Supermajor and subminor

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.

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 definiiton, 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.