List of musical intervals - AbsoluteAstronomy.com

Below is a list of music

Music

Music is an art form whose medium is sound and silence. Its common elements are pitch , rhythm , dynamics, and the sonic qualities of timbre and texture...

al intervals. Some terminology used in the list:

In music, the prime limit
Limit (music)
In music theory, limit or harmonic limit is a way of characterizing the harmony found in a piece or genre of music, or the harmonies that can be made using a particular scale. The term was introduced by Harry Partch, who used it to give an upper bound on the complexity of harmony; hence the name...

(henceforth referred to simply as the limit) is a number measuring the harmony of an interval
Interval (music)
In music theory, an interval is a combination of two notes, or the ratio between their frequencies. Two-note combinations are also called dyads...

. The lower the number, the more consonant
Consonance and dissonance
In music, a consonance is a harmony, chord, or interval considered stable, as opposed to a dissonance , which is considered to be unstable...

the interval is considered to be. It is defined as the largest prime number
Prime number
A prime number is a natural number greater than 1 that has no positive divisors other than 1 and itself. A natural number greater than 1 that is not a prime number is called a composite number. For example 5 is prime, as only 1 and 5 divide it, whereas 6 is composite, since it has the divisors 2...

occurring in the factorizations
Integer factorization
In number theory, integer factorization or prime factorization is the decomposition of a composite number into smaller non-trivial divisors, which when multiplied together equal the original integer....

of the numerator and denominator of the frequency ratio. The limit of the just perfect fourth
Perfect fourth
In classical music from Western culture, a fourth is a musical interval encompassing four staff positions , and the perfect fourth is a fourth spanning five semitones. For example, the ascending interval from C to the next F is a perfect fourth, as the note F lies five semitones above C, and there...

(4 : 3) is 3, but the just minor tone (10 : 9) has a limit of 5, because 9 can be factorized into 3×3, and 10 into 2×5. There exists another type of limit, the odd limit, which differs slightly from the prime limit, but is not used here.
Equal-tempered refers to 12-tone equal temperament
Equal temperament
An equal temperament is a musical temperament, or a system of tuning, in which every pair of adjacent notes has an identical frequency ratio. As pitch is perceived roughly as the logarithm of frequency, this means that the perceived "distance" from every note to its nearest neighbor is the same for...

with intervals corresponding to 100 cent
Cent (music)
The cent is a logarithmic unit of measure used for musical intervals. Twelve-tone equal temperament divides the octave into 12 semitones of 100 cents each...

multiples (e.g., 100, 200, 300, etc.).
Pythagorean
Pythagorean tuning
Pythagorean tuning is a system of musical tuning in which the frequency relationships of all intervals are based on the ratio 3:2. This interval is chosen because it is one of the most consonant...

means 3-limit just intonation
Just intonation
In music, just intonation is any musical tuning in which the frequencies of notes are related by ratios of small whole numbers. Any interval tuned in this way is called a just interval. The two notes in any just interval are members of the same harmonic series...

—a ratio of numbers with prime factors no higher than three.
Just means 5-limit just intonation—a ratio of numbers with prime factor
Prime factor
In number theory, the prime factors of a positive integer are the prime numbers that divide that integer exactly, without leaving a remainder. The process of finding these numbers is called integer factorization, or prime factorization. A prime factor can be visualized by understanding Euclid's...

s no higher than five.
Similarly, septimal, undecimal, tridecimal, and septendecimal mean, respectively, 7, 11, 13, and 17-limit just intonation.
By definition every tone in a 3-limit unit can also be part of a 5-limit tuning and so on. By sorting the limit column all tones of that limit can be brought together (tip: sort backwards by clicking the button twice).
Meantone refers to meantone temperament
Meantone temperament
Meantone temperament is a musical temperament, which is a system of musical tuning. In general, a meantone is constructed the same way as Pythagorean tuning, as a stack of perfect fifths, but in meantone, each fifth is narrow compared to the ratio 27/12:1 in 12 equal temperament, the opposite of...

, the most common of which is quarter-comma meantone
Quarter-comma meantone
Quarter-comma meantone, or 1/4-comma meantone, was the most common meantone temperament in the sixteenth and seventeenth centuries, and was sometimes used later. This method is a variant of Pythagorean tuning...

. In general, a meantone is constructed the same way as Pythagorean tuning, as a stack of perfect fifths, but in a meantone, each fifth is narrowed by the same small amount (a portion of the syntonic comma
Syntonic comma
In music theory, the syntonic comma, also known as the chromatic diesis, the comma of Didymus, the Ptolemaic comma, or the diatonic comma is a small comma type interval between two musical notes, equal to the frequency ratio 81:80, or around 21.51 cents...

such as 1/4).
Since the table is sortable, you can also sort the table by frequency ratio, by cents or alphabetically.

