The Philosophy of Hermes on Numbers

The philosophy of Hermes Trismegistus on numbers.

So quotes Camerarius from the ancients. Most of what Hermes Trismegistus (whoever he was) impressed on his son Tatius agrees with it.

He wrote: Unity embraces the Tenfold on the basis of ratio, and again the tenfold embraces Unity.

Next, he makes up the faculty of the soul which is responsible for desire from the 12 avengers, or ethical vices, in accordance with the 12 the signs of the zodiac. He makes the body, and this power of the soul which is closest to the body, subject to it. Whereas the same man makes up the rational faculty of the soul from the tenfold ethical virtues.

The Pythagoreans celebrate the Tetractys as the source of souls.

Camerarius says that there is more than one Tetractys, not only that which from the fourfold as base rises to a total of 10, but also above all the other which from the eightfold as base up to its vertex adds up to a total of 36, the said Tatius also hints at the same thing from the teaching of his father Hermes when he says it was the time when he himself was still in the Eighth Level, the Eightfold.

The father sent the son back to Pimander singing of the eightfold. There in fact occur the eightfold ethical casts of soul, seven corresponding with the 7 planets, as is apparent, starting from the Moon; but the eighth, more divine and more at rest, to the idea, I think, of the sphere of the fixed stars.

Furthermore, everything is carried out through harmonies. There is much impressing of silence, much mention of mind and truth.

Also the cave, the foundation, the inner sanctum, the mixing bowl of spirits, and many other things are evinced, so that there can be no doubt that either Pythagoras is playing Hermes or Hermes Pythagoras.

For there is the additional fact that Hermes expounds a particular theology, or cult of a divine power. Often he paraphrases Moses, often the Evangelist John in his sentiments, especially on regeneration.

He im- John 3 . presses on his disciple certain ceremonies; whereas the authorities declare the same of the Pythagoreans, that part of them were given over to theology and to various ceremonies and superstitions, and

Proclus the Pythagorean locates his theology in the contemplation of numbers.

The error of the Pythagoreans in the Number of Harmonies

Let us now return to the Pythagorean demonstration of the harmonious proportions.

The Pythagoreans were so much given over to this form of philosophizing through numbers that they did not even stand by the judgment of their ears, though it was by their evidence that they had number of originally gained entry to philosophy.

But from their numbers alone, they marked out what was:

• melodic and unmelodic
• consonant and dissonant

This did violence to the natural prompting of hearing.

This harmonic tyranny of theirs lasted up until Ptolemy, who was the first, 1,500 years ago, to uphold the sense of hearing against the Pythagorean philosophy. He accepted as melodic:

• the proportions stated above
• the proportion of one and an eighth to one as equivalent to a Tone

But he also admitted the proportion of one and a ninth to one as equivalent to a minor tone, and that of one and a fifteenth to one as equivalent to a semitone.’^'

He added other proportions of one and a single aliquot part of one, which were sanctioned by the ears, such as one to one and a quarter or one to one and a fifth. But he also added some of the proportions of several aliquot parts, such as the proportion of 3 to 5 and 5 to 8 and others.

Ptolemy did indeed correct the Pythagorean speculation on the origin of the harmonic proportions as forced. But he did not completely eliminate it as false.

He restored the judgement of the ears to its rightful place in words and doctrine. Nevertheless, he deserted it again, as even he adhered to the contemplation of abstract numbers.

For the cause of the number of the harmonic proportions and of the individual proportions is not, even so, adequate for its effect.

But in designating the consonances it falls short, in the case of the other melodic intervals it goes too far.

Ptolemy still denies that the thirds and sixths, minor and major (which are covered by the proportions 4:5, 5:6, 3:5 and 5:8) are consonances, which all musicians of today who have good ears say they are.

On the other hand he accepts the proportions 6:7, 7:8 and others among the melodic musical intervals, so that if a tune proceeds from UT to FA, a note is constituted, intermediate between RE and MI, in the proportion in which 7 is the middle term between 6 and 8 .

Let this note be RI, so that we can refer to it. Then it is possible to sound just as it is possible to sound UT, RE, Ml, FA, which is utterly abhorrent to the ears of all men and the usages of singing, even though it may be possible for strings to be tuned in that way, seeing that as they are inanimate they do not interpose their own judgement but follow the hand of the foolish theorist without the least resistance.

Furthermore if both the cause which was sought in abstract numbers, and the effect, that of consonance, were as far as possible equal in scope, and it could without absurdity be seen as the archetypal cause, bearing witness that it was from the contemplation of those numbers that the Father of things, the Eternal Mind, took the idea of notes and intervals, and so that they should be pleasing to human spirits He had to arrange them in the shape of those spirits, yet it would still not be very clear why the numbers 1, 2, 3, 4, 5, 6 , etc., conform with musical intervals, but 7, 11, 13, and the like do not conform.

Also, the cause of this fact would not be revealed by the numbers, as numbers, from within themselves. Eor the cause drawn from the Threefold basic principles, and the family of squares and cubes derived from them, is no cause, since the Eivefold is foreign to it, although it refuses to have its rights of citizenship in the origin of musical intervals torn from it.

Yet not even this is satisfactory to the theorist, for he knows that the numbers 1, 2, 3 are symbols of the basic principles of which natural things consist. Eor an interval is not a natural thing, but a geometrical one. Hence unless these numbers number something else, which is more akin to the intervals, the philosopher will not be able to put any confidence in this cause but will suspect it of not being a cause.

This is why, in order to work this out fully for the last 20 years I have set myself the task of illuminating this part of Mathematics and Physics.

I do this by discovering causes which on the one hand would satisfy the judgement of the ears, in establishing the number of the consonances, and the other melodic intervals, without trespassing beyond what the ears bear, but which on the other hand would set up a clear and overt criterion between the numbers which form musical intervals and those which have nothing to do with the matter, and lastly which, with respect both to the archetype and to the Mind which uses the archetype to shape things to fit it, would have a kinship with the intervals, and so would rest on the clearest probability.

Since the terms of the consonant intervals are continuous quantities, the causes which set them apart from the discords must also be sought among the family of continuous quantities, not among abstract numbers, that is in discrete quantity;

It is Mind which shaped human intellects in such a way that they would delight in such an interval (which is the true definition of consonance and discordance) the differences between one and the other, and the causes of such intervals’ being harmonious, should also have a mental and intellectual essence, that is that the terms of the consonant intervals are properly knowable, but those of the dissonant intervals either cannot be prop­ erly known or are unknowable.

If they are knowable, then they can enter the Mind and into the shaping of the archetype. But if they are unknowable (in the sense which has been explained in Book I), then they have remained outside the Mind of the eternal Craftsman, and have in no way matched the archetype.

Throughout we shall indeed speak of melody, that is harmonious intervals which are not abstract but realized in sound; yet to the educated ears of the mind the underlying reference throughout will be to the intervals abstracted from the sounds.

For it is not only in sounds and in human melody that they yield their charm, but also in other things which are soundless, as we shall hear in Books 4 and 5.