18edo: Difference between revisions

Line 26:

18edo can be notated with [[ups and downs]]. The notational 5th is the 2nd-best approximation of 3/2, 10\18. This is only 4¢ worse that the best approximation, which becomes the up-fifth. Using this 5th allows conventional notation to be used, including the staff, note names, relative notation, etc. There are two ways to do this:

The first ~~way 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. e.g. M2 + M2 isn't M3, and D + M2 isn't E. ~~Chord names are different because C - E - G isn't P1 - M3 - P5.~~

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. Chord names don't follow diatonic nominals because {{dash|C, E, G|med}} is not {{dash|P1, M3, P5|med}}.

~~The second way preserves~~ the ~~<u>harmonic</u> 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. While this approach may seem bizarre at first~~, ~~interval arithmetic and chord names work as usual. Furthermore~~, ~~conventional 12edo music can be directly translated to 18edo "on the fly"~~.

The second approach is to essentially pretend 18edo'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 18edo "on the fly", and it carries over the way interval arithmetic and chord names work from diatonic notation.

{| class="wikitable center-all right-2"

! Degree

@@ Line 26: / Line 26: @@
 edo can be notated with [[ups and downs]]. The notational 5th is the 2nd-best approximation of 3/2, 10\18. This is only 4¢ worse that the best approximation, which becomes the up-fifth. Using this 5th allows conventional notation to be used, including the staff, note names, relative notation, etc. There are two ways to do this:
-The first way 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. e.g. M2 + M2 isn't M3, and D + M2 isn't E. Chord names are different because C - E - G isn't P1 - M3 - P5.
+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. Chord names don't follow diatonic nominals because {{dash|C, E, G|med}} is not {{dash|P1, M3, P5|med}}.
-The second way preserves the <u>harmonic</u> 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. While this approach may seem bizarre at first, interval arithmetic and chord names work as usual. Furthermore, conventional 12edo music can be directly translated to 18edo "on the fly".
+The second approach is to essentially pretend 18edo'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 18edo "on the fly", and it carries over the way interval arithmetic and chord names work from diatonic notation.
 {| class="wikitable center-all right-2"
 ! Degree