No-fives subgroup temperaments: Difference between revisions

{{See also| Whitewood }}

Subgrouo-val mapping: {{mapping| 1 0 -6 10 | 0 1 6 -4 }}

Subgrouo-val mapping: {{mapping| 1 0 -6 -6 | 0 2 12 13 }}

Music:

: sval mapping generators: ~17/12, ~3

: [[gencom]]: [17/12 3; 289/288]

[[Optimal tuning]] ([[CTE]]): ~17/12 = 1\2, ~3/2 = 702.3472 (~17/16 = 102.3472)

{{Optimal ET sequence|legend=1| 12, 58, 70, 82, 94, 106, 118, 224g }}

[[Tp tuning #T2 tuning|RMS error]]: 0.2247 cents

[[Subgroup]]: 2.3.85

[[Comma list]]: 2.3.85 {{val|-40 1 6 }}

 

 

[[Optimal tuning]] ([[CTE]]): ~2 = 1\1, ~85/64 = 483.034

 

[[Support]]ing [[ET]]s: 5, 47, 52, 57, 62, 67, 72, 77*, 82*, 87*, 92*, 139*, 149*, 159**

 

==== 2.3.7.85 subgroup ====

[[Subgroup]]: 2.3.7.85

[[Comma list]]: 1029/1024, 7225/7203

 

 

 

[[Optimal tuning]] ([[CTE]]): ~2 = 1\1, ~85/64 = 483.031

 

 

The dog temperament is based by [[2L 5s]] or [[7L 2s]] scale that makes [[81/76]] vanish, so [[19/16]] is a major third. It can be viewed as a 2.3.19 subgroup analogue of [[Pelogic family|mavila]].

Subgroup: 2.3.19

 

 

 

 

 

 

 

 

{{Mapping|legend=2| 1 0 9 | 0 1 -3 }}

[[Optimal tuning]] (CTE): ~2 = 1200.0000{{c}}, ~3/2 = 701.3288{{c}}

{{Optimal ET sequence|legend=1| 5, 7, 12, 41, 53, 65, 77, 219, 296 }}

[[Badness]] (Smith): 0.000374

Lipsett temperament is a pleasantly melodic little temperament with a highly useable 5-tone and 9-tone mos. It is audibly similar to [[semaphore]] temperament, so it could be thought of as semaphore but for the 23rd harmonic instead of the 7th. It is named for Arthur Lipsett, the director off the Canadian short film ’21-87’. Leia’s prison cell in Star Wars is numbered ‘2187’, as a nod to the influence the film had on George Lucas.

[[Comma list]]: [[2187/2116]]

{{Mapping|legend=2| 1 0 -1 | 0 2 7}}

[[Optimal tuning]] ([[CTE]]): ~2 = 1\1, ~46/27 = 948.526

[[Badness]] (Smith): 8.998 × 10^-3

[[Mapping]]: [{{val|1 2 5}}, {{val|0 3 -1}}]

[[CTE tuning|CTE generator]]: ~32/29 = 166.067

This temperament tempers out 4107/4096 and thus equates 2 [[37/32]]'s with [[4/3]].

[[Gencom]]: [2 37/32; 4107/4096]

[[Mapping]]: [{{val|1 1 5}}, {{val|0 -2 1}}]

 

[[POTE generator]]: ~[[37/32]] = 249.075

 

{{Optimal ET sequence|legend=1| 5, 14, 19, 24, 53, 77, 130 }}

 

==== 2.3.7.37 subgroup ====

[[Subgroup]]: 2.3.7.37

 

 

[[Gencom]]: [2 37/32; 4107/4096 259/256]

 

[[Mapping]]: [{{val|1 1 1 5}}, {{val|0 -2 -1 1}}]

 

[[POTE generator]]: ~[[37/32]] = 247.782

 

{{Optimal ET sequence|legend=1| 5, 14, 19, 24, 53d }}

 

==== 2.3.5.37 subgroup ====

It is difficult to extend sematology to include 5, due the 5th harmonic being quite high-complexity.

 

[[Subgroup]]: 2.3.5.37

 

 

[[Mapping]]: [{{val|1 1 4 5}}, {{val|0 -2 -8 1}}]

[[POTE generator]]: ~[[37/32]] = 251.393

 

 

 

 

 

[[Mapping]]: [{{val|1 1 4 1 5}}, {{val|0 -2 -8 -1 1}}]

 

[[POTE generator]]: ~[[37/32]] = 251.204

 

[[Gencom]]: [2 4/3; 81/74]

[[Mapping]]: [{{val|1 1 0}}, {{val|0 -1 12}}]

[[POTE generator]]: ~4/3 = 521.397

Subgroup: 2.3.41

[[Gencom]]: [2 4/3; 82/81]

[[Mapping|Sval mapping]]: [{{val|1 2 7}}, {{val|0 -1 -4}}]

 

[[Tp tuning|POL2 generator]]: ~4/3 = 494.509

 

{{Optimal ET sequence|legend=1| 5, 12, 17 }}

 

==== 2.3.7.41 subgroup ====

Subgroup: 2.3.7.41

 

[[Comma list]]: 64/63, 82/81

 

 

[[Mapping|Sval mapping]]: [{{val| 1 2 2 7 }}, {{val| 0 -1 2 -4 }}]

 

[[POTE generator]]: ~4/3 = 490.0323

 

[[TOP tuning|TOP generator]]s: ~2 = 1197.2342, ~4/3 = 488.9029

 

{{Optimal ET sequence|legend=1| 5, 12, 17, 22, 49 }}

 

 

 

[[Gencom]]: [2 4/3; 64/63 82/81 99/98]

 

[[Mapping|Sval mapping]]: [{{val| 1 2 2 1 7 }}, {{val| 0 -1 2 6 -4 }}]

 

[[TOP tuning|TOP generator]]s: ~2 = 1197.9683, ~4/3 = 491.3454