343edo: Difference between revisions

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Wery named the temperament "lucite" because musically, it sounds like frosted glass (perhaps to do with the timbre/partials of struck glass).

Some ~~coincidence~~ that make the name "lucite" particularly fitting

Some coincidences that make the name "lucite" particularly fitting

* Lucite is often installed in double layers in building, and lucite temperament has two sizes of perfect fifth-like interval.

* Lucite[23] is close to ripple[23], but turned inside out; and lucite is reflective and clear like water, but solid instead of liquid

* Lucite is an especially lightweight material, and lucite temperament is lightweight in the way it only needs 18 generators to reach every 17-limit prime.

; Subsets

* [[Modmos]] of lucite[6]: 60 60 30 40 93 60

=== Other MOS scales ===

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* Amity[39]: 7 7 17 7 7 7 7 7 17 7 7 7 7 17 7 7 7 7 7 17 7 7 7 7 7 17 7 7 7 7 17 7 7 7 7 7 17 7 7

* Amity[53]: 7 7 7 3 7 7 7 7 7 7 7 3 7 7 7 7 7 7 3 7 7 7 7 7 7 7 3 7 7 7 7 7 7 7 3 7 7 7 7 7 7 3 7 7 7 7 7 7 7 3 7 7 7

** ''Try approximating scales fron 53edo ([[53edo#Scales]]) within the ~~lucite~~[23] scale''

** ''Try approximating scales fron 53edo ([[53edo#Scales]]) within the amity[53] scale''

* Amity[99]: 3 4 3 4 3 4 3 4 3 4 3 4 3 4 3 3 4 3 4 3 4 3 4 3 4 3 4 3 3 4 3 4 3 4 3 4 3 4 3 4 3 4 3 3 4 3 4 3 4 3 4 3 4 3 4 3 3 4 3 4 3 4 3 4 3 4 3 4 3 4 3 3 4 3 4 3 4 3 4 3 4 3 4 3 3 4 3 4 3 4 3 4 3 4 3 4 3 4 3

** ''Try approximating scales fron 99edo ([[99edo#Scales]]) within the ~~lucite~~[23] scale''

** ''Try approximating scales fron 99edo ([[99edo#Scales]]) within the amity[99] scale''

* Lucite[23]: 13 17 13 17 13 17 13 17 13 17 13 17 13 17 13 17 13 17 13 17 13 17 13

** ''Try approximating scales fron 23edo ([[23edo#Scales]]) within the lucite[23] scale''

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{{Harmonics in equal|86|2|1|intervals=integer|columns=12|collapsed=1|title=86edo for comparison}}

=== 34.3edo ===

'''34.3edo''' is contained within 343edo (it is every 10th step of 343edo). It is like [[34edo]] with the [[octave shrinking|octave compressed]] by 11.51 [[cents]].

It has a step size of 34.985{{c}}.

It was discovered by chaseofspades513 and [[YoVariable]] on the [[Xenharmonic Alliance]] Discord server and further described by [[Gordon Wery]].

Compared to 34edo it improves harmonics 7, 11 and 13, at the expense of 2, 3 and 5. Its mappings of multiple-of-2 and multiple-of-3 harmonics are very inconsistent, though some composers may enjoy this due to the potential to play tricks on the listener by having [[octave equivalence]] fall on a scale step one might not expect.

Many temperaments and [[34edo#Scales|scales from 34edo]] can be used here in 34.3edo too.

{{Harmonics in cet|34.985|intervals=integer|columns=12|title=Approximation of harmonics in 34.3edo}}

{{Harmonics in equal|34|2|1|intervals=integer|columns=12|collapsed=1|title=34edo for comparison}}

=== Scales approximated from JI ===

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=== Other scales ===

* [[Equiheptatonic]] (as from [[7edo]]): 49 49 49 49 49 49 49

* [[Modmos]] of frost[6]: 60 60 30 40 93 60

* [[49edo]]: 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7

== Music ==

; [[Budjarn Lambeth]]

* [https://youtu.be/aWqdWHSk5J4 ''Odd Findings in the Caves''] (2025) - ''uses two copies of lucite[23]''

