4L 3s/Temperaments: Difference between revisions

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== Myna (27&31) ==
== Myna ==
Subgroup: 2.3.5.7
 
[[Comma list]]: 126/125, 1728/1715
 
[[Mapping]]: [{{val| 1 9 9 8 }}, {{val| 0 -10 -9 -7 }}]
 
Mapping generators: ~2, ~5/3
 
{{Multival|legend=1| 10 9 7 -9 -17 -9 }}
 
[[POTE generator]]: ~6/5 = 310.146
 
[[Minimax tuning]]:
* 7- and [[9-odd-limit]]
: [{{monzo| 1 0 0 0 }}, {{monzo| 0 1 0 0 }}, {{monzo| 9/10 9/10 0 0 }}, {{monzo| 17/10 7/10 0 0 }}]
: [[Eigenmonzo]]s: 2, 3
 
{{Val list|legend=1| 27, 31, 58, 89 }}
 
[[Badness]]: 0.0270
 
== Kleismic ==
== Kleismic ==
Subgroup: 2.3.5
Subgroup: 2.3.5
Line 16: Line 37:
{{Val list|legend=1| 15, 19, 34, 53, 458, 511c, …, 882c }}
{{Val list|legend=1| 15, 19, 34, 53, 458, 511c, …, 882c }}


== Orgone (15&11, 2.7.11) ==
== Orgone ==
{{main|Orgone}}
{{main|Orgone}}
Commas:65536/65219
Commas:65536/65219
Line 28: Line 49:
EDOs: 7, 11, 15, 26, 37, 63, 89, 115, 141, 167, 308, 475bc, 783bc
EDOs: 7, 11, 15, 26, 37, 63, 89, 115, 141, 167, 308, 475bc, 783bc


== Sixix (18&25) ==
== Dual-3 Sixix ==
[[Sixix]] can be viewed as a [[dual-fifth temperaments|dual-fifth temperament]], i.e. a temperament on the 2.3+.3-.5 "subgroup" (3+ = sharp 3, 3- = flat 3):
Subgroup: 2.3⁻.9.5
* It has both a sharp fifth and a flat fifth but no near-just 3/2.  
 
* Combining the sharp fifth and the flat fifth yields a good approximation of 9/8; two 9/8's make a 5/4, so it tempers out 81/80 in the underlying 2.9.5 subgroup.
Comma list: 81/80, {{monzo| 2 -3 0 1 }}
* The chroma of sixix[7] is the difference between the sharp fifth and the flat fifth, and functions much like a(n untempered) comma in sixix harmony, giving two slightly different flavors of fifths, minor thirds, major thirds, etc, much like in [[porcupine]] harmony. Tempering out this comma leads to [[7edo]].
 
Mapping: [{{val| 1 2 4 4 }}, {{val| 0 -2 -3 -6 }}]
 
2.9.5 POTE generator: 335.8409
 
{{Val list|legend=1| 18, 25, 43 }}
== Sixix ==
 
Subgroup: 2.3.5
 
Comma list: 3125/2916
 
Mapping: [{{val| 1 3 4 }}, {{val| 0 -5 -6 }}]
 
POTE generator: ~6/5 = 338.365
 
{{Val list|legend=1| 7, 25, 32 }}
 
Badness: 0.1531
 
[[Category:Smitonic|T]]
[[Category:Smitonic|T]]
[[Category:Temperament]]
[[Category:Temperament]]

Revision as of 22:42, 19 April 2021

Myna

Subgroup: 2.3.5.7

Comma list: 126/125, 1728/1715

Mapping: [⟨1 9 9 8], ⟨0 -10 -9 -7]]

Mapping generators: ~2, ~5/3

Wedgie: ⟨⟨ 10 9 7 -9 -17 -9 ]]

POTE generator: ~6/5 = 310.146

Minimax tuning:

[[1 0 0 0⟩, [0 1 0 0⟩, [9/10 9/10 0 0⟩, [17/10 7/10 0 0⟩]
Eigenmonzos: 2, 3

Template:Val list

Badness: 0.0270

Kleismic

Subgroup: 2.3.5

Comma list: 15625/15552

Mapping: [⟨1 0 1], ⟨0 6 5]]

POTE generator: ~6/5 = 317.007

Tuning ranges:

  • valid range: [300.000, 327.273] (4 to 11b)
  • nice range: [315.641, 317.263]
  • strict range: [315.641, 317.263]

Template:Val list

Orgone

Main article: Orgone

Commas:65536/65219

Subgroup: 2.7.11

POTE generator: ~77/64 = 323.372

Sval map: [<1 2 4|, <0 3 -2|]

EDOs: 7, 11, 15, 26, 37, 63, 89, 115, 141, 167, 308, 475bc, 783bc

Dual-3 Sixix

Subgroup: 2.3⁻.9.5

Comma list: 81/80, [2 -3 0 1⟩

Mapping: [⟨1 2 4 4], ⟨0 -2 -3 -6]]

2.9.5 POTE generator: 335.8409

Template:Val list

Sixix

Subgroup: 2.3.5

Comma list: 3125/2916

Mapping: [⟨1 3 4], ⟨0 -5 -6]]

POTE generator: ~6/5 = 338.365

Template:Val list

Badness: 0.1531

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