Kite's ups and downs notation: Difference between revisions
Wikispaces>TallKite **Imported revision 593594684 - Original comment: ** |
Wikispaces>TallKite **Imported revision 593632740 - 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>2016-09-29 | : This revision was by author [[User:TallKite|TallKite]] and made on <tt>2016-09-29 13:56:36 UTC</tt>.<br> | ||
: The original revision id was <tt> | : The original revision id was <tt>593632740</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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In 22edo, the major chord is 0-8-13 = 0¢-436¢-709¢. In 19edo, it's 0-6-11 = 0¢-379¢-695¢. The two chords sound quite different, because "major 3rd" is defined only in terms of the fifth, not in terms of what JI ratios it approximates. To describe the sound of the chord, color notation can be used. 22edo major chords sound red and 19edo major chords sound yellow. | In 22edo, the major chord is 0-8-13 = 0¢-436¢-709¢. In 19edo, it's 0-6-11 = 0¢-379¢-695¢. The two chords sound quite different, because "major 3rd" is defined only in terms of the fifth, not in terms of what JI ratios it approximates. To describe the sound of the chord, color notation can be used. 22edo major chords sound red and 19edo major chords sound yellow. | ||
A chord quality like "major" refers not to the sound but to the function of the chord. If you want to play a I - VIm - IIm - V - I progression without pitch shifts or tonic drift, you can do that in any edo, as long as you use only major and minor chords. The notation tells you what kind of chord can be used to play that progression. In 22edo, the chord that you need sounds like a red chord. | |||
In other words, I - VIm - IIm - V - I in just intonation implies Iy - VIg - IIg - Vy - Iy, but this implication only holds in those EDOs in which major sounds yellow. If 22edo's downmajor chord 0-7-13 = 0¢-382¢-709¢ were called "major", you wouldn't know that it doesn't work in that progression. | In other words, I - VIm - IIm - V - I in just intonation implies Iy - VIg - IIg - Vy - Iy, but this implication only holds in those EDOs in which major sounds yellow. If 22edo's downmajor chord 0-7-13 = 0¢-382¢-709¢ were called "major", you wouldn't know that it doesn't work in that progression. | ||
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The third approach is to use some interval other than the fifth to generate the notation. Earlier I said notating 22edo using an even distribution of note names such as C _ _ D _ _ E _ _ F _ _ _ G _ _ A _ _ B _ _ C was a bad idea because the G-D and the A-E fifths looked perfect but were actually diminished. The reasoning is that 3/2 is an important ratio, and any decent approximation of 3/2 should look like a perfect fifth. But these EDOs don't approximate 3/2 well, so they can be thought of as having both a major fifth and a minor fifth. This negates any expectations of what a fifth should look like. | The third approach is to use some interval other than the fifth to generate the notation. Earlier I said notating 22edo using an even distribution of note names such as C _ _ D _ _ E _ _ F _ _ _ G _ _ A _ _ B _ _ C was a bad idea because the G-D and the A-E fifths looked perfect but were actually diminished. The reasoning is that 3/2 is an important ratio, and any decent approximation of 3/2 should look like a perfect fifth. But these EDOs don't approximate 3/2 well, so they can be thought of as having both a major fifth and a minor fifth. This negates any expectations of what a fifth should look like. | ||
