35edo: Difference between revisions
m →Intervals: typo |
updated ups/down notation, added color names to the comma list, a little general cleanup |
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= Theory = | |||
35-tET or 35-[[EDO]] refers to a tuning system which divides the octave into 35 steps of approximately [[cent|34.29¢]] each. | 35-tET or 35-[[EDO]] refers to a tuning system which divides the octave into 35 steps of approximately [[cent|34.29¢]] each. | ||
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| style="text-align:center;" | up unison | | style="text-align:center;" | up unison | ||
| style="text-align:center;" | ^1 | | style="text-align:center;" | ^1 | ||
| style="text-align:center;" | D | | style="text-align:center;" | ^D | ||
|- | |- | ||
| style="text-align:center;" | 2 | | style="text-align:center;" | 2 | ||
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| style="text-align:center;" | double-up unison | | style="text-align:center;" | double-up unison | ||
| style="text-align:center;" | ^^1 | | style="text-align:center;" | ^^1 | ||
| style="text-align:center;" | | | style="text-align:center;" | ^^D | ||
|- | |- | ||
| style="text-align:center;" | 3 | | style="text-align:center;" | 3 | ||
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| style="text-align:center;" | double-down 2nd | | style="text-align:center;" | double-down 2nd | ||
| style="text-align:center;" | vv2 | | style="text-align:center;" | vv2 | ||
| style="text-align:center;" | | | style="text-align:center;" | vvE | ||
|- | |- | ||
| style="text-align:center;" | 4 | | style="text-align:center;" | 4 | ||
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| style="text-align:center;" | down 2nd | | style="text-align:center;" | down 2nd | ||
| style="text-align:center;" | v2 | | style="text-align:center;" | v2 | ||
| style="text-align:center;" | | | style="text-align:center;" | vE | ||
|- | |- | ||
| style="text-align:center;" | 5 | | style="text-align:center;" | 5 | ||
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| style="text-align:center;" | up 2nd | | style="text-align:center;" | up 2nd | ||
| style="text-align:center;" | ^2 | | style="text-align:center;" | ^2 | ||
| style="text-align:center;" | E | | style="text-align:center;" | ^E | ||
|- | |- | ||
| style="text-align:center;" | 7 | | style="text-align:center;" | 7 | ||
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| style="text-align:center;" | double-up 2nd | | style="text-align:center;" | double-up 2nd | ||
| style="text-align:center;" | ^^2 | | style="text-align:center;" | ^^2 | ||
| style="text-align:center;" | | | style="text-align:center;" | ^^E | ||
|- | |- | ||
| style="text-align:center;" | 8 | | style="text-align:center;" | 8 | ||
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| style="text-align:center;" | double-down 3rd | | style="text-align:center;" | double-down 3rd | ||
| style="text-align:center;" | vv3 | | style="text-align:center;" | vv3 | ||
| style="text-align:center;" | | | style="text-align:center;" | vvF | ||
|- | |- | ||
| style="text-align:center;" | 9 | | style="text-align:center;" | 9 | ||
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| style="text-align:center;" | down 3rd | | style="text-align:center;" | down 3rd | ||
| style="text-align:center;" | v3 | | style="text-align:center;" | v3 | ||
| style="text-align:center;" | | | style="text-align:center;" | vF | ||
|- | |- | ||
| style="text-align:center;" | 10 | | style="text-align:center;" | 10 | ||
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| style="text-align:center;" | up 3rd | | style="text-align:center;" | up 3rd | ||
| style="text-align:center;" | ^3 | | style="text-align:center;" | ^3 | ||
| style="text-align:center;" | F | | style="text-align:center;" | ^F | ||
|- | |- | ||
| style="text-align:center;" | 12 | | style="text-align:center;" | 12 | ||
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| style="text-align:center;" | double-up 3rd | | style="text-align:center;" | double-up 3rd | ||
| style="text-align:center;" | ^^3 | | style="text-align:center;" | ^^3 | ||
| style="text-align:center;" | | | style="text-align:center;" | ^^F | ||
|- | |- | ||
| style="text-align:center;" | 13 | | style="text-align:center;" | 13 | ||
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| style="text-align:center;" | double-down 4th | | style="text-align:center;" | double-down 4th | ||
