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== Definition ==
== Definition ==
Ups and Downs (or ^v) is a notation system invented by [[Kite Giedraitis]] that can notate almost every [[EDO|EDO]]. The up symbol "^" and the down symbol "v" indicate raising/lowering a note (or widening/narrowing an interval) by one EDOstep. The mid symbol, "~" is for intervals exactly midway between major and minor, e.g. 3\24 is a mid 2nd. The mid 4th (~4) is midway between perfect and augmented, i.e. halfway-augmented, and the mid 5th (~5) is a halfway-diminished 5th.  
Ups and Downs (or ^v) is a notation system invented by [[Kite Giedraitis]] that can notate almost every [[EDO|edo]]. The up symbol "^" and the down symbol "v" indicate raising/lowering a note (or widening/narrowing an interval) by one EDOstep. The mid symbol, "~" is for intervals exactly midway between major and minor, e.g. 3\24 is a mid 2nd. The mid 4th (~4) is midway between perfect and augmented, i.e. halfway-augmented, and the mid 5th (~5) is a halfway-diminished 5th.  


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 15-edo and 22-edo, and both EDOs map 81/80 to one EDOstep. Thus if Triyo is tuned to 15-edo, 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 22edo, 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 22edo by simply writing "22edo" on the top of the page.  


Ups and downs can also be used to notate rank-3 just intonation subgroups such as 2.3.5 or 2.3.7 or 2.3.11. See [[Ups and Downs Notation for Rank-3 JI]].  
Ups and downs can also be used to notate rank-3 just intonation subgroups such as 2.3.5 or 2.3.7 or 2.3.11. See [[Ups and Downs Notation for Rank-3 JI]].  


'''<u>This page only discusses notation of EDOs.</u>''' However the notation of chords and chord progressions applies to all situations. For notation of rank-2 and rank-3 temperaments, see the [[pergen|pergens]] article.   
'''<u>This page only discusses notation of edos.</u>''' However the notation of chords and chord progressions applies to all situations. 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, slash chords, staff notation, key signatures, and scale trees.  
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, slash chords, staff notation, key signatures, and scale trees.  


==Explanation -- a 22-edo example==
==Explanation -- a 22edo example==


To understand the ups and downs notation, let's start with an EDO that doesn't need it. 19-edo is easy to notate because 7 fifths reduced by 4 octaves adds up to one EDOstep. C# is right next to C, and the keyboard runs C C# Db D D# Eb E etc. Conventional notation works perfectly with 19-edo as long as you remember that C# and Db are different notes.
To understand the ups and downs notation, let's start with an edo that doesn't need it. 19edo is easy to notate because 7 fifths reduced by 4 octaves adds up to one EDOstep. C# is right next to C, and the keyboard runs C C# Db D D# Eb E etc. Conventional notation works perfectly with 19edo as long as you remember that C# and Db are different notes.


In contrast, 22-edo is hard to notate because 7 fifths reduces to <u>three</u> EDOsteps, and the usual chain of fifths Eb-Bb-F-C-G-D-A-E-B-F#-C# etc. creates the scale C Db B# C# D Eb Fb D# E F. That's very confusing because B#-Db looks ascending on the page but sounds descending. Also a 4:5:6 chord is written C-D#-G, and the 5/4, usually a major 3rd, becomes an aug 2nd. Some people forgo the chain of fifths for a maximally even scale like C _ _ D _ _ E _ _ F _ _ _ G _ _ A _ _ B _ _ C. But that's confusing because G-D and A-E are dim 5ths. And if your piece is in G or A, that's really confusing. A notation system should work in every key!
In contrast, 22edo is hard to notate because 7 fifths reduces to <u>three</u> EDOsteps, and the usual chain of fifths Eb-Bb-F-C-G-D-A-E-B-F#-C# etc. creates the scale C Db B# C# D Eb Fb D# E F. That's very confusing because B#-Db looks ascending on the page but sounds descending. Also a 4:5:6 chord is written C-D#-G, and the 5/4, usually a major 3rd, becomes an aug 2nd. Some people forgo the chain of fifths for a maximally even scale like C _ _ D _ _ E _ _ F _ _ _ G _ _ A _ _ B _ _ C. But that's confusing because G-D and A-E are dim 5ths. And if your piece is in G or A, that's really confusing. A notation system should work in every key!


The solution is to use the sharp symbol to mean "raised by 7 fifths", and to use the up-arrow symbol to mean "sharpened by one EDOstep". 22-edo can be written C - Db - ^Db - vD - D - Eb - ^Eb - vE - E - F etc. The notes are pronounced up-D-flat, down-D, etc. Now the notes run in order. There's a pattern that's not too hard to pick up on, if you remember that there's 3 ups to a sharp. The up or down comes <u>before</u> the note name to make naming chords easy.
The solution is to use the sharp symbol to mean "raised by 7 fifths", and to use the up-arrow symbol to mean "sharpened by one EDOstep". 22edo can be written C - Db - ^Db - vD - D - Eb - ^Eb - vE - E - F etc. The notes are pronounced up-D-flat, down-D, etc. Now the notes run in order. There's a pattern that's not too hard to pick up on, if you remember that there's 3 ups to a sharp. The up or down comes <u>before</u> the note name to make naming chords easy.


The names change depending on the key, just like in conventional notation where F# in D major becomes Gb in Db major. So the B scale is B - C - ^C - vC# - C# - D - ^D - vD# - D# - E etc.
The names change depending on the key, just like in conventional notation where F# in D major becomes Gb in Db major. So the B scale is B - C - ^C - vC# - C# - D - ^D - vD# - D# - E etc.
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=== Relative notation and interval arithmetic ===
=== Relative notation and interval arithmetic ===
Ups and downs can be used not only for absolute notation (note names) but also for relative notation (intervals, chords and scales). Relative notation for 22-edo intervals: P1 - m2 - ^m2 - vM2 - M2 - m3 - ^m3 - vM3 - M3 - P4 - ^4/d5 - vA4/^d5 - A4/v5 - P5 etc. That's pronounced upminor 2nd, downmajor 3rd, etc. You can apply this pattern to any 22-edo key. The '''plain''' notes (those without ups or downs) always form a chain of fifths.
Ups and downs can be used not only for absolute notation (note names) but also for relative notation (intervals, chords and scales). Relative notation for 22edo intervals: P1 - m2 - ^m2 - vM2 - M2 - m3 - ^m3 - vM3 - M3 - P4 - ^4/d5 - vA4/^d5 - A4/v5 - P5 etc. That's pronounced upminor 2nd, downmajor 3rd, etc. You can apply this pattern to any 22edo key. The '''plain''' notes (those without ups or downs) always form a chain of fifths.


