Diatonic scale
Encyclopedia
In music theory
, a diatonic scale (from the Greek διατονικός, meaning "[progressing] through tones", also known as the heptatonia prima) is a seven note, octave
-repeating musical scale
comprising five whole steps and two half steps for each octave
, in which the two half steps are separated from each other by either two or three whole steps. This pattern ensures that, in a diatonic scale spanning more than one octave
, all the half steps are maximally separated from each other (i.e. separated by at least two whole steps).
The term diatonic originally referred to the diatonic genus
, one of the three genera of the ancient Greeks. In musical set theory, Allen Forte
classifies diatonic scales as set form 7-35.
al tradition. The modern major
and minor
scales are diatonic, as were all of the 'church modes'. What are now called major and minor were in reality - during the medieval and Renaissance periods - only two of seven modes ('church modes') based on the same diatonic notes (but forming different scales when the starting note was changed). Depending on which of the seven notes is used as the beginning, the positions of the intervals, the half-steps, end at different distances from the starting tone, hence obtaining seven different scales or modes that are, as already mentioned, deduced from the diatonic scale. By the start of the Baroque
period, the notion of musical key
was established—based on a central triad
rather than a central tone. Major and minor scales came to dominate until at least the start of the 20th century, partly because their intervallic patterns are suited to the reinforcement of a central triad. Some church modes survived into the early 18th century, as well as appearing occasionally in classical
and 20th century music
, and later in modal jazz
.
flute" (Divje Babe flute) found at Divje Babe
. Although there is no consensus that this is a musical instrument, there has been one claim that it played a diatonic scale.
There is evidence that the Sumer
ians and Babylonians used some version of the diatonic scale. This derives from surviving inscriptions that contain a tuning system and musical composition. Despite the conjectural nature of reconstructions of the piece known as the Hurrian hymn from the surviving score, the evidence that it used the diatonic scale is much more soundly based. This is because instructions for tuning the scale involve tuning a chain of six fifths, so that the corresponding circle of seven major
and minor
thirds are all consonant-sounding, and this is a recipe for tuning a diatonic scale. See Music of Mesopotamia
.
9,000-year-old flutes
found in Jiahu
, China indicate the evolution, over a period of 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.
, twelve of each of the three major scales (Ionian, Lydian, and Mixolydian), twelve of each of the three minor scales (Dorian, Phrygian, and Aeolian), and twelve Locrian scales can be played, totaling eighty-four diatonic scales. The modern musical keyboard
, with its black keys grouped in twos and threes, is essentially diatonic; this arrangement not only helps musicians to find their bearings on the keyboard, but simplifies the system of key signature
s compared with what would be necessary for a continuous alternation of black and white keys. The black (or "short") keys were an innovation that allows the adjacent positioning of most of the diatonic whole-steps (all in the case of C major), with significant physical and conceptual advantages.
In music of the broadly western classical tradition
the pattern of seven intervals separating the eight notes of an octave (see heptatonic scale
) can be represented in three ways, which are equivalent to each other. For instance, for a major scale these intervals are:
The major scale
starts on the key note and proceeds by scale degree
s (or steps) to the first octave
. In solfege
, the syllables for each degree are "Do–Re–Mi–Fa–Sol–La–Si–Do". Including the example of C-major (piano white notes), this can be viewed as:
The degrees of the scale are also known by traditional names. These names, starting from the bottom of the scale, are the tonic, the supertonic, the mediant, the subdominant, the dominant, the submediant, and the leading tone.
The natural minor scale
can be thought of as the relative minor of the major scale, beginning on the sixth degree of the major scale and proceeding step by step to the first octave of the sixth degree:
The degrees of the natural minor scale have the same names, except that the seventh degree is known as the subtonic, rather than the leading tone.
In solfege
this is regarded in two different ways: either as "La–Si–Do–Re–Mi–Fa–Sol–La" or as "Do–Re–Mi–Fa–Sol–La–Si–Do."
Western harmony
from the Renaissance
until the late 19th century
is based on the diatonic scale and the unique hierarchical
relationships, or diatonic functionality, created by this system of organizing seven notes. Most longer pieces of common practice music change key
, which leads to a hierarchical relationship of diatonic scales in one key with those in another.
