59ed6: Difference between revisions
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{{ED intro}} It | {{ED intro}} | ||
== 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]]. | |||
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 in equal|59|6|1|intervals=integer|columns=11}} | |||
{{Harmonics in equal|59|6|1|intervals=integer|columns=12|start=12|collapsed=true|title=Approximation of harmonics in 59ed6 (continued)}} | |||
=== Subsets and supersets === | |||
59ed6 is the 17th [[prime equal division|prime ed6]], so it does not contain any nontrivial subset ed6's. | |||
== Intervals == | == Intervals == | ||
{{Interval table}} | {{Interval table}} | ||
== | == Scales == | ||
* [[Maeve Gutierrez#Gutierrez-Lambeth quasi-subharmonic pentatonic|Gutierrez-Lambeth quasi-subharmonic pentatonic]] | |||
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== See also == | |||
* [[36edt]] – relative edt | |||