A core principle of ups and downs notation is that '''interval arithmetic is always preserved'''. Ups and downs are simply added in:
A core principle of ups and downs notation is that '''interval arithmetic is always preserved'''. Ups and downs are simply added in:
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=== Enharmonic equivalents ===
=== Enharmonic equivalents ===
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, or '''dup''' B for short, rhymes with "cup").  
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 22edo, Db can be spelled ^C or vB# or even ^^B (double-up B, or '''dup''' B for short, rhymes with "cup").  


From the [[Pergen|pergens]] article: "Conventional notation is generated by the octave and the 5th, and the notation (not the tuning itself) is rank-2. Each additional pair of accidentals increases the notation's rank by one, analogous to adding primes to a JI subgroup. Enharmonic intervals are like commas in that each one reduces the notation's rank by one (assuming they are linearly independent). Obviously, the notation's rank must match the actual tuning's rank. Therefore the minimum number of enharmonics needed always equals the difference between the notation's rank and the tuning's rank."  
From the [[Pergen|pergens]] article: "Conventional notation is generated by the octave and the 5th, and the notation (not the tuning itself) is rank-2. Each additional pair of accidentals increases the notation's rank by one, analogous to adding primes to a JI subgroup. Enharmonic intervals are like commas in that each one reduces the notation's rank by one (assuming they are linearly independent). Obviously, the notation's rank must match the actual tuning's rank. Therefore the minimum number of enharmonics needed always equals the difference between the notation's rank and the tuning's rank."  
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=== Key signatures ===
=== Key signatures ===
Key signatures follow the conventional practice, expanded to allow for double-sharps and double flats in some EDOs. For example, 19-edo 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. See also [[Kite Guitar originals#Scales and key signatures]] for the use of '''arrow stacks'''.
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. 24edo 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. See also [[Kite Guitar originals#Scales and key signatures]] for the use of '''arrow stacks'''.


=== Placement of the arrow ===
=== Placement of the arrow ===
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=== Further notes ===
=== Further notes ===
EDO intervals are often written as 7\22. This can also be written as vM3\22. This is useful when comparing EDOs, e.g. vM3\22 vs. vM3\15.
Edo intervals are often written as 7\22. This can also be written as vM3\22. This is useful when comparing edos, e.g. vM3\22 vs. vM3\15.


==Examples: EDOs 12-24==
==Examples: edos 12-24==


Sharp-1, flat-2, etc. refer to the [[sharpness]], the number of arrows made by seven 5ths minus four 8ves. All sharp-1 and flat-1 edos can be notated without ups and downs, because the up is exactly equivalent to a sharp or flat.  
Sharp-1, flat-2, etc. refer to the [[sharpness]], the number of arrows made by seven 5ths minus four 8ves. All sharp-1 and flat-1 edos can be notated without ups and downs, because the up is exactly equivalent to a sharp or flat.  
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A ring is a circle of 5ths. In multi-ring (aka ringy) edos like 14, 15 and 24, a single ring doesn't contain all the edo's notes. In contrast, edos like 12, 19 and 22 are single-ring. It's possible to notate any single-ring edo with conventional notation if notes are permitted to be out of order (e.g. 22edo could have C Db B# C# D). But multi-ring edos absolutely require ups and downs.  
A ring is a circle of 5ths. In multi-ring (aka ringy) edos like 14, 15 and 24, a single ring doesn't contain all the edo's notes. In contrast, edos like 12, 19 and 22 are single-ring. It's possible to notate any single-ring edo with conventional notation if notes are permitted to be out of order (e.g. 22edo could have C Db B# C# D). But multi-ring edos absolutely require ups and downs.  


13-edo and 18-edo aren't compatible with heptatonic notation, because the minor 2nd is descending. Thus the minor 3rd is flatter than the major 2nd, the 4th is flatter than the major 3rd, etc. These edos are best notated using the 2nd best fifth, as 13b and 18b.  
13edo and 18edo aren't compatible with heptatonic notation, because the minor 2nd is descending. Thus the minor 3rd is flatter than the major 2nd, the 4th is flatter than the major 3rd, etc. These edos are best notated using the 2nd best fifth, as 13b and 18b.  


There are four flat-N edos on this list. 16-edo and 23-edo are flat-1, 18b is flat-2 and 13b is flat-3. There are two ways to notate such edos: with sharp lowering the pitch, and major/aug narrower than minor/dim, or with sharp raising the pitch, and major/aug wider than minor/dim. Both notations are shown. In the 2nd notation, note that a fifth above B is Fb, not F#.   
There are four flat-N edos on this list. 16edo and 23edo are flat-1, 18b is flat-2 and 13b is flat-3. There are two ways to notate such edos: with sharp lowering the pitch, and major/aug narrower than minor/dim, or with sharp raising the pitch, and major/aug wider than minor/dim. Both notations are shown. In the 2nd notation, note that a fifth above B is Fb, not F#.   


