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== Definition ==
== Definition ==
Ups and Downs (or ^v) is a notation system developed by [[KiteGiedraitis|Kite]] that works with almost all [[EDO|EDOs]]. When extended with lifts and drops (/ and \), it works with all rank-2 temperaments (see the [[pergen|pergens]] page). The up symbol "^" and the down symbol "v" indicate raising or 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. half-augmented, and the mid 5th ~5 is half-diminished.  
Ups and Downs (or ^v) is a notation system developed by [[KiteGiedraitis|Kite]] that can notate almost every [[EDO|EDO]]. The up symbol "^" and the down symbol "v" indicate raising or 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. half-augmented, and the mid 5th (~5 )is a half-diminished 5th.  


The notation is fully described 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 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.  


==Explanation -- a 22-edo example==
==Explanation -- a 22-edo example==
Line 26: Line 28:
<u>'''Interval arithmetic'''</u>
<u>'''Interval arithmetic'''</u>


Interval arithmetic is <u>always</u> preserved. Ups and downs are just added in:
A core principle of ups and downs notation is that '''interval arithmetic is <u>always</u> preserved'''. Ups and downs are just added in:
 
{| class="wikitable"
C to E = M3, ^C to E = vM3, C to ^E = ^M3
|+
 
!
C + M3 = E, ^C + M3 = ^E, C + ^M3 = ^E
!conventional
 
! colspan="2" |with ups and downs
M2 + m2 = m3, M2 + ^m2 = ^m3, vM2 + m2 = vm3
|-
|interval between two notes
|C to E = M3
|^C to E = vM3
|C to ^E = ^M3
|-
|note plus an interval
|C + M3 = E
|^C + M3 = ^E
|C + ^M3 = ^E
|-
|sum of two intervals
|M2 + m2 = m3
|M2 + ^m2 = ^m3
|vM2 + m2 = vm3
|}


==EDOs 12-24, 31 and 41==
==EDOs 12-24, 31 and 41==
Line 172: Line 189:
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, never use lower case roman numerals for minor chords. Write either vIIm or VIIm, never 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, never use lower case roman numerals for minor chords. Write either vIIm or VIIm, never vii.  


<span style="display: block; text-align: left;">The major chord and its alterations:</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")
Line 237: Line 254:
|Cvaug(v5)
|Cvaug(v5)
|}
|}
Many EDOs have notes between the major 3rd and the perfect 4th, creating such triads as:
Many EDOs have notes between the major 3rd and the perfect 4th, creating triads impossible in 12-edo, such as:
 
C Fb G = C(d4) or C(b4) = "C dim-four" or "C flat-four"


C D# G = C(A2) or C(#2) = "C aug-two" or "C sharp-two"
C E# G = C(A3) or C(#3) = "C aug-three" or "C sharp-three"


C Ebb G = C(d3) or C(bb3) = "C dim-three" or "C double-flat-three"
C Ebb G = C(d3) or C(bb3) = "C dim-three" or "C double-flat-three"


C E# G = C(A3) or C(#3) = "C aug-three" or "C sharp-three"
C D# G = C(A2) or C(#2) = "C aug-two" or "C sharp-two"


C Fb G = C(d4) or C(b4) = "C dim-four" or "C flat-four"
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 = 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 D# Gb = C(A2,d5) or C(#2,b5) = "C aug-two dim-five" or "C sharp-two, flat-five"
Line 253: Line 270:
C Ebb Gb = Cdim(d3) or Cdim(bb3) = "C dim dim-three" or "C dim double-flat-three"
C Ebb Gb = Cdim(d3) or Cdim(bb3) = "C dim dim-three" or "C dim double-flat-three"


C Eb G# is Cmin(#5) = "C minor sharp-five"
C Eb G# = Cmin(#5) = "C minor sharp-five"


C E# G# is Caug(#3) = "C aug sharp-three"
C E# G# = Caug(#3) = "C aug sharp-three"


C Fb G# is C(b4,#5) = "C flat-four sharp-five"
C Fb G# = C(b4,#5) = "C flat-four sharp-five"


<u>'''Sixth and seventh chords:'''</u>
<u>'''Sixth and seventh chords:'''</u>


If the 3rd and 7th are not a perfect 5th or a dim 5th apart, the chord is named as a triad with an added 7th.
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.


C E G Bb = C7 = "C seven"
C E G Bb = C7 = "C seven"
Line 271: Line 288:
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 ^Bbb. But the slash-circle abbreviation for half-dim is untypable, so half-dim is problematic.
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 ^Bbb. But half-dim is problematic because the slash-circle abbreviation for half-dim is untypable.


In the table below, if a chord is '''bolded''', the comma must be spoken as "add". A dim 7th could be written either d7 or o7.
In the table below, if a chord is '''bolded''', the comma must be spoken as "add".  
 
''Question: should a dim 7th be written as d7 or o7?''
 