| style="text-align:center;" | vv4 | | style="text-align:center;" | vv4 | ||
| style="text-align:center;" | | | style="text-align:center;" | vvG | ||
|- | |- | ||
| style="text-align:center;" | 14 | | style="text-align:center;" | 14 | ||
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| style="text-align:center;" | down 4th | | style="text-align:center;" | down 4th | ||
| style="text-align:center;" | v4 | | style="text-align:center;" | v4 | ||
| style="text-align:center;" | | | style="text-align:center;" | vG | ||
|- | |- | ||
| style="text-align:center;" | 15 | | style="text-align:center;" | 15 | ||
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| style="text-align:center;" | up 4th | | style="text-align:center;" | up 4th | ||
| style="text-align:center;" | ^4 | | style="text-align:center;" | ^4 | ||
| style="text-align:center;" | G | | style="text-align:center;" | ^G | ||
|- | |- | ||
| style="text-align:center;" | 17 | | style="text-align:center;" | 17 | ||
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| style="text-align:center;" | double-up 4th | | style="text-align:center;" | double-up 4th | ||
| style="text-align:center;" | ^^4 | | style="text-align:center;" | ^^4 | ||
| style="text-align:center;" | | | style="text-align:center;" | ^^G | ||
|- | |- | ||
| style="text-align:center;" | 18 | | style="text-align:center;" | 18 | ||
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| style="text-align:center;" | double-down 5th | | style="text-align:center;" | double-down 5th | ||
| style="text-align:center;" | vv5 | | style="text-align:center;" | vv5 | ||
| style="text-align:center;" | | | style="text-align:center;" | vvA | ||
|- | |- | ||
| style="text-align:center;" | 19 | | style="text-align:center;" | 19 | ||
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| style="text-align:center;" | down 5th | | style="text-align:center;" | down 5th | ||
| style="text-align:center;" | v5 | | style="text-align:center;" | v5 | ||
| style="text-align:center;" | | | style="text-align:center;" | vA | ||
|- | |- | ||
| style="text-align:center;" | 20 | | style="text-align:center;" | 20 | ||
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| style="text-align:center;" | up 5th | | style="text-align:center;" | up 5th | ||
| style="text-align:center;" | ^5 | | style="text-align:center;" | ^5 | ||
| style="text-align:center;" | A | | style="text-align:center;" | ^A | ||
|- | |- | ||
| style="text-align:center;" | 22 | | style="text-align:center;" | 22 | ||
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| style="text-align:center;" | double-up 5th | | style="text-align:center;" | double-up 5th | ||
| style="text-align:center;" | ^^5 | | style="text-align:center;" | ^^5 | ||
| style="text-align:center;" | | | style="text-align:center;" | ^^A | ||
|- | |- | ||
| style="text-align:center;" | 23 | | style="text-align:center;" | 23 | ||
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| style="text-align:center;" | double-down 6th | | style="text-align:center;" | double-down 6th | ||
| style="text-align:center;" | vv6 | | style="text-align:center;" | vv6 | ||
| style="text-align:center;" | | | style="text-align:center;" | vvB | ||
|- | |- | ||
| style="text-align:center;" | 24 | | style="text-align:center;" | 24 | ||
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| style="text-align:center;" | down 6th | | style="text-align:center;" | down 6th | ||
| style="text-align:center;" | v6 | | style="text-align:center;" | v6 | ||
| style="text-align:center;" | | | style="text-align:center;" | vB | ||
|- | |- | ||
| style="text-align:center;" | 25 | | style="text-align:center;" | 25 | ||
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| style="text-align:center;" | up 6th | | style="text-align:center;" | up 6th | ||
| style="text-align:center;" | ^6 | | style="text-align:center;" | ^6 | ||
| style="text-align:center;" | B | | style="text-align:center;" | ^B | ||
|- | |- | ||
| style="text-align:center;" | 27 | | style="text-align:center;" | 27 | ||
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| style="text-align:center;" | double-up 6th | | style="text-align:center;" | double-up 6th | ||
| style="text-align:center;" | ^^6 | | style="text-align:center;" | ^^6 | ||
| style="text-align:center;" | | | style="text-align:center;" | ^^B | ||
