Okay, here’s a notation issue.
Consider a musical passage that begins with a simple meter in which the quarter note gets the beat, then alternates regularly with a compound meter in which the subdivided beat is equivalent to the triplet eighth of the prevailing simple meter and in which extra subdivided beats are occasionally added or subtracted. Or to put it another way, consider the alternation between a prevailing simple meter in which the quarter note gets the beat and a compound meter, with occasional asymmetrical meters (e.g. 7/8, 5/8) thrown in, in which the eighth note is equivalent to the triplet eighth of the prevailing simple meter.
Here’s a possible example. (Click on the image to enlarge)
Audio (Forgive the poor midi!)
What is the best way to notate such a passage so that it is most easily read? It seems to me that there are at least four different possibilities, not all of which are sensible:
1. The TEMPO CHANGE method
I suppose one could notate such a passage by indicating a tempo change at each shift. After all, that is essentially what is going on here—the shift between two different musics of two different tempi.
But surely this won’t do. In addition to it simply being extremely unwieldy, it fails to adequately show the correspondence between the triplet eighth of the prevailing simple meter and the eighth of the new compound meter.
2. The TEMPO MODULATION Method
One could indicate the correspondence of note values just mentioned by showing the equivalence each time a shift occurs.
But this, too, proves to be unwieldy and awkward. And if the two musics came to resemble one another on the page more closely, reading the duration equivalency equations become even more difficult to read. There must be a better method.
3. The BOULEZ Method
In Le Marteau sans maître, Boulez used fractional time signatures (such as 4/3 over 2) which, perhaps after a few moments of utter confusion, make perfect sense.
The “Boulez” method certainly makes sense, but is the awkwardness of reading fractional time signatures simply too much trouble?
4. The FERNEYHOUGH Method
I first came across the “Ferneyhough” method when looking at a piano piece by Thomas Adès called Traced Overhead (1995-96). I later realized that Ferneyhough used this method before Adès in his Etudes Transcendantales from the early 1980s. In this method, unusual “denominators” of the time signature such as 12 or 20 are used. Just as the lower “4″ of a 4/4 meter indicates that the quarter note gets the beat since it is 1/4 of a whole note, the denominator “12″ would indicate that that note value which is 1/12 of a whole note is what gets the beat. That note value would be the triplet eighth. So a 5/12 time signature means that 5 beats (or beat divisions, more accurately) fill the measure and the beat is the triplet-eighth. A 9/20 time signature would mean that 9 quintuplet-sixteenths fill the measure. Like the “Boulez” method, the “Ferneyhough” method makes perfect sense once you get your head around it. Here is what it would look like:
Of the four, methods 3 and 4 are better, and while it is extremely odd to use “Ferneyough” and “clarity” in the same sentence, it does appear that Method 4 is the neatest of the four, though it perhaps requires the most “figuring out” at the beginning. Furthermore, it seems to me that with some practice, one could become quite fluent at reading time signatures with “12,” “20″ and “24″ denominators.
So what do you say? What would you prefer to see as a performer? Are there any better “methods”? Do you know of other composers who have tackled this issue?