Kite's ups and downs notation: Difference between revisions

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.  

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.  

'''<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.  

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.

In contrast, 22-edo is hard to notate because 7 fifths are <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 bad. 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 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.

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].

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

|Cm,v6

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.

This suffices for many but not all edos, as some require triple sharps or quadruple ups.