143edo: Difference between revisions

(6 intermediate revisions by 4 users not shown)

Line 1:

~~'''143edo''' is the [[equal division of the octave]] into 143 parts of approximately 8.392¢ each. 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]] and [[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 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.

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.

~~[[Category:Equal divisions of the octave|###]] ~~

== Intervals ==

@@ Line 1: / Line 1: @@
 {{Infobox ET}}
-'''143edo''' is the [[equal division of the octave]] into 143 parts of approximately 8.392¢ each. The 143b val provides a tuning almost identical with that of the POTE tuning for 7-limit meantone.
+{{ED intro}}
-As 143 is 11*13, 143edo allows the [[Polymicrotonality|polymicrotonal]] juxtaposition of [[11edo]] and [[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 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.
+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.
-[[Category:Equal divisions of the octave|###]] <!-- 3-digit number -->
+== Intervals ==
+{{Interval table}}