Saturday, June 9, 2012
Fux Workbook Update
I finished a first draft of a Fux workbook (PDF) to accompany the Mann translation. I've typeset all the exercises, though there might be some cases in which my use of staves and octaves differs from the examples in the book. I'm proofreading and adding short summaries of the newly introduced rules as I work through it. I've finished proofing the section on 2-voice counterpoint, and hope to start back up with three voices this summer.
Sunday, May 20, 2012
3-voice, 1st-species, Dorian mode
The academic year is over, hooray! I fired up my score editor earlier today, and found that before I got busy last summer I managed to complete the exercises in 3-voice, 1st-species, Dorian mode. I'll need to do a fair amount of review before I can get back up to speed, and confirm that this is correct. But even if it's incorrect, I still like the way it sounds.I hope it won't be another eleven months before the next update...
Thursday, June 30, 2011
Rarely asked questions: tritones and modes
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.
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.
Thursday, March 24, 2011
Quality of tools and standards of success
I was assigned about a dozen exercises from Fux as a Sophomore at St. John's. I remember them going very quickly, maybe ten minutes each, and so thought I could tear through the sixty two-voice exercises in a week. It's actually taken me about six weeks. Why?
I think there's an interesting interplay between my workflow and my standards of success. When I did these as a 19-year-old, I worked on paper in a dorm room. I'd usually show up for class a little early so I could play my exercises on the piano. (I've never been able really to read music, so the only way I can know what they sound like is to play them.) Every time I played one, I was impressed that some part of it sounded neat. I was following these rules, marking down notes that I couldn't hear, making nice-looking patterns on the page, and when I played them, some part always sounded nice.
Now, as soon as I finish a first pass, I do it up in my score editor and have the computer play it back for me. It's still the case that some parts sound nice, but it's always the case that some parts could be nicer. So I fiddle with it, which is easy to do. I move some notes around on the screen, then hit "play" again, then fiddle some more. So, instead of being happy that some bit of it sounds nice, I keep working on it until I'm basically satisfied with the whole thing. This can take a long time-- I spent three hours on one of the fifth species exercises. Because tweaking my work is much easier now, I'm much less willing to be satisfied with mixed results.
The new way is probably the better way to learn, but it's definitely made the project more daunting than I thought it would be. I hope I have the stamina to make it through all 90 of the three-voice exercises. I'd love to do that. But I don't expect I'll do more than a handful of the four-voice exercises. Unless I somehow get much, much faster, there's no way I'm going to do all 120 of those.
I think there's an interesting interplay between my workflow and my standards of success. When I did these as a 19-year-old, I worked on paper in a dorm room. I'd usually show up for class a little early so I could play my exercises on the piano. (I've never been able really to read music, so the only way I can know what they sound like is to play them.) Every time I played one, I was impressed that some part of it sounded neat. I was following these rules, marking down notes that I couldn't hear, making nice-looking patterns on the page, and when I played them, some part always sounded nice.
Now, as soon as I finish a first pass, I do it up in my score editor and have the computer play it back for me. It's still the case that some parts sound nice, but it's always the case that some parts could be nicer. So I fiddle with it, which is easy to do. I move some notes around on the screen, then hit "play" again, then fiddle some more. So, instead of being happy that some bit of it sounds nice, I keep working on it until I'm basically satisfied with the whole thing. This can take a long time-- I spent three hours on one of the fifth species exercises. Because tweaking my work is much easier now, I'm much less willing to be satisfied with mixed results.
The new way is probably the better way to learn, but it's definitely made the project more daunting than I thought it would be. I hope I have the stamina to make it through all 90 of the three-voice exercises. I'd love to do that. But I don't expect I'll do more than a handful of the four-voice exercises. Unless I somehow get much, much faster, there's no way I'm going to do all 120 of those.
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.
Tuesday, March 22, 2011
Marking my own work
It's getting harder to be confident in marking my own work. I've adopted a multiple pass technique that seems reliable so far. I'll edit this post if I end up changing my approach.
First pass: check for fifths, eighths, and unisons on the first beat, and make sure they're entered via contrary motion. (I'm especially prone to error when entering the penultimate bar.)
Second pass: scan through for bs and fs. They're always dissonant against each other, so double check any b-f harmonies. Also check for exposed tritones in the counterpoint any time a b or f appears at the peak or trough of a melodic run. If the counterpoint uses any accidentals (for example, in the closing formula) run the same set of tritone leap/exposed tritone checks on the accidental.
Third pass: locate all dissonances, and double check that they are entered and left stepwise, or are part of a cambiata formula.
Fourth pass: scan through the counterpoint and note every jump larger than a fifth. Double check that none of those leaps are forbidden. Also double check that any leap larger than a fifth is "recovered."
First pass: check for fifths, eighths, and unisons on the first beat, and make sure they're entered via contrary motion. (I'm especially prone to error when entering the penultimate bar.)
Second pass: scan through for bs and fs. They're always dissonant against each other, so double check any b-f harmonies. Also check for exposed tritones in the counterpoint any time a b or f appears at the peak or trough of a melodic run. If the counterpoint uses any accidentals (for example, in the closing formula) run the same set of tritone leap/exposed tritone checks on the accidental.
Third pass: locate all dissonances, and double check that they are entered and left stepwise, or are part of a cambiata formula.
Fourth pass: scan through the counterpoint and note every jump larger than a fifth. Double check that none of those leaps are forbidden. Also double check that any leap larger than a fifth is "recovered."
Saturday, March 19, 2011
5th Species Dorian
Fifth species combines all the rules of the previous species: whole notes, halves, quarters, and ligatures. Moving from fourth species, in which there's next to no flexibility, to fifth, in which there's a huge amount of flexibility, is a time-consuming relief. With so many possibilities, I can mess around indefinitely with bars I don't like until I find an approach that's better. This first exercise, in Dorian mode, took more than an hour to write 11 bars, but I like the result:
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