Explanation of Order

We have set out the harmonic proportions, considered in the abstract, in the first three books.

• Book 1 exhibited the geometrical properties of the individual shapes.
• Book 2 exhibited their congruences in combination
• Book 3 developed the harmonic proportions from the shapes.

Three other books explained how to apply the harmonies to the cosmos.

• Book 1 attributes the harmonies to God, as the Creator
• Book 2 attributes them to Nature, as the director of the differing motions
• Book 3 attributes them to Man the controller of his voice, which originates from motion.

However, the requirements of stating the arguments have persuaded us to reverse the order.

• It starts from human song
• Then it passes to the works of Nature
• Then it passes to the work of Creation, the first and most perfect of all..

We also to combine the end of abstract speculation with the beginning of actual harmonies in melody, also in Book 3.

Book 3 started this application to the cosmos and transferred the harmonies to human melody, which others usually call Art.

Book 4, in this reverse order, attributes to Nature the second part in actual harmony.

Book 3 also discussed the metaphysical essence of the harmonies here and there. It will be fully discussed in the beginning of Book 4.

The philosophers commonly look for harmonies nowhere else but in melody. Many people it is an unexpected treat when they are told that sounds are something different from the harmonies which are thought to be in the sounds,something had to be conceded to the weakness of our understanding, and the origin of the harmonies had to be explained by the terms which are commonly known to musicians:

The eagerness of the reader had not to be disturbed by the uncomfortable subtlety of metaphysical investigations.

I shall next reveal the harmonies in Nature and in the motions of the heavens. The common herd of philosophers at the first mention of harmony immediately conceives the singing music of the stars, which can be perceived by the hearing.

Along with Cicero’s Scipio stands with its ears pricked to catch “so great and so sweet a sound.”

It is easy for those who are inexperienced in these matters to conclude with Cicero the dreamer himself that “Motions so great cannot rush on in silence,” and with the Pythagoreans according to Aristotle give an explanation why the sound of the heavens is not heard upon earth.’

These preconceived opinions are a considerable obstacle to readers who are striving towards the inner secrets of Nature, and could frighten off many who have great powers of judgement and are seekers after truth, to such an extent that they would disdain those Pythagorean pipedreams, scarcely recognized at arm’s length, and throw away the book unread.

For these reasons this seemed to me a suitable place to assign to this highly necessary discussion.

I was also moved by the example of Ptolemy.^ When in the first 2 books of his work on Harmony he had completed the exposition of the harmony which concerns melody, and had already embarked in the third book on his demonstration that all perfect natures participate in the force of harmony,he too began his examination with this same question “To what class of things should the nature or force of harmony, and the knowledge of it, be assigned?”

Therefore, although I have relegated examination and judgment of Ptolemy to the appendix of this work of mine, yet for the reason stated the reply which it seems ought to be made in accordance with my basic principles to this question of Ptolemy’s had to be placed at the start of this Book 4.

Nor does that relate only to forearming the reader and avoiding adverse opinions, but also to the fundamental theme of Book 4.

Hence, because we are going to state of the harmonies of the stellar rays-’ what they are and how many they are in number, and on what geometrical principles they are formed, we should first know what the essence of the harmonies is, apart from consideration either of sounds, which are here of no importance, or even of the rays themselves, what their proper subject and their terms are, whether they are among those things which are outside our understanding, or only in our soul, by what medium they are perceived, and inwardly received, by what agency they are discriminated, and what effect follows this perception and recognition, by what originator or prime mover.

When these points have been explained, both generally and by the comparison of particular features, it will then be easy for us to discuss metaphysically the essence and properties of minds and of sublunary nature itself, and to show the secrets of Nature in rather clearer light than hitherto.