11edo: Difference between revisions
Cmloegcmluin (talk | contribs) →Intervals and notation: add more Sagittal notation |
Dave Keenan (talk | contribs) →Intervals and notation: Remove Sagittal duplication. Add Ups and downs heading. |
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[[File:0-8-16-20 chord.wav|thumb|A 0-8-16-20 chord in 11edo illustrating harmony generated from stacking 9/7 intervals.]] | [[File:0-8-16-20 chord.wav|thumb|A 0-8-16-20 chord in 11edo illustrating harmony generated from stacking 9/7 intervals.]] | ||
== | == Notation == | ||
=== Ups and downs notation === | |||
11edo can be notated using ups and downs. Conventional notation, including the staff, note names, relative notation, etc. can be used in two ways. The first preserves the ''melodic'' meaning of sharp/flat, major/minor and aug/dim, in that sharp is higher pitched than flat, and major/aug is wider than minor/dim. The disadvantage to this approach is that conventional interval arithmetic no longer works. e.g. M2 + M2 isn't M3, and D + M2 isn't E. Chord names are different because C - E - G isn't P1 - M3 - P5. | 11edo can be notated using ups and downs. Conventional notation, including the staff, note names, relative notation, etc. can be used in two ways. The first preserves the ''melodic'' meaning of sharp/flat, major/minor and aug/dim, in that sharp is higher pitched than flat, and major/aug is wider than minor/dim. The disadvantage to this approach is that conventional interval arithmetic no longer works. e.g. M2 + M2 isn't M3, and D + M2 isn't E. Chord names are different because C - E - G isn't P1 - M3 - P5. | ||
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! Solfege | ! Solfege | ||
! Approximate Ratios* | ! Approximate Ratios* | ||
! colspan="2" | [[Ups and Downs Notation|Up/down notation]] <br> with major wider <br> than minor | ! colspan="2" | [[Ups and Downs Notation|Up/down notation]] <br> with major wider <br> than minor | ||
! colspan="2" | Up/down notation <br> with major narrower <br> than minor | ! colspan="2" | Up/down notation <br> with major narrower <br> than minor | ||
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| '''do''' | | '''do''' | ||
| 1/1 | | 1/1 | ||
| P1 | | P1 | ||
| A | | A | ||
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| '''ra''' | | '''ra''' | ||
| [[15/14]], [[16/15]], [[17/16]], [[18/17]] | | [[15/14]], [[16/15]], [[17/16]], [[18/17]] | ||
| ^1, m2 | | ^1, m2 | ||
| ^A, B | | ^A, B | ||
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| '''re''' | | '''re''' | ||
| [[8/7]], [[9/8]], [[17/15]] | | [[8/7]], [[9/8]], [[17/15]] | ||
| ~2, m3 | | ~2, m3 | ||
| ^B, Cb | | ^B, Cb | ||
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| '''me''' | | '''me''' | ||
| [[6/5]], [[11/9]], [[17/14]] | | [[6/5]], [[11/9]], [[17/14]] | ||
| M2, ~3 | | M2, ~3 | ||
| B#, vC | | B#, vC | ||
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| '''mo''' | | '''mo''' | ||
| [[9/7]], [[14/11]], [[22/17]] | | [[9/7]], [[14/11]], [[22/17]] | ||
| M3, v4 | | M3, v4 | ||
| C, vD | | C, vD | ||
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| '''fu''' | | '''fu''' | ||
| [[11/8]], [[15/11]] | | [[11/8]], [[15/11]] | ||
| P4, v5 | | P4, v5 | ||
| D, vE | | D, vE | ||
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| '''su''' | | '''su''' | ||
| [[16/11]], [[22/15]] | | [[16/11]], [[22/15]] | ||
| ^4, P5 | | ^4, P5 | ||
| ^D, E | | ^D, E | ||
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| '''lo''' | | '''lo''' | ||
| [[14/9]], [[11/7]], [[17/11]] | | [[14/9]], [[11/7]], [[17/11]] | ||
| ^5, m6 | | ^5, m6 | ||
| ^E, Fb | | ^E, Fb | ||
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| '''la''' | | '''la''' | ||
| [[5/3]], [[18/11]], [[28/17]] | | [[5/3]], [[18/11]], [[28/17]] | ||
| ~6, m7 | | ~6, m7 | ||
| vF, Gb | | vF, Gb | ||
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| '''ta''' | | '''ta''' | ||
| [[7/4]], [[16/9]], [[30/17]] | | [[7/4]], [[16/9]], [[30/17]] | ||
| M6, ~7 | | M6, ~7 | ||
| F, vG | | F, vG | ||
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| '''ti''' | | '''ti''' | ||
| [[15/8]], [[17/9]], [[28/15]], [[32/17]] | | [[15/8]], [[17/9]], [[28/15]], [[32/17]] | ||
| M7, v8 | | M7, v8 | ||
| G, vAv | | G, vAv | ||
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| '''do''' | | '''do''' | ||
| 2/1 | | 2/1 | ||
| P8 | | P8 | ||
| A | | A | ||
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*in 2.7.9.11.15.17 subgroup | *in 2.7.9.11.15.17 subgroup | ||
The ups and downs notations above are heptatonic systems generated by 5ths (~3/2). Alternative notations include pentatonic 5th-generated, octatonic 5th-generated, nonatonic 5th-generated, heptatonic 3rd-generated, and hexatonic 2nd-generated. | |||
'''<u>Pentatonic 5th-generated:</u>''' '''D * * E G * * A C * * D''' ([[Sensoid]] generator = wide 3/2 = 7\11 = perfect 5thoid) | '''<u>Pentatonic 5th-generated:</u>''' '''D * * E G * * A C * * D''' ([[Sensoid]] generator = wide 3/2 = 7\11 = perfect 5thoid) | ||