List

Code	Legend
E	12 tone equal temperament.
Q	24 tone equal temperament, or Arab tone system Arab tone system The modern Arab tone system, or system of musical tuning, is based upon the theoretical division of the octave into twenty-four equal divisions or 24-tone equal temperament , the distance between each successive note being a quarter tone . Each tone has its own name not repeated in different... .
2	2-limit tones (only fundamental Fundamental frequency The fundamental frequency, often referred to simply as the fundamental and abbreviated f0, is defined as the lowest frequency of a periodic waveform. In terms of a superposition of sinusoids The fundamental frequency, often referred to simply as the fundamental and abbreviated f0, is defined as the... and octave Octave In music, an octave is the interval between one musical pitch and another with half or double its frequency. The octave relationship is a natural phenomenon that has been referred to as the "basic miracle of music", the use of which is "common in most musical systems"... s).
2 3	3-limit just intonation, or Pythagorean.
2 3 5	5-limit (not 3-limit) just intonation, or just.
2 3 5 7	7-limit (not 5-limit) just intonation, or septimal.
2 3 5 7 11	11-limit (not 7-limit) just intonation, or undecimal.
2 3 5 7 11 13	13-limit (not 11-limit) just intonation, or tridecimal.
2 3 5 7 11 13 17	17-limit (not 13-limit) just intonation, or septendecimal.
2 3 5 7 11 13 17 19	19-limit (not 17-limit) just intonation.
M	Meantone temperament.
U	A unit of measurement.

List of musical intervals
Cents	Freq. Ratio	Factors	Interval Name	E	Q	2	3	5	7	11	13	17	19	M	U
	1 : 1	1 : 1		E	Q	2	3	5	7	11	13	17	19	M
	4375 : 4374								7	11	13	17	19
	2401 : 2400								7	11	13	17	19
	2^1/1200 : 1														U
	2 ^1/1000 : 1														U
		3⁸·5 : 2¹⁵						5	7	11	13	17	19
	10^1/1000 : 1														U
	225 : 224								7	11	13	17	19
	15625 : 15552	5⁶ : 2⁶·3⁵						5	7	11	13	17	19
	2109375 : 2097152	3³·5⁷ : 2²¹						3	5
	2^1/96 : 1														U
	1728:1715	2⁶·3³ : 5·7³							7	11	13	17	19
	126 : 125	2·3²·7 : 5³							7	11	13	17	19
	121 : 120	11² : 2³·3·5								11	13	17	19
	2^1/72 : 1														U
	2048 : 2025							5	7	11	13	17	19
	81 : 80	3⁴ : 2⁴·5						5	7	11	13	17	19
	2^1/53 : 1														U
	531441:524288	3¹² : 2¹⁹					3	5	7	11	13	17	19
	2^1/48 : 1														U
	64 : 63	2⁶ : 3²·7							7	11	13	17	19
	2^1/41 : 1														U
	56 : 55	2³·7 : 5·11								11	13	17	19
	2^1/36 : 1														U
	50 : 49	2·5² : 7²							7	11	13	17	19
	49 : 48	7² : 2⁴·3							7	11	13	17	19
	2^1/31 : 1														U
	2^1/30 : 1														U
	128 : 125	2⁷ : 5³						5	7	11	13	17	19
	36 : 35	2²·3² : 5·7							7	11	13	17	19
	2^1/24 : 1				Q										U
															U
	27 : 26														U
	2^1/18 : 1														U
	25 : 24	5² : 2³·3						5	7	11	13	17	19
															U
	21 : 20	3·7 : 2²·5							7	11	13	17	19
	256 : 243	2⁸ : 3⁵					3	5	7	11	13	17	19
	135 : 128	3³·5 : 2⁷						5	7	11	13	17	19
	2^1/12 : 1			E	Q										U
	16 : 15	2⁴ : 3·5						5	7	11	13	17	19
	2187 : 2048	3⁷ : 2¹¹					3	5	7	11	13	17	19
	18^1/19 : 5^1/19														U
	15 : 14	3·5 : 2·7							7	11	13	17	19
	27 : 25	3³ : 5²						5	7	11	13	17	19
	2^3/24 : 1				Q
	12 : 11	2²·3 : 11								11	13	17	19
	11 : 10	11 : 2·5								11	13	17	19
	2^1/7 : 1														U
	65536 : 59049	2¹⁶ : 3¹⁰					3	5	7	11	13	17	19
	10 : 9	2·5 : 3²						5	7	11	13	17	19
	2^2/12 : 1			E	Q
	9 : 8	3² : 2³					3	5	7	11	13	17	19
	8 : 7	2³ : 7							7	11	13	17	19
	2^1/5 : 1														U
	7 : 6	7 : 2·3							7	11	13	17	19
	32 : 27	2⁵ : 3³					3	5	7	11	13	17	19
	19 : 16	19 : 2⁴											19
	2^3/12 : 1			E	Q
	6:5÷(81:80)^1/4													M

