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Kite's ups and downs notation: Difference between revisions

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Using quip and quid (> and <) in larger edos
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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").  
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 vanishing 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."  


Since 22edo is rank-1, and conventional notation plus ups and downs is rank-3, two enharmonic intervals are needed to define the notation: v<sup>3</sup>A1 and vm2. Either interval can be added to or subtracted from any note to respell the note. For example, ^C + vm2 = Db and ^^Eb + v<sup>3</sup>A1 = vE. Any combination of these two enharmonic intervals is also an enharmonic interval, for example their sum v<sup>4</sup>M2. Thus ^^F = vvG (double-down G, or '''dud''' G for short, rhymes with "cud").  
Since 22edo is rank-1, and conventional notation plus ups and downs is rank-3, two enharmonic intervals are needed to define the notation: v<sup>3</sup>A1 and vm2. Either interval can be added to or subtracted from any note to respell the note. For example, ^C + vm2 = Db and ^^Eb + v<sup>3</sup>A1 = vE. Any combination of these two enharmonic intervals is also an enharmonic interval, for example their sum v<sup>4</sup>M2. Thus ^^F = vvG (double-down G, or '''dud''' G for short, rhymes with "cud").  


In larger edos, triple-arrows, quadruple-arrows, etc. can occur, and are names thusly:
=== Larger EDOs ===
In larger edos, triple-arrows, quadruple-arrows, etc. can occur. Up, dup, trup and quup all rhyme, as do dud, trud and quud.
{| class="wikitable"
{| class="wikitable"
|+words for multiple arrows
|+symbols and words for multiple arrows
!written
!spoken
!etymology
!
!written
!spoken
!etymology
|-
|^
|up
|
!1 arrow
!1 arrow
|v
|down
|
|-
|^^
|dup
|'''<u>d</u>'''ouble-'''<u>up</u>'''
!2 arrows
!2 arrows
|vv
|dud
| rowspan="4" |"-d" for down
replaces
"-p" for up
|-
|^^^
|trup
|'''<u>tr</u>'''iple-'''<u>up</u>'''
!3 arrows
!3 arrows
|vvv
|trud
|-
|^<sup>4</sup> <u>or</u>
v>
|quup
"kwup"
|'''<u>qu</u>'''adruple-'''<u>up</u>'''
!4 arrows
!4 arrows
|v<sup>4</sup> <u>or</u>
^<
|quud
"kwud"
|-
|>
|quip
|'''<u>qui</u>'''ntuple-u'''<u>p</u>'''
!5 arrows
!5 arrows
|<
|quid
|}
Very large edos can go well beyond 5 arrows. The sequence of names resembles tally counting I, II, III, IIII, <s>||||</s>. But the sequence of ''symbols'' might resemble roman numerals I, II, III, IV, V. Thus 4 ups is spoken quup but might be written v>.
{| class="wikitable"
|+
!1
!2
!3
!4
!5
!6
!7
!8
!9
!10
!11
!12
!...
|-
|-
|up
|up
|dup (rhymes
^
with "up")
|dup
|trup (rhymes
^^
with "up")
|trup
^^^
|quup
|quup
("kwup")
v>
|quip
|quip
>
|upquip
^>
|dupquip
^^>
|trupquip
^^^>
|quupquip
v>>
|quipquip
>>
|upquipquip
^>>
|dupquipquip
^^>>
|...
|-
|-
|down
|down
v
|dud
|dud
|trud (rhymes
vv
with "dud")
|trud
vvv
|quud
|quud
("kwud")
^<
|quid
|quid
<
|downquid
v<
|dudquid
vv<
|trudquid
vvv<
|quudquid
^<<
|quidquid
<<
|downquidquid
v<<
|dudquidquid
vv<<
|...
|}
|}
Lifts and drops (/ and \) can be used for microinflections of less than an edostep, since they look like part of an arrow.


=== Staff Notation ===
=== Staff Notation ===
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|  etc.
|  etc.
|}
|}
== Extremely large edos ==
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]].


==Chords and chord progressions==
==Chords and chord progressions==
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