MUSIC VS SOUND: MATHEMATICAL LOGIC FOR A CORRELATION THEME A metre is a measure of length. It is the basic unit of length in the metric system and in the International System of Units (SI). It is defined by the International Bureau of Weights and Measures as the distance travelled by light in absolute vacuum in 1/299,792,458 of a second. A nanometre is a unit of length in the metric system, equal to one thousand-millionth of a metre, which is the current SI base unit of length. It can be written as 1 m / 1,000,000,000. Light waves have wavelengths generally referred to in nanometers. A perfect fifth, in Pythagorean terms, is calculated as having a ratio of 3:2 to the reference octave. Put another way, the frequency a perfect fifth above a given tone vibrates at 1.5 times the frequency of the tonic. So (TONIC FREQ) x (1.5) = (PERFECT 5th FREQ) where the 5th is assumed to be the higher tone. We have to be specific about the 5th being the one above the tonic, because a tone exists below the tonic at an interval of a perfect fifth distant. That tone in fact is the harmonic fourth of the tonic scale. All reference harmonic interval expressions in music are assumed to be oriented in accordance with increasing pitch. In the real world this means that if we have a tonic note C256Hz, the perfect fifth is 256 x 1.5 = 384. Therefore the G above the C is G384Hz. And so on. (Greater detail has been presented in a prior post.) Lets apply this computation to light just for kicks. As mentioned, light travels at 299,792,458 meters per second. So pretty slow. ;) As nothing can travel in excess of this speed, we’ll establish this “optic octave” as the highest theoretically possible. Its optic root tonic would be half this value: 299,792,458/2 = 149,896,229. Now all we have to do is apply the Pythagorean ratios as detailed in previous posts to generate values for each harmonic interval, and thereby derive our Optical Music Scale. Starting with the perfect 5th, we multiply 149,896,229 by 1.5, which gives us 224,844,343.5 as the G. Below are the results derived via applying the Pythagorean ratios used in music: C 1:2 149,896,229 C# 16:15 159889310.93 D 9:8 1.125 D# 6:5 179875474.8 E 5:4 187,370,286.25 F 4:3 199861638.67 F# 45:32 210791572.031 G 3:2 224844343.5 G# 8:5 239833966.4 A 5:3 249827048.33 A# 9:5 269813212.2 B 15:8 281055429.38 C 1:1 299792458 Remember, these values are presently expressed in meters per second. Right away we have an issue, that being that the velocity of light is a universal constant, which we have allowed to be adjusted so as to permit correlation. But since it makes things easier its okay. Right? No. I’m sorry. No. If we are attempting to derive a common denominator for purpose of demonstrating correlations of principle, we must implement said principle(s) from the beginning and operate in accordance throughout. We don’t just ‘theoretically adjust’ a universal constant. So how do we justify changing the numbers? Answer: by changing the units in accordance with the known velocity. Most obvious example would be changing the number to 186,000. Almost everyone will immediately understand that this number describes velocity in units of miles per hour. And that’s how its done. But what if we don’t know the units that go with those particular numbers? Doesn’t matter, we know they are by definition ‘distances’, and that none of the numbers are negative values, so we don’t need to know the actual terms, we can just call it a ‘unit of certain length’ and leave it at that. Capice? But we have another immediate problem. Wave frequency is expressed in terms of vibrations per second. That’s not velocity, that’s periodicity. A vibrating guitar string doesn’t travel…well, back and forth, sure. Does that mean we have to determine the actual distance the center of the string travels in each individual vibration? Because each subsequent vibration gets smaller, in accordance with properties of the string, the guitar, room temperature, integrity of oscillation, limits of distortional torque…WTF??? No. I’m sorry. No. Lets back up. What are we seeking again, specifically? The correlation between the series of harmonic intervals generated by the fundamental frequency. Right. Since we know light speed is a constant, we know that no matter what we do to the term, we cant change the speed it represents. So we can adjust the numerical value as long as we adjust the units to reflect the correct speed. Most obvious example is if we want to change the number to 186,000, we change the units to ‘miles per hour’ – 186,000 mph is the same speed, in different terms. Ah… So whats the most obvious common factor here? Right away both are expressed in meters per second. Sound travels at 343 mps, so we just divide each into the other to obtain each in terms of the other. 299,792,458/343 = 874,030.4898 meaning light travels at 874,030.5 times the speed of sound. Conversely, 343/299,792,458 = 1.1441 x 10^-6, or .0000011441 so sound travels at .00000115 times light. So if we propose a numerical value of 149,896,229 as our light part, we must apply the same process by which we derived that number to the sound part. In this case I just divided it in half, since the octave below a sound tone is half the frequency of the reference tone. In this post I’ve established our scale as a sort of scientific/Pythagorean hybrid, so the notes can be expressed in simple whole number ratios. Some call this Verdi tuning, which is…close enough. The primary notes are: C 256 D 288 E 324 F 352 G 384 A 432 B 486 C 512 C256Hz is ‘middle C’ in this tuning. That means its four octaves below the high C on a piano. So if we want a correlation establishing light speed as the highest C note (of course this is not the case – I’ll address this aspect in a future installment) we just reduce light speed by four octaves, or cut it in half four times in a row: 299792458/2 149896229/2 74948114.5/2 37474057.25/2 = 18737028.625 Hz as the theoretical light wave frequency analogous to middle C256Hz. Remember, these are equivalencies based on the assumption of the specified ratios and reference tones of our musical scale, as well as light speed representing limit velocity, so as it stands this assumes no tones above high C. I did this to center us on the keyboard for reference to be used in determining alignment, because we have yet to identify with precision the corresponding hues. I will demonstrate this process in the next installment. Be patient peeps, we’re almost there. And if you have been following this series of posts, you will soon possess a genuinely valid scientific basis upon which one may correlate hue to pitch – and remember, this has yet to be formally accomplished in the real world. I don’t sell information that is readily observable in nature, nor do I make demands or solicit promises from people to whom I present such information. Do with this what you will. None of this is plagiarized, and sources of information used will be thoroughly listed when we’re done so no misunderstandings occur and to help you accomplish further research in the areas you want to without having to comb the whole damn internet. As to the idea entire…there is a great deal here that you won’t find online elsewhere. Peace.
Posted on: Tue, 24 Sep 2013 13:54:59 +0000