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| The [[interval qualities]] "'''supermajor'''" and "'''subminor'''" essentially refer to [[interval]]s sharper than major and flatter than minor, respectively; a supermajor interval is sharper than the corresponding ~[[12edo]] interval by approximately a sixth-tone or [[diesis]], and a subminor interval is flat of the corresponding ~12edo interval by approximately a sixth-tone or diesis. | | The [[interval qualities]] "'''supermajor'''" and "'''subminor'''" refer to [[interval]]s sharper than major or flatter than minor, respectively; a supermajor interval is sharper than the corresponding ~[[12edo]] interval by approximately a sixth-tone or [[diesis]], and a subminor interval is flat of the corresponding ~12edo interval by approximately a sixth-tone or diesis. |
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| For example, supermajor thirds may be found between about 429-446 cents, and subminor thirds may be found between about 256-273 cents. | | For example, supermajor thirds may be found between about 429-446 cents, and subminor thirds may be found between about 256–273{{cent}}. |
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| Common supermajor and subminor intervals may be found as simple 7-limit intervals, and include: | | Common supermajor and subminor intervals may be found as simple 7-limit intervals, and include: |
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| * [[8/7]] (231c), supermajor second | | * [[8/7]] (231{{c}}), supermajor second |
| * [[7/6]] (267c), subminor third | | * [[7/6]] (267{{c}}), subminor third |
| * [[9/7]] (435c), supermajor third | | * [[9/7]] (435{{c}}), supermajor third |
| * [[14/9]] (765c), subminor sixth | | * [[14/9]] (765{{c}}), subminor sixth |
| * [[12/7]] (933c), supermajor sixth | | * [[12/7]] (933{{c}}), supermajor sixth |
| * [[7/4]] (969c), subminor seventh | | * [[7/4]] (969{{c}}), subminor seventh |
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| Supermajor and subminor intervals are found in diatonic scales where the fifth is tuned significantly sharper than just - depending on the desired interval category, between 709 and 715 cents. For a given [[neutral]] interval ''k'' in cents, the supermajor quality ranges from around k+78 to k+95, and the subminor quality ranges from around k-95 to k-78.
| | More examples may be found in the {{subpage|tunings|u}} subpage. |
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| Optionally, the category of supermajor or subminor may be split into two smaller categories. Tuning ranges have been provided in terms of thirds:
| | Supermajor and subminor intervals are found in diatonic scales where the fifth is tuned significantly sharper than just—depending on the desired interval category, between 709 and 715{{c}}. For a given [[neutral]] interval ''k'' in cents, the supermajor quality ranges from around {{nowrap|''k'' + 78}} to {{nowrap|''k'' + 95}}, and the subminor quality ranges from around {{nowrap|''k'' − 95}} to {{nowrap|''k'' − 78}}. |
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| * Supermajor and subminor, for thirds, may more precisely refer to the ranges between about 429-438 and 264-273, respectively. These are the ranges more closely focused around septimal intervals. Supermajor seconds, under this definition, range from about 225 to 234 cents. For a given [[neutral]] interval ''k'' in cents, the supermajor version in this sense is found at around k+84, and the subminor version is found at around k-84.
| | Supermajor and subminor intervals are associated with [[Ploidacot/Tricot|tricot]] systems, as one generator represents a supermajor second, and four stacked downward represent a subminor third. |
| * '''Sensamajor''' and '''sensaminor''', for thirds, refer to the ranges between about 438-446 and 256-264 cents, respectively. These are more extreme than the septimal ranges. Sensamajor seconds, under this definiiton, range from about 234 to 242 cents, containing the 5edo second of 240 cents. For a given [[neutral]] interval ''k'' in cents, the sensamajor version is found at around k+90, and the sensaminor version is found at around k-90.
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| == In just intonation ==
| | Optionally, the category of supermajor or subminor may be split into two smaller categories. Tuning ranges have been provided in terms of thirds: |
| 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).
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| == In other notations ==
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| In, say, [[41edo]] or [[53edo]] (or other similar systems), "upmajor" corresponds to "supermajor", and "downminor" to "subminor".
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| 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.
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| {| class="wikitable"
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| |+
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| !EDO
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| !Major
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| !Upmajor/supermajor
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| |-
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| |16
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| |375
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| |450
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| |-
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| |19
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| |379
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| |442
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| |-
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| |24
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| |400
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| |450
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| |-
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| |25b
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| |384
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| |432
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| |-
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| |29
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| |414
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| |455
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| |-
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| |31
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| |387
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| |426
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| |-
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| |32
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| |413
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| |450
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| |-
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| |36
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| |400
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| |433
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| |-
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| |41
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| |410
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| |439
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| |-
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| |48
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| |400
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| |425
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| |-
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| |53
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| |408
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| |430
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| |-
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| |58
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| |414
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| |434
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| |-
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| |70
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| |411
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| |429
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| |-
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| |87
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| |414
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| |427
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| |}
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| Similarly, as mentioned, [[diatonic]] thirds can be supermajor, and thus other diatonic intervals supermajor or subminor:
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| 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).
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| {| class="wikitable"
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| |+
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| !EDO
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| !Major
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| |-
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| |22
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| |436
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| |-
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| |27
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| |444
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| |-
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| |32
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| |450
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| |-
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| |37
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| |454
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| |-
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| |39
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| |431
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| |-
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| |42
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| |457
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| |-
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| |49
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| |441
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| |-
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| |56
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| |429
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| |-
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| |59
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| |447
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| |-
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| |61
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| |433
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| |-
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| |71
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| |439
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| |-
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| |73
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| |427
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| |-
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| |83
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| |434
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| |-
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| |90
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| |426
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| |-
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| |95
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| |430
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| |-
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| |107
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| |426
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| |-
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| |124
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| |426
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| |}
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| == See also ==
| | * Supermajor and subminor, for thirds, may more precisely refer to the ranges between about 429–438 and 264–273, respectively. These are the ranges more closely focused around septimal intervals. Supermajor seconds, under this definition, range from about 225 to 234{{c}}. For a given [[neutral]] interval ''k'' in cents, the supermajor version in this sense is found at around {{nowrap|''k'' + 78}}, and the subminor version is found at around {{nowrap|''k'' − 84}}. |
| | * '''Sensamajor''' and '''sensaminor''', for thirds, refer to the ranges between about 438–446 and 256–264 cents, respectively. These are more extreme than the septimal ranges. Sensamajor seconds, under this definition, range from about 234 to 242{{c}}, containing the 5edo second of 240{{c}}. For a given [[neutral]] interval ''k'' in cents, the sensamajor version is found at around {{nowrap|''k'' + 90}}, and the sensaminor version is found at around {{nowrap|''k'' − 90}}. |
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| * [[Neutral (interval quality)]] - halfway between major and minor
| | {{Navbox intervals}} |
| * [[Submajor and supraminor]] - roughly 10 to 24 cents sharp or flat of neutral
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| * [[Pental major and minor]] - roughly 24 to 43 cents sharp or flat of neutral
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| * [[Novamajor and novaminor]] - roughly 43 to 60 cents sharp or flat of neutral
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| * [[Neogothic major and minor]] - roughly 60 to 78 cents sharp or flat of neutral
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| * [[Ultramajor and inframinor]] - more extreme than 95 cents sharp or flat of neutral
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| [[Category:Interval naming]] | | [[Category:Interval naming]] |