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Hemimage temperaments: Difference between revisions

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m Units, misc. cleanup, - redundant category
Switch to Sintel's badness, WE & CWE tunings
Line 27: Line 27:
: mapping generators: ~63/50, ~28/27
: mapping generators: ~63/50, ~28/27


[[Optimal tuning]] ([[POTE]]): ~63/50 = 400.000{{c}}, ~28/27 = 60.528{{c}}
[[Optimal tuning]]s:
* [[WE]]: ~63/50 = 399.9549{{c}}, ~28/27 = 60.5216{{c}}
: [[error map]]: {{val| -0.135 +0.473 +0.241 -0.751 }}
* [[CWE]]: ~63/50 = 400.0000{{c}}, ~28/27 = 60.5162{{c}}
: error map: {{val| 0.000 +0.626 +0.397 -0.567 }}


{{Optimal ET sequence|legend=1| 39d, 60, 99, 258, 357, 456 }}
{{Optimal ET sequence|legend=1| 39d, 60, 99, 258, 357, 456 }}


[[Badness]] (Smith): 0.057499
[[Badness]] (Sintel): 1.46


=== 11-limit ===
=== 11-limit ===
Line 40: Line 44:
Mapping: {{mapping| 3 4 5 6 6 | 0 5 13 16 29 }}
Mapping: {{mapping| 3 4 5 6 6 | 0 5 13 16 29 }}


Optimal tuning (POTE): ~44/35 = 400.000{{c}}, ~28/27 = 60.430{{c}}
Optimal tunings:
* WE: ~44/35 = 400.0359{{c}}, ~28/27 = 60.4357{{c}}
* CWE: ~44/35 = 400.0000{{c}}, ~28/27 = 60.4375{{c}}


{{Optimal ET sequence|legend=0| 60e, 99e, 159, 258, 417d }}
{{Optimal ET sequence|legend=0| 60e, 99e, 159, 258 }}


Badness (Smith): 0.050379
Badness (Sintel): 1.67


==== 13-limit ====
==== 13-limit ====
Line 53: Line 59:
Mapping: {{mapping| 3 4 5 6 6 4 | 0 5 13 16 29 47 }}
Mapping: {{mapping| 3 4 5 6 6 4 | 0 5 13 16 29 47 }}


Optimal tuning (POTE): ~44/35 = 400.000{{c}}, ~28/27 = 60.428{{c}}
Optimal tunings:
* WE: ~44/35 = 400.0382{{c}}, ~28/27 = 60.4342{{c}}
* CWE: ~44/35 = 400.0000{{c}}, ~28/27 = 60.4331{{c}}


{{Optimal ET sequence|legend=0| 99ef, 159, 258, 417d }}
{{Optimal ET sequence|legend=0| 60eff, 99ef, 159, 258, 417d }}


Badness (Smith): 0.046006
Badness (Sintel): 1.90


===== 17-limit =====
===== 17-limit =====
Line 66: Line 74:
Mapping: {{mapping| 3 4 5 6 6 4 10 | 0 5 13 16 29 47 15 }}
Mapping: {{mapping| 3 4 5 6 6 4 10 | 0 5 13 16 29 47 15 }}


Optimal tuning (POTE): ~44/35 = 400.000{{c}}, ~28/27 = 60.438{{c}}
Optimal tunings:
* WE: ~44/35 = 399.9982{{c}}, ~28/27 = 60.4374{{c}}
* CWE: ~44/35 = 400.0000{{c}}, ~28/27 = 60.4375{{c}}


{{Optimal ET sequence|legend=0| 99ef, 159, 258, 417dg }}
{{Optimal ET sequence|legend=0| 99ef, 159, 258, 417dg }}


Badness (Smith): 0.031678
Badness (Sintel): 1.61


==== Catachrome ====
==== Catachrome ====
Line 79: Line 89:
Mapping: {{mapping| 3 4 5 6 6 12 | 0 5 13 16 29 -6 }}
Mapping: {{mapping| 3 4 5 6 6 12 | 0 5 13 16 29 -6 }}


