Benchmarks

1

We investigate the score of Example 7.6.3, and the three progressions in Example 7.6.4 from A Geometry of Music by Dmitri Tymoczko. The author argues that each feature

"contrapuntally unobjectionable progressions that are quite rare in functionally tonal music. All feature efficient melodic motion, avoid forbidden parallel fifths and octaves, and resolve the leading tone upward by step; all would be perfectly acceptable in sixteenth- or twentieth-century music. Yet Figure 7.6.5 shows that they are virtually absent in Mozart's piano sonatas. The challenge for the monist is to explain this using recognizably contrapuntal principles."
Example 7.6.3 by Dmitri Tymoczko.
Example 7.6.4 by Dmitri Tymoczko
Library configuration with Bach and Mozart

The Pirate Fugues uses neither explicitely the rules of counterpoint, or chord analysis. Therefore, the question is: Does The Pirate Fugues software indicate that these scores are weak, and are not associated to Bach or Mozart? ... Indeed! As can be seen by the zeros in the blue squares, and the red c's which indicate that the transitions do not occur in the database: Example 7.6.3 is weak in 4 locations; each progression in Example 7.6.4 contains exactly one flaw.


2

The resolution of dissonances

We quote from the translation of Johann Joseph Fux's Gradus ad Parnassum by Alfred Mann, chapter The Fourth Species of Counterpoint in subsection The resolution of dissonances:

Joseph. - Why do you omit the seventh? [...] Aloys. - I have intentionally omitted the seventh. However, there is hardly any reason to be given except the model of the great masters, to which we should always pay the utmost attention in our work. There is no one among them who has used the seventh resolving in this way to the octave:

Indeed, the database of the pirate fugues does not contain the verbatim measures that Fux notates. However, the transition from {b-1, a0} to {a-1, a0 (held)} occurs with b-1 as a passing note in three instances: Well-Tempered Clavier 1, Prelude 3 in measure 14, also in measure 31. Well-Tempered Clavier 2, Prelude 10 in measure 90. Important: Each of the scores were transposed to C major, or a minor respectively for a fair comparison.