Law and Theory in Science

It is a law in acoustics that when you pluck two strings, and only relevant difference is one being half as short as other (check same string on a wellmade guitar: once open and once on twelfth fret), the swinging will be twice as fast and the sound go one octave to the discant. From other direction (twelfth fret first, then open), as you go to twice the length, otherwise exactly the same, the swings will be twice as slow and the sound go one octave to the bass. For a fifth check relations 2:3 (same string once open once seventh fret or reverse). Those are for any intervals natural laws, tying it to a relation of x times or x/y times as fast or slow swings or shorter and longer string. Of course shortening the string is not the only way to get a more acute sound, you can also take a thinner string (check strings on guitar: the thicker the bassier, the thinner the more acute), and there too the more discant goes with faster swings and the more bass with slower ones.

That is a natural law. It does not change. I do not know if God would even make a miracle in which it changed, because what would be the point of that miracle? Would it heal someone or raise someone from the dead?

Fastness of swings or oscillation is measured in Herz, abbreviated Hz. The frequency of swings known as 440 Hz is also known as the tone A. That is a fact, but it can change insofar as at other times A has been rather 420 Hz or 432 Hz. It is a fact that musical notation only covers a selection of all possible sounds and that the spectrum of different Hz measures is selected as a finite number of points on that line. And such can do and have historically also done some re-definition of location. But if you change the location of that A, you have to change all the other locations as well. If 440 Hz is an A, 880 Hz must also be an A, and so must 220 Hz. If the A is 432 Hz, it is 864 Hz and 216 Hz which are those other A. If you remember the previously said, you will see in either way As are an octave apart, because they are half or double the Hz number apart. That is a law of music and of musical notation and terminology. Unlike the natural law previously referred to, it is arbitrary. One has historically called them bass to discant A - H - P (unless P was rather 432 than 864, in which case A was as bassy as 108).

Now, there are different theories of what sound is. Mersenne explored the laws above referred to in a much finer and more scientific way than Pythagoras had. Though he favoured the theory "sound is nothing other than the movement" (by which he meant the oscillations, which he had not yet quite identified as such) he also mentioned the theory "sound is a quality, not identical to the movement, but caused by it and proportional to it". There is also the theory that if oscillations go far enough up in speed you get light and electromagnetic waves of which Hz are measured in millions - mHz meaning mega-Herz and mega meaning one million times basic unity. But there is the observation that a thing like air would hardly be able to vibrate that fast, so if that is the case, what is vibrating? Ether? Or a quasi-vibration by different strength in emitted photons? Those also are two different theories. As is the one which says that matter in itself is also a frequency and some add "so is spirit", and so on and so forth. But whichever of these theories is true, as long as we talk about vibrations in air or in instruments, it is a law that 330 Hz and 440 Hz are exactly apart as 3:4 which gives the intervall one fourth (fifth fret and open string), which is an audible inflection of sounds.

Mersenne's theory about sound being physically identical and only subjectively different from movement by being percieved in the ear rather than otherwise, is the one that has most favour with the scientific community. It would not have been quite as fashionable with St Thomas Aquinas. If you remember previous essay, think of the physical line of ink on the paper: is it really continuous even between the molecules, or is the space between molecules, even if it is only nooks and corners, quite empty space? In other words, is there or is there not something in physics which corresponds to the continuousness of geometry, of geometric lines? Are nuclei plus very little electrons all that is matter - or are nuclei "heavy matter" and the distance between them, within a body like air or liquid or solid or ink line or paper, filled by some kind of "light matter" with the characteristic "light" opposed to the characteristic "heavy"? Are sounds vibrations in nuclei and light vibrations in light matter also known as aether or maybe even sound vibrations those in nuclei and sound itself a quality of the surrounding "light matter" - or does one accept the modern standard theory?

Those are theoretic choices not often asked in classrooms. I guess that (along with theoretic preference for creationism) is why I bailed out of studying sciences and studied Latin Language and Literature, which in Sweden has quite a Medieval focus. And why I would hardly be welcome as a science teacher in a classroom.

Hans-Georg Lundahl
Mouffetard, Paris
Our Lady of Sorrows /
Nuestra Señora de Dolores
15 - IX - 2012

PS, Mersenne was a Minim, a kind of very strict Franciscan. He ate basically one meal a day, year round, as other Catholics try to do in Lent. But he did get curious about acoustics and music and he did his experimental work very well for all that. Or, why am I saying "but" or "for all that"? That is just one bow to modern prejudices!