Kite's ups and downs notation: Difference between revisions
Wikispaces>TallKite **Imported revision 558786899 - Original comment: ** |
Wikispaces>TallKite **Imported revision 558808109 - 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- | : This revision was by author [[User:TallKite|TallKite]] and made on <tt>2015-09-10 01:25:52 UTC</tt>.<br> | ||
: The original revision id was <tt> | : The original revision id was <tt>558808109</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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8edo octatonic (every note is a generator) | 8edo octatonic (every note is a generator) | ||
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 heptatonic narrow-fifth-based, fourthwards, # is ^^ (3/2 maps to 6\11 perfect 5th): | 11edo heptatonic narrow-fifth-based, fourthwards, # is ^^ (3/2 maps to 6\11 perfect 5th): | ||
D E * * F G A B * * C D | |||
fourthwards chain of fifths: M2 - M6 - M3 - M7 - P4 - P1 - P5 - m2 - m6 - m3 - m7 | fourthwards chain of fifths: M2 - M6 - M3 - M7 - P4 - P1 - P5 - m2 - m6 - m3 - m7 | ||
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 | ||
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11edo pentatonic wide-fifth-based, fifthwards, # is ^^ (3/2 maps to 7\11 6th): | 11edo pentatonic wide-fifth-based, fifthwards, # is ^^ (3/2 maps to 7\11 6th): | ||
D * * E G * * A C * * D | |||
pentatonic fifthwards chain of fifthoids: m2 - m6 - m3 - m7 - P4 - P1 - P5 - M2 - M6 - M3 - M7 | pentatonic fifthwards chain of fifthoids: m2 - m6 - m3 - m7 - P4 - P1 - P5 - M2 - M6 - M3 - M7 | ||
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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requires learning octatonic interval arithmetic and notation | requires learning octatonic interval arithmetic and notation | ||
13edo heptatonic narrow-fifth-based, fourthwards, | 13edo heptatonic narrow-fifth-based, fourthwards, sharp = ^^^ (3/2 maps to 7\13 perfect 5th): | ||
D E * * * F G A B * * * C D | |||
fourthwards chain of fifths: M2 - M6 - M3 - M7 - P4 - P1 - P5 - m2 - m6 - m3 - m7 | fourthwards chain of fifths: M2 - M6 - M3 - M7 - P4 - P1 - P5 - m2 - m6 - m3 - m7 | ||
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 | ||
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13edo undecatonic narrow-fifth-based, fourthwards, 3/2 maps to 7\13 = perfect 7th | 13edo 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 | ||
P1 - m2 - M2/m3 - M3/m4 - M4/m5 - M5 - P6 - P7 - m8 - M8/m9 - M9/m10 - M10/m11 - M11 - P12 | P1 - m2 - M2/m3 - M3/m4 - M4/m5 - M5 - P6 - P7 - m8 - M8/m9 - M9/m10 - M10/m11 - M11 - P12 | ||
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18edo heptatonic narrow-fifth-based, fourthwards, sharp = ^^ (3/2 maps to 10\18 perfect 5th) | 18edo heptatonic narrow-fifth-based, fourthwards, sharp = ^^ (3/2 maps to 10\18 perfect 5th) | ||
D * E * * * F * G * A * B * * * C * D | |||
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 | fourthwards plus ups and downs plus closed is triply confusing! | ||
18edo nonatonic narrow-fifth-based (3/2 maps to 10\18 = perfect 6th) | 18edo nonatonic narrow-fifth-based (3/2 maps to 10\18 = perfect 6th) | ||
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__**Alternate notation for other edos:**__ | __**Alternate notation for other edos:**__ | ||
23edo pentatonic wide-fifth-based, fifthwards, 3/2 maps to 14\23 = perfect fifthoid | 23edo pentatonic wide-fifth-based, fifthwards, 3/2 maps to 14\23 = perfect fifthoid: | ||
35edo heptatonic wide-fifth-based, sharp = seven ups, 3/2 maps to 21\35 = perfect fifth | D * * * * E * * * G * * * * A * * * C * * * * D | ||
42edo heptatonic narrow-fifth-based, 3/2 maps to 24\42 = perfect fifth | 35edo heptatonic wide-fifth-based, sharp = seven ups, 3/2 maps to 21\35 = perfect fifth: | ||
D * * * * * * E/F * * * * * * G * * * * * * A * * * * * * B/C * * * * * * D | |||
42edo heptatonic narrow-fifth-based, sharp = six ups, 3/2 maps to 24\42 = perfect fifth: | |||
D * * * * * E * * * * * F * * * * * G * * * * * A * * * * * B * * * * * C * * * * * D | |||
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The first two categories never use ups and downs, the next two always do (except for 5edo and 7edo). The sweet EDOs may or may not. | The first two categories never use ups and downs, the next two always do (except for 5edo and 7edo). The sweet EDOs may or may not. | ||
To summarize an EDO, a scale fragment from C to D is shown, including C# and Db. Examples: | To summarize an EDO, a scale fragment from C to D is shown, including C# and Db. Examples: | ||
C C#/Db D (12edo) | C C#/Db D (12edo) | ||
C Db C# D (17edo) | C Db C# D (17edo) | ||
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C _ C# Db _ D (31edo) | C _ C# Db _ D (31edo) | ||
The scale fragment concisely conveys the "flavor" of the EDO's notation. The C-C# interval is the augmented unison, and if the 2nd key in the fragment isn't C#, ups and downs are required. The only exception is 7edo. For most EDOs, the C-Db interval is the minor 2nd and the C-D interval is the major 2nd. For perfect EDOs, C-Db = d2 and C-D = P2. For fourthward EDOs, C-Db = d2 and C-D = m2. | The scale fragment concisely conveys the "flavor" of the EDO's notation. The C-C# interval is the augmented unison, and if the 2nd key in the fragment isn't C#, ups and downs are required. The only exception is 7edo. For most EDOs, the C-Db interval is the minor 2nd and the C-D interval is the major 2nd. For perfect EDOs, C-Db = d2 and C-D = P2. For fourthward EDOs, C-Db = d2 and C-D = m2. D# is included for these EDOs because C-D# is a M2 just like E-F. For fifthless EDOs, the scale fragment isn't as helpful because you can't deduce the entire keyboard layout from it. | ||
Every EDO contains a unique scale fragment, and every scale fragment implies a unique EDO. Furthermore, this uniqueness applies to EDOs with alternate fifths: "wide-fifth" 35edo (which uses 21\35 as a fifth) has a different scale fragment than "narrow-fifth" 35edo with 20\35. If an EDO has a fifth of keyspan F and an octave of keyspan O (i.e. it's O-EDO), the minor 2nd's keyspan is m2 = -5F + 3O, and the augmented unison's is A1 = 7F - 4O. These equations can be reversed: F = 4(m2) + 3(A1) and O = 7(m2) + 5(A1). (For perfect and fourthwards EDOs, substitute M2 for m2.) | |||
||= 5edo ||= pentatonic ||= ||= C/Db ||= C#/D ||= ||= ||= ||= ||= ||= ||= ||= || | |||
||= 7edo ||= perfect ||= ||= C/C# ||= Db/D ||= ||= ||= ||= ||= ||= ||= ||= || | |||
||= 8edo ||= fifthless ||= ||= ||= ||= ||= ||= ||= ||= ||= ||= ||= || | |||
||= 9edo ||= fourthward ||= ||= C/Db ||= C#/D ||= D# ||= ||= ||= ||= ||= ||= ||= || | |||
||= 10edo ||= pentatonic ||= ||= C/Db ||= * ||= C#/D ||= ||= ||= ||= ||= ||= ||= || | |||
||= 11edo ||= fifthless ||= ||= ||= ||= ||= ||= ||= ||= ||= ||= ||= || | |||
||= 12edo ||= sweet ||= ||= C ||= C#/Db ||= D ||= ||= ||= ||= ||= ||= ||= || | |||
||= 13edo ||= fifthless ||= ||= ||= ||= ||= ||= ||= ||= ||= ||= ||= || | |||
