Xenharmonic Wiki

Semicomma family: Difference between revisions

← Older editNewer edit →
VisualWikitext
Xenwolf (talk | contribs)
autopatrolled, Bureaucrats, confirmaccount-notify, Interface administrators, Sysops
8,705 edits
recat
Xenllium (talk | contribs)
autopatrolled, emailconfirmed
4,516 edits
No edit summary
Line 19: Line 19:
{{Val list|legend=1| 22, 31, 53, 190, 243, 296, 645c }}
{{Val list|legend=1| 22, 31, 53, 190, 243, 296, 645c }}


[[Badness]]: 0.0408
[[Badness]]: 0.040807


== Seven limit children ==
== Seven limit children ==
The second comma of the [[Normal lists #Normal interval list|normal comma list]] defines which 7-limit family member we are looking at. Adding 65536/65625 leads to orwell, but we could also add
The second comma of the [[Normal lists #Normal interval list|normal comma list]] defines which 7-limit family member we are looking at. Adding 65536/65625 leads to orwell, but we could also add
* 1029/1024, leading to the 31&159 temperament with wedgie {{multival| 21 -9 -7 -63 -70 9 }}, or  
* 1029/1024, leading to the 31&159 temperament (triwell) with wedgie {{multival| 21 -9 -7 -63 -70 9 }}, or  
* 67528125/67108864, giving the 31&243 temperament with wedgie {{multival| 28 -12 1 -84 -77 36 }}, or  
* 2401/2400, giving the 31&243 temperament with wedgie {{multival| 28 -12 1 -84 -77 36 }}, or  
* 4375/4374, giving the 53&243 temperament with wedgie {{multival| 7 -3 61 -21 77 150 }}.
* 4375/4374, giving the 53&243 temperament (sabric) with wedgie {{multival| 7 -3 61 -21 77 150 }}.


= Orwell =
= Orwell =
Line 61: Line 61:
[[Algebraic generator]]: Sabra3, the real root of 12''x<sup>3</sup> - 7''x'' - 48.
[[Algebraic generator]]: Sabra3, the real root of 12''x<sup>3</sup> - 7''x'' - 48.


{{Val list|legend=1| 22, 31, 53, 84, 137, 221d, 358d }}
{{Val list|legend=1| 9, 22, 31, 53, 84, 137, 221d, 358d }}


[[Badness]]: 0.0207
[[Badness]]: 0.020735


== 11-limit ==
== 11-limit ==
Subgroup: 2.3.5.7.11
Subgroup: 2.3.5.7.11


Line 85: Line 84:
* strict range: [270.968, 272.727]
* strict range: [270.968, 272.727]


{{Val list|legend=1| 22, 31, 53, 84e }}
Vals: {{Val list| 9, 22, 31, 53, 84e }}


Badness: 0.0152
Badness: 0.015231


=== 13-limit ===
=== 13-limit ===
Subgroup: 2.3.5.7.11.13
Subgroup: 2.3.5.7.11.13


Line 104: Line 102:
* strict range: [270.968, 271.698]
* strict range: [270.968, 271.698]


{{Val list|legend=1| 22, 31, 53, 84e, 137e }}
Vals: {{Val list| 22, 31, 53, 84e, 137e }}


Badness: 0.0197
Badness: 0.019718


=== Blair ===
=== Blair ===
Subgroup: 2.3.5.7.11.13
Subgroup: 2.3.5.7.11.13


Line 118: Line 115:
POTE generator: ~7/6 = 271.301
POTE generator: ~7/6 = 271.301


Tuning ranges:  
Vals: {{Val list| 9, 22, 31f }}
* valid range: []
* nice range: [265.357, 289.210]
* strict range: []
 
{{Val list|legend=1| 9, 22, 31f }}


Badness: 0.0231
Badness: 0.023086


=== Winston ===
=== Winston ===
Subgroup: 2.3.5.7.11.13
Subgroup: 2.3.5.7.11.13


Line 142: Line 133:
* strict range: [270.968, 272.727]
* strict range: [270.968, 272.727]


{{Val list|legend=1| 22f, 31 }}
Vals: {{Val list| 22f, 31 }}


Badness: 0.0199
Badness: 0.019931


=== Doublethink ===
=== Doublethink ===
Subgroup: 2.3.5.7.11.13
Subgroup: 2.3.5.7.11.13


Line 161: Line 151:
* strict range: [135.484, 136.364]
* strict range: [135.484, 136.364]


{{Val list|legend=1| 9, 35, 44, 53, 62, 115ef, 168ef }}
Vals: {{Val list| 9, 35bd, 44, 53, 62, 115ef, 168eef }}


Badness: 0.0271
Badness: 0.027120


== Newspeak ==
== Newspeak ==
Subgroup: 2.3.5.7.11
Subgroup: 2.3.5.7.11


Line 180: Line 169:
* strict range: [270.968, 271.698]
* strict range: [270.968, 271.698]


{{Val list|legend=1| 31, 84, 115, 376b, 491bd, 606bde }}
Vals: {{Val list| 31, 84, 115, 376b, 491bd, 606bde }}


Badness: 0.0314
Badness: 0.031438


== Borwell ==
== Borwell ==
Subgroup: 2.3.5.7.11
Subgroup: 2.3.5.7.11


Line 194: Line 182:
POTE generator: ~55/36 = 735.752
POTE generator: ~55/36 = 735.752


{{Val list|legend=1| 31, 106, 137, 442bd }}
Vals: {{Val list| 31, 106, 137, 442bd }}


Badness: 0.0384
Badness: 0.038377


= Triwell =
= Triwell =
Subgroup: 2.3.5.7
Subgroup: 2.3.5.7


Line 212: Line 199:
{{Val list|legend=1| 31, 97, 128, 159, 190 }}
{{Val list|legend=1| 31, 97, 128, 159, 190 }}


[[Badness]]: 0.0806
[[Badness]]: 0.080575


== 11-limit ==
== 11-limit ==
Subgroup: 2.3.5.7.11
Subgroup: 2.3.5.7.11


Line 224: Line 210:
POTE generator: ~448/375 = 309.471
POTE generator: ~448/375 = 309.471


{{Val list|legend=1| 31, 97, 128, 159, 190 }}
Vals: {{Val list| 31, 97, 128, 159, 190 }}
 
Badness: 0.029807
 
= Sabric =
The ''sabric'' temperament (53&amp;190, named by [[User:Xenllium]]) tempers out the [[4375/4374|ragisma]], 4375/4374. It is so named because it is closely related to the '''Sabra2 tuning''' (generator: 271.607278 cents).
 
Subgroup: 2.3.5.7
 
[[Comma list]]: 4375/4374, 2109375/2097152
 
[[Mapping]]: [{{val| 1 0 3 -11 }}, {{val| 0 7 -3 61 }}]
 
{{multival|legend=1| 7 -3 61 -21 77 150 }}
 
[[POTE generator]]: ~75/64 = 271.607
 
{{Val list|legend=1| 53, 137d, 190, 243 }}


Badness: 0.0298
[[Badness]]: 0.088355


[[Category:Regular temperament theory]]
[[Category:Regular temperament theory]]
Retrieved from "https://en.xen.wiki/w/Semicomma_family"