The Universal Art of Music, Volume II (1650) - Page 18

A A L A L A L A A

You see, therefore, in this example, that this name Kircher uses "name" or "voice" to refer to a string of letters. does not allow more than three changes because the letter A is placed twice. For if you place the two AAs at the beginning once; then one at the beginning and the other at the end; and thirdly, both at the end; the entire combination will be exhausted. Likewise, if you wish to know the combinations of a four-letter name tetragrammatona word consisting of four letters with two similar letters, you divide 24 by 2; the resulting 12 will be the sought-after combination of said name.

Example of a four-letter name in which two letters are twice repeated.


1	יהוה	7	החוי
2	יההו	8	החיו
3	יוהה	9	הויח
4	ויהה	10	חיהו
5	וחיה	11	חיוה
6	וההי	12	הוחה

The table shows permutations of the Hebrew Tetragrammaton (Y-H-V-H). In this name, the letter He (ה) appears twice. In the permutations shown, Kircher explores the 12 possible arrangements of these four characters.

You see in this example that this name is not combinable except twelve times, as the example teaches. There you see the letter He (ה) placed six times at the beginning, Vav (ו) three times, and Yod (י) three times, which joined together constitute the sought number of 12 for the combinations of this four-letter name. The same is to be said of any other four-letter name. If, however, some four-letter name had three similar letters—that is, the same ones—24 divided by 6 will give the sought change of combination, as is clear in the second example. There you see it is impossible for it to admit more than 4 changes.

Example of a four-letter name in which three letters are similar; they can only be changed four times, as in AAAL.

A A A L A A L A A L A A L A A A

Again, let there be a five-letter word pentagrammaton which has three similar letters, such as AMARA. You will have its combination thus: if you divide the combination of five things—namely 120—by the combination of the number three which is 6, according to the previous table, which you will find in the sixth table. For the quotient will give 20, the sought combination of the name, as appears in the example, in which you see this name cannot admit any other combination.


1	AMARA	11	AAARM
2	AMAAR	12	AAAMR
3	AMRAA	13	MAARA
4	ARMAA	14	MAAAR
5	ARAAM	15	MARAA
6	ARAMA	16	MRAAA
7	AARAM	17	RAAAM
8	AAMRA	18	RAAMA
9	AAMAR	19	RAMAA
10	AARMA	20	RMAAA

I wished to place these few examples here so that the truth might become known through small instances. But so that the curious Reader may have the combination of any other things ready at hand, we have wished to add a table here, in which you will see more quickly than said all things that have been discussed up to this point.