User:Moremajorthanmajor/Ed9/4: Difference between revisions

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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.
 
== Properties ==
=== Relation to edfs ===
An ed9/4 can be generated by taking every other tone of an [[edf]], so even-numbered ed9/4's are integer edfs.
 
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]].
 
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.
 
=== Relation to common practice ===
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.
 
=== Equivalence ===
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.
 
== Important ed9/4s ==
 
=== 5ed9/4 ===
Completely misses [[3/2]], [[2/1]], [[3/2]] and [[4/1]], but aproximates [[5/1]], [[6/1]] and [[7/1]] well for its size. This makes it still posess useful consonances, but with no strong [[equivalence interval]] to pull the listener's ear — making it a prime candidate for perceptual 9/4-equivalence, if such a thing is even possible.
 
Every other step of [[5edf]].
{{Harmonics in equal|5|9|4|intervals=integer}}
 
=== 9ed9/4 ===
{{main|9ed9/4}}
Every other step of [[9edf]] (almost exactly every other step of [[Carlos Alpha]]).
 
=== 11ed9/4 ===
{{main|11ed9/4}}
Every other step of [[11edf]] (almost exactly every other step of [[Carlos Beta]]).
 
=== 20ed9/4 ===
Every other step of [[20edf]] (almost exactly every other step of [[Carlos Gamma]]).
{{Harmonics in equal|11|9|4|intervals=integer}}
 
=== 29ed9/4 ===
A compromise between [[39edt]] (triple Bohlen-Pierce) and [[25edo]], combining the benefits and drawbacks of both systems while being audibly different from either.
 
Every other step of [[29edf]].
{{Harmonics in equal|29|9|4|intervals=prime}}
 
=== 43ed9/4 ===
A compromise between [[58edt]] and [[37edo]], combining the benefits and drawbacks of both systems while being audibly different from either.
 
Every other step of [[43edf]].
{{Harmonics in equal|43|9|4|intervals=prime}}
 
=== 45ed9/4 ===
Very similar to [[61edt]] but improves on its approximations of [[JI]].
 
Every other step of [[45edf]].
{{Harmonics in equal|45|9|4|intervals=prime}}
 
=== 47ed9/4 ===
A compromise between [[64edt]] and [[40edo]], combining the benefits and drawbacks of both systems while being audibly different from either.
 
Every other step of [[47edf]].
{{Harmonics in equal|47|9|4|intervals=prime}}
 
=== 57ed9/4 ===
A compromise between [[77edt]] and [[49edo]], combining the benefits and drawbacks of both systems while being audibly different from either.
 
Every other step of [[57edf]].
{{Harmonics in equal|57|9|4|intervals=prime}}
 
== Individual pages for ed9/4's ==
{| class="wikitable center-all"
|+ style=white-space:nowrap | 1…99
| [[1ed9/4|1]]
| [[3ed9/4|3]]
| [[5ed9/4|5]]
| [[7ed9/4|7]]
| [[9ed9/4|9]]
| [[11ed9/4|11]]
| [[13ed9/4|13]]
| [[15ed9/4|15]]
| [[17ed9/4|17]]
| [[19ed9/4|19]]
|-
| [[21ed9/4|21]]
| [[23ed9/4|23]]
| [[25ed9/4|25]]
| [[27ed9/4|27]]
| [[29ed9/4|29]]
| [[31ed9/4|31]]
| [[33ed9/4|33]]
| [[35ed9/4|35]]
| [[37ed9/4|37]]
| [[39ed9/4|39]]
|-
| [[41ed9/4|41]]
| [[43ed9/4|43]]
| [[45ed9/4|45]]
| [[47ed9/4|47]]
| [[49ed9/4|49]]
| [[51ed9/4|51]]
| [[53ed9/4|53]]
| [[55ed9/4|55]]
| [[57ed9/4|57]]
| [[59ed9/4|59]]
|-
| [[61ed9/4|61]]
| [[63ed9/4|63]]
| [[65ed9/4|65]]
| [[67ed9/4|67]]
| [[69ed9/4|69]]
| [[71ed9/4|71]]
| [[73ed9/4|73]]
| [[75ed9/4|75]]
| [[77ed9/4|77]]
| [[79ed9/4|79]]
|-
| [[81ed9/4|81]]
| [[83ed9/4|83]]
| [[85ed9/4|85]]
| [[87ed9/4|87]]
| [[89ed9/4|89]]
| [[91ed9/4|91]]
| [[93ed9/4|93]]
| [[95ed9/4|95]]
| [[97ed9/4|97]]
| [[99ed9/4|99]]
|}
 
== See also ==
* [[User:Moremajorthanmajor/Ruhf's Ed9/4 theory]]
 
[[Category:Ed9/4| ]] <!-- main article -->
[[Category:Edonoi]]
[[Category:Lists of scales]]
 
 
{{todo|review}}

Latest revision as of 03:23, 22 May 2025

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