Optimal tuning (POTE): ~44/35 = 400.000{{c}}, ~28/27 = 60.378{{c}}
Optimal tunings:
* WE: ~44/35 = 400.1386{{c}}, ~28/27 = 60.3986{{c}}
* CWE: ~44/35 = 400.0000{{c}}, ~28/27 = 60.3929{{c}}


{{Optimal ET sequence|legend=0| 60e, 99e, 159 }}
{{Optimal ET sequence|legend=0| 60e, 99e, 159 }}


Badness (Smith): 0.043844
Badness (Sintel): 1.81


===== 17-limit =====
===== 17-limit =====
Line 92: Line 104:
Mapping: {{mapping| 3 4 5 6 6 12 10 | 0 5 13 16 29 -6 15 }}
Mapping: {{mapping| 3 4 5 6 6 12 10 | 0 5 13 16 29 -6 15 }}


Optimal tuning (POTE): ~44/35 = 400.000{{c}}, ~28/27 = 60.377{{c}}
Optimal tunings:
* WE: ~44/35 = 400.1115{{c}}, ~28/27 = 60.3935{{c}}
* CWE: ~44/35 = 400.0000{{c}}, ~28/27 = 60.3893{{c}}


{{Optimal ET sequence|legend=0| 60e, 99e, 159 }}
{{Optimal ET sequence|legend=0| 60e, 99e, 159 }}


Badness (Smith): 0.030218
Badness (Sintel): 1.54


==== Chromic ====
==== Chromic ====
Line 105: Line 119:
Mapping: {{mapping| 3 4 5 6 6 9 | 0 5 13 16 29 14 }}
Mapping: {{mapping| 3 4 5 6 6 9 | 0 5 13 16 29 14 }}


Optimal tuning (POTE): ~44/35 = 400.000{{c}}, ~27/26 = 60.456{{c}}
Optimal tunings:
* WE: ~44/35 = 399.9082{{c}}, ~28/27 = 60.4425{{c}}
* CWE: ~44/35 = 400.0000{{c}}, ~28/27 = 60.4380{{c}}


{{Optimal ET sequence|legend=0| 60e, 99ef, 159f, 258ff }}
{{Optimal ET sequence|legend=0| 60e, 99ef, 159f }}


Badness (Smith): 0.049857
Badness (Sintel): 2.06


===== 17-limit =====
===== 17-limit =====
Line 118: Line 134:
Mapping: {{mapping| 3 4 5 6 6 9 10 | 0 5 13 16 29 14 15 }}
Mapping: {{mapping| 3 4 5 6 6 9 10 | 0 5 13 16 29 14 15 }}


Optimal tuning (POTE): ~63/50 = 400.000{{c}}, ~27/26 = 60.459{{c}}
Optimal tunings:
* WE: ~44/35 = 399.8948{{c}}, ~28/27 = 60.4435{{c}}
* CWE: ~44/35 = 400.0000{{c}}, ~28/27 = 60.4385{{c}}


{{Optimal ET sequence|legend=0| 60e, 99ef, 159f, 258ff }}
{{Optimal ET sequence|legend=0| 60e, 99ef, 159f }}


Badness (Smith): 0.031043
Badness (Sintel): 1.58


=== Hemichromat ===
=== Hemichromat ===
Line 131: Line 149:
Mapping: {{mapping| 3 4 5 6 10 | 0 10 26 32 5 }}
Mapping: {{mapping| 3 4 5 6 10 | 0 10 26 32 5 }}


Optimal tuning (CTE): ~63/50 = 400.0000{{c}}, ~55/54 = 30.2511{{c}}
Optimal tunings:
* WE: ~63/50 = 399.9750{{c}}, ~55/54 = 30.2568{{c}}
* CWE: ~63/50 = 400.0000{{c}}, ~55/54 = 30.2561{{c}}


{{Optimal ET sequence|legend=0| 39d, 120cd, 159, 198, 357, 912b }}
{{Optimal ET sequence|legend=0| 39d, 120cd, 159, 198, 357, 912b }}


