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Ups and downs can also notate any [[Tour of Regular Temperaments|rank-2 temperament]], although some temperaments require an additional pair of accidentals, lifts and drops (/ and \). In this context, an up or a lift represents sharpening by a [[comma]] that has been tempered, but not tempered out. For example, in [[Porcupine|Triyo aka Porcupine]], an up/down represents raising/lowering by a tempered 81/80, and lifts/drops aren't used. In practice, the two uses of the notation often coincide perfectly. Triyo is supported by both 15edo and 22edo, and both edos map 81/80 to one edostep. Thus if Triyo is tuned to 15edo, an up simultaneously means both a tempered 81/80 and 1\15. Likewise, if tuned to 22-edo, the up means both 81/80 and 1\22. If not tuned to an edo at all, then the up only means 81/80. Thus a piece written in Triyo can be converted to a piece written in 22-edo by simply writing "22-edo" on the top of the page.  
Ups and downs can also notate any [[Tour of Regular Temperaments|rank-2 temperament]], although some temperaments require an additional pair of accidentals, lifts and drops (/ and \). In this context, an up or a lift represents sharpening by a [[comma]] that has been tempered, but not tempered out. For example, in [[Porcupine|Triyo aka Porcupine]], an up/down represents raising/lowering by a tempered 81/80, and lifts/drops aren't used. In practice, the two uses of the notation often coincide perfectly. Triyo is supported by both 15edo and 22edo, and both edos map 81/80 to one edostep. Thus if Triyo is tuned to 15edo, an up simultaneously means both a tempered 81/80 and 1\15. Likewise, if tuned to 22-edo, the up means both 81/80 and 1\22. If not tuned to an edo at all, then the up only means 81/80. Thus a piece written in Triyo can be converted to a piece written in 22-edo by simply writing "22-edo" on the top of the page.  


Ups and downs notation as it applies to edos is fully documented in the [http://tallkite.com/misc_files/notation%20guide%20for%20edos%205-72.pdf Notation guide for edos 5-72], which also covers chord names, staff notation, key signatures, and scale trees. Ups and downs notation as it applies to rank-2 and rank-3 temperaments is fully documented in the [[pergen|pergens]] article.  
'''<u>This page only discusses notation of edos.</u>''' For notation of rank-2 and rank-3 temperaments, see the [[pergen|pergens]] article. For more on edo notation, see the [http://tallkite.com/misc_files/notation%20guide%20for%20edos%205-72.pdf Notation guide for edos 5-72], which also covers chord names, staff notation, key signatures, and scale trees.  


==Explanation -- a 22-edo example==
==Explanation -- a 22-edo example==
Line 25: Line 25:


Conventionally, in C you use D# instead of Eb when you have a Gaug chord. You have the freedom to spell your notes how you like, to make your chords look right. Likewise, in 22-edo, Db can be spelled ^C or vB# or even ^^B (double-up B).  
Conventionally, in C you use D# instead of Eb when you have a Gaug chord. You have the freedom to spell your notes how you like, to make your chords look right. Likewise, in 22-edo, Db can be spelled ^C or vB# or even ^^B (double-up B).  
'''<u>Staff Notation</u>'''
For staff notation, put an up or down to the left of the note and any sharp or flat it might have. Like sharps and flats, an up or down applies to any similar note that follows in the measure. If F is upped, any other F in the same octave inherits the up, but an F# doesn't. Key signatures follow the conventional practice, expanded to allow for double-sharps and double flats in some edos. For example, 19edo has the key of Bbb with a key signature of Bbb Ebb Ab Db Gb Cb Fb. Some edos have upped/downed tonics, e.g. 24-edo has the key of vD with a key signature of F# C# (v). The (v) is a "global down" that downs all 7 notes of the vD scale. For more on staff notation, see the [http://tallkite.com/misc_files/notation%20guide%20for%20edos%205-72.pdf Notation Guide for EDOs 5-72].


