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Quartonic family: Difference between revisions

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Switch to Sintel's badness, WE & CWE tunings (1/)
Switch to Sintel's badness, WE & CWE tunings (2/2)
 
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== Yarman I ==
== Yarman I ==
Yarman I is the first interpretation of [[Ozan Yarman]]'s proposed tuning for the Turkish makam.
[[Subgroup]]: 2.3.5.7
[[Subgroup]]: 2.3.5.7


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{{Mapping|legend=1| 1 2 3 4 | 0 -33 -54 -95 }}
{{Mapping|legend=1| 1 2 3 4 | 0 -33 -54 -95 }}
: mapping generators: ~2, ~126/125


[[Optimal tuning]] ([[CTE]]): ~2 = 1200.0000{{c}}, ~126/125 = 15.0714{{c}}
[[Optimal tuning]]s:
* [[WE]]: ~2 = 1199.8726{{c}}, ~126/125 = 15.0651{{c}}
: [[error map]]: {{val| -0.127 +0.641 -0.213 -0.523 }}
* [[CWE]]: ~2 = 1200.0000{{c}}, ~126/125 = 15.0689{{c}}
: error map: {{val| 0.000 +0.771 -0.036 -0.374 }}


{{Optimal ET sequence|legend=1| 79d, 80, 159, 239, 398, 637 }}
{{Optimal ET sequence|legend=1| 79d, 80, 159, 239, 637, 876b }}


[[Badness]] (Smith): 0.193315
[[Badness]] (Sintel): 4.89


=== 11-limit ===
=== 11-limit ===
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Mapping: {{mapping| 1 2 3 4 4 | 0 -33 -54 -95 -43 }}
Mapping: {{mapping| 1 2 3 4 4 | 0 -33 -54 -95 -43 }}


Optimal tuning (CTE): ~2 = 1200.0000{{c}}, ~100/99 = 15.0724{{c}}
Optimal tunings:
* WE: ~2 = 1199.8339{{c}}, ~100/99 = 15.0637{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~100/99 = 15.0685{{c}}


{{Optimal ET sequence|legend=0| 79d, 80, 159, 239, 398, 637, 1035bd }}
{{Optimal ET sequence|legend=0| 79d, 80, 159, 239, 876be }}


Badness (Smith): 0.049170
Badness (Sintel): 1.63


=== 13-limit ===
=== 13-limit ===
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Mapping: {{mapping| 1 2 3 4 4 4 | 0 -33 -54 -95 -43 -24 }}
Mapping: {{mapping| 1 2 3 4 4 4 | 0 -33 -54 -95 -43 -24 }}


Optimal tuning (CTE): ~2 = 1200.0000{{c}}, ~91/90 = 15.0707{{c}}
Optimal tunings:
* WE: ~2 = 1200.1080{{c}}, ~100/99 = 15.0766{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~100/99 = 15.0737{{c}}


{{Optimal ET sequence|legend=0| 79d, 80, 159, 239, 398f, 637ff }}
{{Optimal ET sequence|legend=0| 79d, 80, 159, 239, 398f }}


Badness (Smith): 0.040929
Badness (Sintel): 1.69


=== 17-limit ===
=== 17-limit ===
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Mapping: {{mapping| 1 2 3 4 4 4 4 | 0 -33 -54 -95 -43 -24 7 }}
Mapping: {{mapping| 1 2 3 4 4 4 4 | 0 -33 -54 -95 -43 -24 7 }}


Optimal tuning (CTE): ~2 = 1200.0000{{c}}, ~91/90 = 15.0706{{c}}
Optimal tunings:
* WE: ~2 = 1200.0222{{c}}, ~100/99 = 15.0718{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~100/99 = 15.0713{{c}}


{{Optimal ET sequence|legend=0| 79d, 80, 159, 239, 398f, 637ff }}
{{Optimal ET sequence|legend=0| 79d, 80, 159, 239, 398f }}