|- | |- | ||
| style="text-align:center;" | 28 | | style="text-align:center;" | 28 | ||
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| style="text-align:center;" | double-down 7th | | style="text-align:center;" | double-down 7th | ||
| style="text-align:center;" | vv7 | | style="text-align:center;" | vv7 | ||
| style="text-align:center;" | | | style="text-align:center;" | vvC | ||
|- | |- | ||
| style="text-align:center;" | 29 | | style="text-align:center;" | 29 | ||
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| style="text-align:center;" | down 7th | | style="text-align:center;" | down 7th | ||
| style="text-align:center;" | v7 | | style="text-align:center;" | v7 | ||
| style="text-align:center;" | | | style="text-align:center;" | vC | ||
|- | |- | ||
| style="text-align:center;" | 30 | | style="text-align:center;" | 30 | ||
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| style="text-align:center;" | up 7th | | style="text-align:center;" | up 7th | ||
| style="text-align:center;" | ^7 | | style="text-align:center;" | ^7 | ||
| style="text-align:center;" | C | | style="text-align:center;" | ^C | ||
|- | |- | ||
| style="text-align:center;" | 32 | | style="text-align:center;" | 32 | ||
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| style="text-align:center;" | double-up 7th | | style="text-align:center;" | double-up 7th | ||
| style="text-align:center;" | ^^7 | | style="text-align:center;" | ^^7 | ||
| style="text-align:center;" | | | style="text-align:center;" | ^^C | ||
|- | |- | ||
| style="text-align:center;" | 33 | | style="text-align:center;" | 33 | ||
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| style="text-align:center;" | double-down 8ve | | style="text-align:center;" | double-down 8ve | ||
| style="text-align:center;" | vv8 | | style="text-align:center;" | vv8 | ||
| style="text-align:center;" | | | style="text-align:center;" | vvD | ||
|- | |- | ||
| style="text-align:center;" | 34 | | style="text-align:center;" | 34 | ||
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| style="text-align:center;" | down 8ve | | style="text-align:center;" | down 8ve | ||
| style="text-align:center;" | v8 | | style="text-align:center;" | v8 | ||
| style="text-align:center;" | | | style="text-align:center;" | vD | ||
|- | |- | ||
| style="text-align:center;" | 35 | | style="text-align:center;" | 35 | ||
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|} | |} | ||
== | ==Chord Names== | ||
Ups and downs can be used to name 35edo chords. Because every interval is perfect, the quality can be omitted, and the words major, minor, augmented and diminished are never used. | Ups and downs can be used to name 35edo chords. Because every interval is perfect, the quality can be omitted, and the words major, minor, augmented and diminished are never used. An up or down immediately after the chord root affects the 3rd, 6th, 7th, and/or the 11th (every other note of a stacked-3rds chord 6-1-3-5-7-9-11-13). Alterations are always enclosed in parentheses, additions never are. | ||
0-10-20 = C E G = C = C or C perfect | 0-10-20 = C E G = C = C or C perfect | ||
0-9-20 = C | 0-9-20 = C vE G = Cv = C down | ||
0-11-20 = C E | 0-11-20 = C ^E G = C^ = C up | ||
0-10-19 = C E | 0-10-19 = C E vG = C(v5) = C down-five | ||
0-11-21 = C E^ G | 0-11-21 = C ^E ^G = C^(^5) = C up up-five | ||
0-10-20-30 = C E G B = C7 = C seven | 0-10-20-30 = C E G B = C7 = C seven | ||
0-10-20-29 = C E G | 0-10-20-29 = C E G vB = C,v7 = C add down-seven | ||
0-9-20-30 = C | 0-9-20-30 = C vE G B = Cv,7 = C down add-seven | ||
0-9-20-29 = C | 0-9-20-29 = C vE G vB = Cv7 = C down seven | ||
For a more complete list, see [[ | For a more complete list, see [[Ups and Downs Notation#Chords and Chord Progressions|Ups and Downs Notation - Chords and Chord Progressions]]. | ||
=Intervals= | =JI Intervals= | ||
(Bolded ratio indicates that the ratio is most accurately tuned by the given 35-edo interval.) | (Bolded ratio indicates that the ratio is most accurately tuned by the given 35-edo interval.) | ||
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=Commas= | =Commas= | ||
35EDO tempers out the following commas. (Note: This assumes the val < 35 55 81 98 121 130|.) | 35EDO tempers out the following [[commas]]. (Note: This assumes the val < 35 55 81 98 121 130|.) | ||
{| class="wikitable" | {| class="wikitable" | ||
