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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
|}
|}
Retrieved from "https://en.xen.wiki/w/Supermajor_and_subminor/Tunings"