Supermajor and subminor: Difference between revisions

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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.


== In just intonation ==
For example, supermajor thirds may be found between about 429-446 cents, and subminor thirds may be found between about 256–273{{cent}}.
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 ==
Common supermajor and subminor intervals may be found as simple 7-limit intervals, and include:
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 <415 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).
* [[8/7]] (231{{c}}), supermajor second
{| class="wikitable"
* [[7/6]] (267{{c}}), subminor third
|+
* [[9/7]] (435{{c}}), supermajor third
!EDO
* [[14/9]] (765{{c}}), subminor sixth
!Major
* [[12/7]] (933{{c}}), supermajor sixth
|-
* [[7/4]] (969{{c}}), subminor seventh
|22
 
|436
More examples may be found in the {{subpage|tunings|u}} subpage.
|-
 
|27
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}}.
|444
 
|-
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.
|32
 
|450
Optionally, the category of supermajor or subminor may be split into two smaller categories. Tuning ranges have been provided in terms of thirds:
|-
 
|37
* 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}}.
|454
* '''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}}.
|-
 
|39
{{Navbox intervals}}
|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
|}


[[Category:Interval naming]]
[[Category:Interval naming]]

Latest revision as of 22:04, 30 October 2025

The interval qualities "supermajor" and "subminor" refer to intervals 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.

For example, supermajor thirds may be found between about 429-446 cents, and subminor thirds may be found between about 256–273 ¢.

Common supermajor and subminor intervals may be found as simple 7-limit intervals, and include:

  • 8/7 (231 ¢), supermajor second
  • 7/6 (267 ¢), subminor third
  • 9/7 (435 ¢), supermajor third
  • 14/9 (765 ¢), subminor sixth
  • 12/7 (933 ¢), supermajor sixth
  • 7/4 (969 ¢), subminor seventh

More examples may be found in the tunings subpage.

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 ¢. 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.

Supermajor and subminor intervals are associated with tricot systems, as one generator represents a supermajor second, and four stacked downward represent a subminor third.

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, 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 ¢. For a given neutral interval k in cents, the supermajor version in this sense is found at around k + 78, and the subminor version is found at around 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 ¢, containing the 5edo second of 240 ¢. 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.


View • Talk • EditInterval classification
Interval regions
Unison and octave Unison • Comma and diesis • Octave
Seconds Minor second • Neutral second • Major second
Thirds Minor third • Neutral third • Major third
Fourths and fifths Perfect fourth • Superfourth • Tritone • Subfifth • Perfect fifth
Sixths Minor sixth • Neutral sixth • Major sixth
Sevenths Minor seventh • Neutral seventh • Major seventh
Interseptimal intervals Interseptimal 2nd-3rd • Interseptimal 3rd-4th • Interseptimal 5th-6th • Interseptimal 6th-7th
Interval qualities
Diatonic qualities Diminished • Minor • Perfect • Major • Augmented
Tuning ranges Neutral (interval quality) • Submajor and supraminor • Pental major and minor • Novamajor and novaminor • Neogothic major and minor • Supermajor and subminor • Ultramajor and inframinor
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