Why the specific pattern of white keys on a standard piano?
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.
Why those seven notes?
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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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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