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Encyclopedia > Interval (music)

In music theory, the term interval describes the difference in pitch between two notes. Although frequently used in connection with intervals, the term "distance" does not adequately describe the physics and subjective effects of two interacting frequencies. Image File history File links Gnome-globe. ... Music Theory is a field of study that investigates the nature or mechanics of music. ... Pitch is the perceived fundamental frequency of a sound. ... Distance may refer to: Distance in the mathematical and physical sense. ...


Intervals may be described as:

  • vertical (or harmonic) if the two notes sound simultaneously
  • linear (or melodic), if the notes sound successively.[1]

Interval class is a system of labelling intervals when the order of the notes is left unspecified, therefore describing an interval in terms of the shortest distance possible between its two pitch classes.[2] Harmony is the result of polyphony (more than one note being played simultaneously). ... Look up melody in Wiktionary, the free dictionary. ... In music, specifically, musical set theory an interval class, or unordered pitch-class interval, is an interval measured by the distance between its two pitch classes ordered so they are as close as possible. ... In music and music theory a pitch class contains all notes that have the same name; for example, all Es, no matter which octave they are in, are in the same pitch class. ...

Contents

Frequency ratios

Intervals may be labelled according to the ratio of frequencies of the two pitches. Important intervals are those using the lowest integers, such as 1/1, 2/1, 3/2, etc. This system is frequently used to describe intervals in non-Western music. This method is also often used in just intonation, and in theoretical explanations of equal-tempered intervals used in European tonal music which explain their use through their approximation of just intervals. A ratio is a dimensionless, or unitless, quantity denoting an amount or magnitude of one quantity relative to another. ... FreQuency is a music video game developed by Harmonix and published by SCEI. It was released in November 2001. ... In music, just intonation, also called rational intonation, is any musical tuning in which the frequencies of notes are related by ratios of whole numbers. ...


Interval number and quality

Interval namesU = unison; 8ve = octave
Interval names
U = unison; 8ve = octave

In Western harmonic theory, intervals are labeled according to the number of scale steps or staff positions they encompass, as shown at right. Interval numbers This image is ineligible for copyright and therefore in the public domain, because it consists entirely of information that is common property and contains no original authorship. ... In music or music theory a scale degree is an individual note of a scale, both its pitch and its diatonic function. ... In musical notation, the staff or stave is a set of five horizontal lines on which note symbols are placed to indicate pitch and rhythm. ...


Intervals larger than an octave are called compound intervals; for example, a tenth is known as a compound third. Intervals larger than a thirteenth are rarely spoken of, since going above this by stacking thirds would result in a double octave (but see 8va for use of 15ma). In music, an octave (sometimes abbreviated 8ve or 8va) is the interval between one musical note and another with half or double the frequency. ... For the numerical computation software, see GNU Octave. ...


The name or the label of an interval is determined by counting the number of degrees between the two notes beginning with one for the lower note. The number of degrees between F and B for example is 4, therefore the interval is a fourth.


The name of any interval is further qualified using the terms perfect, major, minor, augmented, and diminished. This is called its interval quality. Look up Perfect in Wiktionary, the free dictionary. ... Major may mean: Major, a military rank. ... Look up minor in Wiktionary, the free dictionary. ... In music and music theory augmentation is the lengthening or widening of rhythms, melodies, intervals, chords. ... Diminution, from Italian diminuimento, is a musical term used to mean different things in the context of melodies and intervals or chords. ...

  • Unison, fourth, fifth, octave. These intervals may be perfect, augmented, or diminished.
    • They are called perfect because of their extremely simple pitch relationships resulting in a high degree of consonance.
    • A perfect fourth is five semitones.
    • A perfect fifth is seven semitones.
    • A perfect octave is twelve semitones.
    • A perfect unison occurs between notes of the same pitch, so it is zero semitones.
    • In each case, an augmented interval contains one more semitone, a diminished interval one fewer.
  • Second, third, sixth, seventh. These intervals may be major, minor, augmented, or diminished.