__**Pentatonic notation for | __**Pentatonic notation for 8edo, 11b-edo, 13edo and 18edo**__ | ||
All three EDOs use the same pentatonic fifthwards chain of fifths: ms3 - ms7 - P4d - P1 - P5d - Ms3 - Ms7 - A4d etc. | All three EDOs use the same pentatonic fifthwards chain of fifths: ms3 - ms7 - P4d - P1 - P5d - Ms3 - Ms7 - A4d etc. | ||
| Line 878: | Line 878: | ||
P1 - ms3 - Ms3 - P4d - A4d/d5d - P5d - ms7 - Ms7 - P8d | P1 - ms3 - Ms3 - P4d - A4d/d5d - P5d - ms7 - Ms7 - P8d | ||
__** | __**11b-edo**__**:** (generator = 7\11 = perfect 5thoid) C Db C# D, # is ^^ | ||
D * * E G * * A C * * D | D * * E G * * A C * * D | ||
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 | ||
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P1 - A1 - ds3 - ms3 - Ms3 - As3 - d4d - P4d - A4d - AA4d/dd5d - d5d - P5d - A5d - ds7 - ms7 - Ms7 - As7 - d8d - P8d | P1 - A1 - ds3 - ms3 - Ms3 - As3 - d4d - P4d - A4d - AA4d/dd5d - d5d - P5d - A5d - ds7 - ms7 - Ms7 - As7 - d8d - P8d | ||
__**Other non-heptatonic notations for 8edo, 11edo, 13edo and 18edo**__ | __**Other non-heptatonic notations for 8edo, 11edo, 13edo and 18edo**__ | ||
8edo octatonic (every note is a generator) | __**8edo**__ octatonic (every note is a generator) | ||
D E F G H A B C D | D E F G H A B C D | ||
P1 - P2 - P3 - P4 - P5 - P6 - P7 - P8 - P9 | P1 - P2 - P3 - P4 - P5 - P6 - P7 - P8 - P9 | ||
requires learning octatonic interval arithmetic and staff notation | requires learning octatonic interval arithmetic and staff notation | ||
11edo nonotonic narrow-fifth-based, fifthwards with no ups and downs (3/2 maps to 6\11 = perfect 6th): | __**11edo**__ nonotonic narrow-fifth-based, fifthwards with no ups and downs (3/2 maps to 6\11 = perfect 6th): | ||
nonotonic fifthwards chain of sixths: M2 - M7 - M3 - M8 - M4 - M9 - P5 - P1 - P6 - m2 - m7 - m3 - m8 - m4 - m9 | nonotonic fifthwards chain of sixths: M2 - M7 - M3 - M8 - M4 - M9 - P5 - P1 - P6 - m2 - m7 - m3 - m8 - m4 - m9 | ||
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 staff notation | requires learning nonotonic interval arithmetic and staff notation | ||
__**11b-edo**__ 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 | ||
__**13b-edo**__ undecatonic narrow-fifth-based, fourthwards, 3/2 maps to 7\13 = perfect 7th | |||
undecatonic sixthwards chain of sevenths: | undecatonic sixthwards chain of sevenths: | ||
M2 - M8 - M3 - M9 - M4 - M10 - M5 - M11 - P6 - P1 - P7 - m2 - m8 - m3 - m9 - m4 - m10 - m5 - m11 | M2 - M8 - M3 - M9 - M4 - M10 - M5 - M11 - P6 - P1 - P7 - m2 - m8 - m3 - m9 - m4 - m10 - m5 - m11 | ||
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requires learning undecatonic interval arithmetic and notation | requires learning undecatonic interval arithmetic and notation | ||
13edo octatonic wide-fifth-based, fourthwards, 3/2 maps to 8\13 = perfect 6th | __**13edo**__ octatonic wide-fifth-based, fourthwards, 3/2 maps to 8\13 = perfect 6th | ||
octotonic chain of sixths: M3 - M8 - M5 - M2 - M7 - P4 - P1 - P6 - m3 - m8 - m5 - m2 - m7 | octotonic chain of sixths: 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 | ||
