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Compton family: Difference between revisions

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m →Duodecim: update
+CTE tunings; +error maps; spell 1\12 etc. in decimal; note the badness metric being used
Line 12: Line 12:
: mapping generators: ~256/243, ~5
: mapping generators: ~256/243, ~5


[[Optimal tuning]] ([[POTE]]): ~256/243 = 1\12, ~5/4 = 384.884 (~81/80 = 15.116)
[[Optimal tuning]]s:
* [[CTE]]: ~256/243 = 100.000, ~5/4 = 386.314 (~81/80 = 13.686)
: [[error map]]: {{val| 0.000 -1.955 0.000 }}
* [[POTE]]: ~256/243 = 100.000, ~5/4 = 384.884 (~81/80 = 15.116)
: error map: {{val| 0.000 -1.955 -1.431 }}


{{Optimal ET sequence|legend=1| 12, 48, 60, 72, 84, 156, 240, 396b, 636bbc }}
{{Optimal ET sequence|legend=1| 12, 48, 60, 72, 84, 156, 240, 396b, 636bbc }}


[[Badness]]: 0.094494
[[Badness]] (Smith): 0.094494


== Septimal compton ==
== Septimal compton ==
Line 31: Line 35:
{{Mapping|legend=1| 12 19 0 -22 | 0 0 1 2 }}
{{Mapping|legend=1| 12 19 0 -22 | 0 0 1 2 }}


Wedgie: {{Multival| 0 12 24 19 38 22 }}
{{Multival|legend=1| 0 12 24 19 38 22 }}


[[Optimal tuning]] ([[POTE]]): ~256/243 = 1\12, ~5/4 = 383.7752 (~126/125 = 16.2248)
[[Optimal tuning]]s:
* [[CTE]]: ~200/189 = 100.000, ~5/4 = 384.922 (~126/125 = 15.078)
: [[error map]]: {{val| 0.000 -1.955 -1.392 -1.017 }}
* [[POTE]]: ~200/189 = 100.000, ~5/4 = 383.775 (~126/125 = 16.225)
: error map: {{val| 0.000 -1.955 -2.538 -1.275 }}


{{Optimal ET sequence|legend=1| 12, 48d, 60, 72, 228, 300c, 372bc, 444bc }}
{{Optimal ET sequence|legend=1| 12, 48d, 60, 72, 228, 300c, 372bc, 444bc }}


[[Badness]]: 0.035686
[[Badness]] (Smith): 0.035686


=== 11-limit ===
=== 11-limit ===
Line 48: Line 56:
Wedgie: {{Multival| 0 12 24 36 19 38 57 22 42 18 }}
Wedgie: {{Multival| 0 12 24 36 19 38 57 22 42 18 }}


Optimal tuning (POTE): ~256/243 = 1\12, ~5/4 = 383.2660 (~100/99 = 16.7340)
Optimal tunings:
* CTE: ~35/33 = 100.000, ~5/4 = 384.324 (~100/99 = 15.676)
* POTE: ~35/33 = 100.000, ~5/4 = 383.266 (~100/99 = 16.734)


{{Optimal ET sequence|legend=1| 12, 48dee, 60e, 72 }}
{{Optimal ET sequence|legend=0| 12, 48dee, 60e, 72 }}


Badness: 0.022235
Badness (Smith): 0.022235


==== 13-limit ====
==== 13-limit ====
Line 63: Line 73:
Wedgie: {{Multival| 0 12 24 36 48 19 38 57 76 22 42 67 18 46 33 }}
Wedgie: {{Multival| 0 12 24 36 48 19 38 57 76 22 42 67 18 46 33 }}


Optimal tuning (POTE): ~256/243 = 1\12, ~5/4 = 383.9628 (~105/104 = 16.0372)
Optimal tunings:
* CTE: ~35/33 = 100.000, ~5/4 = 384.685 (~105/104 = 15.315)
* POTE: ~35/33 = 100.000, ~5/4 = 383.963 (~105/104 = 16.037)


