Talk:Kite's thoughts on fifthspans: Difference between revisions
→Fifthward and fourthward distances for multi-ring EDOs?: (Adjust wording, fix typo) |
→Fifthward and fourthward distances for multi-ring EDOs?: (Also see Talk:Antipodes.) |
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It occurred to me that it should be possible to define fifthward and fourthward distances for multi-ring EDOs if fractional distances are allowed. For instance, 34EDO has 2 rings of fifths, so with only integer fifthwards and fourthwards distances, the fifthwards/fourthwards antipode is undefined. But if we divide the perfect fifth (20\34) in 4 (5\34), we get the odd number of 1\34 increments we need to move between rings of fifths. Then we can define a fifthward distance for any interval in 34EDO, for instance its best approximation to 5/4, which is 11\34: Moving upwards by 9 quarter-fifths (9/4 fifths) gives us 45\34, which octave-reduces to 11\34. Since Tetracot temperament divides the (tempered) perfect fifth into 4 equal parts, this provides a reason in favor of using the Tetracot generalized/isomorphic keyboard mapping for facilitating use of the excellent 5-limit harmony of 34EDO. | It occurred to me that it should be possible to define fifthward and fourthward distances for multi-ring EDOs if fractional distances are allowed. For instance, 34EDO has 2 rings of fifths, so with only integer fifthwards and fourthwards distances, the fifthwards/fourthwards antipode is undefined. But if we divide the perfect fifth (20\34) in 4 (5\34), we get the odd number of 1\34 increments we need to move between rings of fifths. Then we can define a fifthward distance for any interval in 34EDO, for instance its best approximation to 5/4, which is 11\34: Moving upwards by 9 quarter-fifths (9/4 fifths) gives us 45\34, which octave-reduces to 11\34. Since Tetracot temperament divides the (tempered) perfect fifth into 4 equal parts, this provides a reason in favor of using the Tetracot generalized/isomorphic keyboard mapping for facilitating use of the excellent 5-limit harmony of 34EDO. | ||
(Also see [[Talk:Antipodes]] for another example of potentially useful fractional distances.) | |||
[[User:Lucius Chiaraviglio|Lucius Chiaraviglio]] ([[User talk:Lucius Chiaraviglio|talk]]) 21:37, 20 June 2024 (UTC) | [[User:Lucius Chiaraviglio|Lucius Chiaraviglio]] ([[User talk:Lucius Chiaraviglio|talk]]) 21:37, 20 June 2024 (UTC) | ||