16edo: Difference between revisions

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== Intervals ==

16edo can be notated with conventional notation, including the staff, note names, relative notation, etc. in two ways. The first ~~preserves the <u>melodic</u> meaning of~~ sharp/flat, major/minor and aug/dim, in that sharp is higher pitched than flat, and major/aug is wider than minor/dim. The disadvantage to this approach is that conventional interval arithmetic no longer ~~works—this shouldn't be surprising as conventional interval arithmetic is designed for meantone/(super)pythagorean systems and 16edo is neither—e~~.g. {{nowrap|M2 + M2}} isn't M3, and {{nowrap|D + M2}} isn't E. Chord names are different because {{dash|C, E, G|med}} is not {{dash|P1, M3, P5|med}}. (But see below in "Chord Names".)

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. The disadvantage to this approach is that, 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. Chord names are different because {{dash|C, E, G|med}} is not {{dash|P1, M3, P5|med}}. (But see below in "Chord Names".)

The second approach is to preserve the *harmonic* meaning of sharp~~/flat, major/minor and aug/dim, in that the former is always further fifthwards on the chain of fifths than the latter. Sharp~~ is lower in pitch than flat, and major/aug is narrower than minor/dim. This ~~approach may seem bizarre at first. However~~, it carries over the way interval arithmetic and chord names work from diatonic notation~~. Furthermore, conventional 12edo music can be directly translated to 16edo "on the fly"~~.

The second approach is to essentially pretend 16edo's antidiatonic scale is a normal diatonic, meaning that sharp is lower in pitch than flat (since the "S" step is larger than the "L" step) and major/aug is narrower than minor/dim. This allows music notated in 12edo or another diatonic system to be directly translated to 16edo "on the fly", and it carries over the way interval arithmetic and chord names work from diatonic notation.

Alternatively, one can use Armodue nine-nominal notation; see [[Armodue theory]]

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 == Intervals ==
-edo can be notated with conventional notation, including the staff, note names, relative notation, etc. in two ways. The first preserves the <u>melodic</u> meaning of sharp/flat, major/minor and aug/dim, in that sharp is higher pitched than flat, and major/aug is wider than minor/dim. The disadvantage to this approach is that conventional interval arithmetic no longer works—this shouldn't be surprising as conventional interval arithmetic is designed for meantone/(super)pythagorean systems and 16edo is neither—e.g. {{nowrap|M2 + M2}} isn't M3, and {{nowrap|D + M2}} isn't E. Chord names are different because {{dash|C, E, G|med}} is not {{dash|P1, M3, P5|med}}. (But see below in "Chord Names".)
+edo 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. The disadvantage to this approach is that, 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. Chord names are different because {{dash|C, E, G|med}} is not {{dash|P1, M3, P5|med}}. (But see below in "Chord Names".)
-The second approach is to preserve the *harmonic* meaning of sharp/flat, major/minor and aug/dim, in that the former is always further fifthwards on the chain of fifths than the latter. Sharp is lower in pitch than flat, and major/aug is narrower than minor/dim. This approach may seem bizarre at first.  However, it carries over the way interval arithmetic and chord names work from diatonic notation. Furthermore, conventional 12edo music can be directly translated to 16edo "on the fly".
+The second approach is to essentially pretend 16edo's antidiatonic scale is a normal diatonic, meaning that sharp is lower in pitch than flat (since the "S" step is larger than the "L" step) and major/aug is narrower than minor/dim. This allows music notated in 12edo or another diatonic system to be directly translated to 16edo "on the fly", and it carries over the way interval arithmetic and chord names work from diatonic notation.
 Alternatively, one can use Armodue nine-nominal notation; see [[Armodue theory]]