User:Moremajorthanmajor/Ed9/4: Difference between revisions
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''' | The '''equal division of 9/4''' ('''ed9/4''') is a [[tuning]] obtained by dividing the [[9/4|Pythagorean ninth (9/4)]] in a certain number of [[equal]] steps. | ||
== Properties == | == Properties == | ||
Division of | Division of 9/4 into equal parts does not necessarily imply directly using this interval as an [[equivalence]]. The question of equivalence has not even been posed yet. The utility of 9/4 or another major 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]] tuning, as the root position of its regular triad. Many, though not all, of these scales have a 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 | 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 has not been named yet. | ||
The branches of the Napoli family are named thus: | The branches of the Napoli family are named thus: | ||
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Surprisingly, though sort of obviously, due to 9/4 being the primary attractor for Neapolitan temperaments, 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). | Surprisingly, though sort of obviously, due to 9/4 being the primary attractor for Neapolitan temperaments, 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 ed9/ | == Individual pages for ed9/4's == | ||
* [[8ed9/4]] | * [[8ed9/4]] | ||
* [[9ed9/4]] | * [[9ed9/4]] | ||
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* [[17ed9/4]] | * [[17ed9/4]] | ||
[[Category:Ed9/4]] | [[Category:Ed9/4| ]] <!-- main article --> | ||
[[Category:Equal-step tuning]] | [[Category:Equal-step tuning]] | ||