1. L'Artusi overo delle imperfettioni della moderna musica (Venice, 1600), ff. 21-21v. The complete text, together with full graphics, is available online at the following URL: http://WWW.music.indiana.edu/smi/seicento/ARTIMP_TEXT.html.
2. The two voices as printed by Artusi can be viewed online at the following URL: http://www.music.indiana.edu/smi/seicento/ARTIMP_04GF.gif.
3. Edward Lowinsky, "Adrian Willaert's Chromatic 'duo' Re-examined", Tijdschrift voor Muziekwetenschap, 18 (1956-9), pp. 1-36.
4. Joseph S. Levitan, "Adrian Willaert's Famous Duo Quidnam ebrietas", Tijdschrift der Vereeniging voor Nederlandshe Muziekgescheidenis, 15 (1938-9), pp. 166-233.
5. Margaret Bent, "Diatonic Ficta", Early Music History 4 (1984), pp 16-20.
6. Dorothy Keiser, "The Character of Exploration: Adrian Willaert's 'Quid non ebrietas'", Musical Repercussions of 1492 ed. Carol E. Robertson (1992), p. 185.
7. Rob Wegman, "Music Ficta", Companion to Medieval and Renaissance Music ed. T. Knighton and D. Fallows (London 1992), pp. 270-1.
8. This, and many other observations derived from the correspondences between Spataro and Aron, is discussed in greater length in Edward Lowinsky, "Adrian Willaert's Chromatic 'duo' Re-examined".
9. When a melody arises from the use of diatonic tetrachords its resulting diatonicism regulates the disposition of tones and semitones so that each semitone is surrounded (if the pitch material is presented as a scale) by a minimum of two and a maximum of three undivided tones. If the tetrachords are disjunct, there will be three undivided tones in the series. Where tetrachords are conjunct there will be only two.
10. Similarly (though irrelevant to this composition) the most distant pitch in the chain sharpwards to which ficta notation could be applied is A-sharp (occurring between the two recta notes A and B).
11. All voices are given a default signature of one flat and this indicates that the default pitch material will be a scale that employs the synemmenon tetrachord with the B-flat and not the Diezeugmenon with B-natural. This will assert a disjunction of tetrachords on the notes D-E (D being the highest note of the synemmenon and E the lowest note of the Meson). Only the Tenor voice applies structured modifications to this default as it adds its further flats. The other voices remain faithful to the default, thereby retaining the simple "white-note" scale with an added B-flat.
12. A full account of Syntonic tuning is given by Willaert's distinguished pupil, the theorist Zarlino in his Le Istitutioni Harmoniche, part 3. Full texts and graphics of this work are available online at http://www.music.indiana.edu/smi/cinquecento. This will not be discussed in this essay, but will form part of the supporting evidence presented in a later essay that develops further the findings revealed here.
13. The singer of the Tenor will still be reading these semitones as F-G flat and B flat-C flat (sung a semitone lower by double ficta).
14. These flats are also shown in Example 7 above near the end of staff 1.
15. Altus partbook of Libro primo de la fortuna discussed in Edward Lowinsky, "Adrian Willaert's Chromatic 'duo' Re-examined".
16. His Tenor was correct, but for the wrong reasons. His four-voice rendition made the Tenor's interval structure more or less inevitable, but the insertion of multiple editorial flats and double-flats obscures the simplicity and clarity of the original notation, and misunderstands the structural purpose of the resulting melodic inflections in terms of the transformation to Syntonic tuning. Indeed, Lowinsky assumed the use of equal temperament. The editorial flats also presume that the notational default (in the second half) is "white-note" whereas we can now see that an understanding of the tetrachord structure reveals it to be essentially "black-note".
17. The pitches are computer generated, and a detailed explanation of the processes used to produce this, and all other Audio examples accompanying this study, will be offered in a future article.
18. Lowinsky's Bassus adopted a range of an octave plus a sixth, and this was much greater than that found in the other voices.
End of footnotes