Notation


11
Nov 13

JI Composers: Taylor Brook

This is the second in a series of conversations with composers who work in just intonation, and other microtonal systems. Questions from Ekmeles are bolded, the composer’s responses follow. This is a special edition, since we’re premiering Brook’s Motorman Sextet this Friday, November 15th, at the DiMenna Center.

Composer Taylor Brook

Composer Taylor Brook

Why not 12-note equal temperament?

I do sometimes use 12tet, however I consider 12tet as one possibility among many. Perhaps a better question for most composers would be: why use any temperament at all? I look to just intonation as a default tuning system because it is not a temperament, but the most direct way to think about intervals. Indeed, all temperaments are in relation to just intonation, a deformation of JI that serves an end that may have to do with the music or the construction of the instrument. With this in mind, if I choose to use a temperament then it should be a meaningful part of the composition. For example, in my new work for Ekmeles, Motorman Sextet, I employed pythagorean tuning in quotations of an organ prelude by Buxtehude in order to better invoke how the tuning of a Buxtehude piece would be realized by voices as well as create a division between the quotations of Buxtehude and my music.

Taylor Brook - Motorman Sextet score excerpt

Taylor Brook – Motorman Sextet score excerpt

Why the systems and pitches you use?

I tend to approach each new piece I write from as fundamental a place as possible. Most of my pieces begin with an idea that has nothing to do with pitch, and so pitch will then be controlled to serve some larger goal. Not until I have a clear idea of what I want to do with a piece, will I begin to think about how I will use pitch. This means that many of my pieces use very different systems or sometimes no system at all for pitch. With this said, I always think about pitch from the basis of just intonation. It’s important to remember that just intonation isn’t a system, just a way to measure the acoustic consonance of an interval, and so one must carve out a system from it as many composers do with 12tet.

What was your first encounter with microtones?

The first piece I heard with microtones was James Tenney’s Bridge and Flocking for two pianos tuned a quarter-tone apart. I was in high-school at the time and I was good friends with Tenney’s daughter and so was curious about his music and bought a CD of his works. I must say that I didn’t really understand or enjoy his music until years later and this encounter was not so meaningful to me other than bringing forward the idea that such a thing would be possible.

What piece of microtonal music that you didn’t write is most important to you?

I’m not sure about it being the most important, but the most meaningful microtonal piece for me is LaMonte Young’s The Well-Tuned Piano. During my undergraduate studies I spent a lot of time in the electronic music studio with another composer named Jacob Sudol. Jacob was doing his masters and gave me a lot of great recordings. One time he played The Well-Tuned Piano for my on the super-hi-fi speakers at the studio and it had a very strong effect on me. This piece is very direct and allows for enough time to deeply feel all of the pitch relationships as they are presented in different combinations and textures. It somehow invents and completes a genre of music all its own. Many composers have attempted to write pieces like this, but in my opinion, The Well-Tuned Piano is one of these truly unique works.


4
Nov 13

JI Composers: Christopher Trapani

This is the first in a series of conversations with composers who work in just intonation, and other microtonal systems. Questions from Ekmeles are bolded, the composer’s responses follow.

Why not 12-note equal temperament?

It comes down to this question, one I ask myself often: What exactly enchants me as a listener in the music I love? More often than not, it’s small expressive details that capture my attention, the fleeting surface gestures or stylistic inflections that make a performance distinctive. Replicating that kind of expressivity requires a full palette of pitch material; my works often run the gamut, mixing highly-detailed microtonality with tempered passages. Microtones are a vital component of almost every musical tradition: jazz, blues, country, electronic music, many folk styles, early music — almost everywhere except in the mainstream art music of the last few centuries.

Speaking more broadly, I’m captivated by the idea of consonance, and devoted to pushing the boundaries of what can be considered to “sound good.” Just intonation sparks my imagination because what appears to be a complex network of pitch relationships can be boiled down to multiples of whole numbers, simplest ratios that require extreme precision in tuning. I’m very attracted to this idea that simplicity and complexity can be a matter of perspective.

Why the systems and pitches you use?

My approach is simple: the system has to fit the project. I’m very concerned with making my music practical form a performance standpoint, so that the microtones can be reliably performed — whatever that might mean in a given context. I’ve often used the trick of retuning winds, plucked strings (guitar, mandolin, autoharp), or bowed strings (playing only harmonics and open strings) down by a quarter-tone, so that a player can use “normal” fingerings but still play reliable microtones.

