No-twos subgroup temperaments: Difference between revisions

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* Deneb has a ~11/9 generator, three of which give the ~9/5.

* Canopus has a ~15/7 generator, five of which give the ~45/1 (5/1 up two tritaves).

* Miaplacidus has a ~7/5 generator, eight of which give the ~15/1 (5/1 up one tritave).

* Alnilam has a ~55/27 generator, ten of which give the ~1215/1 (5/1 up five tritaves).

* Izar has a ~30375/16807 generator, twelve of which give the ~1215/1 (5/1 up five tritaves).

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Badness (Sintel): 0.542

== Miaplacidus ==

Miaplacidus tempers out [[5859375/5764801]], the amount by which eight [[7/5]]'s fall short of [[15/1]]. It thus tunes the chord 7:9:15 accurately. Having a generator of ~7/5, it possesses [[mos scale]]s of the families {{mos scalesig|link=true|3L 4s<3/1>}}, {{mos scalesig|link=true|3L 7s<3/1>}}, {{mos scalesig|link=true|3L 10s<3/1>}}, and {{mos scalesig|link=true|13L 3s<3/1>}}. Good tunings for this temperament are [[13edt]], [[16edt]], and [[29edt]].

[[Subgroup]]: 3.5.7

[[Comma list]]: 5859375/5764801

: mapping generators: ~3, ~7/5

[[Optimal tuning]]s:

* [[WE]]: ~3 = 1901.8789{{c}}, ~7/5 = 585.8428{{c}}

: [[error map]]: {{val| -0.076 -1.450 +1.880 }}

* [[CWE]]: ~3 = 1901.9550{{c}}, ~7/5 = 585.8590{{c}}

: error map: {{val| 0.000 -1.396 +1.950 }}

[[Badness]] (Sintel): 1.24

== Izar ==

@@ Line 12: / Line 12: @@
 * Deneb has a ~11/9 generator, three of which give the ~9/5.
 * Canopus has a ~15/7 generator, five of which give the ~45/1 (5/1 up two tritaves).
+* Miaplacidus has a ~7/5 generator, eight of which give the ~15/1 (5/1 up one tritave).
 * Alnilam has a ~55/27 generator, ten of which give the ~1215/1 (5/1 up five tritaves).
 * Izar has a ~30375/16807 generator, twelve of which give the ~1215/1 (5/1 up five tritaves).
@@ Line 456: / Line 457: @@
 Badness (Sintel): 0.542
+== Miaplacidus ==
+Miaplacidus tempers out [[5859375/5764801]], the amount by which eight [[7/5]]'s fall short of [[15/1]]. It thus tunes the chord 7:9:15 accurately. Having a generator of ~7/5, it possesses [[mos scale]]s of the families {{mos scalesig|link=true|3L 4s<3/1>}}, {{mos scalesig|link=true|3L 7s<3/1>}}, {{mos scalesig|link=true|3L 10s<3/1>}}, and {{mos scalesig|link=true|13L 3s<3/1>}}. Good tunings for this temperament are [[13edt]], [[16edt]], and [[29edt]].
+[[Subgroup]]: 3.5.7
+[[Comma list]]: 5859375/5764801
+{{Mapping|legend=3| 1 -1 -1 | 0 8 9 }}
+: mapping generators: ~3, ~7/5
+[[Optimal tuning]]s:
+* [[WE]]: ~3 = 1901.8789{{c}}, ~7/5 = 585.8428{{c}}
+: [[error map]]: {{val| -0.076 -1.450 +1.880 }}
+* [[CWE]]: ~3 = 1901.9550{{c}}, ~7/5 = 585.8590{{c}}
+: error map: {{val| 0.000 -1.396 +1.950 }}
+[[Optimal ET sequence]]: [[13edt|b13]], [[120edt|b120]], [[133edt|b133]], …, [[211edt|b211]], [[224edt|b224]]
+[[Badness]] (Sintel): 1.24
 == Izar ==