12-edo is sharp-1, thus doesn't need ups and downs. Enharmonic interval: d2.  
12edo is sharp-1, thus doesn't need ups and downs. Enharmonic interval: d2.  
{| class="wikitable" style="text-align:center;"  
{| class="wikitable" style="text-align:center;"  
| rowspan="2" |[[12-edo|'''12-edo''']]
| rowspan="2" |[[12-edo|'''12edo''']]
sharp-1
sharp-1
|'''D'''
|'''D'''
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|}
|}


Because every 14-edo interval is perfect, the quality can be omitted. Sharps and flats can also be omitted. 14-edo contains 2 rings of 7-edo: an up/down-ring and a plain-ring. Enharmonic intervals: A1 and vvm2.
Because every 14edo interval is perfect, the quality can be omitted. Sharps and flats can also be omitted. 14edo contains 2 rings of 7edo: an up/down-ring and a plain-ring. Enharmonic intervals: A1 and vvm2.
{| class="wikitable" style="text-align:center;"  
{| class="wikitable" style="text-align:center;"  
| rowspan="2" |'''[[14-edo]]'''
| rowspan="2" |'''[[14-edo|14edo]]'''
sharp-0
sharp-0
|'''D'''   
|'''D'''   
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|8
|8
|}
|}
15-edo contains 3 rings of 5-edo: an up-ring, a down-ring, and a plain-ring. Enharmonic intervals: v<sup>3</sup>A1 and m2.
15edo contains 3 rings of 5edo: an up-ring, a down-ring, and a plain-ring. Enharmonic intervals: v<sup>3</sup>A1 and m2.
{| class="wikitable" style="text-align:center;"  
{| class="wikitable" style="text-align:center;"  
| rowspan="2" |'''[[15-edo]]'''
| rowspan="2" |'''[[15-edo|15edo]]'''
sharp-3   
sharp-3   
|'''D'''   
|'''D'''   
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|  P8
|  P8
|}
|}
16-edo is flat-1, thus doesn't need ups and downs. There are two ways to notate it. Enharmonic interval: either AA2 or dd2.  
16edo is flat-1, thus doesn't need ups and downs. There are two ways to notate it. Enharmonic interval: either AA2 or dd2.  
{| class="wikitable" style="text-align:center;"  
{| class="wikitable" style="text-align:center;"  
| rowspan="4" |'''[[16-edo]]'''
| rowspan="4" |'''[[16-edo|16edo]]'''
flat-1
flat-1
| rowspan="2" |sharp lowers the pitch,
| rowspan="2" |sharp lowers the pitch,
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| P8
| P8
|}
|}
17-edo is sharp-2 and thus has mid intervals. Enharmonic intervals: vvA1 and vm2.
17edo is sharp-2 and thus has mid intervals. Enharmonic intervals: vvA1 and vm2.
{| class="wikitable" style="text-align:center;"  
{| class="wikitable" style="text-align:center;"  
| rowspan="2" |'''[[17edo|17-edo]]'''
| rowspan="2" |'''[[17edo]]'''
sharp-2   
sharp-2   
|'''D'''  
|'''D'''  
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|  P8  
|  P8  
|}
|}
18b-edo contains 2 rings of 9-edo: an up/down-ring and a plain-ring. There are two ways to notate it. Enharmonic intervals: either ^^A1 and vvM2, or vvA1 and vvm2.
18b-edo contains 2 rings of 9edo: an up/down-ring and a plain-ring. There are two ways to notate it. Enharmonic intervals: either ^^A1 and vvM2, or vvA1 and vvm2.
{| class="wikitable" style="text-align:center;"  
{| class="wikitable" style="text-align:center;"  
| rowspan="4" |'''[[18-edo|18b-edo]]'''
| rowspan="4" |'''[[18-edo|18b-edo]]'''
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|  P8
|  P8
|}
|}
19-edo is sharp-1, thus doesn't need ups and downs. Enharmonic interval: dd2.
19edo is sharp-1, thus doesn't need ups and downs. Enharmonic interval: dd2.
{| class="wikitable" style="text-align:center;"  
{| class="wikitable" style="text-align:center;"  
| rowspan="2" |'''[[19-edo]]'''
| rowspan="2" |'''[[19-edo|19edo]]'''
sharp-1
sharp-1
|'''D'''  
|'''D'''  
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|  P8
|  P8
|}
|}
20-edo contains 4 rings of 5-edo: an up-ring, a down-ring, a dup/dud-ring, and a plain-ring. Enharmonic intervals: v<sup>4</sup>A1 and m2.
20edo contains 4 rings of 5edo: an up-ring, a down-ring, a dup/dud-ring, and a plain-ring. Enharmonic intervals: v<sup>4</sup>A1 and m2.
{| class="wikitable" style="text-align:center;"  
{| class="wikitable" style="text-align:center;"  
| rowspan="2" |'''[[20-edo]]'''
| rowspan="2" |'''[[20-edo|20edo]]'''
sharp-4
sharp-4
|'''D'''  
|'''D'''  
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|  P8
|  P8
|}
|}
Because every 21-edo interval is perfect, the quality can be omitted. 21-edo contains 3 rings of 7-edo: an up-ring, a down-ring and a plain-ring. Enharmonic intervals: A1 and v<sup>3</sup>m2.
Because every 21edo interval is perfect, the quality can be omitted. 21edo contains 3 rings of 7edo: an up-ring, a down-ring and a plain-ring. Enharmonic intervals: A1 and v<sup>3</sup>m2.
{| class="wikitable" style="text-align:center;"  
{| class="wikitable" style="text-align:center;"  
| rowspan="2" |'''[[21-edo]]'''
| rowspan="2" |'''[[21-edo|21edo]]'''
sharp-0
sharp-0
|'''D'''   
|'''D'''   
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|  8
|  8
|}
|}
22-edo is sharp-3. Enharmonic intervals: v<sup>3</sup>A1 and vm2.
22edo is sharp-3. Enharmonic intervals: v<sup>3</sup>A1 and vm2.
{| class="wikitable" style="text-align:center;"  
{| class="wikitable" style="text-align:center;"  
| rowspan="2" |'''[[22-edo]]'''
| rowspan="2" |'''[[22-edo|22edo]]'''
sharp-3
sharp-3
|'''D'''   
|'''D'''   
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| etc.
| etc.
|}
|}
23-edo is flat-1, thus doesn't need ups and downs. There are two ways to notate it. Enharmonic interval: either A<sup>3</sup>2 or d<sup>3</sup>2.
23edo is flat-1, thus doesn't need ups and downs. There are two ways to notate it. Enharmonic interval: either A<sup>3</sup>2 or d<sup>3</sup>2.
{| class="wikitable" style="text-align:center;"  
{| class="wikitable" style="text-align:center;"  
| rowspan="4" |'''[[23-edo]]'''
| rowspan="4" |'''[[23-edo|23edo]]'''
flat-1
flat-1
| rowspan="2" |sharp lowers,
| rowspan="2" |sharp lowers,
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| P8
| P8
|}
|}
24-edo contains 2 rings of 12-edo: an up/down-ring and a plain-ring. Enharmonic intervals: vvA1 and d2.
24edo contains 2 rings of 12edo: an up/down-ring and a plain-ring. Enharmonic intervals: vvA1 and d2.
{| class="wikitable" style="text-align:center;"  
{| class="wikitable" style="text-align:center;"  
| rowspan="2" | '''[[24-edo]]'''
| rowspan="2" | '''[[24-edo|24edo]]'''
sharp-2
sharp-2
|  '''D'''   
|  '''D'''   
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|}
|}


