Intervals & Scales on Music Theory Print

Aeolian mode

Mon, 01 Jan 0001 00:00:00 +0000

History#

The word Aeolian, like the names for the other ancient Greek tonoi and harmoniai, is an ethnic designation: in this case, for the inhabitants of Aeolis (), a coastal district of Anatolia. In the music theory of ancient Greece, it was an alternative name (used by some later writers, such as Cleonides) for what Aristoxenus called the Low Lydian tonos (in the sense of a particular overall pitching of the musical system—not a scale), nine semitones higher than the lowest “position of the voice”, which was called Hypodorian. In the mid-16th century, this name was given by Heinrich Glarean to his newly defined ninth mode, with the diatonic octave species of the natural notes extending one octave from A to A—corresponding to the modern natural minor scale. Up until this time, chant theory recognized eight musical modes: the relative natural scales in D, E, F and G, each with their authentic and plagal counterparts, and with the option of B instead of B in several modes. In 1547, Heinrich Petri published Heinrich Glarean’s Dodecachordon in Basel. His premise had as its central idea the existence of twelve diatonic modes rather than eight, including a separate pair of modes each on the finals A and C. Finals on these notes, as well as on B, had been recognized in chant theory at least since Hucbald in the early tenth century, but they were regarded as merely transpositions from the regular finals a fifth lower. In the eleventh century, Guido d’Arezzo, in chapter 8 of his Micrologus, designated these transposed finals A, B, and C as “affinals”, and later still the term “confinal” was used in the same way. In 1525, Pietro Aaron was the first theorist to explain polyphonic modal usage in terms of the eightfold system, including these transpositions. As late as 1581, Illuminato Aiguino da Brescia published the most elaborate theory defending the eightfold system for polyphonic music against Glarean’s innovations, in which he regarded the traditional plainchant modes 1 and 2 (Dorian and Hypodorian) at the affinal position (that is, with their finals on A instead of D) as a composite of species from two modes, which he described as “mixed modes”. Glarean added Aeolian as the name of the new ninth mode: the relative natural mode in A with the perfect fifth as its dominant, reciting tone, reciting note, or tenor. The tenth mode, the plagal version of the Aeolian mode, Glarean called Hypoaeolian (“under Aeolian”), based on the same relative scale, but with the minor third as its tenor, and having a melodic range from a perfect fourth below the tonic to a perfect fifth above it. Scholars for the past three centuries have regarded the modes added by Glarean as the basis of the minor/major division of classical European music, as homophonic music replaced Renaissance polyphony. Howard S Powers considers this to be an oversimplification, since the key of A minor is as closely related to the old transposed modes 1 and 2 (Dorian and Hypodorian) with finals on A—as well as to mode 3 (Phrygian)—as it is to Glarean’s Aeolian. In modern usage, the Aeolian mode is the sixth mode of the major scale and has the following formula: :1, 2, 3, 4, 5, 6, 7, 8 The Aeolian mode is the sixth mode of the major scale, that is, it is formed by starting on the sixth degree (submediant) of the major scale. For example, if the Aeolian mode is used in its all-white-note pitch based on A, this would be an A-minor triad, which would be the submediant in the relative major key of C major. : \override Score.TimeSignature #‘stencil = ##f \relative c’ \clef treble \time 7/4 \hide Staff.TimeSignature a4^\markup A Aeolian scale b c d e f g a2

Blues scale

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Hexatonic#

The hexatonic, or six-note, blues scale consists of the minor pentatonic scale plus the 5th degree of the original heptatonic scale. This added note can be spelled as either a 5 or a 4. The first known published instance of this scale is Jamey Aebersold’s How to Play Jazz and Improvise Volume 1 (1970 revision, p. 26), and Jerry Coker claims that David Baker may have been the first educator to organise this particular collection of notes pedagogically as a scale to be taught in helping beginners evoke the sound of the blues. : \override Score.TimeSignature #‘stencil = ##f \relative c’ \clef treble \time 6/4 c4 es f ges g bes c2 A major feature of the blues scale is the use of blue notes—notes that are played or sung microtonally, at a slightly higher or lower pitch than standard. However, since blue notes are considered alternative inflections, a blues scale may be considered to not fit the traditional definition of a scale. At its most basic, a single version of this blues scale is commonly used over all changes (or chords) in a twelve-bar blues progression. Likewise, in contemporary jazz theory, its use is commonly based upon the key rather than the individual chord. The latter is the same as the hexatonic scale described above. In the Movable do solfège, the hexatonic major blues scale is solmized as “do-re-me-mi-sol-la”; In the La-based minor movable do solfège, the hexatonic minor blues scale is solmized as “la-do-re-me-mi-sol”.

Chromatic scale

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Definition#

The chromatic scale is a musical scale with twelve pitches, each a semitone, also known as a half-step, above or below its adjacent pitches. As a result, in 12-tone equal temperament (the most common tuning in Western music), the chromatic scale covers all 12 of the available pitches. Thus, there is only one chromatic scale in this tuning. The ratio of the frequency of one note in the scale to that of the preceding note is given by \sqrt 12 2 \approxeq 1.06 . In equal temperament, all the semitones have the same size (100 cents), and there are twelve semitones in an octave (1200 cents). As a result, the notes of an equal-tempered chromatic scale are equally-spaced. The ascending and descending chromatic scale is shown below. : \override Score.TimeSignature #‘stencil = ##f \relative c’ \clef treble \time 12/4 c4^\markup Ascending cis d dis e f fis g gis a ais b c^\markup Descending b bes a aes g ges f e es d des c

Chromaticism

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Development of chromaticism#

