Xenharmonic Wiki

Orwellismic temperaments: Difference between revisions

← Older edit
VisualWikitext
Xenllium (talk | contribs)
autopatrolled, emailconfirmed
4,516 edits
No edit summary
 
(5 intermediate revisions by 5 users not shown)
Line 1: Line 1:
{{Technical data page}}
These temper out {{monzo| 6 3 -1 -3 }} = 1728/1715, the orwellisma.
These temper out {{monzo| 6 3 -1 -3 }} = 1728/1715, the orwellisma.


Line 9: Line 10:
* [[Orwell]] (+225/224) → [[Semicomma family #Orwell|Semicomma family]]
* [[Orwell]] (+225/224) → [[Semicomma family #Orwell|Semicomma family]]
* ''[[Secund]]'' (+405/392 or 525/512) → [[Greenwoodmic temperaments #Secund|Greenwoodmic temperaments]]
* ''[[Secund]]'' (+405/392 or 525/512) → [[Greenwoodmic temperaments #Secund|Greenwoodmic temperaments]]
* ''[[Quartonic]]'' (+4000/3969) → [[Quartonic family]]
* ''[[Buzzard]]'' (+5120/5103) → [[Vulture family #Buzzard|Vulture family]]
* ''[[Buzzard]]'' (+5120/5103) → [[Vulture family #Buzzard|Vulture family]]
* ''[[Trisensory]]'' (+78732/78125) → [[Sensipent family #Trisensory|Sensipent family]]
* ''[[Trisensory]]'' (+78732/78125) → [[Sensipent family #Trisensory|Sensipent family]]
Line 21: Line 23:


: Mapping generators: ~567/400, ~10/9
: Mapping generators: ~567/400, ~10/9
{{Multival|legend=1| 14 30 4 15 -33 -75 }}


[[Optimal tuning]] ([[POTE]]): ~567/400 = 1\2, ~10/9 = 185.885
[[Optimal tuning]] ([[POTE]]): ~567/400 = 1\2, ~10/9 = 185.885
Line 90: Line 90:


: Mapping generators: ~2, ~12/7
: Mapping generators: ~2, ~12/7
{{Multival|legend=1| 16 -3 17 -42 -18 48 }}


[[Optimal tuning]] ([[POTE]]): ~2 = 1\1, ~7/6 = 269.032
[[Optimal tuning]] ([[POTE]]): ~2 = 1\1, ~7/6 = 269.032
Line 124: Line 122:


