In musical tuning theory, a Pythagorean interval is a musical interval with a frequency ratio equal to a power of two divided by a power of three, or vice...

Pythagorean tuning is a system of musical tuning in which the frequency ratios of all intervals are determined by choosing a sequence of fifths which...

semitone (augmented unison), or in Pythagorean tuning, where the diatonic semitone is smaller instead. See Interval (music) § Number for more details about...

mathematician and philosopher Pythagoras, is the small interval (or comma) existing in Pythagorean tuning between two enharmonically equivalent notes such...

(or Pythagorean minor third) is the interval 32:27 (approximately 294.13 cents). It is the minor third in Pythagorean tuning. The 32:27 Pythagorean minor...

ear could possibly prefer 45/32 to a small-number interval of about the same width. In the Pythagorean ratio 81/64 both numbers are multiples of 3 or under...

used to refer to similar intervals (of close, but variable magnitudes) produced by other tuning systems, including Pythagorean and most meantone temperaments...

instance, in Pythagorean tuning the diminished second is a descending interval (524288:531441, or about −23.5 cents), and the Pythagorean comma is its...

The Pythagorean ditone is the major third in Pythagorean tuning, which has an interval ratio of 81:64, which is 407.82 cents. The Pythagorean ditone...

endlessly in pitch Pseudo-octave – Musical interval which is not a perfect harmonic Pythagorean interval – Musical interval Short octave – Musical keyboard layout...

Two major tones equal a ditone. In Pythagorean music theory, the epogdoon (Ancient Greek: ἐπόγδοον) is the interval with the ratio 9 to 8. The word is...

conventional notation does not distinguish Pythagorean intervals from 5-limit intervals. Other intervals are considered commas because of the enharmonic...

In music, an interval ratio is a ratio of the frequencies of the pitches in a musical interval. For example, a just perfect fifth (for example C to G)...

inversion of the Pythagorean minor third, and corresponds to the interval between the 27th and the 16th harmonics. The 27:16 Pythagorean major sixth arises...

septimal comma, the ratio of 64:63, is a 7 limit interval which is the distance between the Pythagorean semi-ditone, ⁠ 32 / 27 ⁠, and the septimal minor...

fifth in Pythagorean tuning or meantone temperament is actually not a perfect fifth but a diminished sixth (for instance G♯–E♭). Perfect intervals are also...

In music theory, a minor seventh is one of two musical intervals that span seven staff positions. It is minor because it is the smaller of the two sevenths...

the table below, all intervals of a given limit can be brought together (sort backwards by clicking the button twice). Pythagorean tuning means 3-limit...

In music theory, a neutral interval is an interval that is neither a major nor minor, but instead in between. For example, in equal temperament, a major...

A fourth is a musical interval encompassing four staff positions in the music notation of Western culture, and a perfect fourth (Play) is the fourth spanning...

file? See media help. The Pythagorean augmented fifth is the ratio 6561:4096, or about 815.64 cents. List of meantone intervals Benward & Saker (2003)....

musical parts that sound either the same pitch or pitches separated by intervals of one or more octaves, usually at the same time. Rhythmic unison is another...

in Pythagorean tuning were flattened or sharpened to produce just minor and major thirds. In Pythagorean tuning, the only highly consonant intervals were...

Benward & Saker (2003), p. 92. Paul, Oscar (1885). ""Pythagorean major third" (musical interval)". A Manual of Harmony. Translated by Schirmer, G. Theodore...

In Western classical music, an augmented second is an interval created by widening a major second by a chromatic semitone, spanning three semitones and...

Pythagoreanism originated in the 6th century BC, based on and around the teachings and beliefs held by Pythagoras and his followers, the Pythagoreans...

the schisma (also spelled skhisma) is the interval between the syntonic comma (81:80) and the Pythagorean comma ( 531 441 : 524 288 ), which is slightly...

In music theory, a minor sixth is a musical interval encompassing six staff positions (see Interval number for more details), and is one of two commonly...

intervals. Twelve-tone equal temperament divides the octave into 12 semitones of 100 cents each. Typically, cents are used to express small intervals...

to the just major third than the Pythagorean major third. In just intonation the usual diminished fourth: the interval C♯ to F, a diatonic minor second...