16edo: Difference between revisions

16edo can be notated with conventional notation, including the staff, note names, relative notation, etc. in two ways. The first defines sharp/flat, major/minor and aug/dim in terms of the native antidiatonic scale, such that sharp is higher pitched than flat, and major/aug is wider than minor/dim, as would be expected. Because it does not follow diatonic conventions, conventional interval arithmetic no longer works, e.g. {{nowrap|M2 + M2}} isn't M3, and {{nowrap|D + M2}} isn't E. Because antidiatonic is the sister scale to diatonic, you can solve this by swapping major and minor in interval arithmetic rules (see [[16edo#Interval_arithmetic_examples]]). Chord names don't follow diatonic nominals because {{dash|C, E, G|med}} is not {{dash|P1, M3, P5|med}}. (But see below in "Chord Names".)

! colspan="2" | Antidiatonic

! colspan="2" | Diatonic

16edo chords can be named using ups and downs. Using diatonic interval names, the names correspond to diatonic names, but they bear little relationship to the sound: a minor chord (spelled {{dash|A, C, E|med}}) sounds like [[4:5:6]], the classical major triad, and a major chord (spelled {{dash|C, E, G|med}}) sounds like [[10:12:15]], a classical minor triad! Instead, using antidiatonic names, the chord names will match the sound—but finding the name from the spelling follows the rules of antidiatonic rather than diatonic interval arithmetic.

! colspan="3" | Diatonic

! colspan="3" | Antidiatonic

Using antidiatonic names, if you're used to diatonic interval arithmetic, you can do antidiatonic interval arithmetic by following the simple guideline that qualities are '''reversed''' from standard diatonic. As in, just as adding two major seconds gives you a major third in 12edo, adding two minor seconds gives a minor third in 16edo.

That is, reversing means exchanging major for minor, aug for dim, and sharp for flat. Perfect and natural are unaffected.

 

This Layout places mavila[7] on the black keys and mavila[9] on the white keys, according to antidiatonic notation.