There was an interesting article in the Boston Globe today, “Symphony in J Flat” , about a local clarinetist, Amy Advocat, who is learning a strange new tuning, the Bohlen-Pierce scale. This is a scale where every octave is 3 times the frequency of the one below instead of 2 times as in the standard tuning. Instead of 12 intervals in the octave, there are 13 in the “tritave”. The ratios of chords are 5/3 and 7/3 instead of 3/2 and 4/3. It has an eerie sound, but not as discordant as you might think.
There’s a conference, The Bohlen-Pierce Symposium, going on about it right now in Boston. It can be played on synthesizers, of course, but people are now building real instruments for it. The clarinet is particularly suitable because it has odd-numbered harmonics already.
The Wikipedia article is incomprehensible, but is does mention a bit about the inventors. What’s odd is that they weren’t musicians – they were engineers, and microwave communication engineers at that. And they came upon this idea independently!
Heinz Bohlen working on a synthesizer in ’73. Note the odd pattern of black keys
Heinz Bohlen worked on klystrons in Germany and only started fooling around with the math behind tunings when some friends asked him to help with their recordings.
John R Pierce (1910-2002) came up with the same scheme about 6 years later, only to discover that Bohlen had done it first. He’s actually a significant figure in electrical engineering – he headed the group that developed the transistor at Bell Labs (and in fact named it) and was crucial in putting up the first telecom satellites. He even wrote science fiction under the name “J. J. Coupling”, which is a term in quantum mechanics having something to do with electron interactions. He sold stories to Hugo Gernsback in the 30s and non-fiction articles to John W. Campbell at Astounding (later Analog) in the 40s and 50s. When he retired from Caltech, he joined the computer music lab at Stanford, CCRMA, where he discovered this scale.
Oh, and he was also an expert glider pilot, and he and his wife threw terrific parties at their house in Palo Alto. So there he is: bon vivant, musician, author, teacher, manager, space pioneer. Some people’s careers make you despair of your own.