19edt: Difference between revisions

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| de = Bernhard Stopper

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

~~''Italic text'''''~~[[~~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.~~

== Theory ==

~~=Division of 3/1 into 19 equal parts=~~

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]].

[~~http:~~/~~/www~~.~~piano~~-~~stopper.de~~/~~html/onlypure_tuning~~.~~html Bernhard Stopper's OnlyPure tuning]{{Dead link}}~~

~~Note: 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 "harmonic" tuning framed in a tritave equivalence, the~~ "default" approach to it is as ~~the tritave twin of~~ godzilla temperament (with a generator of 400.4 cents and a

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.

~~[[category:macrotonal]]~~

3:1 ratio ~~superdiatonic~~ scale, ~~weird~~ coincidence how 17edt and 19edt tonality have the same "default" scheme with two tones more or less)~~, which has little connection to standard 12-tone practice in spite of using the 12-tone interval set~~. Beyond this, it is also the tritave twin of ~~sensi or~~ meantone temperament ~~<span style="background-color: rgba(255,255,255,0);">~~(with a generator of 700.7 or </~~span~~>~~1101.1 <span style~~=~~"background-color: rgba(255,255,255,0);">cents and a 2:~~1 ~~ratio superdiatonic~~ scale~~)</span>~~.

~~==See also==~~

*[[12edo]]: relative EDO

*[[28ed5]]: relative ED5

*[[31ed6]]: relative ED6

*[[34ed7]]: relative ED7

*[[40ed10]]: relative ED10

[[~~Category~~:~~edonoi]~~]

=== Harmonics ===

[[Category:~~edt~~]]

[[Category:~~equal~~]]

{{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 ==

* [[7edf]] – relative edf

* [[12edo]] – relative edo

* [[28ed5]] – relative ed5

* [[31ed6]] – relative ed6

* [[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]]

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 {{interwiki
-|de=Bernhard_Stopper
+| en = 19ed3
-|en=19ed3
+| de = Bernhard Stopper
 }}
+{{Infobox ET}}
+{{ED intro}} It is also known as '''Stopper tuning'''.
-''Italic text'''''[[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.
+== Theory ==
-=Division of 3/1 into 19 equal parts=
+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]].
-[http://www.piano-stopper.de/html/onlypure_tuning.html Bernhard Stopper's OnlyPure tuning]{{Dead link}}
-Note: 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 "harmonic" tuning framed in a tritave equivalence, the "default" approach to it is as the tritave twin of godzilla temperament (with a generator of 400.4 cents and a
+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.
-[[category:macrotonal]]
-:1 ratio superdiatonic scale, weird coincidence how 17edt and 19edt tonality have the same "default" scheme with two tones more or less), which has little connection to standard 12-tone practice in spite of using the 12-tone interval set. Beyond this, it is also the tritave twin of sensi or meantone temperament <span style="background-color: rgba(255,255,255,0);">(with a generator of 700.7 or </span>1101.1 <span style="background-color: rgba(255,255,255,0);">cents and a 2:1 ratio superdiatonic scale)</span>.
-==See also==
-*[[12edo]]: relative EDO
-*[[28ed5]]: relative ED5
-*[[31ed6]]: relative ED6
-*[[34ed7]]: relative ED7
-*[[40ed10]]: relative ED10
-[[Category:edonoi]]
+=== Harmonics ===
-[[Category:edt]]
+{{Harmonics in equal|steps=19|num=3|denom=1|intervals=integer}}
-[[Category:equal]]
+{{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 ==
+* [[7edf]] – relative edf
+* [[12edo]] – relative edo
+* [[28ed5]] – relative ed5
+* [[31ed6]] – relative ed6
+* [[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]]