	6 : 5	2·3 : 5						5	7	11	13	17	19
	19683 : 16384	3⁹ : 2¹⁴					3	5	7	11	13	17	19
	2^2/7 : 1
	11 : 9	11 : 3²								11	13	17	19
	2^7/24 : 1				Q
	16 : 13	2⁴ : 13									13	17	19
	8192 : 6561	2¹³ : 3⁸					3	5	7	11	13	17	19
	5 : 4	5 : 2²						5	7	11	13	17	19	M
	2^4/12 : 1			E	Q
	81 : 64	3⁴ : 2⁶					3	5	7	11	13	17	19
	14 : 11	2·7 : 11								11	13	17	19
	9 : 7	3² : 7							7	11	13	17	19
	21 : 16
	2^2/5 : 1
	4 : 3	2² : 3					3	5	7	11	13	17	19
	2^5/12 : 1			E	Q

	2^3/7 : 1
	27 : 20	3³ : 2²·5						5	7	11	13	17	19
	177147:131072	3¹¹ : 2¹⁷					3	5	7	11	13	17	19
	11 : 8	11 : 2³								11	13	17	19
	25 : 18	5² : 2·3²						5	7	11	13	17	19
	7 : 5								7	11	13	17	19
	1024 : 729	2¹⁰ : 3⁶					3	5	7	11	13	17	19
	45 : 32						3	5
	2^6/12 : 1			E	Q
	729 : 512	3⁶ : 2⁹					3	5	7	11	13	17	19
	10 : 7	2·5 : 7							7	11	13	17	19
	16 : 11	2⁴ : 11								11	13	17	19
	262144:177147	2¹⁸ : 3¹¹					3	5	7	11	13	17	19
	40 : 27	2³·5 : 3³						5	7	11	13	17	19
	3:2÷(81:80)^1/4													M
	2^7/12 : 1			E	Q
	3 : 2	3 : 2					3	5	7	11	13	17	19
	14 : 9	2·7 : 3²							7	11	13	17	19
	11 : 7	11 : 7								11	13	17	19
	128 : 81	2⁷ : 3⁴					3	5	7	11	13	17	19
	2^8/12 : 1			E	Q
	8 : 5	2³ : 5						5	7	11	13	17	19
	6561 : 4096	3⁸ : 2¹²					3	5	7	11	13	17	19
	13 : 8	13 : 2³									13	17	19
	2^17/24 : 1				Q
	18 : 11	2·3² : 11								11	13	17	19
	2^5/7 : 1
	32768 : 19683	2¹⁵ : 3⁹					3	5	7	11	13	17	19
	5 : 3	5 : 3						5	7	11	13	17	19
	2^9/12 : 1			E	Q
	27 : 16	3³ : 2⁴					3	5	7	11	13	17	19
	12 : 7	2²·3 : 7							7	11	13	17	19

	2^4/5 : 1
	7 : 4	7 : 2²							7	11	13	17	19
	16 : 9	2⁴ : 3²					3	5	7	11	13	17	19
	2^10/12 : 1			E	Q
	9 : 5	3² : 5						5	7	11	13	17	19
	59049 : 32768	3¹⁰ : 2¹⁵					3	5	7	11	13	17	19
	2^6/7 : 1
	20 : 11	2²·5 : 11								11	13	17	19
	11 : 6	11 : 2·3								11	13	17	19
	2^21/24 : 1				Q
	4096 : 2187	2¹² : 3⁷					3	5	7	11	13	17	19
	15 : 8	3·5 : 2³						5	7	11	13	17	19
	2^11/12 : 1			E	Q
	243 : 128	3⁵ : 2⁷					3	5	7	11	13	17	19
	2 : 1	2 : 1		E	Q	2	3	5	7	11	13	17	19	M	U
	531441:262144	3¹² : 2¹⁸					3	5	7	11	13	17	19
	3 : 1	3 : 1					3	5	7	11	13	17	19
	4 : 1	2² : 1		E	Q	2	3	5	7	11	13	17	19	M

External links

"Names of seven-limit commas", Xenharmony.org. (Archived copy)
"Anatomy of an Octave", KyleGann.com.

The source of this article is wikipedia, the free encyclopedia. The text of this article is licensed under the GFDL.

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See also

External links