pythagorean comma
ditonic comma

More exactly, it will be about a quarter of a semitone larger (see Pythagorean comma).

This implies that ε can be also defined as one twelfth of a Pythagorean comma.

A Pythagorean comma is the difference between twelve justly tuned perfect fifths and seven octaves.

This discrepancy, of about 23.46 cents, or nearly one quarter of a semitone, is known as a Pythagorean comma.

Another frequently encountered comma is the Pythagorean comma.

Take the just fifth to the twelfth power, then subtract seven octaves, and you get the Pythagorean comma (about 1.4% difference).

Between the enharmonic notes at both ends of this sequence, is a difference in pitch of nearly 24 cents, known as the Pythagorean comma.

The small interval between equivalent notes, such as F-sharp and G-flat, is the Pythagorean comma.

His book was also concerned with mathematics and music, making use of the "Pythagorean comma" and listing the first known Chinese 12 musical tone tuning.

This difference between the initial "c" and final "c" that is derived from performing a series of perfect tunings is generally referred to as the Pythagorean comma.

Notice that the Pythagorean comma (PC) and the syntonic comma (SC) are basic intervals which can be used as yardsticks to define some of the other commas.

For instance, in Pythagorean tuning they are all equal to the opposite of a Pythagorean comma, and in quarter-comma meantone they are all equal to a diesis.

In Pythagorean tuning, however, the interval actually shows a descending direction, i.e. a ratio below unison, and thus a negative size ( 23.46 cents), equal to the opposite of a Pythagorean comma.

Leap-year days - plus those few nasty seconds - are our solution to the temporal problem, just as the practical division of the Pythagorean comma into tempered tuning is our solution to the musical.

Equal temperament, today the most common tuning system used in the West, accomplished this by flattening each fifth by a twelfth of a Pythagorean comma (approximately 2 cents), thus producing perfect octaves.

Thus, ascending by justly intonated fifths fails to close the circle by an excess of approximately 23.46 cents, roughly a quarter of a semitone, an interval known as the Pythagorean comma.

Although the limma and the apotome are both represented by one step of 12-pitch equal temperament, they are not equal in Pythagorean tuning, and their difference, 531441/524288, is known as the Pythagorean comma.

For example, to make the 12-note chromatic scale in Pythagorean tuning close at the octave, one fifth must be out of tune by the Pythagorean comma; this altered fifth is called a wolf fifth.

A series of 12 just fifths as in Pythagorean tuning does not return to the original pitch, but rather differs by a Pythagorean comma, which makes that tonal area of the system more or less unusable.

Unlike meantone temperament, which alters the fifth to temper out the Syntonic comma, 12-TET tempers out the Pythagorean comma, thus creating a cycle of fifths that repeats itself exactly after 12 steps.

Werckmeister was not explicit about whether the syntonic comma or Pythagorean comma was meant: the difference between them, the so-called schisma, is almost inaudible and he stated that it could be divided up among the fifths.

When the perfect fifth is exactly 700 cents wide (that is, tempered by approximately 1/11 of a syntonic comma, or exactly 1/12 of a Pythagorean comma) then the tuning is identical to the familiar 12-tone equal temperament.

They presuppose a Pythagorean division of the octave taking the Pythagorean comma (about an 8th of the tempered tone, actually closer to 24 cents, defined as the difference between 7 octaves and 12 just-intonation fifths) as the basic interval.

The Pythagorean limma and Pythagorean apotome are enharmonic equivalents (chromatic semitones) and only a Pythagorean comma apart, in contrast to diatonic and chromatic semitones in meantone temperament and 5-limit just intonation.