43edo: Difference between revisions
ArrowHead294 (talk | contribs) No edit summary |
ArrowHead294 (talk | contribs) m →Scales |
||
| Line 851: | Line 851: | ||
=== Harmonic scales === | === Harmonic scales === | ||
43edo represents the first 16 overtones of the [[harmonic series]] well (written as a ratio of 8:9:10:11:12:13:14:15:16 in [[just intonation]]) with degrees 0, 7, 14, 20, 25, 30, 35, 39, and 43, and scale steps of 7, 7, 6, 5, 5, 5, 4, and 4. | 43edo represents the first 16 overtones of the [[harmonic series]] well (written as a ratio of 8:9:10:11:12:13:14:15:16 in [[just intonation]]) with degrees 0, 7, 14, 20, 25, 30, 35, 39, and 43, and scale steps of 7, 7, 6, 5, 5, 5, 4, and 4. | ||
*7\43 (195.349¢) stands in for frequency ratio [[9/8]] (203.910¢) and [[10/9]] (182.404¢). | |||
* 7\43 (195.349¢) stands in for frequency ratio [[9/8]] (203.910¢) and [[10/9]] (182.404¢). | *6\43 (156.522¢) stands in for [[11/10]] (165.004¢) | ||
* 6\43 (156.522¢) stands in for [[11/10]] (165.004¢) | |||
* 5\46 (130.435¢) stands in for [[12/11]] (150.637¢), [[13/12]] (138.573¢), and [[14/13]] (128.298¢). | * 5\46 (130.435¢) stands in for [[12/11]] (150.637¢), [[13/12]] (138.573¢), and [[14/13]] (128.298¢). | ||
* 4\43 (111.628¢) stands in for [[15/14]] (119.443¢) and [[16/15]] (111.731¢). | *4\43 (111.628¢) stands in for [[15/14]] (119.443¢) and [[16/15]] (111.731¢). | ||
{| class="wikitable center-all" | {| class="wikitable center-all" | ||
|- | |- | ||
! Harmonic | ! Harmonic | ||
! Note (starting from C) | |||
|- | |||
! 1 | ! 1 | ||
| style="font-size: 16px;" | C | |||
|- | |||
! 3 | ! 3 | ||
| style="font-size: 16px;" | G | |||
|- | |||
! 5 | ! 5 | ||
| style="font-size: 16px;" | E | |||
|- | |||
! 7 | ! 7 | ||
| style="font-size: 16px;" | B{{flatdown|40x40px}} | |||
|- | |||
! 9 | ! 9 | ||
| style="font-size: 16px;" | D | |||
|- | |||
! 11 | ! 11 | ||
| style="font-size: 16px;" | F{{sharpdown|40x40px}} | |||
|- | |||
! 13 | ! 13 | ||
| style="font-size: 16px;" | A{{flatup|40x40px}} | |||
|- | |||
! 15 | ! 15 | ||
|- | | style="font-size: 16px;" | B | ||
| B | |||
|} | |} | ||
== Music == | ==Music== | ||
=== Modern renderings === | ===Modern renderings=== | ||
; {{W|Johann Sebastian Bach}} | ;{{W|Johann Sebastian Bach}} | ||
* [https://www.youtube.com/watch?v=E7W-t2KDeSs "Contrapunctus 4" from ''The Art of Fugue'', BWV 1080] (1742–1749) – rendered by Claudi Meneghin (2024) | *[https://www.youtube.com/watch?v=E7W-t2KDeSs "Contrapunctus 4" from ''The Art of Fugue'', BWV 1080] (1742–1749) – rendered by Claudi Meneghin (2024) | ||
; {{W|Nicolaus Bruhns}} | ;{{W|Nicolaus Bruhns}} | ||
* [https://www.youtube.com/watch?v=GkuUVQYpjo4 ''Prelude in E Minor "The Great"''] – rendered by Claudi Meneghin (2023) | *[https://www.youtube.com/watch?v=GkuUVQYpjo4 ''Prelude in E Minor "The Great"''] – rendered by Claudi Meneghin (2023) | ||
=== 21st century === | ===21st century=== | ||
; [[Bryan Deister]] | ;[[Bryan Deister]] | ||
