Tag Archives: Pythagoras

QOTD: Pythagoras

The moral test was a more serious one. Suddenly, without the least preparation, the would-be disciple would one fine morning find himself imprisoned in an empty, dismal-looking cell. A slate was given him and he was coldly ordered to discover the meaning of one of the Pythagorean symbols, as, for instance: What is the signification of the triangle inscribed in a circle? or: Why is the dodecahedron, confined within the sphere, the symbol of the universe? He spent a dozen hours in his cell with his slate and the problem, and no other companion than a vase of water and a piece of dry bread. Then he was taken into a room to face the assembled novices. Under these circumstances the order had been passed round that they should ridicule without pity the wretched youth, who, hungry and sullen, stood before them like a culprit. “So this is the new philosopher,” they would say. “How inspired he looks! He will now tell us of his meditations. Do not conceal from us what you have discovered. You will in the same way go through all the symbols in turn. A month of this régime and you will have become a great sage!”

At this point the master would attentively observe the young man’s attitude and expression. Irritated by his fast, overwhelmed with these sarcastic words, and humiliated at not being able to solve an incomprehensible problem, no small effort was needed to control himself. Some would weep with rage, others gave sarcastic replies, whilst others again, unable to control themselves, dashed their slate madly to the ground and burst out in imprecations against school, master, and disciples alike. Then Pythagoras came forward and calmly said that, as they had failed in the test of self-respect, they were begged not to return to a school of which they had so bad an opinion, in which friendship and respect for the masters should be the most elementary of virtues. The rejected candidate would shamefacedly retire and sometimes become a redoubtable enemy of the order, like the well-known Cylon who, later on, excited the people against the Pythagoreans and brought about their downfall. On the other hand, those who bore everything with firmness, and gave just and witty replies to the provoking words they listened to, declaring they were ready to repeat the test a hundred times if only they could attain to the least degree of wisdom, were solemnly welcomed into the novitiate and received the enthusiastic congratulations of their new companions.

via Pythagoras and the Delphic Mysteries: Chapter IV. The Order and the Doctrine.

domino

Leave a comment

January 9, 2014 · 12:56 pm

Music In Theory & Practice, part 4

Pythagoras

The Harmonic Method

I will just briefly mention this because it is vaguely to do with the theme of associating colours and musical tones mentioned in the preceding blog posts in this series. The main problem with this method is that it was an idea ahead of its time and therefore, as far as I can make out was not taken up in a great way in the past. Ironically however, living in the twenty-first century we are now technologically advanced enough to develop the idea for the future. The basis of the idea lies in Harmonics.

Musicians who play stringed instruments like the guitar or violin will be familiar the concept straightaway – they are the bell-like tones produced by lightly touching a string at the 4th, 5th, 7th, 12th etc frets or the equivalent positions. What you actually have here is a tone which is equal in frequency to that of the open string, multiplied by a whole number. Hence:

Frequency Known as Where on guitar
x The First Harmonic (Fundamental) 0 (Open string)
2x The Second Harmonic 12
3x The Third Harmonic 7
4x The Fourth Harmonic 5
5x The Fifth Harmonic 4
6x The Sixth Harmonic 3 *
7x The Seventh Harmonic 15 *
8x The Eighth Harmonic 17 *

* These harmonics are not as easy to play on a guitar as the other harmonics. But if they were easy, then it wouldn’t be a guitar!

As a sort of aside, it is worth noting that going by Pythagorean Temperament, the various Harmonics would thus be equivalent to: –

Harmonic Note
1st I
2nd I’
3rd V’
4th I”
5th III” **
6th V”
7th b VII” **
8th I”’

** NB: The note-equivalents of the 5th & 7th Harmonics are approximations – probably more suited to a Just Tempered scale, as opposed to a strict Pythagorean one. The strict Pythagorean versions of these notes would be several cents sharper than the corresponding harmonics.

It is here that Madame Blavatsky shoved her oar in: she asserted that the colours of the spectrum correspond to Harmonically to one another, hence:

Harmonic Note Colour
1st I Red
2nd I’ Orange
3rd V’ Yellow
4th I” Green
5th III” Blue
6th V” Indigo
7th b VII” Violet
8th I”’ “The Ghost Ray”

“The Ghost Ray…” Yes indeed, Blavatsky postulated that there was an eighth, mysterious colour of the spectrum, which is where Terry Pratchett got the idea for Octarine from. Hence Chaos magicians have incorporated this into Chaos Magic thinking they are being really ironic, when in fact they are just re-cycling hundred year-old Theosophy!

Anyhoo… now that we have a basis for assigning colours to harmonics, it is possible to analyse the timbre of a musical instrument in astrological terms – e.g. if one particular harmonic is stronger than the rest, one could say that the sound of the instrument is more under the presidency of the corresponding planet or planets than the others. However, in terms of using this for practical magic, this system would have had limited functionality in the late 19th century when it was first proposed. For a particular planetary working one would have to hunt high and low for the particular instruments that sounded just right. Pipe organs would have been more useful in this regard – unfortunately, most organs were not and indeed are not built to accommodate the full range of harmonics as listed above.

Fairlight CMI

So, to fully make use of the system in the 1880s would have been very inconvenient. However: fast forward one hundred years, and the invention of digital synthesisers from the 1980s onwards does now allow one to pick and choose the harmonics with which to imbue your tone. This of course is only if you are prepared to actually synthesise instead of just use the presets. However, such synthesisers can do far more sophisticated things than just “pick a harmonic” – for example, by creating dynamic tones in which the levels of different harmonics alters in real time, thus reflecting that as in music, so in astrology, and so in Life – the influences of the various planets are not constant, but are modulating continually.

Leave a comment

Filed under Supernatural

Donald In Mathemagic Land


Donald Duck teaches your children all about the Pentagram. Thanks to Frater Peter for sending me this link.

2 Comments

Filed under Supernatural