Kite's ups and downs notation: Difference between revisions
Wikispaces>TallKite **Imported revision 558195589 - Original comment: ** |
Wikispaces>TallKite **Imported revision 558211375 - Original comment: ** |
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<h2>IMPORTED REVISION FROM WIKISPACES</h2> | <h2>IMPORTED REVISION FROM WIKISPACES</h2> | ||
This is an imported revision from Wikispaces. The revision metadata is included below for reference:<br> | This is an imported revision from Wikispaces. The revision metadata is included below for reference:<br> | ||
: This revision was by author [[User:TallKite|TallKite]] and made on <tt>2015-09-03 | : This revision was by author [[User:TallKite|TallKite]] and made on <tt>2015-09-03 17:42:02 UTC</tt>.<br> | ||
: The original revision id was <tt> | : The original revision id was <tt>558211375</tt>.<br> | ||
: The revision comment was: <tt></tt><br> | : The revision comment was: <tt></tt><br> | ||
The revision contents are below, presented both in the original Wikispaces Wikitext format, and in HTML exactly as Wikispaces rendered it.<br> | The revision contents are below, presented both in the original Wikispaces Wikitext format, and in HTML exactly as Wikispaces rendered it.<br> | ||
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The other approach is to use some interval other than the fifth to generate the notation. Above I said 22edo using an even distribution of note names such as C _ _ D _ _ E _ _ F _ _ _ G _ _ A _ _ B _ _ C. | The other approach is to use some interval other than the fifth to generate the notation. Above I said 22edo using an even distribution of note names such as C _ _ D _ _ E _ _ F _ _ _ G _ _ A _ _ B _ _ C. | ||
8edo | __**Theoretical alternatives for 8edo, 11edo, 13edo and 18edo**__ | ||
8edo octatonic (every note | 8edo octatonic (every note is a generator) | ||
P1 - P2 - P3 - P4 - P5 - P6 - P7 - P8 - P9 | P1 - P2 - P3 - P4 - P5 - P6 - P7 - P8 - P9 | ||
11edo heptatonic narrow-fifth-based, fourthwards with ^/v, 2 keys per #/b (3/2 maps to 6\11 5th): | 11edo heptatonic narrow-fifth-based, fourthwards with ^/v, 2 keys per #/b (3/2 maps to 6\11 5th): | ||
P1 m2 vM2/m3 M2/^m3 M3 P4 P5 m6 vM6/m7 M6/^m7 M7 P8 | P1 - m2 - vM2/m3 - M2/^m3 - M3 - P4 - P5 - m6 - vM6/m7 - M6/^m7 - M7 - P8 | ||
problematic because m3 = 2\11 is narrower than M2 = 3\11 | problematic because m3 = 2\11 is narrower than M2 = 3\11 | ||
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P1 m2 M2/m3 M3/m4 M4 P5 P6 m7 M7/m8 M8/m9 M9 P8 | P1 m2 M2/m3 M3/m4 M4 P5 P6 m7 M7/m8 M8/m9 M9 P8 | ||
requires learning nonotonic interval arithmetic and devising a nonotonic staff notation | requires learning nonotonic interval arithmetic and devising a nonotonic staff notation | ||
11edo pentatonic wide-fifth-based, fifthwards using ^/v, 2 keys per #/b (3/2 maps to 7\11 6th): | 11edo pentatonic wide-fifth-based, fifthwards using ^/v, 2 keys per #/b (3/2 maps to 7\11 6th): | ||
P1 - ms3 - ^ms3/vMs3 - Ms3 - P4d - ^P4d/d5d - A4d/vP5d - P5d - ms7 - ^ms7/vMs7 - Ms7 - P8d | P1 - ms3 - ^ms3/vMs3 - Ms3 - P4d - ^P4d/d5d - A4d/vP5d - P5d - ms7 - ^ms7/vMs7 - Ms7 - P8d | ||
pentatonic plus ups and downs is doubly confusing! | |||
11edo octatonic wide-fifth-based, fifthwards, no ^/v (3/2 maps to 7\11 6th): | 11edo octatonic wide-fifth-based, fifthwards, no ^/v (3/2 maps to 7\11 = perfect 6th): | ||
octatonic chain of 6ths: m3 - m8 - m5 - m2 - m7 - P4 - P1 - P6 - M3 - M8 - M5 - M2 - M7 | octatonic chain of 6ths: m3 - m8 - m5 - m2 - m7 - P4 - P1 - P6 - M3 - M8 - M5 - M2 - M7 | ||
P1 - m2 - M2/m3 - M3 - P4 - m5 - M5 - P6 - m7 - M7/m8 - M8 - P9 | P1 - m2 - M2/m3 - M3 - P4 - m5 - M5 - P6 - m7 - M7/m8 - M8 - P9 | ||
requires learning octatonic interval arithmetic and notation | requires learning octatonic interval arithmetic and notation | ||
13edo heptatonic narrow-fifth-based, fourthwards, 3 keys per #/b, (3/2 maps to 7\13 = perfect 5th): | |||
13edo heptatonic narrow-fifth-based, fourthwards, 3 keys per #/b, (3/2 maps to 7\13 5th): | |||
P1 - m2 - m3 - vM2/^m3 - M2 - M3 - P4 - P5 - m6 - m7 - vM6/^m7 - M6 - M7 - P8 | P1 - m2 - m3 - vM2/^m3 - M2 - M3 - P4 - P5 - m6 - m7 - vM6/^m7 - M6 - M7 - P8 | ||
problematic because m3 = 2\13 is narrower than M2 = 4\13 | problematic because m3 = 2\13 is narrower than M2 = 4\13 | ||
(13edo undecatonic narrow-fifth-based, 3/2 maps to 7\13 7th) | (13edo undecatonic narrow-fifth-based, 3/2 maps to 7\13 = perfect 7th) | ||
(13edo octatonic wide-fifth-based, fourthwards) | (13edo octatonic wide-fifth-based, fourthwards) | ||
18edo heptatonic narrow-fifth-based, fourthwards, 2 keys per #/b (3/2 maps to 10\18 = perfect 5th) | |||
18edo heptatonic narrow-fifth-based, fourthwards, 2 keys per #/b (3/2 maps to 10\18) | |||
P1 - vm2 - m2 - vM2 - M2/m3 - vM3 - M3 - ^M3 - P4 - ^P4/vP5 - P5 - vm6 - m6 - vM6 - M6/m7 - vM7 - M7 - ^M7 - P8 | P1 - vm2 - m2 - vM2 - M2/m3 - vM3 - M3 - ^M3 - P4 - ^P4/vP5 - P5 - vm6 - m6 - vM6 - M6/m7 - vM7 - M7 - ^M7 - P8 | ||
fourthwards plus ups and downs is doubly confusing! | fourthwards plus ups and downs is doubly confusing! | ||
18edo nonatonic narrow-fifth-based | 18edo nonatonic narrow-fifth-based (3/2 maps to 10\18 = perfect 6th) | ||
