19edt: Difference between revisions
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{{interwiki | {{interwiki | ||
|en = 19ed3 | | en = 19ed3 | ||
|de = | | de = Bernhard Stopper | ||
}} | }} | ||
{{Infobox ET}} | {{Infobox ET}} | ||
{{ED intro}} It is also known as '''Stopper tuning'''. | {{ED intro}} It is also known as '''Stopper tuning'''. | ||
== | == Theory == | ||
19edt is not a truly [[xenharmonic]] tuning; it is a slightly stretched version (with an octave of 1201.2 cents) of the normal [[12edo|12-tone scale]]. Although it is really just the normal 12edo framed in a pure-3 tuning, it can still be used as a temperament with no twos like other tritave-equivalent tunings, although limited in [[accuracy]], with [[5/3]] approximated as 9 steps and [[7/3]] approximated by 15 steps. It completely misses the next tritave-reduced prime harmonic, [[11/9]]. | |||
This approach can create very non-standard chords and scales such as the approximation of the 5:7:9 chord as | This approach can create very non-standard chords and scales such as the approximation of the 5:7:9 chord as 0–600–1000 cents. These could be considered xenharmonic in a sense, since they have little connection to standard 12-tone practice in spite of using the 12-tone interval set. The "default" approach to it is as a "macro-[[godzilla]]" temperament (with a generator of 400.4 cents and a 3:1 ratio {{mos scalesig|5L 4s<3/1>|link=1}} scale, and it is an interesting coincidence how [[17edt]] and 19edt tonality have the same "default" scheme with two tones more or less). Beyond this, it also contains the tritave twin of [[meantone]] temperament (with a generator of 700.7 or 1201.2 cents), producing a basic {{mos scalesig|8L 3s<3/1>|link=1}} scale. | ||
== Harmonics == | === Harmonics === | ||
{{Harmonics in equal | {{Harmonics in equal|steps=19|num=3|denom=1|intervals=integer}} | ||
| steps = 19 | {{Harmonics in equal|steps=19|num=3|denom=1|intervals=integer|start=12|columns=12|collapsed=1|title=Approximation of harmonics in 19edt (continued)}} | ||
| num = 3 | |||
| denom = 1 | === Subsets and supersets === | ||
| intervals = integer | 19edt is the 8th [[prime equal division|prime edt]], following [[17edt]] and before [[23edt]]. | ||
}} | |||
{{Harmonics in equal | |||
| steps = 19 | |||
| num = 3 | |||
| denom = 1 | |||
| start = 12 | |||
| collapsed = 1 | |||
| | |||
}} | |||
== Intervals == | == Intervals == | ||
| Line 31: | Line 22: | ||
== See also == | == See also == | ||
* [[7edf | * [[7edf]] – relative edf | ||
* [[12edo | * [[12edo]] – relative edo | ||
* [[28ed5 | * [[28ed5]] – relative ed5 | ||
* [[31ed6 | * [[31ed6]] – relative ed6 | ||
* [[34ed7 | * [[34ed7]] – relative ed7 | ||
* [[40ed10 | * [[40ed10]] – relative ed10 | ||
* [[43ed12| | * [[43ed12]] – relative ed12 | ||
* [[76ed80]] – close to the zeta-optimized tuning for 12edo | |||
* [[1ed18/17|AS18/17]] – relative [[AS|ambitonal sequence]] | |||
== External links == | == External links == | ||
* [[Bernhard Stopper]]'s [https://piano-stopper.de/?page_id=107&lang=en OnlyPure tuning]{{dead link}} | * [[Bernhard Stopper]]'s [https://piano-stopper.de/?page_id=107&lang=en OnlyPure tuning]{{dead link}} | ||
[[Category:12edo]] | |||
[[Category:Macrotonal]] | [[Category:Macrotonal]] | ||