== Extremely Large EDOs ==
== Extremely large edos ==
In theory, every edo can be notated with ups and downs only. For example, in 159-edo, 11/8 above C would be ^<sup>7</sup>F. But large exponents can be avoided if the edo is multi-ring (if the circle of 5ths doesn't include every note). Ups and downs are used within a ring, and lifts and drops (/ and \, see the [[pergen]] article) are used to label each ring. 159-edo has 3 rings of 53-edo. Many people who work with 159-edo are familiar with 53-edo, and can read the lifts and drops as small inflections of the familiar 53-edo notation. 11/8 becomes ^^/F. See the [[159edo notation#Ups-and-Downs-based notation|159edo notation]] page for the complete notation. In this situation, "arrow" refers to 1\53 and "slant" refers to 1\159.
In theory, every edo can be notated with ups and downs only. For example, in 159edo, 11/8 above C would be ^<sup>7</sup>F. But large exponents can be avoided if the edo is multi-ring (if the circle of 5ths doesn't include every note). Ups and downs are used within a ring, and lifts and drops (/ and \, see the [[pergen]] article) are used to label each ring. 159edo has 3 rings of 53edo. Many people who work with 159edo are familiar with 53edo, and can read the lifts and drops as small inflections of the familiar 53edo notation. 11/8 becomes ^^/F. See the [[159edo notation#Ups-and-Downs-based notation|159edo notation]] page for the complete notation. In this situation, "arrow" refers to 1\53 and "slant" refers to 1\159.


Even if the edo isn't multi-ring, lifts and drops can still be used for single EDOsteps and ups and downs can be used for a group of EDOsteps. See [[311edo#Ups and downs notation]].
Even if the edo isn't multi-ring, lifts and drops can still be used for single EDOsteps and ups and downs can be used for a group of EDOsteps. See [[311edo#Ups and downs notation]].


==Chords and Chord Progressions==
==Chords and chord progressions==


Chord names are based on jazz chord names. See Jim Aiken's book ''A Player's Guide to Chords & Harmony''. Alterations are enclosed in parentheses, additions never are. Examples:
Chord names are based on jazz chord names. See Jim Aiken's book ''A Player's Guide to Chords & Harmony''. Alterations are enclosed in parentheses, additions never are. Alterations always come last in the chord name. Examples:


* [[19edo Chord Names]]
* [[19edo Chord Names]]
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* [[Kite Guitar Chord Shapes (downmajor tuning)]]
* [[Kite Guitar Chord Shapes (downmajor tuning)]]


In perfect EDOs (7, 14, 21, 28 and 35), every interval is perfect, and there is no major or minor. In the following list of chord names, omit major, minor, dim and aug. Substitute up for upmajor and upminor, and down for downmajor and downminor. The C-E-G chord is called "C perfect" or simply "C".
In [[Sharpness|sharp-0]] edos aka perfect edos (7, 14, 21, 28 and 35), every interval is perfect, and there is no major or minor. In the following lists of chord names, omit major, minor, dim and aug. Substitute up for upmajor and upminor, and down for downmajor and downminor. The C-E-G chord is called "C perfect" or simply "C".
 
An arrow between the chord root and the chord type (e.g. C^m7) raises or lowers the 3rd, and also the 6th, 7th or 11th, if present. Thus C down-nine is the usual C9 chord with the 3rd and 7th downed: Cv9 = C vE G vBb D. A mid-something chord has a mid 3rd, 6th, 7th, and/or 11th. Mnemonic: every other note of a stacked-3rds chord is affected: '''<u>6th</u>''' - root - '''<u>3rd</u>''' - 5th - '''<u>7th</u>''' - 9th - '''<u>11th</u>''' - 13th. Note that the 6th is affected, but the 13th is not.
 
The rationale for this rule is that a chord often has a note a perfect fourth or fifth above the 3rd. Furthermore, in larger EDOs, upfifths, downfifths, upfourths and downfourths will all be quite dissonant and rarely used in chords. Thus if the 3rd is upped or downed, the 6th or 7th likely would be too. However the 9th likely wouldn't, because that would create an upfifth or a downfifth with the 5th. By the same logic, if the 7th is upped or downed, the 11th would be too.
 
Every conventional chord can accept such a "global" arrow, with one exception: it's pointless for a C5 chord, because there is no 3rd, 6th or 7th to alter. Thus Cv5 is invalid. But C(v5) is valid, and if someone says "C down-5", it means C(v5) = C E vG.


Chord progressions use ups/downs notation to name the roots, e.g. Cv - Gv - vA^m - F or Iv - Vv - vVI^m - IVv. In relative notation, <u>'''never use lower case roman numerals'''</u> for minor chords, because both vIIm and VIIm would be written vii.  
Chord progressions use ups/downs notation to name the roots, e.g. Cv - Gv - vA^m - F or Iv - Vv - vVI^m - IVv. In relative notation, <u>'''never use lower case roman numerals'''</u> for minor chords, because both vIIm and VIIm would be written vii.  


