Category: 5-limit tuning and intervals

Semantic System
The Semantic System is based on a microtonal musical scale tuned in just intonation, developed by Alain Daniélou. For Alain Daniélou the subtleties of the intervals of music of oral traditions cannot
The diaschisma (or diacisma) is a small musical interval defined as the difference between three octaves and four perfect fifths plus two major thirds (in just intonation). It can be represented by th
Ptolemy's intense diatonic scale
Ptolemy's intense diatonic scale, also known as the Ptolemaic sequence,justly tuned major scale, Ptolemy's tense diatonic scale, or the syntonous (or syntonic) diatonic scale, is a tuning for the diat
In music theory and tuning, the kleisma (κλείσμα), or semicomma majeur, is a minute and barely perceptible comma type interval important to musical temperaments. It is the difference between six justl
Five-limit tuning
Five-limit tuning, 5-limit tuning, or 5-prime-limit tuning (not to be confused with 5-odd-limit tuning), is any system for tuning a musical instrument that obtains the frequency of each note by multip
The semicomma, also Fokker's comma (after 31-TET pioneer Adriaan Fokker), is type of small musical interval, or comma, in microtonal music equivalent to 2109375:2097152, or 33×57 : 221. This is a rati
In music, the schisma (also spelled skhisma) is the interval between a Pythagorean comma (531441:524288) and a syntonic comma (81:80) and equals 5(38)⁄215 or 32805:32768 = 1.00113, which is 1.9537 cen
Syntonic comma
In music theory, the syntonic comma, also known as the chromatic diesis, the Didymean comma, the Ptolemaic comma, or the diatonic comma is a small comma type interval between two musical notes, equal
List of intervals in 5-limit just intonation
The intervals of 5-limit just intonation (prime limit, not odd limit) are ratios involving only the powers of 2, 3, and 5. The fundamental intervals are the superparticular ratios 2/1 (the octave), 3/
Sonata for Microtonal Piano (Ben Johnston)
Sonata for Microtonal Piano is a sonata for specifically microtonally tuned piano by Ben Johnston written in 1964 (see also just intonation). When the movements are played in an alternate order the pi