||= 14edo ||= perfect ||= ||= C/C# ||= * ||= Db/D ||= ||= ||= ||= ||= ||= ||= || | |||
||= 15edo ||= pentatonic ||= ||= C/Db ||= * ||= * ||= C#/D ||= ||= ||= ||= ||= ||= || | |||
||= 16edo ||= fourthward ||= ||= C ||= C#/Db ||= D ||= D# ||= ||= ||= ||= ||= ||= || | |||
||= 17edo ||= sweet ||= ||= C ||= Db ||= C# ||= D ||= ||= ||= ||= ||= ||= || | |||
||= 18edo ||= fifthless ||= ||= ||= ||= ||= ||= ||= ||= ||= ||= ||= || | |||
||= 19edo ||= sweet ||= ||= C ||= C# ||= Db ||= D ||= ||= ||= ||= ||= ||= || | |||
||= 20edo ||= pentatonic ||= ||= C/Db ||= * ||= * ||= * ||= C#/D ||= ||= ||= ||= ||= || | |||
||= 21edo ||= perfect ||= ||= C/C# ||= * ||= * ||= Db/D ||= ||= ||= ||= ||= ||= || | |||
||= 22edo ||= sweet ||= ||= C ||= Db ||= * ||= C# ||= D ||= ||= ||= ||= ||= || | |||
||= 23edo ||= fourthward ||= ||= C ||= C# ||= Db ||= D ||= D# ||= ||= ||= ||= ||= || | |||
||= 24edo ||= sweet ||= ||= C ||= * ||= C#/Db ||= * ||= D ||= ||= ||= ||= ||= || | |||
||= 25edo ||= pentatonic ||= ||= C/Db ||= * ||= * ||= * ||= * ||= C#/D ||= ||= ||= ||= || | |||
||= 26edo ||= sweet ||= ||= C ||= C# ||= * ||= Db ||= D ||= ||= ||= ||= ||= || | |||
||= 27edo ||= sweet ||= ||= C ||= Db ||= * ||= * ||= C# ||= D ||= ||= ||= ||= || | |||
||= 28edo ||= perfect ||= ||= C/C# ||= * ||= * ||= * ||= Db/D ||= ||= ||= ||= ||= || | |||
||= 29edo ||= sweet ||= ||= C ||= * ||= Db ||= C# ||= * ||= D ||= ||= ||= ||= || | |||
||= 30edo ||= pentatonic ||= ||= C/Db ||= * ||= * ||= * ||= * ||= * ||= C#/D ||= ||= ||= || | |||
||= 31edo ||= sweet ||= ||= C ||= * ||= C# ||= Db ||= * ||= D ||= ||= ||= ||= || | |||
||= 32edo ||= sweet ||= ||= C ||= Db ||= * ||= * ||= * ||= C# ||= D ||= ||= ||= || | |||
||= 33edo ||= sweet ||= ||= C ||= C# ||= * ||= * ||= Db ||= D ||= ||= ||= ||= || | |||
||= 34edo ||= sweet ||= ||= C ||= * ||= Db ||= * ||= C# ||= * ||= D ||= ||= ||= || | |||
||= 35edo ||= perfect ||= ||= C/C# ||= * ||= * ||= * ||= * ||= Db/D ||= ||= ||= ||= || | |||
||= 36edo ||= sweet ||= ||= C ||= * ||= * ||= C#/Db ||= * ||= * ||= D ||= ||= ||= || | |||
||= 37edo ||= sweet ||= ||= C ||= Db ||= * ||= * ||= * ||= * ||= C# ||= D ||= ||= || | |||
||= 38edo ||= sweet ||= ||= C ||= * ||= C# ||= * ||= Db ||= * ||= D ||= ||= ||= || | |||
||= 39edo ||= sweet ||= ||= C ||= * ||= Db ||= * ||= * ||= C# ||= * ||= D ||= ||= || | |||
||= 40edo ||= sweet ||= ||= C ||= C# ||= * ||= * ||= * ||= Db ||= D ||= ||= ||= || | |||
||= 41edo ||= sweet ||= ||= C ||= * ||= * ||= Db ||= C# ||= * ||= * ||= D ||= ||= || | |||
||= 42edo ||= sweet ||= ||= C ||= Db ||= * ||= * ||= * ||= * ||= * ||= C# ||= D ||= || | |||
||= 43edo ||= sweet ||= ||= C ||= * ||= * ||= C# ||= Db ||= * ||= * ||= D ||= ||= || | |||
||= 44ddo ||= sweet ||= ||= C ||= * ||= Db ||= * ||= * ||= * ||= C# ||= * ||= D ||= || | |||
||= 45edo ||= sweet ||= ||= C ||= * ||= Db ||= * ||= * ||= C# ||= * ||= D ||= ||= || | |||
||= 46edo ||= sweet ||= ||= C ||= * ||= * ||= Db ||= * ||= C# ||= * ||= * ||= D ||= || | |||
||= 47edo ||= sweet ||= ||= C ||= C# ||= * ||= * ||= * ||= * ||= Db ||= D ||= ||= || | |||
||= 48edo ||= sweet ||= ||= C ||= * ||= * ||= * ||= C#/Db ||= * ||= * ||= * ||= D ||= || | |||
||= 49edo ||= sweet ||= ||= C ||= * ||= Db ||= * ||= * ||= * ||= * ||= C# ||= * ||= D || | |||
||= 50edo ||= sweet ||= ||= C ||= * ||= * ||= C# ||= * ||= Db ||= * ||= * ||= D ||= || | |||
||= 51edo ||= sweet ||= ||= C ||= * ||= * ||= Db ||= * ||= * ||= C# ||= * ||= * ||= D || | |||
||= 52edo ||= sweet ||= ||= C ||= * ||= C# ||= * ||= * ||= * ||= Db ||= * ||= D ||= || | |||
||= 53edo ||= sweet ||= ||= C ||= * ||= * ||= * ||= Db ||= C# ||= * ||= * ||= * ||= D || | |||
===__**"Fifth-less" EDOs (8, 11, 13 and 18)**__=== | ===__**"Fifth-less" EDOs (8, 11, 13 and 18)**__=== | ||
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IIvM,m7 = &quot;two downmajor, minor seven&quot;<br /> | IIvM,m7 = &quot;two downmajor, minor seven&quot;<br /> | ||
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<!-- ws:start:WikiTextHeadingRule:6:&lt;h2&gt; --><h2 id="toc3"><a name="Naming Chords-Chord names in other EDOs"></a><!-- ws:end:WikiTextHeadingRule:6 --><u>Chord names in other EDOs</u></h2> | <!-- ws:start:WikiTextHeadingRule:6:&lt;h2&gt; --><h2 id="toc3"><a name="Naming Chords-Chord names in other EDOs"></a><!-- ws:end:WikiTextHeadingRule:6 --><u>Chord names in other EDOs</u></h2> | ||
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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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<br /> | <br /> | ||
8edo octatonic (every note is a generator)<br /> | 8edo octatonic (every note is a generator)<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 heptatonic narrow-fifth-based, fourthwards, # is ^^ (3/2 maps to 6\11 perfect 5th):<br /> | 11edo heptatonic narrow-fifth-based, fourthwards, # is ^^ (3/2 maps to 6\11 perfect 5th):<br /> | ||
D E * * F G A B * * C D<br /> | |||
fourthwards chain of fifths: M2 - M6 - M3 - M7 - P4 - P1 - P5 - m2 - m6 - m3 - m7<br /> | fourthwards chain of fifths: M2 - M6 - M3 - M7 - P4 - P1 - P5 - m2 - m6 - m3 - m7<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 /> | ||
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<br /> | <br /> | ||
11edo pentatonic wide-fifth-based, fifthwards, # is ^^ (3/2 maps to 7\11 6th):<br /> | 11edo pentatonic wide-fifth-based, fifthwards, # is ^^ (3/2 maps to 7\11 6th):<br /> | ||
D * * E G * * A C * * D<br /> | |||
pentatonic fifthwards chain of fifthoids: m2 - m6 - m3 - m7 - P4 - P1 - P5 - M2 - M6 - M3 - M7<br /> | pentatonic fifthwards chain of fifthoids: m2 - m6 - m3 - m7 - P4 - P1 - P5 - M2 - M6 - M3 - M7<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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requires learning octatonic interval arithmetic and notation<br /> | requires learning octatonic interval arithmetic and notation<br /> | ||
<br /> | <br /> | ||
13edo heptatonic narrow-fifth-based, fourthwards, | 13edo heptatonic narrow-fifth-based, fourthwards, sharp = ^^^ (3/2 maps to 7\13 perfect 5th):<br /> | ||
D E * * * F G A B * * * C D<br /> | |||
fourthwards chain of fifths: M2 - M6 - M3 - M7 - P4 - P1 - P5 - m2 - m6 - m3 - m7<br /> | fourthwards chain of fifths: M2 - M6 - M3 - M7 - P4 - P1 - P5 - m2 - m6 - m3 - m7<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 /> | ||
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13edo undecatonic narrow-fifth-based, fourthwards, 3/2 maps to 7\13 = perfect 7th<br /> | 13edo 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 /> | ||
P1 - m2 - M2/m3 - M3/m4 - M4/m5 - M5 - P6 - P7 - m8 - M8/m9 - M9/m10 - M10/m11 - M11 - P12<br /> | P1 - m2 - M2/m3 - M3/m4 - M4/m5 - M5 - P6 - P7 - m8 - M8/m9 - M9/m10 - M10/m11 - M11 - P12<br /> | ||
| Line 1,076: | Line 1,138: | ||
<br /> | <br /> | ||
18edo heptatonic narrow-fifth-based, fourthwards, sharp = ^^ (3/2 maps to 10\18 perfect 5th)<br /> | 18edo heptatonic narrow-fifth-based, fourthwards, sharp = ^^ (3/2 maps to 10\18 perfect 5th)<br /> | ||
