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Harmonic series, partials 1–5 numbered
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 tuned in this way is said to be pure, and is called a just interval. Just intervals (and chords created by combining them) consist of tones from a single harmonic series of an implied fundamental. For example, in the diagram, if the notes G3 and C4 (labelled 3 and 4) are tuned as members of the harmonic series of the lowest C, their frequencies will be 3 and 4 times the fundamental frequency. The interval ratio between C4 and G3 is therefore 4:3, a just fourth.
In Western musical practice, bowed instruments such as violins, violas, cellos, and double basses are tuned using pure fifths or fourths. In contrast, keyboard instruments are rarely tuned using only pure intervals—the desire for different keys to have identical intervals in Western music makes this impractical. Some instruments of fixed pitch, such as electric pianos, are commonly tuned using equal temperament, in which all intervals other than octaves consist of irrational-number frequency ratios. Acoustic pianos are usually tuned with the octaves slightly widened, and thus with no pure intervals at all.
The phrase "just intonation" is used both to refer to one specific version of a 5-limit diatonic intonation, that is, Ptolemy's intense diatonic, as well to a whole class of tunings which use whole number intervals derived from the harmonic series. In this sense, "just intonation" is differentiated from equal temperaments and the "tempered" tunings of the early renaissance and baroque, such as Well temperament, or Meantone temperament. Since 5-limit has been the most prevalent just intonation used in western music, western musicians have subsequently tended to consider this scale to be the only version of just intonation. In principle, there are an infinite number of possible "just intonations," since the harmonic series is infinite.
In music, justintonation 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 justintonation typically define three or four kinds of semitones. For instance, Asymmetric...
This is a list of a selection of musical compositions in justintonation composed since 1900. List of quarter tone pieces "His Music". harrypartch. Retrieved...
the root and fifth. Another tuning system that is used is justintonation. In justintonation, a major chord is tuned to the frequency ratio 4:5:6. This...
than the 300 cent ET minor third. Other just minor chord tunings include the supertonic triad in justintonation (27:32:40) the false minor triad, Play...
mechanical tuning limitations, sometimes use a tuning much closer to justintonation for acoustic reasons. Other instruments, such as some wind, keyboard...
are tuned with an exact ratio of 3:2 (the system of tuning known as justintonation), this is not the case (the circle does not "close"). The circle of...
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)...
is a tuning system that slightly compromises the pure intervals of justintonation to meet other requirements. Most modern Western musical instruments...
tempered fifth, or by a combination of perfect fifths and perfect thirds (Justintonation), or possibly by a combination of fifths and thirds of various sizes...
sixth ratio. John Fonville (Summer 1991). "Ben Johnston's Extended JustIntonation: A Guide for Interpreters". Perspectives of New Music. 29 (2): 109...
centuries, share a similar asymmetry. In Pythagorean tuning (i.e. 3-limit justintonation) the chromatic scale is tuned as follows, in perfect fifths from G♭...
Pythagorean intonation as that will make the scale sound best in tune, then reverting to other temperaments for other passages (justintonation for chordal...
repeats. Below are Ogg Vorbis files demonstrating the difference between justintonation and equal temperament. You might need to play the samples several times...
it may function as a quarter tone, a fifth-tone or a sixth-tone. In justintonation the quarter tone can be represented by the septimal quarter tone, 36:35...
that are mathematically exact for justintonation, which meantone temperaments seek to approximate. In justintonation, a minor chord is often (but not...
diminished third, are also called tones, whole tones, or whole steps. In justintonation, major seconds can occur in at least two different frequency ratios:...
and Austria to play these notes in position, where they will have justintonation (see harmonic seventh as well for A♭4). The next higher partials—B♭4...
characteristics, and advantages and disadvantages. The main ones are: Justintonation In justintonation, the frequencies of the scale notes are related to one another...
fifth from the root is also present or implied). A minor third, in justintonation, corresponds to a pitch ratio of 6:5 or 315.64 cents. In an equal tempered...
diesis (128:125) less than a perfect octave: A4 + A4 = P8 − diesis. In justintonation several different sizes can be chosen both for the A4 and the d5. For...
\end{alignedat}}} The intervals of 12-ET closely approximate some intervals in justintonation. 12 ET is very accurate in the 3 limit, but as one increases prime...
possible "just ratios" defined for this interval in justintonation (slightly below the width of a minor seventh as tuned in equal temperament). With just intonation...
mean between the major whole tone (9:8 in justintonation) and the minor whole tone (10:9 in justintonation). The meantone is the mean of its major third...
blue notes are intervals of justintonation not derived from European 12-tone equal temperament tuning. Justintonation musical intervals derive directly...
dissonance requiring resolution to a consonance. In justintonation there is both a 16:9 "small just minor seventh", also called the "Pythagorean small...
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