Advanced Rules for the Treatment of Perfect Intervals in Counterpoint Excerpts from Treatises by Albrechtsberger, Berardi, Dressler, Diruta, Fux, Tigrini, Tinctoris, and Zarlino, plus excerpts from Salzer and Schachter and the PhD Dissertation of William Clemmons
Preliminaries: Diruta Moving from one perfect consonance (always contrary motion – not oblique!) is understood differently than moving to a perfect consonance from an imperfect one (contrary and by semitone in one voice). Preliminaries: Salzer and Schachter Unisons only to be used at beginning or end of exercise, or as diminution. On off-beats, should be left by step in the opposite direction to the approach. Directly consecutive perfect intervals of same type are forbidden; use on consecutive accented beats are best avoided, but sometimes permissible (when the melody does not imply polyphonic melody / when the second perfect note in the contrapunctus is the second note of 3+ notes moving in the opposite direction to the approach from the previous perfect consonance? 5-6 technique?) Battuta octaves (not clearly defined) – worst case scenario: leap in upper voice + weak to strong beat. Note that this may also include Battuta fifths. Minimize Perfect Intervals: Zarlino Avoid unisons altogether; use very few octaves. “I do not mean that they should not be used, only that they should be used sparingly. […] He should separate them, however, by other consonances, and he should prefer the octave to the unison …” (Institutione Harmoniche, III:41) Hidden Perfect Intervals: Fux Perfect intervals approached by similar motion imply parallel perfect intervals through diminution by supposition. Hidden Perfect Intervals: Clemmons Side notes: Unisons and octaves discouraged on downbeats except cadences. Repetition of perfect interval by voice-exchange (a la Zarlino) considered amateurish. Same explanation as Salzer & Schachter above, but notes that Fux was early to suggest this manner of explanation, where other theorists gave explanations from speculative theory. Diruta and Tigrini use the same explanation.
Hidden Perfect Intervals: Diruta Explanation is as given by Fux and Schachter. However, Diruta gives the example twice, because it corresponds to each of two rules: movement between two perfect intervals (even of different kinds) and movement from imperfect to perfect. Hidden Perfect Intervals: Tigrini Explanation is again as given above. However, the chart over the following two pages provides several exceptions; these exceptions are not clearly explained. Consecutive Unlike Perfect Intervals: Zarlino In general, follow a perfect consonance by an imperfect consonance (that is, avoid moving directly from one perfect consonance to another, as from an octave to a fifth, even in contrary motion). What about the 2-1 / 5-1 in a PAC? What about 2-1 / 7-6-8 in a Landini Cadence? What about Diruta’s rule, which describes the use of contrary motion between perfect cadences Also, no mention in any of the sources about counter-parallel perfect intervals. Battuta Octaves: Fux Mann Fig. 15, Showing “Battuta Octaves” in m.11
Fux observes that the octaves are approached by contrary motion by step from the outside, and does not know why it is a problem. He contrasts it to Fig. 16, which is allowed, though Fux feels that it shouldn’t be.
Good
Bad
However, compare the same figures from the original Latin edition:
Fux allows his student to make up his own mind about the case in question, but argues that the skip into an octave (or unison) should never be used (except in a bass part). A skip from a unison is also not good. Battuta Octaves: Clemmons Octava Battuta = Beaten Octaves = Downbeat Octaves. “Sixteenth-century Italian theorists viewed even note-against-note counterpoint against a duple background of two semibreves to the bar, in which octaves were allowed only on the second, or upbeat semibreve” (Clemmons, PhD Dissertation, 128). Without this distinction, the idea of Battuta octaves makes no sense in first species. Fux’s sample “error” (figure 17) comes from Berardi (see below). The Berardi example is ambiguously written; Clemmons suggests that the real problem is that both voices move by whole (neither by semitone), hence also violating the rule given by Diruta (above). Therefore, in spite of Berardi’s casual mention of the downbeat, this is not actually a case of Battuta octaves (though it is still an error); on these terms, fig. 16 (as given by Mann) would also be an error (no semitone). Fux’s counter-example (in the original edition) relates to an example by Bononcini, which permits expanding from a fifth to an octave (similar to Diruta rule requiring contrary motion between perfect consonances, but in violation of Zarlino); Fux disagrees with it due to the skip into/from a perfect interval (but not concerned about semitones, which he only worries about at cadences). Battuta Octaves: Berardi Passage quoted by Clemmons above; translation disagrees as regards the position of the downbeat – stressing that this is not Battuta octaves, but rather an inappropriate approach (lacking a semitone). Battuta Octaves: Albrechtsberger Battuta octaves formerly never permitted; Albrechtsberger allows it in three or more parts. Occurs when an octave is approached on an accented beat, especially when the upper part descends by skip of fourth or greater (while lower ascends by step). Perfect Intervals and Modes: Fux A counterpoint below the cantus cannot begin a fifth below, because this contradicts the mode.
Perfect Intervals and Modes: Tinctoris A perfection (perfect interval? Cadence? Same thing?) should not be allowed that contradicts the mode. Perfect Intervals by Mode: Dressler Chart of allowable cadence tones by mode: MODE Dorian Hypodorian Phrygian Hypophrygian Lydian Hypolydian Mixolydian Hypomixolydian
Allowed Scale Degrees 1, 2, 3, 5, 8 1, 2, 3, (5), low 5 1, 3, 4, 5, 6, 8 1, 3, 4, low 6 1, 3, 5, low 5 1, 3, 5, low 5 1, 4, 5, low 5 1, 4, 5, low 5
