What is "abacus harmonicus"

Abacus \Ab"a*cus\ ([a^]b"[.a]*k[u^]s), n.; E. pl. Abacuses; L. pl. Abaci (-s[imac]). [L. abacus, abax, Gr. 'a`bax]

1. A table or tray strewn with sand, anciently used for drawing, calculating, etc. [Obs.]

2. A calculating table or frame; an instrument for performing arithmetical calculations by balls sliding on wires, or counters in grooves, the lowest line representing units, the second line, tens, etc. It is still employed in China.

3. (Arch.)

   1. The uppermost member or division of the capital of a column, immediately under the architrave. See Column.

   2. A tablet, panel, or compartment in ornamented or mosaic work.

4. A board, tray, or table, divided into perforated compartments, for holding cups, bottles, or the like; a kind of cupboard, buffet, or sideboard.

   Abacus harmonicus (Mus.), an ancient diagram showing the structure and disposition of the keys of an instrument.
   --Crabb.

Abacus Harmonicus, or Abacum Arithmetico-Harmonicum is a table and tabular method described in Athanasius Kircher's comprehensive 1650 work on music, the Musurgia Vniversalis. The purpose is to generate counterpoint combinations. Also mentioned in early editions of the Encyclopedia Britannica, it is best described by the author's caption: "wonderful table that reveals all the secret art of counterpoint".