Technically speaking, diatonic scales are obtained from a chain
of six successive fifths
centered at D, in traditional tuning systems such as Pythagorean tuning
or meantone temperament
.
A diatonic scale can be also described as two tetrachord
s separated by a whole tone. For example under this view the two tetrachord structures of C major would be:
and of the natural minor of A would be:
The set of intervals within each tetrachord comprises two tones and a semitone.
conceived of a property of scales he called propriety
, and around the same time Gerald Balzano independently came up with the same definition in the more limited context of equal temperaments, calling it coherence. Rothenberg distinguished proper from a slightly stronger characteristic he called strictly proper. In this vocabulary, there are five proper seven-note scales in 12 equal temperament. None of these is strictly proper, i.e., coherent in the sense of Balzano; but in any system of meantone
tuning with the fifth flatter than 700 cent
s, they are strictly proper. The scales are the diatonic, ascending minor
, harmonic minor
, harmonic major
, and locrian major scales; of these, all but the last are well-known and constitute the backbone of diatonic practice when taken together.
Among these four well-known variants of the diatonic scale, the diatonic scale itself has additional properties of what has been called simplicity, because it is produced by iterations of a single generator, the meantone fifth. The scale, in the vocabulary of Erv Wilson
, who may have been the first to consider the notion, is sometimes called a MOS scale.
The diatonic collection contains each interval class a unique number of times (Browne 1981 cited in Stein 2005, p. 49, 49n12). Diatonic set theory
describes the following properties, aside from propriety: maximal evenness
, Myhill's property
, well formedness, the deep scale property
, cardinality equals variety
, and structure implies multiplicity
.
In just intonation
the diatonic scale is tuned:
In Pythagorean tuning
the diatonic scale is:
Music theory
Music theory is the study of how music works. It examines the language and notation of music. It seeks to identify patterns and structures in composers' techniques across or within genres, styles, or historical periods...
, a diatonic scale (from the Greek διατονικός, meaning "[progressing] through tones", also known as the heptatonia prima) is a seven note, octave
Octave
In music, an octave is the interval between one musical pitch and another with half or double its frequency. The octave relationship is a natural phenomenon that has been referred to as the "basic miracle of music", the use of which is "common in most musical systems"...
-repeating musical scale
Musical scale
In music, a scale is a sequence of musical notes in ascending and descending order. Most commonly, especially in the context of the common practice period, the notes of a scale will belong to a single key, thus providing material for or being used to conveniently represent part or all of a musical...
comprising five whole steps and two half steps for each octave
Octave
In music, an octave is the interval between one musical pitch and another with half or double its frequency. The octave relationship is a natural phenomenon that has been referred to as the "basic miracle of music", the use of which is "common in most musical systems"...
, in which the two half steps are separated from each other by either two or three whole steps. This pattern ensures that, in a diatonic scale spanning more than one octave
Octave
In music, an octave is the interval between one musical pitch and another with half or double its frequency. The octave relationship is a natural phenomenon that has been referred to as the "basic miracle of music", the use of which is "common in most musical systems"...
, all the half steps are maximally separated from each other (i.e. separated by at least two whole steps).
The term diatonic originally referred to the diatonic genus
Diatonic genus
In ancient Greek music theory, the diatonic genus is the division of the tetrachord from which the modern diatonic scale evolved. The distinguishing characteristic of the diatonic genus is that its largest interval is about the size of a major second...
, one of the three genera of the ancient Greeks. In musical set theory, Allen Forte
Allen Forte
Allen Forte is a music theorist and musicologist. He was born in Portland, Oregon and fought in the Navy at the close of World War II before moving to the East Coast. He is now Battell Professor of Music, Emeritus at Yale University...
classifies diatonic scales as set form 7-35.
