In music theory, a comma is a small or very small interval between two enharmonic notes tuned in different ways. For example, an A flat tuned as a major third below C in just intonation, and a G sharp tuned as a major third above E, will not be exactly the same note. The difference between those notes, the diesis, is almost a quarter tone, easily audible. In music theory, an interval is the relationship between two notes or pitches, the lower and higher members of the interval. ... In music, an enharmonic is a note which is the equivalent of some other note, but spelled differently. ... Just intonation is any musical tuning in which the frequencies of notes are related by whole number ratios. ... A diesis is a musical interval. ... A quarter tone is an interval half as wide (aurally, or logarithmically) as a semitone, which is half a whole tone. ...

All of the intervals mentioned below are presumed to be tuned in just intonation. Just intonation is any musical tuning in which the frequencies of notes are related by whole number ratios. ...

There are many commas, notably :

• Pythagorean comma or ditonic comma (difference between 7 octaves and 12 perfect fifths)
• syntonic comma, the difference between four perfect fifths and two major thirds plus two octaves
• schisma, the difference between 8 perfect fifths plus one major third and 5 octaves (equal to the interval between Pythagorean comma and syntonic comma)
• diaschisma, the difference between 4 fifths plus 2 thirds and 3 octaves

Equal temperament was introduced as a way of avoiding commas, since enharmonic notes are tuned identically in that system. When you ascend by a cycle of justly tuned perfect fifths (ratio 3:2), leapfrogging 12 times, you eventually reach a note around seven octaves above the note you started on, which, when lowered to the same octave as your starting point, is 23. ... In music, an octave (sometimes abbreviated 8ve or 8va) is the interval between one musical note and another with half or double the frequency. ... The perfect fifth or diapente is one of three musical intervals that span five diatonic scale degrees; the others being the diminished fifth, which is one semitone smaller, and the augmented fifth, which is one semitone larger. ... The syntonic comma, also known as the comma of Didymus or Ptolemaic comma, is a small interval between two musical notes, equal to the frequency ratio 81:80, or around 21. ... The schisma, also spelled skhisma, is the ratio between a Pythagorean comma and a syntonic comma and equals 32805/32768, which is 1. ... Equal temperament is a scheme of musical tuning in which the octave is divided into a series of equal steps (equal frequency ratios). ...

Also see List of musical intervals. Equal-tempered refers to 12-tone equal temperament. ...