''Question: for all tetrads and pentads, should a comma that needn't be spoken as add be omitted from the written name?''
{| class="wikitable"
{| class="wikitable"
|+
|+
Line 376: Line 397:
|Cvm6(v5)
|Cvm6(v5)
|}
|}
C vE G ^Bb = Cv,^7 = "C down up-seven" (in certain EDOs, C~7 = "C mid-seven")
Some non-12-edo sixth and seventh chords:


C Eb ^Gb Bb = Cm7(^b5) = "C minor seven upflat-five" or "C half-dim up-five" '''or "C dim up-five, 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"
C E G A# = C,#6 or C,A6 = "C add sharp-six" or "C add aug-six"


C E G B# is C,#7 or C,A7 = "C sharp-seven" or "C add aug-seven" (not "C aug-seven" = Caug7)
C vE G ^Bb = Cv,^7 = "C down up-seven" (in certain EDOs, C~7 = "C mid-seven")


C E G Cb = C,b8 or C,d8 = "C flat-eight" or "C dim-eight"
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)


<u>'''Sixth chords:'''</u>
C E G B# is C,#7 or C,A7 = "C add sharp-seven" or "C add aug-seven"


C E G Ab = C,b6 or C,m6 = "C add flat-six" or "C add minor-six"  
C E G Cb = C,b8 or C,d8 = "C add flat-eight" or "C add dim-eight"


C E G A# = C,#6 or C,A6 = "C add sharp-six" or "C add aug-six"
<u>'''Ninth chords:'''</u>


<u>'''Ninth chords:'''</u>
In '''bolded''' chords, the comma is spoken as "add". Double additions need only a single comma, e.g. C E G vBb vD is named C,v7v9. Double alterations need only a single pair of parentheses, e.g. C vE vG B D is named CM9(v3v5).


In '''bolded''' chords, the comma is spoken as "add". Double additions need only a single comma, e.g. C E G vBb vD is C,v7v9
''Question: Should double alterations like (v3v5) be spoken "down three and five"? Should they be written (v3,5) or (v3&5)?''


Double alterations like (v3v5) could be written (v3,5) or (v3&5) and spoken "down three and five".
''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?''
{| class="wikitable"
{| class="wikitable"
|+
|+
Line 404: Line 425:
!dom9
!dom9
!min9
!min9
!dom7,b9
!dom7b9
!
!maj6/9
!maj6/9
!min6/9
!min6/9
!
!half-dim
!dim7
!min-maj
|-
|-
!what's downed
!what's downed
Line 419: Line 435:
!C Eb G Bb D
!C Eb G Bb D
!C E G Bb Db
!C E G Bb Db
!
!C E G A D
!
!C Eb G A D
!
!
!
!
!
|-
|-
|nothing
|nothing
Line 433: Line 444:
|Cm9
|Cm9
|C7,b9
|C7,b9
|
|'''C6,9?'''
|C6/9
|'''Cm6,9?'''
|Cm6/9
|
|'''Co,7'''
|Co7
|Cm,M7
|-
|-
|3rd
|3rd
Line 446: Line 452:
|C9(v3)
|C9(v3)
|Cm9(v3)
|Cm9(v3)
|
|'''Cv,7b9''' or
|
C7(v3)b9 or
|'''Cv,6'''
 
|'''Cvm,6'''
C7,b9(v3)
|
|'''Cv,6,9?'''
|'''Cvo,7'''
|'''Cvm,6,9?'''
|Cvo,d7
|Cvm,M7
|-
|-
|6th/7th
|6th/7th
Line 460: Line 464:
|C9(v7)
|C9(v7)
|Cm9(v7)
|Cm9(v7)
|
|'''C,v7b9'''
|
|'''C,v6,9?'''
|'''C,v6'''
|Cm,v6
|Cm,v6
|
|-
|Co,v7
|3rd, 6th/7th
|Co,vd7
| ---
|Cm,vM7
|CvM9
|Cv9
|Cvm9
|Cv7,b9
|'''Cv6,9?'''
|Cvm6,9
|-
|-
|9th
|9th
Line 474: Line 482:
|C7,v9
|C7,v9
|Cm7,v9
|Cm7,v9
|
|C7,vb9
|
|C6,v9
|
|Cm6,v9
|
|
|
|
|
|-
|3rd, 6th/7th
| ---
|CvM9
|Cv9
|Cvm9
|
|
|Cv6
|Cvm6
|
|Cvo,v7
|Cvo7
|Cvm,vM7
|-
|-
|3rd, 9th
|3rd, 9th
|Cv,v9
|Cv,v9
|
|'''Cv,M7v9''' or
CM7(v3)v9
|'''Cv,7v9''' or
|'''Cv,7v9''' or
C7(v3)v9
C7(v3)v9
|
|'''Cvm,7v9''' or
|
Cm7(v3)v9
|
|'''Cv,7vb9''' or
|
C7(v3)vb9
|
|'''Cv,6v9''' or
|
C6(v3)v9
|
|'''Cvm,6v9''' or
|
 
