Tonal 1.1


	"Music School" ...a huge thanks to Brad Gregory for setting me on this path of discovery...

Frequency Ratios Expressed in Prime Numbers	A Unison is 1/1 An Octave is 2/1 An Octave and a Fifth is 3/1 A Perfect Fifth is 3/2 A Perfect Fourth is 4/3; however, "4" is not a prime number. The accurate description of a Perfect Fourth is 2X2/3 ("X2" meaning up one octave). Since a lower prime number always represents a sound wave to which the wave represented by the higher number will act in a subservient way, we can define the top note ("2" up an octave) in the fourth as the tonic with the bottom note ("3") functioning as the fifth. Esoterically speaking, either note can be viewed as the tonic - it depends upon which tonal structure you set up in your mind. If you view the bottom note in the fourth as the tonic of its own key, then the top note will have extreme "distance" as the lower prime number (2) is exerting a lot of pull. It wants to be the tonic - to make the lower note (3) subservient. The brain naturally identifies the top note as the tonic (lower prime number) with the bottom note being close in distance. Our educational training, however, has identified the bottom note as the tonic with the top note being considered a consonant Perfect Fourth.

Do-Re-Mi	...remember that scale we were all taught? C - D - E - F - G - A - B - C Perhaps the note F was instinctively added to produce an inherent modulation within the scale from the "key of C" to the "key of F" (and back) so that a tune derived from the scale in essence contains two "chord changes". The note within the tonality of C has so much pull that it becomes the tonic of a new key (F represented by the prime number of 2 and C by 3). Therefore our C scale has a built in chord progression (unless one wishes to view F as the tonic at all times).

Speaking of "Pull"...	We can add depth to our perception of tonality by hearing the distance of all 11 notes from their tonic (and not thinking so much in terms of "consonance" and "dissonance"). You can make your own system which will give you the freedom to use and understand all 12 notes according to how you hear their distance. I would say the pentatonic notes (for the key of C): D,E,G,A are close in distance; their inversions (Bb,G#,F,Eb) have significant distance from the tonic and the tritone (F#) would be in-between. I would put the note B in-between the pentatonic notes and the tritone. C# would be far away. It's a bit like a solar system.

The Tonal Cone	Once you've established a yardstick of tonal distance within a key, you can apply your system to all keys. Consider this: any note in a chromatic scale can be the tonic. The tonal distance between a chromatic scale in a "key" and a chromatic scale in any other key is always zero. Triads, on the other hand, have varying distance from each other depending on the keys (or tonal centers) involved. So we could make a 3-D cone-shaped graph which would give us an idea as to the tonal distances between keys in varying degrees of tonal density. The 12 tonics would be plotted around the circle (where the ice cream ball sits) using the circle of fifths while your 12 "tonal distance yardsticks" would run down to merge at the point. The guideline is: "The more notes there are in a tonality, the less is the effect of modulation from another tonality with similar degrees of complexity or density."

"History Class"	A good exercise is to listen to any music to determine the number of notes (out of 12) being used in a tonal center (key) and the extent to which keys are being used around the circle of fifths (not thinking of key signatures in the traditional sense)(our C scale can be viewed as shifting between two tonal centers). Here are a couple of important statements to "chew on" : Miles: "Chick knows where the tonic is" Wayne: "We don't have to build our musical world out of thirds."