Canons calculated through "tabula mirifica"

In this specific, three-voice canon, the artifice (highly praised by musicians of the past) of double counterpoint at the twelfth is employed, in which the two first parts in play lead, by canonical imitation, the third voice; which enters after the pause separating Proposal from Response (in this case after a semibreve).

Adherence to the privative rules that govern this counterpoint, correspond to the deprivation of the sixth interval (understood as consonance) between the two of them (A and B), and allows the dissonances (obviously linked) of

    Fourth and Eleventh above, resolved to the Third and Tenth, as well as
    to the ninth below, resolved to the tenth.

Two types of canon can be realized, depending on the setting of the response pouring, we can realize the canon

    by pouring the proposal a low fifth and recopying the response an octave high 5/8
    by pouring the proposal one octave low and copying the answer one fifth high 8/5.

Thus, the case under consideration is No. 1
In fact, the third voice (C) is the transport of the voice (B), an octave above

Let us see, the comparison section of the tabula, related to the double counterpoint to the twelfth
The green boxes represent consonance shares between B and C, while the colorless boxes mark dissonances
or consonances without mutual correspondence.


C



B
Consonances and dissonances between counterpoint and subject matter

Finally, we can check the nature of the interval relationship, between A and B (the canon matrix) and the added part C,
produced by pouring back to the octave above B, by comparing the consonances and dissonances between the musical score and the numerical superposition given above.
The experience gained allowed to proceed smoothly, but observing the privative rules (without sixth as consonance) that donated the canonical imitation of the third and wanting, of the fourth part.


Line-by-line description of the process in three steps:

  1.     A (proposal) produces the first semibreve
  2.     B (answer 1) repeats the proposal a fifth below
  1.     C (answer 2) repeats B one octave above

The process would go on in the same way (A+B+C) until the composer liked it and end with a cadence to the starting tone,
either with a small coda out of canon or better by bringing the canon to a natural cadence end, without interrupting
the process of imitation.