12 Tertial Dflat-Fsharp (center C)
For a general introduction to Just (Rational) Intonation and these presets, please visit Introduction to Just or Rational Intonation (JI).
About this tuning
Commonly known as Pythagorean tuningPythagorean tuning is an approach to tuning based on stacking pure fifths (i.e. fifths with an exact frequency ratio of 2:3).Visit the link to learn more, attributed to Pythagoras and the Pythagoreans, versions of this system were described by the Akkadian culture of ancient Mesopotamia and in ancient Chinese music texts. It remains a vibrant structural part of modal traditions around the world today, as well as being the tuning system that 12edo most closely approximates.
The Latin-derived terminology "tertialIn Just/Rational Intonation tunings, ratios are often categorized by the prime numbers that constitute them. The Latin-derived terms "tertial" and "quintal," initiated by composer Catherine Lamb, are used to semantically describe the color and function qualities of the specific primes referenced (3 and 5), as well as the chordal and scale structures these primes generate. Higher primes have traditionally been named in similar manner, i.e. "septimal" (7), "undecimal" (11), "tridecimal" (13), etc.Visit the link to learn more," initiated by composer Catherine Lamb, is intended to semantically describe the color and function qualities of the specific prime (in this case, 3) and the chordal and scale structures it generates. "Limit" is a related terminology developed by Harry Partch, indicating the largest prime factors used in frequency ratios defining a rational tuning system. The tertial scale is limited to intervals between partials having only 2 and 3 as prime factors. This may be imagined as generating an infinite sequence or spiral of ascending perfect fifthsPitches a fifth apart have a 2:3 frequency ratio (in just intonation) or a difference of 700 cents (in 12 tone equal temperament).Visit the link to learn more or descending fourthsPitches a fourth apart have a 3:4 frequency ratio (in just intonation) or a difference of 500 cents (in 12 tone equal temperament).Visit the link to learn more, each tuned in the ratio 2:3 or 4:3.
In this particular 12-tone subset, a sequence of eleven perfect fifths - from D♭ through F♯ - is taken, centering the spelling of the chromatic scale degrees around C, by favouring the diatonic intervals (C-D♭-D-E♭-E-F-F♯-G-A♭-A-B♭-B). The missing "13th note", C♯, would lie one Pythagorean commaA comma is a small difference in pitch between the same interval in different tuning systems.Visit the link to learn more (ca. 23.5 cents) higher than D♭. Four diminished fourths – A-D♭, E-A♭, B-E♭, F♯-B♭ – are nearly pure major thirds, measuring one schisma (ca. 2 cents) less than 5/4 ratios.