D * E * * * F * G * A * B * * * C * D<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 | fourthwards plus ups and downs plus closed is triply confusing!<br /> | ||
<br /> | <br /> | ||
18edo nonatonic narrow-fifth-based (3/2 maps to 10\18 = perfect 6th)<br /> | 18edo nonatonic narrow-fifth-based (3/2 maps to 10\18 = perfect 6th)<br /> | ||
| Line 1,085: | Line 1,148: | ||
<br /> | <br /> | ||
<u><strong>Alternate notation for other edos:</strong></u><br /> | <u><strong>Alternate notation for other edos:</strong></u><br /> | ||
23edo pentatonic wide-fifth-based, fifthwards, 3/2 maps to 14\23 = perfect fifthoid<br /> | 23edo pentatonic wide-fifth-based, fifthwards, 3/2 maps to 14\23 = perfect fifthoid: <br /> | ||
35edo heptatonic wide-fifth-based, sharp = seven ups, 3/2 maps to 21\35 = perfect fifth<br /> | D * * * * E * * * G * * * * A * * * C * * * * D<br /> | ||
42edo heptatonic narrow-fifth-based, 3/2 maps to 24\42 = perfect fifth<br /> | 35edo heptatonic wide-fifth-based, sharp = seven ups, 3/2 maps to 21\35 = perfect fifth:<br /> | ||
D * * * * * * E/F * * * * * * G * * * * * * A * * * * * * B/C * * * * * * D<br /> | |||
42edo heptatonic narrow-fifth-based, sharp = six ups, 3/2 maps to 24\42 = perfect fifth:<br /> | |||
D * * * * * E * * * * * F * * * * * G * * * * * A * * * * * B * * * * * C * * * * * D<br /> | |||
<br /> | <br /> | ||
<br /> | <br /> | ||
| Line 1,100: | Line 1,166: | ||
The first two categories never use ups and downs, the next two always do (except for 5edo and 7edo). The sweet EDOs may or may not.<br /> | The first two categories never use ups and downs, the next two always do (except for 5edo and 7edo). The sweet EDOs may or may not.<br /> | ||
<br /> | <br /> | ||
To summarize an EDO, a scale fragment from C to D is shown, including C# and Db. Examples: <br /> | To summarize an EDO, a scale fragment from C to D is shown, including C# and Db. Examples:<br /> | ||
C C#/Db D (12edo)<br /> | C C#/Db D (12edo)<br /> | ||
C Db C# D (17edo)<br /> | C Db C# D (17edo)<br /> | ||
| Line 1,107: | Line 1,173: | ||
C _ C# Db _ D (31edo)<br /> | C _ C# Db _ D (31edo)<br /> | ||
<br /> | <br /> | ||
The scale fragment concisely conveys the &quot;flavor&quot; of the EDO's notation. The C-C# interval is the augmented unison, and if the 2nd key in the fragment isn't C#, ups and downs are required. The only exception is 7edo. For most EDOs, the C-Db interval is the minor 2nd and the C-D interval is the major 2nd. For perfect EDOs, C-Db = d2 and C-D = P2. For fourthward EDOs, C-Db = d2 and C-D = m2.<br /> | The scale fragment concisely conveys the &quot;flavor&quot; of the EDO's notation. The C-C# interval is the augmented unison, and if the 2nd key in the fragment isn't C#, ups and downs are required. The only exception is 7edo. For most EDOs, the C-Db interval is the minor 2nd and the C-D interval is the major 2nd. For perfect EDOs, C-Db = d2 and C-D = P2. For fourthward EDOs, C-Db = d2 and C-D = m2. D# is included for these EDOs because C-D# is a M2 just like E-F. For fifthless EDOs, the scale fragment isn't as helpful because you can't deduce the entire keyboard layout from it.<br /> | ||
<br /> | |||
Every EDO contains a unique scale fragment, and every scale fragment implies a unique EDO. Furthermore, this uniqueness applies to EDOs with alternate fifths: &quot;wide-fifth&quot; 35edo (which uses 21\35 as a fifth) has a different scale fragment than &quot;narrow-fifth&quot; 35edo with 20\35. If an EDO has a fifth of keyspan F and an octave of keyspan O (i.e. it's O-EDO), the minor 2nd's keyspan is m2 = -5F + 3O, and the augmented unison's is A1 = 7F - 4O. These equations can be reversed: F = 4(m2) + 3(A1) and O = 7(m2) + 5(A1). (For perfect and fourthwards EDOs, substitute M2 for m2.)<br /> | |||
<br /> | |||
<table class="wiki_table"> | |||
<tr> | |||
<td style="text-align: center;">5edo<br /> | |||
</td> | |||
<td style="text-align: center;">pentatonic<br /> | |||
</td> | |||
<td style="text-align: center;"><br /> | |||
</td> | |||
<td style="text-align: center;">C/Db<br /> | |||
</td> | |||
<td style="text-align: center;">C#/D<br /> | |||
</td> | |||
<td style="text-align: center;"><br /> | |||
</td> | |||
<td style="text-align: center;"><br /> | |||
</td> | |||
<td style="text-align: center;"><br /> | |||
</td> | |||
<td style="text-align: center;"><br /> | |||
</td> | |||
<td style="text-align: center;"><br /> | |||
</td> | |||
<td style="text-align: center;"><br /> | |||
</td> | |||
<td style="text-align: center;"><br /> | |||
</td> | |||
<td style="text-align: center;"><br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td style="text-align: center;">7edo<br /> | |||
</td> | |||
<td style="text-align: center;">perfect<br /> | |||
</td> | |||
<td style="text-align: center;"><br /> | |||
</td> | |||
<td style="text-align: center;">C/C#<br /> | |||
</td> | |||
<td style="text-align: center;">Db/D<br /> | |||
</td> | |||
<td style="text-align: center;"><br /> | |||
</td> | |||
<td style="text-align: center;"><br /> | |||
</td> | |||
<td style="text-align: center;"><br /> | |||
</td> | |||
<td style="text-align: center;"><br /> | |||
</td> | |||
<td style="text-align: center;"><br /> | |||
</td> | |||
<td style="text-align: center;"><br /> | |||
</td> | |||
<td style="text-align: center;"><br /> | |||
</td> | |||
<td style="text-align: center;"><br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td style="text-align: center;">8edo<br /> | |||
</td> | |||
<td style="text-align: center;">fifthless<br /> | |||
</td> | |||
<td style="text-align: center;"><br /> | |||
</td> | |||
<td style="text-align: center;"><br /> | |||
</td> | |||
<td style="text-align: center;"><br /> | |||
</td> | |||
<td style="text-align: center;"><br /> | |||
</td> | |||
<td style="text-align: center;"><br /> | |||
</td> | |||
<td style="text-align: center;"><br /> | |||
</td> | |||
<td style="text-align: center;"><br /> | |||
</td> | |||
<td style="text-align: center;"><br /> | |||
</td> | |||
<td style="text-align: center;"><br /> | |||
</td> | |||
<td style="text-align: center;"><br /> | |||
</td> | |||
<td style="text-align: center;"><br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td style="text-align: center;">9edo<br /> | |||
</td> | |||
<td style="text-align: center;">fourthward<br /> | |||
</td> | |||
<td style="text-align: center;"><br /> | |||
</td> | |||
<td style="text-align: center;">C/Db<br /> | |||
</td> | |||
<td style="text-align: center;">C#/D<br /> | |||
</td> | |||
<td style="text-align: center;">D#<br /> | |||
</td> | |||
<td style="text-align: center;"><br /> | |||
</td> | |||
<td style="text-align: center;"><br /> | |||
</td> | |||
<td style="text-align: center;"><br /> | |||
</td> | |||
<td style="text-align: center;"><br /> | |||
</td> | |||
<td style="text-align: center;"><br /> | |||
</td> | |||
<td style="text-align: center;"><br /> | |||
</td> | |||
