342edo: Difference between revisions

m Text replacement - "Octave-reduced form, reduced to the first half-octave, and minimal form in parentheses if distinct" to "Octave-reduced form, reduced to the first half-octave, and minimal form in parentheses if distinct"
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== Theory ==
== Theory ==
342edo is a very strong 11-limit system. It is, as one would expect, [[consistency|distinctly consistent]] through the [[11-odd-limit]], but goes no higher; nonetheless, it is a [[zeta peak edo]]. A [[comma basis|basis]] for the 11-limit [[comma]]s consists of [[2401/2400]], [[3025/3024]], [[4375/4374]] and [[32805/32768]]. It is the [[optimal patent val]] for 11-limit [[Breedsmic temperaments #Hemitert|hemitert]] temperament, and [[support]]s hemiennealimmal.
342edo is a very strong 11-limit system. It is, as one would expect, [[consistency|distinctly consistent]] through the [[11-odd-limit]], but goes no higher; nonetheless, it is a [[zeta peak edo]]. A [[comma basis|basis]] for the 11-limit [[comma]]s consists of [[2401/2400]], [[3025/3024]], [[4375/4374]] and [[32805/32768]]. It is the [[optimal patent val]] for 11-limit [[Breedsmic temperaments #Hemitert|hemitert]] temperament, and [[support]]s hemiennealimmal.
If 3.5 cents is taken as the [[just-noticeable difference]], then 342edo may be regarded as the highest EDO whose step size remains individually discernible. However, the [[JND]] is not fixed and depends on the listener and musical context.


=== Prime harmonics ===
=== Prime harmonics ===