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Derek, this is a good question, especially because it is hard to know what is normal before you've had experience with this, and what should happen, what an editor will tell you will happen, and what normally does happen. Keith already gave you an e…
Tymoczko is perfectly clear in his book that the dyad space is modeling voice leading of dyads assuming octave and permutational equivalence. If you think he is saying something about "natural inviolate laws of physics" you are really not reading it…
Hi Carson: Also look up Harald Ferptinger who has worked on these questions. You can actually find a lot more symmetries in the permutation group than are recognized as standard 12-tone operations. This paper from the Math and Computation in Music c…
I put in a vote for the all-numbers camp, with the caveat that I would consider using superscripts for the sixteenth note positions. So 4^4 for the last position in a measure. That's often used in the form (measure number)^(beat number) but I take i…
The lesson we should take from this is: bad music theory pedagogy leads to people (who don't really get much about music theory) pontificating on blogs about what's wrong with music theory. These seem to crop up every spring like so many ephemeral w…
To follow up on Isaac's suggestion, there is an article by Popoff in MCM2015 about the Cage number pieces that might be useful. These would actually be a lot of fun to play with, to imagine all the different possible realizations and what aspecs of …
Mitch,
Jon Kochavi has a great demonstration of the serial design of Nono's Il Canto Sospeso--you might ask him about that. I do things with polyrhythm in Ligeti and Carter in my classes--something you might consider, and Xenakis is also an obvious …
The choice of piece obviously biases the issue--this first movement is unusual in having such a clear two-part main theme with two initiating gestures. Therefore, in a very basic structural sense (tonal and formal structure) there is an excision (of…
Dimitar,
This is your opinion but you should recognize that some of the issues you raise have been debated for hundreds of years--specifically the binary vs. ternary issue. Some people feel very strongly one way or another. In my opinion the whole d…
Very interesting! Thanks, Rick. But if I read this correctly the meaning is so different that the correspondance is purely accidental. Cone wouldn't necessarily have known of how the term is used in reference to poetic meter--if he had one imagines …
David,
Ravel's "Chanson de Rouet" is an excellent example. There is a literal spinning motive throughout to reflect the spinning wheel, but it also "spins" on multiple levels to reflect the cycles of day and night and the cycle of life, which is all…
Zac,
My first reaction when you describe your approach is "gosh, that sounds time consuming." It's impossible to say for sure, not having seen how you do it, but I wonder if maybe the issue is just one of proportionality, spending too much time on t…
Scott,
I don't have anything to add to Andrew's answer, but am interested in what you're doing with the time-span GIS because I've presented on this in the past and have also written about it in some not-yet-published work. One of the points I make …
Ronald,
Glancing at your webpage it looks like there is a lot of re-inventing the wheel going on here: the objects of your system are ordered pcsets (or Tn-type set classes). What is novel is just the system of nomenclature, but there were well-rehe…
Conor,
I use lilypond all the time for my research and teaching. It would be nice to have some better tools for Schenkerian notation, because it takes a lot of tweaking and I end up doing most of it after exporting the notation to image processing s…
Tim,
Not sure if this counts by your lights, but after perusing some Corelli, the best I can find is Op. 6, no. 10, allegro, mm. 16–18. He much prefers to do ascending fifths with root position and 4–3 and/or 9–8 suspensions.