<td style="text-align: center;"><br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td style="text-align: center;">10edo<br /> | |||
</td> | |||
<td style="text-align: center;">pentatonic<br /> | |||
</td> | |||
<td style="text-align: center;"><br /> | |||
</td> | |||
<td style="text-align: center;">C/Db<br /> | |||
</td> | |||
<td style="text-align: center;">*<br /> | |||
</td> | |||
<td style="text-align: center;">C#/D<br /> | |||
</td> | |||
<td style="text-align: center;"><br /> | |||
</td> | |||
<td style="text-align: center;"><br /> | |||
</td> | |||
<td style="text-align: center;"><br /> | |||
</td> | |||
<td style="text-align: center;"><br /> | |||
</td> | |||
<td style="text-align: center;"><br /> | |||
</td> | |||
<td style="text-align: center;"><br /> | |||
</td> | |||
<td style="text-align: center;"><br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td style="text-align: center;">11edo<br /> | |||
</td> | |||
<td style="text-align: center;">fifthless<br /> | |||
</td> | |||
<td style="text-align: center;"><br /> | |||
</td> | |||
<td style="text-align: center;"><br /> | |||
</td> | |||
<td style="text-align: center;"><br /> | |||
</td> | |||
<td style="text-align: center;"><br /> | |||
</td> | |||
<td style="text-align: center;"><br /> | |||
</td> | |||
<td style="text-align: center;"><br /> | |||
</td> | |||
<td style="text-align: center;"><br /> | |||
</td> | |||
<td style="text-align: center;"><br /> | |||
</td> | |||
<td style="text-align: center;"><br /> | |||
</td> | |||
<td style="text-align: center;"><br /> | |||
</td> | |||
<td style="text-align: center;"><br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td style="text-align: center;">12edo<br /> | |||
</td> | |||
<td style="text-align: center;">sweet<br /> | |||
</td> | |||
<td style="text-align: center;"><br /> | |||
</td> | |||
<td style="text-align: center;">C<br /> | |||
</td> | |||
<td style="text-align: center;">C#/Db<br /> | |||
</td> | |||
<td style="text-align: center;">D<br /> | |||
</td> | |||
<td style="text-align: center;"><br /> | |||
</td> | |||
<td style="text-align: center;"><br /> | |||
</td> | |||
<td style="text-align: center;"><br /> | |||
</td> | |||
<td style="text-align: center;"><br /> | |||
</td> | |||
<td style="text-align: center;"><br /> | |||
</td> | |||
<td style="text-align: center;"><br /> | |||
</td> | |||
<td style="text-align: center;"><br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td style="text-align: center;">13edo<br /> | |||
</td> | |||
<td style="text-align: center;">fifthless<br /> | |||
</td> | |||
<td style="text-align: center;"><br /> | |||
</td> | |||
<td style="text-align: center;"><br /> | |||
</td> | |||
<td style="text-align: center;"><br /> | |||
</td> | |||
<td style="text-align: center;"><br /> | |||
</td> | |||
<td style="text-align: center;"><br /> | |||
</td> | |||
<td style="text-align: center;"><br /> | |||
</td> | |||
<td style="text-align: center;"><br /> | |||
</td> | |||
<td style="text-align: center;"><br /> | |||
</td> | |||
<td style="text-align: center;"><br /> | |||
</td> | |||
<td style="text-align: center;"><br /> | |||
</td> | |||
<td style="text-align: center;"><br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td style="text-align: center;">14edo<br /> | |||
</td> | |||
<td style="text-align: center;">perfect<br /> | |||
</td> | |||
<td style="text-align: center;"><br /> | |||
</td> | |||
<td style="text-align: center;">C/C#<br /> | |||
</td> | |||
<td style="text-align: center;">*<br /> | |||
</td> | |||
<td style="text-align: center;">Db/D<br /> | |||
</td> | |||
<td style="text-align: center;"><br /> | |||
</td> | |||
<td style="text-align: center;"><br /> | |||
</td> | |||
<td style="text-align: center;"><br /> | |||
</td> | |||
<td style="text-align: center;"><br /> | |||
</td> | |||
<td style="text-align: center;"><br /> | |||
</td> | |||
<td style="text-align: center;"><br /> | |||
</td> | |||
<td style="text-align: center;"><br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td style="text-align: center;">15edo<br /> | |||
</td> | |||
<td style="text-align: center;">pentatonic<br /> | |||
</td> | |||
<td style="text-align: center;"><br /> | |||
</td> | |||
<td style="text-align: center;">C/Db<br /> | |||
</td> | |||
<td style="text-align: center;">*<br /> | |||
</td> | |||
<td style="text-align: center;">*<br /> | |||
</td> | |||
<td style="text-align: center;">C#/D<br /> | |||
</td> | |||
<td style="text-align: center;"><br /> | |||
</td> | |||
<td style="text-align: center;"><br /> | |||
</td> | |||
<td style="text-align: center;"><br /> | |||
</td> | |||
<td style="text-align: center;"><br /> | |||
</td> | |||
<td style="text-align: center;"><br /> | |||
</td> | |||
<td style="text-align: center;"><br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td style="text-align: center;">16edo<br /> | |||
</td> | |||
<td style="text-align: center;">fourthward<br /> | |||
</td> | |||
<td style="text-align: center;"><br /> | |||
</td> | |||
<td style="text-align: center;">C<br /> | |||
</td> | |||
<td style="text-align: center;">C#/Db<br /> | |||
</td> | |||
<td style="text-align: center;">D<br /> | |||
</td> | |||
<td style="text-align: center;">D#<br /> | |||
</td> | |||
<td style="text-align: center;"><br /> | |||
</td> | |||
<td style="text-align: center;"><br /> | |||
</td> | |||
<td style="text-align: center;"><br /> | |||
</td> | |||
<td style="text-align: center;"><br /> | |||
</td> | |||
<td style="text-align: center;"><br /> | |||
</td> | |||
<td style="text-align: center;"><br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td style="text-align: center;">17edo<br /> | |||
</td> | |||
<td style="text-align: center;">sweet<br /> | |||
</td> | |||
<td style="text-align: center;"><br /> | |||
</td> | |||
<td style="text-align: center;">C<br /> | |||
</td> | |||
<td style="text-align: center;">Db<br /> | |||
</td> | |||
<td style="text-align: center;">C#<br /> | |||
</td> | |||
<td style="text-align: center;">D<br /> | |||
</td> | |||
<td style="text-align: center;"><br /> | |||
</td> | |||
<td style="text-align: center;"><br /> | |||
</td> | |||
<td style="text-align: center;"><br /> | |||
</td> | |||
<td style="text-align: center;"><br /> | |||
</td> | |||
<td style="text-align: center;"><br /> | |||
</td> | |||
<td style="text-align: center;"><br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td style="text-align: center;">18edo<br /> | |||
</td> | |||
<td style="text-align: center;">fifthless<br /> | |||
</td> | |||
<td style="text-align: center;"><br /> | |||
</td> | |||
<td style="text-align: center;"><br /> | |||
</td> | |||
<td style="text-align: center;"><br /> | |||
</td> | |||
<td style="text-align: center;"><br /> | |||
</td> | |||
<td style="text-align: center;"><br /> | |||
</td> | |||
<td style="text-align: center;"><br /> | |||
</td> | |||
<td style="text-align: center;"><br /> | |||
</td> | |||
<td style="text-align: center;"><br /> | |||
</td> | |||
<td style="text-align: center;"><br /> | |||
</td> | |||
