Messing around with Pythagorean ratios. The Tetractys is one of the wonders of Pythagoras. It represents the combination of the elements at creation, and how the words of God in the beginning folded and expanded inwards in the musical scale. This scale is the electromagnetic spectrum, and in these programs I am mostly exploring the musical ratios. Something very cool I realized, is that, on string instruments, the longer and thicker the string, the lower the note. I was looking at a harp tuning device which uses the Pythagorean ratios on a string of length 120mm. The 7 white notes (and the sharps/flats) of the root (lowest octave on string) all exist as a fraction of the maximum length (120) so that C = 1max, D = 8/9max etc. These ratios are all greater than 1/2 of max (120).
the root octave on a string is therefore measures via the max length of the string, and all octaves therein may be measured the same if they are passed their respective max (octave2.max = octave1.max/2). The root octave in this operation only takes up half of the string given so that the higher octaves may be contained in the higher half. As the max is recursively halved in these operations, we can see the beauty of polarity. As the length and size of the string decreases, the tone of the note is higher. The original string is of a finite measurement, yet as the max folds in half when assessing higher octaves, we can essentially fit an infinite amount of octaves in any length string.
I am writing some proofs for option 4, as it shows that if octaves are represented as polygons with sides n+1, there are very interesting intersections when drawing these bound by a circle with radius=note value (noteratio * respective_max).