Greenwoodmic temperaments: Difference between revisions

From Xenharmonic Wiki
Jump to navigation Jump to search
← Older editNewer edit →
VisualWikitext
m Units, misc. cleanup, - redundant category
Switch to Sintel's badness, WE & CWE tunings
Line 21: Line 21:


[[Optimal tuning]]s:  
[[Optimal tuning]]s:  
* [[CTE]]: ~2 = 1200.000{{c}}, ~16/15 = 138.454{{c}}
* [[WE]]: ~2 = 1203.6786{{c}}, ~16/15 = 138.3805{{c}}
: [[error map]]: {{val| 0.000 -9.684 -17.038 +0.353 }}
: [[error map]]: {{val| +3.679 -6.374 -5.561 +7.195 }}
* [[POTE]]: ~2 = 1200.000{{c}}, ~16/15 = 137.958{{c}}
* [[CWE]]: ~2 = 1200.0000{{c}}, ~16/15 = 138.0648{{c}}
: error map: {{val| 0.000 -12.167 -14.059 -3.123 }}
: error map: {{val| 0.000 -11.631 -14.702 -2.372 }}


{{Optimal ET sequence|legend=1| 9, 17, 26, 61bc, 87bcc }}
{{Optimal ET sequence|legend=1| 9, 17, 26, 61bc, 87bcc }}


[[Badness]] (Smith): 0.089840
[[Badness]] (Sintel): 2.27


=== 11-limit ===
=== 11-limit ===
Line 38: Line 38:


Optimal tunings:  
Optimal tunings:  
* CTE: ~2 = 1200.000{{c}}, ~12/11 = 138.420{{c}}
* WE: ~2 = 1202.9415{{c}}, ~12/11 = 138.2377{{c}}
* POTE: ~2 = 1200.000{{c}}, ~12/11 = 137.900{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~12/11 = 137.9970{{c}}


{{Optimal ET sequence|legend=0| 9, 17, 26, 61bc }}
{{Optimal ET sequence|legend=0| 9, 17, 26, 61bc }}


Badness (Smith): 0.042562
Badness (Sintel): 1.41


==== 13-limit ====
==== 13-limit ====
Line 53: Line 53:


Optimal tunings:  
Optimal tunings:  
* CTE: ~2 = 1200.000{{c}}, ~12/11 = 137.455{{c}}
* WE: ~2 = 1202.4465{{c}}, ~12/11 = 137.2165{{c}}
* POTE: ~2 = 1200.000{{c}}, ~12/11 = 136.937{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~12/11 = 137.0309{{c}}


{{Optimal ET sequence|legend=0| 9, 35 }}
{{Optimal ET sequence|legend=0| 9, 35 }}


Badness (Smith): 0.049684
Badness (Sintel): 2.05


==== Secundly ====
==== Secundly ====
Line 68: Line 68:


Optimal tunings:  
Optimal tunings:  
* CTE: ~2 = 1200.000{{c}}, ~13/12 = 138.583{{c}}
* WE: ~2 = 1203.0195{{c}}, ~13/12 = 138.2642{{c}}
* POTE: ~2 = 1200.000{{c}}, ~13/12 = 137.917{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~13/12 = 138.0317{{c}}


{{Optimal ET sequence|legend=0| 9, 17, 26, 61bcf }}
{{Optimal ET sequence|legend=0| 9, 17, 26, 61bcf }}


Badness (Smith): 0.026212
Badness (Sintel): 1.08


== Semishallowtone ==
== Semishallowtone ==
Line 86: Line 86:


[[Optimal tuning]]s:  
[[Optimal tuning]]s:  
* [[CTE]]: ~189/128 = 600.000{{c}}, ~3/2 = 681.532{{c}} (~64/63 = 81.532{{c}})
* [[WE]]: ~189/128 = 603.1653{{c}}, ~3/2 = 686.6365{{c}} (~64/63 = 83.4712{{c}})
: [[error map]]: {{val| 0.000 -20.423 -1.629 -13.421 }}
: [[error map]]: {{val| +6.331 -8.988 -2.034 -0.248 }}
* [[CWE]]: ~189/128 = 600.000{{c}}, ~3/2 = 682.650{{c}} (~64/63 = 82.650{{c}})
* [[CWE]]: ~189/128 = 600.0000{{c}}, ~3/2 = 682.6498{{c}} (~64/63 = 82.6498{{c}})
: error map: {{val| 0.000 -19.305 -12.811 -16.775 }}
: error map: {{val| 0.000 -19.305 -12.811 -16.775 }}


Line 103: Line 103:


Optimal tunings:  
Optimal tunings:  
* CTE: ~189/128 = 600.000{{c}}, ~3/2 = 681.438{{c}} (~64/63 = 81.438{{c}})
* WE: ~189/128 = 603.0536{{c}}, ~3/2 = 686.6175{{c}} (~64/63 = 83.5640{{c}})
* CWE: ~189/128 = 600.000{{c}}, ~3/2 = 682.724{{c}} (~64/63 = 82.724{{c}})
* CWE: ~189/128 = 600.0000{{c}}, ~3/2 = 682.7238{{c}} (~64/63 = 82.7238{{c}})


{{Optimal ET sequence|legend=0| 14c, 44bd, 58bcde, 72bbccddee }}
{{Optimal ET sequence|legend=0| 14c, 44bd, 58bcde, 72bbccddee }}
Line 118: Line 118:


