The Great Art of Consonance & Dissonance.

CHAPTER II.

On the Requirements for our Musarithmic Method of Composing.

A musarithm, as was said in the definitions, is, we say, nothing more than some particular aggregation of harmonic numbers. And when metrometric notes are applied to this musarithm, a perfect harmony is produced. Concerning which, if it is to come out well, then these things are required:

Requirement I.

The Phonotactic Palimpsest.

Since every mathematical science consists more in discovering truth through demonstrations than in the vague and obnoxious style of arguing characterized by the many obscurities of opinions, therefore, in order to better perceive these demonstrations, it was necessary to represent them with discernible markings. Hence points, surfaces, volumes and the infinite different characters for numbers that were devised by the masters of primeval wisdom. And when these were drawn on paper, they would produce sensations in the mind and a signification of things conceived. By no different a method do musurgists invent certain signs in order to reduce speculations to action and to provide demonstrations to the senses, whereby sounds which otherwise are imperceptible are made known through the position of visible markings. So likewise do we, for the purpose of putting these speculations of ours into practice, first set up the phonotactic palimpsest. A palimpsest is nothing but a leather membrane made from donkey hide out of which notepads or writing tablets are commonly made and which modern musicians generally are accustomed to use for this business, regarding it as the most suitable in preference to everything else. For it’s just as easy to write upon as it is to erase what’s written. And we give it the name 'phonotactic' because the individual voices on it may be fit to scales and keys which are suitable for each voice, each on their own pentagrams (for so we call those groups of five lines on which musical notes are inserted for indicating harmonic intervals).

Hard or Natural Song Soft or Wrought Song
Bass Pentagram

Designation of the Bass' Pentagram

Tenor Pentagram

Designation of the Tenor's Pentagram

Alto Pentagram

Designation of the Alto's Pentagram

Canto Pentagram

Designation of the Canto's Pentagram

The pentagrams are marked by three signs in particular which are named the principles of the musical scale and these are F, C, & G. The sign or principle of the scale F in the Bass' pentagram is placed either on the middle line or on the fourth or fifth line. In transposing melodies it is generally placed in the middle & then the bass is intoned higher. If it is placed on the fourth line then it indicates that the central and especially the most natural of the voices is intoned lower by a semiditone;1The interval 32:27; a (Pythagorean) minor third. if on the fifth line, which rarely happens, it denotes an intonation that is very deep and lower by a semiditone from the preceding case. The markings of the remaining voices follow the structure of the bass as was made clear a little bit earlier. And this is the first designation which is called 'hard' or 'natural'. The other is 'soft', which is also called 'wrought', and is no different than before except that a ♭ is placed on each of the voices in a convenient location as is clear in the second series.

Note here that everywhere you find this symbol Key of F placed on the bass' pentagram you know that the key there is F. For by counting upwards or downwards from this we arrive at a knowledge of the seat of the 7 keys or principal characters ABCDEFG, just as if by these keys the door to every modulation is opened.

For the Tenor, everywhere this symbol Key of C is found you will know that the key there is C. Then by counting either up or down from this you will arrive at a knowledge of whatever other key is sought. And these things may likewise be applied to the Alto, or Countertenor, & the Canto. In the case of the Canto, or higher voice, you will initiate the seats of the remaining keys from the line upon which you find the key of G has been placed. But these things are said for those who are ignorant of practical music, for whose sake we have decided to add here the complete system of the phonotactic palimpsest.

Characterization, or the various ways of marking in the phonotactic system.

1 2 3 4 5 6 7 8
For music which is For music which is For music which is For music which is For music which is For music which is For music which is For music which is

Hard
natural
Soft
natural
Hard
unnatural
Soft
unnatural
Hard
unnatural
Soft
unnatural
Hard
transposed
Soft
transposed
Canto's Pentagram Canto's Pentagram
Alto's Pentagram Tenor's Pentagram
Tenor's Pentagram Alto's Pentagram
Bass' Pentagram Bass Pentagram

And these are the ways used everywhere of marking the 4 voices upon which we, just as if upon a base & foundation, shall establish our Musurgy. And although still other markings may be applied, nevertheless since they denote intonations that are either higher or deeper than the human voice can reach they are consequently rejected everywhere. And so, having explained the phonotactic system, let us now proceed to the next requirement.

What a palimpsest is.

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