The Second Annual Pacific Pythagorean Music Festival had originally been scheduled to take place on March 21, 2020. Organized by the Del Sol Quartet of Samuel Weiser (violin), Benjamin Kreith (violin), Charlton Lee (viola), and Kathryn Bates (cello) and hosted by Old First Concerts (O1C), the event was planned to highlight the work of experimental innovators and traditional masters of integer-ratio harmonies. The Festival finally took place over the course of four hours as yesterday afternoon’s O1C offering. Almost all of the content involved streaming pre-recorded video, although it may well have been the case that all the appearances of Del Sol players were “live.”
The good news is that there was an impressive diversity of approaches to both composition and performance that unfolded during the eleven sets of the afternoon. The bad news is that much of the overall approach to presentation left much to be desired, beginning with the fact that all four Del Sol players were totally unprepared to provide useful introductions for all of the sets that following their own opening offering. However, just as problematic was a program book that devoted five pages to an “About the artists” section with absolutely nothing to say about the music being performed, beginning with the motivation behind the Festival itself.
The basic idea behind the Festival involved a departure from the conventional approach to tuning a piano. That technique is known as equal temperament, meaning that the size of the interval between any two adjacent keys is the same as that between any other two adjacent keys. The uniform size of that interval is the twelfth root of two. What is important is that, in mathematics, that amount is an irrational number, which simply means that it cannot be represented by an integer numerator divided by an integer denominator.
Pythagorean tuning is a system in which all intervals are represented by rational numbers with both numerator and denominator being multiples of the integers two and three. The 3:2 ratio is known as the perfect fifth; and, from an engineering point of view, it is very close to the ratio that defines any fifth on an equal temperament piano keyboard. Other intervals on that piano keyboard are harder to match with the limitations of Pythagorean numerators and denominators. The name of the system refers to the Greek philosopher Pythagoras, who was active in the sixth century BC and is credited with many mathematical insights (as well as influencing Plato).
The idea of ratios of integers that involve more than two and three probably emerged in the second century (AD), which seems to have the earliest document (by Claudius Ptolemy) that adds five to the mix. This extension marked the beginning of what is now known as just intonation, whose systems are all based on the integers that define the overtones. These systems are defined in terms of a “limit,” which designates the highest overtone number included among the integers. Thus, in the language of just intonation, Pythagorean tuning is called “3-limit tuning.”
Unless I am mistaken, there were no instances of Pythagorean tuning in yesterday’s Festival. For the most part, the compositions were based on just intonation, with only one exception documented on the program sheet. To be fair, however, there was a generous amount of glissando work in many of the compositions, which basically dispenses entirely with integers in favor of the real-number line.
The problem, however, is that the curious listener unfamiliar with all of this background was given little (if any) orientation to guide any attempts at following the music perceptively. One problem seems to have been that the four Del Sol players provided ad hoc introductions that rambled when they should have been informing. Given that almost all (if not the entirety) of the content was pre-recorded, there was no excuse for such a casual (if not sloppy) approach to introducing the selections begin performed. (At least one of the performers, Ellen Fullman, provided her own introduction that served as a useful, if not fully adequate, remedy.)
In addition, the paucity of background accompanied an overabundance of foreground. Considering that each of the offerings had its own distinctive novelty in dealing with intonation, the entire four-hour package was just too much for all but the most obsessive listeners. Citing, again, the fact that most of the content had been previously recorded, O1C could just as easily presented this as two two-hour programs (nothing had be scheduled for the preceding Friday slot), which would have made for a more “digestible” approach.
The good news is that yesterday’s live-stream has now been uploaded in its entirety to a YouTube Web page. The bad news is that the program details of composers and compositions has not been included on this Web page. As of this writing, there is a Web page on the O1C Web site giving all the program content information that is available. For those that prefer flipping pages to scrolling, there is also a hyperlink for downloading a PDF file with the same content.
I apologize to readers for not going into the specifics of any of the works that were performed. Unfortunately, memory was overwhelmed by the TMI (Too Much Information) phenomenon. Were I more curious, I would probably take the time to revisit at least some of the selections through YouTube. However, I can at least refer readers to the account on this site of the penultimate selection on the program, Catherine Lamb’s “point/wave,” which guitarist Giacomo Fiore released as a self-produced album. For that matter, I have had so many positive experiences in listening to alternatives to a well-tempered piano keyboard, particularly through MicroFest Records, that I feel I already have a wealth of resources available to appreciate music based on just intonation.
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