31edo: Difference between revisions
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<span style="display: block; text-align: right;">[[:de:31edo|Deutsch]]</span> | <span style="display: block; text-align: right;">[[:de:31edo|Deutsch]]</span> | ||
__FORCETOC__ | __FORCETOC__ | ||
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| style="text-align:center;" | 18.242 | | style="text-align:center;" | 18.242 | ||
|} | |} | ||
===Patent val mapping=== | ===Patent val mapping=== | ||
| Line 3,881: | Line 3,881: | ||
|- | |- | ||
! | quality | ! | quality | ||
! | color | ! | [[Kite's color notation|color]] | ||
! | monzo format | ! | monzo format | ||
! | examples | ! | examples | ||
|- | |- | ||
| style="text-align:center;" | downminor | | style="text-align:center;" | downminor | ||
| style="text-align:center;" | | | style="text-align:center;" | zo | ||
| style="text-align:center;" | {a, b, 0, 1} | | style="text-align:center;" | {a, b, 0, 1} | ||
| style="text-align:center;" | 7/6, 7/4 | | style="text-align:center;" | 7/6, 7/4 | ||
|- | |- | ||
| style="text-align:center;" | minor | | style="text-align:center;" | minor | ||
| style="text-align:center;" | fourthward | | style="text-align:center;" | fourthward wa | ||
| style="text-align:center;" | {a, b}, b < -1 | | style="text-align:center;" | {a, b}, b < -1 | ||
| style="text-align:center;" | 32/27, 16/9 | | style="text-align:center;" | 32/27, 16/9 | ||
|- | |- | ||
| style="text-align:center;" | " | | style="text-align:center;" | " | ||
| style="text-align:center;" | | | style="text-align:center;" | gu | ||
| style="text-align:center;" | {a, b, -1} | | style="text-align:center;" | {a, b, -1} | ||
| style="text-align:center;" | 6/5, 9/5 | | style="text-align:center;" | 6/5, 9/5 | ||
|- | |- | ||
| style="text-align:center;" | mid | | style="text-align:center;" | mid | ||
| style="text-align:center;" | | | style="text-align:center;" | lova | ||
| style="text-align:center;" | {a, b, 0, 0, 1} | | style="text-align:center;" | {a, b, 0, 0, 1} | ||
| style="text-align:center;" | 11/9, 11/6 | | style="text-align:center;" | 11/9, 11/6 | ||
|- | |- | ||
| style="text-align:center;" | " | | style="text-align:center;" | " | ||
| style="text-align:center;" | | | style="text-align:center;" | lu | ||
| style="text-align:center;" | {a, b, 0, 0, -1} | | style="text-align:center;" | {a, b, 0, 0, -1} | ||
| style="text-align:center;" | 12/11, 18/11 | | style="text-align:center;" | 12/11, 18/11 | ||
|- | |- | ||
| style="text-align:center;" | major | | style="text-align:center;" | major | ||
| style="text-align:center;" | | | style="text-align:center;" | yo | ||
| style="text-align:center;" | {a, b, 1} | | style="text-align:center;" | {a, b, 1} | ||
| style="text-align:center;" | 5/4, 5/3 | | style="text-align:center;" | 5/4, 5/3 | ||
|- | |- | ||
| style="text-align:center;" | " | | style="text-align:center;" | " | ||
| style="text-align:center;" | fifthward | | style="text-align:center;" | fifthward wa | ||
| style="text-align:center;" | {a, b}, b > 1 | | style="text-align:center;" | {a, b}, b > 1 | ||
| style="text-align:center;" | 9/8, 27/16 | | style="text-align:center;" | 9/8, 27/16 | ||
|- | |- | ||
| style="text-align:center;" | upmajor | | style="text-align:center;" | upmajor | ||
