Р.Луллий/И.Зальцингер об элементах музыки

[jayrandom]

The Teacher:
As ignorance means difficulty and science means facility, something most difficult for the ignorant is perfectly easy for someone who knows. But as ignorance comes in the beginning and science comes at the end, "and one cannot get from the beginning to the end without a medium etc. which means that you, as you begin to learn this Art, cannot destroy your ignorance of this Art without a means, and this means consists in the conditions of the above Trees and Figures, through which your intellect must pass if you want to know this Art in the end. (Doctor Illumin. in Lib. Princ. Med. Dist. 2, cap. 8. fol. 11.) But lest I appear to be placing the entirety of this burden on your arms, let me explain what was said up to now with the following metaphor, and at the same time show you the method, or art of descending from universals to particulars, by taking an example from Grammar and Music. In Grammar there are twenty-four letters of the alphabet which suffice for the entire grammatical System, and which I now call the scale of Grammar; and in music there are seven sonorous letters which suffice for the complete musical System, and I call this the musical scale. These two scales are the universal from which you descend to any particular. Therefore the method, or art of descending consists in correctly combining the letters with each other.

The Disciple:
It is easy to do this correctly in Grammar, but not so easy in Music.

The Teacher:
Why?

The Disciple:
Because grammatical letters can be combined at pleasure, insofar as a syllable is produced by joining a consonant to a vowel, or conversely, or by not joining a consonant to another consonant without a vowel, these combinations will always yield syllables, but musical syllables cannot be produced so easily by art.

The Teacher:
As easily, or if you prefer, even more easily.

The Disciple:
Please demonstrate.

The Teacher:
Given that Art is a habit which operates with right reason, "the Art, as such, is the right measure for carrying out operations, inasmuch as it revolves around them in order to regulate them and predefine or predetermine their methods." (Doctor Illum. in Introd. Art. Dem. cap. 1. fol. 2. To. 3.) and as such, it directs the rational Artist to operate correctly and easily. "Now Art and Science have this in common: they both make it easier for powers to do their work." (Doctor Illum. ibid.) And if this applies to the haphazard discovery of artificial things where reason plays no role, it applies even more to natural works, and to works that are both natural and artificial, as these two are never done without reason, because they are governed by D of the Principles of Philosophy, namely Intelligence.

Let me illustrate this with an example. You see, my Son, how easily and quickly someone who has learned to play the organ and is a Master in the Art, can move the keys of the keyboard to express any given theme, even though your keyboard has not up to now been formed according to natural rules, and the entire musical System is not rational, as will be demonstrated in the next Chapter; then what do you think he could do with a perfectly ordered System? Further, in the musical alphabet there are only four letters and three syllables, whereas the grammatical alphabet has twenty-four, and many more syllables, it is obvious to the senses that working with four is easier than working with twenty-four.

The Disciple:
Father, you just enumerated seven musical letters or seven degrees, and now you only have four. How can this be right?

The Teacher:
This is a Secret of the Art which you should understand as follows. Given that the supreme principle of ternary number belongs to GOD alone, and the number four comes right next after three, the fourfold principle is the first and supreme principle belonging to creatures; and thus there are four elements in corporeal nature, and there are four sounds in Music, which are the four Elements of Music, namely unison, the third, the fifth and the octave. And as all natural corporeal particulars are necessarily composed of these four elements, so likewise all natural musical particulars are composed of the four. Understand, my Son, that this property is common not only to Physics and Music, but to every Art and Science, for every proportion found in any one of them must necessarily be found in all the others.

Further, you should note that conversely, just as in Music, the seven letters constituting the diatonic scale are produced from the four letters mentioned earlier, likewise, in nature, through the four Elements, are produced seven elements which constitute the natural scale through which, in which and from which, as from a universal, spring all natural particulars, in the same way as all musical particulars originate in the musical scale.

-- Иво Зальцингер, "Раскрытие секретов Искусства", гл. "Секрет чертежа V" (выделение моё - jayrandom).

Унисон, терция (очевидно, большая), квинта и октава соответствуют числам 1, 5, 3, 2.
Если набирать из которых, получим не пифагорейский, а скорее строй из ВПЧ (1, 9/8, 5/4, 4/3, 3/2, 5/3, 15/8, 2).