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Encyclopedia > Diatonic scale

In music theory, a diatonic scale (from the Greek diatonikos, "to stretch out"; also known as the heptatonia prima; set form 7-35) is a seven-note musical scale comprising five whole-tone and two half-tone steps, in which the half tones are maximally separated. The modern Western concept of diatonicism developed from the writings of Guido d'Arezzo; diatonic scales are therefore sometimes referred to as Guido scales. Music theory is a field of study that describes the elements of music and includes the development and application of methods for analyzing and composing music, and the interrelationship between the notation of music and performance practice. ... Musical set theory is an atonal or post-tonal method of musical analysis and composition which is based on explaining and proving musical phenomena, taken as sets and subsets, using mathematical rules and notation and using that information to gain insight to compositions or their creation. ... In music, a scale is a set of musical notes in order by pitch, either ascending or descending. ... Guido of Arezzo or Guido Monaco (995-1050) is regarded as the inventor of modern musical notation (staff notation) that replaced neumatic notation. ...


These scales are the fundamental building blocks of the European musical tradition. The modern major and minor scales are diatonic, as are all of the so-called 'church' modes. The seven notes of a diatonic scale—repeated in each octave—correspond to the white keys on a piano. The modern musical keyboard, with its black notes 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 signatures compared with what would be necessary for a continuous alternation of black and white notes. Music is an art, entertainment, or other human activity which involves structured and audible sound, though definitions vary. ... In music, a mode is an ordered series of musical intervals, which, along with the key or tonic, define the pitches. ... In music, an octave (sometimes abbreviated 8ve or 8va) is the interval between one musical note and another with half or double the frequency. ... A grand piano A piano is a keyboard instrument, which is widely used in western music for solo performance, chamber music, and accompaniment, and also as a convenient aid to composing and rehearsal. ...

Contents


Technical composition of diatonic scales

Technically speaking, diatonic scales are obtained from a chain of six successive fifths in some version of meantone temperament, and resulting in two tetrachords separated by intervals of a whole tone. If our version of meantone is the twelve tone equal temperament the pattern of intervals in semitones will be 2-2-1-2-2-2-1; these numbers stand for whole tones (2 semitones) and half tones (1 semitone). The major scale starts on the first note and proceeds by steps to the first octave. In solfege, the syllables for each scale degree are "Do-Re-Mi-Fa-So-La-Ti-Do". In music, interval cycles, unfold a single recurrent interval in a series that closes with a return to the initial pitch class, and are notated by George Perle using the letter C, for cycle, with an interval class integer to distinguish the interval. ... The perfect fifth or diapente is one of three musical intervals that span five diatonic scale degrees; the others being the diminished fifth, which is one semitone smaller, and the augmented fifth, which is one semitone larger. ... Meantone temperament is a system of musical tuning. ... The tetrachord is a concept of music theory borrowed from ancient Greece. ... In music theory, an interval is the relationship between two notes or pitches, the lower and higher members of the interval. ... The musical interval of a major second — also called a whole-tone — is the relationship between the first note (the root or tonic) and the second note in a major scale (and also a minor scale). ... Equal temperament is a scheme of musical tuning in which the octave is divided into a series of equal steps (equal frequency ratios). ... A semitone (also known in the USA as a half step) is a musical interval. ... In music theory, the major scale (or major mode) is one of the diatonic scales. ... Solfege table in an Irish classroom In music and sight singing solfege or solmization is a way of assigning syllables to degrees or steps of the diatonic scale. ...


The natural minor scale can be thought of in two ways, the first is as the relative minor of the major scale, beginning on the sixth degree of the scale and proceeding step by step through the same tetrachords to the first octave of the sixth degree. In solfege "La-Ti-Do-Re-Mi-Fa-So-La." Alternately, the natural minor can be seen as a composite of two different tetrachords of the pattern 2-1-2-2-1-2-2. In solfege "Do-Re-Mé-Fa-So-Lé-Té-Do." A minor scale in musical theory is a diatonic scale whose third scale degree is an interval of a minor third above the tonic. ...


Western harmony from the Renaissance up 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, but this leads to a hierarchical relationship of diatonic scales in one key with those in another. Harmony is the use and study of pitch simultaneity and chords, actual or implied, in music. ... Renaissance music is European classical music written during the Renaissance, approximately 1400 to 1600. ... The era of Romantic music is defined as the period of European classical music that runs roughly from the early 1800s to the first decade of the 20th century, as well as music written according to the norms and styles of that period. ... For the various types of hierarchy, see hierarchy (disambiguation) A hierarchy (in Greek: Ιεραρχία, it is derived from ιερός-hieros, sacred, and άρχω-arkho, rule) is a system of ranking and organizing things or people, where each element of the system (except for the top element) is subordinate to a single other element. ... See also: function and functional. ... In music, modulation is most commonly the act or process of changing from one key (tonic, or tonal center) to another. ...


