Why are there 7 white and 5 black keys per octave on the piano?

A comment I posted at:

http://math.stackexchange.com/questions/11669/mathematical-difference-between-white-and-black-notes-in-a-piano/11873#11873

The math of frequency relationships here is sound (pun intended) but they don’t help explain the white vs black key piano layout.

Here’s the historical imperitive that led to this layout for “Western Music”.

First consider the major triad:

root + third + fifth notes of the “diatonic scale”.

They follow the harmonic series:

  1. root
  2. octave (doubling of root frequency)
  3. fifth (triple of the root – 3:2 relationship to the octave)
  4. double octave (4x)
  5. 10th (double octave of a third)
  6. octave fifth

The Bugle notes: These are notes a static length of tubing can produce by blowing into it and producing standing resonant waves of 1x, 2x, 3x, etc.

Combinations of these notes create frequencies that make choirs sound heaven-ly. The frequencies align and blend into pure complex vibraations that are the sum and the differencies (harmonic overtones) of these relationships.

Choirs can tune themselves dynamically to create these frequency alignments that are percieved as being perfectly consonant. Upbeat western music focus on the 3 major chords found in the diatonic scale:

  • 1+3+5 root major chord – white keys C – E – G 4+6+1
  • 4th chord – white keys F – A – C 5+7+2
  • 5th chord – whote keys G – B – D

The basics of western folk music are the 1 – 4 – 5 sequences of chords. Learn C, F and G on a guitar and you can play the bulk of the classic Country song book.

Put the notes of these chords into a scale and you get that row of 7 white keys: C – D – E – F – G – A – B (repeat until you can’t hear it).

So, they western scale is based upon frequency relationships that make combinations of notes “ring” in consonance in it’s purest form… like the Gregorian Chants of the Roman Church.

So, a basic “western keyboard” could be made from just these 7 notes repeated across the frequency spectrum. Look at the layout of a Greek Lyre (a harp) and that’s what you will find. A sequence following the diatonic scale which sounds pleasant if you just strum across the strings due to the tuning of even multiples (adjusted by octaves).

OK… now adding the black keys is a compromise of tuning specific notes so that you can build these 1+3+5 chords from any starting point and thus play a song adjusted up or down to any starting point. The piano will never achieve that sonic mathematical glimpse into the “music of the spheres” that the self-adjusting choir can to make a chord mathematically perfect in alignment but it’s the “keyboard” for the modern composer… the effective “musical qwerty” that a composer or a pianist begins to visualize chord “shapes” as hand positions.

With a lot of practice a pianist can pre-visualize sound in terms of finger and hand movements much like a solid touch typist starts to set words and sentences as a sequence of movements.

The addition of the black keys was called a “Well Tempered” tuning and Bach was one of the first composers to create whole bodies of compositions that worked through the Major and Minor keys of the 12 scales that you noticed intially when inspecting the keyboard.

If you look into other musical cultures you will find a different approaches to standardizing sound relationships that do not focus on the 1 – 4 – 5 chords. This music to a culturally trained western ear is less predicatable in nature and that lack of predictablility can make the music frustrating or exciting… music “speaks” to us in terms of pure sensory inputs that can move, excite, bore or confuse us.

So, the piano keyboard is designed to be the perfect delivery system for an individual to produce the range of complexity that western music has achieved.

The modern keyboard synthesizers are now able to produce the full range of the western orchestra in terms of “instruments” and I’m hoping someone create one that micro-adjusts notes based upon the surrounding context… shifting a note up or down slightly from the “well tempered” compromise to the pitch that makes a chord “ring” and produce the upper harmonic overtones that make a great orchestra truly “heavenly”.

Maybe it’s already been done.

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