31edo: Difference between revisions
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{| class="wikitable center-all mw-collapsible mw-collapsed" | {| class="wikitable center-all mw-collapsible mw-collapsed" | ||
|+style="white-space:nowrap"| 15-odd-limit intervals by direct mapping (even if inconsistent) | |+ style="white-space: nowrap; font-size: 110%;" | 15-odd-limit intervals by direct mapping (even if inconsistent) | ||
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! Interval, complement | ! Interval, complement | ||
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31edo approximates Mode 8 of the [[harmonic series]] okay, but many intervals between the harmonics aren't distinguished, most importantly 9/8 (major tone) and 10/9 (minor tone), as 31EDO is a meantone temperament. The interval between the 8th and 11th harmonics is approximated okay, but the intervals between the 11th harmonic and closer harmonics such as the 12th and 9th harmonics are approximated even better. 31's version of 13/8 is quite wide and only vaguely suggests the [[13-limit]]. | 31edo approximates Mode 8 of the [[harmonic series]] okay, but many intervals between the harmonics aren't distinguished, most importantly 9/8 (major tone) and 10/9 (minor tone), as 31EDO is a meantone temperament. The interval between the 8th and 11th harmonics is approximated okay, but the intervals between the 11th harmonic and closer harmonics such as the 12th and 9th harmonics are approximated even better. 31's version of 13/8 is quite wide and only vaguely suggests the [[13-limit]]. | ||
The steps are: 5 5 4 4 4 3 3 3 | The steps are: 5 5 4 4 4 3 3 3. | ||
{| class="wikitable" | {| class="wikitable" | ||
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==Instruments== | ==Instruments== | ||
=== Keyboard Instruments === | === Keyboard Instruments === | ||
* [https://www.huygens-fokker.org/instruments/fokkerorgan.html Fokker Organ] | * [https://www.huygens-fokker.org/instruments/fokkerorgan.html Fokker Organ] | ||
* [https://www.huygens-fokker.org/instruments/instrumentshuygensfokker/archiphone.html Archiphone] | * [https://www.huygens-fokker.org/instruments/instrumentshuygensfokker/archiphone.html Archiphone] | ||
=== String Instruments === | === String Instruments === | ||
* [https://www.huygens-fokker.org/instruments/instrumentshuygensfokker/31-toneguitar.html Guitar] | * [https://www.huygens-fokker.org/instruments/instrumentshuygensfokker/31-toneguitar.html Guitar] | ||
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[[File:31edo array kalimba.jpg|none|thumb|640x640px|31edo array kalimba built by Tristan Bay; 3 octaves, 94 keys, and laid out in circle-of-fourths meantone tuning]] | [[File:31edo array kalimba.jpg|none|thumb|640x640px|31edo array kalimba built by Tristan Bay; 3 octaves, 94 keys, and laid out in circle-of-fourths meantone tuning]] | ||
==Music== | == Music == | ||
{{Main| 31edo/Music }} | {{Main| 31edo/Music }} | ||
{{Catrel|31edo tracks}} | {{Catrel|31edo tracks}} | ||
==See also == | == See also == | ||
*[[Lumatone mapping for 31edo]] | * [[Lumatone mapping for 31edo]] | ||
*[[List of 31edo Chords]] | * [[List of 31edo Chords]] | ||
*[[Skip fretting system 31 2 9]] | * [[Skip fretting system 31 2 9]] | ||
*[[Pentachords of 31edo]] | * [[Pentachords of 31edo]] | ||
*[[Tricesimoprimal Tetrachordal Tesseract]] | * [[Tricesimoprimal Tetrachordal Tesseract]] | ||
*[[MicroPedagogyCollective]] - is at work (as of 2012) producing demonstrative material which will encourage and enable more people to learn this system. There have been two [[ThirtyOneToneSinginCamp]]s as well. | * [[MicroPedagogyCollective]] - is at work (as of 2012) producing demonstrative material which will encourage and enable more people to learn this system. There have been two [[ThirtyOneToneSinginCamp]]s as well. | ||
==Further reading== | == Further reading == | ||
===Books=== | === Books === | ||
*Coates, Bill. ''[https://scribd.com/document/32296502/31-tone-equal-temperament Diesis: An Introduction to the Temperament of 31 Notes to Each Octave]''. Self-published, 1992. | *Coates, Bill. ''[https://scribd.com/document/32296502/31-tone-equal-temperament Diesis: An Introduction to the Temperament of 31 Notes to Each Octave]''. Self-published, 1992. | ||