History
These scales are the foundation of the European musicMusic
Music is an art form whose medium is sound and silence. Its common elements are pitch , rhythm , dynamics, and the sonic qualities of timbre and texture...
al tradition. The modern major
Major scale
In music theory, the major scale or Ionian scale is one of the diatonic scales. It is made up of seven distinct notes, plus an eighth which duplicates the first an octave higher. In solfege these notes correspond to the syllables "Do, Re, Mi, Fa, Sol, La, Ti/Si, ", the "Do" in the parenthesis at...
and minor
Minor scale
A minor scale in Western music theory includes any scale that contains, in its tonic triad, at least three essential scale degrees: 1) the tonic , 2) a minor-third, or an interval of a minor third above the tonic, and 3) a perfect-fifth, or an interval of a perfect fifth above the tonic, altogether...
scales are diatonic, as were all of the 'church modes'. What are now called major and minor were in reality - during the medieval and Renaissance periods - only two of seven modes ('church modes') based on the same diatonic notes (but forming different scales when the starting note was changed). Depending on which of the seven notes is used as the beginning, the positions of the intervals, the half-steps, end at different distances from the starting tone, hence obtaining seven different scales or modes that are, as already mentioned, deduced from the diatonic scale. By the start of the Baroque
Baroque music
Baroque music describes a style of Western Classical music approximately extending from 1600 to 1760. This era follows the Renaissance and was followed in turn by the Classical era...
period, the notion of musical key
Key (music)
In music theory, the term key is used in many different and sometimes contradictory ways. A common use is to speak of music as being "in" a specific key, such as in the key of C major or in the key of F-sharp. Sometimes the terms "major" or "minor" are appended, as in the key of A minor or in the...
was established—based on a central triad
Triad (music)
In music and music theory, a triad is a three-note chord that can be stacked in thirds. Its members, when actually stacked in thirds, from lowest pitched tone to highest, are called:* the Root...
rather than a central tone. Major and minor scales came to dominate until at least the start of the 20th century, partly because their intervallic patterns are suited to the reinforcement of a central triad. Some church modes survived into the early 18th century, as well as appearing occasionally in classical
Classical period (music)
The dates of the Classical Period in Western music are generally accepted as being between about 1750 and 1830. However, the term classical music is used colloquially to describe a variety of Western musical styles from the ninth century to the present, and especially from the sixteenth or...
and 20th century music
20th century music
20th century music is defined by the sudden emergence of advanced technology for recording and distributing music as well as dramatic innovations in musical forms and styles...
, and later in modal jazz
Modal jazz
Modal jazz is jazz that uses musical modes rather than chord progressions as a harmonic framework. Originating in the late 1950s and 1960s, modal jazz is characterized by Miles Davis's "Milestones" Kind of Blue and John Coltrane's classic quartet from 1960–64. Other important performers include...
.
Prehistory
The earliest claimed occurrence of diatonic tuning is in the 45,000 year-old so-called "NeanderthalNeanderthal
The Neanderthal is an extinct member of the Homo genus known from Pleistocene specimens found in Europe and parts of western and central Asia...
flute" (Divje Babe flute) found at Divje Babe
Divje Babe
The Divje Babe flute is a cave bear femur pierced by spaced holes that was found at the Divje Babe archeological park located near Cerkno in northwestern Slovenia. It has been suggested that it is the world's oldest known musical instrument, but this is in dispute...
. Although there is no consensus that this is a musical instrument, there has been one claim that it played a diatonic scale.
There is evidence that the Sumer
Sumer
Sumer was a civilization and historical region in southern Mesopotamia, modern Iraq during the Chalcolithic and Early Bronze Age....
ians and Babylonians used some version of the diatonic scale. This derives from surviving inscriptions that contain a tuning system and musical composition. Despite the conjectural nature of reconstructions of the piece known as the Hurrian hymn from the surviving score, the evidence that it used the diatonic scale is much more soundly based. This is because instructions for tuning the scale involve tuning a chain of six fifths, so that the corresponding circle of seven major
Major third
In classical music from Western culture, a third is a musical interval encompassing three staff positions , and the major third is one of two commonly occurring thirds. It is qualified as major because it is the largest of the two: the major third spans four semitones, the minor third three...
and minor
Minor third
In classical music from Western culture, a third is a musical interval encompassing three staff positions , and the minor third is one of two commonly occurring thirds. The minor quality specification identifies it as being the smallest of the two: the minor third spans three semitones, the major...
thirds are all consonant-sounding, and this is a recipe for tuning a diatonic scale. See Music of Mesopotamia
Music of Mesopotamia
This article treats the music of Ancient Mesopotamia.Cuneiform sources reveal an orderly organized system of diatonic depending on the tuning of stringed instruments in alternating fifths and fourths. Whether this reflects all types of music we do not know...
.