Badness (Smith): 0.031015
Badness (Sintel): 1.58


=== 19-limit ===
=== 19-limit ===
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Mapping: {{mapping| 1 2 3 4 4 4 4 5 | 0 -33 -54 -95 -43 -24 7 -60 }}
Mapping: {{mapping| 1 2 3 4 4 4 4 5 | 0 -33 -54 -95 -43 -24 7 -60 }}


Optimal tuning (CTE): ~2 = 1200.0000{{c}}, ~91/90 = 15.0683{{c}}
Optimal tunings:
* WE: ~2 = 1200.0698{{c}}, ~100/99 = 15.0722{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~100/99 = 15.0706{{c}}


{{Optimal ET sequence|legend=0| 79dh, 80, 159, 239, 637ffh }}
{{Optimal ET sequence|legend=0| 79dh, 80, 159, 239, 398fh }}


Badness (Smith): 0.023193
Badness (Sintel): 1.41


=== 23-limit ===
=== 23-limit ===
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Mapping: {{mapping| 1 2 3 4 4 4 4 5 5 | 0 -33 -54 -95 -43 -24 7 -60 -38 }}
Mapping: {{mapping| 1 2 3 4 4 4 4 5 5 | 0 -33 -54 -95 -43 -24 7 -60 -38 }}


Optimal tuning (CTE): ~2 = 1200.0000{{c}}, ~91/90 = 15.0676{{c}}
Optimal tunings:
* WE: ~2 = 1200.0946{{c}}, ~100/99 = 15.0732{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~100/99 = 15.0710{{c}}


{{Optimal ET sequence|legend=0| 79dh, 80, 159, 239, 637ffhi }}
{{Optimal ET sequence|legend=0| 79dh, 80, 159, 239, 398fh }}


Badness (Smith): 0.017682
Badness (Sintel): 1.27


=== 29-limit ===
=== 29-limit ===
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Mapping: {{mapping| 1 2 3 4 4 4 4 5 5 6 | 0 -33 -54 -95 -43 -24 7 -60 -38 -91 }}
Mapping: {{mapping| 1 2 3 4 4 4 4 5 5 6 | 0 -33 -54 -95 -43 -24 7 -60 -38 -91 }}


Optimal tuning (CTE): ~2 = 1200.0000{{c}}, ~91/90 = 15.0667{{c}}
Optimal tunings:
* WE: ~2 = 1200.0995{{c}}, ~100/99 = 15.0726{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~100/99 = 15.0703{{c}}


{{Optimal ET sequence|legend=0| 79dhj, 80, 159, 239 }}
{{Optimal ET sequence|legend=0| 79dhj, 80, 159, 239, 398fh }}


Badness (Smith): 0.014289
Badness (Sintel): 1.19


== Yarman II ==
== Yarman II ==
Yarman II is the other interpretation of [[Ozan Yarman]]'s proposed tuning for the Turkish makam.
[[Subgroup]]: 2.3.5.7
[[Subgroup]]: 2.3.5.7


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{{Mapping|legend=1| 1 2 3 2 | 0 -33 -54 64 }}
{{Mapping|legend=1| 1 2 3 2 | 0 -33 -54 64 }}
: mapping generators: ~2, ~875/864


[[Optimal tuning]] ([[CTE]]): ~2 = 1200.0000{{c}}, ~875/864 = 15.0995{{c}}
[[Optimal tuning]]s:
* [[WE]]: ~2 = 1200.4734{{c}}, ~875/864 = 15.1122{{c}}
: [[error map]]: {{val| +0.473 +0.291 -0.950 -0.701 }}
* [[CWE]]: ~2 = 1200.0000{{c}}, ~875/864 = 15.1048{{c}}
: error map: {{val| 0.000 -0.412 -1.971 -2.121 }}


{{Optimal ET sequence|legend=1| 79, 159 }}
{{Optimal ET sequence|legend=1| 79, 159, 397cd, 556cd, 715ccdd }}