Badness (Smith): 0.067173
Badness (Sintel): 2.22


==== 13-limit ====
==== 13-limit ====
Line 144: Line 164:
Mapping: {{mapping| 3 4 5 6 10 8 | 0 10 26 32 5 41 }}
Mapping: {{mapping| 3 4 5 6 10 8 | 0 10 26 32 5 41 }}


Optimal tuning (CTE): ~63/50 = 400.0000{{c}}, ~55/54 = 30.2527{{c}}
Optimal tunings:
* WE: ~63/50 = 399.9741{{c}}, ~55/54 = 30.2584{{c}}
* CWE: ~63/50 = 400.0000{{c}}, ~55/54 = 30.2577{{c}}


{{Optimal ET sequence|legend=0| 39df, 120cdff, 159, 198, 357, 912b }}
{{Optimal ET sequence|legend=0| 39df, 120cdff, 159, 198, 357, 912b }}


Badness (Smith): 0.033420
Badness (Sintel): 1.38


== Bisupermajor ==
== Bisupermajor ==
Line 160: Line 182:
: mapping generators: ~1225/864, ~192/175
: mapping generators: ~1225/864, ~192/175


[[Optimal tuning]] ([[POTE]]): ~1225/864 = 600.000{{c}}, ~192/175 = 162.806{{c}}
[[Optimal tuning]]s:
* [[WE]]: ~1225/864 = 600.0294{{c}}, ~192/175 = 162.8141{{c}}
: [[error map]]: {{val| +0.059 +0.587 -0.208 -0.957 }}
* [[CWE]]: ~1225/864 = 600.0000{{c}}, ~192/175 = 162.8082{{c}}
: error map: {{val| 0.000 +0.510 -0.355 -1.087 }}


{{Optimal ET sequence|legend=1| 22, 74d, 96d, 118, 140, 258, 398, 656d }}
{{Optimal ET sequence|legend=1| 22, 74d, 96d, 118, 140, 258, 398, 656d }}


[[Badness]] (Smith): 0.065492
[[Badness]] (Sintel): 1.66


=== 11-limit ===
=== 11-limit ===
Line 173: Line 199:
Mapping: {{mapping| 2 1 6 1 8 | 0 8 -5 17 -4 }}
Mapping: {{mapping| 2 1 6 1 8 | 0 8 -5 17 -4 }}


Optimal tuning (POTE): ~99/70 = 600.000{{c}}, ~11/10 = 162.773{{c}}
Optimal tunings:
* WE: ~99/70 = 600.1224{{c}}, ~11/10 = 162.8065{{c}}
* CWE: ~99/70 = 600.0000{{c}}, ~11/10 = 162.7788{{c}}


{{Optimal ET sequence|legend=0| 22, 74d, 96d, 118, 258e, 376de }}
{{Optimal ET sequence|legend=0| 22, 74d, 96d, 118, 258e, 376de, 634dee }}


Badness (Smith): 0.032080
Badness (Sintel): 1.06


== Bicommatic ==
== Bicommatic ==
Line 189: Line 217:
: mapping generators: ~567/400, ~81/80
: mapping generators: ~567/400, ~81/80


[[Optimal tuning]] ([[POTE]]): ~567/400 = 600.000{{c}}, ~81/80 = 20.377{{c}}
[[Optimal tuning]]s:
* [[WE]]: ~567/400 = 600.0497{{c}}, ~81/80 = 20.3790{{c}}
: [[error map]]: {{val| +0.099 +0.089 +1.085 -1.756 }}
* [[CWE]]: ~567/400 = 600.0000{{c}}, ~81/80 = 20.3837{{c}}
: error map: {{val| 0.000 -0.037 +0.976 -1.920 }}


{{Optimal ET sequence|legend=1| 58, 118, 294, 412d, 530d }}
{{Optimal ET sequence|legend=1| 58, 118, 294, 412d }}


[[Badness]] (Smith): 0.084317
[[Badness]] (Sintel): 2.13


=== 11-limit ===
=== 11-limit ===
Line 202: Line 234:
Mapping: {{mapping| 2 3 4 5 6 | 0 5 19 18 27 }}
Mapping: {{mapping| 2 3 4 5 6 | 0 5 19 18 27 }}