__**18b-edo**__ 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 staff notation | requires learning nonotonic interval arithmetic and staff notation | ||
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In 22edo, the major chord is 0-8-13 = 0¢-436¢-709¢. In 19edo, it's 0-6-11 = 0¢-379¢-695¢. The two chords sound quite different, because &quot;major 3rd&quot; is defined only in terms of the fifth, not in terms of what JI ratios it approximates. To describe the sound of the chord, color notation can be used. 22edo major chords sound red and 19edo major chords sound yellow.<br /> | In 22edo, the major chord is 0-8-13 = 0¢-436¢-709¢. In 19edo, it's 0-6-11 = 0¢-379¢-695¢. The two chords sound quite different, because &quot;major 3rd&quot; is defined only in terms of the fifth, not in terms of what JI ratios it approximates. To describe the sound of the chord, color notation can be used. 22edo major chords sound red and 19edo major chords sound yellow.<br /> | ||
<br /> | <br /> | ||
A chord quality like &quot;major&quot; refers not to the sound but to the function of the chord. If you want to play a I - VIm - IIm - V - I progression without pitch shifts or tonic drift, you can do that in any edo, as long as you use only major and minor chords. The notation tells you what kind of chord can be used to play that progression. In 22edo, the chord that you need sounds like a red chord.<br /> | |||
<br /> | <br /> | ||
In other words, I - VIm - IIm - V - I in just intonation implies Iy - VIg - IIg - Vy - Iy, but this implication only holds in those EDOs in which major sounds yellow. If 22edo's downmajor chord 0-7-13 = 0¢-382¢-709¢ were called &quot;major&quot;, you wouldn't know that it doesn't work in that progression.<br /> | In other words, I - VIm - IIm - V - I in just intonation implies Iy - VIg - IIg - Vy - Iy, but this implication only holds in those EDOs in which major sounds yellow. If 22edo's downmajor chord 0-7-13 = 0¢-382¢-709¢ were called &quot;major&quot;, you wouldn't know that it doesn't work in that progression.<br /> | ||
| Line 3,519: | Line 3,517: | ||
The third approach is to use some interval other than the fifth to generate the notation. Earlier I said notating 22edo using an even distribution of note names such as C _ _ D _ _ E _ _ F _ _ _ G _ _ A _ _ B _ _ C was a bad idea because the G-D and the A-E fifths looked perfect but were actually diminished. The reasoning is that 3/2 is an important ratio, and any decent approximation of 3/2 should look like a perfect fifth. But these EDOs don't approximate 3/2 well, so they can be thought of as having both a major fifth and a minor fifth. This negates any expectations of what a fifth should look like.<br /> | The third approach is to use some interval other than the fifth to generate the notation. Earlier I said notating 22edo using an even distribution of note names such as C _ _ D _ _ E _ _ F _ _ _ G _ _ A _ _ B _ _ C was a bad idea because the G-D and the A-E fifths looked perfect but were actually diminished. The reasoning is that 3/2 is an important ratio, and any decent approximation of 3/2 should look like a perfect fifth. But these EDOs don't approximate 3/2 well, so they can be thought of as having both a major fifth and a minor fifth. This negates any expectations of what a fifth should look like.<br /> | ||
<br /> | <br /> | ||
<u><strong>Pentatonic notation for | <u><strong>Pentatonic notation for 8edo, 11b-edo, 13edo and 18edo</strong></u><br /> | ||
<br /> | <br /> | ||
All three EDOs use the same pentatonic fifthwards chain of fifths: ms3 - ms7 - P4d - P1 - P5d - Ms3 - Ms7 - A4d etc.<br /> | All three EDOs use the same pentatonic fifthwards chain of fifths: ms3 - ms7 - P4d - P1 - P5d - Ms3 - Ms7 - A4d etc.<br /> | ||
