Musicology

This page contains excerpts from conversations with musicologist Roger Blumberg:  TheCipher.com
There is probably a deep connection between Spectrum Harmonics and musical harmonics but the subject awaits research.

The reader is encouraged to contribute.

In response to [ Bases article]:

When you say "harmonics", you are speaking of classical physics yes? i.e. harmonic series, partials, calculation of intervals, overtones, undertones et al? -- at least initially?
What background/topics/fields would one need to understand your stuff?
And, where's the departure from classical physics, which is metaphysics, which is classical?

Yes! you have the right idea! Periodic functions, fundamentals, Fourier analysis and such are all valid for Spectrum science, even though we don't know what is even vibrating.

This site: (site is gone) gives a partial list of harmonics but is in poor arrangement. Also it only goes down to the 24th, which is 360÷2÷3÷4. Spectrumology goes down to 360÷9÷9, and this is only the radix spectrum (first order).

The astrological harmonics were rediscovered in modern times by an Englishman named John Addey, but were the basis for Hindu and Semitic astrology long before the Hellenites corrupted it.

Here is a page which discusses the Harmonic biology
I have not examined this material closely but truth be told, it makes no sense to me. It is based on the work in this book:
Schonberger, M.,(1976)"The I Ching and the Genetic Code", which is the seminal work in the field.

Roger said:
> The octaves are 12°, 24°, 36°, etc -- rather than 13, 25, etc.
These numbers are familiar from Harmonic Astrology, in which;
12° is the 532 harmonic (360÷5÷3÷2) AKA Quintile Trine opposition.
24° is the 53 harmonic (360÷5÷3) AKA Quintile Trine.
36° is the 52 harmonic (360÷5÷2) AKA Quintile Opposition.

What you described here is a triad of harmonics. The 52 and 53 are discrete, but the opposition links them harmonically. This astrologically is called a "Quincunx". Part of the mystery of 6 (3÷2).

For example, 3/5 ths of a phase (lambda) is 360/3/5 which is 24° (degrees). In my harmonic math this is "35". Now that you know this, you could translate all harmonic numbers to degrees of angle. Except that the wave is a periodic function which means 24, 48, 72, 96, 120, 144 and168° are all the same phase angle.

"The Cipher" is a "counting-number translation" of Western music theory, chord construction, etc, where music's typically meaningless numbers become meaningful -- to anyone who can count to twelve.
e.g.
Standard chord formula -- Major Triad = R, 3, 5
Cipher chord formula ----- Major Triad = 0°, 4° , 7°

They're "half-step" value (or chromatic) numbers. The translation key is a "zero-based" chromatic number-line (rather than starting at 1, very important), 0° through 12°, marking the 12 chromatic steps of any chromatic scale. The octaves are 12°, 24°, 36°, etc -- rather than 13, 25, etc.

The Cipher formula numbers are applied to the Guitar fretboard -- as illustration vehicle, rather than keyboard. Works like a charm. Bottom line, you don't have to learn how to read staff notation in order to get "the goods", just use "real" (counting) numbers. It's pretty pedestrian stuff, the number translations, but very functional -- as a learning and teaching tool.

> Just for your files;
> The "tri-tone" interval [being three whole-"tones" wide](Aug-4th/Dim-5th),
> AKA the "Devils interval", is 6° using zero-based chromatic numbers -- i.e.
> 6 half-steps, cuts the octave in half 0°_ 6°_ 12°
Hmmm... I wonder if my 8 sequence harmonic is analogous the octave?
> It also lies right between the so called "Perfect" intervals P-4th and
> P-5th. --- P-4th__aug-4th/dim-5th__P-5th

I don't know what this means. What I have been looking for all my life is a degree by degree description of chords and their associated "feeling". this would help me to describe chords as harmonics and appeal to the more "proof oriented" viewer.
Calculating where every wave of a chord coincides in the period is a huge job, I don't have it in me.

> I spent several hours on the Set Theory page but failed to make any sense of
> it (trying to understand the set of 12).

Number the tones of any chromatic scale 0-11 --- 12 is the octave of 0.
On the clock-face analogue the clock reads 0 to 11 but 12 would be sharing the 0 spot (they're synonymous, octaves, like all C notes or all A notes), so that single spot functions as both 0 and 12.

The inversion numbers (representing inverted pairs of intervals), e.g. 2-10, 5-7, 3-9 . . . all add up to 12 (because there's twelve chromatic steps [half-steps] per octave). In classical music theory this is like saying "up a 4th/down a 5th" they're pairs of intervals that add up to one octave, called inversions.

Examples:

Number the tones of any chromatic scale 0-11 --- 12 is the octave of 0.
On the clock-face analogue (if it was on that site) the clock reads 0 to 11 but 12 would be sharing the 0 spot (they're synonymous. Octaves, like all C notes or all A notes), so that single spot functions as both 0 and 12.

Chromatic;     inverted interval pair 5-7:
C												C
C	C#	D	D#	E	F	F#	G	G#	A	A#	B	C	C#	D	D#	E	F
These Chromatic numbers are the kind used in Pitch-Class Set Theory					F							C					F
												0	1	2	3	4	5
					7	6	5	4	3	2	1	0
					0	1	2	3	4	5	6	7	8	9	10	11	12

Diatonic -- (seven tone) inverted interval pairs -- "up a 4th/down a 5th".
Here 4-5 are inverted interval pairs (always add up to 9 using seven tone scales and 1-7 numbers (THE COUNT STARTS AT 1), here the octave is 8, so 1 and 8 are synonymous)

Chromatic -- (twelve tone) inverted interval pairs -- "up 5/down 7"
Here 5-7 are inverted interval pairs (always add up to 12 using twelve tone scales and 0-11 numbers (THE COUNT STARTS AT 0), here the octave is 12, so 0 and 12 are synonymous)
Pitch-Class sets and atonal music analysis use these later chromatic numbers (zero-based chromatic numbers and using Modula 12 arithmetic)

> What I need is a list of the frequencies of the notes, then I can extract
> their ratio relative to a fundamental, then I can calculate the degree
> periodicity of interference and maybe it will fall into place then.

Subject: Re: pitch-class set numbers

> Sorry Rog, no breakthrough on this. I am looking for a revolutionary way to
> understand acoustic waves and this doesn't do it for me. Maybe in the future
> I can spend time picking at this stuff until it yields.

I was actually hunting down some frequency tables (of chromatic scale tones) for you. I got pretty far in the hunt so let me know if/when you want. One thing to be aware of are the units of measure when dealing with acoustics and "calculation of intervals" (frequency ratios). There are three "temperaments": Pathagorean, Just, and Equal -- and all will yield slightly different values. The unit "Cents" is generally prefered over frequency. One cent is equal to 1/100th of an equal tempered semi-tone. 100 cents per semi-tone, 1200 cents per octave. The frequency ratio corresponding to one cent is 1.0005778