As I observed above, the musical context of ex.3 suggests that the sign 3 denotes sesquialtera
(3:2) in relation to [cts.].
The major fifth is that which contains three whole tones with one semitone and is that fifth which is counted among the perfect consonances, and which musical authors define as consisting of the sesquialtera
proportion; the minor fifth is that which contains two whole tones with two semitones and is not a consonant interval but is counted among the intervals that are truly discordant.
The blackened semibreve plus blackened minim therefore occupies the time of the unblackened semibreve occurring in adjacent music in integer valor, so producing the sesquialtera
proportion of 'three in the time of two'.(7) A conventional and straightforward interpretation of this notation in these instances produces satisfactory results that appear to give no cause for misgivings.
These were normally known by the Latin names inherited from Cicero and Boethius; however, one musician called the proportion 3:4 'subdiatessaron' instead of subsequitertia and 3:2 'diapente' instead of sesquialtera
, another defined 'diapason', 'diapente', and 'diatessaron' not merely as the intervals, harmonic and melodic, of octave, fifth, and fourth, but as the proportions 2:1, 3:2, and 4:3, properly dupla, sesquialtera
, and sesquitertia.(22) Not knowing that the dia- names, with their subintended
12, "Also hat Gott die Welt geliebt," containing the only triple sections notated by Schutz at the minim level instead of the semibreve level, under the time signature "3"; here a sesquialtera
interpretation, as Kuster notes (p.
B 115 diagram diatesseron in sesquialtera
: <tonus> in sesquioctava
Newcomb interprets all signs of triple meter as sesquialtera
proportions (three notes in the time of two) without comment.
Even in straightforward pieces, singers were accustomed to construing from the context whether a coloured minim in the same piece and under the same signature meant a semiminim, or was part of an imperfection group, or was subject to triplet sesquialtera