Figure 9. Unused permutations of intervals comprising the 5th in the chromatic and enharmonic genera. Whereas all permutations of the diatonic species of 4ths, 5ths, and 8ves, and all permutations of the chromatic and enharmonic 4ths are used in Vicentino’s theories, the chromatic and enharmonic 5ths in Figure 8 above could be generalized to include these. Berger believes the chromatic 5th shown here, and the last of the enharmonic 5ths shown here, to be the correct structures intended by Vicentino for the G–d 5th instead of the structures that appear in L’Antica musica; see my notes 29 and 31 for discussion.

The abstract templates (aaabaaa etc.) could be realized in more than one way depending on the distribution of major and minor dieses (major and minor semitones in the case of the chromatic genus). Here I have chosen ways that correspond most closely to Vicentino’s practices.