Pental major and minor
This article is about the interval quality. For 5-limit major and minor intervals, see 5/4, 6/5, 8/5, and 5/3. For other uses of "pental", see Perfect fifth and 5-limit.
Pental major intervals are an interval quality denoting tunings close to ptolemaic major intervals. They are sharper than submajor intervals and flatter than novamajor intervals. Likewise, pental minor intervals are an interval quality denoting tunings close to ptolemaic minor intervals. They are sharper than novaminor intervals and flatter than supraminor intervals. Pental major intervals range from about 375 to 394 cents, and pental minor intervals range from about 308 to 327 cents.
Common pental major/minor intervals can be found as simple 5-limit intervals, and include:
- 10/9 (182c), pental major second
- 6/5 (316c), pental minor third
- 5/4 (386c), pental major third
- 8/5 (814c), pental minor sixth
- 5/3 (884c), pental major sixth
- 9/5 (1018c), pental minor seventh
Pental major/minor intervals are found in diatonic sales where the fifth is tuned slightly flat of just. If these intervals are interpreted as the 5-limit, the result is meantone temperament. For a given neutral interval k in cents, the pental major quality ranges from around k+24 to k+43, and the pental minor quality ranges from around k-43 to k-24.
Optionally, the category of pental may be split into two smaller categories. Tuning ranges have been provided in terms of thirds:
- Magimajor and magiminor, for thirds, range between about 375-382 and 320-327 cents, respectively. These are flat of the 5-limit thirds, and appear in 5-limit temperaments where the chromatic semitone 25/24 is tempered narrow, like in garibaldi, magic (hence the name), or the minor third in flattone. Magimajor seconds range from 171-178 cents, and thus contain the upper part of the "equable heptatonic" region. For a given neutral interval k in cents, the magimajor version is found at around k+28, and the magiminor version is found at around k-28.
- Pentamajor and pentaminor, for thirds, range between about 382-394 and 308-320 cents, respectively. These are the regions containing 5-limit intervals. Pentamajor seconds range from 178-190 cents. For a given neutral interval k in cents, the pentamajor version is found at around k+35, and the pentaminor version is found at around k-35.
See also
- Neutral (interval quality) - halfway between major and minor
- Submajor and supraminor - roughly 15 to 24 cents sharp or flat of neutral
- Novamajor and novaminor - roughly 43 to 60 cents sharp or flat of neutral
- Neogothic major and minor - roughly 60 to 78 cents sharp or flat of neutral
- Supermajor and subminor - roughly 78 to 95 cents sharp or flat of neutral
- Ultramajor and inframinor - more extreme than 95 cents sharp or flat of neutral