Now we will delve again into our box of loose, informational jig-saw pieces and connect some of the more technical aspects: Brain wave chart; tone/tone chart; use of the tempered scale (irrational numbered ratios) - regretfully suggested by Plato; and Zodiac sign/colour/tone correlation. The last will be first.
The spectrum of colour lies within a very small band on the Electro-Magnetic continuum; various vibrations, wave-lengths and cycles: the force, the energy that exist in all things. When something vibrates within the frequency of colour, it can be seen with our eyes, it possesses corporeality. If it vibrates faster (ultra-violet) it disappears: thought, telepathy, esp, radar, sonar, gamma & x-rays are up on those frequencies. If it beats slower (infra-red), then it again disappears: toward the realm of radio, t.v., and micro waves.1
The standard sign/colour correlation is RED to ARIES, around to GOLD to LEO and BLUE to SAGITTARIUS. These three FIRE signs form a equilateral triangle within a circle of 12 signs a.k.a. the Zodiac. Likewise, the signs between receive the colour appropriate to their position; e.g., LIBRA, between LEO and SAGITTARIUS, is GREEN; PISCES, between ARIES and AQUARIUS receives MAGENTA (a blend of RED and VIOLET). See figure.
Moving down the vibratory scale we reach sound, tone, and audible oddities of bombastic blasphemies. Average hearing lies within 16 to 20,000 vibrations or cycles per second. That's a good range, some animals and people hear higher - ever gone into a department store that left on their high-frequency motion detector - ouch. The common piano sounds between 27 and 4300 c/s (amazing - 400 yrs. of music played within a range covered by 88 different tones, sometimes less, within a subsequent shorter range; e.g., the virginal, harpsichord and clavichord).
PARTIAL NUMBER
NOTE ONE TWO THREE FOUR FIVE SIX EIGHT C3 130.8 261.6 392.4 523.3 654.1 784.9 1046.5 C#3 138.6 277.2 415.8 554.4 693.0 831.5 1108.7 D3 146.8 293.7 440.5 587.3 734.2 881.0 1174.7 D#3 155.6 311.1 466.7 622.3 777.8 933.4 1244.5 E3 164.8 329.6 494.4 659.3 824.1 988.9 1318.5 F3 174.6 349.2 523.8 698.5 873.1 1047.7 1396.9 F#3 185.0 370.0 555.0 740.0 925.0 1110.0 1480.0 G3 196.0 392.0 588.0 784.0 980.0 1176.0 1568.0 G#3 207.7 415.3 623.0 830.6 1038.3 1245.9 1661.2 A3 220.0 440.0 660.0 880.0 1100.0 1320.0 1760.0 A#3 233.1 466.2 699.2 932.3 1165.4 1398.5 1864.7 B3 246.9 493.9 740.8 987.8 1234.7 1481.6 1975.5 C4 261.6 523.3 784.9 1046.5 1308.1 1569.8 2093.0 C#4 277.2 554.4 831.5 1108.7 1385.9 1663.1 2217.5 D4 293.7 587.3 881.0 1174.7 1468.3 1762.0 2349.3 D#4 311.1 622.3 933.4 1244.5 1555.6 1866.8 2489.0 E4 329.6 659.3 988.9 1318.5 1648.1 1977.8 2637.0 F4 349.2 698.5 1047.7 1396.9 1746.1 2095.4 2793.8 F#4 370.0 740.0 1110.0 1480.0 1850.0 2220.0 2960.0 G4 392.0 784.0 1176.0 1568.0 1960.0 2352.0 3136.0 G#4 415.3 830.6 1245.9 1661.2 2076.5 2491.8 3322.4 A4 440.0 880.0 1320.0 1760.0 2200.0 2640.0 3520.0 A#4 446.2 932.3 1398.5 1864.7 2330.8 2797.0 3729.3 B4 493.9 987.8 1481.6 1975.5 2469.4 2963.3 3951.1 C5 523.3 1046.5 1569.8 2093.0 2616.3 3139.5 4186.0
Since both sound and colour can be represented by a frequency, then it's an easy task to establish a similarity between them. Picture the piano keyboard as a part of the electro-magnetic spectrum; colour lies somewhere way up beyond the high end. How far? Well, let's see....