P1 - vP2 - P2 - vP3 - P3 - vP4- P4 - vP5 - P5 - vP6 - P6 - vP7 - P7 - vP8 - P8 - vP9 - P9 - vP10 - P10 | P1 - vP2 - P2 - vP3 - P3 - vP4- P4 - vP5 - P5 - vP6 - P6 - vP7 - P7 - vP8 - P8 - vP9 - P9 - vP10 - P10 | ||
requires learning nonotonic interval arithmetic and devising a nonotonic staff notation | requires learning nonotonic interval arithmetic and devising a nonotonic staff notation | ||
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=__**Summary of EDO notation**__= | =__**Summary of EDO notation**__= | ||
There are five EDO categories, based on the size of the fifth: | |||
"Fifth-less" EDOs (8, 11, 13 and 18) | "Fifth-less" EDOs (8, 11, 13 and 18) | ||
Fourthward EDOs (9, 16 and 23) | Fourthward EDOs (9, 16 and 23) | ||
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Pentatonic EDOs (5, 10, 15, 20, 25 and 30) | Pentatonic EDOs (5, 10, 15, 20, 25 and 30) | ||
"Sweet" EDOs (all others) | "Sweet" EDOs (all others) | ||
The first two categories never use ups and downs, the next two always do (except for 5edo and 7edo). | The first two categories never use ups and downs, the next two always do (except for 5edo and 7edo). The last may or may not. | ||
To summarize an EDO, a scale fragment from C to D is shown, including C# and Db. The C-C# interval is the augmented unison, and if they are not adjacent, ups and downs are required.The C-Db interval is the minor 2nd | |||
The C-D interval is the major 2nd (P2 for perfect EDOs, m2 for fourthward EDOs). | |||
===__**"Fifth-less" EDOs (8, 11, 13 and 18)**__=== | ===__**"Fifth-less" EDOs (8, 11, 13 and 18)**__=== | ||
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sixthwards chain of thirds: M5 - M7 - M2 - M4 - P6 - P1 - P3 - m5 - m7 - m2 - m4 - d6 etc. | sixthwards chain of thirds: M5 - M7 - M2 - M4 - P6 - P1 - P3 - m5 - m7 - m2 - m4 - d6 etc. | ||
E# - G# - B# - D# - F# - A# - C# - E - G - B - D - F - A - C - Eb - Gb - Bb - Db - Fb - Ab - Cb | E# - G# - B# - D# - F# - A# - C# - E - G - B - D - F - A - C - Eb - Gb - Bb - Db - Fb - Ab - Cb | ||
===__**Alternate pentatonic notation for EDOs 8, 13 and 18**__=== | |||
All three EDOs use the same pentatonic fifthwards chain of fifths: ms3 - ms7 - P4d - P1 - P5d - Ms3 - Ms7 - A4d etc. | |||
Cb - Gb - Db - Ab - Eb - C - G - D - A - E - C# - G# - D# - A# - E# etc. | |||
__**8edo**__**:** (generator = 5\8 = perfect 5thoid) C C#/Db D | |||
D * E G * A C * D | |||
D - D#/Eb - E - G - G#/Ab - A - C - C#/Db - D | |||
P1 - ms3 - Ms3 - P4d - A4d/d5d - P5d - ms7 - Ms7 - P8d | |||
__**13edo**__**:** (generator = 8\13 = perfect 5thoid) C C# Db D | |||
D * * E * G * * A * C * * D | |||
D - D# - Eb - E - E#/Gb - G - G# - Ab - A - A#/Cb - C - C# - Db - D | |||
P1 - A1/ds3 - ms3 - Ms3 - As3/d4d - P4d - A4d - d5d - P5d - A5d/ds7 - ms7 - Ms7 - As7/d8d - P8d | |||
__**18edo**__**:** (generator = 11\18 = perfect 5thoid) C C# * Db D | |||
D * * * E * * G * * * A * * C * * * D | |||
D - D# - Dx/Ebb - Eb - E - E# - Gb - G - G# - Gx/Abb - Ab - A - A# - Cb - C - C# - Cx/Dbb - Db - D | |||
P1 - A1 - ds3 - ms3 - Ms3 - As3 - d4d - P4d - A4d - AA4d/dd5d - d5d - P5d - A5d - ds7 - ms7 - Ms7 - As7 - d8d - P8d | |||
===__Fourthward EDOs (9, 16 and 23)__=== | ===__Fourthward EDOs (9, 16 and 23)__=== | ||
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F# - C# - G# - D# - A# - E# - B# - F - C - G - D - A - E - B - Fb - Cb - Gb - Db - Ab - Eb - Bb - Fbb etc. | F# - C# - G# - D# - A# - E# - B# - F - C - G - D - A - E - B - Fb - Cb - Gb - Db - Ab - Eb - Bb - Fbb etc. | ||
**__9edo__:** D E * F G A B * C D | **__9edo__:** C/Db C#/D | ||
D E * F G A B * C D | |||
D - E - E#/Fb - F - G - A - B - B#/Cb - C - D | D - E - E#/Fb - F - G - A - B - B#/Cb - C - D | ||
P1 - m2 - M2/m3 - M3 - P4 - P5 - m6 - M6/m7 - M7 - P8 | P1 - m2 - M2/m3 - M3 - P4 - P5 - m6 - M6/m7 - M7 - P8 | ||
**__16edo__:** D * E * * F * G * A * B * * C * D | **__16edo__:** C C#/Db D | ||
D * E * * F * G * A * B * * C * D | |||
D - D#/Eb - E - E# - Fb - F F#/Gb - G - G#/Ab - A - A#/Bb - B - B# - Cb - C - C#/Db - D | D - D#/Eb - E - E# - Fb - F F#/Gb - G - G#/Ab - A - A#/Bb - B - B# - Cb - C - C#/Db - D | ||
P1 - A1/d2 - m2 - M2 - m3 - M3 - A3/d4 - P4 - A4/d5 - P5 - A5/d6 - m6 - M6 - m7 - M7 - A7/d8 - P8 | P1 - A1/d2 - m2 - M2 - m3 - M3 - A3/d4 - P4 - A4/d5 - P5 - A5/d6 - m6 - M6 - m7 - M7 - A7/d8 - P8 | ||
**__23edo__:** D * * E * * * F * * G * * A * * B * * * C * * D | **__23edo__:** C C# * Db D | ||
D * * E * * * F * * G * * A * * B * * * C * * D | |||
D - D# - Eb - E - E# - Ex/Fbb - Fb - F - F# - Gb - G - G# - Ab - A - A# - Bb - B - B# - Bx/Cbb - Cb - C - C# - Db - D | D - D# - Eb - E - E# - Ex/Fbb - Fb - F - F# - Gb - G - G# - Ab - A - A# - Bb - B - B# - Bx/Cbb - Cb - C - C# - Db - D | ||
P1 - A1 - d2 - m2 - M2 - A2/d3 - m3 - M3 - A3 - d4 - P4 - A4 - d5 - P5 - A5 - d6 - m6 - M6 - A6/d7 - m7 - M7 - A7 - d8 - P8 | P1 - A1 - d2 - m2 - M2 - A2/d3 - m3 - M3 - A3 - d4 - P4 - A4 - d5 - P5 - A5 - d6 - m6 - M6 - A6/d7 - m7 - M7 - A7 - d8 - P8 | ||
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F - C - G - D - A - E - B - F - C - G - D - A - E - B etc. | F - C - G - D - A - E - B - F - C - G - D - A - E - B etc. | ||
