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Main article: [[Porcupine_intervals|Porcupine intervals]]
Main article: [[Porcupine_intervals|Porcupine intervals]]


{| class="wikitable"
{| class="wikitable" style="text-align:center"
|-
! Generators
! | Generators
! Cents
! | Cents
! Ratios
! | Ratios
! Ups and Downs <br> notation
! | Ups and Downs
! Generators
 
! 2/1 inverse
notation
! Ratios
! | Generators
! Ups and Downs <br> notation
! | 2/1 inverse
! | Ratios
! | Ups and Downs
 
notation
|-
|-
| style="text-align:center;" | 0
| 0
| style="text-align:right;" | 0.00
| style="text-align:right;" | 0.00
| style="text-align:center;" | 1/1
| 1/1
| style="text-align:center;" | P1
| P1
| style="text-align:center;" | 0
| 0
| style="text-align:right;" | 1200.00
| style="text-align:right;" | 1200.00
| style="text-align:center;" | 2/1
| 2/1
| style="text-align:center;" | P8
| P8
|-
|-
| style="text-align:center;" | 1
| 1
| style="text-align:right;" | 162.75
| style="text-align:right;" | 162.75
| style="text-align:center;" | 12/11~11/10~10/9
| 12/11~11/10~10/9
| style="text-align:center;" | vM2 = ^^m2
| vM2 = ^^m2
| style="text-align:center;" | -1
| -1
| style="text-align:right;" | 1037.25
| style="text-align:right;" | 1037.25
| style="text-align:center;" | 9/5~20/11~11/6
| 9/5~20/11~11/6
| style="text-align:center;" | ^m7 = vvM7
| ^m7 = vvM7
|-
|-
| style="text-align:center;" | 2
| 2
| style="text-align:right;" | 325.50
| style="text-align:right;" | 325.50
| style="text-align:center;" | 6/5~11/9
| 6/5~11/9
| style="text-align:center;" | ^m3 = vvM3
| ^m3 = vvM3
| style="text-align:center;" | -2
| -2
| style="text-align:right;" | 874.50
| style="text-align:right;" | 874.50
| style="text-align:center;" | 18/11~5/3
| 18/11~5/3
| style="text-align:center;" | vM6 = ^^m6
| vM6 = ^^m6
|-
|-
| style="text-align:center;" | 3
| 3
| style="text-align:right;" | 488.25
| style="text-align:right;" | 488.25
| style="text-align:center;" | 4/3
| 4/3
| style="text-align:center;" | P4
| P4
| style="text-align:center;" | -3
| -3
| style="text-align:right;" | 711.75
| style="text-align:right;" | 711.75
| style="text-align:center;" | 3/2
| 3/2
| style="text-align:center;" | P5
| P5
|-
|-
| style="text-align:center;" | 4
| 4
| style="text-align:right;" | 651.00
| style="text-align:right;" | 651.00
| style="text-align:center;" | 16/11~22/15
| 16/11~22/15
| style="text-align:center;" | v5 = ^^d5
| v5 = ^^d5
| style="text-align:center;" | -4
| -4
| style="text-align:right;" | 549.00
| style="text-align:right;" | 549.00
| style="text-align:center;" | 15/11~11/8
| 15/11~11/8
| style="text-align:center;" | ^4 = vvA4
| ^4 = vvA4
|-
|-
| style="text-align:center;" | 5
| 5
| style="text-align:right;" | 813.75
| style="text-align:right;" | 813.75
| style="text-align:center;" | 8/5
| 8/5
| style="text-align:center;" | ^m6 = vvM6
| ^m6 = vvM6
| style="text-align:center;" | -5
| -5
| style="text-align:right;" | 386.25
| style="text-align:right;" | 386.25
| style="text-align:center;" | 5/4
| 5/4
| style="text-align:center;" | vM3 = ^^m3
| vM3 = ^^m3
|-
|-
| style="text-align:center;" | 6
| 6
| style="text-align:right;" | 976.50
| style="text-align:right;" | 976.50
| style="text-align:center;" | 7/4~16/9
| 7/4~16/9
| style="text-align:center;" | m7
| m7
| style="text-align:center;" | -6
| -6
| style="text-align:right;" | 223.50
| style="text-align:right;" | 223.50
