At the end of the two-voice part of the book, I had two theory questions. I think I now have educated guesses at the answers.
Q: Why is there no mode corresponding to B?
A: Because this would be a mode without a perfect 5th. (B-F is an augmented 4th. B-G is an augmented 5th. The perfect 5th above B requires an accidental-- that's the only white key for which this is true.) Aloysius seems adamant that the perfect 5th is the interval that establishes the mode in the listener's ear, and so there can be no mode associated with B.
Q: What's the difference between an augmented 4th, a diminished 5th, and a tritone?
Augmented 4th and diminished 5th refer to the same degree in every mode. They are synonyms. "Tritone" refers to this same degree, and is, in an equi-tempered world, a third synonym. Near as I can tell, it has its own name because, in a world of different temperings, there were some keys in which the augmented 4th/diminished 5th was especially hard on the ears. It was sometimes called "the wolf," after the terrifying howl it made. I assume "tritone" or "devil's interval" was reserved for these particularly heinous instances of the augmented 4th (which is not, in equi-temperament, especially hard on the ears).
This answer is extrapolated from an excellent and fascinating article on tuning by Jan Swafford: The Wolf at Our Heels.
Showing posts with label counterpoint. Show all posts
Showing posts with label counterpoint. Show all posts
Thursday, June 30, 2011
Thursday, March 24, 2011
Recap: two voices
Last night I finished the 60 exercises that make up Part I of the Fux book. Musical lessons learned:
1. Occasional skips greater than a third help change the character of a line from an accompaniment to a melody. This is counterintuitive to me-- my instinct is to use steps whenever possible.
2. Parallel motion really does serve to undermine the momentum of the counterpoint and the interest of the harmony. Fux isn't kidding when he says that in florid counterpoint, parallel motion should be generally avoided.
3. However, I find parallel motion can be a nice effect near the end. It's a kind of pre-resolution calming. Like the piece has found its stride before it resolves.
4. Skips in the cantus firmus-- especially skips of more than a third-- introduce the possibility of collapsing the distinction with the counterpoint. This problem is acute when the skip narrows the distance between the two lines. One way to deal with this in florid counterpoint is to "cover" the skip with quarter notes. A run of quarter notes keeps the ear focused on the counterpoint, and helps keep it distinct from the cantus firmus.
5. In florid counterpoint, Fux allows eighth notes on the second and fourth beats. I tried using them in a bunch of exercises and always hated the way they sounded. I didn't end up keeping any eights.
6. I don't yet know if it's the nature of the modes, or the particulars of the cantus firmi Fux supplies for them, but there's no doubt that some modes are easier to write and pleasanter sounding than others. I've found that Dorian, Phrygian, and Ionian modes usually come together pretty easily. Lydian and Mixolydian are tough slogs that often sound bland. Aeloian is sometimes hard to get right, but I usually like sound of the result.
7. A lesson I learned from Wire's "Pink Flag" that is recapitulated by counterpoint exercises: with music, familiarity fosters enjoyment. If I spend two hours getting an exercise into a form I like a lot, then let it sit for a few days, I might dislike it when I listen to it with fresh ears. But if I listen to it four or five times in a row, I start to like it again. This helps explain why so much old classical music is formulaic, and so much popular music is repetitious. When you aren't dealing with a 30-second snippet that can be heard six times in short order, you've got to find some other way to secure the familiarity that fosters enjoyment.
1. Occasional skips greater than a third help change the character of a line from an accompaniment to a melody. This is counterintuitive to me-- my instinct is to use steps whenever possible.
2. Parallel motion really does serve to undermine the momentum of the counterpoint and the interest of the harmony. Fux isn't kidding when he says that in florid counterpoint, parallel motion should be generally avoided.
3. However, I find parallel motion can be a nice effect near the end. It's a kind of pre-resolution calming. Like the piece has found its stride before it resolves.
4. Skips in the cantus firmus-- especially skips of more than a third-- introduce the possibility of collapsing the distinction with the counterpoint. This problem is acute when the skip narrows the distance between the two lines. One way to deal with this in florid counterpoint is to "cover" the skip with quarter notes. A run of quarter notes keeps the ear focused on the counterpoint, and helps keep it distinct from the cantus firmus.
5. In florid counterpoint, Fux allows eighth notes on the second and fourth beats. I tried using them in a bunch of exercises and always hated the way they sounded. I didn't end up keeping any eights.
6. I don't yet know if it's the nature of the modes, or the particulars of the cantus firmi Fux supplies for them, but there's no doubt that some modes are easier to write and pleasanter sounding than others. I've found that Dorian, Phrygian, and Ionian modes usually come together pretty easily. Lydian and Mixolydian are tough slogs that often sound bland. Aeloian is sometimes hard to get right, but I usually like sound of the result.