Using a nice round tone like A-440 c/s we move up through the octaves: 880, 1760, 3520, ah, that's it for the piano...let's skip a few: 14080....suffice to say, it brings us to the realm of colour: 4.07 - 7.68 X 1014 c/s. Between A-440 and 483.79 X 1012 is 40 octaves; i.e., we doubled 440 40 times to arrive within the ballpark of colour. Thus 440 c/s correlates to a orangish-yellow. Test my results with a simple pocket calculator. Using my Texas Instrument SR-40, I found that 2 to the 40th power would give me a constant to transpose any tone into colour. Try it.2 Another is the 12th square root of 2: That moves you between individual tones or colours (21/12 = 1.0594631); e.g., 440 X 1.0594631 = 466.16, that's Bb.
| ARIES | RED (4.068 X 1014 c/s) | F#/Gb (370 c/s) |
| TAURUS | G (392 c/s) | |
| GEMINI | ORANGE (4.566 X 1014 c/s) | G#/Ab (415.3 c/s) |
| CANCER | A (440 c/s) | |
| LEO | YELLOW (5.126 X 1014 c/s) | A#/Bb (466.2 c/s) |
| VIRGO | B (493.9 c/s) | |
| LIBRA | GREEN (5.754 X 1014 c/s) | C (523.3 c/s) |
| SCORPIO | C#/Db (554.4 c/s) | |
| SAGITTARIUS | BLUE (6.457 X 1014 c/s) | D (587.3 c/s) |
| CAPRICORN | D#/Eb (622.3 c/s) | |
| AQUARIUS | VIOLET (7.249 X 1014 c/s) | E (659.3 c/s) |
| PISCES | F (698.5 c/s) |
Plato was frustrated on his inability to establish a "perfect system" of rational numbers to represent musical tone. That is, earlier scholars like Pythagoras had suggested such rational integers as 2/3 to represent the interval of a fifth: D to A, or 4/5 for the third: D to F#. Later investigation by Plato and others found that mathematically AND practically - actually attempting to tune an instrument with these intervals didn't work, the instrument though achieving perfect 4ths and 5ths sounded altogether discordant. In other words, some intervals had to suffer, be jeopardized for the benefit of others. Plato regretfully suggested the use of irrational numbers to represent musical intervals and a tempered scale by which to tune.3
Proof: Mathematically, 3/212 does not = 27 ; i.e., 12 fifths do not equal seven octaves (129.75 does not = 128); e.g., the tone of C (32.7 c/s) taken up through 12 fifths (C-G-D-A-E-B-F#-C#-G#-D#-A#-F-C) does not equal C taken up through 7 octaves (i.e., doubled seven times): 32.7 X 3/2 = 49.05, that's G; 49.05 X 3/2 = 73.575, the D tone. To continue up the keyboard we find high C equals 4242.825, while C (32.7 c/s) doubled seven times equals 4185.6. Utilizing the interval 3/2 - while producing a pure fifth pleasant to the ear - does not provide a set of harmonically equal-distance tones. Thus here in the West, we use the tempered scale hammered out and demonstrated by J.S. Bach. (Hear: The Well-Tempered Clavier.)4
An Octave & its tones: 1/1, 6/5 (-3rd), 5/4 (3rd), 4/3 (4th), 3/2 (5th), 8/5 (-6th), 5/3 (6th), 2/1(8th).