*[[Sword, Ron]]. ''[https://ronsword.bigcartel.com/product/tricesimoprimal-scales-for-guitar Tricesimoprimal Scales for Guitar: Scales for 31-EDO]''. 2009. ([http://www.metatonalmusic.com/books.html Metatonal Music link]) (A comprehensive approach to 31edo and all the families associated for guitar. Features over 300 scale charts/scale examples.) | *[[Sword, Ron]]. ''[https://ronsword.bigcartel.com/product/tricesimoprimal-scales-for-guitar Tricesimoprimal Scales for Guitar: Scales for 31-EDO]''. 2009. ([http://www.metatonalmusic.com/books.html Metatonal Music link]) (A comprehensive approach to 31edo and all the families associated for guitar. Features over 300 scale charts/scale examples.) | ||
===Articles=== | === Articles === | ||
*[http://www.huygens-fokker.org/docs/beerart.html ''The Development of 31-tone Music''] [https://www.webcitation.org/5xeFzBM9b Permalink] by [[Anton de Beer]] | *[http://www.huygens-fokker.org/docs/beerart.html ''The Development of 31-tone Music''] [https://www.webcitation.org/5xeFzBM9b Permalink] by [[Anton de Beer]] | ||
*[http://www.huygens-fokker.org/docs/fokkerorg.html ''Equal Temperament and the Thirty-one-keyed organ''] [https://www.webcitation.org/5xeG6Tmli Permalink] by [[Adriaan Daniël Fokker]] | *[http://www.huygens-fokker.org/docs/fokkerorg.html ''Equal Temperament and the Thirty-one-keyed organ''] [https://www.webcitation.org/5xeG6Tmli Permalink] by [[Adriaan Daniël Fokker]] | ||
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*[http://juhanpuhmmusic.ca/Juhan-Puhm-Compendium-Musica-Harmonic-Resources-31Et-EMT-31EBMT.pdf ''Harmonic Resources of 31Et EMT and 31EBMT''] by [[Juhan Puhm]] (2016) | *[http://juhanpuhmmusic.ca/Juhan-Puhm-Compendium-Musica-Harmonic-Resources-31Et-EMT-31EBMT.pdf ''Harmonic Resources of 31Et EMT and 31EBMT''] by [[Juhan Puhm]] (2016) | ||
==External links== | == External links == | ||
===Videos=== | === Videos === | ||
*[https://youtu.be/E_VD3tqwCAM ''Quarter sharps and flats in the same diatonic key signature'' – Youtube] by [[Stephen Weigel]] – a list of diatonic key signatures and major scales in 31edo (including semi- and sesqui-sharps); and docs in its description. | * [https://youtu.be/E_VD3tqwCAM ''Quarter sharps and flats in the same diatonic key signature'' – Youtube] by [[Stephen Weigel]] – a list of diatonic key signatures and major scales in 31edo (including semi- and sesqui-sharps); and docs in its description. | ||
*[https://www.youtube.com/watch?v=7cv-nuSjbY4&list=PLiWv7dE90L6CsQmQySVdAiRSIIDaAymiJ&pp=iAQB Playlist of 31edo music theory videos on YouTube] by [[Zhea Erose]] | * [https://www.youtube.com/watch?v=7cv-nuSjbY4&list=PLiWv7dE90L6CsQmQySVdAiRSIIDaAymiJ&pp=iAQB Playlist of 31edo music theory videos on YouTube] by [[Zhea Erose]] | ||
===Software=== | === Software === | ||
*[http://31et.com/keyboard.php Virtual Piano Keyboard in 31-Tone Equal Temperament] | * [http://31et.com/keyboard.php Virtual Piano Keyboard in 31-Tone Equal Temperament] | ||
*[http://www.warmplace.ru/forum/viewtopic.php?f=9&t=4750 31EDO Piano — Mini synthesizer in Pixilang] | * [http://www.warmplace.ru/forum/viewtopic.php?f=9&t=4750 31EDO Piano — Mini synthesizer in Pixilang] | ||
===Diagrams=== | === Diagrams === | ||
*[http://juhanpuhmmusic.ca/Juhan-Puhm-Compendium-Musica-Keys-and-Modes-of-31Et.pdf ''Keys and Modes of 31Et''] by Juhan Puhm (2016) | * [http://juhanpuhmmusic.ca/Juhan-Puhm-Compendium-Musica-Keys-and-Modes-of-31Et.pdf ''Keys and Modes of 31Et''] by Juhan Puhm (2016) | ||
*[http://juhanpuhmmusic.ca/Juhan-Puhm-Compendium-Musica-Keyboard-Mapping-for-31Et.pdf ''Keyboard Mapping for 31Et''] by Juhan Puhm (2017) | * [http://juhanpuhmmusic.ca/Juhan-Puhm-Compendium-Musica-Keyboard-Mapping-for-31Et.pdf ''Keyboard Mapping for 31Et''] by Juhan Puhm (2017) | ||
*[http://juhanpuhmmusic.ca/Juhan-Puhm-Compendium-Musica-Mapping-Range-for-31Et.pdf ''Mapping Range for 31Et''] by Juhan Puhm (2017) | * [http://juhanpuhmmusic.ca/Juhan-Puhm-Compendium-Musica-Mapping-Range-for-31Et.pdf ''Mapping Range for 31Et''] by Juhan Puhm (2017) | ||
[[Category:Golden meantone]] | [[Category:Golden meantone]] | ||