Diatonic scale

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: Any sequence of seven successive natural notes, such as C–D–E–F–G–A–B, and any transposition thereof, is a diatonic scale.

Most likely, it refers to the intervals being "stretched out" in that tuning, in contrast to the other two genera (chromatic and enharmonic).

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.

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.

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.

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).

Of Glarean's six natural scales, three have a major third/first triad: (Ionian, Lydian, and Mixolydian), and three have a minor one: Dorian, Phrygian, and Aeolian).

[4] The black keys were progressively added for several purposes: The pattern of elementary intervals forming the diatonic scale can be represented either by the letters T (tone) and S (semitone) respectively.

The term leading tone is generally reserved for seventh degrees that are a half step (semitone) below the tonic, as is the case in the major scale.

If the scale is produced by the iteration of six perfect fifths, for instance F–C–G–D–A–E–B, the result is Pythagorean tuning: This tuning dates to Ancient Mesopotamia[5] (see Music of Mesopotamia § Music theory), and was done by alternating ascending fifths with descending fourths (equal to an ascending fifth followed by a descending octave), resulting in the notes of a pentatonic or heptatonic scale falling within an octave.

The notes of the top line, A, E and B, are lowered by the syntonic comma, 81⁄80, and the "wolf" fifth D–A is too narrow by the same amount.

Since the frequency ratios are based on simple powers of the prime numbers 2, 3, and 5, this is also known as five-limit tuning.