=== Triads ===
<span style="display: block; text-align: left;">The major chord and various alterations of it:</span>
<span style="display: block; text-align: left;">The major chord and various alterations of it:</span>
* C E G = C = "C" or "C major" (in perfect EDOs, "C" or "C perfect")
* C E G = C = "C" or "C major" (in perfect edos, "C" or "C perfect")
* C ^E G = C^ = "C up" or "C upmajor"
* C ^E G = C^ = "C up" or "C upmajor"
* C vE G = Cv = "C down" or "C downmajor" (in EDOs 10, 17, 24, 31, etc., C~ = "C mid")
* C vE G = Cv = "C down" or "C downmajor" (in sharp-2 edos, C~ = "C mid")
* C vvE G = Cvv = "C dud" or "C dudmajor" (in EDOs 20, 27, 34, 41, etc., C~ = "C mid", in EDOs 30, 37, 44, 51, etc. C^~ = "C upmid")
* C vvE G = Cvv = "C dud" or "C dudmajor" (in sharp-4 edos, C~ = "C mid", in sharp-6 edos, C^~ = "C upmid")
This table shows how altering the 3rd or the 5th affects the name of the triad. The conventional abbreviations for aug and dim are + and o. These are rather cryptic, and can be replaced with the more obvious and intuitive a and d. Likewise the symbols Δ and − can be replaced with M and m.
This table shows how altering the 3rd or the 5th affects the name of the triad. The conventional abbreviations for aug and dim are + and <sup>o</sup>. These are rather cryptic, and can be replaced with the more obvious and intuitive a and d. Likewise the symbols Δ and − can be replaced with M and m.
{| class="wikitable" style="text-align:center;"  
{| class="wikitable" style="text-align:center;"  
|+
|+
Line 998: Line 993:
|Cv<sup>o</sup>(v5)
|Cv<sup>o</sup>(v5)
|}
|}
Many EDOs have notes between the major 3rd and the perfect 4th, creating triads impossible in 12-edo, such as:
Note that the dim chord is a triad, not a tetrad. A dim tetrad should always be written C<sup>o</sup>7, never C<sup>o</sup>. In jazz, the 7 is omitted because dim triads are so much rarer than dim tetrads. But ups and downs notation is meant to work for all genres, not just jazz. So the dim triad and the dim tetrad need different names.
 
Many edos have notes between the major 3rd and the perfect 4th, creating triads impossible in 12edo, such as:
* C Fb G = C(d4) or C(b4) = "C dim-four" or "C sus-flat-four"
* C Fb G = C(d4) or C(b4) = "C dim-four" or "C sus-flat-four"
* C E# G = C(A3) or C(#3) = "C aug-three" or "C sus-sharp-three"
* C E# G = C(a3) or C(#3) = "C aug-three" or "C sus-sharp-three"
* C Ebb G = C(d3) or C(bb3) = "C dim-three" or "C sus-double-flat-three"
* C Ebb G = C(d3) or C(bb3) = "C dim-three" or "C sus-double-flat-three"
* C D# G = C(A2) or C(#2) =  "C aug-two" or "C sus-sharp-two"
* C D# G = C(a2) or C(#2) =  "C aug-two" or "C sus-sharp-two"
The "sus" is needed so that C(#2) doesn't sound like C#2, which is C# D# G#.  
The "sus" is needed so that C(#2) doesn't sound like C#2, which is C# D# G#.  


<u>'''Sixth and seventh chords:'''</u>
=== Global arrows ===
A global arrow occurs between the chord root and the conventional chord type (e.g. C^m7). It raises or lowers the 3rd, and also the 6th, 7th or 11th, if present. Thus C down-nine is the usual C9 chord with the 3rd and 7th downed: Cv9 = C vE G vBb D. A global-mid chord has a mid 3rd, 6th, 7th, and/or 11th. Mnemonic: every other note of a stacked-3rds chord is affected: '''<u>6th</u>''' - root - '''<u>3rd</u>''' - 5th - '''<u>7th</u>''' - 9th - '''<u>11th</u>''' - 13th. Note that the 6th is affected, but the 13th is not.
 
The rationale for this rule is that a chord often has a note a perfect fourth or fifth above the 3rd. Furthermore, in larger edos, upfifths, downfifths, upfourths and downfourths will all be quite dissonant and rarely used in chords. Thus if the 3rd is upped or downed, the 6th or 7th likely would be too. However the 9th likely wouldn't, because that would create an upfifth or a downfifth with the 5th. By the same logic, if the 7th is upped or downed, the 11th would be too.
 
A 2nd or 4th in a sus chord is also affected: C4 = C F G but Cv4 = C vF G = "C down-four" or "C sus-down-four". But Cv7(4) = C F G vBb
 
Every conventional chord can accept a global arrow, with one exception: it's pointless for a C5 chord, because there is no 3rd, 6th or 7th to alter. Thus Cv5 is invalid. But C(v5) is valid, and if someone says "C down five", it means C(v5) = C E vG.


If the 7th is not a perfect 5th or a dim 5th above the 3rd, the chord is named as a triad with an added 7th.
=== Sixth and seventh chords ===
* C E G Bb = C7 = "C seven"
If the 7th is not a perfect 5th or a dim 5th above the 3rd, the chord is named as a triad with an added 7th. An added 7th is usually preceded by a comma (the actual punctuation mark, not an interval), which is spoken as "add":
* C E G Bb = C7 = "C seven" (conventional chord)
* C vE G Bb = Cv,7 = "C down add-seven"
* C vE G Bb = Cv,7 = "C down add-seven"
* C E G vBb = C,v7 = "C add down-seven"
* C E G vBb = C,v7 = "C add down-seven"
* C vE G vBb = Cv7 = "C down seven"
* C vE G vBb = Cv7 = "C down seven" (global down)
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" and the illogical "half-dim" can both be replaced with "dim add-7", written Cd,7.   
All 7th chords follow this same pattern. Likewise, if the 6th is not a perfect 4th or aug 4th above the 3rd, it's an add-6 chord. Permitting add-7 chords has the added benefit that the wordy "minor-7 flat-5" and the illogical "half-dim" can both be replaced with "dim add-7", written Cd,7.   