It is possible to have doubly-diminished and doubly-augmented intervals, but these are quite rare. For other uses, see Unison (disambiguation). ... The perfect fourth or diatessaron, abbreviated P4, is one of two musical intervals that span four diatonic scale degrees; the other being the augmented fourth, which is one semitone larger. ... The perfect fifth or diapente is one of three musical intervals that span five diatonic scale degrees; the others being the diminished fifth, which is one semitone smaller, and the augmented fifth, which is one semitone larger. ... In music, an octave (sometimes abbreviated 8ve or 8va) is the interval between one musical note and another with half or double the frequency. ... In music and music theory augmentation is the lengthening or widening of rhythms, melodies, intervals, chords. ... Diminution, from Italian diminuimento, is a musical term used to mean different things in the context of melodies and intervals or chords. ... The perfect fourth or diatessaron, abbreviated P4, is one of two musical intervals that span four diatonic scale degrees; the other being the augmented fourth, which is one semitone larger. ... The perfect fifth or diapente is one of three musical intervals that span five diatonic scale degrees; the others being the diminished fifth, which is one semitone smaller, and the augmented fifth, which is one semitone larger. ... In music, an octave (sometimes abbreviated 8ve or 8va) is the interval between one musical note and another with half or double the frequency. ... In music, a unison is an interval, the ratio of 1:1 or 0 halfsteps and zero cents. ... A major second is one of three commonly occuring musical intervals that span two diatonic scale degrees; the others being the minor second, which is one semitone smaller, and the augmented second, which is one semitone larger. ... A minor second is the smallest of three commonly occuring musical intervals that span two diatonic scale degrees; the others being the major second and the augmented second, which are larger by one and two semitones respectively. ... A major third is the larger of two commonly occuring musical intervals that span three diatonic scale degrees. ... A minor third is the smaller of two commonly occurring musical intervals that span three diatonic scale degrees. ... The musical interval of a major sixth is the relationship between the first note (the root or tonic) and the sixth note in a Major scale. ... A minor sixth is the smaller of two commonly occuring musical intervals that span six diatonic scale degrees. ... The musical interval of a Major seventh the first note (the root or tonic) and the seventh, the leading tone, in a major scale. ... The musical interval of a minor seventh the first note (the root or tonic) and the seventh in a minor scale. ...


The name of an interval cannot be determined by counting semitones alone. There are four semitones between B and E♭ but this interval is not a major third, but rather an diminished fourth, a relatively rare interval (but which does appear naturally as part of the harmonic minor scale). In equal-tempered tuning, as on a piano, these intervals are indistinguishable by sound, but the diatonic function of the notes incorporated might be very different. In music, a scale is a set of musical notes in order by pitch, either ascending or descending. ... An equal temperament is a musical temperament -- that is, a system of tuning intended to approximate some form of just intonation -- in which an interval, usually the octave, is divided into a series of equal steps (equal frequency ratios). ... A diatonic function, in tonal music theory, is the specific, recognized roles of notes or chords in relation to the key. ...


Diatonic and chromatic intervals

The intervals contained in the table are diatonic to C major. All other intervals are chromatic to C major.
The intervals contained in the table are diatonic to C major. All other intervals are chromatic to C major.

A diatonic interval is an interval formed by two notes of a diatonic scale. The table on the right depicts all diatonic intervals for C major. As the diatonic functions are similarly common to each and every major key, the contents of the table can be summarised as follows: Image File history File links No higher resolution available. ...

  • All perfect, major and minor intervals are diatonic.
  • Additionally, the tritone and the diminished 5th are diatonic.
  • All other intervals are chromatic.

Shorthand notation

Intervals are often abbreviated with a P for perfect, m for minor, M for major, d for diminished, A for augmented, followed by the diatonic interval number. The indication M and P are often omitted. The octave is P8, and a unison is usually referred to simply as "a unison" but can be labeled P1. The tritone, an augmented fourth or diminished fifth is often π or TT. Examples: Look up minor in Wiktionary, the free dictionary. ... Major is a military rank the use of which varies according to country. ... Diminution, from Italian diminuimento, is a musical term used to mean different things in the context of melodies and intervals or chords. ... For the linguistic concept, see augment (linguistics). ... In music, an octave (sometimes abbreviated 8ve or 8va) is the interval between one musical note and another with half or double the frequency. ... For other uses, see Unison (disambiguation). ... The augmented fourth between C and F# forms a tritone. ...

