SVP Universal Cosmology

Addendum 7

Pond's Original Notes
on the Scale of Infinite Ninths

 

 

"A truth's initial commotion is directly proportional to how deeply the lie was believed. It wasn't the world being round that agitated people, but that the world wasn't flat. When a well-packaged web of lies has been sold gradually to the masses over generations, the truth will seem utterly preposterous and its speaker a raving lunatic."
~~~Dresden James

[updated 06/06/09]
© Dale Pond, 2007
Delta Spectrum Research
921 Santa Fe Avenue
La Junta, Colorado 81050
720-249-2731

(This is an incomplete presentation. Not every item is as it will be in the final version of these documents. Until the final version is published use the information presented herein at your own risk. In the meantime please peruse the SVP Recommended Reading List for additional background information.)
Section Parts and Addenda

Part 01 - Overall General View
Part 02 - Origin of Polar States
Part 03 - Polarity Creates Rotating Vortex
Part 04 - Rotation on Three Planes
Part 05 - Three Rotating Planes Become Spheres
Part 06 - Formation of Cubes
Part 07A - Origin and Formation of Matter - Part 1
Part 07B - Origin and Formation of Matter - Part 2
Part 08 - What Vibration Is. - Part 1
Part 09 - What Vibration Is. - Part 2
Part 10 - What Sympathy Is
Part 11 - SVP Music Model
Part 12 - Russell's Locked Potentials
Part 13 - Rotation from Vibration/Oscillation
Part 14 - Keely's Mysterious Thirds, Sixths and Ninths
Part 15 - Dissociating Water Acoustically
Part 16 - Electricity and Magnetism
Part 17 - Gravity
Part 18 - Mind as an Engineerable Force
Part 19 - Musical Dynasphere, Historical
Part 20 - Musical Dynasphere, Current
- - - - - - - - - - - -Addenda - - - - - - - - - - - -
01 - Bjerknes Effect
02 - Chart of Locked Potentials
03 - Ether
04 - Origin of Matter
05 - Indig Numbers
06 - One Phase of Keely's Discoveries...
07 - Pond's Original Notes on the Scale of Infinite Ninths
08 - Laws of Being
09 - Table of the Elements
10 - Keely's Forty Laws
11 - Russell's Laws and Principles
12 - What Electricity Is.
13 - Puharich, Water Dissociation via AC
14 - As a Man Thinketh
15 - Genero-Radiative Concept
16 - The Action of Force is Spiro-Vortex
17 - Russell's Optic Dynamo-Generator
18 - Etheric Vibratory Scale
97 - Disclaimer
98 - Footnotes
99 - Compendium and Definitions

Pond's Original Notes on the Scale of Infinite Ninths

 
 
 
2002, 08/31
I’ve been playing around with that interval chart this morning. I "discovered" it only addresses counting by steps. This works pretty well but does not address frequency, etc. When frequency is applied it does not work as expected but totally unexpected. So there is something of importance to be discovered here, I presume. My thoughts are running to things concerning the very most basic premises of what intervals are or supposed to represent. The issues are so convoluted they are appearing as a paradox and the solving of paradoxes always leads to new revelations. The problem is in the definition of "step". Each step throughout the octave has a different size - and we know we can't add apples and oranges. Steps are a generalization and not arithmetical certainties.

For instance if two Mn2 (16:15) are added together AS STEPS they equal a Mj2 (9:8). Very neat.

But if we add 16:15 + 16:15 we get 32:15 which is a Mn9th!!!

The error is apparently the result of a misinterpretation of what 16:15 is. The reality is a Mn2 is NOT 16:15 (in this case). It is 1/15 plus the whole of 1:1 or 15:15 (Unison) which equals 16:15. So 1/15 + 15:15 = 16:15.

Since a Mj2 is 9:8 we must find the common denominator which is 120. 1/15 * 120 = 8. A Mn2 is 8 larger than Unison (120/120)+8/1 = 128/120. So each Mn2 step = 8. Which suggests a Mj2 is 8 larger than a Mn2 which works out to 136/120 where a Mn2 is 128/120. However error begins to creep in due to nonequivalence of fractional parts. In this case the error is 1/120. Because 16:15*120=128/120 and 9:8*120=135/120.

The bottom line is
a Mn2 = 1/15 (8/120) over and above Unison
a Mj2 = 1/8 (15/120) over and above Unison
a Mn2 step (from Unison) = 8/120
a Mj2 step (from Unison) = 15/120
The Mj2 which we consider as 2 X Mn2 is actually smaller than this by 1/120 of the octave.

The two intervals are not octave harmonically equivalent or proportional by 1/120th of the octave.