These unique relationships are as follows: Only certain divisions of the octave, 12 and 20 included, allow uniqueness, coherence, and transpositional simplicity, and that only the diatonic and pentatonic subsets of the 12-tone chromatic set follow these constraints (Balzano, 1980, 1982). 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: maximal evenness, Myhill's property, well formedness, the deep scale property, cardinality equals variety, and structure implies multiplicity. Diatonic set theory is a subdivision or application of musical set theory which applies the techniques and insights of set theory to properties of the diatonic collection such as maximal evenness, Myhills property, well formedness, the deep scale property, cardinality equals variety, and structure implies multiplicity. ... In diatonic set theory maximal evenness is the quality of a collection or scale which for every generic interval there are is either one or two consecutive (adjacent) specific intervals, in other words a scale which is spread out as much as possible. ... In diatonic set theory Myhills property is the quality of 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 collection. ... In diatonic set theory a generated collection is a collection or scale formed by repeatedly adding a constant interval in integer notation, the generator, also known as an interval cycle, around the chromatic circle until a complete collection or scale is formed. ... 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. ... In diatonic set theory cardinality equals variety is quality of a collection or scale for which the number of notes in a series indicates the number of unique interval patterns formed by diatonic transpositions. ... In diatonic set theory structure implies multiplicity is quality of a collection or scale for which 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 (adjacently, rather than around the circle of fifths...


There is significant evidence that the evolution of the diatonic scale is natural, because it is based on the most basic harmonics of any scale's first note, and that it has actually occurred many times over the course of human history, in which the three most common intervals across time and cultures, a tone, its 5th and 4th, produce audible overtones sufficient to influence the formation of the pentatonic, and major/minor diatonic scales. This is called the "Trio" theory [cited in Fink, "On the Origin of Music" (2005)]. There is even circumstantial evidence that a flute used by Neanderthals about 40,000 years ago and found at Divje Babe played the diatonic scale[1], and that a song recorded on a clay tablet in ancient Syria was written in it, 3,400 years ago.[2] Binomial name Homo neanderthalensis The Neanderthal or Neandertal was a species or sub-species of Homo (Homo neanderthalensis) that inhabited Europe and parts of western Asia from about 230,000 to 29,000 years ago, during the Middle Paleolithic period. ... Divje Babe I is an archeological site located near Idrija in northwestern Slovenia. ...


See also

In music, pitch is the perception of the frequency of a note. ... In ancient Greek music theory, the diatonic genus is the division of the tetrachord from which the modern diatonic scale evolved. ... This is a virtual piano with 88 keys tuned to A440, showing the frequencies, in cycles per second (Hz), of each note. ... Divje Babe I is an archeological site located near Idrija in northwestern Slovenia. ...

Further reading

  • Johnson, Timothy (2003). Foundations of Diatonic Theory: A Mathematically Based Approach to Music Fundamentals. Key College Publishing. ISBN 1930190808.
  • Clough, John (1979). "Aspects of Diatonic Sets", Journal of Music Theory 23: 45-61.
  • Gould, Mark (2000). "Balzano and Zweifel: Another Look at Generalised Diatonic Scales", "Perspectives of New Music" 38/2: 88-105
  • Fink, Bob (2005) On the Origin of Music. Greenwich. ISBN 0912424141.

Sources

  • Balzano, Gerald J. (1980). "The Group Theoretic Description of 12-fold and Microtonal Pitch Systems", Computer Music Journal 4: 66-84.
  • Stein, Deborah (2005). Engaging Music: Essays in Music Analysis. New York: Oxford University Press. ISBN 0195170105.
    • Browne, Richmond (1981). "Tonal Implications of the Diatonic Set", In Theory Only 5, nos. 1 and 2: 3-21

External links

Scales in Equally tempered music edit
By interval : diatonic | chromatic | whole tone
By number of pitch classes : ditonic | tritonic | tetratonic | pentatonic | hexatonic | heptatonic | octatonic
Diatonic Scales and Keys
Sharps Flats
major minor major minor
0 C (major), A (minor)
1 G E F D
2 D B B♭ G
3 A F♯ E♭ C
4 E C♯ A♭ F
5 B G♯ D♭ B♭
6 F♯ D♯ G♭ E♭
7 C♯ A♯ C♭ A♭
lower case letters in the circle of fifths are minor
the table indicates the number of sharps or flats in each scale

  Results from FactBites:
 
Diatonic Scale -- from Eric Weisstein's Treasure Trove of Music (270 words)
In particular, all of the church modes (dorian, phrygian, lydian, myxolydian, and aeolian) are rotations of the so-called major scale are diatonic.
In just intonation, the diatonic scale (as well as other scales) work differently for different starting notes, leading to the concept of the key.
The scale used on piano and fretted instruments is actually an approximation to the exact ratios given above because modern western music uses an equal temperament scale, allowing music to be transposed while slightly sacrificing the euphony of chords.
Diatonic scale - Wikipedia, the free encyclopedia (683 words)
In music theory, a diatonic scale (from the Greek diatonikos, "to stretch out"; also known as the heptatonia prima; set form 7-35) is a seven-note musical scale comprising five whole-tone and two half-tone steps, in which the half tones are maximally separated.
The modern major and minor scales are diatonic, as are all of the so-called 'church' modes.
Technically speaking, diatonic scales are obtained from a chain of six successive fifths in some version of meantone temperament, and resulting in two tetrachords separated by intervals of a whole tone.
  More results at FactBites »

 
 

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