Chromaticism began to develop in the late Renaissance period, notably in the 1550s, often as part of musica reservata, in the music of Cipriano de Rore, in Orlando Lasso’s Prophetiae Sibyllarum, and in the theoretical work of Nicola Vicentino. The following timeline is abbreviated from its presentation by Benward & Saker: :Baroque Period (1600—1750) “The system of major and minor scales developed during the early part of the baroque period. This coincided with the emergence of key consciousness in music.” :Classical Period (1750—1825) “The major and minor keys were the basis of music in the classical period. Chromaticism was decorative for the most part and shifts from one key to another…were used to create formal divisions.” :Romantic Period (1825—1900) “Chromaticism increased to the point that the major—minor key system began to be threatened. By the end of the period, keys often shifted so rapidly in the course of a composition that tonality itself began to break down.” :Post-Romantic and Impressionistic Period (1875—1920) “With the breakdown of the major—minor key system, impressionist composers began to experiment with other scales….particularly…pentatonic, modal, and whole-tone scales.” :Contemporary Period (1920—present) “The chromatic scale has predominated in much of the music of our period.” :Jazz and Popular Music (1900—present) “Popular music has remained the last bastion of the major-minor key system… The blues scale “a chromatic variant of the major scale” is often found in jazz and popular music with blues influence.” As tonality began to expand during the last half of the nineteenth century, with new combinations of chords, keys and harmonies being tried, the chromatic scale and chromaticism became more widely used, especially in the works of Richard Wagner, such as the opera “Tristan und Isolde”. Increased chromaticism is often cited as one of the main causes or signs of the “breakdown” of tonality, in the form of increased importance or use of: *mode mixture *leading tones *tonicization of each chromatic step and other secondary key areas *modulatory space *hierarchical organizations of the chromatic set such as George Perle’s *the use of non-tonal chords as tonic “keys”/“scales”/“areas” such as the Tristan chord. As tonal harmony continued to widen and even break down, the chromatic scale became the basis of modern music written using the twelve-tone technique, a tone row being a specific ordering or series of the chromatic scale, and later serialism. Though these styles/methods continue to (re)incorporate tonality or tonal elements, often the trends that led to these methods were abandoned, such as modulation.

Circle of fifths

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Definition#

The circle of fifths organizes pitches in a sequence of perfect fifths, generally shown as a circle with the pitches (and their corresponding keys) in clockwise order. It can be viewed in a counterclockwise direction as a circle of fourths. Harmonic progressions in Western music commonly use adjacent keys in this system, making it a useful reference for musical composition and harmony. The top of the circle shows the key of C Major, with no sharps or flats. Proceeding clockwise, the pitches ascend by fifths. The key signatures associated with those pitches change accordingly: the key of G has one sharp, the key of D has 2 sharps, and so on. Proceeding counterclockwise from the top of the circle, the notes change by descending fifths and the key signatures change accordingly: the key of F has one flat, the key of B has 2 flats, and so on. Some keys (at the bottom of the circle) can be reasonably notated either in sharps or in flats. Starting at any pitch and ascending by a fifth generates all tones before returning to the beginning pitch class (a pitch class consists of all of the notes indicated by a given letter regardless of octave—all “C"s, for example, belong to the same pitch class). Moving counterclockwise, the pitches descend by a fifth, but ascending by a perfect fourth will lead to the same note an octave higher (therefore in the same pitch class). Moving counter-clockwise from C could be thought of as descending by a fifth to F, or ascending by a fourth to F. When notating a circle of fifths, an enharmonic substitution is made for one of the notes. In the clockwise example above, a perfect fifth above A would be E, but is notated as F, which is enharmonically equivalent. This technically creates a diminished sixth between A and F. In the counterclockwise example, a perfect fifth below G should be C, but is replaced with the enharmonic note of B, also creating a diminished sixth.

Diatonic and chromatic

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Greek genera#

In ancient Greece there were three standard tunings (known by the Latin word genus, plural genera) of a lyre. These three tunings were called diatonic, chromatic, and enharmonic, and the sequences of four notes that they produced were called tetrachords (“four strings”). A diatonic tetrachord comprised, in descending order, two whole tones and a semitone, such as A G F E (roughly). In the chromatic tetrachord the second string of the lyre was lowered from G to G, so that the two lower intervals in the tetrachord were semitones, making the pitches A G F E. In the enharmonic tetrachord the second string of the lyre was lowered further to G, so that the two lower interval in the tetrachord were quarter tones, making the pitches A G F E (where F is F lowered by a quarter tone). For all three tetrachords, only the middle two strings varied in their pitch.

Diatonic scale

Mon, 01 Jan 0001 00:00:00 +0000

History#

Western music from the Middle Ages until the late 19th century (see common practice period) is based on the diatonic scale and the unique hierarchical relationships created by this system of organizing seven notes.

Antiquity#

Evidence that the Sumerians and Babylonians used a version of the diatonic scale is found in cuneiform inscriptions that contain both musical compositions and a tuning system. Despite the conjectural nature of reconstructions of the Hurrian songs, the diatonic nature of the tuning system is demonstrated by the fact that it involves a series of six perfect fifths, which is a recipe for the construction of a diatonic scale. The 9,000-year-old flutes found in Jiahu, China, indicate the evolution over 1,200 years of flutes having 4, 5 and 6 holes to having 7 and 8 holes, the latter exhibiting striking similarity to diatonic hole spacings and sounds.

Dorian mode

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Ancient Dorian mode#

The Dorian mode (properly harmonia or tonos) is named after the Dorian Greeks. Applied to a whole octave, the Dorian octave species was built upon two tetrachords (four-note segments) separated by a whole tone, running from the hypate meson to the nete diezeugmenon. In the enharmonic genus, the intervals in each tetrachord are quarter tone–quarter tone–major third. \override Score.TimeSignature #‘stencil = ##f \relative c’ \clef treble \time 4/4 e4^\markup Greek Dorian tonos (enharmonic genus) on E feh geses a b ceh deses e In the chromatic genus, they are semitone–semitone–minor third. \override Score.TimeSignature #‘stencil = ##f \relative c’ \clef treble \time 4/4 e4^\markup Greek Dorian tonos (chromatic genus) on E f ges a b c des e In the diatonic genus, they are semitone–tone–tone. \override Score.TimeSignature #‘stencil = ##f \relative c’ \clef treble \time 4/4 e4^\markup Greek Dorian tonos (diatonic genus) on E f g a b c d e In the diatonic genus, the sequence over the octave is the same as that produced by playing all the white notes of a piano ascending from E to E, a sequence equivalent to the pattern of the modern Phrygian mode, although the temperament differs by small amounts. Placing the single tone at the bottom of the scale followed by two conjunct tetrachords (that is, the top note of the first tetrachord is also the bottom note of the second), produces the Hypodorian (“below Dorian”) octave species: A B C D E (E) F G A. Placing the two conjunct tetrachords together and the single tone at the top of the scale produces the Mixolydian octave species, a note sequence equivalent to modern Locrian mode.