It is presumed similar differences exist throughout the interval chart. Hope the arithmetic doesn't turn you two* off. This may not seem important and may even seem a waste of time. But I submit neither premise is correct. Musicians count by steps because that is the way we've been taught - and it works for practical music purposes. The fact is, steps are unequal and disproporational arithmetically and therefore when we think they create harmony they are actually creating discord. In such suppositions we are operating from a place of illusion and nonreality and therefore we find ourselves fumbling around in the dark and not getting what we want or expect.

*2/23/05: the bulk of this early writing was done via email with Lynda Brazier and Luigi Martinelli. About the time I began mentioning the Scale of Infinite Ninths Luigi gets all upset and antagonistic eventually leaving the conversation. A year or so later he completes his book on music theory, shared it freely over the net and I have not read any of it.

Harmonic / Enharmonic Scale

All difference tones are base 2^3 and will not create discords.

Octave    C" 240/120
Minor 8th Cb 232/120
Major 7th B  224/120
Minor 7th Bb 216/120
Dim.  7th A# 208/120
Major 6th A  200/120
Minor 6th G# 192/120
Major 5th G  184/120
Minor 5th Gb 176/120
Major 4th F# 168/120
Minor 4th F  160/120
Major 3rd E  152/120
Minor 3rd D# 144/120
Major 2nd D  136/120
Minor 2nd C# 128/120
Unison    C  120/120

2002, 09/01
Below is a "new" scale (subject to modification) that accounts for harmony in such a way that all notes are equivalent and proportional. Any note and its immediate harmonics will form harmony with all other notes and their immediate harmonics. No unresolved beats will occur - unresolved beats are a source of dissonance. A beat will resolve when it forms harmony with the notes around it. All beats generated with this scale are multiples of two as are all the notes as also immediate harmonics. So any beats will resolve (form harmony) between themselves and the surrounding notes. If we use conventional music intervals beats occur which are unresolveable which means they may have a base of 1, 2, 3, 5 or 7. These odd numbers do not form harmony or unison with anything other than themselves. Theoretically resolved beats will "disappear" to the ear as they merge with neighboring sounds. I don't know this for a practical thing but arithmetically and vibratorily this appears to be the case. The proof will come in the actually playing and hearing of it.

PS: As far as I know my idea of resolved and unresolved beats is new and unique. I've not read of it in any music theory I've come across. Gee! Maybe I could patent this and charge a fee for it - or I could present it here so we can all get on with some serious and legitimate research of solving some problems out there and creating new possibilities!

-- The Dale Scale --
Interval Note   cps/120
Octave    C""" 2048
Minor 8th Cb   1920
Major 7th B    1856
Minor 7th Bb   1792
Dim.  7th A#   1728
Major 6th A    1664
Minor 6th G#   1600
Major 5th G    1536
Minor 5th Gb   1472
Major 4th F#   1408
Minor 4th F    1344
Major 3rd E    1280
Minor 3rd D#   1216
Major 2nd D    1152
Minor 2nd C#   1088
Octave    C""' 1024
Minor 8th Cb    960
Major 7th B     928
Minor 7th Bb    896
Dim.  7th A#    864
Major 6th A     832
Minor 6th G#    800
Major 5th G     768
Minor 5th Gb    736
Major 4th F#    704
Minor 4th F     672
Major 3rd E     640
Minor 3rd D#    608
Major 2nd D     576
Minor 2nd C#    544
Octave    C""   512
Minor 8th Cb    480
Major 7th B     464
Minor 7th Bb    448
Dim.  7th A#    432
Major 6th A     416
Minor 6th G#    400
Major 5th G     384
Minor 5th Gb    368
Major 4th F#    352
Minor 4th F     336
Major 3rd E     320
Minor 3rd D#    304
Major 2nd D     288
Minor 2nd C#    272
Octave    C'''  256
Minor 8th Cb    240
Major 7th B     232
Minor 7th Bb    224
Dim.  7th A#    216
Major 6th A     208
Minor 6th G#    200
Major 5th G     192
Minor 5th Gb    184
Major 4th F#    176
Minor 4th F     168
Major 3rd E     160
Minor 3rd D#    152
Major 2nd D     144
Minor 2nd C#    136
Octave    C''   128
Minor 8th Cb    120
Major 7th B     116
Minor 7th Bb    112
Dim.  7th A#    108
Major 6th A     104
Minor 6th G#    100
Major 5th G      96
Minor 5th Gb     92
Major 4th F#     88
Minor 4th F      84
Major 3rd E      80
Minor 3rd D#     76
Major 2nd D      72
Minor 2nd C#     68
Octave    C'     64
Minor 8th Cb     60
Major 7th B      58
Minor 7th Bb     56
Dim.  7th A#     54
Major 6th A      52
Minor 6th G#     50
Major 5th G      48
Minor 5th Gb     46
Major 4th F#     44
Minor 4th F      42
Major 3rd E      40
Minor 3rd D#     38
Major 2nd D      36
Minor 2nd C#     34
Unison    C      32

2005, 01/04: This scale was initially called “The Dale Scale” at that time for lack of a better name. That name was changed to “Scale of Infinite Ninths” some time in 2003.