Xenharmonic Wiki

Quintosec family: Difference between revisions

← Older editNewer edit →
VisualWikitext
Cmloegcmluin (talk | contribs)
autopatrolled, emailconfirmed
5,160 edits
"optimal GPV sequence" → "optimal ET sequence", per Talk:Optimal_ET_sequence
Update keys
Line 1: Line 1:
The '''qintosec family''' tempers out the qintosec comma, 140737488355328/140126044921875 = {{monzo|47 -15 -10}}.
The '''qintosec family''' tempers out the qintosec comma, 140737488355328/140126044921875 = {{monzo| 47 -15 -10 }}.


== Qintosec ==
== Qintosec ==
Subgroup: 2.3.5
[[Subgroup]]: 2.3.5


[[Comma]]: 140737488355328/140126044921875
[[Comma list]]: {{monzo| 47 -15 -10 }}


[[Mapping]]: [{{val| 5 1 22 }}, {{val| 0 2 -3 }}]
{{Mapping|legend=1| 5 1 22 | 0 2 -3 }}


Mapping generators: ~524288/455625, ~16384/10125
: mapping generators: ~524288/455625, ~16384/10125


[[POTE generator]]: ~16384/10125 = 831.105 (~16/15 = 111.105)
[[Optimal tuning]] ([[POTE]]): ~524288/455625 = 1\5, ~16384/10125 = 831.105 (~16/15 = 111.105)


{{Optimal ET sequence|legend=1| 10, 55, 65, 140, 205, 270, 1955c, 2225c, 2495bc, 2765bc, 3035bc, 3305bcc, 3575bcc }}
{{Optimal ET sequence|legend=1| 10, 55, 65, 140, 205, 270, 1955c, 2225c, 2495bc, 2765bc, 3035bc, 3305bcc, 3575bcc }}
Line 17: Line 17:


== Septimal qintosec ==
== Septimal qintosec ==
The qintosec temperament can be described as 10&65d temperament, tempering out the [[marvel comma]], 225/224 in the 7-limit.
Qintosec can be described as the 10 & 65d temperament, tempering out the [[marvel comma]], 225/224 in the 7-limit.


Subgroup: 2.3.5.7
[[Subgroup]]: 2.3.5.7


[[Comma list]]: 225/224, 2560000/2470629
[[Comma list]]: 225/224, 2560000/2470629


[[Mapping]]: [{{val| 5 1 22 21 }}, {{val| 0 2 -3 -2 }}]
{{Mapping|legend=1| 5 1 22 21 | 0 2 -3 -2 }}


{{Multival|legend=1| 10 -15 -10 -47 -44 19 }}
{{Multival|legend=1| 10 -15 -10 -47 -44 19 }}


[[POTE generator]]: ~80/49 = 831.553 (~15/14 = 111.553)
[[Optimal tuning]] ([[POTE]]): ~400/343 = 1\5, ~80/49 = 831.553 (~15/14 = 111.553)


{{Optimal ET sequence|legend=1| 10, 55d, 65d, 75, 140d, 215dd }}
{{Optimal ET sequence|legend=1| 10, 55d, 65d, 75, 140d, 215dd }}
Line 38: Line 38:
Comma list: 225/224, 243/242, 3840/3773
Comma list: 225/224, 243/242, 3840/3773


Mapping: [{{val| 5 1 22 21 0 }}, {{val| 0 2 -3 -2 5 }}]
Mapping: {{mapping| 5 1 22 21 0 | 0 2 -3 -2 5 }}


POTE generator: ~80/49 = 831.311 (~15/14 = 111.311)
Optimal tuning (POTE): ~55/48 = 1\5, ~80/49 = 831.311 (~15/14 = 111.311)


{{Optimal ET sequence|legend=1| 10, 55d, 65d, 140de, 205dde }}
{{Optimal ET sequence|legend=1| 10, 55d, 65d, 140de, 205dde }}
Line 51: Line 51:
Comma list: 225/224, 385/384, 332750/321489
Comma list: 225/224, 385/384, 332750/321489


Mapping: [{{val| 5 1 22 21 -7 }}, {{val|0 2 -3 -2 7 }}]
Mapping: {{mapping| 5 1 22 21 -7 | 0 2 -3 -2 7 }}


POTE generator: ~44/27 = 832.448 (~15/14 = 112.448)
Optimal tuning (POTE): ~220/189 = 1\5, ~44/27 = 832.448 (~15/14 = 112.448)


{{Optimal ET sequence|legend=1| 10, 75, 160cde }}
{{Optimal ET sequence|legend=1| 10, 75, 160cde }}
Line 60: Line 60:


== Sengasec ==
== Sengasec ==
The ''sengasec'' temperament (10&55) tempers out the [[cloudy comma]], 16807/16384 and the sengic comma, 686/675 in the 7-limit.
Sengasec can be described as the 10 & 55 temperament, tempering out the [[cloudy comma]], 16807/16384 and the sengic comma, 686/675 in the 7-limit.


