comma list]] defines which [[7-limit]] family member we are looking at. That means [[64/63]], the Archytas comma, for [[#Porcupine|porcupine]], [[36/35]], the septimal quarter tone, for [[#Hystrix|hystrix]], [[50/49]], the jubilisma, for [[#Hedgehog|hedgehog]], and [[49/48]], the slendro diesis, for [[#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]]. 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.
{{main| 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]]. 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: 64/63, 250/243
Commas: 64/63, 250/243
Line 31: Line 33:
strict range: [160.000, 163.636]
strict range: [160.000, 163.636]


[[POTE_tuning|POTE generator]]: ~10/9 = 162.880
[[POTE generator]]: ~10/9 = 162.880


7- and 9-limit minimax eigenmonzo: 9/7
7- and 9-limit minimax eigenmonzo: 9/7
Line 37: Line 39:
Map: [&lt;1 2 3 2|, &lt;0 -3 -5 6|]
Map: [&lt;1 2 3 2|, &lt;0 -3 -5 6|]


EDOs: 7, 15, 22, [[59edo|59]], [[81edo|81bd]], [[140edo|140bbd]]
EDOs: {{EDOs| 7, 15, 22, 59, 81bd, 140bbd }}


Badness: 0.0411
Badness: 0.0411


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


Line 56: Line 58:
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: {{EDOs| 7, 15, 22, 37, 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


Line 75: Line 77:
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: {{EDOs| 7, 15, 22f, 37f }}


Badness: 0.0213
Badness: 0.0213


==Porcupinefish==
=== Porcupinefish ===
See also: [[The_Biosphere|The Biosphere]]
{{see also| The Biosphere }}


Commas: 55/54, 64/63, 91/90, 100/99
Commas: 55/54, 64/63, 91/90, 100/99
Line 96: Line 98:
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: {{EDOs| 15, 22, 37, 59, 96b }}


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


Line 109: Line 111:
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: {{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


Line 122: Line 124:
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: {{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]]. They can try the even sharper fifth of hystrix in [[68edo]] and see how that suits.


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


[[POTE_tuning|POTE generator]]: ~8/7 = 158.868
[[POTE generator]]: ~8/7 = 158.868


7- and 9-limit minimax eigenmonzo: 5/4
7- and 9-limit minimax eigenmonzo: 5/4
Line 137: Line 139:
Map: [&lt;1 2 3 3|, &lt;0 -3 -5 -1|]
Map: [&lt;1 2 3 3|, &lt;0 -3 -5 -1|]


EDOs: 7, 8d, 15d
EDOs: {{EDOs| 7, 8d, 15d }}


Badness: 0.0449
Badness: 0.0449


==11-limit==
== 11-limit ==
Commas: 22/21, 36/35, 80/77
Commas: 22/21, 36/35, 80/77


Line 148: Line 150:
Map: [&lt;1 2 3 3 4|, &lt;0 -3 -5 -1 -4|]
Map: [&lt;1 2 3 3 4|, &lt;0 -3 -5 -1 -4|]


EDOs: 7, 8d, 15d
EDOs: {{EDOs| 7, 8d, 15d }}


Badness: 0.0268
Badness: 0.0268


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


Line 163: Line 165:
Wedgie: &lt;&lt;3 5 16 1 17 23||
Wedgie: &lt;&lt;3 5 16 1 17 23||


EDOs: 7d, 15d, 22, 29, 51, 73c
EDOs: {{EDOs| 7d, 15d, 22, 29, 51, 73c }}


Badness: 0.0544
Badness: 0.0544


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


Line 176: Line 178:
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: 7d, 15d, 22, 29, 51, 73ce
EDOs: {{EDOs| 7d, 15d, 22, 29, 51, 73ce }}


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 187: Line 189:
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: 7d, 22, 29, 51f, 80cdeff
EDOs: {{EDOs| 7d, 22, 29, 51f, 80cdeff }}


Badness: 0.0265
Badness: 0.0265


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


Line 202: Line 204:
Wedgie: &lt;&lt;3 5 -13 1 -29 -44||
Wedgie: &lt;&lt;3 5 -13 1 -29 -44||


EDOs: 7, 29, 65c, 94cd
EDOs: {{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


Line 215: Line 217:
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: {{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


Line 228: Line 230:
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: {{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. 22edo provides the obvious tuning, but if you are looking for an alternative, you could try the &lt;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. 22edo provides the obvious tuning, but if you are looking for an alternative, you could try the &lt;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 243: Line 245:
Wedgie: &lt;&lt;6 10 10 2 -1 -5||
Wedgie: &lt;&lt;6 10 10 2 -1 -5||


EDOs: 8d, 14c, 22, [[146edo|146bccdd]]
EDOs: {{EDOs| 8d, 14c, 22, 146bccdd }}


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 254: Line 256:
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: {{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 265: Line 267:
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: {{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 276: Line 278:
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: {{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 287: Line 289:
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: {{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 303: Line 305:
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: {{EDOs| 15, 29, 43cd, 44d, 59d, 73cd, 102cd }}


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


Line 312: Line 314:
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: {{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 321: Line 323:
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: {{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 332: Line 334:
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: {{EDOs| 14c, 15, 29f, 44df }}


Badness: 0.0298
Badness: 0.0298
Line 338: Line 340:
[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 347: Line 349:
Wedgie: &lt;&lt;9 15 19 3 5 2||
Wedgie: &lt;&lt;9 15 19 3 5 2||


EDOs: 29, 37, 66
EDOs: {{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 358: Line 360:
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: {{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 369: Line 371:
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: {{EDOs| 29, 37, 66 }}


Badness: 0.0272
Badness: 0.0272


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


Line 382: Line 384:
Wedgie: &lt;&lt;9 15 4 3 -19 -33||
Wedgie: &lt;&lt;9 15 4 3 -19 -33||


EDOs: 22
EDOs: {{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 393: Line 395:
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: {{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 404: Line 406:
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: {{EDOs| 22 }}


Badness: 0.0447
Badness: 0.0447
Line 411: Line 413:
[[Category:Temperament family]]
[[Category:Temperament family]]
[[Category:Porcupine]]
[[Category:Porcupine]]
[[Category:Rank 2]]
Retrieved from "https://en.xen.wiki/w/Porcupine_family"