Cthon5m: Difference between revisions

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'''~~Sequar5m~~''' (in [[aberrismic theory|aberrismic]] systematic naming) is the [[~~diregular scale|diregular~~]] 5L5m4s scale pattern '''LmLsmLsmLmsLms''', so named because it is generated by a generator of the [[semiquartal]] MOS and the m step is the offset in its generator-offset structure.

'''Cthon5m''' (in [[aberrismic theory|aberrismic]] systematic naming) is the [[even-regular]] 5L5m4s scale pattern '''LmLsmLsmLmsLms''', so named because it is generated by a generator of the [[semiquartal]] MOS and the m step is the offset in its generator-offset structure.

~~Sequar5m~~ is comprised of two interleaved [[nicetone]]/Zarlino scales of opposite chirality. In the JI preimage below these are 5-limit Zarlino scales.

Cthon5m is comprised of two interleaved [[nicetone]]/Zarlino scales of opposite chirality. In the JI preimage below these are 5-limit Zarlino scales.

== Temperaments ==

=== ~~Cata~~ (2.3.5.13[34&53]) ===

=== 2.3.5.13 Island (2.3.5.13[34&53&58]) ===

~~Sequar5m~~ has the following 2.3.5.13 interpretation in the [[34edo]] (4:2:1) ~~and~~ [[53edo]] (6:3:2) tunings:

Cthon5m has the following 2.3.5.13 interpretation in the [[34edo]] (4:2:1), [[53edo]] (6:3:2), and [[58edo]] (7:3:2) tunings:

13/12

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2/1

~~(Sequar5m hence admits a [[Cata]] temperament interpretation~~.)

Here L = ~13/12, m = ~26/25~27/26, and s = ~40/39.

~~Sequar5m~~ is comparable to the MOS Kleismic[15] in size, but it's "fifthier" than Kleismic[15] and has one fewer note:

(Hence Cthon5m admits an Island (2.3.5.13[ [[676/675]] ] temperament) interpretation.)

* Kleismic[15] has 9 3/2's whereas ~~sequar4s~~ has 10 3/2's.

* 3/2 chains in Kleismic[15] only have at most 3 notes whereas ~~sequar4s~~ interpreted in Kleismic has 3/2 chains with 3 and 4 notes.

As a 2.3.5.13 subgroup scale, cthon5m is comparable to the MOS Kleismic[15] in size, but it's "fifthier" than Kleismic[15] and has one fewer note:

* Kleismic[15] has 9 3/2's whereas cthon5m has 10 3/2's.

* 3/2 chains in Kleismic[15] only have at most 3 notes whereas cthon5m interpreted in Kleismic has 3/2 chains with 3 and 4 notes.

==== Kleismic ====

Kleismic (properly [[Cata]]) tempering corresponds to using Island tempering and then letting L = 2m. This makes Kleismic-tempered cthon5m a subset of a permutation (mmmmmsmmmsmmmmsmmms) of the Kleismic[19] MOS.

== External links ==

* [https://sw3.lumipakkanen.com/scale/~~C7mHFdyHd~~ 34edo (4:2:1) tuning]

* [https://sw3.lumipakkanen.com/scale/Udm0Ix3Kl 34edo (4:2:1) tuning]

* [https://sw3.lumipakkanen.com/scale/~~C7mZtkgOf~~ 53edo (6:3:2) tuning]

* [https://sw3.lumipakkanen.com/scale/UdmzxDxtu 53edo (6:3:2) tuning]

* [https://sw3.lumipakkanen.com/scale/~~C7mTDZFH9~~ 87edo (10:5:3) tuning]

* [https://sw3.lumipakkanen.com/scale/Udmr6q8k8 58edo (7:3:2) tuning]

* [https://sw3.lumipakkanen.com/scale/UdmMBly3k 87edo (10:5:3) tuning]

[[Category:Aberrismic theory]]