| style="text-align:center;" | | | style="text-align:center;" | ru | ||
| style="text-align:center;" | {a, b, 0, -1} | | style="text-align:center;" | {a, b, 0, -1} | ||
| style="text-align:center;" | 9/7, 12/7 | | style="text-align:center;" | 9/7, 12/7 | ||
|} | |} | ||
All 31edo chords can be named using ups and downs. Here are the | All 31edo chords can be named using ups and downs. Here are the zo, gu, lova, yo and ru triads: | ||
{| class="wikitable" | {| class="wikitable" | ||
|- | |- | ||
! | color of the 3rd | ! | [[Kite's color notation|color of the 3rd]] | ||
! | JI chord | ! | JI chord | ||
! | notes as edosteps | ! | notes as edosteps | ||
| Line 3,936: | Line 3,936: | ||
! | spoken name | ! | spoken name | ||
|- | |- | ||
| style="text-align:center;" | | | style="text-align:center;" | zo | ||
| style="text-align:center;" | 6:7:9 | | style="text-align:center;" | 6:7:9 | ||
| style="text-align:center;" | 0-7-18 | | style="text-align:center;" | 0-7-18 | ||
| Line 3,943: | Line 3,943: | ||
| style="text-align:center;" | C downminor | | style="text-align:center;" | C downminor | ||
|- | |- | ||
| style="text-align:center;" | | | style="text-align:center;" | gu | ||
| style="text-align:center;" | 10:12:15 | | style="text-align:center;" | 10:12:15 | ||
| style="text-align:center;" | 0-8-18 | | style="text-align:center;" | 0-8-18 | ||
| Line 3,950: | Line 3,950: | ||
| style="text-align:center;" | C minor | | style="text-align:center;" | C minor | ||
|- | |- | ||
| style="text-align:center;" | | | style="text-align:center;" | lova | ||
| style="text-align:center;" | 18:22:27 | | style="text-align:center;" | 18:22:27 | ||
| style="text-align:center;" | 0-9-18 | | style="text-align:center;" | 0-9-18 | ||
| Line 3,957: | Line 3,957: | ||
| style="text-align:center;" | C mid | | style="text-align:center;" | C mid | ||
|- | |- | ||
| style="text-align:center;" | | | style="text-align:center;" | yo | ||
| style="text-align:center;" | 4:5:6 | | style="text-align:center;" | 4:5:6 | ||
| style="text-align:center;" | 0-10-18 | | style="text-align:center;" | 0-10-18 | ||
| Line 3,964: | Line 3,964: | ||
| style="text-align:center;" | C major or C | | style="text-align:center;" | C major or C | ||
|- | |- | ||
| style="text-align:center;" | | | style="text-align:center;" | ru | ||
| style="text-align:center;" | 14:18:27 | | style="text-align:center;" | 14:18:27 | ||
| style="text-align:center;" | 0-11-18 | | style="text-align:center;" | 0-11-18 | ||
| Line 4,104: | Line 4,104: | ||
|- | |- | ||
| style="text-align:center;" | 34171875/33554432 | | style="text-align:center;" | 34171875/33554432 | ||
| | | -25 7 6 > | | |<nowiki> | -25 7 6 </nowiki>> | ||
| style="text-align:right;" | 31.567 | | style="text-align:right;" | 31.567 | ||
| style="text-align:center;" | [[ampersand|Ampersand's Comma]] | | style="text-align:center;" | [[ampersand|Ampersand's Comma]] | ||
| Line 4,111: | Line 4,111: | ||
|- | |- | ||
| style="text-align:center;" | 81/80 | | style="text-align:center;" | 81/80 | ||
| | | -4 4 -1 > | | |<nowiki> | -4 4 -1 </nowiki>> | ||
| style="text-align:right;" | 21.506 | | style="text-align:right;" | 21.506 | ||
| style="text-align:center;" | [[Syntonic_Comma|Syntonic Comma]] | | style="text-align:center;" | [[Syntonic_Comma|Syntonic Comma]] | ||
