59ed6: Difference between revisions
Cleanup; + subsets and supersets; + see also |
Copypasty (with data for this tuning) from 60ed6 |
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== Theory == | == Theory == | ||
59ed6 corresponds to 22.8243…edo. It can be viewed as a [[stretched and compressed tuning|stretched]] version of [[23edo]] or a compressed version of [[36edt]]. | 59ed6 corresponds to 22.8243…edo. It can be viewed as a [[stretched and compressed tuning|stretched]] version of [[23edo]] or a compressed version of [[36edt]]. | ||
23edo's [[harmonic]]s [[3/1|3]], [[5/1|5]], [[7/1|7]] and [[11/1|11]] are all more than 20 cents away from just, so they exhibit very little [[consonance]]. 59ed6 improves upon all of their tunings, bringing all of them within 10 cents of just. This dramatically increases the number of consonant intervals and chords available in the tuning. | |||
The trade-off is that 59ed6's octave is significantly worse than 23edo. It has just over 9 cents of error, compared to none. For some composers, 9 cents error on the octave may be unacceptable, but for others, it may be considered still close enough for consonance and [[octave equivalence]] to be well preserved, and they may see it a worthwhile sacrifice to unlock so many warm [[11-limit]] harmonies. | |||
=== Harmonics === | === Harmonics === | ||