<u>'''Interval arithmetic'''</u>
<u>'''Interval arithmetic'''</u>
Line 34: Line 38:
!conventional
!conventional
! colspan="2" |with ups and downs
! colspan="2" |with ups and downs
!(cancelling)
!(combining)
|-
|-
|interval between two notes  
|interval between two notes  
Line 39: Line 45:
|^C to E = vM3
|^C to E = vM3
|C to ^E = ^M3
|C to ^E = ^M3
|^C to ^E = M3
|^C to vE = vvM3
|-
|-
|note plus an interval
|note plus an interval
Line 44: Line 52:
|^C + M3 = ^E
|^C + M3 = ^E
|C + ^M3 = ^E
|C + ^M3 = ^E
|^C + vM3 = E
|^C + ^M3 = ^^E
|-
|-
|sum of two intervals
|sum of two intervals
|M2 + m2 = m3
|M2 + M2 = M3
|M2 + ^m2 = ^m3
|M2 + ^M2 = ^M3
|vM2 + m2 = vm3
|vM2 + M2 = vM3
|vM2 + ^M2 = M3
|vM2 + vM2 = vvM3
|}
|}


==EDOs 12-24, 31 and 41==
==Examples: EDOs 12-24==


'''<u>12-edo</u>:'''  D * E F * G * A * B C * D, 1 key per sharp/flat, ups and downs not needed
'''[[12-edo]]:'''  D * E F * G * A * B C * D, 1 key per sharp/flat, ups and downs not needed


D  D#/Eb  E  F  F#/Gb  G  G#/Ab  A  A#/Bb  B  C  C#/Db  D
D  D#/Eb  E  F  F#/Gb  G  G#/Ab  A  A#/Bb  B  C  C#/Db  D
Line 59: Line 71:
P1  m2  M2  m3  M3  P4  A4/d5  P5  m6  M6  m7  M7  P8
P1  m2  M2  m3  M3  P4  A4/d5  P5  m6  M6  m7  M7  P8


'''<u>13b-edo</u>:'''  D E * * * F G A B * * * C D, 2 keys per sharp/flat
'''[[13-edo|13b-edo]]:'''  D E * * * F G A B * * * C D, 2 keys per sharp/flat


with sharp lowering the pitch, and major/aug narrower than minor/dim:
with sharp lowering the pitch, and major/aug narrower than minor/dim:
Line 67: Line 79:
P1  M2  ^M2/M3  vm2/^M3  m2/vm3  m3  P4  P5  M6  ^M6/M7  vm6/^M7  m6/vm7  m7  P8
P1  M2  ^M2/M3  vm2/^M3  m2/vm3  m3  P4  P5  M6  ^M6/M7  vm6/^M7  m6/vm7  m7  P8


'''<u>13b-edo</u>''' with sharp raising the pitch, and major/aug wider than minor/dim:
'''[[13-edo|13b-edo]]''' with sharp raising the pitch, and major/aug wider than minor/dim:


D  E  ^E/Fb  vE#/^Fb  E#/vF  F  G  A  B  ^B/Cb  vB#/^Cb  B#/vC  C  D
D  E  ^E/Fb  vE#/^Fb  E#/vF  F  G  A  B  ^B/Cb  vB#/^Cb  B#/vC  C  D
Line 73: Line 85:
P1  m2  ^m2/m3  vM2/^m3  M2/vM3  M3  P4  P5  m6  ^m6/m7  vM6/^m7  M6/vM7  M7  P8
P1  m2  ^m2/m3  vM2/^m3  M2/vM3  M3  P4  P5  m6  ^m6/m7  vM6/^m7  M6/vM7  M7  P8


<u>'''14-edo'''</u>:  D * E * F * G * A * B * C * D, zero keys per sharp/flat. Because every interval is perfect, the quality can be omitted
'''[[14-edo]]''':  D * E * F * G * A * B * C * D, zero keys per sharp/flat. Because every interval is perfect, the quality can be omitted


D  ^D/vE  E  ^E/vF  F  ^F/vG  G  ^G/vA  A  ^A/vB  B  ^B/vC  C  ^C/vD  D
D  ^D/vE  E  ^E/vF  F  ^F/vG  G  ^G/vA  A  ^A/vB  B  ^B/vC  C  ^C/vD  D
Line 79: Line 91:
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


'''<u>15-edo</u>:'''  D * * E/F * * G * * A * * B/C * * D, 3 keys per sharp/flat
'''[[15-edo]]:'''  D * * E/F * * G * * A * * B/C * * D, 3 keys per sharp/flat