@@ Line 124: / Line 124: @@
 Wery named the temperament "lucite" because musically, it sounds like frosted glass (perhaps to do with the timbre/partials of struck glass).
-Some coincidence that make the name "lucite" particularly fitting
+Some coincidences that make the name "lucite" particularly fitting
 * Lucite is often installed in double layers in building, and lucite temperament has two sizes of perfect fifth-like interval.
 * Lucite[23] is close to ripple[23], but turned inside out; and lucite is reflective and clear like water, but solid instead of liquid
 * Lucite is an especially lightweight material, and lucite temperament is lightweight in the way it only needs 18 generators to reach every 17-limit prime.
+; Subsets
+* [[Modmos]] of lucite[6]: 60 60 30 40 93 60
 === Other MOS scales ===
@@ Line 137: / Line 140: @@
 * Amity[39]: 7 7 17 7 7 7 7 7 17 7 7 7 7 17 7 7 7 7 7 17 7 7 7 7 7 17 7 7 7 7 17 7 7 7 7 7 17 7 7
 * Amity[53]: 7 7 7 3 7 7 7 7 7 7 7 3 7 7 7 7 7 7 3 7 7 7 7 7 7 7 3 7 7 7 7 7 7 7 3 7 7 7 7 7 7 3 7 7 7 7 7 7 7 3 7 7 7
-** ''Try approximating scales fron 53edo ([[53edo#Scales]]) within the lucite[23] scale''
+** ''Try approximating scales fron 53edo ([[53edo#Scales]]) within the amity[53] scale''
 * Amity[99]: 3 4 3 4 3 4 3 4 3 4 3 4 3 4 3 3 4 3 4 3 4 3 4 3 4 3 4 3 3 4 3 4 3 4 3 4 3 4 3 4 3 4 3 3 4 3 4 3 4 3 4 3 4 3 4 3 3 4 3 4 3 4 3 4 3 4 3 4 3 4 3 3 4 3 4 3 4 3 4 3 4 3 4 3 3 4 3 4 3 4 3 4 3 4 3 4 3 4 3
-** ''Try approximating scales fron 99edo ([[99edo#Scales]]) within the lucite[23] scale''
+** ''Try approximating scales fron 99edo ([[99edo#Scales]]) within the amity[99] scale''
 * Lucite[23]: 13 17 13 17 13 17 13 17 13 17 13 17 13 17 13 17 13 17 13 17 13 17 13
 ** ''Try approximating scales fron 23edo ([[23edo#Scales]]) within the lucite[23] scale''
@@ Line 155: / Line 158: @@
 {{Harmonics in equal|343|16|1|intervals=integer|columns=12}}
 {{Harmonics in equal|86|2|1|intervals=integer|columns=12|collapsed=1|title=86edo for comparison}}
+=== 34.3edo ===
+'''34.3edo''' is contained within 343edo (it is every 10th step of 343edo). It is like [[34edo]] with the [[octave shrinking|octave compressed]] by 11.51 [[cents]].
+It has a step size of 34.985{{c}}.
+It was discovered by chaseofspades513 and [[YoVariable]] on the [[Xenharmonic Alliance]] Discord server and further described by [[Gordon Wery]].
+Compared to 34edo it improves harmonics 7, 11 and 13, at the expense of 2, 3 and 5. Its mappings of multiple-of-2 and multiple-of-3 harmonics are very inconsistent, though some composers may enjoy this due to the potential to play tricks on the listener by having [[octave equivalence]] fall on a scale step one might not expect.
+Many temperaments and [[34edo#Scales|scales from 34edo]] can be used here in 34.3edo too.
+{{Harmonics in cet|34.985|intervals=integer|columns=12|title=Approximation of harmonics in 34.3edo}}
+{{Harmonics in equal|34|2|1|intervals=integer|columns=12|collapsed=1|title=34edo for comparison}}
 === Scales approximated from JI ===
@@ Line 168: / Line 184: @@
 === Other scales ===
 * [[Equiheptatonic]] (as from [[7edo]]): 49 49 49 49 49 49 49
-* [[Modmos]] of frost[6]: 60 60 30 40 93 60
 * [[49edo]]: 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7
+== Music ==
+; [[Budjarn Lambeth]]
+* [https://youtu.be/aWqdWHSk5J4 ''Odd Findings in the Caves''] (2025) - ''uses two copies of lucite[23]''