**__7edo__:** D E F G A B C D | **__7edo__:** C/Db C#/D | ||
D E F G A B C D | |||
P1 - P2 - P3 - P4 - P5 - P6 - P7 - P8 | P1 - P2 - P3 - P4 - P5 - P6 - P7 - P8 | ||
Because everything is perfect, the quality can be omitted: 1 - 2 - 3 - 4 - 5 - 6 - 7 - 8 | Because everything is perfect, the quality can be omitted: 1 - 2 - 3 - 4 - 5 - 6 - 7 - 8 | ||
**__14edo__:** D * E * F * G * A * B * C * D | **__14edo__:** 2 keys per sharp/flat: C/C# * Db/D | ||
D * E * F * G * A * B * C * D | |||
D - D^/Ev - E - E/ Fv - F - F^/Gv - G - G^/Av - A - A^/Bv - B - B^/Cv - C - C^/Dv - D | D - D^/Ev - E - E/ Fv - F - F^/Gv - G - G^/Av - A - A^/Bv - B - B^/Cv - C - C^/Dv - D | ||
1 - ^1/v2 - 2 - ^2/v3 - 3 - ^3/v4 - 4 - ^4/v5 - 5 - ^5/v6 - 6 - ^6/v7 - 7 - ^7/v8 - 8 | 1 - ^1/v2 - 2 - ^2/v3 - 3 - ^3/v4 - 4 - ^4/v5 - 5 - ^5/v6 - 6 - ^6/v7 - 7 - ^7/v8 - 8 | ||
**__21edo__:** D * * E * * F * * G * * A * * B * * C * * D | **__21edo__:** 3 keys per sharp/flat: C/C# * * Db/D | ||
D * * E * * F * * G * * A * * B * * C * * D | |||
D - D^ - Ev - E - E^ - Fv - F - F^ - Gv - G - G^ - Av - A - A^ - Bv - B - B^ - Cv - C - C^ - Dv - D | D - D^ - Ev - E - E^ - Fv - F - F^ - Gv - G - G^ - Av - A - A^ - Bv - B - B^ - Cv - C - C^ - Dv - D | ||
1 - ^1 - v2 - 2 - ^2 - v3 - 3 - ^3 - v4 - 4 - ^4 - v5 - 5 - ^5 - v6 - 6 - ^6 - v7 - 7 - ^7 - v8 - 8 | 1 - ^1 - v2 - 2 - ^2 - v3 - 3 - ^3 - v4 - 4 - ^4 - v5 - 5 - ^5 - v6 - 6 - ^6 - v7 - 7 - ^7 - v8 - 8 | ||
**__28edo__:** D * * * E * * * F * * * G * * * A * * * B * * * C * * * D | **__28edo__:** 4 keys per sharp/flat: C/C# * * * Db/D | ||
D * * * E * * * F * * * G * * * A * * * B * * * C * * * D | |||
D - D^ - D^^/Evv - Ev - E - E^ - E^^/Fvv - Fv - F - F^ - F^^/Gvv - Gv - G - G^ - G^^/Avv - Av - A etc. | D - D^ - D^^/Evv - Ev - E - E^ - E^^/Fvv - Fv - F - F^ - F^^/Gvv - Gv - G - G^ - G^^/Avv - Av - A etc. | ||
1 - ^1 - ^^1/vv2 - v2 - 2 - ^2 - ^^2/vv3 - v3 - 3 - ^3 - ^^3/vv4 - v4 - 4 - ^4 - ^^4/vv5 - v5 - 5 etc. | 1 - ^1 - ^^1/vv2 - v2 - 2 - ^2 - ^^2/vv3 - v3 - 3 - ^3 - ^^3/vv4 - v4 - 4 - ^4 - ^^4/vv5 - v5 - 5 etc. | ||
**__35edo__:** D * * * * E * * * * F * * * * G * * * * A * * * * B * * * * C * * * * D | **__35edo__:** 5 keys per sharp/flat: C/C# * * * * Db/D | ||
D * * * * E * * * * F * * * * G * * * * A * * * * B * * * * C * * * * D | |||
D - D^ - D^^ - Evv - Ev - E - E^ - E^^ - Fvv - Fv - F - F^ - F^^ - Gvv - Gv - G - G^ - G^^ - Avv - Av - A etc. | D - D^ - D^^ - Evv - Ev - E - E^ - E^^ - Fvv - Fv - F - F^ - F^^ - Gvv - Gv - G - G^ - G^^ - Avv - Av - A etc. | ||
1 - ^1 - ^^1 - vv2 - v2 - 2 - ^2 - ^^2 - vv3 - v3 - 3 - ^3 - ^^3 - vv4 - v4 - 4 - ^4 - ^^4 - vv5 - v5 - 5 etc.</pre></div> | 1 - ^1 - ^^1 - vv2 - v2 - 2 - ^2 - ^^2 - vv3 - v3 - 3 - ^3 - ^^3 - vv4 - v4 - 4 - ^4 - ^^4 - vv5 - v5 - 5 etc. | ||
===__Pentatonic EDOs (5, 10, 15, 20, 25 and 30)__=== | |||
All pentatonic EDOs use the usual chain of fifths: m2 - m6 - m3 - m7 - P4 - P1 - P5 - M2 - M6 - M3 - M7 etc. | |||
Fb - Cb - Gb - Db - Ab - Eb - Bb - F - C - G - D - A - E - B - F# - C# - G# - D# - A# - E# - B# etc. | |||
In all pentatonic EDOs, the minor 2nd = unison and the major 3rd = perfect fourth. | |||
**__5edo__:** C/Db C#/D | |||
D E/F G A B/C D | |||
P1 - M2/m3 - P4 - P5 - M6/m7 - P8 | |||
**__10edo__:** 2 keys per sharp/flat: C/Db * C#/D | |||
D * E/F * G * A * B/C * D | |||
D - D^/Ev - E/F - F^/Gv - G - G^/Av - A - A^/Bv - B/C - C^/Dv - D | |||
P1/m2 - ^m2/vM2 - M2/m3 - ^m3/vM3 - M3/P4 - ^P4/vP5 - P5/m6 - ^m6/vM6 - M6/m7 - ^m7/vM7 - P8 | |||
**__15edo__:** 3 keys per sharp/flat: C/Db [*] [*] C#/D | |||
D * * E/F * * G * * A * * B/C * * D | |||
D - D^ - Ev - E/F - F^ - Gv - G - G^ - Av - A - A^ - Bv - B/C - C^ - Dv - D | |||
P1/m2 - ^m2 - vM2 - M2/m3 - ^m3 - vM3 - M3/P4 - ^P4 - vP5 - P5/m6 - ^m6 - vM6 - M6/m7 - ^m7 - vM7 - P8 | |||
**__20edo__:** 4 keys per sharp/flat: C/Db * * * C#/D | |||
D * * * E/F * * * G * * * A * * * B/C * * * D | |||
D - D^ - D^^/Evv - Ev - E/F - F^ - F^^/Gvv - Gv - G - G^ - G^^/Avv - Av - A - A^ - A^^/Bvv - Bv - B/C - C^ - C^^/Dvv - Dv - D | |||
P1/m2 - ^m2 - ^^m2/vvM2 - vM2 - M2/m3 - ^m3 - ^^m3/vvM3 - vM3 - M3/P4 - ^P4 - ^^P4/vvP5 - vP5 - P5/m6 - ^m6 - ^^m6/vvM6 - vM6 - M6/m7 - ^m7 - ^^m7/vvM7 - vM7 - P8 | |||
**__25edo__:** 5 keys per sharp/flat: C/Db * * * * C#/D | |||
D * * * * E/F * * * * G * * * * A * * * * B/C * * * * D | |||
D - D^ - D^^ - Evv - Ev - E/F - F^ - F^^ - Gvv - Gv - G - G^ - G^^ - Avv - Av - A - A^ - A^^ - Bvv - Bv - B/C - C^ - C^^ - Dvv - Dv - D | |||
P1/m2 - ^m2 - ^^m2 - vvM2 - vM2 - M2/m3 - ^m3 - ^^m3 - vvM3 - vM3 - M3/P4 - ^P4 - ^^P4 - vvP5 - vP5 - P5/m6 - ^m6 - ^^m6 - vvM6 - vM6 - M6/m7 - ^m7 - ^^m7 - vvM7 - vM7 - P8 | |||
**__30edo__:** 6 keys per sharp/flat: C/Db * * * * * C#/D | |||
D * * * * * E/F * * * * * G * * * * * A * * * * * B/C * * * * * D | |||
D - D^ - D^^ - Evv - Ev - E/F - F^ - F^^ - Gvv - Gv - G - G^ - G^^ - Avv - Av - A - A^ - A^^ - Bvv - Bv - B/C - C^ - C^^ - Dvv - Dv - D | |||
P1/m2 - ^m2 - ^^m2 - vvM2 - vM2 - M2/m3 - ^m3 - ^^m3 - vvM3 - vM3 - M3/P4 - ^P4 - ^^P4 - vvP5 - vP5 - P5/m6 - ^m6 - ^^m6 - vvM6 - vM6 - M6/m7 - ^m7 - ^^m7 - vvM7 - vM7 - P8 | |||
===__"Sweet" EDOs (12, 17, 19, 22, 24, 26, 27, 29, 31, etc.)__=== | |||