Optimal tuning (POTE): ~99/70 = 600.000{{c}}, ~81/80 = 20.390{{c}}
Optimal tunings:
* WE: ~99/70 = 600.0401{{c}}, ~81/80 = 20.3913{{c}}
* CWE: ~99/70 = 600.0000{{c}}, ~81/80 = 20.3948{{c}}


{{Optimal ET sequence|legend=0| 58, 118, 294, 412d }}
{{Optimal ET sequence|legend=0| 58, 118, 294, 412d }}


Badness (Smith): 0.030461
Badness (Sintel): 1.01


=== 13-limit ===
=== 13-limit ===
Line 215: Line 249:
Mapping: {{mapping| 2 3 4 5 6 7 | 0 5 19 18 27 12 }}
Mapping: {{mapping| 2 3 4 5 6 7 | 0 5 19 18 27 12 }}


Optimal tuning (POTE): ~99/70 = 600.000{{c}}, ~66/65 = 20.427{{c}}
Optimal tunings:
* WE: ~99/70 = 599.8514{{c}}, ~66/65 = 20.4215{{c}}
* CWE: ~99/70 = 600.0000{{c}}, ~66/65 = 20.4093{{c}}


{{Optimal ET sequence|legend=0| 58, 118, 176f }}
{{Optimal ET sequence|legend=0| 58, 118, 176f }}


Badness (Smith): 0.026336
Badness (Sintel): 1.09


=== 17-limit ===
=== 17-limit ===
Line 228: Line 264:
Mapping: {{mapping| 2 3 4 5 6 7 8 | 0 5 19 18 27 12 5 }}
Mapping: {{mapping| 2 3 4 5 6 7 8 | 0 5 19 18 27 12 5 }}


Optimal tuning (POTE): ~17/12 = 600.000{{c}}, ~66/65 = 20.378{{c}}
Optimal tunings:
* WE: ~17/12 = 600.0257{{c}}, ~66/65 = 20.3789{{c}}
* CWE: ~17/12 = 600.0000{{c}}, ~66/65 = 20.3804{{c}}


{{Optimal ET sequence|legend=0| 58, 118, 294ffg, 412dffgg }}
{{Optimal ET sequence|legend=0| 58, 118 }}


Badness (Smith): 0.022396
Badness (Sintel): 1.14


== Degrees ==
== Degrees ==
Line 253: Line 291:
: mapping generators: ~28/27, ~3
: mapping generators: ~28/27, ~3


[[Optimal tuning]] ([[POTE]]): ~28/27 = 60.000{{c}}, ~3/2 = 703.015{{c}} (~126/125 = 16.985{{c}})
[[Optimal tuning]]s:
* [[WE]]: ~28/27 = 59.9922{{c}}, ~3/2 = 702.9233{{c}} (~126/125 = 16.9828{{c}})
: [[error map]]: {{val| -0.157 +0.812 -0.647 -0.220 }}
* [[CWE]]: ~28/27 = 60.0000{{c}}, ~3/2 = 702.9324{{c}} (~126/125 = 17.0676{{c}})
: error map: {{val| 0.000 +0.977 -0.449 -0.029 }}


{{Optimal ET sequence|legend=1| 20cd, 60, 80, 140, 640b, 780b }}
{{Optimal ET sequence|legend=1| 60, 80, 140, 640b, 780b }}


[[Badness]] (Sintel): 2.69
[[Badness]] (Sintel): 2.69
Line 266: Line 308:
Mapping: {{mapping| 20 0 -17 -39 -26 | 0 1 2 3 3 }}
Mapping: {{mapping| 20 0 -17 -39 -26 | 0 1 2 3 3 }}


Optimal tuning (POTE): ~28/27 = 60.000{{c}}, ~3/2 = 703.231{{c}} (~100/99 = 16.769{{c}})
Optimal tunings:
* WE: ~28/27 = 59.9929{{c}}, ~3/2 = 703.1478{{c}} (~100/99 = 16.7666{{c}})
* CWE: ~28/27 = 60.0000{{c}}, ~3/2 = 703.1556{{c}} (~100/99 = 16.8444{{c}})


