17-limit: Difference between revisions

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The names tabulated in [[#Intervals]] are common names and do not follow this discussion yet.

== Edo ~~approximations~~ ==

== Edo approximation ==

A list of [[edo]]s with progressively better tunings for 17-limit intervals: {{EDOs| 46, 58, 72, 103, 111, 121, 140, 171, 183, 217, 224, 270, 311, 354, 400, 422, 460, 494, 581, 742, 764, 814, 935, 954 }} and so on.

Here is a list of [[edo]]s with progressively better tunings for 17-limit intervals (decreasing [[TE error]]): {{EDOs| 46, 58, 72, 103, 111, 121, 140, 171, 183, 217, 224, 270, 311, 354, 400, 422, 460, 494, 581, 742, 764, 814, 935, 954 }} and so on.

~~Another~~ list of edos which provides relatively good tunings for 17-limit intervals ([[TE ~~relative error|~~relative error]] < 5.4%): {{EDOs| 46, 58, 72, 87, 94, 103, 111, 121, 130, 140, 171, 183, 190g, 212g, 217, 224, 243e, 270, 282, 301, 311, 320, 328, 342f, 354, 364, 373g, 383, 388, 400, 414, 422, 441, 460, 494, 525, 535, 540, 552g, 566g, 571, 581, 597, 624, 639, 643, 653, 684, 692, 711, 718, 742, 764, 814, 822, 836(f), 863efg, 867, 882, 908, 925, 935, 954 }} and so on.

Here is a list of edos which provides relatively good tunings for 17-limit intervals ([[TE relative error]] < 5.4%): {{EDOs| 46, 58, 72, 87, 94, 103, 111, 121, 130, 140, 171, 183, 190g, 212g, 217, 224, 243e, 270, 282, 301, 311, 320, 328, 342f, 354, 364, 373g, 383, 388, 400, 414, 422, 441, 460, 494, 525, 535, 540, 552g, 566g, 571, 581, 597, 624, 639, 643, 653, 684, 692, 711, 718, 742, 764, 814, 822, 836(f), 863efg, 867, 882, 908, 925, 935, 954 }} and so on.

: '''Note''': [[wart notation]] is used to specify the [[val]] chosen for the edo. In the above list, "190g" means taking the second closest approximation of harmonic 17.

== Intervals ==

@@ Line 18: / Line 18: @@
 The names tabulated in [[#Intervals]] are common names and do not follow this discussion yet.
-== Edo approximations ==
+== Edo approximation ==
-A list of [[edo]]s with progressively better tunings for 17-limit intervals: {{EDOs| 46, 58, 72, 103, 111, 121, 140, 171, 183, 217, 224, 270, 311, 354, 400, 422, 460, 494, 581, 742, 764, 814, 935, 954 }} and so on.
+Here is a list of [[edo]]s with progressively better tunings for 17-limit intervals (decreasing [[TE error]]): {{EDOs| 46, 58, 72, 103, 111, 121, 140, 171, 183, 217, 224, 270, 311, 354, 400, 422, 460, 494, 581, 742, 764, 814, 935, 954 }} and so on.
-Another list of edos which provides relatively good tunings for 17-limit intervals ([[TE relative error|relative error]] < 5.4%): {{EDOs| 46, 58, 72, 87, 94, 103, 111, 121, 130, 140, 171, 183, 190g, 212g, 217, 224, 243e, 270, 282, 301, 311, 320, 328, 342f, 354, 364, 373g, 383, 388, 400, 414, 422, 441, 460, 494, 525, 535, 540, 552g, 566g, 571, 581, 597, 624, 639, 643, 653, 684, 692, 711, 718, 742, 764, 814, 822, 836(f), 863efg, 867, 882, 908, 925, 935, 954 }} and so on.
+Here is a list of edos which provides relatively good tunings for 17-limit intervals ([[TE relative error]] < 5.4%): {{EDOs| 46, 58, 72, 87, 94, 103, 111, 121, 130, 140, 171, 183, 190g, 212g, 217, 224, 243e, 270, 282, 301, 311, 320, 328, 342f, 354, 364, 373g, 383, 388, 400, 414, 422, 441, 460, 494, 525, 535, 540, 552g, 566g, 571, 581, 597, 624, 639, 643, 653, 684, 692, 711, 718, 742, 764, 814, 822, 836(f), 863efg, 867, 882, 908, 925, 935, 954 }} and so on.
 : '''Note''': [[wart notation]] is used to specify the [[val]] chosen for the edo. In the above list, "190g" means taking the second closest approximation of harmonic 17.
 == Intervals ==