Or figure it this way: One third of the octave = the fifth: 1/2÷1/3 = 3/2; the fifth of a fifth = a ninth: 3/4 of 3/2 = 9/8 or C/G/D; 3/2 X 9/8 = 27/16 (6); 3/4 X 27/16 = 81/64 (3). Comparing 5/4 to 81/64 - both are 3rds - lower 81 to 80, divide by 16 = 5/4. Likewise, beginning at 4/3 (4); 4/3 X 4/3 = 16/9 (7); 2/3 X 16/9 = 32/27 (-3); 4/3 X 32/27 = 128/81 (-6). One system is Pythagorean the other Platonic.5 That is, a Pythagorean 3rd (81/64) is slightly higher than a Platonic 3rd (5/4)
Individual tones played in pairs are called intervals. Each of these tones have a frequency or beat rate (c/s or Hertz) by which they are labeled. When two tones are played together they produce a third beat originally nonexistent in the two tones; e.g., F at 349 beats against A-440, the ensuing beat rate is 7 c/s; i.e., the A contained within F beating at 873 c/s is nearly in tune with the A contained within A beating at 880 c/s. See chart below.
MINOR MAJOR
ROOT THIRD THIRD FOURTH FIFTH SIXTH OCTAVE TENTH
NOTE 5/6 4/5 3/4 6/8 2/3 4/6 3/5 1/2 2/4 3/6 4/8 2/5
C3 -7.1 5.2 .6 1.2 -.4 -.9 5.9 0 0 0 0 5.2
C#3 -7.5 5.5 .6 1.3 -.5 -.9 6.3 0 0 0 0 5.5
D3 -7.9 5.8 .7 1.3 -.5 -1.0 6.7 0 0 0 0 5.8
D#3 -8.4 6.1 .7 1.4 -.5 -1.0 7.1 0 0 0 0 6.1
E3 -8.9 6.5 .7 1.5 -.5 -1.1 [7.5] 0 0 0 0 6.5
F3 -9.4 {6.9} .8 1.6 -.6 -1.2 7.9 0 0 0 0 6.9
F#3 -10.0 [7.3] .8 1.7 -.6 -1.2 8.4 0 0 0 0 7.3
G3 -10.6 7.8 .9 1.8 -.7 -1.3 8.9 0 0 0 0 7.8
G#3 -11.2 8.3 .9 1.9 -.7 -1.4 9.4 0 0 0 0 8.3
A3 -11.9 8.7 1.0 2.0 -.7 -1.5 10.0 0 0 0 0
A#3 -12.6 9.3 1.1 2.1 -.8 -1.6 10.6 0 0 0 0
B3 -13.3 9.8 1.1 2.3 -.8 -1.7 11.2 0 0 0 0
C4 -14.1 10.4 1.2 2.4 -.9 -1.8 11.9 0 0 0 0
C#4 -15.0 11.0 1.3 2.5 -.9 -1.9 12.6
D4 -15.9 11.6 1.3 2.7 -1.0 -2.0 13.3
D#4 -16.8 12.3 1.4 2.8 -1.1 -2.1 14.1
E4 -17.8 13.1 1.5 3.0 -1.1 -2.2
F4 -18.8 13.9 1.6 3.2 -1.2 -2.4
F#4 -20.0 14.7 1.7 3.3
G4 -21.2 15.6 1.8 3.5
G#4 -22.4 16.5
A4 -23.7
This is what is called the dynamics of tone; leading to this question: Is part of the magic of music, its power to affect, inherent in the harmonic beat rate set up by the tones played? Could the combination of certain tones be utilized to instill greater self-awareness, alter consciousness and then be passed along down the mind/body experience? It is known the brain/body will attempt to replicate, imitate a beat/pulse.7
Recall, a combination of tones produce a third beat originally nonexistent in the two tones. In fact, not only is this third beat thought as a tone in itself, but due to its low pitch also represents a brain wave frequency. Therefore, could a combination of tones set-off specific states within the brain via brain waves? Could this be the answer to our question? That is, 7.3 b/s would not only correlate to the 2nd A# below A#-29.14, the lowest A# on the piano (29.14 ÷ 4), but would also activate or trigger a meditative state within the listener. See below. Thus, single, sustained tones being played off one another could set-up any harmonic beat rate desired, instilling alertness, easing stress, enhancing learning or creativity.8
BRAIN WAVES in Cycles per Second (C/S) or Hertz (Htz)
From: Michael Wagner, Journal of Music Therapy, Sum. '75, vol. 12, #2,
pp. 46-58.
