 Graham suggests that harmony as a principle required to allow limiters and unlimiteds to combine prefigures Platonic participation and Aristotelian ontological predication (Graham 2014: 53–4). In Fragment 6a Philolaus goes on to describe this harmony and what he describes is a musical scale, the scale known as the Pythagorean diatonic, which was used later by Plato in the Timaeus in the construction of the world soul. This scale provides Philolaus’ only surviving explicit example of the bonding together of limiters and unlimiteds by a harmony. A musical scale presupposes an unlimited continuum of pitches, which must be limited in some way in order for a scale to arise. The crucial point is that not just any set of limiters will do. We cannot just pick pitches at random along the continuum and produce a scale that will be musically pleasing. The scale that Philolaus adopts is such that the ratio of the highest to the lowest pitch is 2 : 1, which produces the interval of an octave. That octave is in turn divided into a fifth and a fourth, which have the ratios of 3 : 2 and 4 : 3 respectively and which, when added, make an octave. If we go up a fifth from the lowest note in the octave and then up a fourth from there, we will reach the upper note of the octave. Finally the fifth can be divided into three whole tones, each corresponding to the ratio of 9 : 8 and a remainder with a ratio of 256 : 243 and the fourth into two whole tones with the same remainder (for more on Fr. 6a see McKirahan 2012 and Huffman 1993: 145–165). Thus, in Philolaus’ system the fitting together of limiters and unlimiteds involves their combination in accordance with ratios of numbers. Similarly the cosmos and the individual things in the cosmos do not arise by a chance combination of limiters and unlimiteds; the limiters and unlimiteds must be fitted together in a pleasing way in accordance with number for an order to arise. Fragment 6a suggests that Philolaus saw the cosmos as put together according to the diatonic scale. This would be very much in accord with the famous conception of the harmony of the spheres according to which the heavenly bodies make harmonious music as they move, but neither in Philolaus nor any other early source do we get an explicit account of how the musical scale corresponds to the astronomical system (Huffman 1993, 279–83; Zhmud 2012: 343–4 denies that there was any connection between the harmony of the spheres and Philolaus’ system ).