  • m2: minor second
  • M3: major third
  • P5: perfect fifth
  • m9: minor ninth

For use in describing chords, the sign + is used for augmented and for diminished. Furthermore the 3 for the third is often omitted, and for the seventh, the plain form stands for the minor interval, while the major is indicated by maj. So for example: In music a chord symbol is an abbreviated notation for chord names and qualities, using letters, numbers, and other symbols. ...

  • m: minor third
  • 7: minor seventh
  • °7: diminished seventh
  • maj7: major seventh
  • +5: augmented fifth
  • −5: diminished fifth

Enharmonic intervals

Two intervals are considered to be enharmonic, or enharmonically equivalent, if they both contain the same pitches spelled in different ways; that is, if the notes in the two intervals are themselves enharmonically equivalent. Enharmonic intervals span the same number of semitones. For example, as shown in the matrix below, F♯–A♯ (a major third), G♭–B♭ (also a major third), F♯–B♭ (a diminished fourth), and G♭–A♯ (a double augmented second) are all enharmonically equivalent — and they all span four semitones. In music, an enharmonic is a note which is the equivalent of some other note, but spelled differently. ... Pitch is the perceived fundamental frequency of a sound. ... A semitone (also known in the USA as a half step) is a musical interval. ... A major third is the larger of two commonly occuring musical intervals that span three diatonic scale degrees. ... A major third is the larger of two commonly occurring musical intervals that span three diatonic scale degrees. ... The musical interval of a minor third is the relationship between the first note (the root or tonic) and the third note in a minor scale. ...

step 1 2 3 4
major third F♯   A♯  
major third   G♭   B♭
diminished fourth F♯     B♭
double augmented second   G♭ A♯  

A major third is the larger of two commonly occuring musical intervals that span three diatonic scale degrees. ... A major third is the larger of two commonly occurring musical intervals that span three diatonic scale degrees. ... The musical interval of a minor third is the relationship between the first note (the root or tonic) and the third note in a minor scale. ...

Steps and skips

Linear (melodic) intervals may be described as steps or skips in a diatonic context. Steps are linear intervals between consecutive scale degrees while skips are not, although if one of the notes is chromatically altered so that the resulting interval is three semitones or more (e.g. C to D♯), that may also be considered a skip. However, the reverse is not true: a diminished third, an interval comprising two semitones, is still considered a skip. In music or music theory a scale degree is an individual note of a scale, both its pitch and its diatonic function. ... In music alteration, an example of chromaticism, is the use of a neighboring pitch in the chromatic scale in place of its diatonic neighbor such as in an altered chord. ... A semitone (also known in the USA as a half step) is a musical interval. ... In music, a diminished third is the interval produced by flattening a minor third by a chromatic semitone. ... A semitone (also known in the USA as a half step) is a musical interval. ...


The words conjunct and disjunct refer to melodies composed of steps and skips, respectively.


Pitch class intervals

Post-tonal or atonal theory, originally developed for equal tempered European classical music written using the twelve tone technique or serialism, integer notation is often used, most prominently in musical set theory. In this system intervals are named according to the number of half steps, from 0 to 11, the largest interval class being 6. Atonality in a general sense describes music that departs from the system of tonal hierarchies that are said to characterized the sound of classical European music from the sixteenth through the nineteenth centuries. ... Twelve-tone technique is a system of musical composition devised by Arnold Schoenberg. ... Serialism is a technique for composing music that uses sets to describe musical elements, and allows the composer manipulations of those sets to create music. ... Music notation is a system of writing for music. ... Musical set theory is an atonal or post-tonal method of musical analysis and composition which is based on explaining and proving musical phenomena, taken as sets and subsets, using mathematical rules and notation and using that information to gain insight to compositions or their creation. ...


Ordered and unordered pitch and pitch class intervals

In atonal or musical set theory there are numerous types of intervals, the first being ordered pitch interval, the distance between two pitches upward or downward. For instance, the interval from C to G upward is 7, but the interval from G to C downward is −7. One can also measure the distance between two pitches without taking into account direction with the unordered pitch interval, somewhat similar to the interval of tonal theory. Musical set theory is an atonal or post-tonal method of musical analysis and composition which is based on explaining and proving musical phenomena, taken as sets and subsets, using mathematical rules and notation and using that information to gain insight to compositions or their creation. ... In musical set theory ordered pitch interval is the distance between two pitches upward or downward. ...