{{Optimal ET sequence|legend=0| 20cd, 60e, 80, 140, 360 }}
{{Optimal ET sequence|legend=0| 60e, 80, 140, 360 }}


Badness (Sintel): 1.55
Badness (Sintel): 1.55
Line 279: Line 323:
Mapping: {{mapping| 20 0 -17 -39 -26 74 | 0 1 2 3 3 0 }}
Mapping: {{mapping| 20 0 -17 -39 -26 74 | 0 1 2 3 3 0 }}


Optimal tuning (POTE): ~28/27 = 600.000{{c}}, ~3/2 = 703.080{{c}} (~100/99 = 16.920{{c}})
Optimal tunings:
* WE: ~28/27 = 59.9996{{c}}, ~3/2 = 703.0749{{c}} (~100/99 = 16.9197{{c}})
* CWE: ~28/27 = 60.0000{{c}}, ~3/2 = 703.0770{{c}} (~100/99 = 16.9230{{c}})


{{Optimal ET sequence|legend=0| 20cde, 60e, 80, 140 }}
{{Optimal ET sequence|legend=0| 60e, 80, 140 }}


Badness (Sintel): 1.35
Badness (Sintel): 1.35
Line 292: Line 338:
Mapping: {{mapping| 20 0 -17 -39 -26 74 50 | 0 1 2 3 3 0 1 }}
Mapping: {{mapping| 20 0 -17 -39 -26 74 50 | 0 1 2 3 3 0 1 }}


Optimal tuning (CTE): ~28/27 = 600.000{{c}}, ~3/2 = 703.107{{c}} (~100/99 = 16.893{{c}})
Optimal tunings:
* WE: ~28/27 = 60.0058{{c}}, ~3/2 = 703.0364{{c}} (~100/99 = 17.0335{{c}})
* CWE: ~28/27 = 60.0000{{c}}, ~3/2 = 703.0061{{c}} (~100/99 = 16.9939{{c}})


{{Optimal ET sequence|legend=0| 20cde, 60e, 80, 140 }}
{{Optimal ET sequence|legend=0| 60e, 80, 140 }}


Badness (Sintel): 1.17
Badness (Sintel): 1.17
Line 305: Line 353:
Mapping: {{mapping| 20 0 -17 -39 -26 74 50 85 | 0 1 2 3 3 0 1 0 }}
Mapping: {{mapping| 20 0 -17 -39 -26 74 50 85 | 0 1 2 3 3 0 1 0 }}


Optimal tuning (CTE): ~28/27 = 600.000{{c}}, ~3/2 = 703.107{{c}} (~100/99 = 16.893{{c}})
Optimal tunings:
* WE: ~28/27 = 59.9961{{c}}, ~3/2 = 703.1523{{c}} (~100/99 = 16.8015{{c}})
* CWE: ~28/27 = 60.0000{{c}}, ~3/2 = 703.1777{{c}} (~100/99 = 16.8223{{c}})


{{Optimal ET sequence|legend=0| 20cde, 60e, 80, 140 }}
{{Optimal ET sequence|legend=0| 60e, 80, 140 }}


Badness (Sintel): 1.27
Badness (Sintel): 1.27
Line 318: Line 368:
Mapping: {{mapping| 20 0 -17 -39 -26 74 50 85 27 | 0 1 2 3 3 0 1 0 2 }}
Mapping: {{mapping| 20 0 -17 -39 -26 74 50 85 27 | 0 1 2 3 3 0 1 0 2 }}


Optimal tuning (CTE): ~28/27 = 600.000{{c}}, ~3/2 = 703.169{{c}} (~100/99 = 16.831{{c}})
Optimal tunings:
* WE: ~28/27 = 59.9990{{c}}, ~3/2 = 703.1804{{c}} (~100/99 = 16.8074{{c}})
* CWE: ~28/27 = 60.0000{{c}}, ~3/2 = 703.1870{{c}} (~100/99 = 16.8130{{c}})