I’ve also written for instruments which are specifically designed to produce microtones, in which case the system is more or less decided for me. I’ve worked extensively with the qanûn for instance, a middle-eastern zither equipped with small levers under the string that can produce microtones by changing the string length. I’ve used both the Syrian version (in Üsküdar and Widening Circles) which gives tempered quarter-tones, as well as a just intonation qanûn designed by Julien Weiss, for whom I wrote a solo part tailored to his particular tuning system in Cognitive Consonance. Or another example: the Fokker Organ, a MIDI-controlled microtonal organ in the Amsterdam Muziekgebouw, for which I also composed a short piece.

Another approach I’ve used is to write strictly tempered music for tempered instruments complemented by electronically created microtonal sounds, aiming for a fusion of live sound and synthesis or retuned samples that sounds like a single microtonal instrument. And there’s also my hexaphonic electric guitar, whose strings can be electronically retuned by a Max/MSP patch. I find that working with electronics offers the broadest range of possibility and precision, and a lot of my most fantastical pitch-related ideas are best realized in that medium.

A qanûn, showing the levers used for tuning

A qanûn, showing the levers used for tuning

What was your first encounter with microtones?

Wow, it’s coming up on a decade now… Shortly after I first moved to Paris in 2003, I caught a complete performance of Gérard Grisey’s Les Espaces Acoustiques. I’d heard Partiels (the third piece in the series) about a year earlier, and (weird to think of this in retrospect) only the theatrics at the end made an impression. But being enveloped by those lush harmonies in the concert hall was life-changing. Microtones were the key, it dawned on me around then, and I started devouring all the French microtonal music I could find, starting with Murail, Hurel, Leroux… For my first piece with microtones — a quartet for four clarinets written in 2004 — I decided I’d consciously train myself to hear microtonal intervals, and started constructing chords from slices of the harmonic series. But even in this first piece, I wasn’t doing just intonation drones, but working towards a richer polyphony, focusing on the voice-leading interactions between multiple microtonal lines.

My second microtonal revelation came when I discovered Turkish music. Often you hear that microtonal music has to be slow to be effective, that it takes the ear a while to attune itself to “unfamiliar” intervals. But in Ottoman classical music I discovered an entire tradition of fast and yet extremely precise microtones. The Turks rely on a combination of specially designed instruments and an internalized tradition that divides the octave (approximately but not quite exactly or consistently) into 53 parts. The idea that a microtonal theoretical framework could exist in tandem with a practice that tolerations deviations (which is in fact the way most supposedly tempered music is performed!) was illuminating for me and a source of inspiration for several pieces to follow.

Excerpt from Trapani's Cognitive Consonance

Excerpt from Trapani’s Cognitive Consonance

What piece of microtonal music that you didn’t write is most important to you?

I’ll go with either Harry Partch’s And on the Seventh Day the Petals Fell in Petaluma or Blind Willie Johnson’s version of “Dark was the Night, Cold was the Ground”


13
May 13

Handwriting and engraving

Furrer's FAMAPreparing the vocal ensemble parts in Beat Furrer’s FAMA has been an athletic physical challenge, and a catalyst for a lot of thinking about music, notation, and the voice. The score to this work is in the composer’s hand, which is becoming less and less common. The ubiquity of Sibelius and Finale have led to most scores being computer-engraved, including scores from major publishing houses who used to go through the painstaking and difficult task of literally engraving music for composers:

Now it is often the composer herself who must submit a score to the publisher, fully edited and formatted in the software of her choosing. For the composer and publisher, computer-engraved scores allow for easier corrections, re-formatting, and extraction and transposition of parts. For the performer, they allow for a standardized legibility that a composer rushing to meet a deadline may not always provide.

I’ve found myself becoming deeply engaged with the visual aspect of scores lately, what with our recent Augenmusik program. Each of the scores from that program has a unique visual world it inhabits, immediately presenting something of the work to the performer. On the other hand, the standardized default computer-engraved formatting of scores can lead to a homogenous visual presentation, which completely ignores the way that a musician will take in the score. While Furrer’s hand is not always as immediately legible as an engraved score, I think it has something to show us about the music. It is angular and sharp, with blocks of repetition across the page. The hard angles of Furrer’s flags and stems seem to communicate the precision with which the rhythms are to be executed. The time-saving device of writing in repeat marks for literal repetitions of measures also serves to illuminate their structural nature.