{{Optimal ET sequence|legend=1| 12f, 48defff, 60eff, 72, 228f }}
{{Optimal ET sequence|legend=0| 12f, 48deefff, 60eff, 72, 228f }}


Badness: 0.021852
Badness (Smith): 0.021852


===== 17-limit =====
===== 17-limit =====
Line 76: Line 88:
Mapping: {{mapping| 12 19 0 -22 -42 -67 49 | 0 0 1 2 3 4 0 }}
Mapping: {{mapping| 12 19 0 -22 -42 -67 49 | 0 0 1 2 3 4 0 }}


Optimal tuning (POTE): ~18/17 = 1\12, ~5/4 = 383.7500 (~105/104 = 16.2500)
Optimal tunings:
* CTE: ~18/17 = 100.000, ~5/4 = 384.685 (~105/104 = 15.315)
* POTE: ~18/17 = 100.000, ~5/4 = 383.750 (~105/104 = 16.250)


{{Optimal ET sequence|legend=1| 12f, 60eff, 72 }}
{{Optimal ET sequence|legend=0| 12f, 60eff, 72 }}


Badness: 0.017131
Badness (Smith): 0.017131


==== Comptone ====
==== Comptone ====
Line 91: Line 105:
Wedgie: {{Multival| 0 12 24 36 -24 19 38 57 -38 22 42 -100 18 -156 -216 }}
Wedgie: {{Multival| 0 12 24 36 -24 19 38 57 -38 22 42 -100 18 -156 -216 }}


Optimal tuning (POTE): ~256/243 = 1\12, ~5/4 = 382.6116 (~100/99 = 17.3884)
Optimal tunings:
* CTE: ~35/33 = 100.000, ~5/4 = 383.552 (~100/99 = 16.448)
* POTE: ~35/33 = 100.000, ~5/4 = 382.612 (~100/99 = 17.388)


{{Optimal ET sequence|legend=1| 12, 60e, 72, 204cdef, 276cdeff }}
{{Optimal ET sequence|legend=0| 12, 60e, 72, 204cdef, 276cdeff }}


Badness: 0.025144
Badness (Smith): 0.025144


===== 17-limit =====
===== 17-limit =====
Line 104: Line 120:
Mapping: {{mapping| 12 19 0 -22 -42 100 49 | 0 0 1 2 3 -2 0 }}
Mapping: {{mapping| 12 19 0 -22 -42 100 49 | 0 0 1 2 3 -2 0 }}


Optimal tuning (POTE): ~18/17 = 1\12, ~5/4 = 382.5968 (~100/99 = 17.4032)
Optimal tunings:
* CTE: ~18/17 = 100.000, ~5/4 = 383.552 (~100/99 = 16.448)
* POTE: ~18/17 = 100.000, ~5/4 = 382.597 (~100/99 = 17.403)


{{Optimal ET sequence|legend=1| 12, 60e, 72, 204cdefg, 276cdeffgg }}
{{Optimal ET sequence|legend=0| 12, 60e, 72, 204cdefg, 276cdeffgg }}


Badness: 0.016361
Badness (Smith): 0.016361


== Catler ==
== Catler ==
Line 123: Line 141:
{{Multival|legend=1| 0 0 12 0 19 28 }}
{{Multival|legend=1| 0 0 12 0 19 28 }}


[[Optimal tuning]] ([[POTE]]): ~16/15 = 1\12, ~7/4 = 973.210 (~64/63 = 26.790)
[[Optimal tuning]]s:
* [[CTE]]: ~16/15 = 100.000, ~7/4 = 968.826 (~64/63 = 31.174)
: [[error map]]: {{val| 0.000 -1.955 +13.686 0.000 }}
* [[POTE]]: ~16/15 = 100.000, ~7/4 = 973.210 (~64/63 = 26.790)
: error map: {{val| 0.000 -1.955 +13.686 +4.384 }}


