Sebald Heyden, Musicae, id est Artis canendl libri duo (Nuremberg: J. Petreius, 1537)
The second of three editions of Heyden’s treatise, each of which was published with a different title; the third edition is De arte canendi.
Source of piece in Choralis Constantinus II: The book was published in the same year that Ott announced the forthcoming publication of Isaac’s Choralis cantus constantiensis. Heyden, working in the same city as Ott, would have had access to his source.
Choralis Constantinus II contents:
- Mass 25
- Sequence, v. 2 (p. 92)
Character of the Choralis Constantinus II example:
The example is without text. It is notated with the most complex set of proportions in any work of the period. The numerical proportions are represented with fractions (2/1, 3/1, 4/1); the corresponding proportions in the print are shown with single numbers (2, 3, 4).
There are no earlier sources for the piece. It is likely that Heyden revised the original notation, as he did that of many of his examples, for the purpose of illustrating his theory. See Ruth I. DeFord, “Who Devised the Proportional Notation in Isaac’s Choralis Constantinus?” in Heinrich Isaac and Polyphony for the Proper of the Mass in the Late Middle Ages and Renaissance, ed. David J. Burn and Stefan Gasch (Turnhout, Belgium, 2011), 167-213.
Heyden's reference mensurations are Օ and Ϲ. Other signs relate to them as follows:
- In Ꙩ and Ͼ a minim equals a semibreve of Օ or Ϲ.
- In Օ2, Ϲ2, and ₵ a breve equals a semibreve of Օ or Ϲ.
- In ₵2 and ₵Ɔ a long equals a semibreve of Օ or Ϲ.
- In 3/1 breves are perfect, and three semibreves equal a semibreve of Օ or Ϲ.
- In 4/1 eight semibreves equal a semibreve of Օ or Ϲ. The sign implicitly presumes a ₵ before the 4/1, but this principle is inconsistent with Heyden's other proportion signs and the explanation of quadruple proportion in his text. The anomaly was probably the cause of the inconsistent errors in both the original and the resolution of the bass in m. 18 (see below).
- Coloration functions mostly to make notes imperfect in perfect mensurations, but at the end of the altus (m. 18) it creates sesquialtera (3/2) proportion of the current 4/1, calling for three black longs (in place of two white longs) in the time of a semibreve of Օ or Ϲ. At the end of the tenor (m. 18) it creates sesquialtera proportion of the new sign 2/1, calling for three black breves (in place of two white breves) in the time of a semibrve of Օ or Ϲ.
Proportions are not cumulative. The above formulas apply regardless of what mensuration precedes a numerical ratio.
Heyden adds a "resolution" of the notation in ₵. The passages in 3/1 in the original version are unchanged in the resolution. The sign 2/1 remains before the coloration in the tenor in m. 18, where a return to ₵ (which has the same meaning as 2/1 in Heyden's system) would be more logical and more consistent with the other voices.
The original notation has two errors:
- B, m. 4: sign is Օ3.
- B, m. 18 n. 4: the note is a long.
The resolved notation has three errors and one minor variant:
- B, m. 2 n. 2: pitch is c' (error).
- B, m. 15: ₵ is missing (error).
- B, m. 18 n. 1-3: rhythm is breve-semibreve-semibreve (error).
- A, m. 14 n. 6-7: semibreve instead of two minims (variant).