History of Music Theory, Part Four
Last night I labored my way through the first chapter of Book II, which is chapter VIII, and it concerns itself with mensural notation to the beginning of the 14th century. I must admit to having less than no interest at all in this particular area of study, and I found myself nodding off from time to time. As a practical musician, I simply use the notational practices handed down to me, and I could hardly tell a neume from a plume of mustard gas if my life depended on it. In any event, Riemann made several incorrect assumptions and there seem to be so many areas of dissagreement and conjecture that I found myself hoplessly confused concerning several points about how neumes were actually employed in the earliest eras in which they appear.
About the only thing that really kept my interest was the continued unfolding pantheon of magnificent names. Hieronymus de Moravia is a cool name, and I didn't previously know it translated to "Jerome". There is a lady I met once with the last name of Hieronymous who is a prominent supporter of the arts, and now I'm wondering if I should address her as Ms. Jerome next time I run into her. Probably not. I also ran into the name of the earliest of the composers I really like, Perotinus Magnus, as well as Petrus de Cruce, the optimus notator. Aribo Scholasticus has to be an envious name among the scholarly class, but my favorite of all so far is without doubt, Prosdocimus de Beldemandis. Say that a few times. It really is delicious.
Fortunately, I have a couple of more points to make about the evolution of consonance and dissonance I'd like to get across. I mentioned yesterday that theorists were having a hard time rationally coming to terms with imperfect consonances because they were trying to relate them to the Pythagorean tuning system, and that practice had gotten ahead of them for this reason. Be reminded that the evolution of consonance was still an incramental process. After the unison, octave, perfect fifth, and perfect fourth that were the original consonances, thirds were next to appear. Sixths were initially treated as dissonances, but then they were admitted as consonances; first the major sixth and then the minor sixth. Note how this progression goes up the natural harmonic overtone series.
If we label the pitches as C1, C2, G2, C3, E3, G3, B-flat3, C4 - which are all the pitches we will need for this demonstration - the point can easily be made. In the beginning of diaphonic music, only the perfect unison C1-C1, the perfect octave C1-C2, the perfect fifth C2-G2, and the perfect fourth G2-C3 were admitted as consonances. Note that these are all found in that part of the series that encompasses the fundamental and the first three overtones. Note also that these intervals retain the appelation of "perfect" to this day.
Next, the thirds were admitted: The major third C3-E3 and the minor third E3-G3. At this point the fundamental and the first five overtones had been explored, but not completely. It may seem strange that the sixths were admitted incramentally until you consider that the major sixth first appears between G2-E3 - within the range of the fundamental and the first five overtones - but the minor sixth not until E3-C4, which requires that the range be extended up to the seventh overtone above the fundamental. Notice that all of the basic elements for invertible counterpoint are now in place, and that these intervals all come down to us with the appelation "imperfect consonances" still attached to them. As for the sixth overtone at B-flat3, the implications that it would have would have to wait for the development of cadential and harmonic concepts. That would take... er... a while.
About the only thing that really kept my interest was the continued unfolding pantheon of magnificent names. Hieronymus de Moravia is a cool name, and I didn't previously know it translated to "Jerome". There is a lady I met once with the last name of Hieronymous who is a prominent supporter of the arts, and now I'm wondering if I should address her as Ms. Jerome next time I run into her. Probably not. I also ran into the name of the earliest of the composers I really like, Perotinus Magnus, as well as Petrus de Cruce, the optimus notator. Aribo Scholasticus has to be an envious name among the scholarly class, but my favorite of all so far is without doubt, Prosdocimus de Beldemandis. Say that a few times. It really is delicious.
Fortunately, I have a couple of more points to make about the evolution of consonance and dissonance I'd like to get across. I mentioned yesterday that theorists were having a hard time rationally coming to terms with imperfect consonances because they were trying to relate them to the Pythagorean tuning system, and that practice had gotten ahead of them for this reason. Be reminded that the evolution of consonance was still an incramental process. After the unison, octave, perfect fifth, and perfect fourth that were the original consonances, thirds were next to appear. Sixths were initially treated as dissonances, but then they were admitted as consonances; first the major sixth and then the minor sixth. Note how this progression goes up the natural harmonic overtone series.
If we label the pitches as C1, C2, G2, C3, E3, G3, B-flat3, C4 - which are all the pitches we will need for this demonstration - the point can easily be made. In the beginning of diaphonic music, only the perfect unison C1-C1, the perfect octave C1-C2, the perfect fifth C2-G2, and the perfect fourth G2-C3 were admitted as consonances. Note that these are all found in that part of the series that encompasses the fundamental and the first three overtones. Note also that these intervals retain the appelation of "perfect" to this day.
Next, the thirds were admitted: The major third C3-E3 and the minor third E3-G3. At this point the fundamental and the first five overtones had been explored, but not completely. It may seem strange that the sixths were admitted incramentally until you consider that the major sixth first appears between G2-E3 - within the range of the fundamental and the first five overtones - but the minor sixth not until E3-C4, which requires that the range be extended up to the seventh overtone above the fundamental. Notice that all of the basic elements for invertible counterpoint are now in place, and that these intervals all come down to us with the appelation "imperfect consonances" still attached to them. As for the sixth overtone at B-flat3, the implications that it would have would have to wait for the development of cadential and harmonic concepts. That would take... er... a while.
posted by Hucbald at 10:54 AM
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