{{Optimal ET sequence|legend=1| 12, 24, 36, 48c }}
{{Optimal ET sequence|legend=1| 12, 24, 36, 48c, 84c }}


[[Badness]]: 0.050297
[[Badness]] (Smith): 0.050297


=== 11-limit ===
=== 11-limit ===
Line 136: Line 158:
Mapping: {{mapping| 12 19 28 0 -26 | 0 0 0 1 2 }}
Mapping: {{mapping| 12 19 28 0 -26 | 0 0 0 1 2 }}


Optimal tuning (POTE): ~16/15 = 1\12, ~7/4 = 977.277 (~64/63 = 22.723)
Optimal tunings:
* CTE: ~16/15 = 100.000, ~7/4 = 973.779 (~64/63 = 26.221)
* POTE: ~16/15 = 100.000, ~7/4 = 977.277 (~64/63 = 22.723)


{{Optimal ET sequence|legend=1| 12, 36e, 48c, 108ccd }}
{{Optimal ET sequence|legend=0| 12, 36e, 48c }}


Badness: 0.058213
Badness (Smith): 0.058213


=== Catlat ===
=== Catlat ===
Line 149: Line 173:
Mapping: {{mapping| 12 19 28 0 109 | 0 0 0 1 -2 }}
Mapping: {{mapping| 12 19 28 0 109 | 0 0 0 1 -2 }}


Optimal tuning (POTE): ~16/15 = 1\12, ~7/4 = 972.136 (~64/63 = 27.864)
Optimal tunings:
* CTE: ~16/15 = 100.000, ~7/4 = 972.823 (~64/63 = 27.177)
* POTE: ~16/15 = 100.000, ~7/4 = 972.136 (~64/63 = 27.864)


{{Optimal ET sequence|legend=1| 36, 48c, 84c }}
{{Optimal ET sequence|legend=0| 12e, 36, 48c, 84c }}


Badness: 0.081909
Badness (Smith): 0.081909


=== Catnip ===
=== Catnip ===
Line 162: Line 188:
Mapping: {{mapping| 12 19 28 0 8 | 0 0 0 1 1 }}
Mapping: {{mapping| 12 19 28 0 8 | 0 0 0 1 1 }}


Optimal tuning (POTE): ~16/15 = 1\12, ~7/4 = 967.224 (~64/63 = 32.776)
Optimal tunings:
* CTE: ~16/15 = 100.000, ~7/4 = 961.874 (~64/63 = 38.126)
* POTE: ~16/15 = 100.000, ~7/4 = 967.224 (~64/63 = 32.776)


{{Optimal ET sequence|legend=1| 12, 24, 36, 72ce }}
{{Optimal ET sequence|legend=0| 12, 24, 36, 72ce }}


Badness: 0.034478
Badness (Smith): 0.034478


==== 13-limit ====
==== 13-limit ====
Line 175: Line 203:
Mapping: {{mapping| 12 19 28 0 8 11 | 0 0 0 1 1 1 }}
Mapping: {{mapping| 12 19 28 0 8 11 | 0 0 0 1 1 1 }}


Optimal tuning (POTE): ~16/15 = 1\12, ~7/4 = 962.778 (~40/39 = 37.232)
Optimal tunings:
* CTE: ~16/15 = 100.000, ~7/4 = 956.375 (~40/39 = 43.625)
* POTE: ~16/15 = 100.000, ~7/4 = 962.778 (~40/39 = 37.232)


{{Optimal ET sequence|legend=1| 12f, 24, 36f, 60cf }}
{{Optimal ET sequence|legend=0| 12f, 24, 36f }}


Badness: 0.028363
Badness (Smith): 0.028363


===== 17-limit =====
===== 17-limit =====
Line 188: Line 218:
Mapping: {{mapping| 12 19 28 0 8 11 49 | 0 0 0 1 1 1 0 }}
Mapping: {{mapping| 12 19 28 0 8 11 49 | 0 0 0 1 1 1 0 }}