|
Cm6(v3)v9
|-
|-
|6th/7th, 9th
|6th/7th, 9th
Line 517: Line 507:
|'''C,v7v9'''
|'''C,v7v9'''
|Cm,v7v9
|Cm,v7v9
|
|'''C,v7vb9'''
|
|'''C,v6v9'''
|
|Cm,v6v9
|
|
|
|
|
|-
|-
|3rd, 6th/7th, 9th
|3rd, 6th/7th, 9th
Line 531: Line 516:
|Cv7,v9
|Cv7,v9
|Cvm7,v9
|Cvm7,v9
|
|Cv7,vb9
|
|Cv6,v9
|
|Cvm6,v9
|
|
|
|
|
|-
|-
|5th
|5th
Line 545: Line 525:
|C9(v5)
|C9(v5)
|Cm9(v5)
|Cm9(v5)
|
|C7(v5)b9
|
|C6(v5)9
|C6(v5)
|Cm6(v5)9
|Cm6(v5)
|
|Co(v5)7
|Co7(v5)
|Cm(v5)M7
|-
|-
|3rd, 5th
|3rd, 5th
Line 559: Line 534:
|C9(v3v5)
|C9(v3v5)
|Cm9(v3v5)
|Cm9(v3v5)
|
|Cv(v5)7b9 or
|
C7(v3v5)b9
|Cv(v5)6
|Cv(v5)6,9
|Cvm(v5)6
|Cvm(v5)6,9
|
|Cvo(v5)7
|Cvo(v5)d7
|Cvm(v5)M7
|-
|-
|5th, 6th/7th
|5th, 6th/7th
Line 573: Line 544:
|C9(v5v7)
|C9(v5v7)
|Cm9(v5v7)
|Cm9(v5v7)
|
|C(v5)v7b9
|
|C(v5)v6,9
|C(v5)v6
|Cm(v5)v6,9
|Cm(v5)v6
|-
|
|3rd, 5th, 6th/7th
|Co(v5)v7
| ---
|Co(v5)vd7
|CvM9(v5)
|Cm(v5)vM7
|Cv9(v5)
|Cvm9(v5)
|Cv7(v5)b9
|Cv6(v5)9
|Cvm6(v5)9
|-
|-
|5th, 9th
|5th, 9th
Line 587: Line 562:
|C7(v5)v9
|C7(v5)v9
|Cm7(v5)v9
|Cm7(v5)v9
|
|C7(v5)vb9
|
|C6(v5)v9
|Cv6(v5)
|Cm6(v5)v9
|Cvm6(v5)
|
|Cvo(v5)v7
|Cvo7(v5)
|Cvm(v5)vM7
|-
|3rd, 5th, 6th/7th
| ---
|
|Cv9(v5)
|
|
|
|
|
|
|
|
|
|-
|-
|3rd, 5th, 9th
|3rd, 5th, 9th
|Cv(v5)v9
|Cv(v5)v9
|
|Cv(v5)M7v9 or
|
CM7(v3v5)v9
|
|Cv(v5)7v9 or
|
C7(v3v5)v9
|
|Cvm(v5)7v9 or
|
Cm7(v3v5)v9
|
|Cv(v5)7vb9 or
|
C7(v3v5)b9
|
|Cv(v5)6v9 or
|
C6(v3v5)v9
|
|Cvm(v5)6v9 or
Cm6(v3v5)v9
|-
|-
|5th, 6th/7th, 9th
|5th, 6th/7th, 9th
| ---
| ---
|
|C(v5)vM7v9
|C(v5)v7v9
|C(v5)v7v9
|
|Cm(v5)v7v9
|
|C(v5)v7vb9
|
|C(v5)v6v9
|
|Cm(v5)v6v9
|
|
|
|
|
|-
|-
|3rd, 5th, 6th/7th, 9th
|3rd, 5th, 6th/7th, 9th
| ---
| ---
|
|CvM7(v5)v9
|Cv7(v5)v9
|Cv7(v5)v9
|
|Cvm7(v5)v9
|
|Cv7(v5)vb9
|
|Cv6(v5)v9
|
|Cvm6(v5)v9
|
|
|
|
|
|}
|}
C Db E G Bb = C7,b9 = "C seven flat-nine" (in perfect EDOs, C9 = "C nine")
C Db vE G Bb = C7,b9(v3) = "C seven flat-nine down-three"
C Db E G vBb = C,v7,b9 = "C add down-seven flat-nine"
C vDb E G Bb = C7,vb9 = "C seven downflat-nine"
C Db vE G vBb = Cv7,b9 = "C down-seven flat-nine"
C vDb vE G Bb = C7(v3)vb9 = "C seven down-three downflat-nine"
C vDb E G vBb = C,v7,vb9 = "C add down-seven downflat-nine"
C vDb vE G vBb = Cv7,vb9 = "C down-seven downflat-nine"
== Staff Notation ==
== Staff Notation ==
For staff notation, just put an up or down to the left of the note and any conventional accidental it might have. Like conventional accidentals, 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.
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-1.png|alt=Tibia in G CORRECTED-1.png|800x1034px|Tibia in G CORRECTED-1.png]]
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