In the table below, if a chord is '''bolded''', the comma (the actual punctuation mark, not the interval) must be spoken as "add".   
In the table below, if a chord is '''bolded''', the comma punctuation is <u>not</u> spoken as "add".   
{| class="wikitable" style="text-align:center;"  
{| class="wikitable" style="text-align:center;"  
|+
|+
Line 1,039: Line 1,044:
|C7
|C7
|Cm7
|Cm7
|'''Cd,7'''
|Cd,7
|Cm7(b5)
|Cm7(b5)
|C<sup>ø</sup>
|C<sup>ø</sup>
Line 1,048: Line 1,053:
|-
|-
!3rd
!3rd
|'''Cv,M7'''
|Cv,M7
|'''Cv,7'''
|Cv,7
|'''Cvm,7'''
|Cvm,7
|'''Cvd,7'''
|Cvd,7
|'''Cvm,7(b5)'''
|Cvm,7(b5)
|C<sup>ø</sup>(v3)
|C<sup>ø</sup>(v3)
|Cvd,d7
|'''Cvd,d7'''
|Cv<sup>o</sup>,d7
|'''Cv<sup>o</sup>,d7'''
|'''Cv,6'''
|Cv,6
|'''Cvm,6'''
|Cvm,6
|-
|-
!5th
!5th
Line 1,063: Line 1,068:
|C7(v5)
|C7(v5)
|Cm7(v5)
|Cm7(v5)
|Cd(v5)7
|Cd,7(v5)
|Cm7(vb5)
|Cm7(vb5)
|C<sup>ø</sup>(v5)
|C<sup>ø</sup>(v5)
Line 1,072: Line 1,077:
|-
|-
!6th/7th
!6th/7th
|'''C,vM7'''
|C,vM7
|'''C,v7'''
|C,v7
|Cmv7
|Cmv7
|Cdv7
|Cdv7
Line 1,080: Line 1,085:
|Cdvd7
|Cdvd7
|C<sup>o</sup>vd7
|C<sup>o</sup>vd7
|'''C,v6'''
|C,v6
|Cmv6
|Cmv6
|-
|-
!3rd, 5th
!3rd, 5th
|'''Cv,M7(v5)'''
|Cv,M7(v5)
|'''Cv,7(v5)'''
|Cv,7(v5)
|'''Cvm,7(v5)'''
|Cvm,7(v5)
|Cvd(v5)7
|Cvd,7(v5)
|'''Cvm,7(vb5)'''
|Cvm,7(vb5)
|C<sup>ø</sup>(v3v5)
|C<sup>ø</sup>(v3v5)
|Cvd(v5)d7
|'''Cvd,d7(v5)'''
|Cv<sup>o</sup>(v5)d7
|'''Cv<sup>o</sup>,d7(v5)'''
|Cv(v5)6
|Cv,6(v5)
|Cvm(v5)6
|Cvm,6(v5)
|-
|-
!3rd, 6th/7th
!3rd, 6th/7th
Line 1,109: Line 1,114:
!5th, 6th/7th
!5th, 6th/7th
|C,vM7(v5)
|C,vM7(v5)
|'''C,v7(v5)'''
|C,v7(v5)
|Cmv7(v5)
|Cmv7(v5)
|Cd(v5)v7
|Cdv7(v5)
|Cmv7(vb5)
|Cmv7(vb5)
|C<sup>ø</sup>(v5v7)
|C<sup>ø</sup>(v5v7)
|Cd(v5)vd7
|Cdvd7(v5)
|C<sup>o</sup>(v5)vd7
|C<sup>o</sup>vd7(v5)
|C(v5)v6
|C,v6(v5)
|Cm(v5)v6
|Cm,v6(v5)
|-
|-
!3rd, 5th, 6th/7th
!3rd, 5th, 6th/7th
Line 1,123: Line 1,128:
|Cv7(v5)
|Cv7(v5)
|Cvm7(v5)
|Cvm7(v5)
|Cvd(v5)v7
|Cvdv7(v5)
|Cvm7(vb5)
|Cvm7(vb5)
|Cv<sup>ø</sup>(v5)
|Cv<sup>ø</sup>(v5)
Line 1,132: Line 1,137:
|}
|}
Various unusual tetrads:
Various unusual tetrads:
* C vE G ^Bb = Cv,^7 = "C down up-seven" (in EDOs 17, 24, 31, etc. C~7 = "C mid-seven")
* C vE G ^Bb = Cv^7 = "C down up-seven" (in sharp-2 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 E G Ab = C,b6 or C,m6 = "C add flat-six" or "C add minor-six"
* 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,bb7 or C,d7 = "C add double-flat-seven" or "C add dim-seven" (19edo's 4:5:6:7 chord)
* C E G B# = C,#7 or C,A7 = "C add sharp-seven" or "C add aug-seven"
* C E G B# = C,#7 or C,A7 = "C add sharp-seven" or "C add aug-seven"
* C E G Cb = C,b8 or C,d8 = "C add flat-eight" or "C add dim-eight"
* C E G Cb = C,b8 or C,d8 = "C add flat-eight" or "C add dim-eight"
<u>'''Ninth chords:'''</u>


In '''bolded''' chords, the comma punctuation is spoken as "add". Double alterations need only a single pair of parentheses, e.g. C vE vG B D is named CM9(v3v5). Double additions mostly need only a single comma, e.g. C E G vBb vD is named C,v7v9. But certain 6/9 chords require two commas. In these chords, marked with an asterisk '''*''', only the first comma is spoken as "add".
=== Ninth chords ===
As in conventional chord naming, a sharp-9 or flat-9 chord is always named as a 7th chord with an added 9th. Thus B D# F# A C is named B7b9 (not Bb9 which would be Bb D F A C). Likewise C#7b9 not C#b9, even thought the latter is clearly the same flat-9 chord as the former. Likewise Cm7b9 not Cmb9, etc.
 