Enharmonic equivalence

Mon, 01 Jan 0001 00:00:00 +0000

Definition#

The predominant tuning system in Western music is twelve-tone equal temperament (12 ), where each octave is divided into twelve equal half-steps, or semitones; each half-step is both a chromatic semitone (a sharp or a flat) and a diatonic semitone (a minor step between two diatonic notes). The notes F and G are a whole step apart, so the note one semitone above F (F) and the note one semitone below G (G) indicate the same pitch. These written notes are enharmonic, or enharmonically equivalent. The choice of notation for a pitch can depend on its role in harmony; this notation keeps modern music compatible with earlier tuning systems, such as meantone temperaments. The choice can also depend on the note’s readability in the context of the surrounding pitches. Multiple sharps or flats can produce other enharmonic equivalents; for example, F (double-sharp) is enharmonically equivalent to G. When other tuning systems were in use, prior to the adoption of 12 equal temperament , the term enharmonic referred to notes that were very close in pitch — closer than the smallest step of a diatonic scale — but not quite identical. In a tuning system without equal half steps, F and G do not indicate the same pitch, although the two pitches would be called enharmonically equivalent. Sets of notes that involve pitch relationships — scales, key signatures, or intervals, for example — can also be referred to as enharmonic (e.g., in the keys of C major and D major contain identical pitches and are therefore enharmonic). Identical intervals notated with different, enharmonically equivalent, written pitches are also referred to as enharmonic. The interval of a tritone above C may be written as a diminished fifth from C to G, or as an augmented fourth (C to F). In modern , notating the C as a B leads to other enharmonically equivalent notations, an option which does not exist in most earlier notation systems. Enharmonic equivalents can be used to improve the readability of music, as when a sequence of notes is more easily read using sharps or flats. This may also reduce the number of accidentals required.

Harmonic minor scale

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Harmony#

The scale is called the harmonic minor scale because it is a common foundation for harmonies (chords) in minor keys. Traditionally, “the main use for harmonic minor, when improvising or creating melodies, is over the V7 chord, not for use over the i chord.” For example, in the key of A minor, the dominant (V) chord (the triad built on the 5th scale degree, E) is a minor triad in the natural minor scale. But when the seventh degree is raised from G to G, the triad becomes a major triad. “In fact, it created even more tension than the major key V7. This is because the scale not only outlines the notes of E7 V7 but also adds new tension notes like the 5 C to B and 9 F to E .” Chords on degrees other than V may also include the raised 7th degree, such as the diminished triad on VII itself (vii), which has a dominant function, as well as an augmented triad on III (III), which is not found in any “natural” harmony (that is, harmony that is derived from harmonizing the seven Western modes, which include “major” and “minor”). This augmented fifth chord (5 chord) played a part in the development of modern chromaticism. The triads built on each scale degree follow a distinct pattern. The Roman numeral analysis is shown below. : \override Score.TimeSignature #‘stencil = ##f \relative c’ \clef treble \time 7/1 \hide Staff.TimeSignature 1_\markup i _\markup ii° _\markup III+ _\markup iv _\markup V _\markup VI \markup vii° An interesting property of the harmonic minor scale is that it contains two chords that are each generated by just one interval: # an augmented triad (III), which is generated by major thirds # a diminished seventh chord (vii 7 ), which is generated by minor thirds Because they are generated by just one interval, the inversions of augmented triads and diminished seventh chords introduce no new intervals (allowing for enharmonic equivalents) that are absent from its root position. That is, any inversion of an augmented triad (or diminished seventh chord) is enharmonically equivalent to a new augmented triad (or diminished seventh chord) in root position. For example, the triad E–G–B in first inversion is G–B–E, which is enharmonically equivalent to the augmented triad G–B–D. One chord, with various spellings, may therefore have various harmonic functions in various keys. The seventh chords built on each scale degree follow a distinct pattern. The Roman numeral analysis is shown in parentheses below. Harmonic minor contains seven types of seventh chords: a minor major seventh chord (i m(maj7) ), a half-diminished seventh chord (ii m7(−5) ), an augmented major seventh chord (III aug(maj7) ), a minor seventh chord (iv m7 ), a dominant seventh chord (V 7 ), a major seventh chord (VI maj7 ), and a diminished seventh chord (vii dim7 ). Natural minor only contains four types of seventh chords: three minor seventh chords (i m7 , iv m7 , and v m7 ), a half-diminished seventh chord (ii m7(-5) ), two major seventh chords (III maj7 and VI maj7 ), and a dominant seventh chord (VII 7 ). : \override Score.TimeSignature #‘stencil = ##f \relative c’ \clef treble \time 7/1 \hide Staff.TimeSignature 1\markup i♮7 _\markup iiø7 _\markup III+7 _\markup ivm7 _\markup V7 _\markup VIM7 _\markup vii°7 * 1st: minor-major seventh chord (i ♮7 ) * 2nd: half diminished seventh chord (ii ø7 ) * 3rd: augmented major seventh chord (III +7 ) * 4th: minor seventh chord (ivm 7 ) * 5th: dominant seventh chord (V 7 ) * 6th: major seventh chord (VIM 7 ) * 7th: diminished seventh chord (vii o7 )

Interval (music)

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Size#

The size of an interval (also known as its width or height) can be represented using two alternative and equivalently valid methods, each appropriate to a different context: frequency ratios or cents.

Frequency ratios#

The size of an interval between two notes may be measured by the 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 ratios, such as 1:1 (unison), 2:1 (octave), 5:3 (major sixth), 3:2 (perfect fifth), 4:3 (perfect fourth), 5:4 (major third), 6:5 (minor third). Intervals with small-integer ratios are often called just intervals, or pure intervals. Most commonly, however, musical instruments are nowadays tuned using a different tuning system, called 12-tone equal temperament. As a consequence, the size of most equal-tempered intervals cannot be expressed by small-integer ratios, although it is very close to the size of the corresponding just intervals. For instance, an equal-tempered fifth has a frequency ratio of 2:1, approximately equal to 1.498:1, or 2.997:2 (very close to 3:2). For a comparison between the size of intervals in different tuning systems, see .

