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| {{Editable user page}}
| | #redirect [[Ed9/4]] |
| 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.
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| == Properties ==
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| === Relation to edfs ===
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| An ed9/4 can be generated by taking every other tone of an [[edf]], so even-numbered ed9/4's are integer edfs.
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| This is the primary use for ed9/4s — to get the same benefits of a particular edf, without having to juggle such a large number of notes per [[period]]. This is a similar principle to using an [[ed4]] in place of a very large [[edo]].
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| Perhaps a composer wanting to explore ''N''edf but daunted by the number of notes, could instead simply use ''N''ed9/4. Otherwise, they could also compose for two instruments, both tuned to ''N''ed9/4, but each tuned one step of ''N''edf apart, making the piece overall in ''N''edf, but each individual instrument ''N''ed9/4. This is a similar strategy to how some composers have approached [[24edo]] — using two [[12edo]] instruments tuned a 24edo-step apart.
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| === Relation to common practice ===
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| 9/4 or another major ninth is a standard replacement for the [[root]] in jazz piano voicings. Perhaps, then, a composer could approach the period of an ed9/4 not as an [[equivalence]], but as a skeleton for chords to be built out of — potentially encouraging an approach that focuses more on individual chords than an overall scale.
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| === Equivalence ===
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| Few would argue that 9/4 itself could be heard as an equivalence. Some might argue that some degree of 3/2 equivalence may be possible in a scale which has no 2/1, 3/1, or 4/1, though this is quite controversial. If that is the case, then perhaps in a similar scale that also has no 3/2, 9/4 may have some form of faint equivalence as it might sound like two periods of 3/2.
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| == Important ed9/4s ==
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| === 5ed9/4 ===
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| Completely misses [[2/1]] and [[3/1]], but aproximates [[5/1]] maybe passably, and [[7/1]] extremely well.
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| This makes it still posess some useful consonances, but with neither an octave nor tritave to pull the listener's ear — making it a prime candidate for perceptual 9/4-equivalence, if such a thing is even possible.
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| Every other step of [[5edf]].
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| {{Harmonics in equal|5|9|4|intervals=prime}}
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| {{Harmonics in equal|5|9|4|intervals=integer}}
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| === 9ed9/4 ===
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| {{main|9ed9/4}}
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| Every other step of [[9edf]] (almost exactly every other step of [[Carlos Alpha]]).
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| === 11ed9/4 ===
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| {{main|11ed9/4}}
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| Every other step of [[11edf]] (almost exactly every other step of [[Carlos Beta]]).
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| === 20ed9/4 ===
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| Every other step of [[20edf]] (almost exactly every other step of [[Carlos Gamma]]).
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| {{Harmonics in equal|11|9|4|intervals=prime}}
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| {{Harmonics in equal|11|9|4|intervals=integer}}
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| === 29ed9/4 ===
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| A compromise between [[39edt]] (triple Bohlen-Pierce) and [[25edo]], combining the benefits and drawbacks of both systems while being audibly different from either.
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| Every other step of [[29edf]].
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| {{Harmonics in equal|29|9|4|intervals=prime}}
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| === 43ed9/4 ===
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| A compromise between [[58edt]] and [[37edo]], combining the benefits and drawbacks of both systems while being audibly different from either.
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| Every other step of [[43edf]].
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| {{Harmonics in equal|43|9|4|intervals=prime}}
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| === 45ed9/4 ===
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| Very similar to [[61edt]] but improves on its approximations of [[JI]].
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| Every other step of [[45edf]].
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| {{Harmonics in equal|45|9|4|intervals=prime}}
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| === 47ed9/4 ===
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| A compromise between [[64edt]] and [[40edo]], combining the benefits and drawbacks of both systems while being audibly different from either.
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| Every other step of [[47edf]].
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| {{Harmonics in equal|47|9|4|intervals=prime}}
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| === 57ed9/4 ===
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| A compromise between [[77edt]] and [[49edo]], combining the benefits and drawbacks of both systems while being audibly different from either.
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| Every other step of [[57edf]].
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| {{Harmonics in equal|57|9|4|intervals=prime}}
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| == Individual pages for ed9/4's ==
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| {| class="wikitable center-all"
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| |+ style=white-space:nowrap | 1…99
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| | [[1ed9/4|1]]
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| | [[3ed9/4|3]]
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| | [[5ed9/4|5]]
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| | [[7ed9/4|7]]
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| | [[9ed9/4|9]]
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| | [[11ed9/4|11]]
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| | [[13ed9/4|13]]
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| | [[15ed9/4|15]]
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| | [[17ed9/4|17]]
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| | [[19ed9/4|19]]
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| |-
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| | [[21ed9/4|21]]
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| | [[23ed9/4|23]]
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| | [[25ed9/4|25]]
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| | [[27ed9/4|27]]
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| | [[29ed9/4|29]]
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| | [[31ed9/4|31]]
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| | [[33ed9/4|33]]
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| | [[35ed9/4|35]]
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| | [[37ed9/4|37]]
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| | [[39ed9/4|39]]
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| |-
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| | [[41ed9/4|41]]
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| | [[43ed9/4|43]]
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| | [[45ed9/4|45]]
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| | [[47ed9/4|47]]
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| | [[49ed9/4|49]]
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| | [[51ed9/4|51]]
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| | [[53ed9/4|53]]
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| | [[55ed9/4|55]]
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| | [[57ed9/4|57]]
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| | [[59ed9/4|59]]
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| |-
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| | [[61ed9/4|61]]
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| | [[63ed9/4|63]]
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| | [[65ed9/4|65]]
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| | [[67ed9/4|67]]
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| | [[69ed9/4|69]]
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| | [[71ed9/4|71]]
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| | [[73ed9/4|73]]
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| | [[75ed9/4|75]]
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| | [[77ed9/4|77]]
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| | [[79ed9/4|79]]
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| |-
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| | [[81ed9/4|81]]
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| | [[83ed9/4|83]]
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| | [[85ed9/4|85]]
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| | [[87ed9/4|87]]
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| | [[89ed9/4|89]]
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| | [[91ed9/4|91]]
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| | [[93ed9/4|93]]
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| | [[95ed9/4|95]]
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| | [[97ed9/4|97]]
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| | [[99ed9/4|99]]
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| |}
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| == See also ==
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| * [[User:Moremajorthanmajor/Ruhf's Ed9/4 theory]]
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| [[Category:Ed9/4| ]] <!-- main article -->
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| [[Category:Edonoi]]
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| [[Category:Lists of scales]]
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| {{todo|review}}
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