10edo: Difference between revisions
Zach Curley (talk | contribs) I removed another one of my tracks that I wasn't proud of. |
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__FORCETOC__ | __FORCETOC__ | ||
=Intervals= | =Intervals= | ||
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! | Degree | ! | Degree | ||
! | Cents | ! | Cents | ||
! | Approximate Ratios* | ! | Approximate Ratios* | ||
! | Additional Ratios* | ! | Additional Ratios* | ||
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! colspan="3" | [[Ups_and_Downs_Notation|ups and downs notation]] | ! colspan="3" | [[Ups_and_Downs_Notation|ups and downs notation]] | ||
|- | |- | ||
| | | 0 | ||
| style="text-align:right;" | 0 | |||
| style="text-align:center;" | 1/1 | | style="text-align:center;" | 1/1 | ||
| | 256/243, 50/49, 25/24 | | | 256/243, 50/49, 25/24 | ||
| Line 35: | Line 32: | ||
| | 1 | | | 1 | ||
| style="text-align:right;" | 120 | | style="text-align:right;" | 120 | ||
| style="text-align:center;" | 16/15, 15/14, 13/14 | | style="text-align:center;" | 16/15, 15/14, 13/14 | ||
| | 10/9, 13/12, 81/80 | | | 10/9, 13/12, 81/80 | ||
| Line 42: | Line 37: | ||
| | mid 2nd | | | mid 2nd | ||
| style="text-align:center;" | ~2 | | style="text-align:center;" | ~2 | ||
| style="text-align:center;" | D | | style="text-align:center;" | ^D, vE | ||
|- | |- | ||
| | 2 | | | 2 | ||
| style="text-align:right;" | 240 | | style="text-align:right;" | 240 | ||
| style="text-align:center;" | 8/7, 15/13, 144/125 | | style="text-align:center;" | 8/7, 15/13, 144/125 | ||
| | 9/8, 7/6 | | | 9/8, 7/6 | ||
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| | 3 | | | 3 | ||
| style="text-align:right;" | 360 | | style="text-align:right;" | 360 | ||
| style="text-align:center;" | 16/13 | | style="text-align:center;" | 16/13 | ||
| | 5/4 | | | 5/4 | ||
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| | mid 3rd | | | mid 3rd | ||
| style="text-align:center;" | ~3 | | style="text-align:center;" | ~3 | ||
| style="text-align:center;" | F | | style="text-align:center;" | ^F, vG | ||
|- | |- | ||
| | 4 | | | 4 | ||
| style="text-align:right;" | 480 | | style="text-align:right;" | 480 | ||
| style="text-align:center;" | 64/49, 169/128 | | style="text-align:center;" | 64/49, 169/128 | ||
| | 4/3, 9/7, 13/10 | | | 4/3, 9/7, 13/10 | ||
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| | 5 | | | 5 | ||
| style="text-align:right;" | 600 | | style="text-align:right;" | 600 | ||
| style="text-align:center;" | 91/64, 128/91, 169/120, 240/169 | | style="text-align:center;" | 91/64, 128/91, 169/120, 240/169 | ||
| | 7/5, 10/7, 13/9, 18/13 | | | 7/5, 10/7, 13/9, 18/13 | ||
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| | up 4th, down 5th | | | up 4th, down 5th | ||
| style="text-align:center;" | ^4,v5 | | style="text-align:center;" | ^4,v5 | ||
| style="text-align:center;" | G | | style="text-align:center;" | ^G, vA | ||
|- | |- | ||
| | 6 | | | 6 | ||
| style="text-align:right;" | 720 | | style="text-align:right;" | 720 | ||
| style="text-align:center;" | 49/32, 256/169 | | style="text-align:center;" | 49/32, 256/169 | ||
| | 3/2, 14/9, 20/13 | | | 3/2, 14/9, 20/13 | ||
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| | 7 | | | 7 | ||
| style="text-align:right;" | 840 | | style="text-align:right;" | 840 | ||
| style="text-align:center;" | 13/8 | | style="text-align:center;" | 13/8 | ||
| | 8/5 | | | 8/5 | ||
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| | mid 6th | | | mid 6th | ||