The interval between pitch classes may be measured with ordered and unordered pitch class intervals. The ordered one, also called directed interval, may be considered the measure upwards, which, since we are dealing with pitch classes, depends on whichever pitch is chosen as 0. For unordered pitch class interval see interval class. In music, specifically, musical set theory an interval class, or unordered pitch-class interval, is an interval measured by the distance between its two pitch classes ordered so they are as close as possible. ...


Generic and specific intervals

In diatonic set theory, specific and generic intervals are distinguished. Specific intervals are the interval class or number of semitones between scale degrees or collection members, and generic intervals are the number of scale steps between notes of a collection or scale. Diatonic set theory is a subdivision or application of musical set theory which applies the techniques and insights of set theory to properties of the diatonic collection such as maximal evenness, Myhills property, well formedness, the deep scale property, cardinality equals variety, and structure implies multiplicity. ... In diatonic set theory a specific interval is the shortest possible clockwise distance between pitch classes on the chromatic circle (interval class), in other words the number of half steps between notes. ... In diatonic set theory a generic interval is the number of scale steps between notes of a collection or scale. ...


Cents

The standard system for comparing intervals of different sizes is with cents. This is a logarithmic scale in which the octave is divided into 1200 equal parts. In equal temperament, each semitone is exactly 100 cents. The value in cents for the interval f1 to f2 is 1200×log2(f2/f1). The cent is a logarithmic unit of measure used for musical intervals. ... A logarithmic scale is a scale of measurement that uses the logarithm of a physical quantity instead of the quantity itself. ... An equal temperament is a musical temperament -- that is, a system of tuning intended to approximate some form of just intonation -- in which an interval, usually the octave, is divided into a series of equal steps (equal frequency ratios). ... A semitone (also known in the USA as a half step) is a musical interval. ...


Comparison of different interval naming systems

# semitones
Interval
class
Generic
interval
Common
diatonic name
Comparable
just interval
Comparison of interval width in cents
equal
temperament
just
intonation
quarter-comma
meantone
0 0 0 perfect unison 1:1 0 0 0
1 1 1 minor second 16:15 100 112 117
2 2 1 major second 9:8 200 204 193
3 3 2 minor third 6:5 300 316 310
4 4 2 major third 5:4 400 386 386
5 5 3 perfect fourth 4:3 500 498 503
6 6 3
4
augmented fourth
diminished fifth
45:32
64:45
600 590
610
579
621
7 5 4 perfect fifth 3:2 700 702 697
wolf fifth 737
8 4 5 minor sixth 8:5 800 814 814
9 3 5 major sixth 5:3 900 884 889
10 2 6 minor seventh 16:9 1000 996 1007
11 1 6 major seventh 15:8 1100 1088 1083
12 0 0 perfect octave 2:1 1200 1200 1200

It is possible to construct just intervals which are closer to the equal-tempered equivalents, but most of the ones listed above have been used historically in equivalent contexts. In particular the tritone (augmented fourth or diminished fifth), could have other ratios; 17:12 (603 cents) is fairly common. The 7:4 interval (the harmonic seventh) has been a contentious issue throughout the history of music theory; it is 31 cents flatter than an equal-tempered minor seventh. Some assert the 7:4 is one of the blue notes used in jazz. When the twelve notes within the octave are tuned using meantone temperament, one of the fifths will be much sharper than the rest. ... In jazz and blues notes added to the major scale for expressive quality, loosely defined by musicians to be an alteration to a scale or chord that makes it sound like the blues. ... Jazz is a style of music which originated in New Orleans, Louisiana, United States at around the start of the 20th century. ...


In the diatonic system, every interval has one or more enharmonic equivalents, such as augmented second for minor third. In music, an enharmonic is a note which is the equivalent of some other note, but spelled differently. ... The musical interval of a minor third is the relationship between the first note (the root or tonic) and the third note in a minor scale. ... A minor third is the smaller of two commonly occurring musical intervals that span three diatonic scale degrees. ...