| style="text-align:center;" | 9/8~8/7
| 9/8~8/7
| style="text-align:center;" | M2
| M2
|-
|-
| style="text-align:center;" | 7
| 7
| style="text-align:right;" | 1139.25
| style="text-align:right;" | 1139.25
| style="text-align:center;" | 48/25~160/81
| 48/25~160/81
| style="text-align:center;" | v8 = ^^d8
| v8 = ^^d8
| style="text-align:center;" | -7
| -7
| style="text-align:right;" | 60.75
| style="text-align:right;" | 60.75
| style="text-align:center;" | 81/80~25/24
| 81/80~25/24
| style="text-align:center;" | ^1 = vvA1
| ^1 = vvA1
|-
|-
| style="text-align:center;" | 8
| 8
| style="text-align:right;" | 102.00
| style="text-align:right;" | 102.00
| style="text-align:center;" | 16/15~21/20
| 16/15~21/20
| style="text-align:center;" | ^m2 = vvM2
| ^m2 = vvM2
| style="text-align:center;" | -8
| -8
| style="text-align:right;" | 1098.00
| style="text-align:right;" | 1098.00
| style="text-align:center;" | 40/21~15/8
| 40/21~15/8
| style="text-align:center;" | vM7 = ^^m7
| vM7 = ^^m7
|-
|-
| style="text-align:center;" | 9
| 9
| style="text-align:right;" | 264.75
| style="text-align:right;" | 264.75
| style="text-align:center;" | 7/6
| 7/6
| style="text-align:center;" | m3
| m3
| style="text-align:center;" | -9
| -9
| style="text-align:right;" | 935.25
| style="text-align:right;" | 935.25
| style="text-align:center;" | 12/7
| 12/7
| style="text-align:center;" | M6
| M6
|-
|-
| style="text-align:center;" | 10
| 10
| style="text-align:right;" | 427.50
| style="text-align:right;" | 427.50
| style="text-align:center;" | 14/11
| 14/11
| style="text-align:center;" | v4 = ^^d4
| v4 = ^^d4
| style="text-align:center;" | -10
| -10
| style="text-align:right;" | 772.50
| style="text-align:right;" | 772.50
| style="text-align:center;" | 11/7
| 11/7
| style="text-align:center;" | ^5 = vvA5
| ^5 = vvA5
|-
|-
| style="text-align:center;" | 11
| 11
| style="text-align:right;" | 590.25
| style="text-align:right;" | 590.25
| style="text-align:center;" | 7/5
| 7/5
| style="text-align:center;" | ^d5 = vv5
| ^d5 = vv5
| style="text-align:center;" | -11
| -11
| style="text-align:right;" | 609.75
| style="text-align:right;" | 609.75
| style="text-align:center;" | 10/7
| 10/7
| style="text-align:center;" | vA4 = ^^4
| vA4 = ^^4
|-
|-
| style="text-align:center;" | 12
| 12
| style="text-align:right;" | 753.00
| style="text-align:right;" | 753.00
| style="text-align:center;" | 14/9
| 14/9
| style="text-align:center;" | m6
| m6
| style="text-align:center;" | -12
| -12
| style="text-align:right;" | 447.00
| style="text-align:right;" | 447.00
| style="text-align:center;" | 9/7
| 9/7
| style="text-align:center;" | M3
| M3
|}
|}
The specific tuning shown is the full 11-limit [[POTE_tuning|POTE tuning]], but of course there is a range of acceptible porcupine tunings that includes generators as small as 160 cents ([[15edo|15edo]]) and as large as 165.5 cents ([[29edo|29edo]]). (However, the 29edo patent val does not support 11-limit porcupine proper, not annihilating 64/63.)
The specific tuning shown is the full 11-limit [[POTE_tuning|POTE tuning]], but of course there is a range of acceptible porcupine tunings that includes generators as small as 160 cents ([[15edo|15edo]]) and as large as 165.5 cents ([[29edo|29edo]]). (However, the 29edo patent val does not support 11-limit porcupine proper, not annihilating 64/63.)
Line 151: Line 146:


{| class="wikitable"
{| class="wikitable"
| [[File:OtonalPentad_JI.mp3]]
| [[File:OtonalPentad_22edo.mp3]]
| [[File:OtonalPentad_29edo.mp3]]
|-
|-
| | [[File:OtonalPentad_JI.mp3]]
| 8:9:10:11:12 chord, in just intonation. <br> All intervals are slightly different.
| | [[File:OtonalPentad_22edo.mp3]]
| Porcupine-tempered 8:9:10:11:12 chord, in [[22edo|22edo]]. <br> Except the first, the intervals are the same.
| | [[File:OtonalPentad_29edo.mp3]]
| Porcupine-tempered 8:9:10:11:12 chord, in [[29edo|29edo]]. <br> Except the first, the intervals are the same.
|-
| | 8:9:10:11:12 chord, in just intonation.
 
All intervals are slightly different.
| | Porcupine-tempered 8:9:10:11:12 chord, in [[22edo|22edo]].
 
Except the first, the intervals are the same.
| | Porcupine-tempered 8:9:10:11:12 chord, in [[29edo|29edo]].
 
Except the first, the intervals are the same.
|}
|}


Line 174: Line 162:


{| class="wikitable"
{| class="wikitable"
! Eigenmonzo
! Neutral Second
!
|-
|-
! | Eigenmonzo
| 13/12
! | Neutral Second
| 138.573
! |  
|-
|-
| | 13/12
| 13/11
| | 138.573
| 144.605
|-
|-
| | 13/11
| 12/11
| | 144.605
| 150.637
|-
|-
| | 12/11
| 13/10
| | 150.637
| 151.405
|-
|-
| | 13/10
| 6/5
| | 151.405
| 157.821
|-
|-
| | 6/5
| 15/13
| | 157.821
| 158.710
|-
|-
| | 15/13
| 18/13
| | 158.710
| 159.154
|-
|-
| | 18/13
| 2\15
| | 159.154
| 160.000
|-
|-
| | 2\15
| 8/7
| | 160.000
| 161.471
|-
|-
| | 8/7
| 14/11
| | 161.471
| 161.751
|-
|-
| | 14/11
| 7/5
| | 161.751
| 162.047
|-
|-
| | 7/5
| 5\37
| | 162.047
| 162.162
|-
|-
| | 5\37
| 11/8
| | 162.162
| 162.171 13- and 15-limit minimax
|-
|-
| | 11/8
| 8\59
| | 162.171 13- and 15-limit minimax
| 162.712
|-
|-
| | 8\59
| 5/4
| | 162.712
| 162.737 5-limit minimax
|-
|-
| | 5/4
| 15/14
| | 162.737 5-limit minimax
| 162.897
|-
|-
| | 15/14
| 7/6
| | 162.897
| 162.986
|-
|-
| | 7/6
| 3\22
| | 162.986
| 163.636
|-
|-
| | 3\22
| 9/7
| | 163.636
| 163.743 7- 9- and 11-limit minimax
|-
|-
| | 9/7
| 16/15
| | 163.743 7- 9- and 11-limit minimax
| 163.966
|-
|-
| | 16/15
| 7\51
| | 163.966
| 164.706
|-
|-
| | 7\51
| 11/10
| | 164.706
| 165.004
|-
|-
| | 11/10
| 4\29
| | 165.004
| 165.517
|-
|-
| | 4\29
| 15/11
| | 165.517
| 165.762
|-
|-
| | 15/11
| 4/3
| | 165.762
| 166.015
|-
|-
| | 4/3
| 14/13
| | 166.015
| 166.037
|-
|-
| | 14/13
| 11/9
| | 166.037
| 173.704
|-
|-
| | 11/9
| 16/13
| | 173.704
| 179.736
|-
|-
| | 16/13
| 10/9
| | 179.736
| 182.404
|-
| | 10/9
| | 182.404
|}
|}
[8/5 12/7] eigenmonzos: [[porcupinewoo15|porcupinewoo15]] [[porcupinewoo22|porcupinewoo22]]
[8/5 12/7] eigenmonzos: [[porcupinewoo15|porcupinewoo15]] [[porcupinewoo22|porcupinewoo22]]


Line 271: Line 259:


