13edo: Difference between revisions
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'''13edo''', or 13 equal divisions of the octave, is the equal tuning featuring steps of (1200/13) ~= 92.308 cents, 13 of which stack to the perfect octave 2/1. It does not approximate many small prime harmonics well at all but approximates 10/9, 11/8, 17/13, 20/17, and 21/13 well for its size. But the approximations do not fit very well in a rank-2 temperament (they fit better in an over-34 [[Glossary#Neji|neji]]), so [[delta-rational chord|DR]]-based interpretations are often preferred among 13edo users. | '''13edo''', or 13 equal divisions of the octave, is the equal tuning featuring steps of (1200/13) ~= 92.308 cents, 13 of which stack to the perfect octave 2/1. It does not approximate many small prime harmonics well at all but approximates 10/9, 11/8, 17/13, 20/17, and 21/13 well for its size. But the approximations do not fit very well in a rank-2 temperament (they fit better in an over-34 [[Glossary#Neji|neji]]), so [[delta-rational chord|DR]]-based interpretations are often preferred among 13edo users. | ||
13edo's greatest melodic strength is its proximity to 12edo, whose most important effect is providing an oneirotonic (5L3s) MOS | 13edo's greatest melodic strength is its proximity to 12edo, whose most important effect is providing an oneirotonic (5L3s) MOS which is a compressed diatonic. A functional system for 13edo oneirotonic is provided below. | ||
== One functional system for 13edo == | |||
13edo's melodically strongest scale is the oneirotonic MOS, so it behooves us to find harmonies that work for it. | |||
* Major ~+1+1 triad: 0-4-7\13: A compressed major triad that sounds desaturated and somewhat bittersweet. | |||
* Minor +1+2 triad: 0-3-8\13: A bright if somewhat hollow-sounding minor triad. | |||
Revision as of 05:52, 4 January 2026
13edo, or 13 equal divisions of the octave, is the equal tuning featuring steps of (1200/13) ~= 92.308 cents, 13 of which stack to the perfect octave 2/1. It does not approximate many small prime harmonics well at all but approximates 10/9, 11/8, 17/13, 20/17, and 21/13 well for its size. But the approximations do not fit very well in a rank-2 temperament (they fit better in an over-34 neji), so DR-based interpretations are often preferred among 13edo users.
13edo's greatest melodic strength is its proximity to 12edo, whose most important effect is providing an oneirotonic (5L3s) MOS which is a compressed diatonic. A functional system for 13edo oneirotonic is provided below.
One functional system for 13edo
13edo's melodically strongest scale is the oneirotonic MOS, so it behooves us to find harmonies that work for it.
- Major ~+1+1 triad: 0-4-7\13: A compressed major triad that sounds desaturated and somewhat bittersweet.
- Minor +1+2 triad: 0-3-8\13: A bright if somewhat hollow-sounding minor triad.
