17-limit: Difference between revisions
→Terminology and notation: rework to sort it topically |
m In color notation, when "so" appears by itself, we need to write "iso" to differenciate it from solfege "so/sol" |
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== Edo approximation == | == Edo approximation == | ||
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. | Here is a list of [[edo]]s with progressively better tunings for 17-limit intervals ([[monotonicity limit]] ≥ 17 and decreasing [[TE error]]): {{EDOs| 31, 38df, 41, 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. For a more comprehensive list, see [[Sequence of equal temperaments by error]]. | ||
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. | 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 == | == Intervals == | ||
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| 104.955 | | 104.955 | ||
| 17o2 | | 17o2 | ||
| | | iso 2nd | ||
| large septendecimal semitone | | large septendecimal semitone | ||
|- | |- | ||
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| 603.000 | | 603.000 | ||
| 17o5 | | 17o5 | ||
| | | iso 5th | ||
| greater septendecimal tritone | | greater septendecimal tritone | ||
|- | |- | ||
| Line 144: | Line 144: | ||
| 1101.045 | | 1101.045 | ||
| 17o8 | | 17o8 | ||
| | | iso octave | ||
| large septendecimal major seventh | | large septendecimal major seventh | ||
|} | |} | ||