343edo: Difference between revisions

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343edo includes every 49edo scale (see [[49edo#Scales]]).

~~''Scales listed below are rotated to modes with lots of consonances.''~~

==== Lucite[23] ====

'''Lucite[23]''' is a 23-tone [[MOS scale]] discovered by [[Gordon Wery]] in October 2025:

==== ~~Frost~~[23] ====

A 23-tone [[MOS scale]] discovered by [[Gordon Wery]] in October 2025:

* 13 17 13 17 13 17 13 17 13 17 13 17 13 17 13 17 13 17 13 17 13 17 13

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It is [[generator|generated]] by 30\343 (104.956{{c}}).

~~Frost~~[23] can be generalised into a 17-limit [[regular temperament]] called [[User:BudjarnLambeth/Regular temperament interpretation of ~~frost23~~|~~frost~~ temperament]].

Lucite[23] can be generalised into a 17-limit [[regular temperament]] called '''[[User:BudjarnLambeth/Regular temperament interpretation of lucite23|lucite temperament]]'''.

; Naming

Wery named it "~~frost~~" because:

Lucite is another name for acrylic glass.

* Musically, it sounds like frosted glass (perhaps to do with the [[timbre]]/~~[[partial]]s~~ of struck glass)

* It is close to [[ripple]][23], but turned inside out, ~~so just as ice~~ is ~~water in~~ an ~~altered state~~, ~~frost~~ is ~~ripple~~ in ~~an altered state~~

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

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 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

* ~~Frost~~[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 99edo ([[99edo#Scales]]) within the amity[99] scale''

* ~~Frost~~[34]: 13 4 13 13 4 13 13 4 13 13 4 13 13 13 4 13 13 4 13 13 4 13 13 4 13 13 4 13 13 4 13 13 4 13

* 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''

* Lucite[34]: 13 4 13 13 4 13 13 4 13 13 4 13 13 13 4 13 13 4 13 13 4 13 13 4 13 13 4 13 13 4 13 13 4 13

** ''Try approximating scales fron 34edo ([[34edo#Scales]]) within the lucite[34] scale''

=== 343ed16 ===

''343ed16'' is contained within 343edo (it is every 4th step of 343edo). It is like [[86edo]] with the [[octave stretching|octave stretched]] by 3.5 [[cents]].

'''343ed16''' is contained within 343edo (it is every 4th step of 343edo). It is like [[86edo]] with the [[octave stretching|octave stretched]] by 3.5 [[cents]].

It is quite similar to [[136edt]].

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

* [[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 102: / Line 102: @@
 edo includes every 49edo scale (see [[49edo#Scales]]).
-''Scales listed below are rotated to modes with lots of consonances.''
+==== Lucite[23] ====
+'''Lucite[23]''' is a 23-tone [[MOS scale]] discovered by [[Gordon Wery]] in October 2025:
-==== Frost[23] ====
-A 23-tone [[MOS scale]] discovered by [[Gordon Wery]] in October 2025:
 * 13 17 13 17 13 17 13 17 13 17 13 17 13 17 13 17 13 17 13 17 13 17 13
@@ Line 119: / Line 117: @@
 It is [[generator|generated]] by 30\343 (104.956{{c}}).
-Frost[23] can be generalised into a 17-limit [[regular temperament]] called [[User:BudjarnLambeth/Regular temperament interpretation of frost23|frost temperament]].
+Lucite[23] can be generalised into a 17-limit [[regular temperament]] called '''[[User:BudjarnLambeth/Regular temperament interpretation of lucite23|lucite temperament]]'''.
 ; Naming
-Wery named it "frost" because:
+Lucite is another name for acrylic glass.
-* Musically, it sounds like frosted glass (perhaps to do with the [[timbre]]/[[partial]]s of struck glass)
-* It is close to [[ripple]][23], but turned inside out, so just as ice is water in an altered state, frost is ripple in an altered state
+Wery named the temperament "lucite" because musically, it sounds like frosted glass (perhaps to do with the timbre/partials of struck glass).
+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 134: / 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 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
-* Frost[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 99edo ([[99edo#Scales]]) within the amity[99] scale''
-* Frost[34]: 13 4 13 13 4 13 13 4 13 13 4 13 13 13 4 13 13 4 13 13 4 13 13 4 13 13 4 13 13 4 13 13 4 13
+* 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''
+* Lucite[34]: 13 4 13 13 4 13 13 4 13 13 4 13 13 13 4 13 13 4 13 13 4 13 13 4 13 13 4 13 13 4 13 13 4 13
+** ''Try approximating scales fron 34edo ([[34edo#Scales]]) within the lucite[34] scale''
 === 343ed16 ===
-''343ed16'' is contained within 343edo (it is every 4th step of 343edo). It is like [[86edo]] with the [[octave stretching|octave stretched]] by 3.5 [[cents]].
+'''343ed16''' is contained within 343edo (it is every 4th step of 343edo). It is like [[86edo]] with the [[octave stretching|octave stretched]] by 3.5 [[cents]].
 It is quite similar to [[136edt]].
@@ Line 148: / 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 162: / Line 185: @@
 * [[Equiheptatonic]] (as from [[7edo]]): 49 49 49 49 49 49 49
 * [[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]''