.5-4 Delta - comatomic or deep sleep
5-7 Theta - light or pre-sleep
8-13 Alpha - daydreaming or inward directed attention
14-50 Beta - alertness or externally orientated attention
Another opinion: 0-4 D. 0.0
4-8 T. 7.5 meditation, removes muscular kinks
8-13 A. right brain 10.5 soothing; boosts immune system
15-30 B. left brain
| A | Ab | G | F# | F | E | Eb | D | C# | C | B | Bb |
| 27.5 | 25.9 | 24.49 | |23.12 | 21.82 | 20.6 | 19.44 | 18.35 | 17.32 | 16.35 | 15.43 | 14.56 |
| 13.75 | |12.97 | 12.25 | 11.56| | 10.91 | 10.3 | 9.72 | 9.17 | 8.66 | 8.175 | 7.72 | 7.28 |
| 6.875 | 6.48| | 6.124 | 5.78 | 5.45 | 5.15 | 4.86 | 4.56 | 4.33 | 4.08 | 3.858 | 3.64 |
Recall, 'A' is 440/220/110/55/27.5/13.75/6.875 c/s; could a sustained A produce these same affects? Some say YES! A sustained E will be soothing and is claimed to boost the immune system and enliven the right brain.9
In this, Scott Makeig of UCSD set-up a study of the "affective quality of musical intervals" and "its consistent tendency to qualitatively influence the imagination of listeners particularly, but not limited to the imagination of personal feeling."10 He found successive fifths (C/G; G/D; D/A; A/E) produced a feeling of active; successive fourths (A/D; D/G; G/C; C/F): passive; thirds (C/E; D/F#; E/G#) were sensitive; major sevenths (C/B; D/C#; E/D#; F/E): an enclosed, potent feeling. Powerful stuff; check it out.11
However, the "affective quality of musical intervals" is not a new idea. Recalling the introductory statement regarding ethos, the "secret power" of music, music's ability to affect the listener, it remains clear the research of Scott Makeig is the baby steps of science confirming what was started but lost and forgotten 3 or 4 thousand years ago.
In this regard, we have four sources that the "...priests hymn the gods through the seven tones".13 There's also the Hebrew way of speaking/chanting a particular psalm depending on the day/week.14 A bit more complex, to the other extreme, we have, from Assur ca. 1100 B.C., a music tablet comprising a song catalogue - Listing more than 360 song titles divided into 31 song types, ranging from royal hymns to work and love songs, with two song types further divided according to tunings.15 All this as an attempt to qualify, to understand music's ability to instill an emotion, a state of being.
This monograph reinstates the ancient idea of music of the spheres by establishing a historical reaffirmation of mode-to-planet through title/label. Such as: The mode OPEN relates to Jupiter; the mode CLOSED, Saturn. See Pt 1. Music theory and the use of music in the Ancient Near East is well-documented. A person born and raised in 1800 B.C. Mesopotamia heard the stories of Ea, Shamash, the Descent of Ishtar, and others. In that - a knowledge of their gods and goddesses was applied to teach music. In turn, music was used to teach math, the interworking of numbers -- what much later, 14th, 15th, 16th century A.D., was known as the Magic of Numbers, taught only to the initiate in Ancient Mystery Schools. How romantic. Rosicrucians, Freemasons. Be that as it may, this is the info. to which Pythagoras traveled "...to Babylonia, studied arithmetic, music and all the other sciences" and brought back to Greece16 -- instructed his students who in turn studied & passed it along; the info. which was subsequently forgotten, then considered & theorized by the Age of Reason, attempted by many and now with the assistance of many has been reestablished as an utility. Not merely for its therapeutic value but as a tool of empowerment, as it was used 4000 yrs ago: To attune the listener to present, the here and now.