|- | |- | ||
! | | ! | [[Ratio]] | ||
! | Monzo | ! | [[Monzo]] | ||
! | | ! | [[Cents]] | ||
![[Color notation/Temperament Names|Color Name]] | |||
! | Name 1 | ! | Name 1 | ||
! | Name 2 | ! | Name 2 | ||
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| |<nowiki> | -11 7 </nowiki>> | | |<nowiki> | -11 7 </nowiki>> | ||
| style="text-align:right;" | 113.69 | | style="text-align:right;" | 113.69 | ||
| style="text-align:center;" |Lawa | |||
| style="text-align:center;" | Apotome | | style="text-align:center;" | Apotome | ||
| style="text-align:center;" | Whitewood comma | | style="text-align:center;" | Whitewood comma | ||
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| |<nowiki> | -1 8 -5 </nowiki>> | | |<nowiki> | -1 8 -5 </nowiki>> | ||
| style="text-align:right;" | 84.07 | | style="text-align:right;" | 84.07 | ||
| style="text-align:center;" |Quingu | |||
| style="text-align:center;" | Ripple comma | | style="text-align:center;" | Ripple comma | ||
| style="text-align:center;" | | | style="text-align:center;" | | ||
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| |<nowiki> | 9 9 -10 </nowiki>> | | |<nowiki> | 9 9 -10 </nowiki>> | ||
| style="text-align:right;" | 54.46 | | style="text-align:right;" | 54.46 | ||
| style="text-align:center;" |Quinbigu | |||
| style="text-align:center;" | Mynic comma | | style="text-align:center;" | Mynic comma | ||
| style="text-align:center;" | | | style="text-align:center;" | | ||
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| |<nowiki> | -10 -1 5 </nowiki>> | | |<nowiki> | -10 -1 5 </nowiki>> | ||
| style="text-align:right;" | 29.61 | | style="text-align:right;" | 29.61 | ||
| style="text-align:center;" |Laquinyo | |||
| style="text-align:center;" | Small diesis | | style="text-align:center;" | Small diesis | ||
| style="text-align:center;" | Magic comma | | style="text-align:center;" | Magic comma | ||
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| |<nowiki> | -3 4 1 -2 </nowiki>> | | |<nowiki> | -3 4 1 -2 </nowiki>> | ||
| style="text-align:right;" | 56.48 | | style="text-align:right;" | 56.48 | ||
| style="text-align:center;" |Ruruyo | |||
| style="text-align:center;" | Greenwoodma | | style="text-align:center;" | Greenwoodma | ||
| style="text-align:center;" | | | style="text-align:center;" | | ||
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| |<nowiki> | -14 0 0 5 </nowiki>> | | |<nowiki> | -14 0 0 5 </nowiki>> | ||
| style="text-align:right;" | 44.13 | | style="text-align:right;" | 44.13 | ||
| style="text-align:center;" |Laquinzo | |||
| style="text-align:center;" | | | style="text-align:center;" | | ||
| style="text-align:center;" | | | style="text-align:center;" | | ||
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| |<nowiki> | -9 1 2 1 </nowiki>> | | |<nowiki> | -9 1 2 1 </nowiki>> | ||
| style="text-align:right;" | 43.41 | | style="text-align:right;" | 43.41 | ||
| style="text-align:center;" |Zoyoyo | |||
| style="text-align:center;" | Avicenna | | style="text-align:center;" | Avicenna | ||
| style="text-align:center;" | | | style="text-align:center;" | | ||
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| |<nowiki> | 1 2 -3 1 </nowiki>> | | |<nowiki> | 1 2 -3 1 </nowiki>> | ||
| style="text-align:right;" | 13.79 | | style="text-align:right;" | 13.79 | ||
| style="text-align:center;" |Zotrigu | |||
| style="text-align:center;" | Starling comma | | style="text-align:center;" | Starling comma | ||
| style="text-align:center;" | Septimal semicomma | | style="text-align:center;" | Septimal semicomma | ||
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| |<nowiki> | -1 2 0 -2 1 </nowiki>> | | |<nowiki> | -1 2 0 -2 1 </nowiki>> | ||
| style="text-align:right;" | 17.58 | | style="text-align:right;" | 17.58 | ||
| style="text-align:center;" |Loruru | |||
| style="text-align:center;" | Mothwellsma | | style="text-align:center;" | Mothwellsma | ||
| style="text-align:center;" | | | style="text-align:center;" | | ||
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| |<nowiki> | 1 1 -1 0 1 -1 </nowiki>> | | |<nowiki> | 1 1 -1 0 1 -1 </nowiki>> | ||
| style="text-align:right;" | 26.43 | | style="text-align:right;" | 26.43 | ||
| style="text-align:center;" |Thulogu | |||
| style="text-align:center;" | | | style="text-align:center;" | | ||
| style="text-align:center;" | | | style="text-align:center;" | | ||