[[Badness]] (Smith): 0.655487
[[Badness]] (Sintel): 16.6


=== 11-limit ===
=== 11-limit ===
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Mapping: {{mapping| 1 2 3 2 4 | 0 -33 -54 64 -43 }}
Mapping: {{mapping| 1 2 3 2 4 | 0 -33 -54 64 -43 }}


Optimal tuning (CTE): ~2 = 1200.0000{{c}}, ~100/99 = 15.0982{{c}}
Optimal tunings:
* WE: ~2 = 1200.4357{{c}}, ~100/99 = 15.1126{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~100/99 = 15.1054{{c}}


{{Optimal ET sequence|legend=0| 79, 159 }}
{{Optimal ET sequence|legend=0| 79, 159, 397cd, 556cd }}


Badness (Smith): 0.143477
Badness (Sintel): 4.74


=== 13-limit ===
=== 13-limit ===
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Mapping: {{mapping| 1 2 3 2 4 4 | 0 -33 -54 64 -43 -24 }}
Mapping: {{mapping| 1 2 3 2 4 4 | 0 -33 -54 64 -43 -24 }}


Optimal tuning (CTE): ~2 = 1200.0000{{c}}, ~100/99 = 15.0952{{c}}
Optimal tunings:
* WE: ~2 = 1200.5028{{c}}, ~100/99 = 15.1135{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~100/99 = 15.1052{{c}}


{{Optimal ET sequence|legend=0| 79, 159 }}
{{Optimal ET sequence|legend=0| 79, 159, 397cdff, 556cdff }}


Badness (Smith): 0.068150
Badness (Sintel): 2.82


=== 17-limit ===
=== 17-limit ===
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Mapping: {{mapping| 1 2 3 2 4 4 4 | 0 -33 -54 64 -43 -24 7 }}
Mapping: {{mapping| 1 2 3 2 4 4 4 | 0 -33 -54 64 -43 -24 7 }}


Optimal tuning (CTE): ~2 = 1200.0000{{c}}, ~100/99 = 15.0950{{c}}
Optimal tunings:
* WE: ~2 = 1200.3840{{c}}, ~100/99 = 15.1086{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~100/99 = 15.1025{{c}}


{{Optimal ET sequence|legend=0| 79, 159 }}
{{Optimal ET sequence|legend=0| 79, 159 }}


Badness (Smith): 0.051019
Badness (Sintel): 2.60


== Tertiseptisix ==
== Tertiseptisix ==
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[[Comma list]]: 2401/2400, 390625000/387420489
[[Comma list]]: 2401/2400, 390625000/387420489


{{Mapping|legend=1| 1 13 21 15 | 0 -44 -72 -47 }}
{{Mapping|legend=1| 1 -31 -51 -32 | 0 44 72 47 }}
: mapping generators: ~2, ~1458/875


[[Optimal tuning]] ([[CTE]]): ~2 = 1200.000{{c}}, ~875/729 = 311.308{{c}}
[[Optimal tuning]]s:
* [[WE]]: ~2 = 1200.0156{{c}}, ~1458/875 = 888.7028{{c}}
: [[error map]]: {{val| +0.016 +0.485 -0.507 -0.293 }}
* [[CWE]]: ~2 = 1200.0000{{c}}, ~1458/875 = 888.6915{{c}}
: error map: {{val| 0.000 +0.472 -0.523 -0.324 }}


{{Optimal ET sequence|legend=1| 27, 131bccd, 158cd, 185c, 212, 239, 451 }}
{{Optimal ET sequence|legend=1| 27, …, 212, 239, 451 }}


[[Badness]] (Smith): 0.155952
[[Badness]] (Sintel): 3.95


== Triquart ==
== Triquart ==
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{{Mapping|legend=1| 3 6 9 10 | 0 -11 -18 -14 }}
{{Mapping|legend=1| 3 6 9 10 | 0 -11 -18 -14 }}
: mapping generators: ~63/50, ~250/243