IN CONCLUSION, the ancients listened to the voice within - they knew a good thing when they heard it. They established a means to conform planetary position into musical tones. A utility in every aspect of life: Worship, love, play, and work. See if it works for you.
Want more? How 'bout a full BIBLIOGRAPHY? Or maybe some Lab Results testing my system of planet to tone transposition. Also available is the Appendix, another step beyond Pt 1 & Pt 2, which incorporates the finest bits of archæological info plus info garnered during the research process. Together, the net result is music produced and set to acoustic or synthezied piano. That is, Musical Astrology goes from mystic probability to implemented reality. For a demonstration click on ASTRO TUNES.
Supplemental regards
Other philosophies, other disciplines of related cultures are easily incorporated into the hierarchy of 7. Here are just a few examples...
The modern-day piano has a few notes more than 7 octaves. Reviewing the planet/tone connection it seemed logical to me that there too was an octave correlation. In other words, since Saturn moves the slowest of the 7, then the lowest G octave of the piano would be ruled by Saturn. Slow planet; slow moving tones. Jupiter then would follow next with the F octave, then Mars, etc. up to Moon at the top A octave. Also...
According to Oriental philosophy, healing & meditation, our body contains 7 major energy wheels or chakras. So too we can correlate these 7 major chakras to the planetary octaves. The lowest tone, the lowest octave is given to the 1st chakra; located at the base of the spine we place Saturn. Then to the 2nd chakra we give the tone of F and the planet Jupiter. The third chakra - Mars. Etc. I strongly recommend we play planet tones w/in the planet octave, as much as can be accepted/tolerated.
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A Universal Tone -- 'F'
Touted by both Hindu and Chinese, it has connotations to the primal, cosmical force. Labeled hwang-tchong or kung by the Chinese or Ma by the Hindu could this refer to "first-mother"? As Rudhyar states... "The tone of nature on earth is F... It is the outcome of all the functional processes of the planet". And, "Ma is the root sound of nature, the Fa of the Western world...The true Chaldean name of Orpheus is Urfa, the primordial Fa"17 To confirm, the tone F refers to the Zodiacal sign of Pisces: the all, everyth18ing encompass-ing; the great ocean. Note the planet Jupiter, given the tone of F, in turn refers to Pisces. Are we then simply confirming the known? Have we discovered the process of original reference, the method of first discovery? That is, the two systems of sign/colour-tone and the planet-tone coincide, are not only confirmed by the results achieved through trial & error but by references found in the course of research. Again, plugging the planets into the sign/colour/tone chart according to their tone we arrive at this, a most interesting conclusion: Jupiter normally an "F" finds itself at Pisces - its old night ruler and current co-ruler. The Moon "A" enters Cancer; Mercury "B" falls into Virgo as it should, and Venus follows with Libra. This leaves Sun in Sagittarius, Mars in Aquarius and Saturn in Taurus and opens a fresh can of worms to be considered.
(See Planets & Signs.)
1. m=E/c2; where m is mass & c is speed of light (3 X1010 cm/s): c÷n (frequency) = wavelength;
Cogan, Sonic Design, pg 434, the electromagnetic spectrum;
Burnet, pp 107, 112n, 285-7 things are number; are made according to...(v=d/t; a=d/t2; f=ma; f=md/t2; e=fd; e=dmd/t2;e=mv2)
2. 240 = 1.099X1012; e.g., 440 c/s X 1.099X1012 = 483,560,000,000,000 c/s. COLOUR!
