Dandrieu's Treatise

Click Here for the Lessons

Each of Dandrieu’s lessons comes in three parts:

  1. Full realizations given via figures;
  2. The figures for those realizations that would be seen in practice; and
  3. No figures at all.

He presents each lesson in a variety of common keys, generally ranging to one or two sharps or flats. When a new type of harmony is introduced, he uses a square note instead of a round one.

The lessons here take this to its logical conclusion: each exercise is given in the three forms (full, figured, unfigured) in all reasonable keys. These are generated using Lilypond via a script that transposes the lessons into each key. Additionally, Dandrieu’s inversions can be constructed from each other via inverting the figures in a regular fashion, with a few exceptions to deal with the occasional 5-voice realization and any doubling. For example, the entire input for generating one lesson is:

L'Acord de la Sixte Majeure jointe à la Fausse Quinte (Mineure)
a1 \square b gis a a a e a
<8 5 3>1 <6+ 5-> <3 6 5-> <8 5 3> <7+ 6 4 2> <8 5 3> <3+ 8 5> <8 5 3>
"
""
s1 <5- 6+> <5-> s <6 7+> s <_+> s

The name, the bassline in Lilypond format, one inversion of the figures, two lines " and "" saying the other inversions don’t have exceptions, and the practical figures.

Caveats

The latter lessons (starting from my #29 on) give everything only in minor keys and F major; this is due to the fact that the harmonies described don’t work in major keys. Nonetheless, Dandrieu gives a harmonization of the major form of that bassline (with different figures) since the bassline works in a major key. As a result, he gives only a single inversion for the major case; I have filled in the other inversions myself. Take particular care here, as I may have missed voice-leading errors.

Dandrieu is very particular in his use of slashed vs. flat 5 figures: he uses a flat figure when it will land on an accidental key and a slashed figure otherwise. This has not been replicated here for two reasons:

  1. This will not be consistent between keys (i.e. additional script-logic is needed, i.e. laziness); and
  2. This is not seen in practice (including in Dandrieu’s own publications).

All exercises here will use flat-5 figures.

Please send me any errors you find: typographical, musical or otherwise.