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| The structural utility of 9/4 or another major ninth 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. | | The structural utility of 9/4 or another major ninth 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. |
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| === Joseph Ruhf's ed9/4 theory ===
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| {{idiosyncratic terms}}
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| In ed9/4 systems, 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.
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| One way to approach some ed9/4 tunings 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 superficially similar to certain versions of the regularly tempered approximate ("full"-status) [[A shruti list|shrutis]]. [[Joseph Ruhf]] proposes the name "macroshrutis" for this reason.
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| The branches of the Napoli family are named thus:
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| 5&3: Grandfather
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| Bipentachordal:
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| * 4&4: Macrodiminshed
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| * 6&2: Macroshrutis
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| The temperament family in the Neapolitan temperament area which has an interlaced enneatonic scale is named for parts of Maryland further west of the Middletown Valley as its generator rises:
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| 3&6: South Mountain Scale
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| 4&5: Hagerstown (particularly in ~9/4)
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| 2&7: Allegany
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| The temperament family in the Neapolitan temperament area which has an octatonic scale of seven generators and a remainder is named Fujiyama (i. e. the volcano viewable from practically anywhere in Japan due to the Japanese archipelago consisting of such flat islands).
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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).
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| == Individual pages for ed9/4's == | | == Individual pages for ed9/4's == |
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| {| class="wikitable center-all" | | {| class="wikitable center-all" |
| |+ style=white-space:nowrap | 1…99 | | |+ style=white-space:nowrap | 1…99 |
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| | [[99ed9/4|99]] | | | [[99ed9/4|99]] |
| |} | | |} |
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| | == See also == |
| | * [[User:Moremajorthanmajor/Ruhf's Ed9/4 theory]] |
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| [[Category:Ed9/4| ]] <!-- main article --> | | [[Category:Ed9/4| ]] <!-- main article --> |