Neogothic major and minor

Neogothic major intervals are between regular major intervals and supermajor intervals, and likewise, neogothic minor intervals are between regular minor intervals and subminor intervals. For example, neogothic thirds may be found between roughly 273 and 291 ¢, and between 411 and 429 ¢. Common neogothic intervals can be found by taking the mediant of a major and supermajor, or minor and subminor, interval, and include:

• 17/15 (217 ¢), neogothic major second
• 13/11 (289 ¢), neogothic minor third
• 14/11 (418 ¢), neogothic major third
• 25/19 (475 ¢), neogothic subfourth
• 38/25 (725 ¢), neogothic superfifth
• 11/7 (782 ¢), neogothic minor sixth
• 22/13 (911 ¢), neogothic major sixth
• 30/17 (983 ¢), neogothic minor seventh

Neogothic intervals are found in diatonic scales where the fifth is tuned sharp of just, but flatter than superpyth tunings, with the most common tunings being 17edo, 29edo, and 46edo. The term is usually applied to thirds (and by extension sixths), but can be generalized to apply to any interval category. For a given neutral interval k in cents, the neogothic major quality ranges from around k + 60 to k + 78, and the neogothic minor quality ranges from around k − 78 to k − 60.

Optionally, the category of neogothic may be split into two smaller categories. Tuning ranges have been provided in terms of thirds:

• Neomajor and neominor, for thirds, range between about 411–421 and 281–291 ¢, respectively. These can be considered "true" neogothic intervals, as the thirds are generated by fifths in the gentle region, a core aspect of neogothic harmony. Neomajor seconds range from about 207-217 cents. For a given neutral interval k in cents, the neomajor version is found at around k + 65, and the neominor version is found at around k − 65.
• Gothmajor (or "shrubmajor") and gothminor, for thirds, range between about 421–429 and 273–281 ¢ respectively, and can be considered flat supermajor or sharp subminor intervals, think 17edo. The thirds are generated by fifths in the inverse-gentle or shrub region (between about 706–708 ¢). Gothmajor seconds are roughly 217–225 ¢. For a given neutral interval k in cents, the goth/shrubmajor version is found at around k + 75, and the gothminor version is found at around k − 75.