13ed8/3: Difference between revisions
Created page with "{{Infobox ET}} {{ED intro}} The first person to explore 13ed8/3 was Maeve Gutierrez in early October 2025, who documented her findings in the Xenharmonic Alliance Discord server. Gutierrez noted that: * 13ed8/3 is like 9edo with the octave compressed by 24 cents * It has a good approximation of the 7/6 subminor third (one of her favourite intervals) * It has a major third close to the familiar 12edo major third * It has no perfect fifth, in..." |
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The first person to explore 13ed8/3 was [[Maeve Gutierrez]] in early October 2025, who documented her findings in the [[Xenharmonic Alliance]] Discord server. | The first person to explore 13ed8/3 was [[Maeve Gutierrez]] in early October 2025, who documented her findings in the [[Xenharmonic Alliance]] Discord server. | ||
== Properties == | |||
Gutierrez noted that: | Gutierrez noted that: | ||
* 13ed8/3 is like [[9edo]] with the octave compressed by 24 [[cents]] | * 13ed8/3 is like [[9edo]] with the octave compressed by 24 [[cents]] | ||
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* 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 | * 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]]. | |||
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== Harmonics == | == Harmonics == | ||
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}} | }} | ||
== Intervals == | |||
{{Interval table}} | |||
== 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]], 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 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 | |||