31
May 11

## Irrational meters

I was going to write a blog post about what are called “irrational meters” (time signatures with denominators that are not powers of 2) – then I re-read a fantastic post by Helen Bledsoe, flutist for MusikFabrik (among others), and realized I should just link to her! She very lucidly explains the mathematical workings of Ferneyhough-style rhythm, complete with “irrational meters”, which really pose very little additional challenge, if you know how to interpret them.

The most basic point to remember about these meters is that the denominator, just like in more familiar time signatures, indicates the number of notes it will take to fill a whole note. 4/8 indicates 4 of something it takes 8 of to fill a whole note (namely eighth notes). A denominator of 5 would indicate that quarter note quintuplets are the basic unit of the bar, and the numerator, as in familiar time signatures, indicates the number of units in the bar. Thus, 3/5 would be a bar of 3 quarter note quintuplets! Of course, you can, instead, treat these changes of denominator as metric modulations and tempo changes – but I’ll leave some of the specifics to Ms. Bledsoe’s lucid explanations!

Head on over to her blog, Flutin’ High, for the full post!

23
May 11

## Equal Temperament

Equal temperament or ET is the current tuning framework for most Western music. It is a kind of acoustical compromise, compared with the pure mathematical relationships of just intonation (JI). No intervals are ‘true’ in the system, but the equality of half-steps allows for free modulation to any key, ensuring that each would be as viable as any other. Pitches which in JI would be derived from the lowest primes are generally the best approximated pitches in ET: perfect fifths (3/2 in JI) are 2 cents low in ET, major thirds (5/4) are 14c+, and minor (7/4) sevenths are 31c+. In JI, all pitches are related intervalically to a fundamental (1/1); in ET, pitches are derived as equal logarithmic subdivisions of an interval, most usually the octave. (An interesting exception in this case is the Bohlen-Pierce system, which divides a perfect 12th into 13 equal steps) Thus, instead of the simple ratios involved in JI, the size of each ET halfstep is derived from the twelveth root of 2. Any ET division of the octave can be reached this way. For example, a 24 note scale’s smallest interval can be derived from the twenty-fourth root of 2.

The ET system used in most Western music is 12 note ET, also called 12ET. However, since the early twentieth century (and with a few notable exceptions, hundreds of years before), composers have worked in other equal subidvisions of the octave. 24ET introduces the quarter tone, 36 the sixth tone, 48 the eighth tone, and 72 the twelfth tone. These are the most common divisions, though there are many musics, composers and cultures who use different divisions (Klaus Huber, for example, in his later works, uses 18ET, creating an equal tempered scale of third tones). 19ET has been used as a better compromise for true JI intervals in tonal music than 12ET, differentiating between sharps and flats as differently tuned. 31ET is a system which was approximated by instrument makers and theorists in Italy in the 16th century via a kind of mean-tone temperament. It allows for diatonic (white note) chromatic (accidentals both sharp and flat) and enharmonic (double sharps and flats) genera, extending the range of possible harmonies greatly. Ekmeles will be experimenting in 31ET tuning in the performance of Gesualdo madrigals this Fall, as historical records indicate that Scipone Stella, a composer in Gesualdo’s court, built replicas of Vicentino’s 31ET keyboard instruments.

### Non-exhaustive list of composers using ET microtones

Charles Ives (24ET), Alois Hába (24ET, 36ET, 72ET) Julián Carillo (18ET, 24ET, 30ET, 36ET, 42ET, 48ET, 54ET, 60ET, 66ET, 12ET, 78ET, 84ET, 90ET, 96ET [if you don’t know him, you should really check him out!]). James Dillon, Brian Ferneyhough, Liza Lim, and many other second modern or complexist composers make liberal use of ET microtones.

### Learning ET microtones

Without the aid of rote learning, ET microtones can be exceptionally difficult to find. Acoustically, further divisions of 12ET rarely become more consonant, with the exception of 11th partial relationships which lie only a few cents away from a quarter tone. I reccommend the use of computer models, and have made use of several. I have occasionally used simple software synths for learning quarter tones. I reprogrammed a fine-tuning knob built into the synth to instead move only in gradations of 50c, and altered the pitches by hand on the fly. This is useful for melodic work, but makes harmonic hearing of quarter tones impossible. OpenMusic is an IRCAM-developed program made for computer assisted composition. A companion program, microplayer, can handle up to 72ET playback in multiple channels. To hear the score of an ET microtonal piece, I can’t just sit down and play it at the piano, so I enter it into OpenMusic, and can hear a completely accurate version of it, harmonically and melodically. When you have a limited amount of time to rehearse with an ensemble for a difficult piece, practicing with a computer model can allow you to devote that rehearsal time to music making, and not to panicking over whether you’re singing the right notes.

16
May 11

## Non-classical voices

Despite the fact that we work mostly with the voice in its classically trained sense, I still have a deep appreciation and love for many non-classical voices. If you don’t know the following, get to know them.

Alfred G. Karnes, preacher and gospel singer;

Mike Patton, erstwhile frontman of Mr. Bungle, Faith No More, collaborator with Zorn;

Tom Waits, singer/songwriter with the most expressive chronic laryngitis you’ll ever hear;

Demetrio Stratos, Greek prog-rocker, researcher, and experimentalist;
and Roy Hart, South African actor who was the star student of avant-garde teacher Alfred Wolfsohn and for whom Eight Songs for a Mad King was written.

08
May 11

## Invisible Cities preview

You’ve got to make it out this weekend to our staged debut with Red Light New Music in Chris Cerrone’s Invisible Cities at the Italian Academy! Preview below.