Vavoom family: Difference between revisions
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The '''vavoom family''' includes [[temperaments]] that [[tempering out|temper out]] the [[vavoom comma]], {{monzo| -68 18 17 }}. | The '''vavoom family''' includes [[temperaments]] that [[tempering out|temper out]] the [[vavoom comma]], {{monzo| -68 18 17 }}. | ||
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Comma list: {{monzo| -68 18 17 }} | Comma list: {{monzo| -68 18 17 }} | ||
{{Mapping|legend=0| 1 0 4 | 0 17 -18 }} | |||
: Mapping generators: ~2, ~16/15 | : Mapping generators: ~2, ~16/15 | ||
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Comma list: 225/224, 41943040/40353607 | Comma list: 225/224, 41943040/40353607 | ||
{{Mapping|legend=0| 1 0 4 3 | 0 17 -18 -2 }} | |||
: Mapping generators: ~2, ~16/15 | : Mapping generators: ~2, ~16/15 | ||
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Comma list: 225/224, 1344/1331, 2420/2401 | Comma list: 225/224, 1344/1331, 2420/2401 | ||
{{Mapping|legend=0| 1 0 4 3 3 | 0 17 -18 -2 5 }} | |||
: Mapping generators: ~2, ~16/15 | : Mapping generators: ~2, ~16/15 | ||
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Comma list: 3136/3125, 33756345/33554432 | Comma list: 3136/3125, 33756345/33554432 | ||
{{Mapping|legend=0| 1 0 4 7 | 0 17 -18 -45 }} | |||
: Mapping generators: ~2, ~16/15 | : Mapping generators: ~2, ~16/15 | ||
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Comma list: 441/440, 3136/3125, 35937/35840 | Comma list: 441/440, 3136/3125, 35937/35840 | ||
{{Mapping|legend=0| 1 0 4 7 7 | 0 17 -18 -45 -38 }} | |||
: Mapping generators: ~2, ~16/15 | : Mapping generators: ~2, ~16/15 | ||
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Comma list: 441/440, 1001/1000, 1188/1183, 3136/3125 | Comma list: 441/440, 1001/1000, 1188/1183, 3136/3125 | ||
{{Mapping|legend=0| 1 0 4 7 7 1 | 0 17 -18 -45 -38 29 }} | |||
: Mapping generators: ~2, ~16/15 | : Mapping generators: ~2, ~16/15 | ||
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Comma list: 65625/65536, 4802000/4782969 | Comma list: 65625/65536, 4802000/4782969 | ||
{{Mapping|legend=0| 1 0 4 -4 | 0 17 -18 73 }} | |||
: Mapping generators: ~2, ~16/15 | : Mapping generators: ~2, ~16/15 | ||
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Comma list: 3025/3024, 12005/11979, 19712/19683 | Comma list: 3025/3024, 12005/11979, 19712/19683 | ||
{{Mapping|legend=0| 1 0 4 -4 -4 | 0 17 -18 73 80 }} | |||
: Mapping generators: ~2, ~16/15 | : Mapping generators: ~2, ~16/15 | ||
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Comma list: 625/624, 1575/1573, 4096/4095, 4459/4455 | Comma list: 625/624, 1575/1573, 4096/4095, 4459/4455 | ||
{{Mapping|legend=0| 1 0 4 -4 -4 12 | 0 17 -18 73 80 -89 }} | |||
: Mapping generators: ~2, ~16/15 | : Mapping generators: ~2, ~16/15 | ||
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Comma list: 4375/4374, [-68 18 17⟩ | Comma list: 4375/4374, [-68 18 17⟩ | ||
{{Mapping|legend=0| 1 0 4 -15 | 0 17 -18 191 }} | |||
: Mapping generators: ~2, ~16/15 | : Mapping generators: ~2, ~16/15 | ||
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Comma list: 4375/4374, 42592/42525, 805255/802816 | Comma list: 4375/4374, 42592/42525, 805255/802816 | ||
{{Mapping|legend=0| 1 0 4 -15 -4 | 0 17 -18 191 80 }} | |||
: Mapping generators: ~2, ~16/15 | : Mapping generators: ~2, ~16/15 | ||
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Comma list: 4375/4374, 496125/495616, 806736/805255 | Comma list: 4375/4374, 496125/495616, 806736/805255 | ||
{{Mapping|legend=0| 1 0 4 -15 -15 | 0 17 -18 191 198 }} | |||
: Mapping generators: ~2, ~16/15 | : Mapping generators: ~2, ~16/15 | ||
Latest revision as of 12:32, 24 September 2026
- This is a list showing technical temperament data. For an explanation of what information is shown here, you may look at the technical data guide for regular temperaments.
The vavoom family includes temperaments that temper out the vavoom comma, [-68 18 17⟩.
