171edo: Difference between revisions
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[[684edo]], which quadruples it, achieves [[17-odd-limit]] consistency. | [[684edo]], which quadruples it, achieves [[17-odd-limit]] consistency. | ||
== Intervals == | |||
{{Main| 171edo/Intervals }} | |||
== Notation == | |||
=== Ups and downs notation === | |||
171edo can be notated using [[Kite's ups and downs notation|ups and downs]] with quarter-tone accidentals: | |||
{{Ups and downs sharpness|171|true}} | |||
== Approximation to JI == | |||
=== 15-odd-limit intervals === | |||
{{Q-odd-limit intervals|171|15}} | |||
=== Consistent circles === | |||
171edo contains consistent circles of [[7/6]], [[6/5]], and [[9/7]], each with 9, 19, and 171 notes respectively. | |||
{| class="wikitable center-all left-5" | |||
|+ style="font-size: 105%;" | Consistent circles in 171edo | |||
|- | |||
! Note<br>count | |||
! [[Interval]] | |||
! [[Closing error|Closing<br>error]] | |||
! [[Circle #Definitions|Consistency]] | |||
! Associated<br>edostep | |||
|- | |||
| 9 | |||
| [[7/6]] | |||
| -26.2% | |||
| Normal | |||
| 2\9 = 38\171 | |||
|- | |||
| 19 | |||
| [[6/5]] | |||
| +40.1% | |||
| Normal | |||
| 5\19 = 45\171 | |||
|- | |||
| 171 | |||
| [[9/7]] | |||
| +8.8% | |||
| Strong | |||
| 62\171 | |||
|} | |||
=== 7-prime-limited odd-limit analysis === | === 7-prime-limited odd-limit analysis === | ||
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The 7-prime-limited 49-odd-limit is where non-distinctness first shows up: namely, ~49/48 = ~50/49 (this is characteristic of all Ennealimmal tunings). However, 171edo remains consistent up to much higher 7-prime-limited odd-limits (much higher than even [[99edo]]). | The 7-prime-limited 49-odd-limit is where non-distinctness first shows up: namely, ~49/48 = ~50/49 (this is characteristic of all Ennealimmal tunings). However, 171edo remains consistent up to much higher 7-prime-limited odd-limits (much higher than even [[99edo]]). | ||
== Regular temperament properties == | == Regular temperament properties == | ||