28
Nov 11

Tuning – Vertical vs. Horizontal

I was talking with Sasha Zamler-Carhart, director of Ascoli Ensemble, about the ways that our ensembles approach tuning. Ekmeles’s approach to tuning Gesualdo in 31-note equal temperament is a mostly harmonically focused – 31ET being a keyboard temperament -and is about aiming for pure verticalities. Sasha’s group, specializing in Medieval music, and often reading from original manuscript parts, approaches tuning in an entirely linear sense. Of course they make sure they begin lines and cadence together, but reading from parts and singing in Pythagorean tuning – which is beautifully melodic, but only harmonically satisfying for major seconds fourths and fifths – has led them to consider tuning in this way.

Our most recent project, the premiere of Randy Gibson‘s “Circular Trance“, was an almost totally vertical experience. Scored for an array of sine wave drones in addition to the seven singers required, the piece’s complex just intonation tuning system requires us to constantly listen vertically, and to subsume our voices into the tuning of the drone. Perhaps the most linearly conceived work that I’ve ever performed is the first movement of Johannes Sch√∂llhorn‘s “Madrigali a Dio”. The pitches for the singers are graphically specified on a 3 line staff representing the full compass of the voice, so that the pitches are only determined relatively within each voice, and are free to interact with the other voices at any interval, tempered or otherwise.

Despite these extreme examples I think I do my best work tuning diagonally, imagining both the melodic contour of my own individual part, and the way it will interact with the other parts as they go along. In reality, tuning with an ensemble of voices is a constant game of listening and subtle adjustments. Rules and approaches to tuning are a jumping-off point and a reference; but in practice, the voice is both a producer of an infinite continuum of pitch, and fallibly organic.


10
Oct 11

The new continuo?

Ekmeles is currently preparing a performance of several of Gesualdo’s madrigals, applying a tuning that is a combination of historical fact and conjecture – Vicentino’s 31-note division of the octave. There is a surfeit of forgotten theories of the tuning of musical instruments and performances, including many that were likely never used in performance.¬†Nicola Vicentino (1511-1575) went a step further than many theorists, actually building and designing instruments capable of producing the scalar divisions he proposed mathematically. He devised the archiorgano, and the archicembalo, respectively an organ and a harpsichord capable of playing 31 (roughly) equal divisions of the octave, allowing free modulation through the keys in a mean-tone tuning, and application of the ancient Greek enharmonic genus. Scipione Stella, a composer at Gesualdo’s court, made a copy of the archicembalo – thus our historical conjecture.

Vicentino himself was a madrigalist, though it is recorded that his enharmonic vocal works were never performed without the harmonic support of a player at the archicembalo. This idea of needing continuo in the context of difficult intonation reminded me of the place singers of contemporary music often find ourselves – ears attached to computer synthesized tracks of our pitches. As readers of the blog will know, I am an advocate for making use of all technological tools possible in the course of learning difficult music. What I am interested in exploring is performing with these computer crutches. Of course, in some cases (like Martin Iddon‘s commission for Ekmeles, Hamadryads, or Aaron Cassidy‘s I, purples, spat blood, laugh of beautiful lips) the in-ear pitch component of the piece is a considered and integral part of the piece.

But what about when the composer hasn’t asked that a pitch track be used, and precise intonation is just too difficult, whether because of short rehearsal time, vocal considerations, or extremely small divisions of the octave? Is performing with a pitch track in our ears just cheating or is it the new continuo? Is the vitality and authenticity of a performance threatened by adherence to a mechanical version of the work which, by literally blocking the ears, supersedes the natural interaction of the performers? Thanks are due to a 16th-century Italian composer for raising these very modern questions – but more importantly, what do you think?


20
Jun 11

The mathematics of tuning

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.

We’ve recently discussed JI and ET tunings, and they differ in mathematical foundations. Absurdly briefly put: JI is based on ratios; ET is based on logarithms.

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.