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Minortone family: Difference between revisions

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{{Technical data page}}
{{Technical data page}}
The '''minortonic family''' tempers out the minortone comma (also known as "minortonma"), {{monzo| -16 35 -17 }}. The head of this family is 5-limit minortone temperament, with generator a minor tone.
The '''minortone family''' of [[regular temperament|temperaments]] [[tempering out|tempers out]] the [[minortone comma]] ({{monzo|legend=1| -16 35 -17 }}).  


== Minortone ==
== Minortone ==
The head of this family is the 5-limit minortone temperament, with generator a minor tone.
[[Subgroup]]: 2.3.5
[[Subgroup]]: 2.3.5


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{{Mapping|legend=1| 1 -1 -3 | 0 17 35 }}
{{Mapping|legend=1| 1 -1 -3 | 0 17 35 }}


[[Optimal tuning]] ([[POTE]]): ~2 = 1\1, ~10/9 = 182.466
[[Optimal tuning]] ([[POTE]]): ~2 = 1200.000{{c}}, ~10/9 = 182.466{{c}}


{{Optimal ET sequence|legend=1| 46, 125, 171, 388, 559, 730, 1289, 2019, 2749, 4768, 16323, 21091 }}
{{Optimal ET sequence|legend=1| 46, 125, 171, 388, 559, 730, 1289, 2019, 2749, 4768, 16323, 21091 }}


[[Badness]]: 0.029765
[[Badness]] (Smith): 0.029765


== Mitonic ==
== Mitonic ==
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{{Mapping|legend=1| 1 -1 -3 6 | 0 17 35 -21 }}
{{Mapping|legend=1| 1 -1 -3 6 | 0 17 35 -21 }}


[[Optimal tuning]] ([[POTE]]): ~2 = 1\1, ~10/9 = 182.458
[[Optimal tuning]] ([[POTE]]): ~2 = 1200.000{{c}}, ~10/9 = 182.458{{c}}


{{Optimal ET sequence|legend=1| 46, 125, 171, 1927d, 2098d, …, 3637bcdd }}
{{Optimal ET sequence|legend=1| 46, 125, 171, 1927d, 2098d, …, 3637bcdd }}


[[Badness]]: 0.025184
[[Badness]] (Smith): 0.025184


=== Mineral ===
=== Mineral ===
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Mapping: {{mapping| 1 -1 -3 6 10 | 0 17 35 -21 -43 }}
Mapping: {{mapping| 1 -1 -3 6 10 | 0 17 35 -21 -43 }}


Optimal tuning (POTE): ~2 = 1\1, ~10/9 = 182.482
Optimal tuning (POTE): ~2 = 1200.000{{c}}, ~10/9 = 182.482{{c}}


{{Optimal ET sequence|legend=1| 46, 125e, 171, 217, 605ee, 822dee }}
{{Optimal ET sequence|legend=0| 46, 125e, 171, 217, 605ee, 822dee }}


Badness: 0.059060
Badness (Smith): 0.059060


==== 13-limit ====
==== 13-limit ====
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Mapping: {{mapping| 1 -1 -3 6 10 11 | 0 17 35 -21 -43 -48 }}
Mapping: {{mapping| 1 -1 -3 6 10 11 | 0 17 35 -21 -43 -48 }}


Optimal tuning (POTE): ~2 = 1\1, ~10/9 = 182.481
Optimal tuning (POTE): ~2 = 1200.000{{c}}, ~10/9 = 182.481{{c}}


{{Optimal ET sequence|legend=1| 46, 125e, 171, 217, 605ee, 822dee }}
{{Optimal ET sequence|legend=0| 46, 125e, 171, 217, 605ee, 822dee }}


Badness: 0.033140
Badness (Smith): 0.033140


==== 17-limit ====
==== 17-limit ====
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Mapping: {{mapping| 1 -1 -3 6 10 11 5 | 0 17 35 -21 -43 -48 -6 }}
Mapping: {{mapping| 1 -1 -3 6 10 11 5 | 0 17 35 -21 -43 -48 -6 }}


Optimal tuning (POTE): ~2 = 1\1, ~10/9 = 182.481
Optimal tuning (POTE): ~2 = 1200.000{{c}}, ~10/9 = 182.481{{c}}


{{Optimal ET sequence|legend=1| 46, 125e, 171, 217, 605ee, 822dee }}
{{Optimal ET sequence|legend=0| 46, 125e, 171, 217, 605ee, 822dee }}


Badness: 0.019792
Badness (Smith): 0.019792


=== Ore ===
=== Ore ===
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Mapping: {{mapping| 1 -1 -3 6 3 | 0 17 35 -21 3 }}
Mapping: {{mapping| 1 -1 -3 6 3 | 0 17 35 -21 3 }}


Optimal tuning (POTE): ~2 = 1\1, ~10/9 = 182.449
Optimal tuning (POTE): ~2 = 1200.000{{c}}, ~10/9 = 182.449{{c}}


{{Optimal ET sequence|legend=1| 46, 125, 171e }}
{{Optimal ET sequence|legend=1| 46, 125, 171e }}


Badness: 0.053662
Badness (Smith): 0.053662


==== 13-limit ====
==== 13-limit ====
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Mapping: {{mapping| 1 -1 -3 6 3 11 | 0 17 35 -21 3 -48 }}
Mapping: {{mapping| 1 -1 -3 6 3 11 | 0 17 35 -21 3 -48 }}


