Quintosec family: Difference between revisions

From Xenharmonic Wiki
Jump to navigation Jump to search
← Older editNewer edit →
VisualWikitext
Fredg999 category edits (talk | contribs)
autopatrolled, Bots, emailconfirmed
4,330 edits
Cmloegcmluin (talk | contribs)
autopatrolled, emailconfirmed
5,160 edits
"optimal GPV sequence" → "optimal ET sequence", per Talk:Optimal_ET_sequence
Line 12: Line 12:
[[POTE generator]]: ~16384/10125 = 831.105 (~16/15 = 111.105)
[[POTE generator]]: ~16384/10125 = 831.105 (~16/15 = 111.105)


{{Val list|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 }}


[[Badness]]: 0.139191
[[Badness]]: 0.139191
Line 29: Line 29:
[[POTE generator]]: ~80/49 = 831.553 (~15/14 = 111.553)
[[POTE generator]]: ~80/49 = 831.553 (~15/14 = 111.553)


{{Val list|legend=1| 10, 55d, 65d, 75, 140d, 215dd }}
{{Optimal ET sequence|legend=1| 10, 55d, 65d, 75, 140d, 215dd }}


[[Badness]]: 0.156764
[[Badness]]: 0.156764
Line 42: Line 42:
POTE generator: ~80/49 = 831.311 (~15/14 = 111.311)
POTE generator: ~80/49 = 831.311 (~15/14 = 111.311)


Optimal GPV sequence: {{Val list| 10, 55d, 65d, 140de, 205dde }}
{{Optimal ET sequence|legend=1| 10, 55d, 65d, 140de, 205dde }}


Badness: 0.077907
Badness: 0.077907
Line 55: Line 55:
POTE generator: ~44/27 = 832.448 (~15/14 = 112.448)
POTE generator: ~44/27 = 832.448 (~15/14 = 112.448)


Optimal GPV sequence: {{Val list| 10, 75, 160cde }}
{{Optimal ET sequence|legend=1| 10, 75, 160cde }}


Badness: 0.127732
Badness: 0.127732
Line 72: Line 72:
[[POTE generator]]: ~45/28 = 831.113 (~16/15 = 111.113)
[[POTE generator]]: ~45/28 = 831.113 (~16/15 = 111.113)


{{Val list|legend=1| 10, 55, 65, 140dd, 205ddd, 270ddd }}
{{Optimal ET sequence|legend=1| 10, 55, 65, 140dd, 205ddd, 270ddd }}


[[Badness]]: 0.156259
[[Badness]]: 0.156259
Line 85: Line 85:
POTE generator: ~45/28 = 830.659 (~16/15 = 110.659)
POTE generator: ~45/28 = 830.659 (~16/15 = 110.659)


Optimal GPV sequence: {{Val list| 10, 55, 65 }}
{{Optimal ET sequence|legend=1| 10, 55, 65 }}


Badness: 0.081607
Badness: 0.081607
Line 98: Line 98:
POTE generator: ~45/28 = 830.910 (~16/15 = 110.910)
POTE generator: ~45/28 = 830.910 (~16/15 = 110.910)


Optimal GPV sequence: {{Val list| 10, 55, 65 }}
{{Optimal ET sequence|legend=1| 10, 55, 65 }}


Badness: 0.056390
Badness: 0.056390
Line 117: Line 117:
[[POTE generator]]: ~8192/4725 = 951.099 (~16/15 = 111.099)
[[POTE generator]]: ~8192/4725 = 951.099 (~16/15 = 111.099)


{{Val list|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 }}


[[Badness]]: 0.033902
[[Badness]]: 0.033902
Line 130: Line 130:
POTE generator: ~400/231 = 951.070 (~16/15 = 111.070)
POTE generator: ~400/231 = 951.070 (~16/15 = 111.070)


Optimal GPV sequence: {{Val list| 10e, 130, 270, 670, 940, 1210, 2150c }}
{{Optimal ET sequence|legend=1| 10e, 130, 270, 670, 940, 1210, 2150c }}


Badness: 0.018735
Badness: 0.018735
Line 143: Line 143:
POTE generator: ~26/15 = 951.083 (~16/15 = 111.083)
POTE generator: ~26/15 = 951.083 (~16/15 = 111.083)


Optimal GPV sequence: {{Val list| 10e, 130, 270, 940, 1210f, 1480cf }}
{{Optimal ET sequence|legend=1| 10e, 130, 270, 940, 1210f, 1480cf }}


Badness: 0.013475
Badness: 0.013475

Revision as of 16:20, 7 May 2023

The qintosec family tempers out the qintosec comma, 140737488355328/140126044921875 = [47 -15 -10⟩.