Ionian mode

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External links#

Ionian mode for guitar at GOSK.com

Key (music)

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Background#

Music is made from audible vibrations, such as from oscillating strings or air moving through reeds. People generally perceive some vibrations as sounding “higher” or “lower” than others, creating a subjective perception called pitch. As a medium vibrates faster, this higher frequency of vibration is perceived as higher pitch. In standard Western tonal music, specific frequencies are grouped into twelve pitch classes. Seven of these are considered “natural” pitches and represented by the letters A, B, C, D, E, F, and G. Humans perceive frequencies logarithmically, not linearly. In other words, the ratio between two frequencies, rather than the absolute difference between them, determines how different they sound. If one vibration has twice the frequency of another, both sound similar and are considered the same pitch class. The distance between the two is called an octave. For clarity, these pitches are sometimes labeled with numbers. For example, the lowest C playable on a standard piano is C1, while the pitch with twice the frequency (one octave higher) is C2. On a piano, each white key represents one of the seven “natural” pitches. These are arranged from A to G, followed by another A one octave higher. Among these pitches, the relative increases in frequency from B to C and from E to F are smaller than the changes between other adjacent pitches. This smaller distance is called a semitone, while the larger distance (e.g. from A to B) is a whole tone. When two natural pitches are a whole tone apart, an intermediate pitch is placed between them—on a piano, these are represented by the smaller black keys. Instead of using separate letters, these intermediate pitches are denoted with the accidentals ♯ (sharp) and ♭ (flat), which represent raising or lowering a natural pitch by one semitone. The pitch between G and A may be denoted as either G♯ (G plus one semitone) or A♭ (A minus one semitone). These two ways of representing the same sound are called enharmonically equivalent. Most Western music is built around major and minor scales. These scales use seven of the twelve pitches, arranged in ascending or descending order, and beginning and ending with the same pitch one octave apart. An ascending major scale moves between pitches with the pattern tone, tone, semitone, tone, tone, tone, semitone. An ascending minor scale instead uses the pattern tone, semitone, tone, tone, semitone, tone, tone, which results in the third, sixth, and seventh pitches being one semitone lower compared to the major scale. A major scale beginning from C and a minor scale beginning from A each contain only natural pitches, and on a piano will use exclusively white keys; the two scales are considered distinct “modes” of the same set of pitches. In contrast, a major scale beginning from A uses the pitches A, B, C♯, D, E, F♯, G♯, A. The pitch on which a given scale begins and ends is called its tonic.

Locrian mode

Mon, 01 Jan 0001 00:00:00 +0000

History#

Locrian is the word used to describe an ancient Greek tribe that inhabited the three regions of Locris. Although the term occurs in several classical authors on music theory, including Cleonides (as an octave species) and Athenaeus (as an obsolete harmonia), there is no warrant for the modern use of Locrian as equivalent to Glarean’s hyperaeolian mode, in either classical, Renaissance, or later phases of modal theory through the 18th century, or modern scholarship on ancient Greek musical theory and practice. The name first came into use in modal chant theory after the 18th century, The final, as its name implies, is the tone on which the chant eventually settles, and corresponds to the tonic in tonal music. The reciting tone is the tone around which the melody principally centers, the term mediant is named from its position between the final tone and the reciting tone, and the participant is an auxiliary note, generally adjacent to the mediant in authentic modes and, in the plagal forms, coincident with the reciting tone of the corresponding authentic mode.

Lydian mode

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Ancient Greek Lydian#

The name Lydian refers to the ancient kingdom of Lydia in Anatolia. In Greek music theory, there was a Lydian scale or “octave species” extending from parhypate hypaton to trite diezeugmenon, equivalent in the diatonic genus to the modern Ionian mode (the major scale). : \key e \major \override Score.TimeSignature #‘stencil = ##f \relative c’ \clef treble \time 7/4 e4^\markup Greek Lydian tonos (diatonic genus) on E fis gis a b cis dis e2 In the chromatic and enharmonic genera, the Lydian scale was equivalent to C D E F G A B C, and C C E F F A B C, respectively, where signifies raising the pitch by approximately a quarter tone. : \key e \major \override Score.TimeSignature #‘stencil = ##f \relative c’ \clef treble \time 7/4 e4^\markup Greek Lydian tonos (chromatic genus) on E f gis a bes cis dis e2 : \key e \major \override Score.TimeSignature #‘stencil = ##f \relative c’ \clef treble \time 7/4 e4^\markup Greek Lydian tonos (enharmonic genus) on E feh gisih a aih cisih disih e2

Major scale

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Natural major scale#

The natural major scale is the diatonic Ionian mode. The simplest major scale to write is C major, the only major scale not requiring sharps or flats. It can be played on the white keys of the piano: The major scale has a central importance in Western music, particularly that of the common practice period and in popular music. In Carnatic music, it is known as Sankarabharanam. In Hindustani classical music, it is known as Bilaval. The sequence of intervals between the notes of a major scale is: : whole, whole, half, whole, whole, whole, half where “whole” stands for a whole tone (a red u-shaped curve in the figure), and “half” stands for a semitone (a red angled line in the figure). Whole steps and half steps are explained mathematically in a related article, Twelfth root of two. Notably, in terms of the sound frequency ratio in equal temperament, a whole tone has twice the sound frequency ratio of a semitone and an octave has twelve half steps (semitones) spaced equally. The sound frequency doubles for corresponding notes from one octave to the next. The ratio is 3/2 = 1.5 for a perfect fifth, for example from C to G on a major scale, and 5/4 = 1.25 for a major third, for example from C to E. A major scale may be seen as two identical tetrachords separated by a whole tone. Each tetrachord consists of two whole tones followed by a semitone (i.e. whole, whole, half). The major scale is maximally even.

Major second

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Major and minor tones#

In tuning systems using just intonation, such as 5-limit tuning, in which major seconds occur in two different sizes, the wider of them is called a major tone or greater tone, and the narrower minor tone or, lesser tone. The difference in size between a major tone and a minor tone is equal to one syntonic comma (about 21.51 cents). The major tone is the 9:8 interval , and it is an approximation thereof in other tuning systems, while the minor tone is the 10:9 ratio The 9:8 major tone arises in the C major scale between C and D, F and G, and A and B. This 9:8 interval was named epogdoon (meaning ‘one eighth in addition’) by the Pythagoreans. Notice that in these tuning systems, a third kind of whole tone, even wider than the major tone, exists. This interval of two semitones, with ratio 256:225, is simply called the diminished third (for further details, see ). Some equal temperaments also produce major seconds of two different sizes, called greater and lesser tones (or major and minor tones). For instance, this is true for 15-ET, 22-ET, 34-ET, 41-ET, 53-ET, and 72-ET. Conversely, in twelve-tone equal temperament, Pythagorean tuning, and meantone temperament (including 19-ET and 31-ET) all major seconds have the same size, so there cannot be a distinction between a greater and a lesser tone. In any system where there is only one size of major second, the terms greater and lesser tone (or major and minor tone) are rarely used with a different meaning. Namely, they are used to indicate the two distinct kinds of whole tone, more commonly and more appropriately called major second (M2) and diminished third (d3). Similarly, major semitones and minor semitones are more often and more appropriately referred to as minor seconds (m2) and augmented unisons (A1), or diatonic and chromatic semitones. Unlike most uses of the terms major and minor, these intervals span the same number of semitones. They both span 2 semitones, while, for example, a major third (4 semitones) and minor third (3 semitones) differ by one semitone. Thus, to avoid ambiguity, it is preferable to call them greater tone and lesser tone (see also greater and lesser diesis). Two major tones equal a ditone.