| style="text-align:center;" | ~6 | | style="text-align:center;" | ~6 | ||
| style="text-align:center;" | A | | style="text-align:center;" | ^A, vB | ||
|- | |- | ||
| | 8 | | | 8 | ||
| style="text-align:right;" | 960 | | style="text-align:right;" | 960 | ||
| style="text-align:center;" | 7/4, 26/15, 125/72 | | style="text-align:center;" | 7/4, 26/15, 125/72 | ||
| | 16/9, 12/7 | | | 16/9, 12/7 | ||
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| | 9 | | | 9 | ||
| style="text-align:right;" | 1080 | | style="text-align:right;" | 1080 | ||
| style="text-align:center;" | 15/8, 28/15, 13/7 | | style="text-align:center;" | 15/8, 28/15, 13/7 | ||
| | 9/5, 24/13, 160/81 | | | 9/5, 24/13, 160/81 | ||
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| | mid 7th | | | mid 7th | ||
| style="text-align:center;" | ~7 | | style="text-align:center;" | ~7 | ||
| style="text-align:center;" | C | | style="text-align:center;" | ^C, vD | ||
|- | |- | ||
| | 10 | | | 10 | ||
| style="text-align:right;" | 1200 | | style="text-align:right;" | 1200 | ||
| style="text-align:center;" | 2/1 | | style="text-align:center;" | 2/1 | ||
| | 243/128, 49/25, 48/25 | | | 243/128, 49/25, 48/25 | ||
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[[:File:10ed2-001.svg|10ed2-001.svg]] | [[:File:10ed2-001.svg|10ed2-001.svg]] | ||
=Linear temperaments= | =Linear temperaments= | ||
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|} | |} | ||
=Images= | |||
[[File:10edo_wheel.png|alt=10edo wheel.png|280x285px|10edo wheel.png]] | |||
=Instruments= | |||
10-EDO lends itself exceptionally well to guitar (and other fretted strings), on account of the fact that five of its flat 4ths (at 480 cents) exactly spans two octaves (480*5=2400), meaning the open strings can be uniformly tuned in 4ths. This allows for greater uniformity in chord and scale fingering patterns than in 12-TET, making it exceptionally easy to learn. For instance, the fingering for an "E" chord would be 0-2-2-1-0-0 (low to high), an "A" chord would be 0-0-2-2-1-0, and a "D" chord would be 1-0-0-2-2-1. This is also the case in all EDOs which are multiples of 5, but in 10-EDO it is particularly simple. | |||
Retuning a conventional keyboard to 10edo may be done in many ways, but neglecting or making redundant the Eb and Ab keys preserves the sLsLsLs scale on the white keys. Redundancy may make modulation easier, but another option is tuning the superfluous keys to selections from [[20edo|20edo]] which approximates the 11th harmonic with relative accuracy, among other features. | |||
{| class="wikitable" | |||
|- | |||
| | [[File:Decaphonic_Classic_Guitar.png|alt=Decaphonic_Classic_Guitar.png|Decaphonic_Classic_Guitar.png]] | |||
|- | |||
| | A Decaphonic (10-EDO) Classical Guitar | |||
|} | |||
[[File:decaphonic-uke.JPG|alt=decaphonic-uke.JPG|526x406px|decaphonic-uke.JPG]] | |||
=Music= | =Music= | ||
[https://www.reverbnation.com/1029821/album/172734 ZIA Space by Elaine Walker] "Who Loves You, Me?," "Champagne," and "Avatar" | [https://www.reverbnation.com/1029821/album/172734 ZIA Space by Elaine Walker] "Who Loves You, Me?," "Champagne," and "Avatar" | ||
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''[https://soundcloud.com/clem-fortuna/10tone 10tone demo]'' by [http://clemfortuna.com Clem Fortuna] | ''[https://soundcloud.com/clem-fortuna/10tone 10tone demo]'' by [http://clemfortuna.com Clem Fortuna] | ||
[[Category:10-tone]] | [[Category:10-tone]] | ||
[[Category:10edo]] | [[Category:10edo]] | ||