The Great Art of Consonance & Dissonance.


On Simple Counterpoint & How It Can Be Made By Anyone, Even Someone Unskilled in Music, Using Musarithms Of The First Syntagma.

Syntagma I contains twelve tablets of polysyllabic musarithms.1Poor Athanasius can't decide if there are 10, 11 or 12 tablets in Syntagma I. Based on the number of tablets illustrated in the text, the correct number appears to be eleven. The first tablet contains polysyllables with a long penult, and the second, polysyllables with a short penult. By means of these, anyone, even someone ἄμουσος [unmusical], may easily prepare every simple counterpoint by a technique that we will explain a little later. And we have started with this syntagma of musarithms since it is simpler than the rest, so that by making a beginning with easier and simpler things we shall feel less difficulty in what follows. And lest we proceed in this business of instruction ἀμεθόδως [unmethodically], it seemed best, following the style of the mathematicians, to demonstrate the handiwork of the whole of our Musurgia by means of some practical propositions or problems. Let us then commence this matter with the good Lord’s favor.

Problem I.

Given any textual theme, & any tone, compose a line of pious music in simple counterpoint using the first tablet.2ex primo pinace. This, however, is not correct. As the text makes clear, the composition will be made from Tablet VI. of Syntagma I. Perhaps 'first syntagma' was intended.

If anyone, then, should desire to make a trial of our art with simple counterpoint, let him before everything else have first prepared the requisite phonotactic palimpsest according to the second chapter of this part of the book; next, the tonographic table; third, let him take a theme of words written down separately. He must select the appropriate tone according to the ‘energy’ of these words.3iuxta quorum verborum energiam. For imploring the grace of the divine Spirit, let the first theme of words be: Veni Creator Spiritus. [Come, creator-spirit.] Since these words denote hope and faith in divine mercy, the sixth, or hypolydian, tone will square with them best. And since this tone is soft, as the title of the tone makes plain on the tonographic table, you will mark the characteristic sign for cantus mollis ['soft-song'] upon the pentagram of voices on the phonotactic palimpsest4The characteristic sign for cantus mollis is ♭.. Then, off to the side, you will place the column of the sixth tone, excerpted individually, next to the colum of the keys in the Tonographic table. The scheme will stand as follows:

Paradigm I.

Musarithm I.5Insofar as this diagram consists of sequences of notes and not of numbers, it seems inappropriate to refer to it as a Musarithm. Melothesia, 'composition', would perhaps be more correct here.
of Keys
Paradigm I
F 8
E 7
D 6
C 5
B 4
A 3
G 2
F 1.8

Having in this way prepared the phonotactic palimpsest & the scale of keys corresponding to the selected 6th tone, we then divide the pentagrams of the four voices into as many spaces as there are syllables in the given theme, as the scheme shows. Then you can order your composition in two ways: with the words of the theme divided or joined together; or, what is the same thing, using several columns corresponding to the different words6diversis thematis vocibus. That vocibus here means 'words' and not 'voices' is clear from the context. of the theme, or using one column corresponding to some whole period of the given theme.7The second method is treated in this section (Problem I). The first method is described in the following section (Problem II), below. By way of example, since the chosen theme is the following four-verse stanza, it may be regarded as consisting of four periods.8This sentence seems to be missing a verb, but its meaning is clear enough.

Veni Creator Spiritus [Come, Creator-Spirit
Mentes tuorum visita Visit the minds of your creations
Imple superna gratia Fill with grace from on high
Quæ tu creasti pectora. The hearts which you created.]

Let each verse, or period, have eight syllables. From the octosyllabic column of the octosyllabic tablet9Tablet VI. take out four musarithms corresponding to the four verses; their sequence in the column can be either in order or out of order, it is the same. Here we have taken musarithms 1, 2, 3 and 4 as follows:10It is somewhat frustrating that the musarithms written-out below do not appear in any of the Tablets illustrated in the text.