All sweet EDOs use the usual chain of fifths: m2 - m6 - m3 - m7 - P4 - P1 - P5 - M2 - M6 - M3 - M7 etc. | |||
Fb - Cb - Gb - Db - Ab - Eb - Bb - F - C - G - D - A - E - B - F# - C# - G# - D# - A# - E# - B# etc. | |||
**__12edo__:** sharp/flat = 1 key, no ups and downs: C C#/Db D | |||
D * E F * G * A * B C * D | |||
D - D#/Eb - E - F - F#/Gb - G - G#/Ab - A - A#/Bb - B - C - C#/Db - D | |||
P1 - m2 - M2 - m3 - M3 - P4 - A4/d5 - P5 - m6 - M6 - m7 - M7 - P8 | |||
**__17edo__:** sharp = 2 keys: C Db C# C | |||
D * * E F * * G * * A * * B C * * D | |||
D - D^/Eb - D#/Ev - Eb - E - F - F^/Gb - F#/Gv - G - G^/Ab - G#/Av - A - A^/Bb - A#/Bv - B - C - C^/Db - C#/Dv - D | |||
P1 - m2 - ^m2/vM2 - M2 - m3 - ^m3/vM3 - M3 - P4 - ^P4/d5 - A4/vP5 - P5 - m6 - ^m6/vM6 - M6 - m7 ^m7/vM7 - M7 - P8 | |||
**__19edo__:** no ups and downs C C# Db D | |||
D * * E * F * * G * * A * * B * C * * D | |||
D - D# - Eb - E - E#/Fb - F - F# - Gb - G - G# - Ab - A - A# - Bb - B - B#/Cb - C - C# - Db - D | |||
P1 - A1/d2 - m2 - M2 - A2/d3 - m3 - M3 - A3/d4 - P4 - A4 - d5 - P5 - A5/d6 - m6 - M6 - A6/d7 - m7 - M7 - A7/d8 - P8 | |||
**__22edo__:** sharp = 3 keys: C Db * C# C | |||
D * * * E F * * * G * * * A * * * B C * * * D | |||
D - D^/Eb - D#v/Eb^ - D#/Ev - E - F - F^/Gb - F#v/Gb^ - F#/Gv - G - G^/Ab - G#v/Ab^ - G#/Av - A etc. | |||
P1 - m2 - ^m2 - vM2 - M2 - m3 - ^m3 - vM3 - M3 - P4 - ^P4/d5 - vA4/^d5 - A4/vP5 - P5 etc. | |||
**__24edo__:** sharp = 2 keys: C * C#/Db * C | |||
D * * * E * F * * * G * * * A * * * B * C * * * D | |||
D - D^/Ebv - D#/Eb - D#^/Ev - E - E^/Fv - F - F^/Gbv - F#/Gb - F#^/Gv - G - G^/Abv - G#/Ab - G#^/Av - A etc. | |||
P1 - ^P1/vm2 - m2 - ^m2/vM2 - M2 - ^M2/vm3 - m3 - ^m3/vM3 - M3 - ^M3/vP4 - P4 - ^P4/vd5 - A4/d5 - ^A4/vP5 - P5 etc.</pre></div> | |||
<h4>Original HTML content:</h4> | <h4>Original HTML content:</h4> | ||
<div style="width:100%; max-height:400pt; overflow:auto; background-color:#f8f9fa; border: 1px solid #eaecf0; padding:0em"><pre style="margin:0px;border:none;background:none;word-wrap:break-word;width:200%;white-space: pre-wrap ! important" class="old-revision-html"><html><head><title>Ups and Downs Notation</title></head><body><!-- ws:start:WikiTextHeadingRule:0:&lt;h1&gt; --><h1 id="toc0"><a name="x&quot;Ups and Downs&quot; Notation"></a><!-- ws:end:WikiTextHeadingRule:0 -->&quot;Ups and Downs&quot; Notation</h1> | <div style="width:100%; max-height:400pt; overflow:auto; background-color:#f8f9fa; border: 1px solid #eaecf0; padding:0em"><pre style="margin:0px;border:none;background:none;word-wrap:break-word;width:200%;white-space: pre-wrap ! important" class="old-revision-html"><html><head><title>Ups and Downs Notation</title></head><body><!-- ws:start:WikiTextHeadingRule:0:&lt;h1&gt; --><h1 id="toc0"><a name="x&quot;Ups and Downs&quot; Notation"></a><!-- ws:end:WikiTextHeadingRule:0 -->&quot;Ups and Downs&quot; Notation</h1> | ||
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Not counting the trivial edos 2, 3, 4 and 6, there are only seven such edos. As seen in this diagram, they are the ones to the left of the central line in the light blue region, plus the ones to the right of the central line in the orange region. The ones on the left edge of the blue region are the fourthward ones like 16edo, and have been dealt with already. 23edo can be notated similarly to 16edo by using a fifth of 13\23 instead of 14\23. That leaves only four edos: 8, 11, 13, and 18.<br /> | Not counting the trivial edos 2, 3, 4 and 6, there are only seven such edos. As seen in this diagram, they are the ones to the left of the central line in the light blue region, plus the ones to the right of the central line in the orange region. The ones on the left edge of the blue region are the fourthward ones like 16edo, and have been dealt with already. 23edo can be notated similarly to 16edo by using a fifth of 13\23 instead of 14\23. That leaves only four edos: 8, 11, 13, and 18.<br /> | ||
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The other approach is to use some interval other than the fifth to generate the notation. Above I said 22edo using an even distribution of note names such as C _ _ D _ _ E _ _ F _ _ _ G _ _ A _ _ B _ _ C.<br /> | The other approach is to use some interval other than the fifth to generate the notation. Above I said 22edo using an even distribution of note names such as C _ _ D _ _ E _ _ F _ _ _ G _ _ A _ _ B _ _ C.<br /> | ||
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8edo | <u><strong>Theoretical alternatives for 8edo, 11edo, 13edo and 18edo</strong></u><br /> | ||
<br /> | <br /> | ||
<br /> | <br /> | ||
8edo octatonic (every note | 8edo octatonic (every note is a generator)<br /> | ||
P1 - P2 - P3 - P4 - P5 - P6 - P7 - P8 - P9<br /> | P1 - P2 - P3 - P4 - P5 - P6 - P7 - P8 - P9<br /> | ||
<br /> | <br /> | ||
11edo heptatonic narrow-fifth-based, fourthwards with ^/v, 2 keys per #/b (3/2 maps to 6\11 5th):<br /> | 11edo heptatonic narrow-fifth-based, fourthwards with ^/v, 2 keys per #/b (3/2 maps to 6\11 5th):<br /> | ||
P1 m2 vM2/m3 M2/^m3 M3 P4 P5 m6 vM6/m7 M6/^m7 M7 P8<br /> | P1 - m2 - vM2/m3 - M2/^m3 - M3 - P4 - P5 - m6 - vM6/m7 - M6/^m7 - M7 - P8<br /> | ||
