Determination of particular musical notes by scalar design is not something which is inherently set in stone, but rather varies according to the scale in question. In popular western music, the octave consists of 7 whole notes and 5 semi-tones, however there are many other ways of determining the notes in an octave, subjectively speaking. Yet our perception of harmony, as when relating one note to another in sequence, may be more of a meeting point between subjectivity and certain objective events. In particular these objective events are dependant on biological functions of our organism and the physical properties of matter, namely the movement of air molecules within our atmosphere and the effect this has on our ears.
For example, the note "A" above "middle C" or "La" above "Do" is conventionally regarded as having a frequency of 440hz (which is actually a very modern designation). This means that we perceive the pressure of air molecules oscillating at 440 cycles per second to sound a certain way which we have termed as the note “A”. The next note of "A" above this, would have a frequency of 880hz, and the next above this would have a frequency of 1760hz, and so on. However, this system of tuning "A" to 440hz was only accepted as a standard in the last few centuries... and it is not by itself a law of nature, per se - that which describes the measurements which build harmonies from a scale of tones that doubles in frequency is known as the "equal tempered scale".
The system of musical notes presented in scalar form is often attributed to Pythagoras, by way of a story in which he was walking along one day and noticed that the clanging sounds of a blacksmith hitting various pieces of metal produced different “tones” directly relative to their length. While the truth of who actually discovered musical scales is probably deeper than this, we have been left other bits of knowledge that are almost certainly from Pythagoras and/or his students. One of these bits is a symbol known as the Tetractys.
It is a triangle consisting of 4 rows of dots, with 10 dots in total. Each row represents a different facet of the 1 reality. This symbol was even more sacred to the Pythagoreans than the pentagram, which was also one of their most widely used designs, often inscribed with the word "Hygieia", the goddess of health and well-being. For Pythagoreans, the pentagram describes an interplay of cosmos, in much the same way as the Wu-Xing, a taoist diagram which describes the interactions of fundamental elements.
Pythagoras was supposedly a man of great internal power, who traveled to Egypt and Persia and other exotic lands to gather their esoteric knowledge before returning to his home in Samos to start his own school. It was a place dedicated to the holistic integration of this knowledge with a healthy lifestyle, along with the study of music, metaphysics and mathematics - culminating in what he supposedly described as a "love of wisdom", i.e. "philosophy". His life (as we know it) has an oddly close parallel to that of another greek of our own modern age, named George Gurdjieff, who also traveled to the east to gather knowledge and then came back to start his own “Institute for the Harmonious Development of Man”. He even brought us his version of the ultimate sacred symbol, which he called the Enneagram.
It is a circle containing nine points, connected by straight lines in various ways. Something that is often overlooked when viewing the Enneagram is the central triangle, which represents the "three forces" which are central to Gurdjieff’s cosmology. These three forces also correspond to the third row of the Tetractys. In fact, regarding the connectivity of the other 2 points, and then the other 4 points, we can even see the explicit legacy of the Tetractys inherent in this design.
Gurdjieff also related these points with musical notes by way of the equal tempered scale, however he only regarded 2 semi-tones and 7 whole notes as part of the "cosmic octave”:
"The period between one do and the next, that is, an octave, is divided into seven unequal parts because the frequency of vibrations does not increase uniformly. "The ratio of the pitch of the notes, or of the frequency of vibrations will be as follows: "If we take do as 1 then re will be 9/8, mi 5/4, fa 4/3, sol 3/2, la 3/2, si 15/8, and do 2. The differences in the notes or the differences in the pitch of the notes are called intervals. We see that there are three kinds of intervals in the octave: 9/8, 10/9, and 16/15, which in whole numbers correspond to 405, 400, and 384. The smallest interval 16/15 occurs between mi and fa and between si and do. These are precisely the places of retardation in the octave.
"In relation to the musical (seven-tone) scale it is generally considered (theoretically) that there are two semitones between each two notes, with the exception of the intervals mi-fa and si-do, which have only one semitone and in which one semitone is regarded as being left out. In this manner twenty notes are obtained, eight of which are fundamental: do, re, mi, fa, sol, la, si, do - and twelve intermediate: two between each of the following two notes: do-re re-mi fa-sol sol-la la-si - and one between each of the following two notes: mi-fa si-do.
"But in practice, that is, in music, instead of twelve intermediate semitones only five are taken, that is one semitone between: do-re re-mi fa-sol sol-la la-si - "Between mi and fa and between si and do the semitone is not taken at all.
"In this way the structure of the musical seven-tone scale gives a scheme of the cosmic law of 'intervals,' or absent semitones. In this respect when octaves are spoken of in a 'cosmic' or a 'mechanical' sense, only those intervals between mi-fa and si-do are called 'intervals'.
- from “In Search Of the Miraculous”
In the Enneagram, the 1 reality is implicit in the circle itself, and the movement of the Enneagram through time is envisioned as a spiral of consecutive cycles, from the Absolute to the Absolute.