Consonant and dissonant intervals

Consonance and dissonance are relative terms referring to the stability, or state of repose, of particular musical effects. Dissonant intervals would be those which cause tension and desire to be resolved to consonant intervals. In music, a consonance (Latin consonare, sounding together) is a harmony, chord, or interval considered stable, as opposed to a dissonance, which is considered unstable. ...


These terms are relative to the usage of different compositional styles.

  • In atonal music all intervals (or interval classes) are considered equally consonant melodically and harmonically.
  • In the middle ages, only the octave and perfect fifth were considered consonant harmonically.
  • In 16th-century usage, perfect fifths and octaves, and major and minor thirds and sixths were considered harmonically consonant, and all other intervals dissonant. In the common practice period, it makes more sense to speak of consonant and dissonant chords, and certain intervals previously thought to be dissonant (such as minor sevenths) became acceptable in certain contexts. However, 16th-century practice continued to be taught to beginning musicians throughout this period.
  • Hermann von Helmholtz (1821–1894) defined a harmonically consonant interval as one in which the two pitches have an overtone in common (specifically excluding the seventh harmonic). This essentially defines all seconds and sevenths as dissonant, while perfect fourths and fifths, and major and minor thirds and sixths, are consonant.
  • Pythagoras defined a hierarchy of consonance based on how small the numbers were which express the ratio. 20th-century composer and theorist Paul Hindemith's system has a hierarchy with the same results as Pythagoras's, but defined by fiat rather than by interval ratios, to better accommodate equal temperament, all of whose intervals (except the octave) would be dissonant using acoustical methods.
  • David Cope (1997, p.40–41) suggests the concept of interval strength, in which an interval's strength, consonance, or stability is determined by its approximation to a lower and stronger, or higher and weaker, position in the harmonic series. See also: Lipps-Meyer law.

All of the above analyses refer to vertical (simultaneous) intervals. Atonality in a general sense describes music that departs from the system of tonal hierarchies that are said to characterized the sound of classical European music from the sixteenth through the nineteenth centuries. ... In music, specifically, musical set theory an interval class, or unordered pitch-class interval, is an interval measured by the distance between its two pitch classes ordered so they are as close as possible. ... This article does not adequately cite its references or sources. ... Renaissance music is European classical music written during the Renaissance, approximately 1400 to 1600. ... In music the common practice period is a long period in western musical history spanning from before the classical era proper to today, dated, on the outside, as 1600-1900. ... Hermann Ludwig Ferdinand von Helmholtz (August 31, 1821 – September 8, 1894) was a German physician and physicist. ... An overtone is a sinusoidal component of a waveform, of greater frequency than its fundamental frequency. ... In acoustics and telecommunication, the harmonic of a wave is a component frequency of the signal that is an integer multiple of the fundamental frequency. ... Pythagoras of Samos (Greek: ; circa 580 BC – circa 500 BC) was an Ionian (Greek) mathematician, astronomer, scientist and philosopher,[1] founder of the mathematical, mystic, religious, and scientific society called Pythagoreans. ... Paul Hindemith (16 November 1895 – 28 December 1963) was a German composer, violist, violinist, teacher, music theorist and conductor. ... David Cope is an author, composer, and professor at UC Santa Cruz. ... In music theory, an interval is the difference (a ratio or logarithmic measure) in pitch between two notes and often refers to those two notes themselves (otherwise known as a dyad). ... The Lipps-Meyer law, named for Max F. Meyer (1873-1967), hypothesizes that the closure of melodic intervals is determined by whether or not the end tone of the interval can be represented by the number two or a power of two, in the frequency ratio between notes. ...


Inversion

An interval may be inverted, by raising the lower pitch an octave, or lowering the upper pitch an octave (though it is less usual to speak of inverting unisons or octaves). For example, the fourth between a lower C and a higher F may be inverted to make a fifth, with a lower F and a higher C. Here are the ways to identify interval inversions: It has been suggested that this article be split into multiple articles accessible from a disambiguation page. ... In music, an octave (sometimes abbreviated 8ve or 8va) is the interval between one musical note and another with half or double the frequency. ...