| Line 4,118: | Line 4,118: | ||
|- | |- | ||
| style="text-align:center;" | 393216/390625 | | style="text-align:center;" | 393216/390625 | ||
| | | 17 1 -8 > | | |<nowiki> | 17 1 -8 </nowiki>> | ||
| style="text-align:right;" | 11.445 | | style="text-align:right;" | 11.445 | ||
| style="text-align:center;" | [[Würschmidt_comma|Würschmidt Comma]] | | style="text-align:center;" | [[Würschmidt_comma|Würschmidt Comma]] | ||
| Line 4,125: | Line 4,125: | ||
|- | |- | ||
| style="text-align:center;" | 2109375/2097152 | | style="text-align:center;" | 2109375/2097152 | ||
| | | -21 3 7 > | | |<nowiki> | -21 3 7 </nowiki>> | ||
| style="text-align:right;" | 10.061 | | style="text-align:right;" | 10.061 | ||
| style="text-align:center;" | [[semicomma|Semicomma]] | | style="text-align:center;" | [[semicomma|Semicomma]] | ||
| Line 4,132: | Line 4,132: | ||
|- | |- | ||
| style="text-align:center;" | 6719816/6714445 | | style="text-align:center;" | 6719816/6714445 | ||
| | | 38 -2 -15 > | | |<nowiki> | 38 -2 -15 </nowiki>> | ||
| style="text-align:right;" | 1.3843 | | style="text-align:right;" | 1.3843 | ||
| style="text-align:center;" | Hemithirds Comma | | style="text-align:center;" | Hemithirds Comma | ||
| Line 4,139: | Line 4,139: | ||
|- | |- | ||
| style="text-align:center;" | 9859966/9733137 | | style="text-align:center;" | 9859966/9733137 | ||
| | | -10 7 8 -7 > | | |<nowiki> | -10 7 8 -7 </nowiki>> | ||
| style="text-align:right;" | 22.413 | | style="text-align:right;" | 22.413 | ||
| style="text-align:center;" | Blackjackisma | | style="text-align:center;" | Blackjackisma | ||
| Line 4,146: | Line 4,146: | ||
|- | |- | ||
| style="text-align:center;" | 64827/64000 | | style="text-align:center;" | 64827/64000 | ||
| | | -9 3 -3 4 > | | |<nowiki> | -9 3 -3 4 </nowiki>> | ||
| style="text-align:right;" | 22.227 | | style="text-align:right;" | 22.227 | ||
| style="text-align:center;" | Squalentine | | style="text-align:center;" | Squalentine | ||
| Line 4,153: | Line 4,153: | ||
|- | |- | ||
| style="text-align:center;" | 2430/2401 | | style="text-align:center;" | 2430/2401 | ||
| | | 1 5 1 -4 > | | |<nowiki> | 1 5 1 -4 </nowiki>> | ||
| style="text-align:right;" | 20.785 | | style="text-align:right;" | 20.785 | ||
| style="text-align:center;" | Nuwell | | style="text-align:center;" | Nuwell | ||
| Line 4,160: | Line 4,160: | ||
|- | |- | ||
| style="text-align:center;" | 50421/50000 | | style="text-align:center;" | 50421/50000 | ||
| | | -4 1 -5 5 > | | |<nowiki> | -4 1 -5 5 </nowiki>> | ||
| style="text-align:right;" | 14.516 | | style="text-align:right;" | 14.516 | ||
| style="text-align:center;" | Trimyna | | style="text-align:center;" | Trimyna | ||
| Line 4,167: | Line 4,167: | ||
|- | |- | ||
| style="text-align:center;" | 126/125 | | style="text-align:center;" | 126/125 | ||
| | | 1 2 -3 1 > | | |<nowiki> | 1 2 -3 1 </nowiki>> | ||
| style="text-align:right;" | 13.795 | | style="text-align:right;" | 13.795 | ||
| style="text-align:center;" | [[126/125|Septimal Semicomma]] | | style="text-align:center;" | [[126/125|Septimal Semicomma]] | ||
| Line 4,174: | Line 4,174: | ||
|- | |- | ||
| style="text-align:center;" | 1728/1715 | | style="text-align:center;" | 1728/1715 | ||