Major third

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Harmonic and non-harmonic thirds#

The major third may be derived from the harmonic series as the interval between the fourth and fifth harmonics. The major scale is so named because of the presence of this interval between its tonic and mediant (1st and 3rd) scale degrees. The major chord also takes its name from the presence of this interval built on the chord’s root (provided that the interval of a perfect fifth from the root is also present). A major third is slightly different in different musical tunings: In just intonation it corresponds to a pitch ratio of 5:4, or () (fifth harmonic in relation to the fourth) or 386.31 cents; in 12 tone equal temperament, a major third is equal to four semitones, a ratio of 2 1/3 :1 (about 1.2599) or 400 cents, 13.69 cents wider than the 5:4 ratio. The older concept of a “ditone” (two 9:8 major seconds) made a dissonant, wide major third with the ratio 81:64 (about 1.2656) or 408 cents (), about 22 cents sharp from the harmonic ratio of 5:4 . The septimal major third is 9:7 (435 cents), the undecimal major third is 14:11 (418 cents), and the tridecimal major third is 13:10 (452 cents). In 12 tone equal temperament three major thirds in a row are equal to an octave. For example, A to C, C to E, and E to G (in the differently written notes G and A both represent the same pitch, but not in most other tuning systems). This is sometimes called the “circle of thirds”. In just intonation, however, three 5:4 major third, the 125th subharmonic, is less than an octave. For example, three 5:4 major thirds from C is B (C to E, to G, to B) ( = \tfrac ; 5^3 \ ; 2^6\ = \tfrac \ 125\ 64 \ ). The difference between this just-tuned B and C, like the interval between G and A, is called the “enharmonic diesis”, about 41 cents, or about two commas (the inversion of the interval : \ \frac \ 128\ 125 = \frac ; 2^7\ ; 5^3 \ ()).

Minor scale

Mon, 01 Jan 0001 00:00:00 +0000

Natural minor#

The natural minor scale is the diatonic Aeolian mode. It can be played on the white keys of the piano as A–B–C–D–E–F–G. Because this A minor scale shares a key signature with the C major scale, the two are considered relatives. The major scale sits a third above its relative minor. The major and natural minor scales have the same collection of intervals: two semitones and five whole tones. Beginning in the 17th century, they were the two dominant modes of tonal music. The resulting harmonies are quite different from the major scale. The tonic chord (A–C–E) is minor, as are the subdominant (D–F–A) and dominant chords (E–G–B). The absence of the leading tone made composing a satisfactory cadence difficult. This problem gave rise to the two common variations of the natural minor scale. The term “natural minor” was not in common use until the twentieth century.

Minor third

Mon, 01 Jan 0001 00:00:00 +0000

In other tunings#

A minor third, in just intonation, corresponds to a pitch ratio of 6:5 or 315.64 cents. In an equal tempered tuning, a minor third is equal to three semitones, a ratio of 2 1/4 :1 (about 1.189), or 300 cents, 15.64 cents narrower than the 6:5 ratio. In other meantone tunings it is wider, and in 19 equal temperament it is very nearly the 6:5 ratio of just intonation; in more complex schismatic temperaments, such as 53 equal temperament, the “minor third” is often significantly flat (being close to Pythagorean tuning ()), although the “augmented second” produced by such scales is often within ten cents of a pure 6:5 ratio. If a minor third is tuned in accordance with the fundamental of the overtone series, the result is a ratio of 19:16 or 297.51 cents (the nineteenth harmonic). The 12-TET minor third (300 cents) more closely approximates the nineteenth harmonic with only 2.49 cents error. M. Ergo mistakenly claimed that the nineteenth harmonic was the highest ever written, for the bass-trumpet in Richard Wagner’s Der Ring des Nibelungen (1848–74), when Robert Schumann’s Op. 86 Konzertstück for 4 Horns and Orchestra (1849) features the twentieth harmonic (four octaves and a major third above the fundamental) in the first horn part three times . Other pitch ratios are given related names, the septimal minor third with ratio 7:6 and the tridecimal minor third with ratio 13:11 in particular.

Mixolydian mode

Mon, 01 Jan 0001 00:00:00 +0000

Ancient Mixolydian#

The idea of a Mixolydian mode comes from the music theory of ancient Greece. The invention of the ancient Greek Mixolydian mode was attributed to Sappho, the poet and musician. However, what the ancient Greeks thought of as Mixolydian is very different from the modern interpretation of the mode. The prefix mixo- (-) means “mixed”, referring to its resemblance to the Lydian mode. In Greek theory, the Mixolydian tonos (the term “mode” is a later Latin term) employs a scale (or “octave species”) corresponding to the Greek Hypolydian mode inverted. In its diatonic genus, this is a scale descending from paramese to hypate hypaton: in the diatonic genus, a whole tone (paramese to mese) followed by two conjunct inverted Lydian tetrachords (each being two whole tones followed by a semitone descending). This diatonic genus of the scale is roughly the equivalent of playing all the white notes of a piano from B to B, which is also known as modern Locrian mode. In the chromatic and enharmonic genera, each tetrachord consists of a minor third plus two semitones, and a major third plus two quarter tones, respectively.

Mode (music)

Mon, 01 Jan 0001 00:00:00 +0000

Mode as a general concept#

Regarding the concept of mode as applied to pitch relationships generally, in 2001 Harold S. Powers proposed that “mode” has “a twofold sense”, denoting either a “particularized scale” or a “generalized tune”, or both: In 1792, Sir Willam Jones applied the term “mode” to the music of “the Persians and the Hindoos”. As early as 1271, Amerus applied the concept to cantilenis organicis (lit. “organic songs”, most probably meaning “polyphony”). It is still heavily used with regard to Western polyphony before the onset of the common practice period, as for example “modale Mehrstimmigkeit” by Carl Dahlhaus or “Alte Tonarten” of the 16th and 17th centuries found by Bernhard Meier. The word encompasses several additional meanings. Authors from the 9th century until the early 18th century (e.g., Guido of Arezzo) sometimes employed the Latin modus for interval, or for qualities of individual notes. In the theory of late-medieval mensural polyphony (e.g., Franco of Cologne), modus is a rhythmic relationship between long and short values or a pattern made from them; in mensural music most often theorists applied it to division of longa into 3 or 2 breves.

