User:Moremajorthanmajor/Ed9/4: Difference between revisions

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Ed9/4 ~~stands for a division~~ of ~~a [[9/4|~~Pythagorean ninth (9/4)]] into n equal parts.

'''Ed9/4''' means '''Division of of the Pythagorean ninth ([[9/4]]) into n equal parts'''.

== Properties ==

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 fourth optionally with a period equivalent to three or six macrotones, in particular ones at least as wide as 101.083 cents) takes 1-3-6, which is not equivalent to a tone cluster as it would be in an [[EDF|edf]] tuning, 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.

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-Ed9/4 stands for a division of a [[9/4|Pythagorean ninth (9/4)]] into n equal parts.
+'''Ed9/4''' means '''Division of of the Pythagorean ninth ([[9/4]]) into n equal parts'''.
+== Properties ==
 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 fourth optionally with a period equivalent to three or six macrotones, in particular ones at least as wide as 101.083 cents) takes 1-3-6, which is not equivalent to a tone cluster as it would be in an [[EDF|edf]] tuning, 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.