43edo: Difference between revisions
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Because 43edo is a meantone system, this makes it easier to adapt traditional Western notation to it than to some other tunings. A# and Bb are distinct and the distance between them is one meride. The whole tone is divided into seven merides so this means we can use "third-sharps", "two-thirds-sharps", "third-flats", and "two-thirds-flats" to reach the remaining notes between A and B; notes elsewhere on the scale can be notated similarly. | Because 43edo is a meantone system, this makes it easier to adapt traditional Western notation to it than to some other tunings. A# and Bb are distinct and the distance between them is one meride. The whole tone is divided into seven merides so this means we can use "third-sharps", "two-thirds-sharps", "third-flats", and "two-thirds-flats" to reach the remaining notes between A and B; notes elsewhere on the scale can be notated similarly. | ||
For people who aren't colorblind, a red-note/blue-note system (similar to that proposed for sixth-tones/[[36edo]]) can be used. (This is a different use of color than Kite's [[color notation]].) Now we have the following sequence of notes, each separated by one meride: A, red A, blue A#, A#, Bb, red Bb, blue B, B. (Note that there are red flats and blue sharps, but no red sharps or blue flats, because the latter are enharmonically equivalent to simpler notes: blue Bb is actually just A#, for instance). | |||
The diatonic semitone is four steps, so for the region between B and C (or, E and F), we can use: B, Cb, red Cb/blue B# (''they are enharmonic equivalents''), B#, and C. All of the notes in 43edo therefore have unambiguous names except for two: red Cb/blue B#, and red Fb/blue E#. It might also be possible to design special symbols for those two notes (resembling a cross between the letters B and C in the former case, and E and F in the latter). | The diatonic semitone is four steps, so for the region between B and C (or, E and F), we can use: B, Cb, red Cb/blue B# (''they are enharmonic equivalents''), B#, and C. All of the notes in 43edo therefore have unambiguous names except for two: red Cb/blue B#, and red Fb/blue E#. It might also be possible to design special symbols for those two notes (resembling a cross between the letters B and C in the former case, and E and F in the latter). | ||
If red Cb and blue B# (and red Fb/blue E#) are instead forced to be distinct, but the requirement that all notes be equally spaced is maintained, then we end up with a ''completely'' unambiguous red-note/blue-note notation for [[45edo]], which is another meantone (actually, a [[flattone]]) system. | If red Cb and blue B# (and red Fb/blue E#) are instead forced to be distinct, but the requirement that all notes be equally spaced is maintained, then we end up with a ''completely'' unambiguous red-note/blue-note notation for [[45edo]], which is another meantone (actually, a [[flattone]]) system. | ||
=== Ups and downs notation === | |||
The following shows how [[ups and downs notation]] can notate the third-sharps and third-flats through extended [[Helmholtz-Ellis notation]] symbols: | |||
{| class="wikitable center-all" | |||
! Semitones | |||
| 2⅓ | |||
| '''2''' | |||
| 1⅔ | |||
| 1⅓ | |||
| '''1''' | |||
| ⅔ | |||
| ⅓ | |||
| '''0''' | |||
|- | |||
! Sharp symbol | |||
| [[File:Heji33.svg|18px|center]] | |||
| [[File:Heji32.svg|18px|center]] | |||
| [[File:Heji31.svg|18px|center]] | |||
| [[File:Heji26.svg|18px|center]] | |||
| [[File:Heji25.svg|17px|center]] | |||
| [[File:Heji24.svg|17px|center]] | |||
| [[File:Heji19.svg|18px|center]] | |||
| rowspan="2" | [[File:Heji18.svg|15px|center]] | |||
|- | |||
! Flat symbol | |||
| [[File:Heji3.svg|24px|center]] | |||
| [[File:Heji4.svg|24px|center]] | |||
| [[File:Heji5.svg|27px|center]] | |||
| [[File:Heji10.svg|19px|center]] | |||
| [[File:Heji11.svg|15px|center]] | |||
| [[File:Heji12.svg|18px|center]] | |||
| [[File:Heji17.svg|15px|center]] | |||
|} | |||
=== Sagittal === | === Sagittal === | ||