Octatonic scale

Mon, 01 Jan 0001 00:00:00 +0000

Nomenclature#

In Saint Petersburg at the turn of the 20th century, this scale had become so familiar in the circle of composers around Nikolai Rimsky-Korsakov that it was referred to as the Korsakovian scale (Корсаковская гамма). As early as 1911, the Russian theorist Boleslav Yavorsky described this collection of pitches as the diminished mode (уменьшённый лад), because of the stable way the diminished fifth functions in it. In more recent Russian theory, the term octatonic is not used. Instead, this scale is placed among other symmetrical modes (total 11) under its historical name Rimsky-Korsakov scale, or Rimsky-Korsakov mode.) In jazz theory, it is called the diminished scale or symmetric diminished scale because it can be conceived as a combination of two interlocking diminished seventh chords, just as the augmented scale can be conceived as a combination of two interlocking augmented triads. The two modes are sometimes referred to as the half-step/whole step diminished scale and the whole step/half-step diminished scale. Because it was associated in the early 20th century with the Dutch composer Willem Pijper, in the Netherlands it is called the Pijper scale.

Octave

Mon, 01 Jan 0001 00:00:00 +0000

Explanation and definition#

An octave is the interval between one musical pitch and another with double or half its frequency. For example, if one note has a frequency of 440 Hz, the note one octave above is at 880 Hz, and the note one octave below is at 220 Hz. The ratio of frequencies of two notes an octave apart is therefore 2:1. Further octaves of a note occur at 2^n times the frequency of that note (where n is an integer), such as 2, 4, 8, 16, etc. and the reciprocal of that series. For example, 55 Hz and 440 Hz are one and two octaves away from 110 Hz because they are (or 2^ -1 ) and 4 (or 2^ 2 ) times the frequency, respectively. The number of octaves between two frequencies is given by the formula: \text Number of octaves = \log_2\left(\frac f_2 f_1 \right) File:Middle_C,_or_262_hertz,_on_a_virtual_oscilloscope.png Oscillogram of middle C (261.62 Hz) (scale: 1 square is equal to 1 millisecond) File:C5_523_Hz_oscillogram.png C 5 , an octave above middle C. The frequency is twice that of middle C (523.25 Hz). File:C3_131_Hz_oscillogram.png C 3 , an octave below middle C. The frequency is half that of middle C (130.81 Hz).

Parallel key

Mon, 01 Jan 0001 00:00:00 +0000

Pentatonic scale

Mon, 01 Jan 0001 00:00:00 +0000

Hemitonic and anhemitonic#

Musicology commonly classifies pentatonic scales as either hemitonic or anhemitonic. Hemitonic scales contain one or more semitones and anhemitonic scales do not contain semitones. (For example, in Japanese music the anhemitonic yo scale is contrasted with the hemitonic in scale.) Hemitonic pentatonic scales are also called “ditonic scales”, because the largest interval in them is the ditone (e.g., in the scale C–E–F–G–B–C, the interval found between C–E and G–B). (This should not be confused with the identical term also used by musicologists to describe a scale including only two notes.)

Perfect fifth

Mon, 01 Jan 0001 00:00:00 +0000

Alternative definitions#

The term perfect identifies the perfect fifth as belonging to the group of perfect intervals (including the unison, perfect fourth, and octave), so called because of their simple pitch relationships and their high degree of consonance. When an instrument with only twelve notes to an octave (such as the piano) is tuned using Pythagorean tuning, one of the twelve fifths (the wolf fifth) sounds severely discordant and can hardly be qualified as “perfect”, if this term is interpreted as “highly consonant”. However, when using correct enharmonic spelling, the wolf fifth in Pythagorean tuning or meantone temperament is actually not a perfect fifth but a diminished sixth (for instance G–E). Perfect intervals are also defined as those natural intervals whose inversions are also natural, where natural, as opposed to altered, designates those intervals between a base note and another note in the major diatonic scale starting at that base note (for example, the intervals from C to C, D, E, F, G, A, B, C, with no sharps or flats); this definition leads to the perfect intervals being only the unison, fourth, fifth, and octave, without appealing to degrees of consonance. The term perfect has also been used as a synonym of just, to distinguish intervals tuned to ratios of small integers from those that are “tempered” or “imperfect” in various other tuning systems, such as equal temperament. The perfect unison has a pitch ratio 1:1, the perfect octave 2:1, the perfect fourth 4:3, and the perfect fifth 3:2. Within this definition, other intervals may also be called perfect, for example a perfect third (5:4) or a perfect major sixth (5:3).

Perfect fourth

Mon, 01 Jan 0001 00:00:00 +0000

History#

The use of perfect fourths and fifths to sound in parallel with and to “thicken” the melodic line was prevalent in music prior to the European polyphonic music of the Middle Ages. In the 13th century, the fourth and fifth together were the concordantiae mediae (middle consonances) after the unison and octave, and before the thirds and sixths. The fourth came in the 15th century to be regarded as dissonant on its own, and was first classed as a dissonance by Johannes Tinctoris in his Terminorum musicae diffinitorium (1473). In practice, however, it continued to be used as a consonance when supported by the interval of a third or fifth in a lower voice. Modern acoustic theory supports the medieval interpretation insofar as the intervals of unison, octave, fifth and fourth have particularly simple frequency ratios. The octave has the ratio of 2:1, for example the interval between a’ at A440 and a at 880 Hz, giving the ratio 880:440, or 2:1. The fifth has a ratio of 3:2, and its complement has the ratio of 3:4. Ancient and medieval music theorists appear to have been familiar with these ratios, see for example their experiments on the monochord. In the years that followed, the frequency ratios of these intervals on keyboards and other fixed-tuning instruments would change slightly as different systems of tuning, such as meantone temperament, well temperament, and equal temperament were developed. In early western polyphony, these simpler intervals (unison, octave, fifth and fourth) were generally preferred. However, in its development between the 12th and 16th centuries: *In the earliest stages, these simple intervals occur so frequently that they appear to be the favourite sound of composers. *Later, the more “complex” intervals (thirds, sixths, and tritones) move gradually from the margins to the centre of musical interest. *By the end of the Middle Ages, new rules for voice leading had been laid, re-evaluating the importance of unison, octave, fifth and fourth and handling them in a more restricted fashion (for instance, the later forbidding of parallel octaves and fifths). The music of the 20th century for the most part discards the rules of “classical” Western tonality. For instance, composers such as Erik Satie borrowed stylistic elements from the Middle Ages, but some composers found more innovative uses for these intervals.