* [https://www.youtube.com/watch?v=pALxebjbhZo ''microtonal improvisation in 43edo''] (2023) | *[https://www.youtube.com/watch?v=pALxebjbhZo ''microtonal improvisation in 43edo''] (2023) | ||
; [[Peter Kosmorsky]] | ;[[Peter Kosmorsky]] | ||
* [[:File:43_edo_counterpoint.mid|43 edo counterpoint.mid]] [http://micro.soonlabel.com/gene_ward_smith/Others/Kosmorsky/43%20edo%20counterpoint.mp3 mp3]{{dead link}} – in meantone (late 2011) | *[[:File:43_edo_counterpoint.mid|43 edo counterpoint.mid]] [http://micro.soonlabel.com/gene_ward_smith/Others/Kosmorsky/43%20edo%20counterpoint.mp3 mp3]{{dead link}} – in meantone (late 2011) | ||
; [[MortisTheneRd]] | ;[[MortisTheneRd]] | ||
* [https://www.youtube.com/watch?v=WyU38ESUBqo Shiro Sagisu - ''Pensées Intimes''] (2024) | *[https://www.youtube.com/watch?v=WyU38ESUBqo Shiro Sagisu - ''Pensées Intimes''] (2024) | ||
; [[Juhan Puhm]] ([http://juhanpuhmmusic.ca site]) | ;[[Juhan Puhm]] ([http://juhanpuhmmusic.ca site]) | ||
* [https://www.youtube.com/watch?v=I68hwh45CyQ ''Meantone Suite V in D Minor''] [http://juhanpuhmmusic.ca/Juhan-Puhm-Meantone-Suite-V-D-Minor.pdf score] (2017) | *[https://www.youtube.com/watch?v=I68hwh45CyQ ''Meantone Suite V in D Minor''] [http://juhanpuhmmusic.ca/Juhan-Puhm-Meantone-Suite-V-D-Minor.pdf score] (2017) | ||
; [[Randy Wells]] | ;[[Randy Wells]] | ||
* [https://www.youtube.com/watch?v=xN-QzI6OgGs ''Time Travel''] (2021) | *[https://www.youtube.com/watch?v=xN-QzI6OgGs ''Time Travel''] (2021) | ||
== Articles == | ==Articles== | ||
* [http://juhanpuhmmusic.ca/Juhan-Puhm-Compendium-Musica-Harmonic-Resources-43Et-EMT-43EBMT.pdf ''Harmonic Resources of 43Et EMT and 43EBMT''] by Juhan Puhm (2018) | *[http://juhanpuhmmusic.ca/Juhan-Puhm-Compendium-Musica-Harmonic-Resources-43Et-EMT-43EBMT.pdf ''Harmonic Resources of 43Et EMT and 43EBMT''] by Juhan Puhm (2018) | ||
== Diagrams == | ==Diagrams== | ||
* [http://juhanpuhmmusic.ca/Juhan-Puhm-Compendium-Musica-Keys-and-Modes-of-43Et.pdf ''Keys and Modes of 43Et''] by Juhan Puhm (2016) | *[http://juhanpuhmmusic.ca/Juhan-Puhm-Compendium-Musica-Keys-and-Modes-of-43Et.pdf ''Keys and Modes of 43Et''] by Juhan Puhm (2016) | ||
* [http://juhanpuhmmusic.ca/Juhan-Puhm-Compendium-Musica-Keyboard-Mapping-for-43Et.pdf ''Keyboard Mapping for 43Et''] by Juhan Puhm (2017) | *[http://juhanpuhmmusic.ca/Juhan-Puhm-Compendium-Musica-Keyboard-Mapping-for-43Et.pdf ''Keyboard Mapping for 43Et''] by Juhan Puhm (2017) | ||
* [http://juhanpuhmmusic.ca/Juhan-Puhm-Compendium-Musica-Mapping-Range-for-43Et.pdf ''Mapping Range for 43Et''] by Juhan Puhm (2017) | *[http://juhanpuhmmusic.ca/Juhan-Puhm-Compendium-Musica-Mapping-Range-for-43Et.pdf ''Mapping Range for 43Et''] by Juhan Puhm (2017) | ||
== Instruments == | ==Instruments== | ||
* [[Lumatone mapping for 43edo]] | *[[Lumatone mapping for 43edo]] | ||
* [[Skip fretting system 43 2 9]] | *[[Skip fretting system 43 2 9]] | ||
== References == | ==References== | ||
<references/> | <references /> | ||
[[Category:Meantone]] | [[Category:Meantone]] | ||