Interval inversions
Interval inversions
  • For diatonically-named intervals".[citation needed], here are two rules, applying to all simple (i.e., non-compound) intervals:
    1. The number of any interval and the number of its inversion always add up to nine (four + five = nine, in the example just given).
    2. The inversion of a major interval is a minor interval (and vice versa); the inversion of a perfect interval is also perfect; the inversion of an augmented interval is a diminished interval (and vice versa); and the inversion of a double augmented interval is a double diminished interval (and vice versa).
A full example: E♭ below and C above make a major sixth. By the two rules just given, C natural below and E flat above must make a minor third.
  • For intervals identified by ratio, the inversion is determined by reversing the ratio and multiplying by 2. For example, the inversion of a 5:4 ratio is an 8:5 ratio.
  • Intervals identified by integer can be simply subtracted from 12. However, since an interval class is the lower of the interval integer or its inversion, interval classes cannot be inverted.

Interval inversions This image is ineligible for copyright and therefore in the public domain, because it consists entirely of information that is common property and contains no original authorship. ...

Interval roots

Although intervals are usually designated in relation to their lower note, David Cope and Hindemith both suggest the concept of interval root. To determine an interval's root, one locates its nearest approximation in the harmonic series. The root of a perfect fourth, then, is its top note because it is an octave of the fundamental in the hypothetical harmonic series. The bottom note of every odd diatonically numbered intervals are the roots, as are the tops of all even numbered intervals. The root of a collection of intervals or a chord is thus determined by the interval root of its strongest interval. David Cope is an author, composer, and professor at UC Santa Cruz. ... Paul Hindemith (16 November 1895 – 28 December 1963) was a German composer, violist, violinist, teacher, music theorist and conductor. ...


As to its usefulness, Cope provides the example of the final tonic chord of some popular music being traditionally analyzable as a "submediant six-five chord" (added sixth chords by popular terminology), or a first inversion seventh chord (possibly the dominant of the mediant V/iii). According the interval root of the strongest interval of the chord (in first inversion, CEGA), the perfect fifth (C–G), is the bottom C, the tonic. Generally speaking, a sixth chord is any chord which contains the interval of a sixth. ...


Interval cycles

Interval cycles, "unfold a single recurrent interval in a series that closes with a return to the initial pitch class", and are notated by George Perle using the letter "C", for cycle, with an interval class integer to distinguish the interval. Thus the diminished seventh chord would be C3 and the augmented triad would be C4. A superscript may be added to distinguish between transpositions, using 0–11 to indicate the lowest pitch class in the cycle. (Perle 1990, p.21) In music, interval cycles, unfold a single recurrent interval in a series that closes with a return to the initial pitch class, and are notated by George Perle using the letter C, for cycle, with an interval class integer to distinguish the interval. ... George Perle (born May 6, 1915 in Bayonne, New Jersey) is a composer and musicologist who has studied with Ernst Krenek. ...


Other intervals

There are also a number of intervals not found in the chromatic scale or labeled with a diatonic function which have names of their own. Many of these intervals describe small discrepancies between notes tuned according to the tuning systems used. Most of the following intervals may be described as microtones. Microtonal music is music using microtones -- intervals of less than a semitone, or as Charles Ives put it, the notes between the cracks of the piano. ...

  • A Pythagorean comma is the difference between twelve justly tuned perfect fifths and seven octaves. It is expressed by the frequency ratio 531441:524288, and is equal to 23.46 cents.
  • A syntonic comma is the difference between four justly tuned perfect fifths and two octaves plus a major third. It is expressed by the ratio 81:80, and is equal to 21.51 cents.
  • A Septimal comma is 64:63, and is the difference between the Pythagorean or 3-limit "7th" and the "harmonic 7th".
  • Diesis is generally used to mean the difference between three justly tuned major thirds and one octave. It is expressed by the ratio 128:125, and is equal to 41.06 cents. However, it has been used to mean other small intervals: see diesis for details.
  • A diaschisma is the difference between three octaves and four justly tuned perfect fifths plus two justly tuned major thirds. It is expressed by the ratio 2048:2025, and is equal to about 19.5 cents.
  • A schisma (also skhisma) is the difference between five octaves and eight justly tuned fifths plus one justly tuned major third. It is expressed by the ratio 32805:32768, and is equal to 1.95 cents. It is also the difference between the Pythagorean and syntonic commas.
    • A schismic major third is a schisma different from a just major third, eight fifths down and five octaves up, F♭ in C.
  • A quarter tone is half the width of a semitone, which is half the width of a whole tone. It is equal to 50 cents.
  • A kleisma is six major thirds up, five fifths down and one octave up, or, sometimes, the septimal kleisma 225:224.
  • A limma is the ratio 256:243, which is the semitone in Pythagorean tuning.
  • A ditone is the pythagorean ratio 81:64, two 9:8 tones.
  • Additionally, some cultures around the world have their own names for intervals found in their music. See: sargam, Bali