<td style="text-align: center;"><br /> | |||
</td> | |||
<td style="text-align: center;"><br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td style="text-align: center;">19edo<br /> | |||
</td> | |||
<td style="text-align: center;">sweet<br /> | |||
</td> | |||
<td style="text-align: center;"><br /> | |||
</td> | |||
<td style="text-align: center;">C<br /> | |||
</td> | |||
<td style="text-align: center;">C#<br /> | |||
</td> | |||
<td style="text-align: center;">Db<br /> | |||
</td> | |||
<td style="text-align: center;">D<br /> | |||
</td> | |||
<td style="text-align: center;"><br /> | |||
</td> | |||
<td style="text-align: center;"><br /> | |||
</td> | |||
<td style="text-align: center;"><br /> | |||
</td> | |||
<td style="text-align: center;"><br /> | |||
</td> | |||
<td style="text-align: center;"><br /> | |||
</td> | |||
<td style="text-align: center;"><br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td style="text-align: center;">20edo<br /> | |||
</td> | |||
<td style="text-align: center;">pentatonic<br /> | |||
</td> | |||
<td style="text-align: center;"><br /> | |||
</td> | |||
<td style="text-align: center;">C/Db<br /> | |||
</td> | |||
<td style="text-align: center;">*<br /> | |||
</td> | |||
<td style="text-align: center;">*<br /> | |||
</td> | |||
<td style="text-align: center;">*<br /> | |||
</td> | |||
<td style="text-align: center;">C#/D<br /> | |||
</td> | |||
<td style="text-align: center;"><br /> | |||
</td> | |||
<td style="text-align: center;"><br /> | |||
</td> | |||
<td style="text-align: center;"><br /> | |||
</td> | |||
<td style="text-align: center;"><br /> | |||
</td> | |||
<td style="text-align: center;"><br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td style="text-align: center;">21edo<br /> | |||
</td> | |||
<td style="text-align: center;">perfect<br /> | |||
</td> | |||
<td style="text-align: center;"><br /> | |||
</td> | |||
<td style="text-align: center;">C/C#<br /> | |||
</td> | |||
<td style="text-align: center;">*<br /> | |||
</td> | |||
<td style="text-align: center;">*<br /> | |||
</td> | |||
<td style="text-align: center;">Db/D<br /> | |||
</td> | |||
<td style="text-align: center;"><br /> | |||
</td> | |||
<td style="text-align: center;"><br /> | |||
</td> | |||
<td style="text-align: center;"><br /> | |||
</td> | |||
<td style="text-align: center;"><br /> | |||
</td> | |||
<td style="text-align: center;"><br /> | |||
</td> | |||
<td style="text-align: center;"><br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td style="text-align: center;">22edo<br /> | |||
</td> | |||
<td style="text-align: center;">sweet<br /> | |||
</td> | |||
<td style="text-align: center;"><br /> | |||
</td> | |||
<td style="text-align: center;">C<br /> | |||
</td> | |||
<td style="text-align: center;">Db<br /> | |||
</td> | |||
<td style="text-align: center;">*<br /> | |||
</td> | |||
<td style="text-align: center;">C#<br /> | |||
</td> | |||
<td style="text-align: center;">D<br /> | |||
</td> | |||
<td style="text-align: center;"><br /> | |||
</td> | |||
<td style="text-align: center;"><br /> | |||
</td> | |||
<td style="text-align: center;"><br /> | |||
</td> | |||
<td style="text-align: center;"><br /> | |||
</td> | |||
<td style="text-align: center;"><br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td style="text-align: center;">23edo<br /> | |||
</td> | |||
<td style="text-align: center;">fourthward<br /> | |||
</td> | |||
<td style="text-align: center;"><br /> | |||
</td> | |||
<td style="text-align: center;">C<br /> | |||
</td> | |||
<td style="text-align: center;">C#<br /> | |||
</td> | |||
<td style="text-align: center;">Db<br /> | |||
</td> | |||
<td style="text-align: center;">D<br /> | |||
</td> | |||
<td style="text-align: center;">D#<br /> | |||
</td> | |||
<td style="text-align: center;"><br /> | |||
</td> | |||
<td style="text-align: center;"><br /> | |||
</td> | |||
<td style="text-align: center;"><br /> | |||
</td> | |||
<td style="text-align: center;"><br /> | |||
</td> | |||
<td style="text-align: center;"><br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td style="text-align: center;">24edo<br /> | |||
</td> | |||
<td style="text-align: center;">sweet<br /> | |||
</td> | |||
<td style="text-align: center;"><br /> | |||
</td> | |||
<td style="text-align: center;">C<br /> | |||
</td> | |||
<td style="text-align: center;">*<br /> | |||
</td> | |||
<td style="text-align: center;">C#/Db<br /> | |||
</td> | |||
<td style="text-align: center;">*<br /> | |||
</td> | |||
<td style="text-align: center;">D<br /> | |||
</td> | |||
<td style="text-align: center;"><br /> | |||
</td> | |||
<td style="text-align: center;"><br /> | |||
</td> | |||
<td style="text-align: center;"><br /> | |||
</td> | |||
<td style="text-align: center;"><br /> | |||
</td> | |||
<td style="text-align: center;"><br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td style="text-align: center;">25edo<br /> | |||
</td> | |||
<td style="text-align: center;">pentatonic<br /> | |||
</td> | |||
<td style="text-align: center;"><br /> | |||
</td> | |||
<td style="text-align: center;">C/Db<br /> | |||
</td> | |||
<td style="text-align: center;">*<br /> | |||
</td> | |||
<td style="text-align: center;">*<br /> | |||
</td> | |||
<td style="text-align: center;">*<br /> | |||
</td> | |||
<td style="text-align: center;">*<br /> | |||
</td> | |||
<td style="text-align: center;">C#/D<br /> | |||
</td> | |||
<td style="text-align: center;"><br /> | |||
</td> | |||
<td style="text-align: center;"><br /> | |||
</td> | |||
<td style="text-align: center;"><br /> | |||
</td> | |||
<td style="text-align: center;"><br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td style="text-align: center;">26edo<br /> | |||
</td> | |||
<td style="text-align: center;">sweet<br /> | |||
</td> | |||
<td style="text-align: center;"><br /> | |||
</td> | |||
<td style="text-align: center;">C<br /> | |||
</td> | |||
<td style="text-align: center;">C#<br /> | |||
</td> | |||
<td style="text-align: center;">*<br /> | |||
</td> | |||
<td style="text-align: center;">Db<br /> | |||
</td> | |||
<td style="text-align: center;">D<br /> | |||
</td> | |||
<td style="text-align: center;"><br /> | |||
</td> | |||
<td style="text-align: center;"><br /> | |||
</td> | |||
<td style="text-align: center;"><br /> | |||
</td> | |||
<td style="text-align: center;"><br /> | |||
</td> | |||
<td style="text-align: center;"><br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td style="text-align: center;">27edo<br /> | |||
</td> | |||
<td style="text-align: center;">sweet<br /> | |||
</td> | |||
<td style="text-align: center;"><br /> | |||
</td> | |||
<td style="text-align: center;">C<br /> | |||
</td> | |||
<td style="text-align: center;">Db<br /> | |||
</td> | |||
<td style="text-align: center;">*<br /> | |||
</td> | |||
<td style="text-align: center;">*<br /> | |||
</td> | |||
<td style="text-align: center;">C#<br /> | |||
</td> | |||
<td style="text-align: center;">D<br /> | |||