Optimal tunings:  
Optimal tunings:  
* CTE: ~91/64 = 600.000{{c}}, ~3/2 = 681.406{{c}} (~64/63 = 81.406{{c}})
* WE: ~91/64 = 601.8872{{c}}, ~3/2 = 684.4774{{c}} (~64/63 = 82.5902{{c}})
* CWE: ~91/64 = 600.000{{c}}, ~3/2 = 682.168{{c}} (~64/63 = 82.168{{c}})
* CWE: ~91/64 = 600.0000{{c}}, ~3/2 = 682.1676{{c}} (~64/63 = 82.1676{{c}})


{{Optimal ET sequence|legend=0| 14c, 30b }}
{{Optimal ET sequence|legend=0| 14c, 30b }}

Revision as of 11:36, 4 July 2026

This is a list showing technical temperament data. For an explanation of what information is shown here, you may look at the technical data guide for regular temperaments.

This is a collection of rank-2 greenwoodmic temperaments, which temper out 405/392, the greenwoodma.

Temperaments discussed elsewhere are

Considered below are secund and semishallowtone.

Secund

Subgroup: 2.3.5.7

Comma list: 405/392, 525/512

Mapping: [⟨1 1 3 2], ⟨0 5 -6 7]]

mapping generators: ~2, ~16/15

Optimal tunings:

  • WE: ~2 = 1203.6786 ¢, ~16/15 = 138.3805 ¢
error map: ⟨+3.679 -6.374 -5.561 +7.195]
  • CWE: ~2 = 1200.0000 ¢, ~16/15 = 138.0648 ¢
error map: ⟨0.000 -11.631 -14.702 -2.372]

Optimal ET sequence: 9, 17, 26, 61bc, 87bcc

Badness (Sintel): 2.27

11-limit

Subgroup: 2.3.5.7.11

Comma list: 45/44, 99/98, 385/384

Mapping: [⟨1 1 3 2 3], ⟨0 5 -6 7 4]]

Optimal tunings:

  • WE: ~2 = 1202.9415 ¢, ~12/11 = 138.2377 ¢
  • CWE: ~2 = 1200.0000 ¢, ~12/11 = 137.9970 ¢

Optimal ET sequence: 9, 17, 26, 61bc

Badness (Sintel): 1.41

13-limit

Subgroup: 2.3.5.7.11.13

Comma list: 27/26, 45/44, 99/98, 385/384

Mapping: [⟨1 1 3 2 3 2], ⟨0 5 -6 7 4 15]]

Optimal tunings:

  • WE: ~2 = 1202.4465 ¢, ~12/11 = 137.2165 ¢
  • CWE: ~2 = 1200.0000 ¢, ~12/11 = 137.0309 ¢

Optimal ET sequence: 9, 35

Badness (Sintel): 2.05

Secundly

Subgroup: 2.3.5.7.11.13

Comma list: 45/44, 65/64, 78/77, 99/98

Mapping: [⟨1 1 3 2 3 3], ⟨0 5 -6 7 4 6]]

Optimal tunings:

  • WE: ~2 = 1203.0195 ¢, ~13/12 = 138.2642 ¢
  • CWE: ~2 = 1200.0000 ¢, ~13/12 = 138.0317 ¢

Optimal ET sequence: 9, 17, 26, 61bcf

Badness (Sintel): 1.08

Semishallowtone

See also: Shallowtone

Subgroup: 2.3.5.7

Comma list: 405/392, 35721/32768

Mapping: [⟨2 0 36 15], ⟨0 1 -10 -3]]

mapping generators: ~189/128, ~3

Optimal tunings:

  • WE: ~189/128 = 603.1653 ¢, ~3/2 = 686.6365 ¢ (~64/63 = 83.4712 ¢)
error map: ⟨+6.331 -8.988 -2.034 -0.248]
  • CWE: ~189/128 = 600.0000 ¢, ~3/2 = 682.6498 ¢ (~64/63 = 82.6498 ¢)
error map: ⟨0.000 -19.305 -12.811 -16.775]

Optimal ET sequence: 14c, 44bd, 58bcd

Badness (Sintel): 8.42

11-limit

Subgroup: 2.3.5.7.11

Comma list: 45/44, 99/98, 35721/32768

Mapping: [⟨2 0 36 15 32], ⟨0 1 -10 -3 -8]]

Optimal tunings:

  • WE: ~189/128 = 603.0536 ¢, ~3/2 = 686.6175 ¢ (~64/63 = 83.5640 ¢)
  • CWE: ~189/128 = 600.0000 ¢, ~3/2 = 682.7238 ¢ (~64/63 = 82.7238 ¢)

Optimal ET sequence: 14c, 44bd, 58bcde, 72bbccddee

Badness (Sintel): 4.15

13-limit

Subgroup: 2.3.5.7.11.13

Comma list: 27/26, 45/44, 99/98, 35721/32768

Mapping: [⟨2 0 36 15 32 -2], ⟨0 1 -10 -3 -8 3]]

Optimal tunings:

  • WE: ~91/64 = 601.8872 ¢, ~3/2 = 684.4774 ¢ (~64/63 = 82.5902 ¢)
  • CWE: ~91/64 = 600.0000 ¢, ~3/2 = 682.1676 ¢ (~64/63 = 82.1676 ¢)

Optimal ET sequence: 14c, 30b

Badness (Sintel): 4.38

Retrieved from "https://en.xen.wiki/index.php?title=Greenwoodmic_temperaments&oldid=233251"