Subgroup: 2.3.5.7
[[Subgroup]]: 2.3.5.7


[[Comma list]]: 686/675, 16807/16384
[[Comma list]]: 686/675, 16807/16384


[[Mapping]]: [{{val| 5 1 22 14 }}, {{val| 0 2 -3 0 }}]
{{Mapping|legend=1| 5 1 22 14 | 0 2 -3 0 }}


{{Multival|legend=1| 10 -15 0 -47 -28 42 }}
{{Multival|legend=1| 10 -15 0 -47 -28 42 }}


[[POTE generator]]: ~45/28 = 831.113 (~16/15 = 111.113)
[[Optimal tuning]] ([[POTE]]): ~8/7 = 1\5, ~45/28 = 831.113 (~16/15 = 111.113)


{{Optimal ET sequence|legend=1| 10, 55, 65, 140dd, 205ddd, 270ddd }}
{{Optimal ET sequence|legend=1| 10, 55, 65, 140dd, 205ddd, 270ddd }}
Line 81: Line 81:
Comma list: 243/242, 385/384, 686/675
Comma list: 243/242, 385/384, 686/675


Mapping: [{{val| 5 1 22 14 0 }}, {{val| 0 2 -3 0 5 }}]
Mapping: {{mapping| 5 1 22 14 0 | 0 2 -3 0 5 }}


POTE generator: ~45/28 = 830.659 (~16/15 = 110.659)
Optimal tuning (POTE): ~8/7 = 1\5, ~45/28 = 830.659 (~16/15 = 110.659)


{{Optimal ET sequence|legend=1| 10, 55, 65 }}
{{Optimal ET sequence|legend=1| 10, 55, 65 }}
Line 94: Line 94:
Comma list: 105/104, 144/143, 243/242, 686/675
Comma list: 105/104, 144/143, 243/242, 686/675


Mapping: [{{val| 5 1 22 14 0 22 }}, {{val| 0 2 -3 0 5 -1 }}]
Mapping: {{mapping| 5 1 22 14 0 22 | 0 2 -3 0 5 -1 }}


POTE generator: ~45/28 = 830.910 (~16/15 = 110.910)
POTE generator: ~45/28 = 830.910 (~16/15 = 110.910)
Line 105: Line 105:
{{See also| Breedsmic temperaments #Decoid }}
{{See also| Breedsmic temperaments #Decoid }}


Subgroup: 2.3.5.7
[[Subgroup]]: 2.3.5.7


[[Comma list]]: 2401/2400, 67108864/66976875
[[Comma list]]: 2401/2400, 67108864/66976875


[[Mapping]]: [{{val| 10 0 47 36 }}, {{val| 0 2 -3 -1 }}]
{{Mapping|legend=1| 10 0 47 36 | 0 2 -3 -1 }}


Mapping generators: ~15/14, ~8192/4725
: mapping generators: ~15/14, ~8192/4725


{{Multival|legend=1| 20 -30 -10 -94 -72 61 }}
{{Multival|legend=1| 20 -30 -10 -94 -72 61 }}


[[POTE generator]]: ~8192/4725 = 951.099 (~16/15 = 111.099)
[[Optimal tuning]] ([[POTE]]): ~15/14 = 1\10, ~8192/4725 = 951.099 (~16/15 = 111.099)


{{Optimal ET sequence|legend=1| 10, 120, 130, 270, 2020c, 2290c, 2560c, 2830bc, 3100bcc, 3370bcc, 3640bcc }}
{{Optimal ET sequence|legend=1| 10, 120, 130, 270, 2020c, 2290c, 2560c, 2830bc, 3100bcc, 3370bcc, 3640bcc }}
Line 126: Line 126:
Comma list: 2401/2400, 5632/5625, 9801/9800
Comma list: 2401/2400, 5632/5625, 9801/9800


Mapping: [{{val| 10 0 47 36 98 }}, {{val| 0 2 -3 -1 -8 }}]
Mapping: {{mapping| 10 0 47 36 98 | 0 2 -3 -1 -8 }}


POTE generator: ~400/231 = 951.070 (~16/15 = 111.070)
Optimal tuning (POTE): ~15/14 = 1\10, ~400/231 = 951.070 (~16/15 = 111.070)


{{Optimal ET sequence|legend=1| 10e, 130, 270, 670, 940, 1210, 2150c }}
{{Optimal ET sequence|legend=1| 10e, 130, 270, 670, 940, 1210, 2150c }}
Line 139: Line 139:
Comma list: 676/675, 1001/1000, 1716/1715, 4096/4095
Comma list: 676/675, 1001/1000, 1716/1715, 4096/4095


Mapping: [{{val| 10 0 47 36 98 37 }}, {{val| 0 2 -3 -1 -8 0 }}]
Mapping: {{mapping| 10 0 47 36 98 37 | 0 2 -3 -1 -8 0 }}


POTE generator: ~26/15 = 951.083 (~16/15 = 111.083)
Optimal tuning (POTE): ~15/14 = 1\10, ~26/15 = 951.083 (~16/15 = 111.083)


{{Optimal ET sequence|legend=1| 10e, 130, 270, 940, 1210f, 1480cf }}
{{Optimal ET sequence|legend=1| 10e, 130, 270, 940, 1210f, 1480cf }}
Retrieved from "https://en.xen.wiki/w/Quintosec_family"