problematic because m3 = 2\11 is narrower than M2 = 3\11<br /> | problematic because m3 = 2\11 is narrower than M2 = 3\11<br /> | ||
<br /> | <br /> | ||
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P1 m2 M2/m3 M3/m4 M4 P5 P6 m7 M7/m8 M8/m9 M9 P8<br /> | P1 m2 M2/m3 M3/m4 M4 P5 P6 m7 M7/m8 M8/m9 M9 P8<br /> | ||
requires learning nonotonic interval arithmetic and devising a nonotonic staff notation<br /> | requires learning nonotonic interval arithmetic and devising a nonotonic staff notation<br /> | ||
<br /> | <br /> | ||
11edo pentatonic wide-fifth-based, fifthwards using ^/v, 2 keys per #/b (3/2 maps to 7\11 6th):<br /> | 11edo pentatonic wide-fifth-based, fifthwards using ^/v, 2 keys per #/b (3/2 maps to 7\11 6th):<br /> | ||
P1 - ms3 - ^ms3/vMs3 - Ms3 - P4d - ^P4d/d5d - A4d/vP5d - P5d - ms7 - ^ms7/vMs7 - Ms7 - P8d<br /> | P1 - ms3 - ^ms3/vMs3 - Ms3 - P4d - ^P4d/d5d - A4d/vP5d - P5d - ms7 - ^ms7/vMs7 - Ms7 - P8d<br /> | ||
pentatonic plus ups and downs is doubly confusing!<br /> | |||
<br /> | <br /> | ||
11edo octatonic wide-fifth-based, fifthwards, no ^/v (3/2 maps to 7\11 6th):<br /> | 11edo octatonic wide-fifth-based, fifthwards, no ^/v (3/2 maps to 7\11 = perfect 6th):<br /> | ||
octatonic chain of 6ths: m3 - m8 - m5 - m2 - m7 - P4 - P1 - P6 - M3 - M8 - M5 - M2 - M7<br /> | octatonic chain of 6ths: m3 - m8 - m5 - m2 - m7 - P4 - P1 - P6 - M3 - M8 - M5 - M2 - M7<br /> | ||
P1 - m2 - M2/m3 - M3 - P4 - m5 - M5 - P6 - m7 - M7/m8 - M8 - P9<br /> | P1 - m2 - M2/m3 - M3 - P4 - m5 - M5 - P6 - m7 - M7/m8 - M8 - P9<br /> | ||
requires learning octatonic interval arithmetic and notation<br /> | requires learning octatonic interval arithmetic and notation<br /> | ||
<br /> | <br /> | ||
13edo heptatonic narrow-fifth-based, fourthwards, 3 keys per #/b, (3/2 maps to 7\13 = perfect 5th):<br /> | |||
13edo heptatonic narrow-fifth-based, fourthwards, 3 keys per #/b, (3/2 maps to 7\13 5th):<br /> | |||
P1 - m2 - m3 - vM2/^m3 - M2 - M3 - P4 - P5 - m6 - m7 - vM6/^m7 - M6 - M7 - P8<br /> | P1 - m2 - m3 - vM2/^m3 - M2 - M3 - P4 - P5 - m6 - m7 - vM6/^m7 - M6 - M7 - P8<br /> | ||
problematic because m3 = 2\13 is narrower than M2 = 4\13<br /> | problematic because m3 = 2\13 is narrower than M2 = 4\13<br /> | ||
<br /> | <br /> | ||
(13edo undecatonic narrow-fifth-based, 3/2 maps to 7\13 7th) | (13edo undecatonic narrow-fifth-based, 3/2 maps to 7\13 = perfect 7th)<br /> | ||
<br /> | <br /> | ||
(13edo octatonic wide-fifth-based, fourthwards)<br /> | (13edo octatonic wide-fifth-based, fourthwards)<br /> | ||
<br /> | <br /> | ||
18edo heptatonic narrow-fifth-based, fourthwards, 2 keys per #/b (3/2 maps to 10\18 = perfect 5th)<br /> | |||
18edo heptatonic narrow-fifth-based, fourthwards, 2 keys per #/b (3/2 maps to 10\18)<br /> | |||
P1 - vm2 - m2 - vM2 - M2/m3 - vM3 - M3 - ^M3 - P4 - ^P4/vP5 - P5 - vm6 - m6 - vM6 - M6/m7 - vM7 - M7 - ^M7 - P8<br /> | P1 - vm2 - m2 - vM2 - M2/m3 - vM3 - M3 - ^M3 - P4 - ^P4/vP5 - P5 - vm6 - m6 - vM6 - M6/m7 - vM7 - M7 - ^M7 - P8<br /> | ||
fourthwards plus ups and downs is doubly confusing!<br /> | fourthwards plus ups and downs is doubly confusing!<br /> | ||
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18edo nonatonic narrow-fifth-based<br /> | 18edo nonatonic narrow-fifth-based (3/2 maps to 10\18 = perfect 6th)<br /> | ||
P1 - vP2 - P2 - vP3 - P3 - vP4- P4 - vP5 - P5 - vP6 - P6 - vP7 - P7 - vP8 - P8 - vP9 - P9 - vP10 - P10<br /> | P1 - vP2 - P2 - vP3 - P3 - vP4- P4 - vP5 - P5 - vP6 - P6 - vP7 - P7 - vP8 - P8 - vP9 - P9 - vP10 - P10<br /> | ||
requires learning nonotonic interval arithmetic and devising a nonotonic staff notation<br /> | requires learning nonotonic interval arithmetic and devising a nonotonic staff notation<br /> | ||
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<!-- ws:start:WikiTextHeadingRule:12:&lt;h1&gt; --><h1 id="toc6"><a name="Summary of EDO notation"></a><!-- ws:end:WikiTextHeadingRule:12 --><u><strong>Summary of EDO notation</strong></u></h1> | <!-- ws:start:WikiTextHeadingRule:12:&lt;h1&gt; --><h1 id="toc6"><a name="Summary of EDO notation"></a><!-- ws:end:WikiTextHeadingRule:12 --><u><strong>Summary of EDO notation</strong></u></h1> | ||
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There are five EDO categories, based on the size of the fifth:<br /> | |||
&quot;Fifth-less&quot; EDOs (8, 11, 13 and 18)<br /> | &quot;Fifth-less&quot; EDOs (8, 11, 13 and 18)<br /> | ||
Fourthward EDOs (9, 16 and 23)<br /> | Fourthward EDOs (9, 16 and 23)<br /> | ||
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Pentatonic EDOs (5, 10, 15, 20, 25 and 30)<br /> | Pentatonic EDOs (5, 10, 15, 20, 25 and 30)<br /> | ||
&quot;Sweet&quot; EDOs (all others)<br /> | &quot;Sweet&quot; EDOs (all others)<br /> | ||
The first two categories never use ups and downs, the next two always do (except for 5edo and 7edo).<br /> | The first two categories never use ups and downs, the next two always do (except for 5edo and 7edo). The last may or may not. <br /> | ||
