Supermajor and subminor: Difference between revisions
Created page with "The interval qualities "supermajor" and "subminor" essentially refer to intervals sharper than major and flatter than minor, respectively. == In just intonation == In some no..." |
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The interval qualities "supermajor" and "subminor" essentially refer to intervals sharper than major and flatter than minor, respectively. | The interval qualities "supermajor" and "subminor" essentially refer to intervals 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. | ||
== In just intonation == | == In just intonation == | ||
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== In other notations == | == In other notations == | ||
In, say, 41edo or 53edo (or other similar systems), "upmajor" corresponds to "supermajor", and "downminor" to "subminor". | 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). | |||
{| 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 | |||
|} | |||