List Of Intervals In 5-limit Just Intonation
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The intervals of 5- limit
just intonation In music, just intonation or pure intonation is a musical tuning, tuning system in which the space between notes' frequency, frequencies (called interval (music), intervals) is a natural number, whole number ratio, ratio. Intervals spaced in thi ...
( prime limit, not odd limit) are ratios involving only the powers of 2, 3, and 5. The fundamental intervals are the superparticular ratios 2/1 (the
octave In music, an octave (: eighth) or perfect octave (sometimes called the diapason) is an interval between two notes, one having twice the frequency of vibration of the other. The octave relationship is a natural phenomenon that has been referr ...
), 3/2 (the
perfect fifth In music theory, a perfect fifth is the Interval (music), musical interval corresponding to a pair of pitch (music), pitches with a frequency ratio of 3:2, or very nearly so. In classical music from Western culture, a fifth is the interval f ...
) and 5/4 (the
major third In music theory, a third is a Interval (music), musical interval encompassing three staff positions (see Interval (music)#Number, Interval number for more details), and the major third () is a third spanning four Semitone, half steps or two ...
). That is, the notes of the
major triad In music theory, a major chord is a chord that has a root, a major third, and a perfect fifth. When a chord comprises only these three notes, it is called a major triad. For example, the major triad built on C, called a C major triad, has pitch ...
are in the ratio 1:5/4:3/2 or 4:5:6. In all tunings, the
major third In music theory, a third is a Interval (music), musical interval encompassing three staff positions (see Interval (music)#Number, Interval number for more details), and the major third () is a third spanning four Semitone, half steps or two ...
is equivalent to two
major second In Western music theory, a major second (sometimes also called whole tone or a whole step) is a second spanning two semitones (). A second is a musical interval encompassing two adjacent staff positions (see Interval number for more de ...
s. However, because just intonation does not allow the irrational ratio of /2, two different frequency ratios are used: the
major tone Major most commonly refers to: * Major (rank), a military rank * Academic major, an academic discipline to which an undergraduate student formally commits * People named Major, including given names, surnames, nicknames * Major and minor in musi ...
(9/8) and the
minor tone In Western music theory, a major second (sometimes also called whole tone or a whole step) is a second spanning two semitones (). A second is a musical interval encompassing two adjacent staff positions (see Interval number for more detai ...
(10/9). The intervals within the
diatonic scale In music theory a diatonic scale is a heptatonic scale, heptatonic (seven-note) scale that includes five whole steps (whole tones) and two half steps (semitones) in each octave, in which the two half steps are separated from each other by eith ...
are shown in the table below.


List

(The Pythagorean minor second is found by adding 5 perfect fourths.) The table below shows how these steps map to the first 31 scientific harmonics, transposed into a single octave. ยง These intervals also appear in the upper table, although with different ratios.


See also

* List of musical intervals * List of pitch intervals *
Pythagorean interval In musical tuning theory, a Pythagorean interval is a musical interval with a Interval ratio, frequency ratio equal to a Exponentiation, power of two divided by a power of three, or vice versa.Benson, Donald C. (2003). ''A Smoother Pebble: Mathe ...


References

{{Musical tuning