Supermajor and subminor: Difference between revisions

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 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, 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.  

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).