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To summarize an EDO, a scale fragment from C to D is shown, including C# and Db. The C-C# interval is the augmented unison, and if they are not adjacent, ups and downs are required.The C-Db interval is the minor 2nd<br /> | |||
The C-D interval is the major 2nd (P2 for perfect EDOs, m2 for fourthward EDOs).<br /> | |||
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<!-- ws:start:WikiTextHeadingRule:14:&lt;h3&gt; --><h3 id="toc7"><a name="Summary of EDO notation--&quot;Fifth-less&quot; EDOs (8, 11, 13 and 18)"></a><!-- ws:end:WikiTextHeadingRule:14 --><u><strong>&quot;Fifth-less&quot; EDOs (8, 11, 13 and 18)</strong></u></h3> | <!-- ws:start:WikiTextHeadingRule:14:&lt;h3&gt; --><h3 id="toc7"><a name="Summary of EDO notation--&quot;Fifth-less&quot; EDOs (8, 11, 13 and 18)"></a><!-- ws:end:WikiTextHeadingRule:14 --><u><strong>&quot;Fifth-less&quot; EDOs (8, 11, 13 and 18)</strong></u></h3> | ||
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E# - G# - B# - D# - F# - A# - C# - E - G - B - D - F - A - C - Eb - Gb - Bb - Db - Fb - Ab - Cb<br /> | E# - G# - B# - D# - F# - A# - C# - E - G - B - D - F - A - C - Eb - Gb - Bb - Db - Fb - Ab - Cb<br /> | ||
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<!-- ws:start:WikiTextHeadingRule:16:&lt;h3&gt; --><h3 id="toc8"><a name="Summary of EDO notation--Fourthward EDOs (9, 16 and 23)"></a><!-- ws:end:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:16:&lt;h3&gt; --><h3 id="toc8"><a name="Summary of EDO notation--Alternate pentatonic notation for EDOs 8, 13 and 18"></a><!-- ws:end:WikiTextHeadingRule:16 --><u><strong>Alternate pentatonic notation for EDOs 8, 13 and 18</strong></u></h3> | ||
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All three EDOs use the same pentatonic fifthwards chain of fifths: ms3 - ms7 - P4d - P1 - P5d - Ms3 - Ms7 - A4d etc.<br /> | |||
Cb - Gb - Db - Ab - Eb - C - G - D - A - E - C# - G# - D# - A# - E# etc.<br /> | |||
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<u><strong>8edo</strong></u><strong>:</strong> (generator = 5\8 = perfect 5thoid) C C#/Db D<br /> | |||
D * E G * A C * D<br /> | |||
D - D#/Eb - E - G - G#/Ab - A - C - C#/Db - D<br /> | |||
P1 - ms3 - Ms3 - P4d - A4d/d5d - P5d - ms7 - Ms7 - P8d<br /> | |||
<br /> | |||
<u><strong>13edo</strong></u><strong>:</strong> (generator = 8\13 = perfect 5thoid) C C# Db D<br /> | |||
D * * E * G * * A * C * * D<br /> | |||
D - D# - Eb - E - E#/Gb - G - G# - Ab - A - A#/Cb - C - C# - Db - D<br /> | |||
P1 - A1/ds3 - ms3 - Ms3 - As3/d4d - P4d - A4d - d5d - P5d - A5d/ds7 - ms7 - Ms7 - As7/d8d - P8d<br /> | |||
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<u><strong>18edo</strong></u><strong>:</strong> (generator = 11\18 = perfect 5thoid) C C# * Db D<br /> | |||
D * * * E * * G * * * A * * C * * * D<br /> | |||
D - D# - Dx/Ebb - Eb - E - E# - Gb - G - G# - Gx/Abb - Ab - A - A# - Cb - C - C# - Cx/Dbb - Db - D<br /> | |||
P1 - A1 - ds3 - ms3 - Ms3 - As3 - d4d - P4d - A4d - AA4d/dd5d - d5d - P5d - A5d - ds7 - ms7 - Ms7 - As7 - d8d - P8d<br /> | |||
<br /> | |||
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<!-- ws:start:WikiTextHeadingRule:18:&lt;h3&gt; --><h3 id="toc9"><a name="Summary of EDO notation--Fourthward EDOs (9, 16 and 23)"></a><!-- ws:end:WikiTextHeadingRule:18 --><u>Fourthward EDOs (9, 16 and 23)</u></h3> | |||
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All fourthwards EDOs use the same chain of fifths: M2 - M6 - M3 - M7 - P4 - P1 - P5 - m2 - m6 - m3 - m7 - A4 etc.<br /> | All fourthwards EDOs use the same chain of fifths: M2 - M6 - M3 - M7 - P4 - P1 - P5 - m2 - m6 - m3 - m7 - A4 etc.<br /> | ||
F# - C# - G# - D# - A# - E# - B# - F - C - G - D - A - E - B - Fb - Cb - Gb - Db - Ab - Eb - Bb - Fbb etc.<br /> | F# - C# - G# - D# - A# - E# - B# - F - C - G - D - A - E - B - Fb - Cb - Gb - Db - Ab - Eb - Bb - Fbb etc.<br /> | ||
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<strong><u>9edo</u>:</strong> D E * F G A B * C D<br /> | <strong><u>9edo</u>:</strong> C/Db C#/D <br /> | ||
D E * F G A B * C D<br /> | |||
D - E - E#/Fb - F - G - A - B - B#/Cb - C - D<br /> | D - E - E#/Fb - F - G - A - B - B#/Cb - C - D<br /> | ||
P1 - m2 - M2/m3 - M3 - P4 - P5 - m6 - M6/m7 - M7 - P8<br /> | P1 - m2 - M2/m3 - M3 - P4 - P5 - m6 - M6/m7 - M7 - P8<br /> | ||
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<strong><u>16edo</u>:</strong> D * E * * F * G * A * B * * C * D<br /> | <strong><u>16edo</u>:</strong> C C#/Db D <br /> | ||
D * E * * F * G * A * B * * C * D<br /> | |||
D - D#/Eb - E - E# - Fb - F F#/Gb - G - G#/Ab - A - A#/Bb - B - B# - Cb - C - C#/Db - D<br /> | D - D#/Eb - E - E# - Fb - F F#/Gb - G - G#/Ab - A - A#/Bb - B - B# - Cb - C - C#/Db - D<br /> | ||
P1 - A1/d2 - m2 - M2 - m3 - M3 - A3/d4 - P4 - A4/d5 - P5 - A5/d6 - m6 - M6 - m7 - M7 - A7/d8 - P8<br /> | P1 - A1/d2 - m2 - M2 - m3 - M3 - A3/d4 - P4 - A4/d5 - P5 - A5/d6 - m6 - M6 - m7 - M7 - A7/d8 - P8<br /> | ||
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<strong><u>23edo</u>:</strong> D * * E * * * F * * G * * A * * B * * * C * * D<br /> | <strong><u>23edo</u>:</strong> C C# * Db D<br /> | ||
D * * E * * * F * * G * * A * * B * * * C * * D<br /> | |||
