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 ==

[[~~Bernhard Stopper~~]]~~'s [https://piano-stopper.de/?page_id=107&lang=en 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, ~~alithough~~ limited 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 ~~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 ~~“macro~~-[[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 1201.1 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 ==
-[[Bernhard Stopper]]'s [https://piano-stopper.de/?page_id=107&lang=en 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, alithough limited 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 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 “macro-[[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 1201.1 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]]