| Line 3,529: | Line 3,527: | ||
P1 - ms3 - Ms3 - P4d - A4d/d5d - P5d - ms7 - Ms7 - P8d<br /> | P1 - ms3 - Ms3 - P4d - A4d/d5d - P5d - ms7 - Ms7 - P8d<br /> | ||
<br /> | <br /> | ||
<u><strong> | <u><strong>11b-edo</strong></u><strong>:</strong> (generator = 7\11 = perfect 5thoid) C Db C# D, # is ^^<br /> | ||
D * * E G * * A C * * D<br /> | D * * E G * * A C * * D<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 /> | ||
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P1 - A1 - ds3 - ms3 - Ms3 - As3 - d4d - P4d - A4d - AA4d/dd5d - d5d - P5d - A5d - ds7 - ms7 - Ms7 - As7 - d8d - P8d<br /> | P1 - A1 - ds3 - ms3 - Ms3 - As3 - d4d - P4d - A4d - AA4d/dd5d - d5d - P5d - A5d - ds7 - ms7 - Ms7 - As7 - d8d - P8d<br /> | ||
<br /> | <br /> | ||
<br /> | <br /> | ||
<u><strong>Other non-heptatonic notations for 8edo, 11edo, 13edo and 18edo</strong></u><br /> | <u><strong>Other non-heptatonic notations for 8edo, 11edo, 13edo and 18edo</strong></u><br /> | ||
<br /> | <br /> | ||
8edo octatonic (every note is a generator)<br /> | <u><strong>8edo</strong></u> octatonic (every note is a generator)<br /> | ||
D E F G H A B C D<br /> | D E F G H A B C D<br /> | ||
P1 - P2 - P3 - P4 - P5 - P6 - P7 - P8 - P9<br /> | P1 - P2 - P3 - P4 - P5 - P6 - P7 - P8 - P9<br /> | ||
requires learning octatonic interval arithmetic and staff notation<br /> | requires learning octatonic interval arithmetic and staff notation<br /> | ||
<br /> | <br /> | ||
11edo nonotonic narrow-fifth-based, fifthwards with no ups and downs (3/2 maps to 6\11 = perfect 6th):<br /> | <u><strong>11edo</strong></u> nonotonic narrow-fifth-based, fifthwards with no ups and downs (3/2 maps to 6\11 = perfect 6th):<br /> | ||
nonotonic fifthwards chain of sixths: M2 - M7 - M3 - M8 - M4 - M9 - P5 - P1 - P6 - m2 - m7 - m3 - m8 - m4 - m9<br /> | nonotonic fifthwards chain of sixths: M2 - M7 - M3 - M8 - M4 - M9 - P5 - P1 - P6 - m2 - m7 - m3 - m8 - m4 - m9<br /> | ||
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 staff notation<br /> | requires learning nonotonic interval arithmetic and staff notation<br /> | ||
<br /> | <br /> | ||
<u><strong>11b-edo</strong></u> 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 /> | ||
<u><strong>13b-edo</strong></u> undecatonic narrow-fifth-based, fourthwards, 3/2 maps to 7\13 = perfect 7th<br /> | |||
undecatonic sixthwards chain of sevenths:<br /> | undecatonic sixthwards chain of sevenths:<br /> | ||
M2 - M8 - M3 - M9 - M4 - M10 - M5 - M11 - P6 - P1 - P7 - m2 - m8 - m3 - m9 - m4 - m10 - m5 - m11<br /> | M2 - M8 - M3 - M9 - M4 - M10 - M5 - M11 - P6 - P1 - P7 - m2 - m8 - m3 - m9 - m4 - m10 - m5 - m11<br /> | ||
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requires learning undecatonic interval arithmetic and notation<br /> | requires learning undecatonic interval arithmetic and notation<br /> | ||
<br /> | <br /> | ||
13edo octatonic wide-fifth-based, fourthwards, 3/2 maps to 8\13 = perfect 6th<br /> | <u><strong>13edo</strong></u> octatonic wide-fifth-based, fourthwards, 3/2 maps to 8\13 = perfect 6th<br /> | ||
octotonic chain of sixths: M3 - M8 - M5 - M2 - M7 - P4 - P1 - P6 - m3 - m8 - m5 - m2 - m7<br /> | octotonic chain of sixths: 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 /> | ||
<u><strong>18b-edo</strong></u> 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 staff notation<br /> | requires learning nonotonic interval arithmetic and staff notation<br /> | ||