Double alterations need only a single pair of parentheses, e.g. C E vG vB D is named CM9(v5v7). Double additions mostly need only a single comma, e.g. C E G vBb vD is named C,v7v9. But certain 6/9 chords require two commas. In '''bolded''' 6/9 chords, the comma between the 6 and the 9 is <u>not</u> spoken as "add". However any comma before "6" is, e.g. Cv,6,9 is "C down add six nine".
{| class="wikitable" style="text-align:center;"  
{| class="wikitable" style="text-align:center;"  
|+
|+
Line 1,162: Line 1,169:
|-
|-
!nothing
!nothing
|'''C,9'''
|C,9
|CM9
|CM9
|C9
|C9
|Cm9
|Cm9
|C7b9
|C7b9
|C6,9
|'''C6,9'''
|Cm6,9
|'''Cm6,9'''
|-
|-
!3rd
!3rd
|'''Cv,9'''
|Cv,9
|CM9(v3)
|CM9(v3)
|C9(v3)
|C9(v3)
|Cm9(v3)
|Cm9(v3)
|'''Cv,7b9'''
|Cv,7b9
|'''Cv,6,9 *'''
|'''Cv,6,9'''
|'''Cvm,6,9 *'''
|'''Cvm,6,9'''
|-
|-
!5th
!5th
|'''C,9(v5)'''
|C,9(v5)
|CM9(v5)
|CM9(v5)
|C9(v5)
|C9(v5)
|Cm9(v5)
|Cm9(v5)
|C7(v5)b9
|C7b9(v5)
|C6(v5)9
|'''C6,9(v5)'''
|Cm6,9(v5)
|'''Cm6,9(v5)'''
|-
|-
!6th/7th
!6th/7th
| ------
| ------
|CM9(v7)
|CM9(v7)
|C9(v7)
|C9(v7)
|Cm9(v7)
|Cm9(v7)
|'''C,v7b9'''
|C,v7b9
|'''C,v6,9 *'''
|'''C,v6,9'''
|Cmv6,9
|'''Cmv6,9'''
|-
|-
!9th
!9th
|'''C,v9'''
|C,v9
|CM7v9
|CM7v9
|C7v9
|C7v9
Line 1,207: Line 1,214:
|-
|-
!3rd, 5th
!3rd, 5th
|'''Cv,9(v5)'''
|Cv,9(v5)
|CM9(v3v5)
|CM9(v3v5)
|C9(v3v5)
|C9(v3v5)
|Cm9(v3v5)
|Cm9(v3v5)
|'''Cv,7b9(v5)'''
|Cv,7b9(v5)
|Cv(v5)6,9
|'''Cv,6,9(v5)'''
|Cvm(v5)6,9
|'''Cvm,6,9(v5)'''
|-
|-
!3rd, 6th/7th
!3rd, 6th/7th
| ------
| ------
|CvM9
|CvM9
|Cv9
|Cv9
|Cvm9
|Cvm9
|Cv7b9
|Cv7b9
|Cv6,9
|'''Cv6,9'''
|Cvm6,9
|'''Cvm6,9'''
|-
|-
!3rd, 9th
!3rd, 9th
|Cv,v9
|Cv,v9
|'''Cv,M7v9''' or
|Cv,M7v9 or
CM7(v3)v9
CM7v9(v3)
|'''Cv,7v9''' or
|Cv,7v9 or
C7(v3)v9
C7v9(v3)
|'''Cvm,7v9''' or
|Cvm,7v9 or
Cm7(v3)v9
Cm7v9(v3)
|'''Cv,7vb9''' or
|Cv,7vb9 or
C7(v3)vb9
C7vb9(v3)
|'''Cv,6v9''' or
|Cv,6v9 or
C6(v3)v9
C6v9(v3)
|'''Cvm,6v9''' or
|Cvm,6v9 or


Cm6(v3)v9
Cm6v9(v3)
|-
|-
!5th, 6th/7th
!5th, 6th/7th
| ------
| ------
|CM9(v5v7)
|CM9(v5v7)
|C9(v5v7)
|C9(v5v7)
|Cm9(v5v7)
|Cm9(v5v7)
|C(v5)v7b9
|C,v7b9(v5)
|C(v5)v6,9
|'''C,v6,9(v5)'''
|Cm(v5)v6,9
|'''Cm,v6,9(v5)'''
|-
|-
!5th, 9th
!5th, 9th
|C(v5)v9
|C,v9(v5)
|CM7(v5)v9
|CM7v9(v5)
|C7(v5)v9
|C7v9(v5)
|Cm7(v5)v9
|Cm7v9(v5)
|C7(v5)vb9
|C7vb9(v5)
|C6(v5)v9
|C6v9(v5)
|Cm6(v5)v9
|Cm6v9(v5)
|-
|-
!6th/7th, 9th
!6th/7th, 9th
| ------
| ------
|'''C,vM7v9'''
|C,vM7v9
|'''C,v7v9'''
|C,v7v9
|Cmv7v9
|Cmv7v9
|'''C,v7vb9'''
|C,v7vb9
|'''C,v6v9'''
|C,v6v9
|Cmv6v9
|Cmv6v9
|-
|-
!3rd, 5th, 6th/7th
!3rd, 5th, 6th/7th
| ------
| ------
|CvM9(v5)
|CvM9(v5)
|Cv9(v5)
|Cv9(v5)
|Cvm9(v5)
|Cvm9(v5)
|Cv7(v5)b9
|Cv7b9(v5)
|Cv6(v5)9
|'''Cv6,9(v5)'''
|Cvm6(v5)9
|'''Cvm6,9(v5)'''
|-
|-
!3rd, 5th, 9th
!3rd, 5th, 9th
|Cv(v5)v9
|Cv,v9(v5)
|Cv(v5)M7v9 or
|Cv,M7v9(v5) or
CM7(v3v5)v9
CM7v9(v3v5)
|Cv(v5)7v9 or
|Cv,7v9(v5) or
C7(v3v5)v9
C7v9(v3v5)
|Cvm(v5)7v9 or
|Cvm,7v9(v5) or
Cm7(v3v5)v9
Cm7v9(v3v5)
|Cv(v5)7vb9 or
|Cv,7vb9(v5) or
C7(v3v5)b9
C7vb9(v3v5)
|Cv(v5)6v9 or
|Cv,6v9(v5) or
C6(v3v5)v9
C6v9(v3v5)
|Cvm(v5)6v9 or
|Cvm,6v9(v5) or
Cm6(v3v5)v9
Cm6v9(v3v5)
|-
|-
!3rd, 6th/7th, 9th
!3rd, 6th/7th, 9th
| ------
| ------
|CvM7v9
|CvM7v9
|Cv7v9
|Cv7v9
Line 1,301: Line 1,308:
|-
|-
!5th, 6th/7th, 9th
!5th, 6th/7th, 9th
| ------
| ------
|C(v5)vM7v9
|C,vM7v9(v5)
|C(v5)v7v9
|C,v7v9(v5)
|Cm(v5)v7v9
|Cmv7v9(v5)
|C(v5)v7vb9
|C,v7vb9(v5)
|C(v5)v6v9
|C,v6v9(v5)
|Cm(v5)v6v9
|Cmv6v9(v5)
|-
|-
!3rd, 5th, 6th/7th, 9th
!3rd, 5th, 6th/7th, 9th
| ------
| ------
|CvM7(v5)v9
|CvM7v9(v5)
|Cv7(v5)v9
|Cv7v9(v5)
|Cvm7(v5)v9
|Cvm7v9(v5)
|Cv7(v5)vb9
|Cv7vb9(v5)
|Cv6(v5)v9
|Cv6v9(v5)
|Cvm6(v5)v9
|Cvm6v9(v5)
|}
 