9,000-year-old flutes
Gudi (instrument)
The Jiahu gǔdí is the oldest known musical instrument from China, dating back to around 6000 BC. Gudi literally means "bone flute".- History :...
found in Jiahu
Jiahu
Jiahu was the site of a Neolithic Yellow River settlement based in the central plains of ancient China, modern Wuyang, Henan Province. Archaeologists consider the site to be one of the earliest examples of the Peiligang culture. Settled from 7000 to 5800 BC, the site was later flooded and abandoned...
, China indicate the evolution, over a period of 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.
Theory
Using the twelve notes of the chromatic scaleChromatic scale
The chromatic scale is a musical scale with twelve pitches, each a semitone apart. On a modern piano or other equal-tempered instrument, all the half steps are the same size...
, twelve of each of the three major scales (Ionian, Lydian, and Mixolydian), twelve of each of the three minor scales (Dorian, Phrygian, and Aeolian), and twelve Locrian scales can be played, totaling eighty-four diatonic scales. The modern musical keyboard
Musical keyboard
A musical keyboard is the set of adjacent depressible levers or keys on a musical instrument, particularly the piano. Keyboards typically contain keys for playing the twelve notes of the Western musical scale, with a combination of larger, longer keys and smaller, shorter keys that repeats at the...
, with its black keys grouped in twos and threes, is essentially diatonic; this arrangement not only helps musicians to find their bearings on the keyboard, but simplifies the system of key signature
Key signature
In musical notation, a key signature is a series of sharp or flat symbols placed on the staff, designating notes that are to be consistently played one semitone higher or lower than the equivalent natural notes unless otherwise altered with an accidental...
s compared with what would be necessary for a continuous alternation of black and white keys. The black (or "short") keys were an innovation that allows the adjacent positioning of most of the diatonic whole-steps (all in the case of C major), with significant physical and conceptual advantages.
Analysis
Common practice period
The common practice period, in the history of Western art music , spanning the Baroque, Classical, and Romantic periods, lasted from c. 1600 to c. 1900.-General characteristics:...
the pattern of seven intervals separating the eight notes of an octave (see heptatonic scale
Heptatonic scale
A heptatonic scale is a musical scale with seven pitches per octave. Among the most famous of these are the major scale, C D E F G A B C; the melodic minor scale, C D E F G A B C ascending, C B A G F E D C descending; the harmonic minor scale, C D E F G A B C; and a scale variously known as the...
) can be represented in three ways, which are equivalent to each other. For instance, for a major scale these intervals are:
- T-T-S-T-T-T-S: where S means semitone; T means tone
- 2–2–1–2–2–2–1: where 1 means semitone; 2 means tone (2 semitones)
- whole-whole-half-whole-whole-whole-half: where half means semitone (half a tone); whole means tone.
The major scale
Major scale
In music theory, the major scale or Ionian scale is one of the diatonic scales. It is made up of seven distinct notes, plus an eighth which duplicates the first an octave higher. In solfege these notes correspond to the syllables "Do, Re, Mi, Fa, Sol, La, Ti/Si, ", the "Do" in the parenthesis at...
starts on the key note and proceeds by scale degree
Degree (music)
In music theory, a scale degree or scale step is the name of a particular note of a scale in relation to the tonic...
s (or steps) to the first octave
Octave
In music, an octave is the interval between one musical pitch and another with half or double its frequency. The octave relationship is a natural phenomenon that has been referred to as the "basic miracle of music", the use of which is "common in most musical systems"...
. In solfege
Solfege
In music, solfège is a pedagogical solmization technique for the teaching of sight-singing in which each note of the score is sung to a special syllable, called a solfège syllable...
, the syllables for each degree are "Do–Re–Mi–Fa–Sol–La–Si–Do". Including the example of C-major (piano white notes), this can be viewed as:
| C major: | C | D | E | F | G | A | B | C | ||||||||
| Solfege: | Do | Re | Mi | Fa | Sol | La | Si | Do | ||||||||
| Interval: | T | T | S | T | T | T | S |
The degrees of the scale are also known by traditional names. These names, starting from the bottom of the scale, are the tonic, the supertonic, the mediant, the subdominant, the dominant, the submediant, and the leading tone.
