I've been studying the basic math behind music theory, especially Pythagorean Temperament vs Equal Temperament, and the relationship it has with base
Hertz frequencies. I find it fascinating. Today our tuning standard is 'A 440Hz'. That means that on any modern piano/keyboard, the A key that follows
'middle C' vibrates at 440Hz. Since 440 is evenly divisible by 8, this is ideal for the western "Octive" model of harmonic resonance. However, in the
past, composers like Bach, Mozart, and Beethoven where known to use A 432Hz, and as far back as the Middle Ages, A 415Hz was in use.
This means the classical masterpieces that you hear recreated today did not sound the same when they were first composed. The chords ring clearer
today due to Equal Temperament coupled with the A 440Hz standard, but the mood shift caused by the tuning imperfections and dissonance is long dead.
Just think about that the next time you hear a timeless classical masterpiece.
Why am I saying this? To inspire the mind of readers in the same way this knowledge inspired me.
I have a programmable chromatic tuning app on my phone: Pitchlab. It allows you to adjust the Hertz standard you want and select one of the many
Temperaments. The ancient civilizations largely used Pythagorean Temperament. It won't work on modern guitars unless you adjust the fretboard.
So I decided to make my own Pentatonic Scale composed of 5 equidistant whole tones per resonance point (pentive).
To achieve this, used A 420Hz as my standard. Why?Because 420 is evenly divisible by 5 (pentive for resonance), 7, 6, 2, and 3.
To distinguish this scale from standard pentatonic scales, my tones are: V, W, X, Y, & Z.
So V = 420Hz.
420÷5=84 Hz whole intervals
From this point, I divided each value by 2 repeatedly until the values where low enough to tune my guitar.
String 1=X 294Hz
String 2=V 210Hz
String 3=Y 168Hz
String 4=W 126Hz
String 5=Z 94.5Hz
String 6=W 63Hz
Now I just have to figure out how to remove my frets.
Playing it is pretty easy. Every 3.5 or so fret spaces is whole step and whole tone (unlike standard tuning). The sound is a bit exotic; a little
bluesy, mildly ancient and moderately alien...but the frets are still getting in the way.
I call it the perfect petatonic becaues each whole step yields a wholetone.
Next project is the perfect heptatonic.
edit on 26-11-2015 by BELIEVERpriest because: corrected calculations
edit on 26-11-2015
by BELIEVERpriest because: typo