Supermajor and subminor/Tunings - Revision history

ArrowHead294 at 22:55, 20 January 2026

2026-01-20T22:55:54Z

← Older revision		Revision as of 22:55, 20 January 2026
Line 6:		Line 6:

	== In other notations ==		== In other notations ==
	In, say, [[41edo]] or [[53edo]] (or other similar systems), "upmajor" corresponds to "supermajor", and "downminor" to "subminor". Here is a rough list of [[EDOs]] where this is true in regards to thirds (i.e. the (anti)diatonic major third is >370{{c}} and <415{{c}} and the upmajor third is >425{{c}} and <460{{c}}). The restriction on normal major thirds is placed to ensure that the chosen diatonic major thirds are not already within the supermajor range.		In, say, [[41edo]] or [[53edo]] (or other similar systems), "upmajor" corresponds to "supermajor", and "downminor" to "subminor". Here is a rough list of [[EDOs]] where this is true in regards to thirds (i.e. the (anti)diatonic major third is >370{{cent}} and <415{{c}} and the upmajor third is >425{{c}} and <460{{c}}). The restriction on normal major thirds is placed to ensure that the chosen diatonic major thirds are not already within the supermajor range.

	{\| class="wikitable"		{\| class="wikitable"
Line 70:		Line 70:
	\| 427		\| 427
	\|}		\|}

	Similarly, as mentioned, [[diatonic]] thirds can be supermajor, and thus other diatonic intervals supermajor or subminor:		Similarly, as mentioned, [[diatonic]] thirds can be supermajor, and thus other diatonic intervals supermajor or subminor:

	With our previously established supermajor range, this corresponds to a diatonic fifth of >706.25 ~~[[cents]]~~ and <715 ~~cents~~; here are all EDOs which have that as a [[patent val]] fifth, excluding contorted EDOs (i.e. those which have the same fifth as a smaller EDO).		With our previously established supermajor range, this corresponds to a diatonic fifth of >706.25{{c}} and <715{{c}}; here are all EDOs which have that as a [[patent val]] fifth, excluding contorted EDOs (i.e. those which have the same fifth as a smaller EDO).

	{\| class="wikitable"		{\| class="wikitable"

ArrowHead294 at 12:33, 3 June 2025

2025-06-03T12:33:19Z

Show changes

VectorGraphics: Created page with "A set of tunings for supermajor and subminor intervals, migrated from the original page. == In just intonation == In some notations and interval naming systems for just intonation, "supermajor" and "subminor" indicate sharping or flatting by a specific predefined comma, such as 64/63 (to reach septimal intervals), 81/80 (to reach acute and grave intervals), or 2048/2025 (to reach 5-limit supermajor and subminor intervals). == In oth..."

2025-06-02T21:16:45Z

Created page with "A set of tunings for supermajor and subminor intervals, migrated from the original page. == In just intonation == In some notations and interval naming systems for just intonation, "supermajor" and "subminor" indicate sharping or flatting by a specific predefined comma, such as 64/63 (to reach septimal intervals), 81/80 (to reach acute and grave intervals), or 2048/2025 (to reach 5-limit supermajor and subminor intervals). == In oth..."

New page

A set of tunings for supermajor and subminor intervals, migrated from the original page.

== In just intonation ==
In some [[Notation|notations]] and interval naming systems for [[just intonation]], "supermajor" and "subminor" indicate sharping or flatting by a specific predefined [[comma]], such as [[64/63]] (to reach septimal intervals), [[81/80]] (to reach acute and grave intervals), or [[2048/2025]] (to reach [[5-limit]] supermajor and subminor intervals).

== In other notations ==
In, say, [[41edo]] or [[53edo]] (or other similar systems), "upmajor" corresponds to "supermajor", and "downminor" to "subminor". Here is a rough list of [[EDOs]] where this is true in regards to thirds (i.e. the (anti)diatonic major third is >370c and <415c and the upmajor third is >425c and <460c). The restriction on normal major thirds is placed to ensure that the chosen diatonic major thirds are not already within the supermajor range.
{| class="wikitable"
|+
!EDO
!Major
!Upmajor/supermajor
|-
|16
|375
|450
|-
|19
|379
|442
|-
|24
|400
|450
|-
|25b
|384
|432
|-
|29
|414
|455
|-
|31
|387
|426
|-
|32
|413
|450
|-
|36
|400
|433
|-
|41
|410
|439
|-
|48
|400
|425
|-
|53
|408
|430
|-
|58
|414
|434
|-
|70
|411
|429
|-
|87
|414
|427
|}
Similarly, as mentioned, [[diatonic]] thirds can be supermajor, and thus other diatonic intervals supermajor or subminor:

With our previously established supermajor range, this corresponds to a diatonic fifth of >706.25 [[cents]] and <715 cents; here are all EDOs which have that as a [[patent val]] fifth, excluding contorted EDOs (i.e. those which have the same fifth as a smaller EDO).
{| class="wikitable"
|+
!EDO
!Major
|-
|22
|436
|-
|27
|444
|-
|32
|450
|-
|37
|454
|-
|39
|431
|-
|42
|457
|-
|49
|441
|-
|56
|429
|-
|59
|447
|-
|61
|433
|-
|71
|439
|-
|73
|427
|-
|83
|434
|-
|90
|426
|-
|95
|430
|-
|107
|426
|-
|124
|426
|}