EDO: Difference between revisions

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EDOs can be further subdivided and classified according to the size of the fifth, such as with [[Margo_Schulter|Margo Schulter]]'s [[Gentle_region|gentle region]] or the distinction between negative, positive, doubly negative and doubly positive of [[RHM_Bosanquet|RHM Bosanquet]]. [[KiteGiedraitis|Kite Giedraitis]] has proposed these six categories, based on the size of the fifth. From narrowest to widest:

<ul><li>'''superflat''' edos (9, 11, 13b, 16, 18b & 23) have a fifth narrower than four-sevenths of an octave = 4\7 = 686¢</li><li>'''perfect''' edos (7, 14, 21, 28 & 35) have a fifth of 4\7 = 686¢</li><li>'''~~regular~~''' edos (12, 17, 19, 22, 24, etc.) have a fifth between 686¢ and 720¢</li><li>'''pentatonic''' edos (5, 10, 15, 20, 25 & 30) have a fifth of three-fifths of an octave = 3\5 = 720¢</li><li>'''supersharp''' edos (8, 13 & 18) have a fifth wider than 3\5 = 720¢</li><li>'''trivial''' edos (1, 2, 3, 4 and 6) are contained in 12-edo</li></ul>

<ul><li>'''superflat''' edos (9, 11, 13b, 16, 18b & 23) have a fifth narrower than four-sevenths of an octave = 4\7 = 686¢</li><li>'''perfect''' edos (7, 14, 21, 28 & 35) have a fifth of 4\7 = 686¢</li><li>'''diatonic''' edos (12, 17, 19, 22, 24, etc.) have a fifth between 686¢ and 720¢</li><li>'''pentatonic''' edos (5, 10, 15, 20, 25 & 30) have a fifth of three-fifths of an octave = 3\5 = 720¢</li><li>'''supersharp''' edos (8, 13 & 18) have a fifth wider than 3\5 = 720¢</li><li>'''trivial''' edos (1, 2, 3, 4 and 6) have a fifth about 100¢ from just, and are contained in 12-edo</li></ul>

==Non-tuning properties==

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 EDOs can be further subdivided and classified according to the size of the fifth, such as with [[Margo_Schulter|Margo Schulter]]'s [[Gentle_region|gentle region]] or the distinction between negative, positive, doubly negative and doubly positive of [[RHM_Bosanquet|RHM Bosanquet]]. [[KiteGiedraitis|Kite Giedraitis]] has proposed these six categories, based on the size of the fifth. From narrowest to widest:
-<ul><li>'''superflat''' edos (9, 11, 13b, 16, 18b &amp; 23) have a fifth narrower than four-sevenths of an octave = 4\7 = 686¢</li><li>'''perfect''' edos (7, 14, 21, 28 &amp; 35) have a fifth of 4\7 = 686¢</li><li>'''regular''' edos (12, 17, 19, 22, 24, etc.) have a fifth between 686¢ and 720¢</li><li>'''pentatonic''' edos (5, 10, 15, 20, 25 &amp; 30) have a fifth of three-fifths of an octave = 3\5 = 720¢</li><li>'''supersharp''' edos (8, 13 &amp; 18) have a fifth wider than 3\5 = 720¢</li><li>'''trivial''' edos (1, 2, 3, 4 and 6) are contained in 12-edo</li></ul>
+<ul><li>'''superflat''' edos (9, 11, 13b, 16, 18b &amp; 23) have a fifth narrower than four-sevenths of an octave = 4\7 = 686¢</li><li>'''perfect''' edos (7, 14, 21, 28 &amp; 35) have a fifth of 4\7 = 686¢</li><li>'''diatonic''' edos (12, 17, 19, 22, 24, etc.) have a fifth between 686¢ and 720¢</li><li>'''pentatonic''' edos (5, 10, 15, 20, 25 &amp; 30) have a fifth of three-fifths of an octave = 3\5 = 720¢</li><li>'''supersharp''' edos (8, 13 &amp; 18) have a fifth wider than 3\5 = 720¢</li><li>'''trivial''' edos (1, 2, 3, 4 and 6) have a fifth about 100¢ from just, and are contained in 12-edo</li></ul>
 ==Non-tuning properties==