Post
by **dave432** » Thu Sep 12, 2013 11:37 am

I am a beginning, non-scientist student of the Reciprocal System and have been working with daniel's papers, the tutorial RS material, the Conscious Hugs forum, and Bruce's Reevaluation book on this site. I also study music and in the last few years have discovered the ratio system for tuning musical scales known as "just intonation." One of the things that initially attracted me to the RS was its use of ratios because I had already been familiarizing myself with them in a musical context

Learning this new approach to scales was revolutionary for me because I discovered that the ratio system is "in tune" with nature, one example being the study of phyllotaxis. Our current system of musical tuning, equal temperament, is not in sync with nature because it does not use ratios. Equal temperament solves the many tuning problems musicians can have with their instruments but at a biological cost. This is due to the musical distance between each consecutive note in the12-note chromatic scale being based on an irrational number - the twelfth root of 2. There is a 24-note equal temperament chromatic scale in the East, but the concept is the same - equal irrational number distance between consecutive notes.

I read one of daniel's replies in a Conscious Hugs forum post entitled "the 13 steps" and combined that concept with bruce's Reevaluation book concept from "note 3" in the chapter entitled "Opposites."

Here is daniel's partial forum reply from "the 13 steps" post: 'A life unit is a stable combination of material and cosmic atoms (Beyond Space and Time), so it has two, 6D systems involved, which give the life unit a total of 12 independent variables, or is 12D. 12D gives rise to 13 "speed ranges", so to transition from a 3D, spatial body in the low speed range, all the way over to the 3D, temporal body in the inverse-low speed range, requires a total of 13 steps.'

Here is Bruce's note "3" in the Reevaluation book: 'A “displacement” is used as a notation to represent atoms and particles, being the displacement (or offset) from unity. Hence a speed of ¼ has a temporal displacement of 3 (1/4-1/1=0/3; numerators (1-1=0) and denominators (4-1=3) are treated independently, not as normal fractions). Spatial displacements are put in parenthesis, so that a speed of 4/1 has a spatial displacement of (3).'

So I set out to calculate the speeds for the 13D biological life unit:

1D, 12s, 0t, 13/1 speed, 13/8 musical ratio (major sixth)

2D, 11s, 1t, 12/2 speed, 3/2 musical ratio (perfect fifth)

3D, 10s, 2t, 11/3 speed, 11/6 musical ratio (major seventh)

4D, 9s, 3t, 10/4 speed. 5/4 musical ratio (major third)

5D, 8s, 4t, 9/5 speed, 9/5 musical ratio (minor seventh)

6D, 7s, 5t, 8/6 speed, 4/3 musical ratio (perfect fourth)

7D, 6s, 6t, 7/7 speed, 1/1 musical ratio (unison)

8D, 5s, 7t, 6/8 speed, 3/2 musical ratio (perfect fifth)

9D, 4s, 8t, 5/9 speed, 10/9 musical ratio (major second)

10D, 3s, 9t, 4/10 speed, 8/5 musical ratio (minor sixth)

11D, 2s, 10t, 3/11 speed, 12/11 musical ratio (minor second)

12D, 1s, 11t, 2/12 speed, 4/3 musical ratio (perfect fourth)

13D 0s,12t, 1/13 speed, 16/13 musical ratio (minor third)

The reciprocal speeds are also reciprocal musical relationships. For example, 2D is a 3/2 perfect fifth and 12D is a 4/3 perfect fourth . A fifth (5) and a fourth (4) add up to 9. All musical reciprocals add up to 9. The musical ratios I used are expressed in an octave where the decimal equivalent is between 1.0 and 2.0.

Another example, 1D is a 13/8 major sixth and 13D is a 16/13 minor third. A sixth (6) and a third (3) add up to 9. Also, the reciprocals of major ratios become minor and vice versa. Perfect ratios remain perfect when in a reciprocal relationship.

I noticed, though, that the diminished fifth tritone was missing and that there were two perfect fifths and two perfect fourths instead of one each.

When looking for frequencies to plug in to the these ratios, I followed some advice from daniel that I might try using frequencies based on 8, because he said light starts at multiples of 8 which are then multiplied by 9 -- based on the 9 degrees of freedom of the photon.

8X9X1 = 72

8X9X2 = 144

8X9X3 = 216

etc.

I noticed that 72 Hz can be thought of as a 1/1 unison, then 144/72 = 2/1.

Then I noticed that 216/144 = 3/2.

I kept going and realized that the harmonic series was developing with the frequencies increasing by factors of 72 Hz. daniel also mentioned that the speed of light (unit speed) can be interpreted as 1 Hz, so I decided to use octaves of 1 Hz to be the unisons 1/1, 2/1, 4/1, 8/1, etc. instead of octaves of 72 Hz. All the harmonic series ratios stayed intact when I made the conversion to octaves of 1 Hz.

Here are frequencies I came up with for a 16-ratio harmonic series scale . I used 256 Hz as one of many possible octaves of 1 Hz to be the 16/1 unison:

16/1, C, 256 Hz (unison) - or think of this as another octave of 1/1

17/16, C#/Db, 272 Hz (minor second)

9/8, D, 288 Hz (major second)

19/16, D#/Eb, 304 Hz (minor third)

5/4, E, 320 Hz (major third)

21/16, F, 336 Hz (major fourth) - a perfect fourth would be 4/3

11/8, F#, 352 Hz (augmented fourth)

23/16, Gb, 368 Hz (diminished fifth) - with the ratio system, an augmented fourth can be a different pitch than a diminished fifth; in equal temperament they are identical

3/2, G, 384 Hz (perfect fifth)

25/16, G#, 400 Hz (augmented fifth)

13/8, Ab, 416 Hz (minor sixth) - same idea as augmented fourth/diminished fifth

27/16, A, 432 Hz (major sixth)

7/4, Bb, 448 Hz (minor seventh)

29/16, Bb, 464 Hz (minor seventh) - or diminished minor seventh

15/8, B, 480 Hz (major seventh)

31/16, B, 496 Hz (major seventh) - or diminished major seventh

32/1, C, 512 Hz (unison) - next octave, which will contain 32 ratios

All the frequencies are 16 Hz apart.

These ratios of the harmonic series, though, are not matching the speeds I came up with earlier, so maybe someone has some suggestions as to a next step.

"just down the road a little way, turn left, cross the drawbridge, and you will be my guest tonight."

-- directions to the grail castle. We'll have some toast.