343edo: Difference between revisions

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** Octave size: 1199.888{{c}}

** TE error: 0.461{{c}}/octave

{{Harmonics in cet|3.498|intervals=odd|title=Odd harmonics in TE-tuned 343cf}}

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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:

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

; Properties

It is very similar to [[23edo]] and can be used as a [[well temperament]] of 23edo.

In his post on Discord describing it, Wery said of the scale:

"''Basically a more complicated version of 23edo, centered around a more minor (less neutral) anti-diatonic scale.''

''This scale has a sort of glassy quality, ample neutral seconds, and two sets of dual fifths--a true dual dual fifth scale.''"

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

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

; Naming

Lucite is another name for acrylic glass.

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

=== MOS scales ===

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 ===

* Amity[7]: 52 52 45 52 45 52 45

* Amity[11]: 45 7 45 45 7 45 7 45 45 7 42

Line 113:

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

** ''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''

* 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''

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

=== 343ed16 ===

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

'''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]].

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

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

Compared to 86edo it improves harmonics 3, 5, 7 and 11. Its mappings of multiple-of-2 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 scales from 86edo can be used here in 343ed16 too.

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

It is ~~very similar to~~ [[~~23edo~~]] ~~and can be used as a~~ [[~~well temperament~~]] ~~of 23edo~~.

=== 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]].

~~In his post on Discord describing it, Wery said~~ of ~~the scale:~~

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

~~"''Basically a more complicated version of 23edo, centered around a more minor (less neutral) anti-diatonic scale~~.''

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

~~''This scale has a sort~~ of ~~glassy quality, ample neutral seconds~~, and ~~two sets~~ of ~~dual fifths~~--a ~~true dual dual fifth~~ scale.~~''"~~

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.

~~It is~~ [[~~generator~~|~~generated~~]] ~~by 30\343 (104~~.~~956~~{{c}}).

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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* [[36afdo]]: 11 10 9 10 9 10 9 9 8 9 8 9 8 8 8 8 7 8 7 8 7 7 7 7 14 13 13 12 12 12 12 11 11 11 11 10

* [[72afdo]]: 5 6 5 5 4 5 5 5 5 4 5 5 4 5 4 5 4 4 5 4 4 4 5 4 4 4 4 4 4 4 4 4 4 3 4 4 4 3 4 4 3 4 4 3 4 3 4 3 7 7 6 7 6 7 6 6 6 6 6 6 6 6 6 5 6 5 6 5 6 5 5 5

~~=== 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]].~~

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

Compared to 86edo it improves harmonics 3, 5, 7 and 11. Its mappings of multiple-of-2 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 scales from 86edo can be used here in 343ed16 too.~~

~~{{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}}~~

=== Other scales ===

* [[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 97: / Line 97: @@
 ** Octave size: 1199.888{{c}}
 ** TE error: 0.461{{c}}/octave
 {{Harmonics in cet|3.498|intervals=odd|title=Odd harmonics in TE-tuned 343cf}}
@@ Line 103: / 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:
+* 13 17 13 17 13 17 13 17 13 17 13 17 13 17 13 17 13 17 13 17 13 17 13
+; Properties
+It is very similar to [[23edo]] and can be used as a [[well temperament]] of 23edo.
+In his post on Discord describing it, Wery said of the scale:
+"''Basically a more complicated version of 23edo, centered around a more minor (less neutral) anti-diatonic scale.''
+''This scale has a sort of glassy quality, ample neutral seconds, and two sets of dual fifths--a true dual dual fifth scale.''"
+It is [[generator|generated]] by 30\343 (104.956{{c}}).
+Lucite[23] can be generalised into a 17-limit [[regular temperament]] called '''[[User:BudjarnLambeth/Regular temperament interpretation of lucite23|lucite temperament]]'''.
+; Naming
+Lucite is another name for acrylic glass.
+Wery named the temperament "lucite" because musically, it sounds like frosted glass (perhaps to do with the timbre/partials of struck glass).
-=== MOS scales ===
+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 ===
 * Amity[7]: 52 52 45 52 45 52 45
 * Amity[11]: 45 7 45 45 7 45 7 45 45 7 42
@@ Line 113: / 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
+** ''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''
+* 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''
-==== ''Frost[23]'' ====
+=== 343ed16 ===
-A 23-tone [[MOS scale]] discovered by [[Gordon Wery]] in October 2025:
+'''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]].
-* 13 17 13 17 13 17 13 17 13 17 13 17 13 17 13 17 13 17 13 17 13 17 13
+It is quite similar to [[136edt]].
+Compared to 86edo it improves harmonics 3, 5, 7 and 11. Its mappings of multiple-of-2 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 scales from 86edo can be used here in 343ed16 too.
+{{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}}
-It is very similar to [[23edo]] and can be used as a [[well temperament]] of 23edo.
+=== 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]].
-In his post on Discord describing it, Wery said of the scale:
+It has a step size of 34.985{{c}}.
-"''Basically a more complicated version of 23edo, centered around a more minor (less neutral) anti-diatonic scale.''
+It was discovered by chaseofspades513 and [[YoVariable]] on the [[Xenharmonic Alliance]] Discord server and further described by [[Gordon Wery]].
-''This scale has a sort of glassy quality, ample neutral seconds, and two sets of dual fifths--a true dual dual fifth scale.''"
+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.
-It is [[generator|generated]] by 30\343 (104.956{{c}}).
+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 138: / Line 181: @@
 * [[36afdo]]: 11 10 9 10 9 10 9 9 8 9 8 9 8 8 8 8 7 8 7 8 7 7 7 7 14 13 13 12 12 12 12 11 11 11 11 10
 * [[72afdo]]: 5 6 5 5 4 5 5 5 5 4 5 5 4 5 4 5 4 4 5 4 4 4 5 4 4 4 4 4 4 4 4 4 4 3 4 4 4 3 4 4 3 4 4 3 4 3 4 3 7 7 6 7 6 7 6 6 6 6 6 6 6 6 6 5 6 5 6 5 6 5 5 5
-=== 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]].
-It is quite similar to [[136edt]].
-Compared to 86edo it improves harmonics 3, 5, 7 and 11. Its mappings of multiple-of-2 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 scales from 86edo can be used here in 343ed16 too.
-{{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}}
 === Other scales ===
 * [[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]''