Optimal tuning (POTE): ~18/17 = 1\12, ~7/4 = 960.223 (~40/39 = 39.777)
Optimal tunings:
* CTE: ~18/17 = 100.000, ~7/4 = 956.375 (~40/39 = 43.625)
* POTE: ~18/17 = 100.000, ~7/4 = 960.223 (~40/39 = 39.777)


{{Optimal ET sequence|legend=1| 12f, 24, 36f, 60cf }}
{{Optimal ET sequence|legend=0| 12f, 24, 36f }}


Badness: 0.023246
Badness (Smith): 0.023246


===== 19-limit =====
===== 19-limit =====
Line 201: Line 233:
Mapping: {{mapping| 12 19 28 0 8 11 49 51 | 0 0 0 1 1 1 0 0 }}
Mapping: {{mapping| 12 19 28 0 8 11 49 51 | 0 0 0 1 1 1 0 0 }}


Optimal tuning (POTE): ~18/17 = 1\12, ~7/4 = 959.835 (~40/39 = 40.165)
Optimal tunings:
* CTE: ~18/17 = 100.000, ~7/4 = 956.375 (~40/39 = 43.625)
* POTE: ~18/17 = 100.000, ~7/4 = 959.835 (~40/39 = 40.165)


{{Optimal ET sequence|legend=1| 12f, 24, 36f, 60cf }}
{{Optimal ET sequence|legend=0| 12f, 24, 36f }}


Badness: 0.018985
Badness (Smith): 0.018985


==== Duodecic ====
==== Duodecic ====
Line 214: Line 248:
Mapping: {{mapping| 12 19 28 0 8 78 | 0 0 0 1 1 -1 }}
Mapping: {{mapping| 12 19 28 0 8 78 | 0 0 0 1 1 -1 }}


Optimal tuning (POTE): ~16/15 = 1\12, ~7/4 = 962.312 (~64/63 = 37.688)
Optimal tunings:
* CTE: ~16/15 = 100.000, ~7/4 = 961.255 (~64/63 = 38.745)
* POTE: ~16/15 = 100.000, ~7/4 = 962.312 (~64/63 = 37.688)


{{Optimal ET sequence|legend=1| 12, 24, 36, 60c }}
{{Optimal ET sequence|legend=0| 12, 24, 36 }}


Badness: 0.038307
Badness (Smith): 0.038307


===== 17-limit =====
===== 17-limit =====
Line 227: Line 263:
Mapping:{{mapping| 12 19 28 0 8 78 49 | 0 0 0 1 1 -1 0 }}
Mapping:{{mapping| 12 19 28 0 8 78 49 | 0 0 0 1 1 -1 0 }}


Optimal tuning (POTE): ~18/17 = 1\12, ~7/4 = 961.903 (~64/63 = 38.097)
Optimal tunings:
* CTE: ~18/17 = 100.000, ~7/4 = 961.255 (~64/63 = 38.745)
* POTE: ~18/17 = 100.000, ~7/4 = 961.903 (~64/63 = 38.097)


{{Optimal ET sequence|legend=1| 12, 24, 36, 60c }}
{{Optimal ET sequence|legend=0| 12, 24, 36, 60c }}


Badness: 0.027487
Badness (Smith): 0.027487


===== 19-limit =====
===== 19-limit =====
Line 240: Line 278:
Mapping: {{mapping| 12 19 28 0 8 78 49 51 | 0 0 0 1 1 -1 0 0 }}
Mapping: {{mapping| 12 19 28 0 8 78 49 51 | 0 0 0 1 1 -1 0 0 }}


Optimal tuning (POTE): ~18/17 = 1\12, ~7/4 = 961.920 (~64/63 = 38.080)
Optimal tunings:
* CTE: ~18/17 = 100.000, ~7/4 = 961.255 (~64/63 = 38.745)
* POTE: ~18/17 = 100.000, ~7/4 = 961.920 (~64/63 = 38.080)


