97edo: Difference between revisions
Cleanup +1 |
"Worst approximation" needs to be defined, replaced with a more vague evaluation. I think emancipation of dissonance is about using concordances of higher complexity rather than lack of concordances. Clarify that the table is using direct approximation and relative error |
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== JI approximation == | == JI approximation == | ||
97edo has | 97edo has very poor 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 [[16/15 equal-step tuning]]. | ||
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 | 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 in this tuning through JI-agnostic approaches. | ||
{| class="wikitable center-all" | {| class="wikitable center-all" | ||
|+ | |+style=white-space:nowrap| Superparticular intervals up to 17/16 by direct approximation (even if inconsistent) | ||
|- | |- | ||
! Interval | ! Interval !! Error (Relative, [[Relative cent|r¢]]) | ||
|- | |- | ||
| 3/2 || 25.9 | | 3/2 || 25.9 | ||