Supermajor and subminor/Tunings: Difference between revisions

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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..."
 
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A set of tunings for supermajor and subminor intervals, migrated from the original page.
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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 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 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 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.
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"
{| class="wikitable"
|+
!EDO
!Major
!Upmajor/supermajor
|-
|-
|16
! EDO
|375
! Major
|450
! Upmajor/supermajor
|-
| 16
| 375
| 450
|-
|-
|19
| 19
|379
| 379
|442
| 442
|-
|-
|24
| 24
|400
| 400
|450
| 450
|-
|-
|25b
| 25b
|384
| 384
|432
| 432
|-
|-
|29
| 29
|414
| 414
|455
| 455
|-
|-
|31
| 31
|387
| 387
|426
| 426
|-
|-
|32
| 32
|413
| 413
|450
| 450
|-
|-
|36
| 36
|400
| 400
|433
| 433
|-
|-
|41
| 41
|410
| 410
|439
| 439
|-
|-
|48
| 48
|400
| 400
|425
| 425
|-
|-
|53
| 53
|408
| 408
|430
| 430
|-
|-
|58
| 58
|414
| 414
|434
| 434
|-
|-
|70
| 70
|411
| 411
|429
| 429
|-
|-
|87
| 87
|414
| 414
|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 [[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"
{| class="wikitable"
|+
!EDO
!Major
|-
|-
|22
! EDO
|436
! Major
|-
| 22
| 436
|-
|-
|27
| 27
|444
| 444
|-
|-
|32
| 32
|450
| 450
|-
|-
|37
| 37
|454
| 454
|-
|-
|39
| 39
|431
| 431
|-
|-
|42
| 42
|457
| 457
|-
|-
|49
| 49
|441
| 441
|-
|-
|56
| 56
|429
| 429
|-
|-
|59
| 59
|447
| 447
|-
|-
|61
| 61
|433
| 433
|-
|-
|71
| 71
|439
| 439
|-
|-
|73
| 73
|427
| 427
|-
|-
|83
| 83
|434
| 434
|-
|-
|90
| 90
|426
| 426
|-
|-
|95
| 95
|430
| 430
|-
|-
|107
| 107
|426
| 426
|-
|-
|124
| 124
|426
| 426
|}
|}

Latest revision as of 12:33, 3 June 2025

< Supermajor and subminor

This subpage describes 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 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 ¢ and <415 ¢ and the upmajor third is >425 ¢ and <460 ¢). The restriction on normal major thirds is placed to ensure that the chosen diatonic major thirds are not already within the supermajor range.

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).

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
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