</td> | |||
<td style="text-align: center;"><br /> | |||
</td> | |||
<td style="text-align: center;"><br /> | |||
</td> | |||
<td style="text-align: center;"><br /> | |||
</td> | |||
<td style="text-align: center;"><br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td style="text-align: center;">28edo<br /> | |||
</td> | |||
<td style="text-align: center;">perfect<br /> | |||
</td> | |||
<td style="text-align: center;"><br /> | |||
</td> | |||
<td style="text-align: center;">C/C#<br /> | |||
</td> | |||
<td style="text-align: center;">*<br /> | |||
</td> | |||
<td style="text-align: center;">*<br /> | |||
</td> | |||
<td style="text-align: center;">*<br /> | |||
</td> | |||
<td style="text-align: center;">Db/D<br /> | |||
</td> | |||
<td style="text-align: center;"><br /> | |||
</td> | |||
<td style="text-align: center;"><br /> | |||
</td> | |||
<td style="text-align: center;"><br /> | |||
</td> | |||
<td style="text-align: center;"><br /> | |||
</td> | |||
<td style="text-align: center;"><br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td style="text-align: center;">29edo<br /> | |||
</td> | |||
<td style="text-align: center;">sweet<br /> | |||
</td> | |||
<td style="text-align: center;"><br /> | |||
</td> | |||
<td style="text-align: center;">C<br /> | |||
</td> | |||
<td style="text-align: center;">*<br /> | |||
</td> | |||
<td style="text-align: center;">Db<br /> | |||
</td> | |||
<td style="text-align: center;">C#<br /> | |||
</td> | |||
<td style="text-align: center;">*<br /> | |||
</td> | |||
<td style="text-align: center;">D<br /> | |||
</td> | |||
<td style="text-align: center;"><br /> | |||
</td> | |||
<td style="text-align: center;"><br /> | |||
</td> | |||
<td style="text-align: center;"><br /> | |||
</td> | |||
<td style="text-align: center;"><br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td style="text-align: center;">30edo<br /> | |||
</td> | |||
<td style="text-align: center;">pentatonic<br /> | |||
</td> | |||
<td style="text-align: center;"><br /> | |||
</td> | |||
<td style="text-align: center;">C/Db<br /> | |||
</td> | |||
<td style="text-align: center;">*<br /> | |||
</td> | |||
<td style="text-align: center;">*<br /> | |||
</td> | |||
<td style="text-align: center;">*<br /> | |||
</td> | |||
<td style="text-align: center;">*<br /> | |||
</td> | |||
<td style="text-align: center;">*<br /> | |||
</td> | |||
<td style="text-align: center;">C#/D<br /> | |||
</td> | |||
<td style="text-align: center;"><br /> | |||
</td> | |||
<td style="text-align: center;"><br /> | |||
</td> | |||
<td style="text-align: center;"><br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td style="text-align: center;">31edo<br /> | |||
</td> | |||
<td style="text-align: center;">sweet<br /> | |||
</td> | |||
<td style="text-align: center;"><br /> | |||
</td> | |||
<td style="text-align: center;">C<br /> | |||
</td> | |||
<td style="text-align: center;">*<br /> | |||
</td> | |||
<td style="text-align: center;">C#<br /> | |||
</td> | |||
<td style="text-align: center;">Db<br /> | |||
</td> | |||
<td style="text-align: center;">*<br /> | |||
</td> | |||
<td style="text-align: center;">D<br /> | |||
</td> | |||
<td style="text-align: center;"><br /> | |||
</td> | |||
<td style="text-align: center;"><br /> | |||
</td> | |||
<td style="text-align: center;"><br /> | |||
</td> | |||
<td style="text-align: center;"><br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td style="text-align: center;">32edo<br /> | |||
</td> | |||
<td style="text-align: center;">sweet<br /> | |||
</td> | |||
<td style="text-align: center;"><br /> | |||
</td> | |||
<td style="text-align: center;">C<br /> | |||
</td> | |||
<td style="text-align: center;">Db<br /> | |||
</td> | |||
<td style="text-align: center;">*<br /> | |||
</td> | |||
<td style="text-align: center;">*<br /> | |||
</td> | |||
<td style="text-align: center;">*<br /> | |||
</td> | |||
<td style="text-align: center;">C#<br /> | |||
</td> | |||
<td style="text-align: center;">D<br /> | |||
</td> | |||
<td style="text-align: center;"><br /> | |||
</td> | |||
<td style="text-align: center;"><br /> | |||
</td> | |||
<td style="text-align: center;"><br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td style="text-align: center;">33edo<br /> | |||
</td> | |||
<td style="text-align: center;">sweet<br /> | |||
</td> | |||
<td style="text-align: center;"><br /> | |||
</td> | |||
<td style="text-align: center;">C<br /> | |||
</td> | |||
<td style="text-align: center;">C#<br /> | |||
</td> | |||
<td style="text-align: center;">*<br /> | |||
</td> | |||
<td style="text-align: center;">*<br /> | |||
</td> | |||
<td style="text-align: center;">Db<br /> | |||
</td> | |||
<td style="text-align: center;">D<br /> | |||
</td> | |||
<td style="text-align: center;"><br /> | |||
</td> | |||
<td style="text-align: center;"><br /> | |||
</td> | |||
<td style="text-align: center;"><br /> | |||
</td> | |||
<td style="text-align: center;"><br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td style="text-align: center;">34edo<br /> | |||
</td> | |||
<td style="text-align: center;">sweet<br /> | |||
</td> | |||
<td style="text-align: center;"><br /> | |||
</td> | |||
<td style="text-align: center;">C<br /> | |||
</td> | |||
<td style="text-align: center;">*<br /> | |||
</td> | |||
<td style="text-align: center;">Db<br /> | |||
</td> | |||
<td style="text-align: center;">*<br /> | |||
</td> | |||
<td style="text-align: center;">C#<br /> | |||
</td> | |||
<td style="text-align: center;">*<br /> | |||
</td> | |||
<td style="text-align: center;">D<br /> | |||
</td> | |||
<td style="text-align: center;"><br /> | |||
</td> | |||
<td style="text-align: center;"><br /> | |||
</td> | |||
<td style="text-align: center;"><br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td style="text-align: center;">35edo<br /> | |||
</td> | |||
<td style="text-align: center;">perfect<br /> | |||
</td> | |||
<td style="text-align: center;"><br /> | |||
</td> | |||
<td style="text-align: center;">C/C#<br /> | |||
</td> | |||
<td style="text-align: center;">*<br /> | |||
</td> | |||
<td style="text-align: center;">*<br /> | |||
</td> | |||
<td style="text-align: center;">*<br /> | |||
</td> | |||
<td style="text-align: center;">*<br /> | |||
</td> | |||
<td style="text-align: center;">Db/D<br /> | |||
</td> | |||
<td style="text-align: center;"><br /> | |||
</td> | |||
<td style="text-align: center;"><br /> | |||
</td> | |||
<td style="text-align: center;"><br /> | |||
</td> | |||
<td style="text-align: center;"><br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td style="text-align: center;">36edo<br /> | |||
</td> | |||
<td style="text-align: center;">sweet<br /> | |||
</td> | |||
<td style="text-align: center;"><br /> | |||
</td> | |||
<td style="text-align: center;">C<br /> | |||
</td> | |||
<td style="text-align: center;">*<br /> | |||
</td> | |||
<td style="text-align: center;">*<br /> | |||
</td> | |||
