User:Hkm/Fifive family: Difference between revisions

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Created page with "{{Technical data page}} The '''fifive family''' of temperaments tempers out the fifive comma ({{monzo|legend=1| -1 -14 10 }}, ratio: 9765625/9565938). The name ''fifive'' was given by Petr Pařízek in 2011 for it splits the perfect fifth in five.<ref>[https://yahootuninggroupsultimatebackup.github.io/tuning/topicId_101780.html Yahoo! Tuning Group | ''Suggested names for the unclasified temperaments'']</ref>..."
 
Hkm (talk | contribs)
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{{Technical data page}}
The '''fifive family''' of [[regular temperament|temperaments]] [[tempering out|tempers out]] the [[fifive comma]] ({{monzo|legend=1| -1 -14 10 }}, [[ratio]]: 9765625/9565938).
The name ''fifive'' was given by [[Petr Pařízek]] in 2011 for it splits the [[3/2|perfect fifth]] in five.<ref>[https://yahootuninggroupsultimatebackup.github.io/tuning/topicId_101780.html Yahoo! Tuning Group | ''Suggested names for the unclasified temperaments'']</ref>
Considered below are crepuscular, fifives, and fourfives.
== Fifive ==
== Fifive ==
[[Subgroup]]: 2.3.5
[[Subgroup]]: 2.3.5
Line 25: Line 18:
* Dirichlet: 4.828
* Dirichlet: 4.828


=== 2.3.5.13 subgroup ===
{{databox
| 141c<0 5 '7 13:6]
| {{normal|
 
Subgroup: 2.3.5.13
Subgroup: 2.3.5.13


Line 44: Line 40:
* Dirichlet: 0.800
* Dirichlet: 0.800


=== 2.3.5.13.17 subgroup ===
{{databox
| 141c<0 5 '7 13:6 17:'5]
| {{normal|
 
Subgroup: 2.3.5.13.17
Subgroup: 2.3.5.13.17


Line 63: Line 62:
* Dirichlet: 0.488
* Dirichlet: 0.488


== Crepuscular ==
}}
}}
 
}}
}}
 
{{databox
| 140c<0 5 '7 7]
| {{normal|
 
{{See also| Jubilismic clan #Crepuscular }}
{{See also| Jubilismic clan #Crepuscular }}


