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Observations placeholder

Joscelyn Godwin - On Plutarch, Ptolemy and Canobus



Type of Spiritual Experience


Two notes with frequencies in a ratio of any power of two (e.g. half, twice, or four times) are perceived as ‘similar’. Because of that, all notes with these kinds of relations are grouped in musical notation schemes with the same ‘pitch class’.

So, for example, where the pitch classes are represented by the first seven letters of the Latin alphabet (A, B, C, D, E, F and G) the eighth note, is given the same name as the first, but has double its frequency. The octave is then used to denote which span of notes – which sets of frequencies - are being used.

How does an ancient shaman or mystic try to preserve pitch – the notes that he has heard as a hum or buzz from which spiritual experience ensued?

He can define the general range of experience – water, earth, air, fire or aether using relative pitch. Thus the proportions between notes and hence between levels. In effect, instead of our hertz numbering system, an equivalent system was devised probably by observing the resonance of the strings of bows or the strings of musical instruments to determine the ratios involved. And in each case, the system used the fact that proportionally similar sounding notes could be perceived as the differentiator of ‘levels’

The Sefer Yetzirah, for example, assigns numbers to each of the letters that symbolically represent the levels. This system is called Gematria or gimatria in the Kabbalah. The numbers used in the Jewish system are

  • Mem - Mem [Water] is represented by the number 600

  • Shin – Shin [Fire] is represented by the number 300

  • Aleph - [Air] is represented by the number 1

A description of the experience

Joscelyn Godwin- Harmonies of Heaven and Earth

According to Plutarch's treatise on 'the Procreation of the Soul in the Timaeus' the notes which bound the five tetrachords are in the same proportion as the intervals between the planets. The fragmentary last chapter of Ptolemy's Harmonics gives a similar system, while an inscription at Canobus in Egypt, recording the mathematical principles of Ptolemy, adds to these the low note proslambanomenos ['added note'] for the elements of Earth and Water, and the high note hyperhyperbolaeon ['above the highest'] for the Fixed stars, giving the intervals in proportional numbers

The source of the experience


Concepts, symbols and science items

Science Items

Activities and commonsteps