{{Optimal ET sequence|legend=0| 20cdei, 60e, 80, 140 }}
{{Optimal ET sequence|legend=0| 60e, 80, 140 }}


Badness (Sintel): 1.21
Badness (Sintel): 1.21
Line 331: Line 383:
Mapping: {{mapping| 20 0 -17 -39 -26 74 50 85 27 2 | 0 1 2 3 3 0 1 0 2 3 }}
Mapping: {{mapping| 20 0 -17 -39 -26 74 50 85 27 2 | 0 1 2 3 3 0 1 0 2 3 }}


Optimal tuning (CTE): ~29/28 = 600.000{{c}}, ~3/2 = 703.171{{c}} (~100/99 = 16.829{{c}})
Optimal tunings:
* WE: ~29/28 = 59.9990{{c}}, ~3/2 = 703.1829{{c}} (~100/99 = 16.8055{{c}})
* CWE: ~29/28 = 60.0000{{c}}, ~3/2 = 703.1891{{c}} (~100/99 = 16.8109{{c}})


{{Optimal ET sequence|legend=0| 20cdeij, 60e, 80, 140 }}
{{Optimal ET sequence|legend=0| 60e, 80, 140 }}


Badness (Sintel): 1.13
Badness (Sintel): 1.13


=== no-31's 37-limit ===
=== 2.3.5.7.11.13.17.19.23.29.37 subgroup ===
Subgroup: 2.3.5.7.11.13.17.19.23.29.37
Subgroup: 2.3.5.7.11.13.17.19.23.29.37


Line 344: Line 398:
Mapping: {{mapping| 20 0 -17 -39 -26 74 50 85 27 2 9 | 0 1 2 3 3 0 1 0 2 3 3 }}
Mapping: {{mapping| 20 0 -17 -39 -26 74 50 85 27 2 9 | 0 1 2 3 3 0 1 0 2 3 3 }}


Optimal tuning (CTE): ~29/28 = 600.000{{c}}, ~3/2 = 703.222{{c}} (~100/99 = 16.778{{c}})
Optimal tunings:
* WE: ~29/28 = 60.0001{{c}}, ~3/2 = 703.2183{{c}} (~100/99 = 16.7827{{c}})
* CWE: ~29/28 = 60.0000{{c}}, ~3/2 = 703.2178{{c}} (~100/99 = 16.7822{{c}})


{{Optimal ET sequence|legend=0| 20cdeijl, 60el, 80, 140 }}
{{Optimal ET sequence|legend=0| 60el, 80, 140 }}


Badness (Sintel): 1.13
Badness (Sintel): 1.13


=== no-31's 41-limit ===
=== 2.3.5.7.11.13.17.19.23.29.37.41 subgroup ===
Subgroup: 2.3.5.7.11.13.17.19.23.29.37.41
Subgroup: 2.3.5.7.11.13.17.19.23.29.37.41


Line 357: Line 413:
Mapping: {{mapping| 20 0 -17 -39 -26 74 50 85 27 2 9 12 | 0 1 2 3 3 0 1 0 2 3 3 3 }}
Mapping: {{mapping| 20 0 -17 -39 -26 74 50 85 27 2 9 12 | 0 1 2 3 3 0 1 0 2 3 3 3 }}


Optimal tuning (CTE): ~29/28 = 600.000{{c}}, ~3/2 = 703.207{{c}}
Optimal tunings:
* WE: ~29/28 = 59.9998{{c}}, ~3/2 = 703.2088{{c}} (~100/99 = 16.7882{{c}})
* CWE: ~29/28 = 60.0000{{c}}, ~3/2 = 703.2104{{c}} (~100/99 = 16.7896{{c}})


{{Optimal ET sequence|legend=0| 20cdeijlm, 60el, 80, 140 }}
{{Optimal ET sequence|legend=0| 60el, 80, 140 }}