D  ^D  vE  E/F  ^F  vG  G  ^G  vA  A  ^A  vB  B/C  ^C  vD  D
D  ^D  vE  E/F  ^F  vG  G  ^G  vA  A  ^A  vB  B/C  ^C  vD  D
Line 85: Line 97:
P1  ^m2  vM2  M2/m3  ^m3  vM3  M3/P4  ^4  v5  P5  ^m6  vM6  M6/m7  ^m7  vM7  P8
P1  ^m2  vM2  M2/m3  ^m3  vM3  M3/P4  ^4  v5  P5  ^m6  vM6  M6/m7  ^m7  vM7  P8


'''<u>16-edo:</u>'''  D * E * * F * G * A * B * * C * D, 1 key per sharp/flat, ups and downs not needed
'''[[16-edo]]:'''  D * E * * F * G * A * B * * C * D, 1 key per sharp/flat, ups and downs not needed


with sharp lowering the pitch, and major/aug narrower than minor/dim:
with sharp lowering the pitch, and major/aug narrower than minor/dim:
Line 93: Line 105:
P1  A2  M2  m2/A3  M3  m3  d3/A4  P4  d4/A5  P5  d5/A6  M6  m6/A7  M7  m7  d7  P8
P1  A2  M2  m2/A3  M3  m3  d3/A4  P4  d4/A5  P5  d5/A6  M6  m6/A7  M7  m7  d7  P8


'''<u>16-edo</u>''' with sharp raising the pitch, and major/aug wider than minor/dim:
'''[[16-edo]]''' with sharp raising the pitch, and major/aug wider than minor/dim:


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
Line 99: Line 111:
P1  d2  m2  M2  m3  M3  A3  P4  A4/d5  P5  d6  m6  M6/d7  m7  M7  A7  P8
P1  d2  m2  M2  m3  M3  A3  P4  A4/d5  P5  d6  m6  M6/d7  m7  M7  A7  P8


'''<u>17edo:</u>'''  D * * E F * * G * * A * * B C * * D, 2 keys per sharp/flat
'''[[17edo]]:'''  D * * E F * * G * * A * * B C * * D, 2 keys per sharp/flat


D  ^D/Eb  D#/vE  E  F ^F/Gb  F#/vG  G  ^G/Ab  G#/vA  A  ^A/Bb  A#/vB  B  C  ^C/Db  C#/vD  D
D  ^D/Eb  D#/vE  E  F ^F/Gb  F#/vG  G  ^G/Ab  G#/vA  A  ^A/Bb  A#/vB  B  C  ^C/Db  C#/vD  D
Line 105: Line 117:
P1  ^1/m2  A1/~2  M2  m3  ~3  M3  P4  ^4/d5  A4/v5  P5  m6  ~6  M6  m7  ~7  M7  P8  
P1  ^1/m2  A1/~2  M2  m3  ~3  M3  P4  ^4/d5  A4/v5  P5  m6  ~6  M6  m7  ~7  M7  P8  


'''<u>18b-edo</u>:'''  D * E * * * F * G * A * B * * * C * D, 2 keys per sharp/flat
'''[[18-edo|18b-edo]]:'''  D * E * * * F * G * A * B * * * C * D, 2 keys per sharp/flat


with sharp lowering the pitch, and major/aug narrower than minor/dim:
with sharp lowering the pitch, and major/aug narrower than minor/dim:
Line 113: Line 125:
P1  ^P1/vM2  M2  ~2  m2/M3  ~3  m3  ^m3/v4  P4  ^4/v5  P5  ^5/vM6  M6  ~6  m6/M7  ~7  m7  ^m2/d8  P8
P1  ^P1/vM2  M2  ~2  m2/M3  ~3  m3  ^m3/v4  P4  ^4/v5  P5  ^5/vM6  M6  ~6  m6/M7  ~7  m7  ^m2/d8  P8


'''<u>18b-edo</u>''' with sharp raising the pitch, and major/aug wider than minor/dim:
'''[[18-edo|18b-edo]]''' with sharp raising the pitch, and major/aug wider than minor/dim:


D  ^D/vE  E  ^E  E#/Fb  vF  F  ^F/vG  G  ^G/vA  A  ^A/vB  B  ^B  B#/Cb  vC  C  ^C/vD  D
D  ^D/vE  E  ^E  E#/Fb  vF  F  ^F/vG  G  ^G/vA  A  ^A/vB  B  ^B  B#/Cb  vC  C  ^C/vD  D
Line 119: Line 131:
P1  ^P1/vm2  m2  ~2  mM2/m3  ~3  M3  ^M3/v4  P4  ^4/v5  P5  ^5/vm6  m6  ~6  M6/m7  ~7  M7  ^M7/d8  P8
P1  ^P1/vm2  m2  ~2  mM2/m3  ~3  M3  ^M3/v4  P4  ^4/v5  P5  ^5/vm6  m6  ~6  M6/m7  ~7  M7  ^M7/d8  P8


'''<u>19-edo:</u>'''  D * * E * F * * G * * A * * B * C * * D, 1 key per sharp/flat, ups and downs not needed
'''[[19-edo]]:'''  D * * E * F * * G * * A * * B * C * * D, 1 key per sharp/flat, ups and downs not needed


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
Line 125: Line 137:
P1  d2  m2  M2  d3  m3  M3  A3  P4  A4  d5  P5  A5  m6  M6  d7  m7  M7  A7  P8
P1  d2  m2  M2  d3  m3  M3  A3  P4  A4  d5  P5  A5  m6  M6  d7  m7  M7  A7  P8


'''<u>20-edo</u>:'''  D * * * E/F * * * G * * * A * * * B/C * * * D, 4 keys per sharp/flat
'''[[20-edo]]:'''  D * * * E/F * * * G * * * A * * * B/C * * * D, 4 keys per sharp/flat


D  ^D  ^^D/vvE  vE  E/F  ^F  ^^F/vvG  vG  G  ^G  ^^G/vvA  vA  A  ^A  ^^A/vvB  vB  B/C  ^C  ^^C/vvD  vD  D
D  ^D  ^^D/vvE  vE  E/F  ^F  ^^F/vvG  vG  G  ^G  ^^G/vvA  vA  A  ^A  ^^A/vvB  vB  B/C  ^C  ^^C/vvD  vD  D
Line 131: Line 143:
P1/m2  ^m2  ~2  vM2  M2/m3  ^m3  ~3  vM3  M3/P4  ^4  ^^4/vv5  v5  P5/m6  ^m6  ~6  vM6  M6/m7  ^m7  ~7  vM7  P8
P1/m2  ^m2  ~2  vM2  M2/m3  ^m3  ~3  vM3  M3/P4  ^4  ^^4/vv5  v5  P5/m6  ^m6  ~6  vM6  M6/m7  ^m7  ~7  vM7  P8


'''<u>21-edo</u>''':  D * * E * * F * * G * * A * * B * * C * * D, zero keys per sharp/flat. Because every interval is perfect, the quality can be omitted
'''[[21-edo]]''':  D * * E * * F * * G * * A * * B * * C * * D, zero keys per sharp/flat. Because every interval is perfect, the quality can be omitted


D  ^D  vE  E  ^E  vF  F  ^F  vG  G  ^G  vA  A  ^A  vB  B  ^B  vC  C  ^C  vD  D
D  ^D  vE  E  ^E  vF  F  ^F  vG  G  ^G  vA  A  ^A  vB  B  ^B  vC  C  ^C  vD  D
Line 137: Line 149:
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


'''<u>22-edo</u>:'''  D * * * E F * * * G * * * A * * * B C * * * D, 3 keys per sharp/flat
[[22-edo|'''22-edo''']]''':'''  D * * * E F * * * G * * * A * * * B C * * * D, 3 keys per sharp/flat


D  ^D/Eb  vD#/^Eb  D#/vE  E  F  ^F/Gb  vF#/^Gb  F#/vG  G  ^G/Ab  vG#/^Ab  G#/vA  A  etc.
D  ^D/Eb  vD#/^Eb  D#/vE  E  F  ^F/Gb  vF#/^Gb  F#/vG  G  ^G/Ab  vG#/^Ab  G#/vA  A  etc.
Line 143: Line 155:
P1  ^1/m2  A1/^m2  vM2  M2  m3  ^m3  vM3  M3  P4  ^4/d5  vA4/^d5  A4/v5  P5  etc.
P1  ^1/m2  A1/^m2  vM2  M2  m3  ^m3  vM3  M3  P4  ^4/d5  vA4/^d5  A4/v5  P5  etc.