See List of Musical Intervals for more. When one ascends by a cycle of justly tuned perfect fifths (ratio 3:2), leapfrogging 12 times, one eventually reaches a note around seven octaves above the note one started on, which, when lowered to the same octave as the starting point, is 23. ... FreQuency is a music video game developed by Harmonix and published by SCEI. It was released in November 2001. ... The cent is a logarithmic unit of measure used for musical intervals. ... The syntonic comma, also known as the comma of Didymus or Ptolemaic comma, is a small interval between two musical notes, equal to the frequency ratio 81:80, or around 21. ... The septimal comma is a small interval between two musical notes, equal to the frequency ratio 36:35, or around 49 cents. ... A diesis is a musical interval. ... A diesis is a musical interval. ... The diaschisma (or diacisma) is a small musical interval defined as the difference between four perfect fifths plus two major thirds (in just intonation) and three octaves. ... The schisma, also spelled skhisma, is the ratio between a Pythagorean comma and a syntonic comma and equals 32805/32768, which is 1. ... A quarter tone is an interval half as wide (aurally, or logarithmically) as a semitone, which is half a whole tone. ... The cent is a logarithmic unit of measure used for musical intervals. ... In music, the ratio 225/224 is called the septimal kleisma. ... In musical harmony, a limma is the interval whose ratio is 256:243 = 28/35. ... In harmony, the semitonium is the ratio 17:16 — or 18:17 — between a pair of frequencies or, equivalently, the ratio 16:17 — or 17:18 — between a pair of wavelengths (or lengths of a monochord). ... Pythagorean tuning is a system of musical tuning in which the frequency relationships of all intervals are based on the ratio 3:2. ... The musical interval of a ditone is literally two tones, whole tones or major seconds, often called a major third. ... It has been suggested that this article or section be merged into Swara. ... Bali is an Indonesian island located at , the westernmost of the Lesser Sunda Islands, lying between Java to the west and Lombok to the east. ... Equal-tempered refers to 12-tone equal temperament. ...


See Musical interval mnemonics at Wikibooks for popular musical fragments that feature common intervals


Notes

  1. ^ Lindley, Mark/Campbell, Murray/Greated, Clive. "Interval", Grove Music Online, ed. L. Macy (accessed 27 February 2007), grovemusic.com (subscription access).
  2. ^ Roeder, John. "Interval Class", Grove Music Online, ed. L. Macy (accessed 27 February 2007), grovemusic.com (subscription access).

The Grove Dictionary of Music and Musicians is an encyclopedic dictionary of music and musicians, considered by most scholars to be the best general reference source on the subject in the English language. ... February 27 is the 58th day of the year in the Gregorian Calendar. ... 2007 (MMVII) is the current year, a common year starting on Monday of the Gregorian calendar and the Anno Domini (common) era. ... The Grove Dictionary of Music and Musicians is an encyclopedic dictionary of music and musicians, considered by most scholars to be the best general reference source on the subject in the English language. ... February 27 is the 58th day of the year in the Gregorian Calendar. ... 2007 (MMVII) is the current year, a common year starting on Monday of the Gregorian calendar and the Anno Domini (common) era. ...

Sources

  • Cope, David (1997). Techniques of the Contemporary Composer, p.40–41. New York, New York: Schirmer Books. ISBN 0-02-864737-8.
  • Perle, George (1990). The Listening Composer. California: University of California Press. ISBN 0-520-06991-9.

David Cope is an author, composer, and professor at UC Santa Cruz. ... George Perle (born May 6, 1915 in Bayonne, New Jersey) is a composer and musicologist who has studied with Ernst Krenek. ...