{| class="wikitable"
{| class="wikitable"
| 12/11
| 150.637
|-
|-
| | 12/11
| 6/5
| | 150.637
| 157.821
|-
| | 6/5
| | 157.821
|-
|-
| | 2\15
| 2\15
| | 160.000
| 160.000
|-
|-
| | 18/13
| 18/13
| | 160.307
| 160.307
|-
|-
| | 15/13
| 15/13
| | 160.860
| 160.860
|-
|-
| | 8/7
| 8/7
| | 161.471
| 161.471
|-
|-
| | 13/12
| 13/12
| | 161.531
| 161.531
|-
|-
| | 14/11
| 14/11
| | 161.751
| 161.751
|-
|-
| | 7/5
| 7/5
| | 162.047
| 162.047
|-
|-
| | 14/13
| 14/13
| | 162.100
| 162.100
|-
|-
| | 13/10
| 13/10
| | 162.149
| 162.149
|-
|-
| | 5\37
| 5\37
| | 162.162
| 162.162
|-
|-
| | 11/8
| 11/8
| | 162.171
| 162.171
|-
|-
| | 16/13
| 16/13
| | 162.322
| 162.322
|-
|-
| | 13/11
| 13/11
| | 162.368 13- and 15-limit minimax
| 162.368 13- and 15-limit minimax
|-
|-
| | 8\59
| 8\59
| | 162.712
| 162.712
|-
|-
| | 5/4
| 5/4
| | 162.737
| 162.737
|-
|-
| | 15/14
| 15/14
| | 162.897
| 162.897
|-
|-
| | 7/6
| 7/6
| | 162.986
| 162.986
|-
|-
| | 3\22
| 3\22
| | 163.636
| 163.636
|-
|-
| | 9/7
| 9/7
| | 163.743
| 163.743
|-
|-
| | 16/15
| 16/15
| | 163.966
| 163.966
|-
|-
| | 7\51
| 7\51
| | 164.706
| 164.706
|-
|-
| | 11/10
| 11/10
| | 165.004
| 165.004
|-
|-
| | 4\29
| 4\29
| | 165.517
| 165.517
|-
|-
| | 15/11
| 15/11
| | 165.762
| 165.762
|-
|-
| | 4/3
| 4/3
| | 166.015
| 166.015
|-
|-
| | 11/9
| 11/9
| | 173.704
| 173.704
|-
|-
| | 10/9
| 10/9
| | 182.404
| 182.404
|}
|}


Line 364: Line 351:


==See also==
==See also==
[[Chords_of_porcupine|Chords of porcupine]]


[[Porcupine_Notation|Porcupine Notation]]
* [[Chords_of_porcupine|Chords of porcupine]]
* [[Porcupine_Notation|Porcupine Notation]]
* [[Porcupine_modes|Porcupine modes]]
* [[Porcupine_Album_Project|Porcupine Album Project]]


[[Porcupine_modes|Porcupine modes]]
==Musical examples==


[[Porcupine_Album_Project|Porcupine Album Project]]
* ''[http://sites.google.com/site/teamouse/home#TOC-Mizarian-music Mizarian Porcupine Overture]'', [[Herman Miller]], 1999. (15edo, namesake of the temperament)
* ''[http://www.myspace.com/paulerlich/music/songs/glassic-in-22-tone-equal-temperament-45202095 Glassic]'', [[Paul Erlich]], [[22edo]] (at least the beginning part is in porcupine).
* ''[http://www.archive.org/download/NightOnPorcupineMountain/Genewardsmithmussorgsky-NightOnPorcupineMountain.mp3 Night on Porcupine Mountain]'', Gene Ward Smith and Modest Mussorgsky, [[22edo]].
* ''[http://soundclick.com/share.cfm?id=8839060 being a]'', Andrew Heathwaite, 2010, 22edo, mode 3 1 3 3 3 3 3 3 of Porcupine[8].
* ''[http://micro.soonlabel.com/15-ET/daily20110619_millers_porcupine_7a.mp3 Playing Gently with Miller's Porcupine]'' by [[Chris Vaisvil]]
* ''[http://micro.soonlabel.com/15-ET/daily20111231-porcupine15-indian.mp3 15 Porcupines in India]'', Sarangi, Tambura and Sitar improvisation by [[Chris Vaisvil]]
* ''[http://micro.soonlabel.com/15-ET/daily20111231-porcupine15-piano.mp3 15 Quills]'' piano solo by Chris Vaisvil
* ''[http://micro.soonlabel.com/15-ET/daily20111231-porcupine15-prickly-side-of-love.mp3 Prickly Side of Love]'' - rock band in Porcupine Temperament with vocals by Chris Vaisvil
* ''[http://micro.soonlabel.com/15-ET/daily20120102-porcupine-organ.mp3 Porcupine Organ Composition]'' by [[Chris Vaisvil]]
* ''[[:File:AmongOtherThings2.mp3|Among Other Things 2]]'' by [[Petr Pařízek]]
* ''[http://micro.soonlabel.com/gene_ward_smith/Others/Freivald/porcupine-comma-pump.mp3 Porcupine Comma Pump]'', by [[Jake Freivald]]
* [http://www.youtube.com/watch?v=DSao0Yg3Tck Life on Mars] by [[Omega9]]
* [https://www.youtube.com/watch?v=se79rdp705Y Flying Straight Down] by [[John Moriarty]]


