In music, just intonation or pure intonation is the tuning of musical intervals as whole number ratios (such as 3:2 or 4:3) of frequencies. An interval...

lesser diesis of ratio 128:125 or 41.1 cents. 12-tone scales tuned in just intonation typically define three or four kinds of semitones. For instance, Asymmetric...

the root and fifth. Another tuning system that is used is just intonation. In just intonation, a major chord is tuned to the frequency ratio 4:5:6. This...

mechanical tuning limitations, sometimes use a tuning much closer to just intonation for acoustic reasons. Other instruments, such as some wind, keyboard...

than the 300 cent ET minor third. Other just minor chord tunings include the supertonic triad in just intonation (27:32:40) the false minor triad, Play...

with an exact frequency ratio of 3:2 (the system of tuning known as just intonation), this is not the case (the circle does not "close"). The circle of...

1934–2006, just intonation, 72-tone equal temperament) Terry Riley (U.S.A., b. 1935, just intonation) La Monte Young (U.S.A., b. 1935, just intonation) John...

proportions (C–G–D–A–E). Considering the anhemitonic scale as a subset of a just diatonic scale, it is tuned thus: 20:24:27:30:36 (A–C–D–E–G = 5⁄6–1⁄1–9⁄8–5⁄4–3⁄2)...

sixth ratio. John Fonville (Summer 1991). "Ben Johnston's Extended Just Intonation: A Guide for Interpreters". Perspectives of New Music. 29 (2): 109...

centuries, share a similar asymmetry. In Pythagorean tuning (i.e. 3-limit just intonation) the chromatic scale is tuned as follows, in perfect fifths from G♭...

repeats. Below are Ogg Vorbis files demonstrating the difference between just intonation and equal temperament. You might need to play the samples several times...

that are mathematically exact for just intonation, which meantone temperaments seek to approximate. In just intonation, a minor chord is often (but not...

is a tuning system that slightly compromises the pure intervals of just intonation to meet other requirements. Most modern Western musical instruments...

This is a list of a selection of musical compositions in just intonation composed since 1900. List of quarter tone pieces "His Music". harrypartch. Retrieved...

characteristics, and advantages and disadvantages. The main ones are: Just intonation In just intonation, the frequencies of the scale notes are related to one another...

ratio of their frequencies. When a musical instrument is tuned using a just intonation tuning system, the size of the main intervals can be expressed by small-integer...

tempered fifth, or by a combination of perfect fifths and perfect thirds (Just intonation), or possibly by a combination of fifths and thirds of various sizes...

it may function as a quarter tone, a fifth-tone or a sixth-tone. In just intonation the quarter tone can be represented by the septimal quarter tone, 36:35...

harmonies. Hence, 5-limit tuning is considered a method for obtaining just intonation. The number of potential intervals, pitch classes, pitches, key centers...

diminished third, are also called tones, whole tones, or whole steps. In just intonation, major seconds can occur in at least two different frequency ratios:...

Pythagorean intonation as that will make the scale sound best in tune, then reverting to other temperaments for other passages (just intonation for chordal...

{\displaystyle 3:2} , in order to bring the major or minor thirds closer to the just intonation ratio of 5 : 4 {\displaystyle 5:4} or 6 : 5 {\displaystyle 6:5} , respectively...

(128:125) less than a perfect octave: Aug 4 + Aug 4 = Perf 8 − diesis. In just intonation several different sizes can be chosen both for the Aug 4 and the dim 5...

fifth from the root is also present or implied). A minor third, in just intonation, corresponds to a pitch ratio of 6:5 or 315.64 cents. In an equal tempered...

\end{alignedat}}} The intervals of 12-ET closely approximate some intervals in just intonation. 12 ET is very accurate in the 3 limit, but as one increases prime...

blue notes are intervals of just intonation not derived from European 12-tone equal temperament tuning. Just intonation musical intervals derive directly...

poorly), while the major seventh chord approximates 8:10:12:15. In just intonation, intervals between pitches are drawn from the rational numbers. Since...

possible "just ratios" defined for this interval in just intonation (slightly below the width of a minor seventh as tuned in equal temperament). With just intonation...

of 28/12:1 or simplified to 22/3:1 (about 1.587), or 800 cents. In just intonation multiple definitions of a minor sixth can exist: In 3-limit tuning...

above-mentioned Pythagorean perfect fifth and fourth are also used in just intonation. Notice that the terms ditone and semiditone are specific for Pythagorean...