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Class of music scales with seven notes

In music theory, a diatonic scale is any heptatonic scale that includes five whole steps (whole tones) and two half steps (semitones) in each octave, in which the two half steps are separated from each other by either two or three whole steps, depending on their position in the scale. 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 seven pitches of any diatonic scale can also be obtained by using a chain of six perfect fifths. For instance, the seven natural pitch classes that form the C major scale can be obtained from a stack of perfect fifths starting from F:
F–C–G–D–A–E–B

Any sequence of seven successive natural notes, such as C–D–E–F–G–A–B, and any transposition thereof, is a diatonic scale. Modern musical keyboards are designed so that the white key notes form a diatonic scale, though transpositions of this diatonic scale require one or more black keys. A diatonic scale can be also described as two tetrachords separated by a whole tone. In musical set theory, Allen Forte classifies diatonic scales as set form 7–35. The term diatonic originally referred to the diatonic genus, one of the three genera of the ancient Greeks, and comes from διατονικός, of uncertain etymology. Most likely, it refers to the intervals being "stretched out" in that tuning, in contrast to the other two genera (chromatic and enharmonic). This article does not concern alternative seven note scales such as the harmonic minor or the melodic minor which, although sometimes called "diatonic", do not fulfill the condition of maximal separation of the semitones indicated above.

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.

Canadian musicologist Bob Fink concluded from his analysis of the 45,000 year old Divje Babe flute that it "could produce four notes of a minor diatonic scale" and that this suggests human perception of "what constitutes harmony is at least partly hard wired". 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.

Heinrich Glarean considered that the modal scales including a B had to be the result of a transposition. In his Dodecachordon, he not only described six "natural" diatonic scales (still neglecting the seventh one with a diminished fifth above the reference note), but also six "transposed" ones, each including a B, resulting in the total of twelve scales that justified the title of his treatise. These were the 6 non Locrian modes of C major and F major.

By the beginning of the Baroque period, the notion of the musical key was established, describing additional possible transpositions of the diatonic scale. 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 in classical and 20th century music, and jazz (see chord scale system).

Diatonic scales can be tuned variously, either by iteration of a perfect or tempered fifth, or by a combination of perfect fifths and perfect thirds (Just intonation), or possibly by a combination of fifths and thirds of various sizes, as in well temperament.

Equal temperament is the division of the octave in twelve equal semitones. The frequency ratio of the semitone then becomes the twelfth root of two ( ≈ 1.059463, 100 cents). The tone is the sum of two semitone. Its ratio is the sixth root of two ( ≈ 1.122462, 200 cents). Equal temperament can be produced by a succession of tempered fifths, each of them with the ratio of 27/12 ≈ 1.498307, 700 cents.

The fifths could be tempered more than in equal temperament, in order to produce better thirds. See quarter comma meantone for a meantone temperament commonly used in the sixteenth and seventeenth centuries and sometimes after, which produces perfect major thirds.