Phrygian mode

Mon, 01 Jan 0001 00:00:00 +0000

Ancient Greek Phrygian#

The octave species (scale) underlying the ancient-Greek Phrygian tonos (in its diatonic genus) corresponds to the medieval and modern Dorian mode. The terminology is based on the Elements by Aristoxenos (fl. ), a disciple of Aristotle. The Phrygian tonos or harmonia is named after the ancient kingdom of Phrygia in Anatolia. In Greek music theory, the harmonia given this name was based on a tonos, in turn based on a scale or octave species built from a tetrachord which, in its diatonic genus, consisted of a series of rising intervals of a whole tone, followed by a semitone, followed by a whole tone. : \key e \dorian \override Score.TimeSignature #‘stencil = ##f \relative c’ \clef treble \time 4/4 e4^\markup Greek Phrygian tonos (diatonic genus) on E fis g a b cis d e In the chromatic genus, this is a minor third followed by two semitones. : \key e \major \override Score.TimeSignature #‘stencil = ##f \relative c’ \clef treble \time 4/4 e4^\markup Greek Phrygian tonos (chromatic genus) on E fisis gis a b cisis dis e In the enharmonic genus, it is a major third and two quarter tones. : \key e \major \override Score.TimeSignature #‘stencil = ##f \relative c’ \clef treble \time 4/4 e4^\markup Greek Phrygian tonos (enharmonic genus) on E gis gisih a b dis disih e A diatonic-genus octave species built upon D is roughly equivalent to playing all the white notes on a piano keyboard from D to D: : \override Score.TimeSignature #‘stencil = ##f \relative c’ \clef treble \time 4/4 d4 e f g a b c d This scale, combined with a set of characteristic melodic behaviours and associated ethe, constituted the harmonia which was given the ethnic name “Phrygian”, after the “unbounded, ecstatic peoples of the wild, mountainous regions of the Anatolian highlands”. This ethnic name was also confusingly applied by theorists such as Cleonides to one of thirteen chromatic transposition levels, regardless of the intervallic makeup of the scale. Since the Renaissance, music theorists have called this same sequence (on a diatonic scale) the “Dorian” mode, due to a mistake interpreting Greek (it is different from the Greek mode called “Dorian”).

Relative key

Mon, 01 Jan 0001 00:00:00 +0000

Distinguishing on the basis of melody#

To distinguish a minor key from its relative major, one can look to the first note/chord of the melody, which usually is the tonic or the dominant (fifth note); The last note/chord also tends to be the tonic. A “raised 7th” is also a strong indication of a minor scale (instead of a major scale): For example, C major and A minor both have no sharps or flats in their key signatures, but if the note G (the seventh note in A minor raised by a semitone) occurs frequently in a melody, then this melody is likely in A harmonic minor, instead of C major.

Scale (music)

Mon, 01 Jan 0001 00:00:00 +0000

Scales, steps, and intervals#

Scales are typically listed from low to high pitch. Most scales are octave-repeating, meaning their pattern of notes is the same in every octave (the Bohlen–Pierce scale is one exception). An octave-repeating scale can be represented as a circular arrangement of pitch classes, ordered by increasing (or decreasing) pitch class. For instance, the increasing C major scale is C–D–E–F–G–A–B– C , with the bracket indicating that the last note is an octave higher than the first note, and the decreasing C major scale is C–B–A–G–F–E–D– C , with the bracket indicating an octave lower than the first note in the scale. The distance between two successive notes in a scale is called a scale step. The notes of a scale are numbered by their steps from the first degree of the scale. For example, in a C major scale the first note is C, the second D, the third E and so on. Two notes can also be numbered in relation to each other: C and E create an interval of a third (in this case a major third); D and F also create a third (in this case a minor third).

Semitone

Mon, 01 Jan 0001 00:00:00 +0000

Minor second#

The minor second (m2 or -2) occurs in the major scale, between the third and fourth degree, (mi (E) and fa (F) in C major), and between the seventh and eighth degree (ti (B) and do (C) in C major). It is also called the diatonic semitone because it occurs between steps in the diatonic scale. Its inversion is the major seventh (M7 or Ma7). Melodically, this interval is very frequently used, and is of particular importance in cadences. In the authentic and deceptive cadences it appears as a resolution of the leading tone to the tonic. In the plagal cadence, it appears as the falling of the subdominant to the mediant. It also occurs in many forms of the imperfect cadence, wherever the tonic falls to the leading tone. Harmonically, the interval usually occurs as some form of dissonance or a nonchord tone that is not part of the functional harmony. It may also appear in inversions of a major seventh chord, and in many added tone chords. In unusual situations, the minor second can add a great deal of character to the music. For instance, Frédéric Chopin’s Étude Op. 25, No. 5 opens with a melody accompanied by a line that plays fleeting minor seconds. These are used to humorous and whimsical effect, which contrasts with its more lyrical middle section. This eccentric dissonance has earned the piece its nickname: the “wrong note” étude. This kind of usage of the minor second appears in many other works of the Romantic period, such as Modest Mussorgsky’s “Ballet of the Unhatched Chicks” from Pictures at an Exhibition. More recently, the music to the movie Jaws exemplifies the minor second.

Transposition (music)

Mon, 01 Jan 0001 00:00:00 +0000

Scalar transpositions#

In scalar transposition, every pitch in a collection is shifted up or down a fixed number of scale steps within some scale. The pitches remain in the same scale before and after the shift. This term covers both chromatic and diatonic transpositions as follows.

Chromatic transposition#

Chromatic transposition is scalar transposition within the chromatic scale, implying that every pitch in a collection of notes is shifted by the same number of semitones. For instance, transposing the pitches C 4 –E 4 –G 4 upward by four semitones, one obtains the pitches E 4 –G 4 –B 4 .