'''<u>23-edo</u>:'''  D * * E * * * F * * G * * A * * B * * * C * * D, 1 key per sharp/flat, ups or downs not needed
'''[[23-edo]]:'''  D * * E * * * F * * G * * A * * B * * * C * * D, 1 key per sharp/flat, ups or downs not needed


with sharp lowering the pitch, and major/aug narrower than minor/dim:
with sharp lowering the pitch, and major/aug narrower than minor/dim:
Line 151: Line 163:
P1  d1  A2  M2  m2  d2/A3  M3  m3  d3  A4  P4  d4  A5  P5  d5  A6  M6  m6  d6/A7  M7  m7  d7  A8  P8
P1  d1  A2  M2  m2  d2/A3  M3  m3  d3  A4  P4  d4  A5  P5  d5  A6  M6  m6  d6/A7  M7  m7  d7  A8  P8


'''<u>23-edo</u>''' with sharp raising the pitch, and major/aug wider than minor/dim:
'''[[23-edo]]''' with sharp raising the pitch, and major/aug wider than minor/dim:


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
Line 157: Line 169:
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


'''<u>24-edo</u>:'''  C * * * D * * * E * F * * * G * * * A * * * B * C, 2 keys per sharp/flat
'''[[24-edo]]:'''  C * * * D * * * E * F * * * G * * * A * * * B * C, 2 keys per sharp/flat


C  ^C/vDb  C#/Db  ^C#/vD  D  ^D/vEb  D#/Eb  ^D#/vE  E  ^E/vF  F  ^F  F#/Gb  vG  G  etc.
C  ^C/vDb  C#/Db  ^C#/vD  D  ^D/vEb  D#/Eb  ^D#/vE  E  ^E/vF  F  ^F  F#/Gb  vG  G  etc.


P1  ^1/vm2  A1/m2  ~2  M2  ^M2/vm3  m3  ~3  M3  ^M3/v4  P4  ^4  A4/d5  v5  P5  etc.
P1  ^1/vm2  A1/m2  ~2  M2  ^M2/vm3  m3  ~3  M3  ^M3/v4  P4  ^4  A4/d5  v5  P5  etc.
'''<u>31-edo</u>:'''  C * * * * D * * * * E * * F * * * * G * * * * A * * * * B * * C, 2 keys per sharp/flat
C  ^C  C#/vDb  ^C#/Db  vD  D  ^D  D#/vEb  ^D#/Eb  vE  E  ^E  vF  F  ^F  F#/vGb  ^F#/Gb  vG  G  etc.
P1  ^1/d2  A1/vm2  m2  ~2  M2  ^M2  vm3  m3  ~3  M3  ^M3  v4  P4  ^4  A4  d5  v5  P5  etc.
'''<u>41-edo</u>:'''  C * * * * * * D * * * * * * E * * F * * * * * * G * * * * * * A * * * * * * B * * C, 4 keys per sharp/flat
P1  ^1  vm2  m2  ^m2  ~2  vM2  M2  ^M2  vm3  m3  ^m3  ~3  vM3  M3  ^M3  v4  P4  ^4  ~4  vA4/d5  A4/^d5  ~5  v5  P5  etc.
C  ^C  vDb  Db  ^Db  vvD  vD  D  ^D  vEb  Eb  ^Eb  vvE  vE  E  ^E  vF  F  ^F  ^^F  vF#/Gb  F#/^Gb  vvG  vG  G  etc.