<td style="text-align: center;">C#/Db<br /> | |||
</td> | |||
<td style="text-align: center;">*<br /> | |||
</td> | |||
<td style="text-align: center;">*<br /> | |||
</td> | |||
<td style="text-align: center;">D<br /> | |||
</td> | |||
<td style="text-align: center;"><br /> | |||
</td> | |||
<td style="text-align: center;"><br /> | |||
</td> | |||
<td style="text-align: center;"><br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td style="text-align: center;">37edo<br /> | |||
</td> | |||
<td style="text-align: center;">sweet<br /> | |||
</td> | |||
<td style="text-align: center;"><br /> | |||
</td> | |||
<td style="text-align: center;">C<br /> | |||
</td> | |||
<td style="text-align: center;">Db<br /> | |||
</td> | |||
<td style="text-align: center;">*<br /> | |||
</td> | |||
<td style="text-align: center;">*<br /> | |||
</td> | |||
<td style="text-align: center;">*<br /> | |||
</td> | |||
<td style="text-align: center;">*<br /> | |||
</td> | |||
<td style="text-align: center;">C#<br /> | |||
</td> | |||
<td style="text-align: center;">D<br /> | |||
</td> | |||
<td style="text-align: center;"><br /> | |||
</td> | |||
<td style="text-align: center;"><br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td style="text-align: center;">38edo<br /> | |||
</td> | |||
<td style="text-align: center;">sweet<br /> | |||
</td> | |||
<td style="text-align: center;"><br /> | |||
</td> | |||
<td style="text-align: center;">C<br /> | |||
</td> | |||
<td style="text-align: center;">*<br /> | |||
</td> | |||
<td style="text-align: center;">C#<br /> | |||
</td> | |||
<td style="text-align: center;">*<br /> | |||
</td> | |||
<td style="text-align: center;">Db<br /> | |||
</td> | |||
<td style="text-align: center;">*<br /> | |||
</td> | |||
<td style="text-align: center;">D<br /> | |||
</td> | |||
<td style="text-align: center;"><br /> | |||
</td> | |||
<td style="text-align: center;"><br /> | |||
</td> | |||
<td style="text-align: center;"><br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td style="text-align: center;">39edo<br /> | |||
</td> | |||
<td style="text-align: center;">sweet<br /> | |||
</td> | |||
<td style="text-align: center;"><br /> | |||
</td> | |||
<td style="text-align: center;">C<br /> | |||
</td> | |||
<td style="text-align: center;">*<br /> | |||
</td> | |||
<td style="text-align: center;">Db<br /> | |||
</td> | |||
<td style="text-align: center;">*<br /> | |||
</td> | |||
<td style="text-align: center;">*<br /> | |||
</td> | |||
<td style="text-align: center;">C#<br /> | |||
</td> | |||
<td style="text-align: center;">*<br /> | |||
</td> | |||
<td style="text-align: center;">D<br /> | |||
</td> | |||
<td style="text-align: center;"><br /> | |||
</td> | |||
<td style="text-align: center;"><br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td style="text-align: center;">40edo<br /> | |||
</td> | |||
<td style="text-align: center;">sweet<br /> | |||
</td> | |||
<td style="text-align: center;"><br /> | |||
</td> | |||
<td style="text-align: center;">C<br /> | |||
</td> | |||
<td style="text-align: center;">C#<br /> | |||
</td> | |||
<td style="text-align: center;">*<br /> | |||
</td> | |||
<td style="text-align: center;">*<br /> | |||
</td> | |||
<td style="text-align: center;">*<br /> | |||
</td> | |||
<td style="text-align: center;">Db<br /> | |||
</td> | |||
<td style="text-align: center;">D<br /> | |||
</td> | |||
<td style="text-align: center;"><br /> | |||
</td> | |||
<td style="text-align: center;"><br /> | |||
</td> | |||
<td style="text-align: center;"><br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td style="text-align: center;">41edo<br /> | |||
</td> | |||
<td style="text-align: center;">sweet<br /> | |||
</td> | |||
<td style="text-align: center;"><br /> | |||
</td> | |||
<td style="text-align: center;">C<br /> | |||
</td> | |||
<td style="text-align: center;">*<br /> | |||
</td> | |||
<td style="text-align: center;">*<br /> | |||
</td> | |||
<td style="text-align: center;">Db<br /> | |||
</td> | |||
<td style="text-align: center;">C#<br /> | |||
</td> | |||
<td style="text-align: center;">*<br /> | |||
</td> | |||
<td style="text-align: center;">*<br /> | |||
</td> | |||
<td style="text-align: center;">D<br /> | |||
</td> | |||
<td style="text-align: center;"><br /> | |||
</td> | |||
<td style="text-align: center;"><br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td style="text-align: center;">42edo<br /> | |||
</td> | |||
<td style="text-align: center;">sweet<br /> | |||
</td> | |||
<td style="text-align: center;"><br /> | |||
</td> | |||
<td style="text-align: center;">C<br /> | |||
</td> | |||
<td style="text-align: center;">Db<br /> | |||
</td> | |||
<td style="text-align: center;">*<br /> | |||
</td> | |||
<td style="text-align: center;">*<br /> | |||
</td> | |||
<td style="text-align: center;">*<br /> | |||
</td> | |||
<td style="text-align: center;">*<br /> | |||
</td> | |||
<td style="text-align: center;">*<br /> | |||
</td> | |||
<td style="text-align: center;">C#<br /> | |||
</td> | |||
<td style="text-align: center;">D<br /> | |||
</td> | |||
<td style="text-align: center;"><br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td style="text-align: center;">43edo<br /> | |||
</td> | |||
<td style="text-align: center;">sweet<br /> | |||
</td> | |||
<td style="text-align: center;"><br /> | |||
</td> | |||
<td style="text-align: center;">C<br /> | |||
</td> | |||
<td style="text-align: center;">*<br /> | |||
</td> | |||
<td style="text-align: center;">*<br /> | |||
</td> | |||
<td style="text-align: center;">C#<br /> | |||
</td> | |||
<td style="text-align: center;">Db<br /> | |||
</td> | |||
<td style="text-align: center;">*<br /> | |||
</td> | |||
<td style="text-align: center;">*<br /> | |||
</td> | |||
<td style="text-align: center;">D<br /> | |||
</td> | |||
<td style="text-align: center;"><br /> | |||
</td> | |||
<td style="text-align: center;"><br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td style="text-align: center;">44ddo<br /> | |||
</td> | |||
<td style="text-align: center;">sweet<br /> | |||
</td> | |||
<td style="text-align: center;"><br /> | |||
</td> | |||
<td style="text-align: center;">C<br /> | |||
</td> | |||
<td style="text-align: center;">*<br /> | |||
</td> | |||
<td style="text-align: center;">Db<br /> | |||
</td> | |||
<td style="text-align: center;">*<br /> | |||
</td> | |||
<td style="text-align: center;">*<br /> | |||
</td> | |||
<td style="text-align: center;">*<br /> | |||
</td> | |||
<td style="text-align: center;">C#<br /> | |||
</td> | |||
<td style="text-align: center;">*<br /> | |||
</td> | |||
<td style="text-align: center;">D<br /> | |||
</td> | |||
<td style="text-align: center;"><br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td style="text-align: center;">45edo<br /> | |||
</td> | |||
<td style="text-align: center;">sweet<br /> | |||
</td> | |||
<td style="text-align: center;"><br /> | |||
</td> | |||
<td style="text-align: center;">C<br /> | |||
</td> | |||