The natural minor scale
Minor scale
A minor scale in Western music theory includes any scale that contains, in its tonic triad, at least three essential scale degrees: 1) the tonic , 2) a minor-third, or an interval of a minor third above the tonic, and 3) a perfect-fifth, or an interval of a perfect fifth above the tonic, altogether...
can be thought of as the relative minor of the major scale, beginning on the sixth degree of the major scale and proceeding step by step to the first octave of the sixth degree:
| A minor: | A | B | C | D | E | F | G | A | ||||||||
| Interval: | T | S | T | T | S | T | T |
The degrees of the natural minor scale have the same names, except that the seventh degree is known as the subtonic, rather than the leading tone.
In solfege
Solfege
In music, solfège is a pedagogical solmization technique for the teaching of sight-singing in which each note of the score is sung to a special syllable, called a solfège syllable...
this is regarded in two different ways: either as "La–Si–Do–Re–Mi–Fa–Sol–La" or as "Do–Re–Mi–Fa–Sol–La–Si–Do."
Western harmony
Harmony
In music, harmony is the use of simultaneous pitches , or chords. The study of harmony involves chords and their construction and chord progressions and the principles of connection that govern them. Harmony is often said to refer to the "vertical" aspect of music, as distinguished from melodic...
from the Renaissance
Renaissance music
Renaissance music is European music written during the Renaissance. Defining the beginning of the musical era is difficult, given that its defining characteristics were adopted only gradually; musicologists have placed its beginnings from as early as 1300 to as late as the 1470s.Literally meaning...
until the late 19th century
Romantic music
Romantic music or music in the Romantic Period is a musicological and artistic term referring to a particular period, theory, compositional practice, and canon in Western music history, from 1810 to 1900....
is based on the diatonic scale and the unique hierarchical
Hierarchy
A hierarchy is an arrangement of items in which the items are represented as being "above," "below," or "at the same level as" one another...
relationships, or diatonic functionality, created by this system of organizing seven notes. Most longer pieces of common practice music change key
Modulation (music)
In music, modulation is most commonly the act or process of changing from one key to another. This may or may not be accompanied by a change in key signature. Modulations articulate or create the structure or form of many pieces, as well as add interest...
, which leads to a hierarchical relationship of diatonic scales in one key with those in another.
Technically speaking, diatonic scales are obtained from a chain
Interval cycle
In music, an interval cycle is a collection of pitch classes created from a sequence of the same interval class. In other words a collection of pitches by starting with a certain note and going up by a certain interval until the original note is reached In music, an interval cycle is a collection...
of six successive fifths
Perfect fifth
In classical music from Western culture, a fifth is a musical interval encompassing five staff positions , and the perfect fifth is a fifth spanning seven semitones, or in meantone, four diatonic semitones and three chromatic semitones...
centered at D, in traditional tuning systems such as Pythagorean tuning
Pythagorean tuning
Pythagorean tuning is a system of musical tuning in which the frequency relationships of all intervals are based on the ratio 3:2. This interval is chosen because it is one of the most consonant...
or meantone temperament
Meantone temperament
Meantone temperament is a musical temperament, which is a system of musical tuning. In general, a meantone is constructed the same way as Pythagorean tuning, as a stack of perfect fifths, but in meantone, each fifth is narrow compared to the ratio 27/12:1 in 12 equal temperament, the opposite of...
.
A diatonic scale can be also described as two tetrachord
Tetrachord
Traditionally, a tetrachord is a series of three intervals filling in the interval of a perfect fourth, a 4:3 frequency proportion. In modern usage a tetrachord is any four-note segment of a scale or tone row. The term tetrachord derives from ancient Greek music theory...
s separated by a whole tone. For example under this view the two tetrachord structures of C major would be:
- [C-D-E-F]-[G-A-B-C]
and of the natural minor of A would be:
- [A-B-C-D]-[E-F-G-A].
The set of intervals within each tetrachord comprises two tones and a semitone.
Temperament and tuning
The diatonic scale has specific properties that mark it out among seven-note scales. David RothenbergDavid Rothenberg
David Rothenberg is a professor of philosophy and music at the New Jersey Institute of Technology, with a special interest in animal sounds as music...
conceived of a property of scales he called propriety
Rothenberg propriety
In music, Rothenberg propriety denotes an important concept in the general theory of scales which was introduced by David Rothenberg in a seminal series of papers in 1978. The concept was independently discovered in a more restricted context by Gerald Balzano, who termed it coherence...