| | | 6 3 -1 -3 > | | |<nowiki> | 6 3 -1 -3 </nowiki>> | ||
| style="text-align:right;" | 13.074 | | style="text-align:right;" | 13.074 | ||
| style="text-align:center;" | Orwellisma | | style="text-align:center;" | Orwellisma | ||
| Line 4,181: | Line 4,181: | ||
|- | |- | ||
| style="text-align:center;" | 1029/1024 | | style="text-align:center;" | 1029/1024 | ||
| | | -10 1 0 3 > | | |<nowiki> | -10 1 0 3 </nowiki>> | ||
| style="text-align:right;" | 8.4327 | | style="text-align:right;" | 8.4327 | ||
| style="text-align:center;" | Gamelisma | | style="text-align:center;" | Gamelisma | ||
| Line 4,188: | Line 4,188: | ||
|- | |- | ||
| style="text-align:center;" | 225/224 | | style="text-align:center;" | 225/224 | ||
| | | -5 2 2 -1 > | | |<nowiki> | -5 2 2 -1 </nowiki>> | ||
| style="text-align:right;" | 7.7115 | | style="text-align:right;" | 7.7115 | ||
| style="text-align:center;" | [[225/224|Septimal Kleisma]] | | style="text-align:center;" | [[225/224|Septimal Kleisma]] | ||
| Line 4,195: | Line 4,195: | ||
|- | |- | ||
| style="text-align:center;" | 16875/16807 | | style="text-align:center;" | 16875/16807 | ||
| | | 0 3 4 -5 > | | |<nowiki> | 0 3 4 -5 </nowiki>> | ||
| style="text-align:right;" | 6.9903 | | style="text-align:right;" | 6.9903 | ||
| style="text-align:center;" | Mirkwai | | style="text-align:center;" | Mirkwai | ||
| Line 4,202: | Line 4,202: | ||
|- | |- | ||
| style="text-align:center;" | 3136/3125 | | style="text-align:center;" | 3136/3125 | ||
| | | 6 0 -5 2 > | | |<nowiki> | 6 0 -5 2 </nowiki>> | ||
| style="text-align:right;" | 6.0832 | | style="text-align:right;" | 6.0832 | ||
| style="text-align:center;" | Hemimean | | style="text-align:center;" | Hemimean | ||
| Line 4,209: | Line 4,209: | ||
|- | |- | ||
| style="text-align:center;" | 6144/6125 | | style="text-align:center;" | 6144/6125 | ||
| | | 11 1 -3 -2 > | | |<nowiki> | 11 1 -3 -2 </nowiki>> | ||
| style="text-align:right;" | 5.3621 | | style="text-align:right;" | 5.3621 | ||
| style="text-align:center;" | Porwell | | style="text-align:center;" | Porwell | ||
| Line 4,216: | Line 4,216: | ||
|- | |- | ||
| style="text-align:center;" | 1065875/1063543 | | style="text-align:center;" | 1065875/1063543 | ||
| | | -26 -1 1 9 > | | |<nowiki> | -26 -1 1 9 </nowiki>> | ||
| style="text-align:right;" | 3.7919 | | style="text-align:right;" | 3.7919 | ||
| style="text-align:center;" | Wadisma | | style="text-align:center;" | Wadisma | ||
| Line 4,223: | Line 4,223: | ||
|- | |- | ||
| style="text-align:center;" | 65625/65536 | | style="text-align:center;" | 65625/65536 | ||
| | | -16 1 5 1 > | | |<nowiki> | -16 1 5 1 </nowiki>> | ||
| style="text-align:right;" | 2.3495 | | style="text-align:right;" | 2.3495 | ||
| style="text-align:center;" | Horwell | | style="text-align:center;" | Horwell | ||
| Line 4,230: | Line 4,230: | ||
|- | |- | ||
| style="text-align:center;" | 703125/702464 | | style="text-align:center;" | 703125/702464 | ||
| | | -11 2 7 -3 > | | |<nowiki> | -11 2 7 -3 </nowiki>> | ||
| style="text-align:right;" | 1.6283 | | style="text-align:right;" | 1.6283 | ||
| style="text-align:center;" | Meter | | style="text-align:center;" | Meter | ||
| Line 4,237: | Line 4,237: | ||
|- | |- | ||
| style="text-align:center;" | 2401/2400 | | style="text-align:center;" | 2401/2400 | ||
