Kite's ups and downs notation: Difference between revisions

The advantage to this notation is that you always know where your fifth is. And hence your 4th, and your major 9th, hence the maj 2nd and the min 7th too. You have convenient landmarks to find your way around, built into the notation. The notation is a map of unfamiliar territory, and we want this map to be as easy to read as possible.

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 notes without ups or downs always form a chain of fifths.

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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 22-edo, Db can be spelled ^C or vB# or even ^^B (double-up B).  

Since 22edo is rank-1, and conventional notation plus ups and downs is rank-3, two enharmonic intervals are needed to define the notation: v³A1 and vm2. Either interval can be added to or subtracted from any note to respell the note. For example, ^C + vm2 = Db and ^^Eb + v³A1 = vE. Any combination of these two enharmonic intervals is also an enharmonic interval, for example their sum v⁴M2.  

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, 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. 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].

It might seem more natural to place the up after the note, for example B^ or Bb^. But the up must come first, to make chord names unambiguous. B^m could mean either a minor chord rooted on B^ or an upminor chord rooted on B. (Chord names are explained fully below.)

Every conventional chord can accept such an up or down, with one exception: it's pointless to down a C5 chord, because there is no 3rd, 6th or 7th to alter. Thus Cv5 is invalid, and "C down-5" means C(v5) = C E vG.

<span style="display: block; text-align: left;">The major chord and various alterations of it:</span>

Imperfect intervals (2nd, 3rd, 6th and 7th): a = mid, e = major, i = aug, o = minor, u = dim

* Ra = ~2, Re = M2, Ri = A2, Ro = m2, Ru = d2

[[Category:notation]]