Ed9/4: Difference between revisions
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An '''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 == | ||
=== Relation to edfs === | === Relation to edfs === | ||
An ed9/4 can be generated by taking every other tone of an [[edf]], so even-numbered ed9/ | 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/ | This is the primary use for ed9/4's – 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]] | 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 === | === 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 | 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 === | === 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 that claim is controversial. If that is the case though, then perhaps in a similar situation, 9/4 may have some form of faint equivalence as it might sound like two periods of 3/2. This is usually not really the point of using ed9/4 though as discussed above. | 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 that claim is controversial. If that is the case though, then perhaps in a similar situation, 9/4 may have some form of faint equivalence as it might sound like two periods of 3/2. This is usually not really the point of using ed9/4 though as discussed above. | ||
== Important ed9/ | == Important ed9/4's == | ||
=== 5ed9/4 === | === 5ed9/4 === | ||
Completely misses [[3/2]], [[2/1]], [[3/1]] 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 | Every other step of [[5edf]]. Completely misses [[3/2]], [[2/1]], [[3/1]] 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. | ||
Its intervals are: | Its intervals are: | ||
* | * 281{{c}} ([[7/6]], [[6/5]]) | ||
* | * 562{{c}} ([[11/8]], [[7/5]]) | ||
* | * 842{{c}} ([[phi]], [[13/8]]) | ||
* | * 1123{{c}} ([[21/11]]) | ||
* | * 1404{{c}} ([[9/4]]) | ||
{{Harmonics in equal|5|9|4|intervals= | {{Harmonics in equal|5|9|4|intervals=prime}} | ||
=== 9ed9/4 === | === 9ed9/4 === | ||
{{ | {{Main| 9ed9/4 }} | ||
Every other step of [[9edf]] (almost exactly every other step of [[Carlos Alpha]]). | Every other step of [[9edf]] (almost exactly every other step of [[Carlos Alpha]]). | ||
=== 11ed9/4 === | === 11ed9/4 === | ||
{{ | {{Main| 11ed9/4 }} | ||
Every other step of [[11edf]] (almost exactly every other step of [[Carlos Beta]]). | Every other step of [[11edf]] (almost exactly every other step of [[Carlos Beta]]). | ||
=== 29ed9/4 === | === 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]]. A compromise between [[39edt]] (triple Bohlen-Pierce) and [[25edo]], combining the benefits and drawbacks of both systems while being audibly different from either. | ||
{{Harmonics in equal|29|9|4|intervals=prime}} | {{Harmonics in equal|29|9|4|intervals=prime}} | ||
=== 43ed9/4 === | === 43ed9/4 === | ||
The smallest ed9/4 with a truly great approximation of full [[11-limit]] JI (let alone all the way up to the full [[23-limit]]). | Every other step of [[43edf]]. The smallest ed9/4 with a truly great approximation of full [[11-limit]] JI (let alone all the way up to the full [[23-limit]]). | ||
A compromise between [[58edt]] and [[37edo]], combining the benefits and drawbacks of both systems while being audibly different from either. | A compromise between [[58edt]] and [[37edo]], combining the benefits and drawbacks of both systems while being audibly different from either. | ||
{{Harmonics in equal|43|9|4|intervals=prime}} | {{Harmonics in equal|43|9|4|intervals=prime}} | ||
=== 45ed9/4 === | === 45ed9/4 === | ||
Very similar to [[61edt]] but improves on its approximations of [[JI]], with slightly better approximations of primes 2, 5, 7, 11, 13, 17, 19 ''and'' 23 compared to 61edt. | Every other step of [[45edf]]. Very similar to [[61edt]] but improves on its approximations of [[JI]], with slightly better approximations of primes 2, 5, 7, 11, 13, 17, 19 ''and'' 23 compared to 61edt. | ||
Compared to the nearest edo ([[38edo]]), it has a much worse prime 2 or course, but it has dramatically better primes 3, 7 and 11, and slightly better 13, 17, 19, 23 and even 29 compared to 38edo. It does however have a worse 5/1, but only slightly. | Compared to the nearest edo ([[38edo]]), it has a much worse prime 2 or course, but it has dramatically better primes 3, 7 and 11, and slightly better 13, 17, 19, 23 and even 29 compared to 38edo. It does however have a worse 5/1, but only slightly. | ||
{{Harmonics in equal|45|9|4|intervals=prime}} | {{Harmonics in equal|45|9|4|intervals=prime}} | ||
=== 47ed9/4 === | === 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]]. A compromise between [[64edt]] and [[40edo]], combining the benefits and drawbacks of both systems while being audibly different from either. | ||
{{Harmonics in equal|47|9|4|intervals=prime}} | {{Harmonics in equal|47|9|4|intervals=prime}} | ||
=== 57ed9/4 === | === 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]]. A compromise between [[77edt]] and [[49edo]], combining the benefits and drawbacks of both systems while being audibly different from either. | ||
{{Harmonics in equal|57|9|4|intervals=prime}} | {{Harmonics in equal|57|9|4|intervals=prime}} | ||
== Individual pages for ed9/ | == Individual pages for ed9/4's == | ||
{| class="wikitable center-all" | {| class="wikitable center-all" | ||
|+ style=white-space:nowrap | 1…99 | |+ style=white-space:nowrap | 1…99 | ||
| Line 134: | Line 123: | ||
* [[User:Moremajorthanmajor/Ruhf's Ed9/4 theory]] | * [[User:Moremajorthanmajor/Ruhf's Ed9/4 theory]] | ||
[[Category:Ed9/4's| ]] | [[Category:Ed9/4's| ]] <!-- main article --> | ||
<!-- main article --> | |||
[[Category:Lists of scales]] | [[Category:Lists of scales]] | ||
{{Todo|inline=1|explain edonoi|text=Most people do not think 9/4 sounds like an equivalence, so there must be some other reason why people are dividing it — some property ''other than'' equivalence that makes people want to divide it. Please add to this page an explanation of what that reason is.}} | |||
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