Lumatone mapping for 72edo: Difference between revisions

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== Diatonic ==

You can use ~~either~~ the second- best alternate fifth, but it is extremely sharp, so much so that "major seconds" become 8/7 instead of 9/8.

You can use the second- best alternate fifth, but it is extremely sharp, so much so that "major seconds" become ~[[8/7]] instead of ~[[9/8]]. If you want to retain patent val mapping with this layout, you can map the generator as a mildly flat ptolemismic fifth ~[[50/33]]. This mapping does not cover the full gamut or make the best-tuned intervals (other than ~8/7) easily accessible.

== Antidiatonic ==

or the third-best:

You can use the third-best fifth, but it is extremely flat, so that "major seconds" are flattened to ~[[11/10]] instead of 9/8 or even [[~[[10/9]]. If you want to retain patent val mapping with this layout, you can map the generator as a mildly sharp grave fifth ~[[40/27]]. This mapping also does not cover the full gamut or make the best-tuned intervals (other than ~11/10) easily accessible.

~~but these do not cover the full gamut or make the best-tuned intervals easily accessible.~~

== Miracle ==

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== Catakleismic-related rank-3 (Harmonic table) ==

[[Bryan Deister]] has demonstrated ~~a [[1L 1s]] (42:23 step ratio)~~ mapping for [[72edo]] in [https://www.youtube.com/shorts/a07Q_zQHe9M ''72edo groove''] (2026). The rightward generator 42\72 is the near-just perfect fifth ~[[3/2]]; the upward generator 19\72 is the near-just classic minor third ~[[6/5]] (as in [[catakleismic]] temperament); this makes the down-right generator 23/72 the near-just classic major third ~[[5/4]] (being derived from the other generators, this does not expand the temperament beyond rank-3). That makes this mapping sort of a harmonic table mapping, although different from that for [[12edo]] since neither the classic major third nor the classic minor third divide 72edo evenly, thus causing comma pumping if either of these is stacked with itself. With such a compressed layout, most notes are not present in any one octave, but all notes are present in some octave, even within the limited part of the Lumatone that was actually mapped in the demonstration video; the synthesized sound used in the demonstration video also ensures that all of the notes are audible, even pushing the brain to do automatic octave-reduction.

[[Bryan Deister]] has demonstrated an ultra-compressed mapping for [[72edo]] in [https://www.youtube.com/shorts/a07Q_zQHe9M ''72edo groove''] (2026). The rightward generator 42\72 is the near-just perfect fifth ~[[3/2]]; the upward generator 19\72 is the near-just classic minor third ~[[6/5]] (as in [[catakleismic]] temperament); this makes the down-right generator 23/72 the near-just classic major third ~[[5/4]] (being derived from the other generators, this does not expand the temperament beyond rank-3). That makes this mapping sort of a harmonic table mapping, although different from that for [[12edo]] since neither the classic major third nor the classic minor third divide 72edo evenly, thus causing comma pumping if either of these is stacked with itself. With such a compressed layout, most notes are not present in any one octave, but all notes are present in some octave, even within the limited part of the Lumatone that was actually mapped in the demonstration video; the synthesized sound used in the demonstration video also ensures that all of the notes are audible, even pushing the brain to do automatic octave-reduction.

@@ Line 2: / Line 2: @@
 == Diatonic ==
-You can use either the second- best alternate fifth, but it is extremely sharp, so much so that "major seconds" become 8/7 instead of 9/8.
+You can use the second- best alternate fifth, but it is extremely sharp, so much so that "major seconds" become ~[[8/7]] instead of ~[[9/8]]. If you want to retain patent val mapping with this layout, you can map the generator as a mildly flat ptolemismic fifth ~[[50/33]]. This mapping does not cover the full gamut or make the best-tuned intervals (other than ~8/7) easily accessible.
 {{Lumatone EDO mapping|n=72|start=24|xstep=14|ystep=-13}}
+== Antidiatonic ==
-or the third-best:
+You can use the third-best fifth, but it is extremely flat, so that "major seconds" are flattened to ~[[11/10]] instead of 9/8 or even [[~[[10/9]]. If you want to retain patent val mapping with this layout, you can map the generator as a mildly sharp grave fifth ~[[40/27]]. This mapping also does not cover the full gamut or make the best-tuned intervals (other than ~11/10) easily accessible.
 {{Lumatone EDO mapping|n=72|start=48|xstep=10|ystep=1}}
-but these do not cover the full gamut or make the best-tuned intervals easily accessible.
 == Miracle ==
@@ Line 31: / Line 28: @@
 == Catakleismic-related rank-3 (Harmonic table) ==
-[[Bryan Deister]] has demonstrated a [[1L&nbsp;1s]] (42:23 step ratio) mapping for [[72edo]] in [https://www.youtube.com/shorts/a07Q_zQHe9M ''72edo groove''] (2026). The rightward generator 42\72 is the near-just perfect fifth ~[[3/2]]; the upward generator 19\72 is the near-just classic minor third ~[[6/5]] (as in [[catakleismic]] temperament); this makes the down-right generator 23/72 the near-just classic major third ~[[5/4]] (being derived from the other generators, this does not expand the temperament beyond rank-3). That makes this mapping sort of a harmonic table mapping, although different from that for [[12edo]] since neither the classic major third nor the classic minor third divide 72edo evenly, thus causing comma pumping if either of these is stacked with itself. With such a compressed layout, most notes are not present in any one octave, but all notes are present in some octave, even within the limited part of the Lumatone that was actually mapped in the demonstration video; the synthesized sound used in the demonstration video also ensures that all of the notes are audible, even pushing the brain to do automatic octave-reduction.
+[[Bryan Deister]] has demonstrated an ultra-compressed mapping for [[72edo]] in [https://www.youtube.com/shorts/a07Q_zQHe9M ''72edo groove''] (2026). The rightward generator 42\72 is the near-just perfect fifth ~[[3/2]]; the upward generator 19\72 is the near-just classic minor third ~[[6/5]] (as in [[catakleismic]] temperament); this makes the down-right generator 23/72 the near-just classic major third ~[[5/4]] (being derived from the other generators, this does not expand the temperament beyond rank-3). That makes this mapping sort of a harmonic table mapping, although different from that for [[12edo]] since neither the classic major third nor the classic minor third divide 72edo evenly, thus causing comma pumping if either of these is stacked with itself. With such a compressed layout, most notes are not present in any one octave, but all notes are present in some octave, even within the limited part of the Lumatone that was actually mapped in the demonstration video; the synthesized sound used in the demonstration video also ensures that all of the notes are audible, even pushing the brain to do automatic octave-reduction.
 {{Lumatone EDO mapping|n=72|start=64|xstep=42|ystep=-19}}
 {{Navbox Lumatone}}

Lumatone mapping for 72edo: Difference between revisions

Lucius Chiaraviglio (talk | contribs)