Perhaps this attraction to hand-written scores is nothing but nostalgia for a craft gradually being left by the wayside, but I think there’s something to the human connection it makes. In the same way that even a scrawled letter can communicate more than a double-spaced Times New Roman printout of the same text, a hand-written score can be a more intimate connection to the composer than a default Sibelius/Finale engraved score can. That isn’t to say that computer engraving precludes communication and individuation of a composer’s visual personality – many tech-savvy composers are doing incredible things with computer engraving. Timothy McCormack for one has managed to bend some notation software to his will to a remarkable degree, displayed in the score excerpt below, from his Mirror Stratum for contrabass clarinet and cello:

An excerpt from Timothy McCormack's Mirror Stratum; click for larger version

An excerpt from Timothy McCormack’s Mirror Stratum; click for larger version


23
Sep 12

Workshopping: Week 1

We’re just getting started workshopping a new piece for our October 13th performance at Issue Project Room (at Our Lady of Lebanon Cathedral). Composer Thanasis Deligiannis is meeting with the 5 singers for the project individually, to get to know our voices and personalities as he assembles the new work, Ignored Manuals.

Our first few meetings have involved the standard “what’s your range” discussions, but quickly moved into a more exciting creative process, with Thanasis singing to us fragments of the piece for us to imitate. Though we are moving towards a written score in the end, starting off with this kind of rote process affords us a kind of musical communication more focused on timbre and other subtle sonic details of vocal sound. In a way it reminds me of learning a language from tapes in the car; we’re beginning with pure sonic mimicry, and eventually getting to analysis and written communication.

Oh, and Thanasis’s isn’t the only voice that might be imitated…


2
Apr 12

Text and IPA for composers

This post is part of a series directed at composers writing for the voice. Something about vocal music feels inherently different from instrumental music; this can be daunting for a composer familiar only with instrumental writing. These posts are intended to be signposts pointing to notational standards and techniques which will allow composers to be as communicative and clear as possible in their writing for singers.

The ability to deliver a text is what sets the voice apart from instruments. There are, of course, occasions on which a more instrumental vocal line is desirable and extremely effective; but when it is at all possible, I prefer to work with words. Text serves as an important cue for musical and vocal interpretation, and can be an immediate way of understanding an otherwise unfamiliar musical style or affect. A text should always be clearly credited as to its source and printed in its entirety somewhere in the score, so that it can be studied and understood away from the music.

Even if it is outside a composer’s aesthetic or intent to use an actual text or even any real words, indicating which vowels or consonants the singers should use can provide an opening for an emotional and interpretive connection to the music. For this reason I would recommend all composers to become familiar with the International Phonetic Alphabet, known as IPA. It is a system which can notate in varying degrees of specificity the sounds of any language, real or imagined.

A fantastical virtuoso use of IPA can be seen in Ligeti’s Aventures and Nouvelles Aventures, for which the composer devised an entire artificial language, notated in great detail. It is of course not necessary to go to these lengths to make use of IPA. It can be used as part of a traditional text to describe a segmentation of words, as in Berio’s A-Ronne, where the text “Aleph is my end” is split between two hocketing singers, one performing only the vowel sounds and one performing only the consonant sounds. Stockhausen uses IPA in Am Himmel wandre ich… to write out nonsense syllables like [tɛgədɛgə] as well as to indicate a kind of echo of a word in the text (often colored by Stockhausen’s German accent!): the word ‘universe’ is echoed by [huhihø], the text ‘of having’ is echoed by [ɔ ɛ ɪ].

IPA is an incredibly flexible and communicative system which can be applied to many ends and aesthetics, and these examples I’ve given only scratch the surface of what is possible. I look forward to seeing how composers of vocal music continue to develop its musical use.