, and around the same time Gerald Balzano independently came up with the same definition in the more limited context of equal temperaments, calling it coherence. Rothenberg distinguished proper from a slightly stronger characteristic he called strictly proper. In this vocabulary, there are five proper seven-note scales in 12 equal temperament. None of these is strictly proper, i.e., coherent in the sense of Balzano; but in any system of meantone
Meantone temperament
Meantone temperament is a musical temperament, which is a system of musical tuning. In general, a meantone is constructed the same way as Pythagorean tuning, as a stack of perfect fifths, but in meantone, each fifth is narrow compared to the ratio 27/12:1 in 12 equal temperament, the opposite of...
tuning with the fifth flatter than 700 cent
Cent (music)
The cent is a logarithmic unit of measure used for musical intervals. Twelve-tone equal temperament divides the octave into 12 semitones of 100 cents each...
s, they are strictly proper. The scales are the diatonic, ascending minor
Minor scale
A minor scale in Western music theory includes any scale that contains, in its tonic triad, at least three essential scale degrees: 1) the tonic , 2) a minor-third, or an interval of a minor third above the tonic, and 3) a perfect-fifth, or an interval of a perfect fifth above the tonic, altogether...
, harmonic minor
Minor scale
A minor scale in Western music theory includes any scale that contains, in its tonic triad, at least three essential scale degrees: 1) the tonic , 2) a minor-third, or an interval of a minor third above the tonic, and 3) a perfect-fifth, or an interval of a perfect fifth above the tonic, altogether...
, harmonic major
Harmonic major scale
In music theory, the harmonic major scale is a musical scale which found occasional use during the common practice era and is now occasionally employed, most often in jazz. It was named by Rimsky-Korsakov...
, and locrian major scales; of these, all but the last are well-known and constitute the backbone of diatonic practice when taken together.
Among these four well-known variants of the diatonic scale, the diatonic scale itself has additional properties of what has been called simplicity, because it is produced by iterations of a single generator, the meantone fifth. The scale, in the vocabulary of Erv Wilson
Erv Wilson
Ervin Wilson is a Mexican/American music theorist. Despite his avoidance of academia, Wilson has been influential on those interested in microtonal music and just intonation, especially in the areas of scale, keyboard, and notation design...
, who may have been the first to consider the notion, is sometimes called a MOS scale.
The diatonic collection contains each interval class a unique number of times (Browne 1981 cited in Stein 2005, p. 49, 49n12). Diatonic set theory
Diatonic set theory
Diatonic set theory is a subdivision or application of musical set theory which applies the techniques and insights of discrete mathematics to properties of the diatonic collection such as maximal evenness, Myhill's property, well formedness, the deep scale property, cardinality equals variety, and...
describes the following properties, aside from propriety: maximal evenness
Maximal evenness
In diatonic set theory maximal evenness is the quality of a collection or scale which for every generic interval there are either one or two consecutive specific intervals, in other words a scale which is "spread out as much as possible." This property was first described by music theorist John...
, Myhill's property
Myhill's property
In diatonic set theory Myhill's property is the quality of musical scales or collections with exactly two specific intervals for every generic interval, and thus also have the properties of maximal evenness, cardinality equals variety, structure implies multiplicity, and be a well formed generated...
, well formedness, the deep scale property
Deep scale property
In diatonic set theory, the deep scale property is the quality of pitch class collections or scales containing each interval class a unique number of times. Examples include the diatonic scale...
, cardinality equals variety
Cardinality equals variety
The musical operation of scalar transposition shifts every note in a melody by the same number of scale steps. The musical operation of chromatic transposition shifts every note in a melody by the same distance in pitch class space...
, and structure implies multiplicity
Structure implies multiplicity
In diatonic set theory structure implies multiplicity is a quality of a collection or scale. This is that for the interval series formed by the shortest distance around a diatonic circle of fifths between member of a series indicates the number of unique interval patterns formed by diatonic...
.