[[Category:Rank-3 scales]]

@@ Line 1: / Line 1: @@
-'''Sequar5m''' (in [[aberrismic theory|aberrismic]] systematic naming) is the [[diregular scale|diregular]] 5L5m4s scale pattern '''LmLsmLsmLmsLms''', so named because it is generated by a generator of the [[semiquartal]] MOS and the m step is the offset in its generator-offset structure.
+'''Cthon5m''' (in [[aberrismic theory|aberrismic]] systematic naming) is the [[even-regular]] 5L5m4s scale pattern '''LmLsmLsmLmsLms''', so named because it is generated by a generator of the [[semiquartal]] MOS and the m step is the offset in its generator-offset structure.
-Sequar5m is comprised of two interleaved [[nicetone]]/Zarlino scales of opposite chirality. In the JI preimage below these are 5-limit Zarlino scales.
+Cthon5m is comprised of two interleaved [[nicetone]]/Zarlino scales of opposite chirality. In the JI preimage below these are 5-limit Zarlino scales.
 == Temperaments ==
-=== Cata (2.3.5.13[34&53]) ===
+=== 2.3.5.13 Island (2.3.5.13[34&53&58]) ===
-Sequar5m has the following 2.3.5.13 interpretation in the [[34edo]] (4:2:1) and [[53edo]] (6:3:2) tunings:
+Cthon5m has the following 2.3.5.13 interpretation in the [[34edo]] (4:2:1), [[53edo]] (6:3:2), and [[58edo]] (7:3:2) tunings:
 /12
@@ Line 22: / Line 22: @@
 /1
-(Sequar5m hence admits a [[Cata]] temperament interpretation.)
+Here L = ~13/12, m = ~26/25~27/26, and s = ~40/39.
-Sequar5m is comparable to the MOS Kleismic[15] in size, but it's "fifthier" than Kleismic[15] and has one fewer note:
+(Hence Cthon5m admits an Island (2.3.5.13[ [[676/675]] ] temperament) interpretation.)
-* Kleismic[15] has 9 3/2's whereas sequar4s has 10 3/2's.
-* 3/2 chains in Kleismic[15] only have at most 3 notes whereas sequar4s interpreted in Kleismic has 3/2 chains with 3 and 4 notes.
+As a 2.3.5.13 subgroup scale, cthon5m is comparable to the MOS Kleismic[15] in size, but it's "fifthier" than Kleismic[15] and has one fewer note:
+* Kleismic[15] has 9 3/2's whereas cthon5m has 10 3/2's.
+* 3/2 chains in Kleismic[15] only have at most 3 notes whereas cthon5m interpreted in Kleismic has 3/2 chains with 3 and 4 notes.
+==== Kleismic ====
+Kleismic (properly [[Cata]]) tempering corresponds to using Island tempering and then letting L = 2m. This makes Kleismic-tempered cthon5m a subset of a permutation (mmmmmsmmmsmmmmsmmms) of the Kleismic[19] MOS.
 == External links ==
-* [https://sw3.lumipakkanen.com/scale/C7mHFdyHd 34edo (4:2:1) tuning]
+* [https://sw3.lumipakkanen.com/scale/Udm0Ix3Kl 34edo (4:2:1) tuning]
-* [https://sw3.lumipakkanen.com/scale/C7mZtkgOf 53edo (6:3:2) tuning]
+* [https://sw3.lumipakkanen.com/scale/UdmzxDxtu 53edo (6:3:2) tuning]
-* [https://sw3.lumipakkanen.com/scale/C7mTDZFH9 87edo (10:5:3) tuning]
+* [https://sw3.lumipakkanen.com/scale/Udmr6q8k8 58edo (7:3:2) tuning]
+* [https://sw3.lumipakkanen.com/scale/UdmMBly3k 87edo (10:5:3) tuning]
 [[Category:Aberrismic theory]]
 [[Category:Rank-3 scales]]