=== Rules for punctuation usage ===
Tetrads, pentads, etc. often require a comma (the actual punctuation mark) to ensure correct parsing of the chord name. Only use a comma when needed, to reduce clutter and standardize chord names. A comma is needed in Cv,7 = C vE G Bb because omitting it makes Cv7 = C vE G vBb, a different chord. But C7,v9 is incorrect because C7v9 is the same chord.
 
The rule is, omit the comma unless doing so changes the chord. This simple rule suffices in most situations. What follows is a detailed analysis, designed to aid in writing computer code that automates chord naming.
 
A comma separates an added note and prevents it from merging with what comes before it. The comma is unneeded in C7v9 because the 7 can't merge with the down to make a 7v. But Cm,7 is incorrect even though the m and the 7 can merge, because Cm7 is the same chord.
 
The various components of a chord name are either numbers (for the 6th, 7th, 9th, etc.) or adjectives (up, down, mid, sharp, flat, major, minor, aug and dim). These adjectives usually modify the following number, but they sometimes modify the preceding root, e.g. Caug or C#7. Up, down and mid can't modify the preceding root.
 
A comma is always needed to separate a number from a number (Cv6,9). It's usually needed to separate an adjective from a number (Cv,7). The only exception is for certain conventional chords like Cm7 where separation is unneeded. A comma is always needed to separate the root of a plain major chord from an adjective (D,v7) or a number (Eb,9). It's never needed to separate a number from an adjective (C7^9). It's needed to separate an adjective from an adjective only if the two adjectives could apply to a single noun. There are six types of such adjective pairs.
 
* up followed by any adjective except down (C^,^9 or C^,~7 or C^,#9 or C^,b9 or C^,M7 or C^,m6 or C^,a7 or C^,d7)
* down followed by any adjective except up
* sharp followed by sharp (C#,#9)
* flat followed by flat (Bb,b9)
* aug followed by aug (Ca,a7)
* dim followed by dim (Cd,d9)
 
No other adjective pair can apply to a single noun, thus the comma is omitted:
 
* Cv^9 = C vE G ^D (an interval can't be both upped and downed)
* CmM7 = C Eb G B (an interval can't be both minor and major)
* Cma7 = C Eb Gb B# (an interval can't be both minor and aug)
* Cm#11 = C Eb G F# (an interval can't be both minor and sharp)
* Cvmm6 = C vEb G Ab (an interval can't be doubly minor)
* Cmv7 = C Eb G vBb (an interval can be downminor, but it can't be minordown)
* C~v7 = C vvE G vBb in a sharp-4 edo (an interval can be downmid, but it can't be middown)
* C~~9 = C vvE G vvD in a sharp-4 edo (an interval can't be doubly mid)
 
In the spoken name, a comma is almost always pronounced as "add". The only exceptions are:
 
* a comma separating two numbers: C6,9 is spoken as "C six nine"
* a comma separating two ups or two downs: Cv,v9 is spoken as "C-down down-nine", since Cvv9 would be "C dud-nine"
* a comma separating two sharps or two flats: C#,#9 is "C sharp sharp-nine" since C##9 would be "C double-sharp nine"
* a comma separating two augs or two dims: Cvd,d7 is "C down-dim dim-seven", since Cvdd7 would be "C down-double-dim-seven"
 
Of course, there's no great harm in saying "add" when it isn't strictly needed.
{| class="wikitable"
|+when to write a comma or say "add"
! colspan="2" rowspan="2" |
! colspan="2" |component after the comma
|-
!adjective
!number
|-
! rowspan="3" |component
before the
 
comma
!root
|comma always
"add" always
|comma always
"add" always
|-
!adjective
|comma sometimes
"add" sometimes if comma,
 
never if no comma
|comma usually
"add" always if comma,
 
never if no comma
|-
!number
|comma never
"add" never
|comma always
"add" never
|}
|}
==Cross-EDO considerations==
More examples, in which the comma is almost always spoken as "add":
 
* B9 = B D# F# AvC#
* B,9 = B D# F# C#
* Bb9 = Bb D F Ab C
* Bb,9 = Bb D F C
* B,b9 = B D# F# C
* Bbb9 = Bbb Db Fb Abb Cb
* Bbb,9 = Bbb Db Fb Cb
* Bb,b9 = Bb D F Cb (no "add", "B flat flat-nine")
* B,bb9 = B D# F# Cbb
 
==Cross-edo considerations==


In 22-edo, the major chord is 0-8-13 = 0¢-436¢-709¢. In 19-edo, 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. 22-edo major chords sound ru (7-under) and 19-edo major chords sound yo (5-over).
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 ru (7-under) and 19edo major chords sound yo (5-over).


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 22-edo, the chord that you need sounds like a ru chord.
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 ru 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 yo. Because 22-edo's yo chord 0-7-13 = 0¢-382¢-709¢ is <u>down</u>major, 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 yo. Because 22edo's yo chord 0-7-13 = 0¢-382¢-709¢ is <u>down</u>major, it doesn't work in that progression.


Another example: I7 - bVII7 - IV7 - I7. To play this progression without shifts or drifts, the 7th in the I7 chord must be a minor 7th. in 22-edo, that 7th sounds zo (7-over, thus 7/4). In 19-edo, it sounds gu (5-under, thus 9/5).
Another example: I7 - bVII7 - IV7 - I7. To play this progression without shifts or drifts, the 7th in the I7 chord must be a minor 7th. in 22edo, that 7th sounds zo (7-over, thus 7/4). In 19edo, it sounds gu (5-under, thus 9/5).


==Ups and downs solfege==
==Ups and downs solfege==
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