97edo: Difference between revisions
→JI approximation: splitting the header in two lines is better by style, one line for each semantic meaning. |
→JI approximation: clarify that maybe there it's direct as well |
||
| Line 12: | Line 12: | ||
== JI approximation == | == JI approximation == | ||
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]]. | 97edo has very poor direct 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 in this tuning through JI-agnostic approaches. | 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. | ||