46edo: Difference between revisions

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<nowiki>*</nowiki> Based on treating 46edo as a 2.3.5.7.11.13.17.23 subgroup, without ratios of 15 (except the superparticulars). 46edo has the 15th harmonic poorly approximated in general, because, while both the 3rd and 5th harmonics are sharp by a fair amount and they add up, all the other primes are flat, making the difference even larger, to the extent that it is not [[consistent]] in the [[15-odd-limit]]. This can be demonstrated with the discrepancy approximating [[15/13]] (and its inversion [[26/15]]). 9\46edo is closer to 15/13 by a hair; 10\46edo represents the difference between, for instance, 46edo's 15/8 and 13/8, and is more likely to appear in chords actually functioning as 15/13.

Combining ups and downs notation with [[~~Kite's_color_notation|~~color notation]], qualities can be loosely associated with colors:

=== Interval quality and chord names in color notation ===

Combining ups and downs notation with [[color notation]], qualities can be loosely associated with colors:

{| class="wikitable center-all"

|-

! ~~quality~~

! Quality

! ~~color~~

! Color

! ~~monzo format~~

! Monzo Format

! ~~examples~~

! Examples

|-

| downminor

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{| class="wikitable center-all"

|-

! ~~color~~ of the 3rd

! Color of the 3rd

! JI ~~chord~~

! JI Chord

! ~~notes~~ as ~~edosteps~~

! Notes as Edosteps

! ~~notes~~ of C ~~chord~~

! Notes of C Chord

! ~~written name~~

! Written Name

! ~~spoken name~~

! Spoken Name

|-

| zo

@@ Line 402: / Line 402: @@
 <nowiki>*</nowiki> Based on treating 46edo as a 2.3.5.7.11.13.17.23 subgroup, without ratios of 15 (except the superparticulars). 46edo has the 15th harmonic poorly approximated in general, because, while both the 3rd and 5th harmonics are sharp by a fair amount and they add up, all the other primes are flat, making the difference even larger, to the extent that it is not [[consistent]] in the [[15-odd-limit]]. This can be demonstrated with the discrepancy approximating [[15/13]] (and its inversion [[26/15]]). 9\46edo is closer to 15/13 by a hair; 10\46edo represents the difference between, for instance, 46edo's 15/8 and 13/8, and is more likely to appear in chords actually functioning as 15/13.
-Combining ups and downs notation with [[Kite's_color_notation|color notation]], qualities can be loosely associated with colors:
+=== Interval quality and chord names in color notation ===
+Combining ups and downs notation with [[color notation]], qualities can be loosely associated with colors:
 {| class="wikitable center-all"
 |-
-! quality
+! Quality
-! color
+! Color
-! monzo format
+! Monzo Format
-! examples
+! Examples
 |-
 | downminor
@@ Line 455: / Line 456: @@
 {| class="wikitable center-all"
 |-
-! color of the 3rd
+! Color of the 3rd
-! JI chord
+! JI Chord
-! notes as edosteps
+! Notes as Edosteps
-! notes of C chord
+! Notes of C Chord
-! written name
+! Written Name
-! spoken name
+! Spoken Name
 |-
 | zo

46edo: Difference between revisions

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