Qintosec

Subgroup: 2.3.5

Comma: 140737488355328/140126044921875

Mapping: [⟨5 1 22], ⟨0 2 -3]]

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

POTE generator: ~16384/10125 = 831.105 (~16/15 = 111.105)

Optimal ET sequence: 10, 55, 65, 140, 205, 270, 1955c, 2225c, 2495bc, 2765bc, 3035bc, 3305bcc, 3575bcc

Badness: 0.139191

Septimal qintosec

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

Subgroup: 2.3.5.7

Comma list: 225/224, 2560000/2470629

Mapping: [⟨5 1 22 21], ⟨0 2 -3 -2]]

Wedgie: ⟨⟨ 10 -15 -10 -47 -44 19 ]]

POTE generator: ~80/49 = 831.553 (~15/14 = 111.553)

Optimal ET sequence: 10, 55d, 65d, 75, 140d, 215dd

Badness: 0.156764

11-limit

Subgroup: 2.3.5.7.11

Comma list: 225/224, 243/242, 3840/3773

Mapping: [⟨5 1 22 21 0], ⟨0 2 -3 -2 5]]

POTE generator: ~80/49 = 831.311 (~15/14 = 111.311)

Optimal ET sequence: 10, 55d, 65d, 140de, 205dde

Badness: 0.077907

Qinto

Subgroup: 2.3.5.7.11

Comma list: 225/224, 385/384, 332750/321489

Mapping: [⟨5 1 22 21 -7], ⟨0 2 -3 -2 7]]

POTE generator: ~44/27 = 832.448 (~15/14 = 112.448)

Optimal ET sequence: 10, 75, 160cde

Badness: 0.127732

Sengasec

The sengasec temperament (10&55) tempers out the cloudy comma, 16807/16384 and the sengic comma, 686/675 in the 7-limit.

Subgroup: 2.3.5.7

Comma list: 686/675, 16807/16384

Mapping: [⟨5 1 22 14], ⟨0 2 -3 0]]

Wedgie: ⟨⟨ 10 -15 0 -47 -28 42 ]]

POTE generator: ~45/28 = 831.113 (~16/15 = 111.113)

Optimal ET sequence: 10, 55, 65, 140dd, 205ddd, 270ddd

Badness: 0.156259

11-limit

Subgroup: 2.3.5.7.11

Comma list: 243/242, 385/384, 686/675

Mapping: [⟨5 1 22 14 0], ⟨0 2 -3 0 5]]

POTE generator: ~45/28 = 830.659 (~16/15 = 110.659)

Optimal ET sequence: 10, 55, 65

Badness: 0.081607

13-limit

Subgroup: 2.3.5.7.11.13

Comma list: 105/104, 144/143, 243/242, 686/675

Mapping: [⟨5 1 22 14 0 22], ⟨0 2 -3 0 5 -1]]

POTE generator: ~45/28 = 830.910 (~16/15 = 110.910)

Optimal ET sequence: 10, 55, 65

Badness: 0.056390

Decoid

See also: Breedsmic temperaments § Decoid

Subgroup: 2.3.5.7

Comma list: 2401/2400, 67108864/66976875

Mapping: [⟨10 0 47 36], ⟨0 2 -3 -1]]

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

Wedgie: ⟨⟨ 20 -30 -10 -94 -72 61 ]]

POTE generator: ~8192/4725 = 951.099 (~16/15 = 111.099)

Optimal ET sequence: 10, 120, 130, 270, 2020c, 2290c, 2560c, 2830bc, 3100bcc, 3370bcc, 3640bcc

Badness: 0.033902

11-limit

Subgroup: 2.3.5.7.11

Comma list: 2401/2400, 5632/5625, 9801/9800

Mapping: [⟨10 0 47 36 98], ⟨0 2 -3 -1 -8]]

POTE generator: ~400/231 = 951.070 (~16/15 = 111.070)

Optimal ET sequence: 10e, 130, 270, 670, 940, 1210, 2150c

Badness: 0.018735

13-limit

Subgroup: 2.3.5.7.11.13

Comma list: 676/675, 1001/1000, 1716/1715, 4096/4095

Mapping: [⟨10 0 47 36 98 37], ⟨0 2 -3 -1 -8 0]]

POTE generator: ~26/15 = 951.083 (~16/15 = 111.083)

Optimal ET sequence: 10e, 130, 270, 940, 1210f, 1480cf

Badness: 0.013475

Retrieved from "https://en.xen.wiki/index.php?title=Quintosec_family&oldid=112498"