[[Optimal tuning]] ([[CTE]]): ~63/50 = 400.0000{{c}}, ~250/243 = 45.2083{{c}}
[[Optimal tuning]]s:
* [[WE]]: ~63/50 = 400.0521{{c}}, ~250/243 = 45.2373{{c}}
: [[error map]]: {{val| +0.156 +0.747 -0.117 -1.628 }}
* [[CWE]]: ~63/50 = 400.0000{{c}}, ~250/243 = 45.2204{{c}}
: error map: {{val| 0.000 +0.621 -0.281 -1.911 }}


{{Optimal ET sequence|legend=1| 27, 105cd, 132d, 159, 186, 345d }}
{{Optimal ET sequence|legend=1| 27, 105cd, 132d, 159, 345d, 506d }}


[[Badness]] (Smith): 0.170062
[[Badness]] (Sintel): 4.30


== Quartiquart ==
== Quartiquart ==
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{{Mapping|legend=1| 4 8 12 15 | 0 -11 -18 -25 }}
{{Mapping|legend=1| 4 8 12 15 | 0 -11 -18 -25 }}
: mapping generators: ~25/21, ~250/243


[[Optimal tuning]] ([[CTE]]): ~25/21 = 300.0000{{c}}, ~250/243 = 45.2411{{c}}
[[Optimal tuning]]s:
* [[WE]]: ~25/21 = 299.9955{{c}}, ~250/243 = 45.2382{{c}}
: [[error map]]: {{val| -0.018 +0.389 -0.655 +0.152 }}
* [[CWE]]: ~25/21 = 300.0000{{c}}, ~250/243 = 45.2400{{c}}
: error map: {{val| 0.000 +0.405 -0.634 +0.174 }}


{{Optimal ET sequence|legend=1| 80, 132d, 212, 292, 504 }}
{{Optimal ET sequence|legend=1| 80, 132d, 212, 292, 504 }}


[[Badness]] (Smith): 0.199116
[[Badness]] (Sintel): 5.04


=== 11-limit ===
=== 11-limit ===
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Mapping: {{mapping| 4 8 12 15 17 | 0 -11 -18 -25 -21 }}
Mapping: {{mapping| 4 8 12 15 17 | 0 -11 -18 -25 -21 }}


Optimal tuning (CTE): ~25/21 = 300.0000{{c}}, ~77/75 = 45.2303{{c}}
Optimal tunings:
* WE: ~25/21 = 300.0140{{c}}, ~77/75 = 45.2398{{c}}
* CWE: ~25/21 = 300.0000{{c}}, ~77/75 = 45.2342{{c}}


{{Optimal ET sequence|legend=0| 80, 132de, 212, 292, 504e }}
{{Optimal ET sequence|legend=0| 80, 132de, 212, 292, 504e }}


Badness (Smith): 0.062450
Badness (Sintel): 2.06


=== 13-limit ===
=== 13-limit ===
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Mapping: {{mapping| 4 8 12 15 17 16 | 0 -11 -18 -25 -21 -8 }}
Mapping: {{mapping| 4 8 12 15 17 16 | 0 -11 -18 -25 -21 -8 }}


Optimal tuning (CTE): ~25/21 = 300.0000{{c}}, ~40/39 = 45.2243{{c}}
Optimal tunings:
* WE: ~25/21 = 300.0805{{c}}, ~40/39 = 45.2812{{c}}
* CWE: ~25/21 = 300.0000{{c}}, ~40/39 = 45.2517{{c}}


{{Optimal ET sequence|legend=0| 80, 132de, 212 }}
{{Optimal ET sequence|legend=0| 80, 132de, 212 }}


Badness (Smith): 0.045028
Badness (Sintel): 1.86


=== 17-limit ===
=== 17-limit ===
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Mapping: {{mapping| 4 8 12 15 17 16 18 | 0 -11 -18 -25 -21 -8 -11 }}
Mapping: {{mapping| 4 8 12 15 17 16 18 | 0 -11 -18 -25 -21 -8 -11 }}