Vavoom
Subgroup: 2.3.5
Comma list: [-68 18 17⟩
Mapping: [⟨1 0 4], ⟨0 17 -18]]
- Mapping generators: ~2, ~16/15
Optimal tuning (POTE): ~2 = 1＼1, ~16/15 = 111.8765
Optimal ET sequence: 32, 43, 75, 118, 429, 547, 665, 783, 901, 1684
Badness: 0.098376
Raccoon
Subgroup: 2.3.5.7
Comma list: 225/224, 41943040/40353607
Mapping: [⟨1 0 4 3], ⟨0 17 -18 -2]]
- Mapping generators: ~2, ~16/15
Optimal tuning (POTE): ~2 = 1＼1, ~16/15 = 111.8960
Optimal ET sequence: 32, 43, 75, 118d
Badness: 0.272586
11-limit
Subgroup: 2.3.5.7.11
Comma list: 225/224, 1344/1331, 2420/2401
Mapping: [⟨1 0 4 3 3], ⟨0 17 -18 -2 5]]
- Mapping generators: ~2, ~16/15
Optimal tuning (POTE): ~2 = 1＼1, ~16/15 = 111.8892
Optimal ET sequence: 32, 43, 75e
Badness: 0.095405
Doubloon
Subgroup: 2.3.5.7
Comma list: 3136/3125, 33756345/33554432
Mapping: [⟨1 0 4 7], ⟨0 17 -18 -45]]
- Mapping generators: ~2, ~16/15
Optimal tuning (POTE): ~2 = 1＼1, ~16/15 = 111.8391
Optimal ET sequence: 43, 75d, 118, 279, 397d
Badness: 0.173974
11-limit
Subgroup: 2.3.5.7.11
Comma list: 441/440, 3136/3125, 35937/35840
Mapping: [⟨1 0 4 7 7], ⟨0 17 -18 -45 -38]]
- Mapping generators: ~2, ~16/15
Optimal tuning (POTE): ~2 = 1＼1, ~16/15 = 111.8368
Optimal ET sequence: 43, 75d, 118, 279, 397d
Badness: 0.049755
13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 441/440, 1001/1000, 1188/1183, 3136/3125
Mapping: [⟨1 0 4 7 7 1], ⟨0 17 -18 -45 -38 29]]
- Mapping generators: ~2, ~16/15
Optimal tuning (POTE): ~2 = 1＼1, ~16/15 = 111.8193
Optimal ET sequence: 43, 75d, 118, 161, 279f
Badness: 0.042899
Kaboom
Subgroup: 2.3.5.7
Comma list: 65625/65536, 4802000/4782969
Mapping: [⟨1 0 4 -4], ⟨0 17 -18 73]]
- Mapping generators: ~2, ~16/15
Optimal tuning (POTE): ~2 = 1＼1, ~16/15 = 111.8950
Optimal ET sequence: 75, 118, 193, 311
Badness: 0.124539
11-limit
Subgroup: 2.3.5.7.11
Comma list: 3025/3024, 12005/11979, 19712/19683
Mapping: [⟨1 0 4 -4 -4], ⟨0 17 -18 73 80]]
- Mapping generators: ~2, ~16/15
Optimal tuning (POTE): ~2 = 1＼1, ~16/15 = 111.8930
Optimal ET sequence: 75e, 118, 193, 311
Badness: 0.038829
13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 625/624, 1575/1573, 4096/4095, 4459/4455
Mapping: [⟨1 0 4 -4 -4 12], ⟨0 17 -18 73 80 -89]]
- Mapping generators: ~2, ~16/15
Optimal tuning (POTE): ~2 = 1＼1, ~16/15 = 111.8979
Optimal ET sequence: 118, 193, 311
Badness: 0.036509
Vacuum
Subgroup: 2.3.5.7
Comma list: 4375/4374, [-68 18 17⟩
Mapping: [⟨1 0 4 -15], ⟨0 17 -18 191]]
- Mapping generators: ~2, ~16/15
Optimal tuning (POTE): ~2 = 1＼1, ~16/15 = 111.8782
Optimal ET sequence: 118, 429d, 547, 665, 783, 1448, 2231, 3679
Badness: 0.092961
Vortex
Subgroup: 2.3.5.7.11
Comma list: 4375/4374, 42592/42525, 805255/802816
Mapping: [⟨1 0 4 -15 -4], ⟨0 17 -18 191 80]]
- Mapping generators: ~2, ~16/15
Optimal tuning (POTE): ~2 = 1＼1, ~16/15 = 111.8786
Optimal ET sequence: 118, 429d, 547, 665e
Badness: 0.108400
Void
Subgroup: 2.3.5.7.11
Comma list: 4375/4374, 496125/495616, 806736/805255
Mapping: [⟨1 0 4 -15 -15], ⟨0 17 -18 191 198]]
- Mapping generators: ~2, ~16/15
Optimal tuning (POTE): ~2 = 1＼1, ~16/15 = 111.8770
Optimal ET sequence: 118, …, 665, 783
Badness: 0.082642