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The white keys are taken in the order of 1-3-5-6-8-10-12 notes from the 12 note chromatic scale. Why only those selective 7 notes and not other sets and why only 7 notes?

Why not the 1-4-5-6-8-9-10 set of seven notes as each of those notes are in consonance with the root note?

Note: I am quite convinced why there are 12 notes in the octave based on the inclusion of perfect fifth but I am curious about the inclusion of other six notes, especially the dissonant ones like major second and major seventh excluding the consonant minor third and minor sixth.

So basically I have two questions.

  1. Why those seven notes?
  2. Why only seven notes?

Edit: The staff notation itself is built on the basis of the pattern of those seven notes.

The interval F-B is called as Augmented Fourth (B is the fourth white key starting from F) and the interval B-F is called as Diminished Fifth ( F is the fifth white key starting from B) when they both have exactly 6 semitones of intervals in between.

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    especially the dissonant ones like major second and major seventh excluding the consonant minor third and minor sixth - those intervals might be dissonant when you isolate them, but in the context of the major scale in its entirety, they create a smooth, 'consonant' sounding scale. A scale is more than just the sum total of its individual intervals - it has its own tonality. The keyboard represents the major scale in its entirety. – Stinkfoot Aug 26 '17 at 0:57
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    Pretty sure this is a dupe, can't pin-point it though. – Tim Aug 26 '17 at 7:50
  • There's also Why did they choose the diatonic scale?, but it doesn't have particularly good answers. – leftaroundabout Aug 26 '17 at 10:22
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The white keys are actually organized as the 7 notes of the any of the medieval modes. For example Dorian (according) is represented as d--e-f-g-a-b-c and Phrygian as e-f-g-a-b--c-d. Each mode can be played on the white keys.

In most (if not all) tunings (Pythagorean or Just for example), there are 5 steps that are approximately double the size of the other gaps. (a-b, c-d, d-e, f-g, and g-a compared to b-c an e-f). The large gaps are interpolated by the black-key notes.

It's all a historical accident so to speak.

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