Optimal tuning (CTE): ~25/21 = 300.000{{c}}, ~40/39 = 45.218{{c}}
Optimal tunings:
* WE: ~25/21 = 300.1108{{c}}, ~40/39 = 45.2990{{c}}
* CWE: ~25/21 = 300.0000{{c}}, ~40/39 = 45.2604{{c}}


{{Optimal ET sequence|legend=0| 52cdeg, 80, 132deg, 212g }}
{{Optimal ET sequence|legend=0| 80, 132deg, 212g }}


Badness (Smith): 0.0312
Badness (Sintel): 1.59


=== 19-limit ===
=== 19-limit ===
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Mapping: {{mapping| 4 8 12 15 17 16 18 20 | 0 -11 -18 -25 -21 -8 -11 20 }}
Mapping: {{mapping| 4 8 12 15 17 16 18 20 | 0 -11 -18 -25 -21 -8 -11 20 }}


Optimal tuning (CTE): ~25/21 = 300.000{{c}}, ~39/38 = 45.210{{c}}
Optimal tunings:
* WE: ~25/21 = 300.1212{{c}}, ~39/38 = 45.3015{{c}}
* CWE: ~25/21 = 300.0000{{c}}, ~39/38 = 45.2590{{c}}


{{Optimal ET sequence|legend=0| 52cdegh, 80, 132degh, 212gh }}
{{Optimal ET sequence|legend=0| 80, 132degh, 212gh }}


Badness (Smith): 0.0224
Badness (Sintel): 1.36


== Quintiquart ==
== Quintiquart ==
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{{Mapping|legend=1| 5 10 15 18 | 0 -11 -18 -21 }}
{{Mapping|legend=1| 5 10 15 18 | 0 -11 -18 -21 }}
: mapping generators: ~35721/31250, ~250/243


[[Optimal tuning]] ([[CTE]]): ~35721/31250 = 240.0000{{c}}, ~250/243 = 45.2563{{c}}
[[Optimal tuning]]s:
* [[WE]]: ~35721/31250 = 239.9950{{c}}, ~250/243 = 45.2520{{c}}
: [[error map]]: {{val| -0.025 +0.223 -0.925 +0.792 }}
* [[CWE]]: ~35721/31250 = 240.0000{{c}}, ~250/243 = 45.2546{{c}}
: error map: {{val| 0.000 +0.244 -0.897 +0.826 }}


{{Optimal ET sequence|legend=1| 80, 185c, 265, 610d, 875cd }}
{{Optimal ET sequence|legend=1| 80, 185c, 265, 610d }}


[[Badness]] (Smith): 0.357387
[[Badness]] (Sintel): 9.04


=== 11-limit ===
=== 11-limit ===
Line 501: Line 561:
Mapping: {{mapping| 5 10 15 18 19 | 0 -11 -18 -21 -9 }}
Mapping: {{mapping| 5 10 15 18 19 | 0 -11 -18 -21 -9 }}


Optimal tuning (CTE): ~8019/7000 = 240.0000{{c}}, ~250/243 = 45.2624{{c}}
Optimal tunings:
* WE: ~8019/7000 = 239.9613{{c}}, ~250/243 = 45.2270{{c}}
* CWE: ~8019/7000 = 240.0000{{c}}, ~250/243 = 45.2460{{c}}


{{Optimal ET sequence|legend=0| 80, 185c, 265, 610de, 875cde }}
{{Optimal ET sequence|legend=0| 80, 185c, 265, 345 }}


Badness (Smith): 0.103496
Badness (Sintel): 3.42


[[Category:Temperament families]]
[[Category:Temperament families]]
[[Category:Quartonic family| ]] <!-- main article -->
[[Category:Quartonic family| ]] <!-- main article -->
[[Category:Rank 2]]
[[Category:Rank 2]]
Retrieved from "https://en.xen.wiki/w/Quartonic_family"