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 Music.
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Music scale.
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*Scale* is any set of musical notes ordered by fundamental frequency or pitch.

Scale ordered by increasing pitch is an *ascending scale*, and a scale ordered
by decreasing pitch is a *descending scale*.

The distance between two successive notes in a scale is called a *scale step*.

For Western music with 12 tones in octave used several definition of steps:

* *semitone*, *half step* is 2^(1/12)
* *whole step*, *whole tone*, *major second* is 2^(2/12)

*Chromatic scale* is a musical scale with twelve pitches, each a semitone
above or below another. On a modern piano or other equal-tempered
instrument, all the semitones have the same size (100 cents). In other
words, the notes of an equal-tempered chromatic scale are equally spaced.

* https://en.wikipedia.org/wiki/Chromatic_scale

*Diatonic scale* (or heptatonia prima) is a scale composed of seven distinct
pitch classes: ``2–2–1–2–2–2–1``.

* https://en.wikipedia.org/wiki/Diatonic_scale

*Minor scale*: ``2-1-2-2-1-2-2``.

* https://en.wikipedia.org/wiki/Minor_scale

Pentatonic major scale: ``1, 2, 3, 5, 6``.
Pentatonic minor scale: ``1, ♭3, 4, 5, ♭7``.

* https://en.wikipedia.org/wiki/Pentatonic_scale

The eight degrees of the diatonic scale are also known by traditional names:

* 1st degree – Tonic (key note)
* 2nd degree – Supertonic
* 3rd degree – Mediant
* 4th degree – Subdominant
* 5th degree – Dominant
* 6th degree – Submediant
* 7th degree – Leading tone
* 8th degree – Tonic (Octave)

Intervals names:

* *Minor second* - 1 semitones.
* *Major second* - 2 semitones.
* *Minor third* - 3 semitones.
* *Major third* - 4 semitones.
* *Perfect fourth* - 5 semitones, 4:3.
* *Perfect fifth* - 7 semitones, 3:2.
* *Minor sixth* - 8 semitones.
* *Major sixth* - 9 semitones.
* *Minor seventh* - 10 semitones.
* *Major seventh* - 11 semitones.

The notes of a scale are numbered by their steps from the root of the scale.

https://en.wikipedia.org/wiki/Scale_%28music%29
  Often, especially in the context of the common practice period, most or all
  of the melody and harmony of a musical work is built using the notes of a
  single scale, which can be conveniently represented on a staff with a
  standard key signature.
https://en.wikipedia.org/wiki/Common_practice_period
  Common-practice harmony is almost always derived from diatonic scales and
  tends to follow particular chord progressions that have withstood the test
  of time.