Tritone

Mon, 01 Jan 0001 00:00:00 +0000

Definition#

A tritone is composed of three whole tones. There are two possible interpretations of this, a narrow definition and a broad definition. Under the narrow definition, only augmented fourths (often abbreviated as A4) are considered tritones, while under the broad definition, augmented fourths and diminished fifths (d5)—as well as rarer intervals like doubly augmented thirds and a doubly diminished sixths—are all considered tritones. The augmented fourth is the interval produced by widening the perfect fourth by one semitone (without changing either letter name), while the diminished fifth is produced by narrowing the perfect fifth by one semitone (without changing either letter name). Under the narrow definition, each of the three whole tones that compose a tritone must be a diatonic step, so only the interval of an augmented fourth is considered a tritone. By this definition, within a diatonic scale (such as a major scale) there is only one tritone per octave. For instance, in the C major scale, the augmented fourth F–B is the only tritone because it is composed of three major seconds (F–G, G–A, and A–B), while its inversion, the diminished fifth B–F, is not considered a tritone because three major seconds above B is E, not F. : \override Score.TimeSignature #‘stencil = ##f \relative c’ \override Score.SpacingSpanner.strict-note-spacing = ##t \set Score.proportionalNotationDuration = #(ly:make-moment 1/4) \time 4/4 \set Score.tempoHideNote = ##t \tempo 1 = 20 1^\markup \abs-fontsize #9 \column “Augmented” “fourth” ^\markup \abs-fontsize #9 \column “Diminished” “fifth” Under the broad definition, however, a tritone may include any interval spanning six semitones, regardless of scale degree. According to this definition, a diatonic scale contains two tritones for each octave. For instance, the C major scale contains the tritones, F–B and B–F. With this broad definition, a tritone can typically be classified as either an augmented fourth or a diminished fifth, though far rarer spellings of the notes in a tritone may be classified as a doubly augmented third, a doubly diminished sixth, etc.

Whole-tone scale

Mon, 01 Jan 0001 00:00:00 +0000

Classical music#

In 1662, Johann Rudolf Ahle wrote a melody to the lyrics of Franz Joachim Burmeister’s “Es ist genug” (It is enough), beginning it with four notes of the whole-tone scale on the four syllables. Johann Sebastian Bach chose the chorale to end his cantata O Ewigkeit, du Donnerwort, BWV 60, set for four parts. The first four measures are shown below. : \new PianoStaff > \new Staff > » Mozart also used the scale in his Musical Joke, for strings and horns. In the 19th century, Russian composers went further with melodic and harmonic possibilities of the scale, often to depict the ominous; examples include the endings of the overtures to Glinka’s opera Ruslan and Lyudmila and Borodin’s Prince Igor, and the Commander’s theme in Dargomyzhsky’s The Stone Guest. Further examples can be found in the works of Rimsky-Korsakov: the sea king’s music in Sadko and also in Scheherazade. Shown below is the opening theme to Scheherazade, which is “simply a descending whole-tone scale with diatonic trimmings.” Notes in the whole-tone scale are highlighted. : \relative c \set Staff.midiInstrument = #“tuba” \set Score.tempoHideNote = ##t \tempo 4 = 130 \clef bass \key g \major \time 2/2 \once \override NoteHead.color = #red e2 \ff b \override NoteHead.color = #red d~ \times 2/3 d4 c \override NoteHead.color = #black b \override NoteHead.color = #red c2.\startTrillSpan c8. \override NoteHead.color = #black g16\stopTrillSpan \override NoteHead.color = #red ais2\accent\staccato fis\accent\staccato (For some short piano pieces written completely in whole-tone scale, see Nos. 1, 6, and 7 from V.A. Rebikov’s Празднество (Une fête), Op. 38, from 1907.) H. C. Colles names as the “childhood of the whole-tone scale” the music of Berlioz and Schubert in France and Austria and then Russians Glinka and Dargomyzhsky. Claude Debussy, who had been influenced by Russians, along with other impressionist composers made extensive use of whole-tone scales. Voiles, the second piece in Debussy’s first book of Préludes, is almost entirely within one whole-tone scale. The opening measures are shown below. : \new PianoStaff 8–(\markup \dynamic p \italic “très doux” 32 8..\ 32 4)> r4! 8–~(\markup \dynamic p 32> ! 4~_\markup \italic “più” \dynamic p 16> )! » \new Staff > » Janáček’s use of the scale in the bracing opening to the second movement of his Sinfonietta is, to quote William W. Austin, “utterly different”. Austin writes, “Janáček’s free chromaticism never loses touch with a diatonic scale for long. Though the whole-tone scale is prominent in much of his music after 1905 when he encountered Debussy, it serves simply to fit the motifs over augmented chords. The same motifs return from the whole-tone to the diatonic scale without emphasizing the contrast.” The first measures of the second movement of Sinfonietta are shown below. Giacomo Puccini used whole-tone scales as well as pentatonic scales in his 1904 opera Madama Butterfly to imitate east Asian music styles. The first of Alban Berg’s Seven Early Songs opens with a whole-tone passage both in the orchestral accompaniment and in the vocal line that enters a bar later. Berg also quotes the Bach chorale setting referred to above in his Violin Concerto. The last four notes of the 12-tone row Berg used are B, C, E and F, which, together with the first note, G, comprise five of the six notes of the scale.) Béla Bartók also uses whole-tone scales in his fifth string quartet. Ferruccio Busoni used the whole-tone scale in the right hand part of the “Preludietto, Fughetta ed Esercizio” of his An die Jugend, and Franz Liszt had used the technique as early as 1831, in the Grande Fantaisie sur La clochette.

Intervals & Scales on Music Theory Print

Aeolian mode

History#

Blues scale

Hexatonic#

Chromatic scale

Definition#

Chromaticism

Development of chromaticism#

Circle of fifths

Definition#

Diatonic and chromatic

Greek genera#

Diatonic scale

History#

Antiquity#

Dorian mode

Ancient Dorian mode#

Enharmonic equivalence

Definition#

Harmonic minor scale

Harmony#

Interval (music)

Size#

Frequency ratios#

Ionian mode

See also#

External links#

Key (music)

Background#

Locrian mode

History#

Lydian mode

Ancient Greek Lydian#

Major scale

Natural major scale#

Major second

Major and minor tones#

Major third

Harmonic and non-harmonic thirds#

Minor scale

Natural minor#

Minor third

In other tunings#

Mixolydian mode

Ancient Mixolydian#

Mode (music)

Mode as a general concept#

Octatonic scale

Nomenclature#

Octave

Explanation and definition#

Parallel key

See also#

Pentatonic scale

Hemitonic and anhemitonic#

Perfect fifth

Alternative definitions#

Perfect fourth

History#

Phrygian mode

Ancient Greek Phrygian#

Relative key

Distinguishing on the basis of melody#

Scale (music)

Scales, steps, and intervals#

Semitone

Minor second#

Transposition (music)

Scalar transpositions#

Chromatic transposition#

Tritone

Definition#

Whole-tone scale

Classical music#