    Musarithm I. II. III. IV.
Verse I. Verse II. Verse III. Verse IV.
C. 55555555 33334334 33297667 54328878
A. 77778778 88888888 88235545 86543523
T. 22233223 55566556 33482222 34568555
B. 55538558 88864884 88765225 82346558

Note first that there are four sequences of numbers in each musarithm and these always correspond to the four voices: Canto, Alto, Tenor & Bass. The last sequence of numbers always and immutably represents the Bass, as if it were a foundation for rest; the remaining three voices can be altered according to the whim of the composer. For it makes no difference whether you regard the first sequence of numbers as the Canto, the Tenor, or the Alto, or the second sequence, or the third (for in certain tones, in order that the progression of voices be preserved naturally, they should be altered repeatedly as will be extensively clarified elsewhere). Here, for the sake of avoiding confusion, we have written down the voices in their natural order next to letters placed off to the side; for by C the highest voice, or Canto, is indicated; by A Alto, by T Tenor, and lastly by B Bass.

These things observed, place before yourself the palimpsest prepared according the the account given a little earlier together with the scale of keys attached to the column of the sixth tone, as shown in the preceding paradigm.

Melothesia of the first voice
or Canto.
5 5 5 5 5 5 5 5

Having done this, you will initiate your melothesia thusly, beginning with the Canto. Because in the first sequence of the first musarithm 5 is repeated eight times, observe what letter in the column of keys 5 (or, the five-fold number11Kircher is making the semantic distinction between the symbol '5' and the number which it represents.) corresponds to, & you will find that C corresponds to it. Therefore, in the Canto’s pentagram, in the space in which you see the letter C inscribed, make eight points next to the 8 syllables and you will have fashioned the Canto.

Secondly, for the voice of the Alto, observe to which letter in the column of keys the numbers 77778778 correspond and you will discover that 7 corresponds

Melothesia of the Alto.
7 7 7 7 8 7 7 8

to the letter E. Accordingly, in the Alto’s pentagram12parallelogrammo is written in the text but this is clearly a printer's error. in the space or line marked with the letter E make 4 points. Additionally, since an 8 follows 4 sevens, observe which letter in the column of keys 8 corresponds to & you will find F. Accordingly, in the space or line of the Alto’s pentagram marked by the letter F make a point. But since after the number eight in the series of numbers two 7's afterwards occur, and 7 corresponds to the letter E, mark two more points in the space of E. And since the final number of the Alto’s musarithm is eight, and F corresponds to this in the column of keys, mark the last point in the space regarded as τῷ13τῷ is the Greek definite article, dative case. Used here by Kircher for no particularly good reason. F, and you will have completed the voice of Alto.

Thirdly, since the musarithm of the Tenor is 22233223, observe to which letter in the column of keys the number two corresponds & you will find it

Melothesia of the Tenor.
2 2 2 3 3 2 2 3

corresponds to τῶ G. Therefore, in the space of the Tenor’s pentagram, in the space assigned to the letter G, mark three points accordingly as the triple two’s which occur in the Tenor’s musarithm. Next, observe which letter in the column of keys 3 corresponds to & you will find A. And since three is given twice, mark on the Tenor’s pentagram in the space denoted14signati read as signato. by the letter A, in the cells that follow in order, two points; & again two more points at G on account of the two two’s that follow & signify the letter G. Finally, since the last number is three, & this corresponds to the letter A in the column of keys, mark the last point in the space denoted by the letter A, and you will have finished the Tenor’s voice.

Fourth, for precisely the same reason, since the Bass’ musarithm contains the numbers 5538558, and in the column of keys 555 correspoinds to the letter C, mark in the Bass’ pentagram, in the space assigned to this letter, three points.

Melothesia of the Bass.
5 5 5 3 8 5 5 8

Then, since 3 occurs in the series of the musarithm, and in the column of keys three corresponds to A, mark in the space in the Bass’ pentagram assigned to the letter A one point. Then, on account of the eight which follows immediately in the musarithm, make another point in the space of the pentagram assigned to F (for 8 corresponds to τῷ letter F in the column of keys), and afterwards another two points on account of the double fives immediately following, two more points in the space of the pentagram assigned to the letter C (for 5 corresponds to the letter C). And finally on account of the 8 corresponding to the letter F, mark the final point in the pentagram in the space for F, and you will have completed the Bass’ voice and in such a way that the harmonic intervals of all four voices are determined by the their points. Accordingly, nothing remains except to clothe the individual points in their metrometric notes. You will do this with this technique:

Because the counterpoint is simple & consequently ἰσόχρονος [isochronous], that is, of equal time, or, what is the same, a counterpoint wherein syllable corresponds to syllable and note to note exactly such that the individual notes of the four voices that pertain to the same syllable are of equal value, you will take from the bottom of the column of octosyllables some series of notes which, unless some error is made, will necessarily have as many notes as there are points marked into the spaces on the pentagrams. Place these notes in order above the points of the Bass. Then you will write these same notes over the points of the Tenor, & the same over the points of the Alto, & finally the same over the points of the Canto, and you will have the first period, or verse, of your theme, complete in every respect.15omnibus numeris absolutam. However, you must diligently make sure that the notes are placed precisely in the spaces indicated by their points. But observe the paradigm exhibited in the preceding text which will show you everything exactly line by line. By precisely the same reason & method you will bring to life16animabis, lit., to endow with a soul. the remaining verses, or periods, into a harmony through their musarithms. Indeed, for all the rest, exactly the same technique will serve. Accordingly, from a given theme of words & a definite tone we have produced a simple counterpoint, which is what we had set out to do. The composition is as follows:

Simple Counterpoint Composition

But here practicing musicians will object that by this system the harmony produced will always be the same & consequently the variety of harmonies alleged by the author will not result. We shall easily shut the mouths of these people when we have demonstrated the amazing diversity even in this one example. Therefore the objection is false. For it will become clear that this theme is capable of infinite variation once we have first addressed certain things.

I say, then, that this aforementioned theme may be varied in four ways. First on account of a transposition of the musarithms; second, on account of the tones; third, on account of the assigned notes; and fourth on account of the columns which, because of the diverse feet which even one verse has, admits infinite combinations. But let us examine each of these separately.

First, since this four-verse theme is made from four polyphonic musarithms, it is certain that on account of properties of the number four, as was extensively demonstrated in Probl. I in the first part of this Musurgia,17Book VIII. Part I. Chapter 1, Problem 1. This section is not included in our translation. it has a twenty-four-fold variability, that is, it admits 24 combinations18The number of permutations of 4 objects is 4! = 4*3*2*1 = 24. whereby a new harmony will always emerge different from the one before. For any of the four given musarithms can occupy the first position in six different ways19That is, by fixing the first musarithm, the total number of combinations becomes 3! = 3*2*1 = 6., with the rest being variable. And since all of this was demonstrated in the location cited, we direct the reader there. This four-verse theme can, therefore, be altered first in twenty-four ways such that the harmony is never the same.20This is correct only if we abandon Kircher's prescription that the bottom sequence of numbers of a musarithm must always be used for the Bass.

Secondly, on account of the tones, it is again changeable in twelve ways. For when the moveable scale of keys is moved to the individual columns of the tones, it will produce harmonies that are always fundamentally different in accordance with the variable system of the tones. If, therefore, you take 24 into 12 you will now have 288 mutations2124*12 = 288. whereby this aforementioned four-verse theme is variable.

Thridly, it can be altered on account of the different notes, and according to the 12 series of notes placed at the foot of the column;22A reference to the sequences of metrometric notes placed at the bottom of each Tablet. But see Kircher's illustration of Tablet VI which contains 13 sequences. first, according to simple position 3,456 mutations will arise23Taking the note sequences as fixed at 12, and taking the previous value of 288 combinations due to musarithm order and tone, there are now 12*288 = 3,456 combinations., but according to the combinations of the notes amongst themselves made in whatever way you please 16,554,298,160,800 will arise.24It's not clear where this number comes from. 3,456*12! = 1,655,429,529,600 which is close to the cited number, albeit smaller by the suspiciously unlikely factor of 10.000002. This suggests that we have a two-fold printer's error: first by adding one too many zeros, and second by mis-transcribing the digits to the right of 9. However, to the extent that any of this is correct, I don't agree with the approach in the first place. Because the verses have eight syllables, my best interpretation of Kircher's intent would suggest a total number of combinations of 3,456*8! = 139,345,920. And by this number of possible ways is this single four-verse stanza variable according to the strict definition of the word. Since all of this was demonstrated in the first book, I reckoned that it would be superfluous to draw this out further here since we have demonstrated all of this in the cited location in such a way that anyone who is ignorant of these things can, and should, in no way doubt of them subsequently.

Fourthly, a mutation can be made that is almost infinitely variable if, indeed, the columns be ordered according to the different feet of a metric verse. I have decided that this should be clarified with an example, and so it is.

A new method of composing.

A technique for composing any line of music in simple counterpoint.

This new method of composing is capable of infinite variation.

Variation on account of the trans-position of musarithms.

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