| | | -5 -1 -2 4 > | | |<nowiki> | -5 -1 -2 4 </nowiki>> | ||
| style="text-align:right;" | 0.72120 | | style="text-align:right;" | 0.72120 | ||
| style="text-align:center;" | Breedsma | | style="text-align:center;" | Breedsma | ||
| Line 4,244: | Line 4,244: | ||
|- | |- | ||
| style="text-align:center;" | 99/98 | | style="text-align:center;" | 99/98 | ||
| | | -1 2 0 -2 1 > | | |<nowiki> | -1 2 0 -2 1 </nowiki>> | ||
| style="text-align:right;" | 17.576 | | style="text-align:right;" | 17.576 | ||
| style="text-align:center;" | Mothwellsma | | style="text-align:center;" | Mothwellsma | ||
| Line 4,251: | Line 4,251: | ||
|- | |- | ||
| style="text-align:center;" | 121/120 | | style="text-align:center;" | 121/120 | ||
| | | -3 -1 -1 0 2 > | | |<nowiki> | -3 -1 -1 0 2 </nowiki>> | ||
| style="text-align:right;" | 14.367 | | style="text-align:right;" | 14.367 | ||
| style="text-align:center;" | Biyatisma | | style="text-align:center;" | Biyatisma | ||
| Line 4,258: | Line 4,258: | ||
|- | |- | ||
| style="text-align:center;" | 176/175 | | style="text-align:center;" | 176/175 | ||
| | | 4 0 -2 -1 1 > | | |<nowiki> | 4 0 -2 -1 1 </nowiki>> | ||
| style="text-align:right;" | 9.8646 | | style="text-align:right;" | 9.8646 | ||
| style="text-align:center;" | Valinorsma | | style="text-align:center;" | Valinorsma | ||
| Line 4,265: | Line 4,265: | ||
|- | |- | ||
| style="text-align:center;" | 243/242 | | style="text-align:center;" | 243/242 | ||
| | | -1 5 0 0 -2 > | | |<nowiki> | -1 5 0 0 -2 </nowiki>> | ||
| style="text-align:right;" | 7.1391 | | style="text-align:right;" | 7.1391 | ||
| style="text-align:center;" | Rastma | | style="text-align:center;" | Rastma | ||
| Line 4,272: | Line 4,272: | ||
|- | |- | ||
| style="text-align:center;" | 385/384 | | style="text-align:center;" | 385/384 | ||
| | | -7 -1 1 1 1 > | | |<nowiki> | -7 -1 1 1 1 </nowiki>> | ||
| style="text-align:right;" | 4.5026 | | style="text-align:right;" | 4.5026 | ||
| style="text-align:center;" | [[385/384|Keenanisma]] | | style="text-align:center;" | [[385/384|Keenanisma]] | ||
| Line 4,279: | Line 4,279: | ||
|- | |- | ||
| style="text-align:center;" | 441/440 | | style="text-align:center;" | 441/440 | ||
| | | -3 2 -1 2 -1 > | | |<nowiki> | -3 2 -1 2 -1 </nowiki>> | ||
| style="text-align:right;" | 3.9302 | | style="text-align:right;" | 3.9302 | ||
| style="text-align:center;" | Werckisma | | style="text-align:center;" | Werckisma | ||
| Line 4,286: | Line 4,286: | ||
|- | |- | ||
| style="text-align:center;" | 540/539 | | style="text-align:center;" | 540/539 | ||
| | | 2 3 1 -2 -1 > | | |<nowiki> | 2 3 1 -2 -1 </nowiki>> | ||
| style="text-align:right;" | 3.2090 | | style="text-align:right;" | 3.2090 | ||
| style="text-align:center;" | Swetisma | | style="text-align:center;" | Swetisma | ||
| Line 4,293: | Line 4,293: | ||
|- | |- | ||
| style="text-align:center;" | 3025/3024 | | style="text-align:center;" | 3025/3024 | ||
| | | -4 -3 2 -1 2 > | | |<nowiki> | -4 -3 2 -1 2 </nowiki>> | ||
| style="text-align:right;" | 0.57240 | | style="text-align:right;" | 0.57240 | ||
| style="text-align:center;" | Lehmerisma | | style="text-align:center;" | Lehmerisma | ||
| Line 4,589: | Line 4,589: | ||