6
Feb 12

Wolfgang Rihm String Quartets

Though it’s not vocal music, it is music by an incredibly prolific and wonderful composer of vocal music, and I think a great decision on the part of a publisher to reach out electronically:

Universal Edition has put online the scores to each of Wolfgang Rihm’s string quartets, celebrating their performance at the 5e Biennale de quatuor à cordes. It’s a wonderful opportunity to peruse these scores at your leisure, without leaving the comfort of your desk!


12
Dec 11

The Exploded Voice

An excerpt from Evan Johnson's "General Interrupter"

The consonant staff

I’m looking right now at a piece by Evan Johnson for solo voice called A general interrupter to ongoing activity. The composer describes it in the performance notes as being “comprised of overlapping, mutually imbricated, sometimes self-canceling structures laid out over a landscape of several different independently treated types of more or less vocal, muscular action…”

A sample from Evan Johnson's "General Interrupter"

An example of the rhythmic structure of the pitch staff

The notation for the piece parses the voice into its component parts – a staff for breath, one for fricative and consonant sounds, teeth clicks, whistles, tongue (pressure and clicks), voicing and vowels, and finally pitch. The amount of information on the page is mind-boggling – add to these concerns a rhythmic language involving tuplets nested 3 or 4 deep, and an extreme degree of specification in dynamics and articulation. Traditional vocal notation involves a staff with the pitches on it, words below, dynamics above, and occasionally articulation markings. This traditional notation is a kind of shorthand, in that it assumes the singer is coming to the score with an understanding of language, phrasing, idiom, style, and a myriad of other historical assumptions. In a way, General interrupter is technically totally prescriptive; an alien musician wouldn’t need to know these traditions to interpret the score. However, the mere quantity of information here demands a kind of interpretation, a filtering of the demands of the score through the ability and body of the performer.

A sparse page from "General Interrupter"

A sparse page from "General Interrupter"

Aside from the idea of the voice expressing manifold levels of often physically self-contradictory musical information, what interests me most in the piece may be the notation itself. While some pages are dense with ink and high prime number tuplets, others are reduced down to a single staff, with rhythm notated proportionally and graceful slurs arcing across the page.

I see in this kind of writing the voice exploded, its infinite variables found so intriguing that it becomes impossible to choose a single possibility. In contrast with say, the string quartets of Aaron Cassidy, whose decoupled instrumental actions create a dramatically physical choreography that produces an explosive music, exploding the voice creates dramatically physical, extremely small inner conflicts, invisible to the audience. I think this distinction is important to note, and that using the voice in this way is a departure on a journey inward – maybe this is really the implosion of the voice – a new hermeticism.


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!


25
Apr 11

IMSLP – sheet music online

IMSLP is a huge repository for public domain sheet music, which is wonderful if you’re looking for older music. Recently their servers had been down, due to a spurious legal challenge from the Music Publisher’s Association. Now they’re back up and running again, and you can find that there’s more than just old music on their servers! Luckily, there are some living composers who have chosen to post their works under Creative Commons licenses, giving us access to newer scores.

Michael Edward Edgerton is one of these living composers who posts his own scores on IMSLP. He is also a researcher into extended vocal techniques, and his works explore a kind of vocal parametric decoupling which includes precise notation of intraoral articulation points for consonants. Cantor’s Dust and Anaphora are two solo voice works worth checking out, if you’re interested at all in the possibilities of notation for vocal music!

It’s hard to know what is lost and what is gained in the move of parametrically decoupled actions from the dramatic choreography of the arms of string players to the movements of the tongue, vocal tract, and larynx of the singer, hidden inside the body. Of course the sonic exploration remains equally valid, but the visual performative intensity is occulted. We are presented with a kind of visual mystery in the performance of any vocal music, where the physicality of sound production is mostly interior and unknowable.


11
Apr 11

Just Intonation

Just Intonation is the tuning of pitches related by whole number ratios. The following will serve as a brief overview and introduction to the system’s theory and practice. The harmonic series is a good place to start when discussing Just Intonation (henceforth JI).

