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 that is a compressed diatonic. A functional system for 13edo oneirotonic | 13edo's greatest melodic strength is its proximity to 12edo, whose most important effect is providing an oneirotonic (5L3s) MOS that is a compressed diatonic. A functional system for 13edo oneirotonic is provided below. | ||
Revision as of 05:49, 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 that is a compressed diatonic. A functional system for 13edo oneirotonic is provided below.
