User:Moremajorthanmajor/Ed9/4: Difference between revisions

Line 1:

~~'''EdIX~~/~~edn''' means '''Division~~ of a ninth (~~nonet~~) ~~interval~~ into n equal parts~~'''~~.

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

~~<font style="font-size: 19.5px;">Division of a ninth (e. g. 9/4) into n equal parts</font>~~

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.

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.

Incidentally, one way to treat 9/4 as an equivalence is the use of the 5:6:8 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 four 9/8 to get to 8/5 (tempering out the schisma). So, doing this yields 6, 8, 14 and 20 or 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.

Line 28:

Line 26:

Surprisingly, though sort of obviously, the golden and pyrite tunings of edIXs must be forced to turn out to divide a (nearly) pure 9:4 (in particular, using Aeolian mode gives the [[2/7-comma meantone]] major ninth as almost exactly the pyrite tuning of the period, or (8φ+6)/(7φ+5).

==Individual pages for ~~EDIXs~~==

==Individual pages for ed9/4s==

* [[8ed9/4]]

* [[9ed9/4]]

@@ Line 1: / Line 1: @@
-'''EdIX/edn''' means '''Division of a ninth (nonet) interval into n equal parts'''.
+Ed9/4 stands for a division of a [[9/4|Pythagorean ninth (9/4)]] into n equal parts.
-<font style="font-size: 19.5px;">Division of a ninth (e. g. 9/4) into n equal parts</font>
+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.
-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.
 Incidentally, one way to treat 9/4 as an equivalence is the use of the 5:6:8 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 four 9/8 to get to 8/5 (tempering out the schisma). So, doing this yields 6, 8, 14 and 20 or 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.
@@ Line 28: / Line 26: @@
 Surprisingly, though sort of obviously, the golden and pyrite tunings of edIXs must be forced to turn out to divide a (nearly) pure 9:4 (in particular, using Aeolian mode gives the [[2/7-comma meantone]] major ninth as almost exactly the pyrite tuning of the period, or (8φ+6)/(7φ+5).
-==Individual pages for EDIXs==
+==Individual pages for ed9/4s==
 * [[8ed9/4]]
 * [[9ed9/4]]