A harmonic series on low C

Partial numbers inside the staff, frequencies below

From a fundamental frequency (here the low C at ~65.4 Hz), the harmonic series ascends in multiples. If we refer to the partials of the tone, rather than the overtones, we can more easily see the math behind the present frequencies. Numbering the fundamental frequency as the 1st partial, the 2nd multiplies the frequency by 2, the 3rd partial by 3, ad infinitum. What does all this have to do with JI? JI deals in tuning intervals by simple whole number frequency ratios, and since we have demonstrated that the number of a partial is a multiplier of the fundamental frequency, we can use the harmonic series to find the intervals of these ratios. 2/1 is an octave, 3/2 the perfect fifth, 4/3 the perfect 4th, 5/4 the major third, 6/5 the minor third. What is significant about these intervals is that they deviate from the tempered intervals one finds on the modern piano. The simpler ratios sound beatless, and ‘pure’. If you are a choral singer or brass player, you probably are already used to finding this beatless sound by tuning wider fifths and lower thirds and sevenths in chords.

JI systems are sometimes referred to as “x-limit” systems, where x is some prime number. For example, a 5-limit system includes no prime numbers higher than 5 in any ratios, allowing for pure major thirds, but not true septimal or 7-limit consonances. 3-limit tuning is often referred to as Pythagorean tuning, and is composed entirely of just fifths. 5-limit tuning can approximate the major-minor system of Western music very well.

A few notable composers using JI

Americans: Ben Johnston, Harry Partch, LaMonte Young, James Tenney. Europeans: Gérard Grisey, Georg Friedrich Haas, György Ligeti. This is of course, no exhaustive list of composers, but a guide for the novice to what might be more familiar music, and an easier entry into the system. For a further discussion of the motivation to use JI, see Colin Holter’s fantastic paper “The Spiritual Construction of Tuning in American Experimental Music” at the Search Journal.

Notation of JI

The notation of JI varies depending on the composer and the circumstances. Ligeti often notated JI intervals simply by the fundamental on which the horn was to play (as in his last work, Hamburg Concerto). James Tenney sometimes notated JI intervals by writing cents deviation from ET. Perhaps the most exhaustive and most widely embraced system yet devised is Ben Johnston’s. Beginning from the assumption that the C Major scale is to be built from interlocking C F and G major triads, all tuned 6:5:4, Johnson introduces novel accidentals to shift these notes to different relationships. For example, in his C major scale, the supertonic D is ~4 cents higher than ET, while the A is ~16 cents low. If we are to use a properly tuned triad based on D, this requires an accidental to raise the A approximately 21 cents, Johnston’s +. Alternately, the D could be lowered, using -. The interval expressed by + or – is called the syntonic comma (81:80), and is the difference between a Pythagorean (or 3-limit) major third (81:64) and a 5:4 (5-limit) major third. Johnston’s system of accidentals continues similarly, with each successive accidental expressing a kind of fundamental shift related to a higher prime ratio.

Learning JI

Just Intonation tunings appear in traditional drone-based musics, like North-Indian Classical music, and can be easily practiced over a drone. If you play any string instrument, you can accompany yourself with a drone for practice, use a recording of a tambura, or even an electronic tone (preferably one rich in harmonics). Singing a just interval correctly feels ‘anchored’ in the fundamental tone and its harmonic spectrum. Aside from going by feel, if you are a string player of any kind you can also use the open harmonics of a string to learn simple just intervals. Being a computer enthusiast, I prefer to practice my microtones with the aid of software. Rote learning is the basis of the oral traditions that function within a JI framework, and is an indispensable tool. I use a program called Scordatura for the playback of JI microtones, and it is extremely flexible. Using CSE, a companion program to Scordatura, I can designate tunings wholly via ratio from any given fundamental at any tuning. It has made the task as simple as entering ratios in scalar order, and assigning them to keys on my midi keyboard. From this point on, I work by transcribing the pitch notation of the score to the re-mapped microtones of the midi keyboard (one octave of pitch extended over more than 4 octaves of keyboard (!) in my most recent JI undertaking, Johnston’s arrangement of Partch’s Barstow). I have a similar setup prepared for learning the tuning of Randy Gibson‘s upcoming work for ekmeles.

Of course, this is but a simplified overview – there are manifold internet resources for learning more about JI theory and practice. I’m happy to address questions or requests for elaboration on any of these points (and to accept corrections from those more deeply involved in JI than I). But if you’re interested, I would recommend as a first step getting your hands on a CD – or better yet, attending a concert – featuring JI music and hearing the difference a few cents here or there can make! Ben Johnston’s fourth String Quartet is a melodic and beautifully lucid introduction to JI.