[https://soundcloud.com/camtaylor-1/back-to-31-hyperchromatic Back to 31: Hyperchromatic progression on C^] by Cam Taylor | [https://soundcloud.com/camtaylor-1/back-to-31-hyperchromatic Back to 31: Hyperchromatic progression on C^] by Cam Taylor | ||
==Thirty-one tone pedagogy== | ==Thirty-one tone pedagogy== | ||
| Line 4,600: | Line 4,598: | ||
=Practical Theory / Books= | =Practical Theory / Books= | ||
<div class= | <div class="external-image-warning" style="background-color:#f8f9fa; border: 1px solid #eaecf0; padding-left: 0.5em; padding-right:0.5em; display:inline-block"> | ||
External image: http://ronsword.com/images/TSG_sm.jpg<br> | External image: http://ronsword.com/images/TSG_sm.jpg<br> | ||
: <small><b>WARNING</b>: MediaWiki doesn't have very good support for external images.</small><br> | : <small><b>WARNING</b>: MediaWiki doesn't have very good support for external images.</small><br> | ||
| Line 4,610: | Line 4,608: | ||
=Other Articles= | =Other Articles= | ||
<ul><li><span style="">[http://www.huygens-fokker.org/docs/beerart.html de Beer, Anton, ''The Development of 31-tone Music]</span> [http://www.webcitation.org/5xeFzBM9b Permalink]</li><li><span style="">[http://www.huygens-fokker.org/docs/fokkerorg.html Fokker, Adriaan Daniël, ''Equal Temperament and the Thirty-one-keyed organ]</span> [http://www.webcitation.org/5xeG6Tmli Permalink]</li><li>Fokker, A.D., "New Music with 31 Notes" translated by Leigh Gerdine</li><li><span style="">[http://www.huygens-fokker.org/docs/rap31.html Rapoport, Paul, ''About 31-tone Equal Temperament]</span> [http://www.webcitation.org/5xeGH4uBH Permalink]</li><li><span style="">[http://www.huygens-fokker.org/docs/terp31.html Terpstra, Siemen, ''Toward a Theory of Meantone (and 31-et) Harmony'']</span> [http://www.webcitation.org/5xeGMeCMd Permalink]</li><li><span style="">[http://tonalsoft.com/enc/number/31edo.aspx Tonalsoft Encyclopedia article]</span> [http://www.webcitation.org/5xeGYj7QU Permalink]</li></ul> | <ul><li><span style="">[http://www.huygens-fokker.org/docs/beerart.html de Beer, Anton, ''The Development of 31-tone Music'']</span> [http://www.webcitation.org/5xeFzBM9b Permalink]</li><li><span style="">[http://www.huygens-fokker.org/docs/fokkerorg.html Fokker, Adriaan Daniël, ''Equal Temperament and the Thirty-one-keyed organ'']</span> [http://www.webcitation.org/5xeG6Tmli Permalink]</li><li>Fokker, A.D., "New Music with 31 Notes" translated by Leigh Gerdine</li><li><span style="">[http://www.huygens-fokker.org/docs/rap31.html Rapoport, Paul, ''About 31-tone Equal Temperament'']</span> [http://www.webcitation.org/5xeGH4uBH Permalink]</li><li><span style="">[http://www.huygens-fokker.org/docs/terp31.html Terpstra, Siemen, ''Toward a Theory of Meantone (and 31-et) Harmony'']</span> [http://www.webcitation.org/5xeGMeCMd Permalink]</li><li><span style="">[http://tonalsoft.com/enc/number/31edo.aspx Tonalsoft Encyclopedia article]</span> [http://www.webcitation.org/5xeGYj7QU Permalink]</li></ul> | ||
[[File:31-edo.svg|alt=alt : Your browser has no SVG support.]] | [[File:31-edo.svg|alt=alt : Your browser has no SVG support.]] | ||
[[:File:31-edo.svg|31-edo.svg]] [[Category:31edo]] | [[:File:31-edo.svg|31-edo.svg]] | ||
[[Category:31edo]] | |||
[[Category:books]] | [[Category:books]] | ||
[[Category:edo]] | [[Category:edo]] | ||