History of Music Theory, Part Six
Immediately after the first great flowering of diaphonic and polyphonic Western Art Music at Notre Dame with Leonin and Perotin, music theory starts working it's way from the Ars Antigua to the Ars Nova and counterpoint as we are accustomed to thinking of it today, versus the older organum. Counterpoint is an anglicisation of the word Contrapunctus, which is itself a contraction of the term Punctus Contra Punctum meaning note-against-note. These terms appear with increasing frequency in treatises of the 13th century until the terminology is mostly standardized by the end of the 14th century into the 15th. The break with older practice is in no way a clean one, and the striving for terminology and "rules" is actually quite a messy affair.
Another term that appears is Puncti Contra Punctum - notes-against-note - and in association with that the term cantu fractibili, which refers to a melody added to the cantus firmus that moves faster in smaller note values. Here we find some of the first attemps at handling dissonance, but it is not treated in a rigorously syatematic way. Rather, it is mentioned more or less in passing that dissonances are allowed after strong-beat consonances on subsequent beats before the next required strong-beat consonance. No doubt this had been a reality of discant practice for many years, as the final musical example I presented earlier shows.
What is of primary interest to me here is the evolution of contrapuntal rules during the 14th and 15th centuries. Previously, I had shown how the evolution of the concept of consonance worked it's way up the natural harmonic overtone series, and the rules of counterpoint relate to the overtone series as well. Prohibitions against parallel movement of unisons and octaves are quite easy to understand, as the effect is that of the cantus firmus simply being doubled: No melodic independence is maintained. The effect of parallel perfect fifths is very close to that of parallel perfect octaves because the low 3/2 ratio of perfect fifths results in a sound second only to the octave in hollowness, and many of the upper partials of a note a perfect fifth above a fundamental are simply absorbed by that fundamental's overtones.
The perfect fourth could possibly be considered the most problematic interval in all of music theory. There are several reasons for this. One is that, of the perfect consonances, it has the highest harmonic density (The thickest sound), and for that reason shares more characteristics with the imperfect consonances and even the dissonance of a major second than it does with the perfect fifth. Another relates to that, and it is that many vocal formants hover around the fourth, and so the voice at the fourth below has it's syllables interfered with and is less than perfectly intelligible. This wasn't a problem in 1:1 ratio early organum where both voices were singing the same text, but it became a consideration as the voices and texts gained independence. The final reason is that the perfect fourth implies the harmony of a 6/4 chord or a 4-3 suspension to us, and those sonorities require a resolution to our ears. Lest you think that is a modern conditioning that the ancients would have been immune to, in some of the earliest treatises dealing with three voice writing, the 6/4 arrangement was singled out as something that was expressly forbidden. If you are familiar with modern voice leading rules as they apply to harmony, you know that parallel perfect fourths are OK in upper voices in three or more parts, but if you are trying to write fully invertible counterpoint in three or more voices, they must be avoided. For our purposes here, that's the way we are going to treat the perfect fourth: Parallels are not allowed. This simplifies the rule to no parallel perfect consonances, which are those found between the fundamental and the first three overtones.
Once the imperfect consonances had been worked out, which I went through in an earlier example, the second rule could be formulated: Parallel imperfect consonances have no restrictions, except those governed by taste. This is very easy to grasp. The interval density of thirds and sixths is higher than octaves and fifths, and no more than two diatonic thirds or sixths in a row are of the same size: Though momentarily coupled, the melodies retain their independence. So, the imperfect consonances found above the third harmonic are allowed to move in parallel, but the perfect consonances below the third harmonic are not. Simple really.
Way down the road from here, when I tackle "The Schillinger System of Musical Composition" again, I will show how these early formulations of rules for the handling of consonance and dissonance in countrapuntal writing were strivings toward the ultimate goal, which is the concept of combining two or more complimentary melodic trajectories into a cohesive whole. It could be years.
Another term that appears is Puncti Contra Punctum - notes-against-note - and in association with that the term cantu fractibili, which refers to a melody added to the cantus firmus that moves faster in smaller note values. Here we find some of the first attemps at handling dissonance, but it is not treated in a rigorously syatematic way. Rather, it is mentioned more or less in passing that dissonances are allowed after strong-beat consonances on subsequent beats before the next required strong-beat consonance. No doubt this had been a reality of discant practice for many years, as the final musical example I presented earlier shows.
What is of primary interest to me here is the evolution of contrapuntal rules during the 14th and 15th centuries. Previously, I had shown how the evolution of the concept of consonance worked it's way up the natural harmonic overtone series, and the rules of counterpoint relate to the overtone series as well. Prohibitions against parallel movement of unisons and octaves are quite easy to understand, as the effect is that of the cantus firmus simply being doubled: No melodic independence is maintained. The effect of parallel perfect fifths is very close to that of parallel perfect octaves because the low 3/2 ratio of perfect fifths results in a sound second only to the octave in hollowness, and many of the upper partials of a note a perfect fifth above a fundamental are simply absorbed by that fundamental's overtones.
The perfect fourth could possibly be considered the most problematic interval in all of music theory. There are several reasons for this. One is that, of the perfect consonances, it has the highest harmonic density (The thickest sound), and for that reason shares more characteristics with the imperfect consonances and even the dissonance of a major second than it does with the perfect fifth. Another relates to that, and it is that many vocal formants hover around the fourth, and so the voice at the fourth below has it's syllables interfered with and is less than perfectly intelligible. This wasn't a problem in 1:1 ratio early organum where both voices were singing the same text, but it became a consideration as the voices and texts gained independence. The final reason is that the perfect fourth implies the harmony of a 6/4 chord or a 4-3 suspension to us, and those sonorities require a resolution to our ears. Lest you think that is a modern conditioning that the ancients would have been immune to, in some of the earliest treatises dealing with three voice writing, the 6/4 arrangement was singled out as something that was expressly forbidden. If you are familiar with modern voice leading rules as they apply to harmony, you know that parallel perfect fourths are OK in upper voices in three or more parts, but if you are trying to write fully invertible counterpoint in three or more voices, they must be avoided. For our purposes here, that's the way we are going to treat the perfect fourth: Parallels are not allowed. This simplifies the rule to no parallel perfect consonances, which are those found between the fundamental and the first three overtones.
Once the imperfect consonances had been worked out, which I went through in an earlier example, the second rule could be formulated: Parallel imperfect consonances have no restrictions, except those governed by taste. This is very easy to grasp. The interval density of thirds and sixths is higher than octaves and fifths, and no more than two diatonic thirds or sixths in a row are of the same size: Though momentarily coupled, the melodies retain their independence. So, the imperfect consonances found above the third harmonic are allowed to move in parallel, but the perfect consonances below the third harmonic are not. Simple really.
Way down the road from here, when I tackle "The Schillinger System of Musical Composition" again, I will show how these early formulations of rules for the handling of consonance and dissonance in countrapuntal writing were strivings toward the ultimate goal, which is the concept of combining two or more complimentary melodic trajectories into a cohesive whole. It could be years.
posted by Hucbald at 8:26 PM
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