Novamajor and novaminor

Novamajor intervals are an interval quality denoting tuning ranges close to or slightly flat of Pythagorean major intervals. They are sharper than pental major intervals and flatter than neogothic major intervals. Likewise, novaminor intervals are an interval quality denoting tuning ranges close to or slightly sharp of Pythagorean minor intervals. They are sharper than neogothic minor intervals and flatter than pental minor intervals. Novamajor thirds range from about 394 to 411 cents, and novaminor thirds range from about 291 to 308 cents.

Common novamajor and novaminor intervals can be found as Pythagorean intervals:

• 9/8 (204c), novamajor second
• 32/27 (294c), novaminor third
• 81/64 (408c), novamajor third
• 128/81 (792c), novaminor sixth
• 27/16 (906c), novamajor sixth
• 16/9 (996c), novaminor seventh

Novamajor and novaminor intervals are usually found in diatonic scales where the fifth is tuned roughly justly, such as in 12edo. For a given neutral interval k in cents, the novamajor quality ranges between about k+43 to k+60, and the novaminor quality ranges between about k-60 to k-43.

Optionally, the category of novamajor or novaminor may be split into two smaller categories, for which tuning ranges have been provided in terms of thirds:

• More precisely, novamajor and novaminor may refer to the range that is, for the case of thirds, between about 394 to 404 cents, or between 298 to 308 cents. Distinctly, these are the tunings provided by 12edo for thirds. As such, they may also be called dodecamajor and dodecaminor to distinguish them. For seconds, the dodeca/novamajor range is about 190 to 200 cents, which is flat of 12edo, but just because neutral intervals are assumed to be hemi-Pythagorean. For a given neutral interval k in cents, the corresponding dodecamajor interval is found at around k+50, and the corresponding dodecaminor interval is found at roughly k-50.
• Trimajor and triminor, for thirds, range between about 404-411 and 291-298 cents respectively. These are the regions containing Pythagorean intervals and are the tunings provided by schismic temperaments or 3-limit just intonation. Trimajor seconds range from 200 to 207 cents. For any given neutral interval k in cents, the corresponding trimajor interval is found at around k+57, and the corresponding triminor interval is found at roughly k-57.