==Musical examples==
<ul><li>"[http://sites.google.com/site/teamouse/home#TOC-Mizarian-music Mizarian Porcupine Overture]", Herman Miller, 1999. (15edo, namesake of the temperament)</li><li>"[http://www.myspace.com/paulerlich/music/songs/glassic-in-22-tone-equal-temperament-45202095 Glassic]", Paul Erlich, [[22edo|22edo]] (at least the beginning part is in porcupine).</li><li>"<span style=""><span style="">''[http://www.archive.org/download/NightOnPorcupineMountain/Genewardsmithmussorgsky-NightOnPorcupineMountain.mp3 Night on Porcupine Mountain]''</span></span>", Gene Ward Smith and Modest Mussorgsky, [[22edo|22edo]].</li><li>"[http://soundclick.com/share.cfm?id=8839060 being a]", Andrew Heathwaite, 2010, 22edo, mode 3 1 3 3 3 3 3 3 of Porcupine[8].</li><li><span style=""><span style="">''[http://micro.soonlabel.com/15-ET/daily20110619_millers_porcupine_7a.mp3 Playing Gently with Miller's Porcupine]''</span></span>, [[Chris_Vaisvil|Chris Vaisvil]]</li><li><span style=""><span style="">''[http://micro.soonlabel.com/15-ET/daily20111231-porcupine15-indian.mp3 15 Porcupines in India]''</span></span>, Sarangi, Tambura and Sitar improvisation by [[Chris_Vaisvil|Chris Vaisvil]]</li><li><span style=""><span style="">''[http://micro.soonlabel.com/15-ET/daily20111231-porcupine15-piano.mp3 15 Quills]''</span></span> piano solo by Chris Vaisvil</li><li><span style=""><span style="">''[http://micro.soonlabel.com/15-ET/daily20111231-porcupine15-prickly-side-of-love.mp3 Prickly Side of Love]''</span></span> - rock band in Porcupine Temperament with vocals by Chris Vaisvil</li><li><span style="">''[http://micro.soonlabel.com/15-ET/daily20120102-porcupine-organ.mp3 Porcupine Organ Composition]''</span> by [[Chris_Vaisvil|Chris Vaisvil]]</li><li>''[[:File:AmongOtherThings2.mp3|Among Other Things 2]]'' by Petr Pařízek</li><li>''[http://micro.soonlabel.com/gene_ward_smith/Others/Freivald/porcupine-comma-pump.mp3 Porcupine Comma Pump]'', by Jake Freivald</li><li>[http://www.youtube.com/watch?v=DSao0Yg3Tck Life on Mars] by Omega9</li><li>[https://www.youtube.com/watch?v=se79rdp705Y Flying Straight Down] by John Moriarty
</li></ul>
==Images==
==Images==
[[File:porcupine8.jpg|alt=porcupine8.jpg|porcupine8.jpg]]       
[[File:porcupine8.jpg|alt=porcupine8.jpg|porcupine8.jpg]]       
[[Category:soft_redirect]]
[[Category:soft_redirect]]
Retrieved from "https://en.xen.wiki/w/Porcupine"