{{Optimal ET sequence|legend=1| 12, 24, 36, 60c }}
{{Optimal ET sequence|legend=0| 12, 24, 36, 60c }}


Badness: 0.020939
Badness (Smith): 0.020939


== Duodecim ==
== Duodecim ==
Line 263: Line 303:
{{Optimal ET sequence|legend=1| 12, 24d, 36d }}
{{Optimal ET sequence|legend=1| 12, 24d, 36d }}


[[Badness]]: 0.030536
[[Badness]] (Smith): 0.030536


== Hours ==
== Hours ==
Line 278: Line 318:
{{Multival|legend=1| 0 24 -24 38 -38 -123 }}
{{Multival|legend=1| 0 24 -24 38 -38 -123 }}


[[Optimal tuning]] ([[POTE]]): ~36/35 = 1\24, ~5/4 = 384.033 (~81/80 = 15.967)
[[Optimal tuning]]s:
* [[CTE]]: ~36/35 = 50.000, ~5/4 = 384.226 (~81/80 = 15.774)
: [[error map]]: {{val| 0.000 -1.955 -2.088 -3.052 }}
* [[POTE]]: ~36/35 = 50.000, ~5/4 = 384.033 (~81/80 = 15.967)
: error map: {{val| 0.000 -1.955 -2.280 -2.859 }}


{{Optimal ET sequence|legend=1| 24, 48, 72, 312bd, 384bcdd, 456bcdd, 528bcdd, 600bccdd }}
{{Optimal ET sequence|legend=1| 24, 48, 72, 312bd, 384bcdd, 456bcdd, 528bcdd, 600bccdd }}


[[Badness]]: 0.116091
[[Badness]] (Smith): 0.116091


=== 11-limit ===
=== 11-limit ===
Line 291: Line 335:
Mapping: {{mapping| 24 38 0 123 83 | 0 0 1 -1 0 }}
Mapping: {{mapping| 24 38 0 123 83 | 0 0 1 -1 0 }}


Optimal tuning (POTE): ~36/35 = 1\24, ~5/4 = 384.054 (~121/120 = 15.946)
Optimal tunings:
* CTE: ~36/35 = 50.000, ~5/4 = 384.226 (~121/120 = 15.774)
* POTE: ~36/35 = 50.000, ~5/4 = 384.054 (~121/120 = 15.946)


{{Multival|legend=1| 0 24 -24 0 38 -38 0 -123 -83 83 }}
{{Multival|legend=1| 0 24 -24 0 38 -38 0 -123 -83 83 }}
Line 297: Line 343:
{{Optimal ET sequence|legend=1| 24, 48, 72, 312bd, 384bcdd, 456bcdde, 528bcdde }}
{{Optimal ET sequence|legend=1| 24, 48, 72, 312bd, 384bcdd, 456bcdde, 528bcdde }}


Badness: 0.036248
Badness (Smith): 0.036248


=== 13-limit ===
=== 13-limit ===
Line 306: Line 352:
Mapping: {{mapping| 24 38 0 123 83 33 | 0 0 1 -1 0 1 }}
Mapping: {{mapping| 24 38 0 123 83 33 | 0 0 1 -1 0 1 }}


Optimal tuning (POTE): ~36/35 = 1\24, ~5/4 = 384.652 (~121/120 = 15.348)
Optimal tunings:
* CTE: ~36/35 = 50.000, ~5/4 = 385.420 (~121/120 = 14.580)
* POTE: ~36/35 = 50.000, ~5/4 = 384.652 (~121/120 = 15.348)


{{Multival|legend=1| 0 24 -24 0 24 38 -38 0 38 -123 -83 -33 83 156 83 }}
{{Multival|legend=1| 0 24 -24 0 24 38 -38 0 38 -123 -83 -33 83 156 83 }}
Line 312: Line 360:
{{Optimal ET sequence|legend=1| 24, 48f, 72, 168df, 240dff }}
{{Optimal ET sequence|legend=1| 24, 48f, 72, 168df, 240dff }}