External links

  • Interval conversion: Frequency ratio to cents and cents to frequency ratio
  • Microtonal music theory: Interval
  • Morphogenesis of chords and scales Chords and scales classification
Diatonic intervals edit
Perfect : unison (0) | fourth (5) | fifth (7) | octave (12)
Major : second (2) | third (4) | sixth (9) | seventh (11)
Minor : second (1) | third (3)| sixth (8) | seventh (10)
Augmented : unison (1) | second (3) | third (5) | fourth (6) | fifth (8) | sixth (10) | seventh (12)
Diminished : second (0) | third (2) | fourth (4) | fifth (6) | sixth (7) | seventh (9) | octave (11)
semitones of equal temperament are given in brackets

For other uses, see Unison (disambiguation). ... The perfect fourth or diatessaron, abbreviated P4, is one of two musical intervals that span four diatonic scale degrees; the other being the augmented fourth, which is one semitone larger. ... The perfect fifth or diapente is one of three musical intervals that span five diatonic scale degrees; the others being the diminished fifth, which is one semitone smaller, and the augmented fifth, which is one semitone larger. ... In music, an octave (sometimes abbreviated 8ve or 8va) is the interval between one musical note and another with half or double the frequency. ... A major second is one of three commonly occuring musical intervals that span two diatonic scale degrees; the others being the minor second, which is one semitone smaller, and the augmented second, which is one semitone larger. ... A major third is the larger of two commonly occuring musical intervals that span three diatonic scale degrees. ... The musical interval of a major sixth is the relationship between the first note (the root or tonic) and the sixth note in a Major scale. ... The musical interval of a Major seventh the first note (the root or tonic) and the seventh, the leading tone, in a major scale. ... A minor second is the smallest of three commonly occuring musical intervals that span two diatonic scale degrees; the others being the major second and the augmented second, which are larger by one and two semitones respectively. ... A minor third is the smaller of two commonly occurring musical intervals that span three diatonic scale degrees. ... A minor sixth is the smaller of two commonly occuring musical intervals that span six diatonic scale degrees. ... The musical interval of a minor seventh the first note (the root or tonic) and the seventh in a minor scale. ... This article is about the musical interval. ... The musical interval of a minor third is the relationship between the first note (the root or tonic) and the third note in a minor scale. ... This article is about the musical interval. ... An augmented fifth is one of three musical intervals that span five diatonic scale degrees. ... An augmented sixth is one of three musical intervals that span six diatonic scale degrees. ... In music, the interval of a diminished second is an interval of a minor second, or diatonic semitone, diminished by a chromatic semitone. ... In music, a diminished third is the interval produced by flattening a minor third by a chromatic semitone. ... A major third is the larger of two commonly occurring musical intervals that span three diatonic scale degrees. ... This article is about the musical interval. ... A seventh chord is a chord or triad which has a note the seventh above the tonic in it. ... A major seventh is the larger of two commonly occurring musical intervals that span seven diatonic scale degrees. ...

See also


  Results from FactBites:
 
Interval (music) - Wikipedia, the free encyclopedia (2249 words)
An interval may be inverted, by raising the lower pitch an octave, or lowering the upper pitch an octave (though it is less usual to speak of inverting unisons or octaves).
The inversion of a major interval is a minor interval (and vice versa); the inversion of a perfect interval is also perfect; the inversion of an augmented interval is a diminished interval (and vice versa); and the inversion of a double augmented interval is a double diminished interval (and vice versa).
Interval cycles, "unfold a single recurrent interval in a series that closes with a return to the initial pitch class", and are notated by George Perle using the letter "C", for cycle, with an interval class integer to distinguish the interval.
Interval (music) - Wikipedia, the free encyclopedia (2556 words)
Intervals may also be labelled according to their diatonic functionality, as is commonly done for tonal music, and according to the number of notes they span in a diatonic scale.
The interval of a note from its tonic is its scale degree, thus the fifth degree of a scale is a fifth from its tonic.
Intervals may also be described as narrow and wide or small and large, consonant and dissonant or stable and unstable, weak and strong, simple and compound, vertical (or harmonic) and linear (or melodic), and, if linear as steps or skips.
  More results at FactBites »

 
 

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