97edo: Difference between revisions
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=== Odd harmonics === | === Odd harmonics === | ||
{{Harmonics in equal|97}} | {{Harmonics in equal|97}} | ||
== JI approximation == | |||
97edo has the worst approximation for [[superparticular]] intervals among edos up to 200. It has errors of well above one standard deviation (about 15.87%) in superparticular intervals with denominators up to 14. The first good approximation is the 16/15 semitone using the 9th note, with an error of 3%, meaning 97edo can be used as a rough version of [[16/15ths equal temperament]]. | |||
Since 97edo is a prime EDO, it lacks specific modulation circles, symmetrical chords or sub-EDOs that are present in composite EDOs. When edos like [[19edo|19]], [[29edo|29]], [[31edo|31]], [[41edo|41]], or [[53edo|53]] have mathematically justified harmony, 97edo is essentially "irredeemable" in terms of either modulation or approximation rationales. However, this might result in interest towards this tuning through emancipation of the dissonance. | |||
{| class="wikitable" | |||
|+ Table of errors for superparticular intervals up to 17/16 | |||
|- | |||
! Interval (JI) !! Error ([[Relative cent|r¢]]) | |||
|- | |||
| 3/2 || 25.9 | |||
|- | |||
| 4/3 || 25.8 | |||
|- | |||
| 5/4 || 22.7 | |||
|- | |||
| 6/5 || 48.6 | |||
|- | |||
| 7/6 || 42.8 | |||
|- | |||
| 8/7 || 31.4 | |||
|- | |||
| 9/8 || 48.2 | |||
|- | |||
| 10/9 || 25.6 | |||
|- | |||
| 11/10 || 33.7 | |||
|- | |||
| 12/11 || 17.6 | |||
|- | |||
| 13/12 || 20.1 | |||
|- | |||
| 14/13 || 37.0 | |||
|- | |||
| 15/14 || 34.6 | |||
|- | |||
| 16/15 || 3.1 | |||
|- | |||
| 17/16 || 48.3 | |||
|} | |||
== Scales == | == Scales == | ||
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|77 | |77 | ||
|20L 57s | |20L 57s | ||
|} | |} | ||