D - D# - Eb - E - E# - Ex/Fbb - Fb - F - F# - Gb - G - G# - Ab - A - A# - Bb - B - B# - Bx/Cbb - Cb - C - C# - Db - D<br /> | D - D# - Eb - E - E# - Ex/Fbb - Fb - F - F# - Gb - G - G# - Ab - A - A# - Bb - B - B# - Bx/Cbb - Cb - C - C# - Db - D<br /> | ||
P1 - A1 - d2 - m2 - M2 - A2/d3 - m3 - M3 - A3 - d4 - P4 - A4 - d5 - P5 - A5 - d6 - m6 - M6 - A6/d7 - m7 - M7 - A7 - d8 - P8<br /> | P1 - A1 - d2 - m2 - M2 - A2/d3 - m3 - M3 - A3 - d4 - P4 - A4 - d5 - P5 - A5 - d6 - m6 - M6 - A6/d7 - m7 - M7 - A7 - d8 - P8<br /> | ||
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<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:20:&lt;h3&gt; --><h3 id="toc10"><a name="Summary of EDO notation--&quot;Perfect&quot; EDOs (7, 14, 21, 28 and 35)"></a><!-- ws:end:WikiTextHeadingRule:20 --><u>&quot;Perfect&quot; EDOs (7, 14, 21, 28 and 35)</u></h3> | ||
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All perfect EDOs use the same chain of fifths: P2 - P6 - P3 - P7 - P4 - P1 - P5 - P2 - P6 - P3 - P7 etc.<br /> | All perfect EDOs use the same chain of fifths: P2 - P6 - P3 - P7 - P4 - P1 - P5 - P2 - P6 - P3 - P7 etc.<br /> | ||
F - C - G - D - A - E - B - F - C - G - D - A - E - B etc.<br /> | F - C - G - D - A - E - B - F - C - G - D - A - E - B etc.<br /> | ||
<br /> | <br /> | ||
<strong><u>7edo</u>:</strong> D E F G A B C D<br /> | <strong><u>7edo</u>:</strong> C/Db C#/D<br /> | ||
D E F G A B C D<br /> | |||
P1 - P2 - P3 - P4 - P5 - P6 - P7 - P8<br /> | P1 - P2 - P3 - P4 - P5 - P6 - P7 - P8<br /> | ||
Because everything is perfect, the quality can be omitted: 1 - 2 - 3 - 4 - 5 - 6 - 7 - 8<br /> | Because everything is perfect, the quality can be omitted: 1 - 2 - 3 - 4 - 5 - 6 - 7 - 8<br /> | ||
<br /> | <br /> | ||
<strong><u>14edo</u>:</strong> D * E * F * G * A * B * C * D<br /> | <strong><u>14edo</u>:</strong> 2 keys per sharp/flat: C/C# * Db/D <br /> | ||
D * E * F * G * A * B * C * D<br /> | |||
D - D^/Ev - E - E/ Fv - F - F^/Gv - G - G^/Av - A - A^/Bv - B - B^/Cv - C - C^/Dv - D<br /> | D - D^/Ev - E - E/ Fv - F - F^/Gv - G - G^/Av - A - A^/Bv - B - B^/Cv - C - C^/Dv - D<br /> | ||
1 - ^1/v2 - 2 - ^2/v3 - 3 - ^3/v4 - 4 - ^4/v5 - 5 - ^5/v6 - 6 - ^6/v7 - 7 - ^7/v8 - 8<br /> | 1 - ^1/v2 - 2 - ^2/v3 - 3 - ^3/v4 - 4 - ^4/v5 - 5 - ^5/v6 - 6 - ^6/v7 - 7 - ^7/v8 - 8<br /> | ||
<br /> | <br /> | ||
<strong><u>21edo</u>:</strong> D * * E * * F * * G * * A * * B * * C * * D<br /> | <strong><u>21edo</u>:</strong> 3 keys per sharp/flat: C/C# * * Db/D<br /> | ||
D * * E * * F * * G * * A * * B * * C * * D<br /> | |||
D - D^ - Ev - E - E^ - Fv - F - F^ - Gv - G - G^ - Av - A - A^ - Bv - B - B^ - Cv - C - C^ - Dv - D<br /> | D - D^ - Ev - E - E^ - Fv - F - F^ - Gv - G - G^ - Av - A - A^ - Bv - B - B^ - Cv - C - C^ - Dv - D<br /> | ||
1 - ^1 - v2 - 2 - ^2 - v3 - 3 - ^3 - v4 - 4 - ^4 - v5 - 5 - ^5 - v6 - 6 - ^6 - v7 - 7 - ^7 - v8 - 8<br /> | 1 - ^1 - v2 - 2 - ^2 - v3 - 3 - ^3 - v4 - 4 - ^4 - v5 - 5 - ^5 - v6 - 6 - ^6 - v7 - 7 - ^7 - v8 - 8<br /> | ||
<br /> | <br /> | ||
<strong><u>28edo</u>:</strong> D * * * E * * * F * * * G * * * A * * * B * * * C * * * D<br /> | <strong><u>28edo</u>:</strong> 4 keys per sharp/flat: C/C# * * * Db/D<br /> | ||
D * * * E * * * F * * * G * * * A * * * B * * * C * * * D<br /> | |||
D - D^ - D^^/Evv - Ev - E - E^ - E^^/Fvv - Fv - F - F^ - F^^/Gvv - Gv - G - G^ - G^^/Avv - Av - A etc.<br /> | D - D^ - D^^/Evv - Ev - E - E^ - E^^/Fvv - Fv - F - F^ - F^^/Gvv - Gv - G - G^ - G^^/Avv - Av - A etc.<br /> | ||
1 - ^1 - ^^1/vv2 - v2 - 2 - ^2 - ^^2/vv3 - v3 - 3 - ^3 - ^^3/vv4 - v4 - 4 - ^4 - ^^4/vv5 - v5 - 5 etc.<br /> | 1 - ^1 - ^^1/vv2 - v2 - 2 - ^2 - ^^2/vv3 - v3 - 3 - ^3 - ^^3/vv4 - v4 - 4 - ^4 - ^^4/vv5 - v5 - 5 etc.<br /> | ||
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<strong><u>35edo</u>:</strong> D * * * * E * * * * F * * * * G * * * * A * * * * B * * * * C * * * * D<br /> | <strong><u>35edo</u>:</strong> 5 keys per sharp/flat: C/C# * * * * Db/D<br /> | ||
D * * * * E * * * * F * * * * G * * * * A * * * * B * * * * C * * * * D<br /> | |||
D - D^ - D^^ - Evv - Ev - E - E^ - E^^ - Fvv - Fv - F - F^ - F^^ - Gvv - Gv - G - G^ - G^^ - Avv - Av - A etc.<br /> | D - D^ - D^^ - Evv - Ev - E - E^ - E^^ - Fvv - Fv - F - F^ - F^^ - Gvv - Gv - G - G^ - G^^ - Avv - Av - A etc.<br /> | ||
1 - ^1 - ^^1 - vv2 - v2 - 2 - ^2 - ^^2 - vv3 - v3 - 3 - ^3 - ^^3 - vv4 - v4 - 4 - ^4 - ^^4 - vv5 - v5 - 5 etc.</body></html></pre></div> | 1 - ^1 - ^^1 - vv2 - v2 - 2 - ^2 - ^^2 - vv3 - v3 - 3 - ^3 - ^^3 - vv4 - v4 - 4 - ^4 - ^^4 - vv5 - v5 - 5 etc.<br /> | ||
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<!-- ws:start:WikiTextHeadingRule:22:&lt;h3&gt; --><h3 id="toc11"><a name="Summary of EDO notation--Pentatonic EDOs (5, 10, 15, 20, 25 and 30)"></a><!-- ws:end:WikiTextHeadingRule:22 --><u>Pentatonic EDOs (5, 10, 15, 20, 25 and 30)</u></h3> | |||
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All pentatonic EDOs use the usual chain of fifths: m2 - m6 - m3 - m7 - P4 - P1 - P5 - M2 - M6 - M3 - M7 etc.<br /> | |||
Fb - Cb - Gb - Db - Ab - Eb - Bb - F - C - G - D - A - E - B - F# - C# - G# - D# - A# - E# - B# etc.<br /> | |||
In all pentatonic EDOs, the minor 2nd = unison and the major 3rd = perfect fourth.<br /> | |||
