05/21/2025
The Tonal Octave is not diatonic and does not contain 7 notes. The tonal Octave resonates at the 9:8 ratio on the note we call the 9th. The 9th and 9:8 ratio complete the Octave resonance as a double of the 3:2 ratio.
The Octave is note the 8th note it is double the tonic root harmonic as 2:1 4:1 and 8:1. The Octave is the 2nd 4th and 8th harmonic overtone.
Half of the Octave is 3:2, what we call the perfect 5th. The P5 is half of the Resonance octave but is not half of the Octave. The P5 is twice as the 9:8 ratio.
In the 5th is the prime 3 of the Resonance. Half way below the 5th is the prime 5 as the Major 3rd. Half way between the upper Octave and the 5th is the prime 7 and the dominant 7th tone
