10edo: Difference between revisions

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Taking the the 360{{c}} large neutral third as a [[generator]] produces a heptatonic [[MOS scales|moment of symmetry scale]] of the form {{nowrap|1 2 1 2 1 2 1}} ([[3L 4s]], or "mosh"), which is the most [[Diatonic scale|diatonic]]-like scale in 10edo excluding the 5edo degenerate diatonic scale.

While not an integral or gap edo, 10edo is a [[The Riemann ~~Zeta Function~~ and ~~Tuning~~ #Zeta edo lists|zeta peak edo]]. 10edo is also the smallest edo that maintains [[minimal consistent EDOs|25% or lower relative error]] on all of the first eight harmonics of the [[harmonic series]].

While not an integral or gap edo, 10edo is a [[The Riemann zeta function and tuning #Zeta edo lists|zeta peak edo]]. 10edo is also the smallest edo that maintains [[minimal consistent EDOs|25% or lower relative error]] on all of the first eight harmonics of the [[harmonic series]].

One way to interpret it in terms of a [[Temperament|temperament of just intonation]] is as a 2.7.13.15 [[subgroup]], such that [[105/104]], [[225/224]], [[43904/43875]], and [[16807/16384]] are [[tempered out]]. It can also be treated as a full [[13-limit]] temperament, but it is a closer match to the aforementioned subgroup.

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 Taking the the 360{{c}} large neutral third as a [[generator]] produces a heptatonic [[MOS scales|moment of symmetry scale]] of the form {{nowrap|1 2 1 2 1 2 1}} ([[3L&nbsp;4s]], or "mosh"), which is the most [[Diatonic scale|diatonic]]-like scale in 10edo excluding the 5edo degenerate diatonic scale.
-While not an integral or gap edo, 10edo is a [[The Riemann Zeta Function and Tuning #Zeta edo lists|zeta peak edo]]. 10edo is also the smallest edo that maintains [[minimal consistent EDOs|25% or lower relative error]] on all of the first eight harmonics of the [[harmonic series]].
+While not an integral or gap edo, 10edo is a [[The Riemann zeta function and tuning #Zeta edo lists|zeta peak edo]]. 10edo is also the smallest edo that maintains [[minimal consistent EDOs|25% or lower relative error]] on all of the first eight harmonics of the [[harmonic series]].
 One way to interpret it in terms of a [[Temperament|temperament of just intonation]] is as a 2.7.13.15 [[subgroup]], such that [[105/104]], [[225/224]], [[43904/43875]], and [[16807/16384]] are [[tempered out]]. It can also be treated as a full [[13-limit]] temperament, but it is a closer match to the aforementioned subgroup.