Optimal tuning (POTE): ~2 = 1\1, ~10/9 = 182.470
Optimal tuning (POTE): ~2 = 1200.000{{c}}, ~10/9 = 182.470{{c}}


{{Optimal ET sequence|legend=1| 46, 125, 171e, 388ee }}
{{Optimal ET sequence|legend=0| 46, 125, 171e, 388ee }}


Badness: 0.046170
Badness (Smith): 0.046170


===== 17-limit =====
===== 17-limit =====
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Mapping: {{mapping| 1 -1 -3 6 3 11 5 | 0 17 35 -21 3 -48 -6 }}
Mapping: {{mapping| 1 -1 -3 6 3 11 5 | 0 17 35 -21 3 -48 -6 }}


Optimal tuning (POTE): ~2 = 1\1, ~10/9 = 182.471
Optimal tuning (POTE): ~2 = 1200.000{{c}}, ~10/9 = 182.471{{c}}


{{Optimal ET sequence|legend=1| 46, 125, 171e, 388ee }}
{{Optimal ET sequence|legend=0| 46, 125, 171e, 388ee }}


Badness: 0.028423
Badness (Smith): 0.028423


==== Goldmine ====
==== Goldmine ====
The goldmine temperament (46 & 79) is another 13-limit extension of ore, equating [[13/12]] with [[14/13]] and [[16/13]] with two [[10/9]]s.
The goldmine temperament (46 & 79) is another 13-limit extension of ore, equating [[13/12]] with [[14/13]] and [[16/13]] with two [[10/9]]s.


Subgroup: 2.3.5.7.11.13
Subgroup: 2.3.5.7.11.13
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Mapping: {{mapping| 1 -1 -3 6 3 4 | 0 17 35 -21 3 -2 }}
Mapping: {{mapping| 1 -1 -3 6 3 4 | 0 17 35 -21 3 -2 }}


Optimal tuning (POTE): ~2 = 1\1, ~10/9 = 182.437
Optimal tuning (POTE): ~2 = 1200.000{{c}}, ~10/9 = 182.437{{c}}


{{Optimal ET sequence|legend=1| 46, 79, 125f, 171ef, 296eff }}
{{Optimal ET sequence|legend=0| 46, 79, 125f, 171ef, 296eff }}


Badness: 0.039302
Badness (Smith): 0.039302


===== 17-limit =====
===== 17-limit =====
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Mapping: {{mapping| 1 -1 -3 6 3 4 5 | 0 17 35 -21 3 -2 -6 }}
Mapping: {{mapping| 1 -1 -3 6 3 4 5 | 0 17 35 -21 3 -2 -6 }}


Optimal tuning (POTE): ~2 = 1\1, ~10/9 = 182.444
Optimal tuning (POTE): ~2 = 1200.000{{c}}, ~10/9 = 182.444{{c}}


{{Optimal ET sequence|legend=1| 46, 125f, 171ef }}
{{Optimal ET sequence|legend=0| 46, 125f, 171ef }}


Badness: 0.027440
Badness (Smith): 0.027440


=== Seminar ===
=== Seminar ===
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Mapping: {{mapping| 2 -2 -6 12 13 | 0 17 35 -21 -20 }}
Mapping: {{mapping| 2 -2 -6 12 13 | 0 17 35 -21 -20 }}


Optimal tuning (POTE): ~2 = 1\1, ~10/9 = 182.457
Optimal tuning (POTE): ~2 = 1200.000{{c}}, ~10/9 = 182.457{{c}}


{{Optimal ET sequence|legend=1| 46, 204c, 250, 296, 342 }}
{{Optimal ET sequence|legend=0| 46, 204c, 250, 296, 342 }}


Badness: 0.026808
Badness (Smith): 0.026808


== Domain ==
== Domain ==
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{{Mapping|legend=1| 3 -3 -9 -8 | 0 17 35 36 }}
{{Mapping|legend=1| 3 -3 -9 -8 | 0 17 35 36 }}


[[Optimal tuning]] ([[POTE]]): ~63/50 = 1\3, ~10/9 = 182.467
[[Optimal tuning]] ([[POTE]]): ~63/50 = 400.000{{c}}, ~10/9 = 182.467{{c}}


{{Optimal ET sequence|legend=1| 171, 1164, 1335, 1506, 1677, 1848, 2019, 11943, 13962, 15981, 18000, 20019, 22038 }}
{{Optimal ET sequence|legend=1| 171, 1164, 1335, 1506, 1677, 1848, 2019, 11943, 13962, 15981, 18000, 20019, 22038 }}


[[Badness]]: 0.013979
[[Badness]] (Smith): 0.013979


=== Hemidomain ===
=== Hemidomain ===
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Mapping: {{mapping| 6 11 17 20 24 | 0 -17 -35 -36 -37 }}
Mapping: {{mapping| 6 11 17 20 24 | 0 -17 -35 -36 -37 }}
 
: mapping generators: ~55/49 = 200.000{{c}}, ~100/99 = 17.533{{c}}
: mapping generators: ~55/49 = 1\6, ~100/99 = 17.533


Optimal tuning (CTE): ~100/99 = 17.533
Optimal tuning (CTE): ~100/99 = 17.533


{{Optimal ET sequence|legend=1| 342, 480, 822, 1164, 1506, 1848, … }}
{{Optimal ET sequence|legend=0| 342, 480, 822, 1164, 1506, 1848, … }}


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