View source for Supermajor and subminor/Tunings

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This subpage describes a set of tunings for supermajor and subminor intervals, migrated from the original page.

== In just intonation ==
In some [[notation]]s 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 &gt;370{{c}} and &lt;415{{c}} and the upmajor third is &gt;425{{c}} and &lt;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"
|-
! 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
|}