User:Moremajorthanmajor/Ed9/4: Difference between revisions

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'''EdIX''' is the short form of '''Division of a ninth ([[9/4]]) into n equal parts'''.

Division of e. g. the 9:4 into equal parts can be conceived of as to directly use this interval as an equivalence, or not. The question of [[equivalence]] has not even been posed yet. The utility of 9:4 or another ninth as a base though, is apparent by being the standard replacement for the root in jazz piano voicings. Also, as a ninth is the double of a fifth, the fifth of normal root position triads will become the common suspension (5-4 or 5-6) of a ninth-based system. However, thirds and sixths are no longer inverses, and thus an [[Pseudo-traditional_harmonic_functions_of_octatonic_scale_degrees|octatonic scale]] (i. e. any of those of the proper Napoli temperament family which are generated by a third or a fourth optionally with a period equivalent to six macrotones, in particular ones at least as wide as 4 degrees of [[45edo]]) takes 1-3-6 as the root position of its regular triad. Many, though not all, of these scales have a pseudo (false) octave, with various degrees of accuracy.

Division of e. g. the 9:4 into equal parts can be conceived of as to directly use this interval as an equivalence, or not. The question of [[equivalence]] has not even been posed yet. The utility of 9:4 or another ninth as a base though, is apparent by being the standard replacement for the root in jazz piano voicings. Also, as a ninth is the double of a fifth, the fifth of normal root position triads will become the common suspension (5-4 or 5-6) of a ninth-based system. However, thirds and sixths are no longer inverses, and thus an [[Pseudo-traditional_harmonic_functions_of_octatonic_scale_degrees|octatonic scale]] (i. e. any of those of the proper Napoli temperament family which are generated by a third or a fourth optionally with a period equivalent to three or six macrotones, in particular ones at least as wide as 4 degrees of [[45edo]]) takes 1-3-6 as the root position of its regular triad. Many, though not all, of these scales have a pseudo (false) octave, with various degrees of accuracy.

Incidentally, one way to treat 9/4 as an equivalence is the use of the 4:5:6:7:[8]:(9) chord as the fundamental complete sonority in a very similar way to the 4:5:6:(8) chord in meantone. Whereas in meantone it takes four 3/2 to get to 5/1, here it takes nine 5/4 to get to the same place as thirteen 7/6 (tempering out the comma |5 -13 9 -13>) or three 7/6 to get between 6/5 and the period of 3/2 (tempering out the comma 1728/1715). So, doing this yields 8 or 10, 12 or 14, and 22 note 2MOS. While the notes are rather farther apart, the scheme is uncannily similar to certain versions of the regularly tempered approximate ("full"-status) [[A_shruti_list|shrutis]]. "Macroshrutis" might be a practically perfect term for it if it hasn't been named yet.

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 '''EdIX''' is the short form of '''Division of a ninth ([[9/4]]) into n equal parts'''.
-Division of e. g. the 9:4 into equal parts can be conceived of as to directly use this interval as an equivalence, or not. The question of [[equivalence]] has not even been posed yet. The utility of 9:4 or another ninth as a base though, is apparent by being the standard replacement for the root in jazz piano voicings. Also, as a ninth is the double of a fifth, the fifth of normal root position triads will become the common suspension (5-4 or 5-6) of a ninth-based system. However, thirds and sixths are no longer inverses, and thus an [[Pseudo-traditional_harmonic_functions_of_octatonic_scale_degrees|octatonic scale]] (i. e. any of those of the proper Napoli temperament family which are generated by a third or a fourth optionally with a period equivalent to six macrotones, in particular ones at least as wide as 4 degrees of [[45edo]]) takes 1-3-6 as the root position of its regular triad. Many, though not all, of these scales have a pseudo (false) octave, with various degrees of accuracy.
+Division of e. g. the 9:4 into equal parts can be conceived of as to directly use this interval as an equivalence, or not. The question of [[equivalence]] has not even been posed yet. The utility of 9:4 or another ninth as a base though, is apparent by being the standard replacement for the root in jazz piano voicings. Also, as a ninth is the double of a fifth, the fifth of normal root position triads will become the common suspension (5-4 or 5-6) of a ninth-based system. However, thirds and sixths are no longer inverses, and thus an [[Pseudo-traditional_harmonic_functions_of_octatonic_scale_degrees|octatonic scale]] (i. e. any of those of the proper Napoli temperament family which are generated by a third or a fourth optionally with a period equivalent to three or six macrotones, in particular ones at least as wide as 4 degrees of [[45edo]]) takes 1-3-6 as the root position of its regular triad. Many, though not all, of these scales have a pseudo (false) octave, with various degrees of accuracy.
 Incidentally, one way to treat 9/4 as an equivalence is the use of the 4:5:6:7:[8]:(9) chord as the fundamental complete sonority in a very similar way to the 4:5:6:(8) chord in meantone. Whereas in meantone it takes four 3/2 to get to 5/1, here it takes nine 5/4 to get to the same place as thirteen 7/6 (tempering out the comma |5 -13 9 -13&gt;) or three 7/6 to get between 6/5 and the period of 3/2 (tempering out the comma 1728/1715). So, doing this yields 8 or 10, 12 or 14, and 22 note 2MOS. While the notes are rather farther apart, the scheme is uncannily similar to certain versions of the regularly tempered approximate ("full"-status) [[A_shruti_list|shrutis]]. "Macroshrutis" might be a practically perfect term for it if it hasn't been named yet.