Badness (Sintel): 1.10
Badness (Sintel): 1.10


== Squarschmidt ==
== Squarschmidt ==
A generator for the squarschimidt temperament is the fourth root of [[5/2]], (5/2)<sup>1/4</sup>, tuned around 396.6 cents. The squarschimidt temperament can be described as {{nowrap| 118 & 239 }} temperament, tempering out the hemimage comma and quasiorwellisma, 29360128/29296875 in the 7-limit. In the 11-limit, 118&amp;239 tempers out 3025/3024, 5632/5625, and 12005/11979, and the generator represents ~44/35.
A generator for the squarschimidt temperament is the fourth root of [[5/2]], (5/2)<sup>1/4</sup>, tuned around 396.6 cents. The squarschimidt temperament can be described as {{nowrap| 118 & 239 }} temperament, tempering out the hemimage comma and quasiorwellisma, 29360128/29296875 in the 7-limit. In the 11-limit, it tempers out 3025/3024, 5632/5625, and 12005/11979, and the generator represents ~44/35.  


[[Subgroup]]: 2.3.5
[[Subgroup]]: 2.3.5
Line 373: Line 431:
: mapping generators: ~2, ~98304/78125
: mapping generators: ~2, ~98304/78125


[[Optimal tuning]] ([[POTE]]): ~2 = 1200.000{{c}}, ~98304/78125 = 396.621{{c}}
[[Optimal tuning]]s:
* [[WE]]: ~2 = 1199.9653{{c}}, ~98304/78125 = 396.6094{{c}}
: [[error map]]: {{val| -0.099 +0.543 +0.029 -0.719 }}
* [[CWE]]: ~2 = 1200.0000{{c}}, ~98304/78125 = 396.6201{{c}}
: error map: {{val| 0.000 +0.653 +0.253 -0.552 }}


{{Optimal ET sequence|legend=1| 118, 593, 711, 829, 947 }}
{{Optimal ET sequence|legend=1| 118, 593, 711, 829, 947, 9588cc, 10535cc, 11482ccc }}


[[Badness]] (Smith): 0.218314
[[Badness]] (Sintel): 5.12


=== 7-limit ===
=== 7-limit ===
Line 386: Line 448:
{{Mapping|legend=1| 1 -8 1 -20 | 0 29 4 69 }}
{{Mapping|legend=1| 1 -8 1 -20 | 0 29 4 69 }}


[[Optimal tuning]] ([[POTE]]): ~2 = 1200.000{{c}}, ~1125/896 = 396.643{{c}}
[[Optimal tuning]]s:
* [[WE]]: ~2 = 1199.9006{{c}}, ~1125/896 = 396.6104{{c}}
: [[error map]]: {{val| -0.099 +0.543 +0.029 -0.719 }}
* [[CWE]]: ~2 = 1200.0000{{c}}, ~1125/896 = 396.6417{{c}}
: error map: {{val| 0.000 +0.653 +0.253 -0.552 }}


{{Optimal ET sequence|legend=1| 118, 239, 357, 596, 1549bd }}
{{Optimal ET sequence|legend=1| 118, 239, 357, 596 }}


[[Badness]] (Smith): 0.132821
[[Badness]] (Sintel): 3.36


=== 11-limit ===
=== 11-limit ===
Line 399: Line 465:
Mapping: {{mapping| 1 -8 1 -20 -21 | 0 29 4 69 74 }}
Mapping: {{mapping| 1 -8 1 -20 -21 | 0 29 4 69 74 }}


Optimal tuning (POTE): ~2 = 1200.000{{c}}, ~44/35 = 396.644{{c}}
Optimal tunings:
* WE: ~2 = 1199.9005{{c}}, ~44/35 = 396.6107{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~44/35 = 396.6419{{c}}


{{Optimal ET sequence|legend=0| 118, 239, 357, 596 }}
{{Optimal ET sequence|legend=0| 118, 239, 357, 596 }}


Badness (Smith): 0.038186
Badness (Sintel): 1.26


[[Category:Temperament collections]]
[[Category:Temperament collections]]
[[Category:Hemimage temperaments| ]] <!-- main article -->
[[Category:Hemimage temperaments| ]] <!-- main article -->
[[Category:Rank 2]]
[[Category:Rank 2]]
Retrieved from "https://en.xen.wiki/w/Hemimage_temperaments"