19edt: Difference between revisions

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|en = 19ed3

| en = 19ed3

|de = ~~Bernhard_Stopper~~

| de = Bernhard Stopper

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~~'''[[EDT|Division of the third harmonic]] into 19 equal parts''' (19ED3) is related to [[12edo|12 EDO]], but with the 3/1 rather than the 2/1 being just.~~ It is also known as '''Stopper tuning'''~~. The octave is about 1.2347 cents stretched and the step size is about 100.1029 cents~~.

{{ED intro}} It is also known as '''Stopper tuning'''.

== ~~Properties~~ ==

== Theory ==

~~[https://piano-stopper.de/?page_id=107&lang=en Bernhard Stopper's OnlyPure tuning]{{Dead link}}~~

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]].

~~19 equal divisions of the tritave~~ is not a ~~"real"~~ 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 ~~tuning~~ framed in a ~~tritave equivalence~~, it can still be used as a temperament with no twos like other tritave tunings. This approach can create very non-standard chords and scales such as the approximation of the 5:7:9 chord as ~~0-600-1100~~ 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 m"~~acro~~-godzilla" temperament (with a generator of 400.4 cents and a 3:1 ratio 5L 4s scale, ~~weird~~ 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 ~~1101~~.1 cents), producing a basic [[8L 3s (3/1~~-equivalent~~)|~~Obikhod~~]] ~~scale~~.

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 in equal|steps=19|num=3|denom=1|intervals=integer|start=12|columns=12|collapsed=1|title=Approximation of harmonics in 19edt (continued)}}

=== Subsets and supersets ===

19edt is the 8th [[prime equal division|prime edt]], following [[17edt]] and before [[23edt]].

== Intervals ==

== See also ==

* [[12edo~~|12EDO~~]] - relative ~~EDO~~

* [[7edf]] – relative edf

* [[28ed5~~|28ED5~~]] - relative ~~ED5~~

* [[12edo]] – relative edo

* [[31ed6~~|31ED6~~]] - relative ~~ED6~~

* [[28ed5]] – relative ed5

* [[34ed7~~|34ED7~~]] - relative ~~ED7~~

* [[31ed6]] – relative ed6

* [[40ed10|~~40ED10~~]] - ~~relative ED10~~

* [[34ed7]] – relative ed7

* [[40ed10]] – relative ed10

* [[43ed12]] – relative ed12

* [[76ed80]] – close to the zeta-optimized tuning for 12edo

* [[1ed18/17|AS18/17]] – relative [[AS|ambitonal sequence]]

== External links ==

* [[Bernhard Stopper]]'s [https://piano-stopper.de/?page_id=107&lang=en OnlyPure tuning]{{dead link}}

[[Category:12edo]]

[[Category:Macrotonal]]

~~[[Category:Edonoi]]~~

~~[[Category:Edt]]~~

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 {{interwiki
-|en = 19ed3
+| en = 19ed3
-|de = Bernhard_Stopper
+| de = Bernhard Stopper
 }}
 {{Infobox ET}}
-'''[[EDT|Division of the third harmonic]] into 19 equal parts''' (19ED3) is related to [[12edo|12 EDO]], but with the 3/1 rather than the 2/1 being just. It is also known as '''Stopper tuning'''. The octave is about 1.2347 cents stretched and the step size is about 100.1029 cents.
+{{ED intro}} It is also known as '''Stopper tuning'''.
-== Properties ==
+== Theory ==
-[https://piano-stopper.de/?page_id=107&lang=en Bernhard Stopper's OnlyPure tuning]{{Dead link}}
+edt 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]].
-equal divisions of the tritave is not a "real" 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 tuning framed in a tritave equivalence, it can still be used as a temperament with no twos like other tritave tunings. This approach can create very non-standard chords and scales such as the approximation of the 5:7:9 chord as 0-600-1100 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 m"acro-godzilla" temperament (with a generator of 400.4 cents and a 3:1 ratio 5L 4s scale, weird 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 1101.1 cents), producing a basic [[8L 3s (3/1-equivalent)|Obikhod]] scale.
+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 in equal|steps=19|num=3|denom=1|intervals=integer}}
+{{Harmonics in equal|steps=19|num=3|denom=1|intervals=integer|start=12|columns=12|collapsed=1|title=Approximation of harmonics in 19edt (continued)}}
+=== Subsets and supersets ===
+edt is the 8th [[prime equal division|prime edt]], following [[17edt]] and before [[23edt]].
+== Intervals ==
+{{Interval table}}
 == See also ==
-* [[12edo|12EDO]] - relative EDO
+* [[7edf]] – relative edf
-* [[28ed5|28ED5]] - relative ED5
+* [[12edo]] – relative edo
-* [[31ed6|31ED6]] - relative ED6
+* [[28ed5]] – relative ed5
-* [[34ed7|34ED7]] - relative ED7
+* [[31ed6]] – relative ed6
-* [[40ed10|40ED10]] - relative ED10
+* [[34ed7]] – relative ed7
+* [[40ed10]] – relative ed10
+* [[43ed12]] – relative ed12
+* [[76ed80]] – close to the zeta-optimized tuning for 12edo
+* [[1ed18/17|AS18/17]] – relative [[AS|ambitonal sequence]]
+== External links ==
+* [[Bernhard Stopper]]'s [https://piano-stopper.de/?page_id=107&lang=en OnlyPure tuning]{{dead link}}
+[[Category:12edo]]
 [[Category:Macrotonal]]
-[[Category:Edonoi]]
-[[Category:Edt]]