==Chords and Chord Progressions==
==Chords and Chord Progressions==
Line 198: Line 198:


C vvE G = Cvv = "C double-down" (in EDOs 20, 27, 34, 41, etc., C~ = "C mid", in EDOs 25, 32, 39, 46, etc. C^~ = "C upmid")
C vvE G = Cvv = "C double-down" (in EDOs 20, 27, 34, 41, etc., C~ = "C mid", in EDOs 25, 32, 39, 46, etc. C^~ = "C upmid")
C E vG = C(v5) = "C down-five" (in EDOs 10, 17, 24, 31, etc., same or C(~5) = "C mid-five")
C vE vG = Cv(v5) = "C down down-five" (in EDOs 10, 17, 24, 31, etc., C~(~5) = "C mid mid-five")


All triads follow a similar pattern.
All triads follow a similar pattern.
Line 228: Line 224:
|C2
|C2
|Co
|Co
|Caug
|C+
|-
|-
|3rd
|3rd
Line 236: Line 232:
|Cv2
|Cv2
|Cvo
|Cvo
|Cvaug
|Cv+
|-
|-
|5th
|5th
Line 244: Line 240:
|C2(v5)
|C2(v5)
|Co(v5)
|Co(v5)
|Caug(v5)  
|C+(v5)  
|-
|-
|3rd, 5th
|3rd, 5th
Line 252: Line 248:
|Cv2(v5)
|Cv2(v5)
|Cvo(v5)
|Cvo(v5)
|Cvaug(v5)
|Cv+(v5)
|}
|}
Many EDOs have notes between the major 3rd and the perfect 4th, creating triads impossible in 12-edo, such as:
Many EDOs have notes between the major 3rd and the perfect 4th, creating triads impossible in 12-edo, such as:
Line 264: Line 260:
C D# G = C(A2) or C(#2) =  "C aug-two" or "C sharp-two"
C D# G = C(A2) or C(#2) =  "C aug-two" or "C sharp-two"


Care must be taken in pronouncing the latter of the two names, that C(#2) doesn't sound like C#2 = C# D# G#. More non-12-edo triads:
Care must be taken in pronouncing the latter of the two names, that C(#2) doesn't sound like C#2, which is C# D# G#.  
 
C D# Gb = C(A2,d5) or C(#2,b5) = "C aug-two dim-five" or "C sharp-two, flat-five"
 
C Ebb Gb = Cdim(d3) or Cdim(bb3) = "C dim dim-three" or "C dim double-flat-three"
 
C Eb G# = Cmin(#5) = "C minor sharp-five"
 
C E# G# = Caug(#3) = "C aug sharp-three"
 
C Fb G# = C(b4,#5) = "C flat-four sharp-five"


<u>'''Sixth and seventh chords:'''</u>
<u>'''Sixth and seventh chords:'''</u>
Line 288: Line 274:
C vE G vBb = Cv7 = "C down seven"
C vE G vBb = Cv7 = "C down seven"


All 7th chords follow this same pattern. Likewise, if a 6th is not a P4 or A4 above the 3rd, it's an "add-6" chord. Permitting add-7 chords has the added benefit that the wordy "minor-7 flat-5" can be replaced with the more concise "dim add-7", written Co,7. "Half-dim" can still be used, e.g. C uphalf-dim is C ^Eb Gb ^Bb. But half-dim is problematic because the slash-circle abbreviation for half-dim is untypable.
All 7th chords follow this same pattern. Likewise, if a 6th is not a P4 or A4 above the 3rd, it's an "add-6" chord. Permitting add-7 chords has the added benefit that the wordy "minor-7 flat-5" can be replaced with the more concise "dim add-7", written Co,7. "Half-dim" can still be used, e.g. C uphalf-dim is C ^Eb Gb ^Bb. But half-dim is problematic because the slash-circle abbreviation for half-dim is hard to type.


In the table below, if a chord is '''bolded''', the comma must be spoken as "add".  
In the table below, if a chord is '''bolded''', the comma must be spoken as "add".  
Line 397: Line 383:
|Cvm6(v5)
|Cvm6(v5)
|}
|}
Some non-12-edo sixth and seventh chords:
More examples:


C E G Ab = C,b6 or C,m6 = "C add flat-six" or "C add minor-six"
C vE G ^Bb = Cv,^7 = "C down up-seven" (in EDOs 17, 24, 31, etc. C~7 = "C mid-seven")


C E G A# = C,#6 or C,A6 = "C add sharp-six" or "C add aug-six"
C E G A# = C,#6 or C,A6 = "C add sharp-six" or "C add aug-six"