7. A lesson I learned from Wire's "Pink Flag" that is recapitulated by counterpoint exercises: with music, familiarity fosters enjoyment. If I spend two hours getting an exercise into a form I like a lot, then let it sit for a few days, I might dislike it when I listen to it with fresh ears. But if I listen to it four or five times in a row, I start to like it again. This helps explain why so much old classical music is formulaic, and so much popular music is repetitious. When you aren't dealing with a 30-second snippet that can be heard six times in short order, you've got to find some other way to secure the familiarity that fosters enjoyment.
Saturday, February 19, 2011
Melodic Rules
These rules governing the melodic flow of each counterpoint are common to every species. I'll add to the list, or clarify the wording, as I come to understand them better.
1. Forbidden skips: augmented fourth, major sixth (up or down), minor sixth (down only), seventh, any interval greater than an octave.
2. "Exposed" tritones are forbidden. That is, no run of notes in a single direction should be an augmented 4th from end to end.
[NOTE: Since all of these exercises are written in their natural modes, the special notes to watch out for are F and B-- an augmented fourth when taken together. There can be no jumps between F and B, and no runs that begin on one can end on the other. Beware of F and B!]
3. Leaps of an ascending minor sixth or octave, or a descending octave must be "recovered." That is, such a large skip must be followed immediately by a step back into the range covered by the leap. (Fux often "recovers" using a skip of a third back into the big leap.)
4. Do not repeat notes. (Though Fux makes many exceptions in Species One, repeated notes are rare in the other species.)
5. Avoid multiple skips in the same direction. (This is a guideline-- Fux contradicts this advice all the time. See, e.g., page 46, in the 2nd species phrygian example, he skips 4th, 5th, and 4th in the same direction: c-f-c'-f'.)
1. Forbidden skips: augmented fourth, major sixth (up or down), minor sixth (down only), seventh, any interval greater than an octave.
2. "Exposed" tritones are forbidden. That is, no run of notes in a single direction should be an augmented 4th from end to end.
[NOTE: Since all of these exercises are written in their natural modes, the special notes to watch out for are F and B-- an augmented fourth when taken together. There can be no jumps between F and B, and no runs that begin on one can end on the other. Beware of F and B!]
3. Leaps of an ascending minor sixth or octave, or a descending octave must be "recovered." That is, such a large skip must be followed immediately by a step back into the range covered by the leap. (Fux often "recovers" using a skip of a third back into the big leap.)
4. Do not repeat notes. (Though Fux makes many exceptions in Species One, repeated notes are rare in the other species.)
5. Avoid multiple skips in the same direction. (This is a guideline-- Fux contradicts this advice all the time. See, e.g., page 46, in the 2nd species phrygian example, he skips 4th, 5th, and 4th in the same direction: c-f-c'-f'.)
Thursday, February 10, 2011
Definitions, and the only rule of counterpoint...
This is the only background information Fux expects.
Intervals
Perfect consonances: Unison, fifth, and octave.
Imperfect consonances: Six and third.
Dissonances: Second, fourth, diminished fifth, tritone, and seventh.
I have a question: What's a tritone, if neither a fourth nor a diminished fifth?
Motion
"Direct motion results when two or more parts ascend or descend in the same direction by step or skip."
"Contrary motion results when one part ascends by step or skip and the other descends-- or vice versa."
"Oblique motion results when one part moves by step or skip while the other remains stationary."
The four rules of counterpoint
Intervals
Perfect consonances: Unison, fifth, and octave.
Imperfect consonances: Six and third.
Dissonances: Second, fourth, diminished fifth, tritone, and seventh.
I have a question: What's a tritone, if neither a fourth nor a diminished fifth?
Motion
"Direct motion results when two or more parts ascend or descend in the same direction by step or skip."
"Contrary motion results when one part ascends by step or skip and the other descends-- or vice versa."
"Oblique motion results when one part moves by step or skip while the other remains stationary."
The four rules of counterpoint
1. From one perfect consonance to another perfect consonance one must proceed in contrary or oblique motion.It seems to me the four rules are a roundabout way of saying one thing: never use direct motion to enter a perfect consonance.
2. From a perfect consonance to an imperfect consonance one may proceed in any of the three motions.
3. From an imperfect consonance to a perfect consonance one must proceed in contrary or oblique motion.
4. From one imperfect consonance to another imperfect consonance one may proceed in any of the three motions.
It is necessary for you to know that in earlier times, instead of our modern notes, dots or points were used. Thus one used to call a composition in which point was set against or counter to point, counterpoint; this usage is still followed today, even though the form of the notes has been changed. By the term counterpoint therefore is understood a composition which is written strictly according to technical rules.
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