Badness: 0.023683
Badness: 0.023683
== Quartonic ==
Quartonic tempers out the quartonic comma, {{monzo| 3 -18 11 }} = 390625000/387420489 in the 5-limit. This temperament can be described as 26 & 27 temperament, which tempers out the orwellisma and the octagar comma, 4000/3969. The name "quartonic" means quarter-tone, which is the generator of this temperament (representing ~[[36/35]] and ~[[40/39]]). Alternative extension [[Turkish maqam music temperaments|yarman]] (80 & 159) slices the quartonic generator in three.
[[Subgroup]]: 2.3.5
[[Comma list]]: 390625000/387420489
{{Mapping|legend=1| 1 2 3 | 0 -11 -18 }}
: Mapping generators: ~2, ~250/243
[[Optimal tuning]] ([[POTE]]): ~2 = 1\1, ~250/243 = 45.233
{{Optimal ET sequence|legend=1| 26, 27, 53, 239, 292, 345, 398, 451 }}
[[Badness]]: 0.117250
=== 7-limit ===
[[Subgroup]]: 2.3.5.7
[[Comma list]]: 1728/1715, 4000/3969
{{Mapping|legend=1| 1 2 3 3 | 0 -11 -18 -5 }}
{{Multival|legend=1| 11 18 5 3 -23 -39 }}
[[Optimal tuning]] ([[POTE]]): ~2 = 1\1, ~36/35 = 45.139
{{Optimal ET sequence|legend=1| 26, 27, 53, 80, 133d, 186d, 319d }}
[[Badness]]: 0.042632
=== 11-limit ===
Subgroup: 2.3.5.7.11
Comma list: 176/175, 540/539, 2200/2187
Mapping: {{mapping| 1 2 3 3 5 | 0 -11 -18 -5 -41 }}
Optimal tuning (POTE): ~2 = 1\1, ~36/35 = 45.041
{{Optimal ET sequence|legend=1| 26e, 27e, 53, 80, 213d, 293bcd }}
Badness: 0.034031
==== 13-limit ====
Subgroup: 2.3.5.7.11.13
Comma list: 169/168, 176/175, 325/324, 540/539
Mapping: {{mapping| 1 2 3 3 5 4 | 0 -11 -18 -5 -41 -8 }}
Optimal tuning (POTE): ~2 = 1\1, ~36/35 = 45.080
{{Optimal ET sequence|legend=1| 26e, 27e, 53, 80, 133d, 213d}}
Badness: 0.023875
=== Quarto ===
Subgroup: 2.3.5.7.11
Comma list: 100/99, 245/242, 864/847
Mapping: {{mapping| 1 2 3 3 4 | 0 -11 -18 -5 -14 }}
Optimal tuning (POTE): ~2 = 1\1, ~36/35 = 45.132
{{Optimal ET sequence|legend=1| 26, 27e, 53e, 80e }}
Badness: 0.041786
==== 13-limit ====
Subgroup: 2.3.5.7.11.13
Comma list: 78/77, 100/99, 144/143, 245/242
Mapping: {{mapping| 1 2 3 3 4 4 | 0 -11 -18 -5 -14 -8 }}
Optimal tuning (POTE): ~2 = 1\1, ~36/35 = 45.205
{{Optimal ET sequence|legend=1| 26, 27e, 53e }}
Badness: 0.027692
=== Quartz ===
Subgroup: 2.3.5.7.11
Comma list: 99/98, 385/384, 4000/3969
Mapping: {{mapping| 1 2 3 3 3 | 0 -11 -18 -5 12 }}
Optimal tuning (POTE): ~2 = 1\1, ~36/35 = 45.385
{{Optimal ET sequence|legend=1| 26, 53 }}
Badness: 0.053285
==== 13-limit ====
Subgroup: 2.3.5.7.11.13
Comma list: 99/98, 169/168, 275/273, 385/384
Mapping: {{mapping| 1 2 3 3 3 4 | 0 -11 -18 -5 12 -8 }}
Optimal tuning (POTE): ~2 = 1\1, ~36/35 = 45.387
{{Optimal ET sequence|legend=1| 26, 53, 132e, 185cdef, 238cdef}}
Badness: 0.028818
=== Biquartonic ===
Subgroup: 2.3.5.7.11
Comma list: 1728/1715, 2420/2401, 2560/2541
Mapping: {{mapping| 2 4 6 6 7 | 0 -11 -18 -5 -1 }}
Optimal tuning (POTE): ~99/70 = 1\2, ~36/35 = 45.129
{{Optimal ET sequence|legend=1| 26, 54c, 80, 186de, 266dde }}
Badness: 0.060737
==== 13-limit ====
Subgroup: 2.3.5.7.11.13
Comma list: 169/168, 325/324, 364/363, 640/637
Mapping: {{mapping| 2 4 6 6 7 8 | 0 -11 -18 -5 -1 -8 }}
Optimal tuning (POTE): ~55/39 = 1\2, ~36/35 = 45.153
{{Optimal ET sequence|legend=1| 26, 54c, 80, 106, 186de }}
Badness: 0.039891
=== Yarm ===
Subgroup: 2.3.5.7.11
Comma list: 1331/1323, 1728/1715, 4000/3969
Mapping: {{mapping| 1 2 3 3 4 | 0 -33 -54 -15 -43 }}
Optimal tuning (POTE): ~2 = 1\1, ~100/99 = 15.046
{{Optimal ET sequence|legend=1| 79, 80, 239dd, 319dd }}
Badness: 0.099950
==== 13-limit ====
Subgroup: 2.3.5.7.11.13
Comma list: 169/168, 325/324, 640/637, 1331/1323
Mapping: {{mapping| 1 2 3 3 4 4 | 0 -33 -54 -15 -43 -24 }}
Optimal tuning (POTE): ~2 = 1\1, ~100/99 = 15.060
{{Optimal ET sequence|legend=1| 79, 80, 159d, 239dd }}
Badness: 0.061645
==== 17-limit ====
Subgroup: 2.3.5.7.11.13.17
Comma list: 169/168, 325/324, 561/560, 640/637, 850/847
Mapping: {{mapping| 1 2 3 3 4 4 4 | 0 -33 -54 -15 -43 -24 7 }}
Optimal tuning (POTE): ~2 = 1\1, ~100/99 = 15.066
{{Optimal ET sequence|legend=1| 79, 80, 159d, 239dd }}
Badness: 0.046718


== Sentinel ==
== Sentinel ==
Line 310: Line 133:


: Mapping generators: ~2, ~9/7
: Mapping generators: ~2, ~9/7
{{Multival|legend=1| 4 -15 9 -33 3 63 }}


[[Optimal tuning]] ([[POTE]]): ~2 = 1\1, ~9/7 = 425.596
[[Optimal tuning]] ([[POTE]]): ~2 = 1\1, ~9/7 = 425.596
Line 355: Line 176:


: Mapping generators: ~2, ~36/35
: Mapping generators: ~2, ~36/35
{{Multival|legend=1| 13 21 6 3 -27 -45 }}


[[Optimal tuning]] ([[POTE]]): ~2 = 1\1, ~36/35 = 38.567
[[Optimal tuning]] ([[POTE]]): ~2 = 1\1, ~36/35 = 38.567
Line 400: Line 219:


: Mapping generators: ~81/56, ~3
: Mapping generators: ~81/56, ~3
{{Multival|legend=1| 2 -18 8 -33 7 69 }}


[[Optimal tuning]] ([[POTE]]): ~81/56 = 1\2, ~3/2 = 691.174
[[Optimal tuning]] ([[POTE]]): ~81/56 = 1\2, ~3/2 = 691.174
Line 432: Line 249:


: Mapping generators: ~15/14, ~3
: Mapping generators: ~15/14, ~3
{{Multival|legend=1| 13 0 13 -30 -16 30 }}


[[Optimal tuning]] ([[POTE]]): ~15/14 = 1\13, ~3/2 = 694.143
[[Optimal tuning]] ([[POTE]]): ~15/14 = 1\13, ~3/2 = 694.143
Line 472: Line 287:
[[Comma list]]: 1728/1715, 179200/177147
[[Comma list]]: 1728/1715, 179200/177147


{{Mapping|legend=1| 5 8 12 14 | 0 -1 -6 1 }}
{{Mapping|legend=1| 5 0 -36 22 | 0 1 6 -1 }}


[[Optimal tuning]] ([[POTE]]): ~280/243 = 1\5, ~7/4 = 975.0872
[[Optimal tuning]]s:
* [[CTE]]: ~280/243 = 1\5, ~3/2 = 704.3709 (~64/63 = 15.6291)
* [[POTE]]: ~280/243 = 1\5, ~3/2 = 704.9128 (~64/63 = 15.0872)


{{Optimal ET sequence|legend=1| 5, 75, 80 }}
{{Optimal ET sequence|legend=1| 5, 75, 80 }}
Line 485: Line 302:
Comma list: 896/891, 1728/1715, 2200/2187
Comma list: 896/891, 1728/1715, 2200/2187


Mapping: {{mapping| 5 8 12 14 17 | 0 -1 -6 1 5 }}
Mapping: {{mapping| 5 0 -36 22 57 | 0 1 6 -1 -5 }}


Optimal tuning (POTE): ~55/48 = 1\5, ~7/4 = 975.1212
Optimal tunings:
* CTE: ~55/48 = 1\5, ~3/2 = 704.8440 (~99/98 = 15.1560)
* POTE: ~55/48 = 1\5, ~3/2 = 704.8788 (~99/98 = 15.1212)


Optimal ET sequence: {{Optimal ET sequence| 5, 75e, 80 }}
Optimal ET sequence: {{Optimal ET sequence| 75e, 80, 315bcdddee }}


Badness: 0.071702
Badness: 0.071702
=== 13-limit ===
Subgroup: 2.3.5.7.11.13
Comma list: 325/324, 352/351, 364/363, 1728/1715
Mapping: {{mapping| 5 0 -36 22 57 82 | 0 1 6 -1 -5 -8 }}
Optimal tunings:
* CTE: ~55/48 = 1\5, ~3/2 = 704.7636 (~99/98 = 15.2364)
* CWE: ~55/48 = 1\5, ~3/2 = 704.7112 (~99/98 = 15.2882)
Optimal ET sequence: {{Optimal ET sequence| 75e, 80, 155de }}
Badness: 0.0557


[[Category:Temperament collections]]
[[Category:Temperament collections]]
[[Category:Pages with mostly numerical content]]
[[Category:Orwellismic temperaments| ]] <!-- main article -->
[[Category:Orwellismic temperaments| ]] <!-- main article -->
[[Category:Orwellismic| ]] <!-- key article -->
[[Category:Orwellismic| ]] <!-- key article -->
[[Category:Rank 2]]
[[Category:Rank 2]]
Retrieved from "https://en.xen.wiki/w/Orwellismic_temperaments"