File talk:Major triad.svg
This picture has errors as far as I can determine.
If a given note X has a frequency of x hz., then that means that the note an octave above X is 2x hz.
For centuries, the 12 notes comprising the chromatic octave have been equalized.
Thus if a note Z is z hz.,, then that means the note an octave above Z is 2z hz.
The only way this can be true is if there is a logarithmic relationship between X and Z, and hence their respective frequencies.
In western music, we have a chromatic octave of 12 notes.
That means that the frequency of each note is the frequency of the one immediately previous times the twelfth root of 2.
To get a perfect 5th, we have 7 semitones. So we multiply the twelfth root of 2 by itself 7 times.
This means that a perfect 5th has a frequency of 1.4983070 times the tonic, and not 1.5 times more.
A major third, then, which is 4 semitones above the tonic, would have a frequency of 1.224620 times the tonic.
If our tonic has a frequency of 200 hz, our perfect 5th would have a frequency of 299.6614 hz, and its major third would be
244.924 hz. or thereabouts.
John A. Matheson
Band Leader, the Dorks.
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