Line 80: Line 88:
[[Badness]]: 0.086669
[[Badness]]: 0.086669


=== 11-limit ===
{{databox
| 141c<0 5 '7 7 4]
| {{normal|
 
Subgroup: 2.3.5.7.11
Subgroup: 2.3.5.7.11


Line 93: Line 104:
Badness: 0.040758
Badness: 0.040758


=== 13-limit ===
{{databox
| 141c<0 5 '7 7 4 6]
| {{normal|
 
Subgroup: 2.3.5.7.11.13
Subgroup: 2.3.5.7.11.13


Line 106: Line 120:
Badness: 0.024368
Badness: 0.024368


=== 17-limit ===
Subgroup: 2.3.5.7.11.13.17
Comma list: 50/49, 78/77, 85/84, 99/98, 144/143
Mapping: {{mapping| 2 2 3 4 6 6 7 | 0 5 7 7 4 6 5 }}
Optimal tuning (POTE): ~7/5 = 1\2, ~12/11 = 140.405
{{Optimal ET sequence|legend=1| 8d, 26, 34d, 60d }}
Badness: 0.018567
== Fifives ==
[[Subgroup]]: 2.3.5.7
[[Comma list]]: 875/864, 83349/81920
{{Mapping|legend=1| 2 2 3 7 | 0 5 7 -6 }}
[[Optimal tuning]] ([[POTE]]): ~567/400 = 1\2, ~27/25 = 139.909
{{Optimal ET sequence|legend=1| 8, 26, 34, 60 }}
[[Badness]]: 0.130589
=== 11-limit ===
Subgroup: 2.3.5.7.11
Comma list: 100/99, 385/384, 3969/3872
Mapping: {{mapping| 2 2 3 7 6 | 0 5 7 -6 4 }}
Optimal tuning (POTE): ~63/44 = 1\2, ~12/11 = 139.884
{{Optimal ET sequence|legend=1| 8, 26, 34, 60 }}
Badness: 0.080306
=== 13-limit ===
Subgroup: 2.3.5.7.11.13
Comma list: 100/99, 105/104, 144/143, 1352/1331
Mapping: {{mapping| 2 2 3 7 6 6 | 0 5 7 -6 4 6 }}
Optimal tuning (POTE): ~55/39 = 1\2, ~12/11 = 139.867
{{Optimal ET sequence|legend=1| 8, 26, 34, 60 }}
Badness: 0.044253
=== 17-limit ===
Subgroup: 2.3.5.7.11.13.17
Comma list: 100/99, 105/104, 144/143, 170/169, 221/220
Mapping: {{mapping| 2 2 3 7 6 6 7 | 0 5 7 -6 4 6 5 }}
Optimal tuning (POTE): ~17/12 = 1\2, ~12/11 = 139.868
{{Optimal ET sequence|legend=1| 8, 26, 34, 60 }}
Badness: 0.029429
== Fourfives ==
{{See also| Sensamagic clan }}
[[Subgroup]]: 2.3.5.7
[[Comma list]]: 245/243, 235298/234375
{{Mapping|legend=1| 4 4 6 7 | 0 5 7 9 }}
: mapping generators: ~25/21, ~27/25
[[Optimal tuning]] ([[POTE]]): ~25/21 = 1\4, ~27/25 = 140.754
{{Optimal ET sequence|legend=1| 8d, 60, 68, 128 }}
[[Badness]]: 0.114143
=== 11-limit ===
Subgroup: 2.3.5.7.11
Comma list: 245/243, 385/384, 235298/234375
Mapping: {{mapping| 4 4 6 7 19 | 0 5 7 9 -11 }}
Optimal tuning (POTE): ~25/21 = 1\4, ~27/25 = 140.771
{{Optimal ET sequence|legend=1| 8de, 60, 68, 128, 196 }}
Badness: 0.120165
==== 13-limit ====
Subgroup: 2.3.5.7.11.13
Comma list: 196/195, 245/243, 385/384, 20000/19773
Mapping: {{mapping| 4 4 6 7 19 12 | 0 5 7 9 -11 6 }}
Optimal tuning (POTE): ~25/21 = 1\4, ~13/12 = 140.760
{{Optimal ET sequence|legend=1| 8de, 60, 68, 128, 196f }}
Badness: 0.067365
=== Quadrafives ===
Subgroup: 2.3.5.7.11
Comma list: 121/120, 245/243, 1375/1372
Mapping: {{mapping| 4 4 6 7 11 | 0 5 7 9 6 }}
Optimal tuning (POTE): ~25/21 = 1\4, ~27/25 = 140.630
{{Optimal ET sequence|legend=1| 8d, 60e, 68, 128e }}
Badness: 0.057268
==== 13-limit ====
Subgroup: 2.3.5.7.11.13
Comma list: 121/120, 196/195, 245/243, 275/273
Mapping: {{mapping| 4 4 6 7 11 12 | 0 5 7 9 6 6 }}
Optimal tuning (POTE): ~25/21 = 1\4, ~13/12 = 140.728
{{Optimal ET sequence|legend=1| 8d, 60e, 68, 128e }}
Badness: 0.036128
==== 17-limit ====
Subgroup: 2.3.5.7.11.13.17
Comma list: 121/120, 154/153, 170/169, 196/195, 245/243
Mapping: {{mapping| 4 4 6 7 11 12 14 | 0 5 7 9 6 6 5 }}
Optimal tuning (POTE): ~25/21 = 1\4, ~13/12 = 140.718
{{Optimal ET sequence|legend=1| 8d, 60e, 68, 128e }}


Badness: 0.024796
}}
}}


== Notes ==
}}
}}


[[Category:Temperament families]]
}}
[[Category:Fifive family| ]] <!-- main article -->
}}
[[Category:Fifive| ]] <!-- key article -->
[[Category:Rank 2]]

Latest revision as of 04:07, 14 April 2025

Fifive

Subgroup: 2.3.5

Comma list: 9765625/9565938

Mapping: [⟨2 2 3], ⟨0 5 7]]

mapping generators: ~78125/50421, ~27/25

Optimal tunings:

  • CTE: ~78125/50421 = 1\2, ~27/25 = 140.6349
  • POTE: ~78125/50421 = 1\2, ~27/25 = 140.624

Optimal ET sequence: 8, 18bc, 26, 34, 94, 128

Badness:

  • Smith: 0.205812
  • Dirichlet: 4.828
141c<0 5 '7 13:6]
{{{1}}}
140c<0 5 '7 7]
{{{1}}}
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