<td style="text-align: center;">*<br /> | |||
</td> | |||
<td style="text-align: center;">Db<br /> | |||
</td> | |||
<td style="text-align: center;">*<br /> | |||
</td> | |||
<td style="text-align: center;">*<br /> | |||
</td> | |||
<td style="text-align: center;">C#<br /> | |||
</td> | |||
<td style="text-align: center;">*<br /> | |||
</td> | |||
<td style="text-align: center;">D<br /> | |||
</td> | |||
<td style="text-align: center;"><br /> | |||
</td> | |||
<td style="text-align: center;"><br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td style="text-align: center;">46edo<br /> | |||
</td> | |||
<td style="text-align: center;">sweet<br /> | |||
</td> | |||
<td style="text-align: center;"><br /> | |||
</td> | |||
<td style="text-align: center;">C<br /> | |||
</td> | |||
<td style="text-align: center;">*<br /> | |||
</td> | |||
<td style="text-align: center;">*<br /> | |||
</td> | |||
<td style="text-align: center;">Db<br /> | |||
</td> | |||
<td style="text-align: center;">*<br /> | |||
</td> | |||
<td style="text-align: center;">C#<br /> | |||
</td> | |||
<td style="text-align: center;">*<br /> | |||
</td> | |||
<td style="text-align: center;">*<br /> | |||
</td> | |||
<td style="text-align: center;">D<br /> | |||
</td> | |||
<td style="text-align: center;"><br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td style="text-align: center;">47edo<br /> | |||
</td> | |||
<td style="text-align: center;">sweet<br /> | |||
</td> | |||
<td style="text-align: center;"><br /> | |||
</td> | |||
<td style="text-align: center;">C<br /> | |||
</td> | |||
<td style="text-align: center;">C#<br /> | |||
</td> | |||
<td style="text-align: center;">*<br /> | |||
</td> | |||
<td style="text-align: center;">*<br /> | |||
</td> | |||
<td style="text-align: center;">*<br /> | |||
</td> | |||
<td style="text-align: center;">*<br /> | |||
</td> | |||
<td style="text-align: center;">Db<br /> | |||
</td> | |||
<td style="text-align: center;">D<br /> | |||
</td> | |||
<td style="text-align: center;"><br /> | |||
</td> | |||
<td style="text-align: center;"><br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td style="text-align: center;">48edo<br /> | |||
</td> | |||
<td style="text-align: center;">sweet<br /> | |||
</td> | |||
<td style="text-align: center;"><br /> | |||
</td> | |||
<td style="text-align: center;">C<br /> | |||
</td> | |||
<td style="text-align: center;">*<br /> | |||
</td> | |||
<td style="text-align: center;">*<br /> | |||
</td> | |||
<td style="text-align: center;">*<br /> | |||
</td> | |||
<td style="text-align: center;">C#/Db<br /> | |||
</td> | |||
<td style="text-align: center;">*<br /> | |||
</td> | |||
<td style="text-align: center;">*<br /> | |||
</td> | |||
<td style="text-align: center;">*<br /> | |||
</td> | |||
<td style="text-align: center;">D<br /> | |||
</td> | |||
<td style="text-align: center;"><br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td style="text-align: center;">49edo<br /> | |||
</td> | |||
<td style="text-align: center;">sweet<br /> | |||
</td> | |||
<td style="text-align: center;"><br /> | |||
</td> | |||
<td style="text-align: center;">C<br /> | |||
</td> | |||
<td style="text-align: center;">*<br /> | |||
</td> | |||
<td style="text-align: center;">Db<br /> | |||
</td> | |||
<td style="text-align: center;">*<br /> | |||
</td> | |||
<td style="text-align: center;">*<br /> | |||
</td> | |||
<td style="text-align: center;">*<br /> | |||
</td> | |||
<td style="text-align: center;">*<br /> | |||
</td> | |||
<td style="text-align: center;">C#<br /> | |||
</td> | |||
<td style="text-align: center;">*<br /> | |||
</td> | |||
<td style="text-align: center;">D<br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td style="text-align: center;">50edo<br /> | |||
</td> | |||
<td style="text-align: center;">sweet<br /> | |||
</td> | |||
<td style="text-align: center;"><br /> | |||
</td> | |||
<td style="text-align: center;">C<br /> | |||
</td> | |||
<td style="text-align: center;">*<br /> | |||
</td> | |||
<td style="text-align: center;">*<br /> | |||
</td> | |||
<td style="text-align: center;">C#<br /> | |||
</td> | |||
<td style="text-align: center;">*<br /> | |||
</td> | |||
<td style="text-align: center;">Db<br /> | |||
</td> | |||
<td style="text-align: center;">*<br /> | |||
</td> | |||
<td style="text-align: center;">*<br /> | |||
</td> | |||
<td style="text-align: center;">D<br /> | |||
</td> | |||
<td style="text-align: center;"><br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td style="text-align: center;">51edo<br /> | |||
</td> | |||
<td style="text-align: center;">sweet<br /> | |||
</td> | |||
<td style="text-align: center;"><br /> | |||
</td> | |||
<td style="text-align: center;">C<br /> | |||
</td> | |||
<td style="text-align: center;">*<br /> | |||
</td> | |||
<td style="text-align: center;">*<br /> | |||
</td> | |||
<td style="text-align: center;">Db<br /> | |||
</td> | |||
<td style="text-align: center;">*<br /> | |||
</td> | |||
<td style="text-align: center;">*<br /> | |||
</td> | |||
<td style="text-align: center;">C#<br /> | |||
</td> | |||
<td style="text-align: center;">*<br /> | |||
</td> | |||
<td style="text-align: center;">*<br /> | |||
</td> | |||
<td style="text-align: center;">D<br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td style="text-align: center;">52edo<br /> | |||
</td> | |||
<td style="text-align: center;">sweet<br /> | |||
</td> | |||
<td style="text-align: center;"><br /> | |||
</td> | |||
<td style="text-align: center;">C<br /> | |||
</td> | |||
<td style="text-align: center;">*<br /> | |||
</td> | |||
<td style="text-align: center;">C#<br /> | |||
</td> | |||
<td style="text-align: center;">*<br /> | |||
</td> | |||
<td style="text-align: center;">*<br /> | |||
</td> | |||
<td style="text-align: center;">*<br /> | |||
</td> | |||
<td style="text-align: center;">Db<br /> | |||
</td> | |||
<td style="text-align: center;">*<br /> | |||
</td> | |||
<td style="text-align: center;">D<br /> | |||
</td> | |||
<td style="text-align: center;"><br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td style="text-align: center;">53edo<br /> | |||
</td> | |||
<td style="text-align: center;">sweet<br /> | |||
</td> | |||
<td style="text-align: center;"><br /> | |||
</td> | |||
<td style="text-align: center;">C<br /> | |||
</td> | |||
<td style="text-align: center;">*<br /> | |||
</td> | |||
<td style="text-align: center;">*<br /> | |||
</td> | |||
<td style="text-align: center;">*<br /> | |||
</td> | |||
<td style="text-align: center;">Db<br /> | |||
</td> | |||
<td style="text-align: center;">C#<br /> | |||
</td> | |||
<td style="text-align: center;">*<br /> | |||
</td> | |||
<td style="text-align: center;">*<br /> | |||
</td> | |||
<td style="text-align: center;">*<br /> | |||
</td> | |||
<td style="text-align: center;">D<br /> | |||
</td> | |||
</tr> | |||
</table> | |||
<br /> | <br /> | ||
<br /> | <br /> | ||
<!-- 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> | ||