12 Sounds, 21 Symbols and 15 Keys – by Mike Overly

Math ParabolaOne octave has 12 sounds and 21 letter, tone, and staff note symbols: 7 (natural) + 7# (sharp) + 7b (flat) = 21 symbols. Now, the question becomes: are there 21 major scales?  The simple answer is yes – but to spell them we need more than 21 symbols. For example, we can easily play a G# major scale, but to spell it we need a double sharp symbol: G# A# B# C# D# E# F##.  The same is true for the Fb major scale: easy to play, but to spell it a double flat is needed: Fb Gb Ab Bbb Cb Db Eb.  Said a different way, the reason why there are only 15 traditional major scales is because there are only 21 symbols from which to spell – and you can only spell 15 major scales with those 21 symbols! In other words, to spell any other major scales, not listed below, we would need additional double sharp and double flat symbols.

Notice that even though each major scale has a different letter spelling, they all have the same tone number spelling: 1 2 3 4 5 6 7. Traditional music theory call tone numbers, scale degrees. The different letter spellings are the result of applying the major scale interval pattern (2 frets – 2 frets – 1 fret, 2 frets – 2 frets – 2 frets – 1 fret) to each of the 15 traditional major scale letter spellings. In other words, there are 15 major scales, in 15 major keys, that are known by their 15 major key signatures. See Guitar EncycloMedia page 15.

15 Major Scale

For now, key will simple be the letter of tone 1, also known as the root or the tonic. For example, if we are in the key of C major, then the letter C is tone 1, and the key signature is 7 naturals. In the next lesson we will learned how to connect 12 sounds and 21 symbols on the fretboard, in a perfect 4th and perfect 5th interval sawtooth pattern. But for now, let’s illustrate this 4th and 5th interval pattern as a “circle” of 15 perfect 4th and perfect 5th related major keys and relative minor keys.

Parabola

It’s important to remember that up a perfect fourth arrives at the same letter as down a perfect fifth, but sounds one octave higher in pitch. In contrast, down a perfect fourth arrives at the same letter as up a perfect fifth, but sounds one octave lower in pitch. This is known as the rule of nine. What becomes apparent as we look at this new parabolic view of of 4ths and 5ths, is that the “circle” of 4th & 5th intervals is not a circle at all, but rather a parabola! Simply stated, a parabola is two curved lines that start at the same place, in this case C, but end at two different places, in this case Cb and C#. The parabola view shows us an important fact — the only way to create a circular motion is to modulate (change keys) at one of the three enharmonic keys: Db/C#, Gb/F# or Cb/B and continue in the same direction toward “home.”  See Guitar EncycloMedia page 42.

The point of all this will become more meaningful when we begin to explore harmony progressions.

’til next time, have some parabolic fun, no matter what key you’re in… I’ll be listening!

http://www.12tonemusic.com/guitar/encyclomedia

One Response to 12 Sounds, 21 Symbols and 15 Keys – by Mike Overly

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