Badness: 0.026931
Badness (Smith): 0.026931


== Decades ==
== Decades ==
Line 327: Line 375:
{{Multival|legend=1| 0 36 0 57 0 -101 }}
{{Multival|legend=1| 0 36 0 57 0 -101 }}


[[Optimal tuning]] ([[POTE]]): ~49/48 = 1\36, ~5/4 = 384.764 (~81/80 = 15.236)
[[Optimal tuning]]s:
* [[CTE]]: ~49/48 = 33.333, ~5/4 = 386.314 (~81/80 = 13.686)
: [[error map]]: {{val| 0.000 -1.955 0.000 -2.159 }}
* [[POTE]]: ~49/48 = 33.333, ~5/4 = 384.764 (~81/80 = 15.236)
: error map: {{val| 0.000 -1.955 -1.549 -2.159 }}


{{Optimal ET sequence|legend=1| 36, 72, 252, 324bd, 396bd }}
{{Optimal ET sequence|legend=1| 36, 72, 252, 324bd, 396bd }}


[[Badness]]: 0.108016
[[Badness]] (Smith): 0.108016


=== 11-limit ===
=== 11-limit ===
Line 340: Line 392:
Mapping: {{mapping| 36 57 0 101 41 | 0 0 1 0 1 }}
Mapping: {{mapping| 36 57 0 101 41 | 0 0 1 0 1 }}


Optimal tuning (POTE): ~49/48 = 1\36, ~5/4 = 384.150 (~81/80 = 15.850)
Optimal tunings:
* CTE: ~49/48 = 33.333, ~5/4 = 385.797 (~81/80 = 14.203)
* POTE: ~49/48 = 33.333, ~5/4 = 385.150 (~81/80 = 14.850)


{{Optimal ET sequence|legend=1| 36, 72, 396bd, 468bcd, 540bcd, 612bccdd, 684bbccdd, 756bbccdd }}
{{Optimal ET sequence|legend=1| 36, 72, 396bd, 468bcd, 540bcd, 612bccdd, 684bbccdd, 756bbccdd }}


Badness: 0.043088
Badness (Smith): 0.043088


== Omicronbeta ==
== Omicronbeta ==
[[Subgroup]]: 2.3.5.7.11.13
[[Subgroup]]: 2.3.5.7.11.13


[[Comma list]]: 225/224, 243/242, 441/440, 4000/3993
[[Comma list]]: 225/224, 243/242, 385/384, 4000/3993


{{Mapping|legend=1| 72 114 167 202 249 0 | 0 0 0 0 0 1 }}
{{Mapping|legend=1| 72 114 167 202 249 0 | 0 0 0 0 0 1 }}
Line 357: Line 411:
{{Multival|legend=1| 0 0 0 0 72 0 0 0 114 0 0 167 0 202 249 }}
{{Multival|legend=1| 0 0 0 0 72 0 0 0 114 0 0 167 0 202 249 }}


[[Optimal tuning]] ([[POTE]]): ~100/99 = 1\72, ~13/8 = 837.814 (~364/363 = 4.481)
[[Optimal tuning]]s:
* [[CTE]]: ~100/99 = 16.667, ~13/8 = 840.528 (~325/324 = 7.194)
: [[error map]]: {{val| 0.000 -1.955 -2.980 -2.159 -1.318 0.000 }}
* [[POTE]]: ~100/99 = 16.667, ~13/8 = 837.814 (~364/363 = 4.481)
: error map: {{val| 0.000 -1.955 -2.980 -2.159 -1.318 -2.713 }}


{{Optimal ET sequence|legend=1| 72, 144, 216c, 288cdf, 504bcdef }}
{{Optimal ET sequence|legend=1| 72, 144, 216c, 288cdf }}


[[Badness]]: 0.029956
[[Badness]] (Smith): 0.029956


[[Category:Temperament families]]
[[Category:Temperament families]]
Retrieved from "https://en.xen.wiki/w/Compton_family"