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<strong><u>5edo</u>:</strong> C/Db C#/D<br /> | |||
D E/F G A B/C D<br /> | |||
P1 - M2/m3 - P4 - P5 - M6/m7 - P8<br /> | |||
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<strong><u>10edo</u>:</strong> 2 keys per sharp/flat: C/Db * C#/D<br /> | |||
D * E/F * G * A * B/C * D<br /> | |||
D - D^/Ev - E/F - F^/Gv - G - G^/Av - A - A^/Bv - B/C - C^/Dv - D<br /> | |||
P1/m2 - ^m2/vM2 - M2/m3 - ^m3/vM3 - M3/P4 - ^P4/vP5 - P5/m6 - ^m6/vM6 - M6/m7 - ^m7/vM7 - P8<br /> | |||
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<strong><u>15edo</u>:</strong> 3 keys per sharp/flat: C/Db [*] [*] C#/D<br /> | |||
D * * E/F * * G * * A * * B/C * * D<br /> | |||
D - D^ - Ev - E/F - F^ - Gv - G - G^ - Av - A - A^ - Bv - B/C - C^ - Dv - D<br /> | |||
P1/m2 - ^m2 - vM2 - M2/m3 - ^m3 - vM3 - M3/P4 - ^P4 - vP5 - P5/m6 - ^m6 - vM6 - M6/m7 - ^m7 - vM7 - P8<br /> | |||
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<strong><u>20edo</u>:</strong> 4 keys per sharp/flat: C/Db * * * C#/D<br /> | |||
D * * * E/F * * * G * * * A * * * B/C * * * D<br /> | |||
D - D^ - D^^/Evv - Ev - E/F - F^ - F^^/Gvv - Gv - G - G^ - G^^/Avv - Av - A - A^ - A^^/Bvv - Bv - B/C - C^ - C^^/Dvv - Dv - D<br /> | |||
P1/m2 - ^m2 - ^^m2/vvM2 - vM2 - M2/m3 - ^m3 - ^^m3/vvM3 - vM3 - M3/P4 - ^P4 - ^^P4/vvP5 - vP5 - P5/m6 - ^m6 - ^^m6/vvM6 - vM6 - M6/m7 - ^m7 - ^^m7/vvM7 - vM7 - P8<br /> | |||
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<strong><u>25edo</u>:</strong> 5 keys per sharp/flat: C/Db * * * * C#/D<br /> | |||
D * * * * E/F * * * * G * * * * A * * * * B/C * * * * D<br /> | |||
D - D^ - D^^ - Evv - Ev - E/F - F^ - F^^ - Gvv - Gv - G - G^ - G^^ - Avv - Av - A - A^ - A^^ - Bvv - Bv - B/C - C^ - C^^ - Dvv - Dv - D<br /> | |||
P1/m2 - ^m2 - ^^m2 - vvM2 - vM2 - M2/m3 - ^m3 - ^^m3 - vvM3 - vM3 - M3/P4 - ^P4 - ^^P4 - vvP5 - vP5 - P5/m6 - ^m6 - ^^m6 - vvM6 - vM6 - M6/m7 - ^m7 - ^^m7 - vvM7 - vM7 - P8<br /> | |||
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<strong><u>30edo</u>:</strong> 6 keys per sharp/flat: C/Db * * * * * C#/D<br /> | |||
D * * * * * E/F * * * * * G * * * * * A * * * * * B/C * * * * * D<br /> | |||
D - D^ - D^^ - Evv - Ev - E/F - F^ - F^^ - Gvv - Gv - G - G^ - G^^ - Avv - Av - A - A^ - A^^ - Bvv - Bv - B/C - C^ - C^^ - Dvv - Dv - D<br /> | |||
P1/m2 - ^m2 - ^^m2 - vvM2 - vM2 - M2/m3 - ^m3 - ^^m3 - vvM3 - vM3 - M3/P4 - ^P4 - ^^P4 - vvP5 - vP5 - P5/m6 - ^m6 - ^^m6 - vvM6 - vM6 - M6/m7 - ^m7 - ^^m7 - vvM7 - vM7 - P8<br /> | |||
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<!-- ws:start:WikiTextHeadingRule:24:&lt;h3&gt; --><h3 id="toc12"><a name="Summary of EDO notation--&quot;Sweet&quot; EDOs (12, 17, 19, 22, 24, 26, 27, 29, 31, etc.)"></a><!-- ws:end:WikiTextHeadingRule:24 --><u>&quot;Sweet&quot; EDOs (12, 17, 19, 22, 24, 26, 27, 29, 31, etc.)</u></h3> | |||
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All sweet EDOs use the usual chain of fifths: m2 - m6 - m3 - m7 - P4 - P1 - P5 - M2 - M6 - M3 - M7 etc.<br /> | |||
Fb - Cb - Gb - Db - Ab - Eb - Bb - F - C - G - D - A - E - B - F# - C# - G# - D# - A# - E# - B# etc.<br /> | |||
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<strong><u>12edo</u>:</strong> sharp/flat = 1 key, no ups and downs: C C#/Db D<br /> | |||
D * E F * G * A * B C * D<br /> | |||
D - D#/Eb - E - F - F#/Gb - G - G#/Ab - A - A#/Bb - B - C - C#/Db - D<br /> | |||
P1 - m2 - M2 - m3 - M3 - P4 - A4/d5 - P5 - m6 - M6 - m7 - M7 - P8<br /> | |||
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<strong><u>17edo</u>:</strong> sharp = 2 keys: C Db C# C<br /> | |||
D * * E F * * G * * A * * B C * * D<br /> | |||
D - D^/Eb - D#/Ev - Eb - E - F - F^/Gb - F#/Gv - G - G^/Ab - G#/Av - A - A^/Bb - A#/Bv - B - C - C^/Db - C#/Dv - D<br /> | |||
P1 - m2 - ^m2/vM2 - M2 - m3 - ^m3/vM3 - M3 - P4 - ^P4/d5 - A4/vP5 - P5 - m6 - ^m6/vM6 - M6 - m7 ^m7/vM7 - M7 - P8<br /> | |||
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<strong><u>19edo</u>:</strong> no ups and downs C C# Db D<br /> | |||
D * * E * F * * G * * A * * B * C * * D<br /> | |||
D - D# - Eb - E - E#/Fb - F - F# - Gb - G - G# - Ab - A - A# - Bb - B - B#/Cb - C - C# - Db - D<br /> | |||
P1 - A1/d2 - m2 - M2 - A2/d3 - m3 - M3 - A3/d4 - P4 - A4 - d5 - P5 - A5/d6 - m6 - M6 - A6/d7 - m7 - M7 - A7/d8 - P8<br /> | |||
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<strong><u>22edo</u>:</strong> sharp = 3 keys: C Db * C# C<br /> | |||
D * * * E F * * * G * * * A * * * B C * * * D<br /> | |||
D - D^/Eb - D#v/Eb^ - D#/Ev - E - F - F^/Gb - F#v/Gb^ - F#/Gv - G - G^/Ab - G#v/Ab^ - G#/Av - A etc.<br /> | |||
P1 - m2 - ^m2 - vM2 - M2 - m3 - ^m3 - vM3 - M3 - P4 - ^P4/d5 - vA4/^d5 - A4/vP5 - P5 etc.<br /> | |||
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<strong><u>24edo</u>:</strong> sharp = 2 keys: C * C#/Db * C<br /> | |||
D * * * E * F * * * G * * * A * * * B * C * * * D<br /> | |||
D - D^/Ebv - D#/Eb - D#^/Ev - E - E^/Fv - F - F^/Gbv - F#/Gb - F#^/Gv - G - G^/Abv - G#/Ab - G#^/Av - A etc.<br /> | |||
P1 - ^P1/vm2 - m2 - ^m2/vM2 - M2 - ^M2/vm3 - m3 - ^m3/vM3 - M3 - ^M3/vP4 - P4 - ^P4/vd5 - A4/d5 - ^A4/vP5 - P5 etc.</body></html></pre></div> | |||