I’ve just stumbled across the Vimeo page of Daryl Buckley, guitarist and artistic director of ELISION Ensemble, and among the many treasures to be found there, recommend this recent Liza Lim piece. I had the pleasure of singing the US Premiere of her piece Chang-O and love the timbral detail in her music.
Since we’re about to embark on a season of non-standard tunings, ranging from columns of septimal JI intervals (thanks to Mr. Randy Gibson) to 31-note ET (a speculative historical journey with everyone’s favorite musical murderer, Don Carlo Gesualdo da Venosa), I thought it might be interesting to have a quick review of the mathematics of tuning.
I highly recommend Kyle Gann’s Just Intonation Explained for a basic background on ratio tunings, and to be able to hear exactly what all those numbers mean.
And though I hesitate to link to it for obvious reasons, Wikipedia actually has a very clear writeup on the math of equal temperament! I’ve linked you past the rambling and somewhat questionable narrative section straight to the goods, starting with the Chinese discovery of the logarithmic solution to equal temperament.
If you’re not knowing him, I’m here to let you know. Georges Aperghis has developed one of the most distinct styles of vocal writing of any composer, and is rather prolific to boot! Check out his website and blog, do some listening at UbuWeb to his famous Recitations and see below for several YouTube clips of his Machinations.