13ed8/3: Difference between revisions

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* Its 1437{{c}} major 9th interval is about an octave above the [[8/7]] septimal whole tone (so it approximates [[16/7]])

* The sharp [[perfect fourth]] of 522{{c}} is very dissonant in a triad with either fifth, but with the major 6th instead it makes a very pretty chord

13ed8/3 can be thought of as a 2.12.15.7.11.13.19 [[subgroup]] tuning. It has under 22% [[relative error]] (under 29{{c}} abs. error) on each of those [[harmonic]]s, which is comparable to [[12edo]]'s approximation of the full [[7-limit]].

== Harmonics ==

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== Related tunings ==

13ed8/3 is a bit like [[9edo]] but with extreme [[octave shrinking]] (the octave is about 24 [[cents]] flat). As a [[23-limit]] equal [[temperament]] it could be considered a tuning for 9bdefhi (see [[wart]]s).

13ed8/3 is a bit like [[9edo]] but with extreme [[octave shrinking]] (the octave is about 24 [[cents]] flat). As a [[23-limit]] equal [[temperament]], 13ed8/3 could be considered a tuning for 9bdefhi (''see [[wart]]s'').

13ed8/3 is quite close to [[23zpi]] (''see [[ZPI]]'') but 13ed8/3 has a much better [[2/1]] than 23zpi, at the expense of most other [[prime]]s being a little worse than 23zpi.

13ed8/3 is ~~quite close~~ to [[~~zpi|23zpi~~]] ~~but 13ed8/3 has a much better~~ [[~~2/1~~]] ~~than 23zpi, at the expense of most other [[prime]]s being a little worse than 23zpi~~.

13ed8/3 is identical (octave less than 1{{c}} different) to ''every second step of'' [[62zpi]] (''see [[ZPI]]'').

== Scales ==

; Described by [[Budjarn Lambeth]]

''Tested by ear in [[Scale Workshop]] using the "jublag", "ugal", and "silver" aperiodic waveforms, and the "percussive (medium)" preset.''

* 5-tone [[pelog]]-like scale: 1 1 3 1 3

* 7-tone [[pelog]]-like scale: 1 1 2 1 1 2 1

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 * Its 1437{{c}} major 9th interval is about an octave above the [[8/7]] septimal whole tone (so it approximates [[16/7]])
 * The sharp [[perfect fourth]] of 522{{c}} is very dissonant in a triad with either fifth, but with the major 6th instead it makes a very pretty chord
+ed8/3 can be thought of as a 2.12.15.7.11.13.19 [[subgroup]] tuning. It has under 22% [[relative error]] (under 29{{c}} abs. error) on each of those [[harmonic]]s, which is comparable to [[12edo]]'s approximation of the full [[7-limit]].
 == Harmonics ==
@@ Line 33: / Line 35: @@
 == Related tunings ==
-ed8/3 is a bit like [[9edo]] but with extreme [[octave shrinking]] (the octave is about 24 [[cents]] flat). As a [[23-limit]] equal [[temperament]] it could be considered a tuning for 9bdefhi (see [[wart]]s).
+ed8/3 is a bit like [[9edo]] but with extreme [[octave shrinking]] (the octave is about 24 [[cents]] flat). As a [[23-limit]] equal [[temperament]], 13ed8/3 could be considered a tuning for 9bdefhi (''see [[wart]]s'').
+ed8/3 is quite close to [[23zpi]] (''see [[ZPI]]'') but 13ed8/3 has a much better [[2/1]] than 23zpi, at the expense of most other [[prime]]s being a little worse than 23zpi.
-ed8/3 is quite close to [[zpi|23zpi]] but 13ed8/3 has a much better [[2/1]] than 23zpi, at the expense of most other [[prime]]s being a little worse than 23zpi.
+ed8/3 is identical (octave less than 1{{c}} different) to ''every second step of'' [[62zpi]] (''see [[ZPI]]'').
 == Scales ==
 ; Described by [[Budjarn Lambeth]]
+''Tested by ear in [[Scale Workshop]] using the "jublag", "ugal", and "silver" aperiodic waveforms, and the "percussive (medium)" preset.''
 * 5-tone [[pelog]]-like scale: 1 1 3 1 3
 * 7-tone [[pelog]]-like scale: 1 1 2 1 1 2 1