In just intonation
Just intonation
In music, just intonation is any musical tuning in which the frequencies of notes are related by ratios of small whole numbers. Any interval tuned in this way is called a just interval. The two notes in any just interval are members of the same harmonic series...
the diatonic scale is tuned:
| C | D | E | F | G | A | B | C |
|---|---|---|---|---|---|---|---|
| 1 | 9/8 | 5/4 | 4/3 | 3/2 | 5/3 | 15/8 | 2 |
In Pythagorean tuning
Pythagorean tuning
Pythagorean tuning is a system of musical tuning in which the frequency relationships of all intervals are based on the ratio 3:2. This interval is chosen because it is one of the most consonant...
the diatonic scale is:
| C | D | E | F | G | A | B | C |
|---|---|---|---|---|---|---|---|
| 1 | 9/8 | 81/64 | 4/3 | 3/2 | 27/16 | 243/128 | 2 |
See also
- Circle of fifths text tableCircle of fifths text tableThe Circle of fifths, text table, shows the number of flats or sharps in each of the diatonic musical scales and keys. Both C major and A minor keys have no flats or sharps....
- PitchPitch (music)Pitch is an auditory perceptual property that allows the ordering of sounds on a frequency-related scale.Pitches are compared as "higher" and "lower" in the sense associated with musical melodies,...
- Piano key frequenciesPiano key frequenciesThis is a virtual keyboard showing the absolute frequencies in hertz of the notes on a modern piano in twelve-tone equal temperament, with the 49th key, the fifth A , tuned to 440 Hz...
- History of musicHistory of musicMusic is found in every known culture, past and present, varying wildly between times and places. Around 50,000 years ago, early modern humans began to disperse from Africa, reaching all the habitable continents...
- Prehistoric musicPrehistoric musicPrehistoric music is a term in the history of music for all music produced in preliterate cultures , beginning somewhere in very late geological history...
- Musical AcousticsMusical acousticsMusical acoustics or music acoustics is the branch of acoustics concerned with researching and describing the physics of music – how sounds employed as music work...
- JiahuJiahuJiahu was the site of a Neolithic Yellow River settlement based in the central plains of ancient China, modern Wuyang, Henan Province. Archaeologists consider the site to be one of the earliest examples of the Peiligang culture. Settled from 7000 to 5800 BC, the site was later flooded and abandoned...
Site of oldest still-playable flute—Neolithic - Diatonic and chromaticDiatonic and chromaticDiatonic and chromatic are terms in music theory that are most often used to characterize scales, and are also applied to intervals, chords, notes, musical styles, and kinds of harmony...
Further reading
- Balzano, Gerald J. (1980). "The Group Theoretic Description of 12-fold and Microtonal Pitch Systems", Computer Music Journal 4 66-84.
- Balzano, Gerald J. (1982). "The Pitch Set as a Level of Description for Studying Musical Pitch Perception", Music, Mind, and Brain, Manfred Clynes, ed., Plenum press.
- Clough, John (1979). "Aspects of Diatonic Sets", Journal of Music Theory 23: 45-61.
- Franklin, John C. (2002). "Diatonic Music in Greece: a Reassessment of its Antiquity", MnemosyneMnemosyne (journal)Mnemosyne is an academic journal of Classical Studies published by Brill Publishers. It was established in 1852 as a journal of textual criticism. It publishes articles in English, French, German, and Latin. The journal is abstracted and indexed in the Arts and Humanities Citation Index, Current...
56.1, 669-702 http://www.kingmixers.com/Franklin%20PDF%20files%20copy/DiatonicmusicinGreece.pdf - Gould, Mark (2000). "Balzano and Zweifel: Another Look at Generalised Diatonic Scales", "Perspectives Of New Music" 38/2, 88-105
- Johnson, Timothy (2003). Foundations Of Diatonic Theory: A Mathematically Based Approach to Music Fundamentals. Key College Publishing. ISBN 1-930190-80-8.
- Kilmer, A.D. (1971) "The Discovery of an Ancient Mesopotamian Theory of Music'". Proceedings of the American Philosophical Society 115, 131-149.
- David Rothenberg (1978). "A Model for Pattern Perception with Musical Applications Part I: Pitch Structures as order-preserving maps", Mathematical Systems Theory 11 199-234 http://lumma.org/tuning/rothenberg/AModelForPatternPerception.pdf
External links
- Diatonic Scale on Eric Weisstein's Treasure trove of Music
- The diatonic scale on the guitar