C vE G ^Bb = Cv,^7 = "C down up-seven" (in certain EDOs, C~7 = "C mid-seven")
C E G Ab = C,b6 or C,m6 = "C add flat-six" or "C add minor-six"


C E G Bbb = C,d7 or C,bb7 = "C add dim-seven" or "C add double-flat-seven" (19-edo's 4:5:6:7 chord)
C E G Bbb = C,d7 or C,bb7 = "C add dim-seven" or "C add double-flat-seven" (19-edo's 4:5:6:7 chord)
Line 418: Line 404:


''Question: What to do when the 3rd is downed but the 7th isn't? Is it a down chord with an added 7th, or a 7th chord with a downed 3rd?''
''Question: What to do when the 3rd is downed but the 7th isn't? Is it a down chord with an added 7th, or a 7th chord with a downed 3rd?''
''Question: How to name 6/9 chords?''
{| class="wikitable"
{| class="wikitable"
|+
|+
Line 452: Line 440:
|C9(v3)
|C9(v3)
|Cm9(v3)
|Cm9(v3)
|'''Cv,7b9''' or
|'''Cv,7b9'''  
C7(v3)b9 or
 
C7,b9(v3)
|'''Cv,6,9?'''
|'''Cv,6,9?'''
|'''Cvm,6,9?'''
|'''Cvm,6,9?'''
|-
|-
|6th/7th
|6th/7th
| ----
| ------
|CM9(v7)
|CM9(v7)
|C9(v7)
|C9(v7)
Line 469: Line 454:
|-
|-
|3rd, 6th/7th
|3rd, 6th/7th
| ---
| ------
|CvM9
|CvM9
|Cv9
|Cv9
Line 503: Line 488:
|-
|-
|6th/7th, 9th
|6th/7th, 9th
| ---
| ------
|'''C,vM7v9'''
|'''C,vM7v9'''
|'''C,v7v9'''
|'''C,v7v9'''
Line 512: Line 497:
|-
|-
|3rd, 6th/7th, 9th
|3rd, 6th/7th, 9th
| ---
| ------
|CvM7,v9
|CvM7,v9
|Cv7,v9
|Cv7,v9
Line 534: Line 519:
|C9(v3v5)
|C9(v3v5)
|Cm9(v3v5)
|Cm9(v3v5)
|Cv(v5)7b9 or
|Cv(v5)7b9
C7(v3v5)b9
|Cv(v5)6,9
|Cv(v5)6,9
|Cvm(v5)6,9
|Cvm(v5)6,9
|-
|-
|5th, 6th/7th
|5th, 6th/7th
| ---
| ------
|CM9(v5v7)
|CM9(v5v7)
|C9(v5v7)
|C9(v5v7)
Line 549: Line 533:
|-
|-
|3rd, 5th, 6th/7th
|3rd, 5th, 6th/7th
| ---
| ------
|CvM9(v5)
|CvM9(v5)
|Cv9(v5)
|Cv9(v5)
Line 582: Line 566:
|-
|-
|5th, 6th/7th, 9th
|5th, 6th/7th, 9th
| ---
| ------
|C(v5)vM7v9
|C(v5)vM7v9
|C(v5)v7v9
|C(v5)v7v9
Line 591: Line 575:
|-
|-
|3rd, 5th, 6th/7th, 9th
|3rd, 5th, 6th/7th, 9th
| ---
| ------
|CvM7(v5)v9
|CvM7(v5)v9
|Cv7(v5)v9
|Cv7(v5)v9
Line 599: Line 583:
|Cvm6(v5)v9
|Cvm6(v5)v9
|}
|}
== Staff Notation ==
For staff notation, put an up or down to the left of the note and any sharp or flat it might have. Like sharps and flats, an up or down applies to any similar note that follows in the measure. If F is upped, any other F in the same octave inherits the up, but an F# doesn't.
[[File:Tibia_in_G_CORRECTED-1.png|alt=Tibia in G CORRECTED-1.png|800x1034px|Tibia in G CORRECTED-1.png]]
[[File:Tibia_in_G_CORRECTED-2.png|alt=Tibia in G CORRECTED-2.png|800x1035px|Tibia in G CORRECTED-2.png]]
==Cross-EDO considerations==
==Cross-EDO considerations==


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