143edo: Difference between revisions

(13 intermediate revisions by 7 users not shown)

Line 1:

143edo is a scale which divides the [[Octave|octave]] into 143 equal divisions of approximately 8.392¢. The 143b val provides a tuning almost identical with that of the POTE tuning for 7-limit meantone.

As 143 is 11*13, 143edo allows the [[~~Polymicrotonality~~|polymicrotonal]] ~~juxtaposition~~ of [[~~11edo|~~11edo]] and [[~~13edo|~~13edo]]:

== Theory ==

143edo is only [[consistent]] to the [[5-odd-limit]], and the error of the [[harmonic]] [[3/1|3]] is quite large. With the patent sharp fifth and flat 7, it supports a sharp form of [[slendric]] and [[hemithirds]] through to the [[13-limit]], while the 143b val provides a tuning almost identical with that of the [[POTE tuning]] for 7-limit [[meantone]].

=== Odd harmonics ===

=== Subsets and supersets ===

As 143 is {{nowrap| 11 × 13 }}, 143edo allows the [[polymicrotonality|polymicrotonal juxtaposition]] of [[11edo]] and [[13edo]]:

[[File:13_against_11.gif|alt=13_against_11.gif|800x312px|13_against_11.gif]]

If the 11edo and 13edo ~~sub-~~scales share ~~one tone~~ (as in the diagram above), the resulting scale would have 23 tones in the octave; otherwise, it would have 24.

If the 11edo and 13edo subsets are analyzed as two scales that share the [[tonic]] and are then combined (as in the diagram above), the resulting scale would have 23 tones in the octave; otherwise, it would have 24.

== Intervals ==

@@ Line 1: / Line 1: @@
-edo is a scale which divides the [[Octave|octave]] into 143 equal divisions of approximately 8.392¢. The 143b val provides a tuning almost identical with that of the POTE tuning for 7-limit meantone.
+{{Infobox ET}}
+{{ED intro}}
-As 143 is 11*13, 143edo allows the [[Polymicrotonality|polymicrotonal]] juxtaposition of [[11edo|11edo]] and [[13edo|13edo]]:
+== Theory ==
+edo is only [[consistent]] to the [[5-odd-limit]], and the error of the [[harmonic]] [[3/1|3]] is quite large. With the patent sharp fifth and flat 7, it supports a sharp form of [[slendric]] and [[hemithirds]] through to the [[13-limit]], while the 143b val provides a tuning almost identical with that of the [[POTE tuning]] for 7-limit [[meantone]].
+=== Odd harmonics ===
+{{Harmonics in equal|143}}
+=== Subsets and supersets ===
+As 143 is {{nowrap| 11 × 13 }}, 143edo allows the [[polymicrotonality|polymicrotonal juxtaposition]] of [[11edo]] and [[13edo]]:
 [[File:13_against_11.gif|alt=13_against_11.gif|800x312px|13_against_11.gif]]
-If the 11edo and 13edo sub-scales share one tone (as in the diagram above), the resulting scale would have 23 tones in the octave; otherwise, it would have 24.
+If the 11edo and 13edo subsets are analyzed as two scales that share the [[tonic]] and are then combined (as in the diagram above), the resulting scale would have 23 tones in the octave; otherwise, it would have 24.
+== Intervals ==
+{{Interval table}}