And each of these colours in turn, create a charge of electron Volts (eV): Red, 1.6; Orange, 1.8; Yellow, 2.0; Green, 2.2; Blue, 2.4; Violet, 2.7
3. McClain, Pythagorean Plato, pp 53-5
4. McClain, op cit, pg 169, paper-folding math;
Partch, pp 135-6; I use equal-temperment because it is;
Cogan, op cit, pg 145, the circle of 5ths
5. ibid., pp 80, 88-90. 2/3 = 6 tones of actual, visual octave; 1/1:a 1/3 of; a 1/3 of; a 1/3 of;
6. Walser, Robert "...the choice of one note..." Esquire, vol 116 #5, pg 130
7. Schafer, pp 98-9, brain/body resonates. Sympathetic vibrations?;
"Study: Patients learn even when they're out cold", Press Democrat 4/25/92;
Since the early 1990's, with the creation of this website and these pages, there have been many truly, legit scientific studies into what is now called brainwave entrainment (en-trance-ment?). Most, one can ONLY find by searching out various sci journals that cover such subjects. Be warned: The Internet coughs off repeated useless mumbo jumbo re: the four or five levels of brainwaves, but NOOO hard data.. see fn #9.
8. Or, is it the quantity or the quality of tonal interplay that generally signifies musical effect?
9. The reader is reminded of the many studies on the effects of ELFs and the Schumann research that found the Earth's electro-magnet field to radiate at 7.83 cps. That's "C";
John Wilson's book, The Mind (1980, pg 170), alpha waves credited w/ a feeling of well-being and refreshment;
Here's two articles (hard data) re: brainwave entrainment...
"Brain wave synchronization and entrainment to periodic acoustic stimuli", Neuroscience Letters, Aug '07, pp 55-60;
"Alpha Brainwave Entrainment as a Cognitive Performance Activator", Cognition, Brain, Behavior, Sept '13, pp 249-261. They used a 10.2Hz frequency, a pulse going 10.2 beats a second. Relates to "E". And was found "... to have a positive effect on cognitive performance...", pg 257. That is, it enlivens the BRAIN!
10. Clynes, chap xii (Scott Makeig) pp 235, affective quality, definition; 241-2, interval affect explained.
11. ibid., chap xii, Affective vs. Analytic Perception of Musical Intervals; pp 229, et. al.
12. Crossley-Holland, op cit, pp 14, 17;
Farmer, op cit, pg 126, all that issued from the scheme of "cosmical music", the harmony of the spheres, the theory of numbers, the doctrine of the ethos, & musical therapy would appear to have been introduced to the Greeks by Pythagoras or Pythagoreans from Babylon & Egypt - Farmer, Influence of Music from Arabic Sources, p 5;
Grove's, op cit, (Jewish music) on theory of ethos: vol iv, pg 623, "...each of these modes is capable of evoking in the listeners a specific ethos." - emotion. "It encompasses both the expression & effect of these modes." - from R. Lachmann, Musik des Orients, Breslau '29;
Winnington-Ingram, pp 8, 14, 14n;
Helmholtz, pg 551;
See also pp 56-63 of M. West's 'Music Therapy in Antiquity' and A. Voss's 'Marsilio Ficino', particularly concerning Ficino's contemporary Ramos de Pareja, pg 168. Both in Music as Medicine, Peregrine Horden, ed, Ashgate, 2000
13. Stege, pg 126, "...7 tones.";
pseudo-Demetrius Phalereus, de elocutione (On style), pg 71, "...7 vowels.";
Dionysius of Halicarnassus, History of Music, pg 53;
Seligmann, pg 245; see also "the Complete Yoga Book" by J. Hewitt, pg 446
14. Lewittes, op cit, pp 274-5, psalm/day
15. Kilmer, "A Musical Tablet..." pp 69-80. See also "Music", International Standard Bible Encyclopedia, pg 447; AS 16 (1965), pg 267n & PAPS 115 (1971), pg 137n
16. Guthrie, loc cit, "...to Babylonia, ..."
17. Hamel, pg 87, hwang-tchong; pg 191, maternal power of the centre;
Crossley-Holland, op cit, pg 45, "huang-chung, literally 'yellow bell', foundation tone will be conventionally taken as fa (F)." Egypt: Maat??? Semite: Matu???;
Schafer, loc cit, "yellow bell" estab. 239 B.C.;
Rudhyar, pp 46, 62
18. The suffix of -ing possesses corporeality. Receptivity/Yin(g)ness. Everything - ing = eve-r(h)yth(m). Moving w/ life? Quickening?