Showing posts with label psychoacoustics. Show all posts
Showing posts with label psychoacoustics. Show all posts

Sunday, May 20, 2012

Terry Riley’s Aleph (א): Music to Code By

Terry Riley
A  leph in Jewish mysticism represents the oneness of the Divine. The letter can been seen as being composed of an upper yud, a lower yud, and a vav leaning on a diagonal. The upper yud represents the hidden and ineffible aspects of God while the lower yud represents God’s revelation and presence in the world. The vav connects the two realms.”
  — Wikipedia.

T he 1-hour 53-min recording of Terry Riley’s solo synth performance of his composition, ‘א’, is beautiful—and precisely the sort of experience you would expect from Riley.

B ut, apart from whatever else it may be and apart from its merits as a composition and as a performance, I have found it to be especially conducive to my own productivity when working on complex math problems and coding software to solve them. For me, silence works only up to a point, after which I need minimalist music.

B ut not just any minimalist music. For example, Michael Nyman’s music interferes with concentration. La Monte Young’s music contains, for me, too many distractions. I do find Ellen Fullman’s recent work conducive, though, in the same way that Terry Riley’s ‘Aleph’ is conducive.

T he timbre of the Korg Triton Studio 88 Synth is bright like a Chinese single-reed or double-reed, but with a lot of spectral flux like a car horn... or a choir of Chinese tenor and bass suonas. Spectral flux and spectral irregularity are distinguishing features in car horns (see Lemaitre 2003, link below).

T he two-hour performance is filled with dense, organic, continually-changing textures—nimble car horns, if car horns can ever be nimble, and these are supernaturally nimble. The automaticity of preschool kids’ trying out their fingers on a keyboard, enjoying the raw pleasure of making notes and reproducing patterns and sequences... reflexive movements of their fingers and arms, yielding arpeggiation that involves just those notes that are within easy reach without stretching.

T he effect, some minutes into listening to it, evokes a freedom from intention and planning that is unknown to sober adults, and this is what facilitates my problem-solving and coding mind. The uncertain continuation of woodwind-like fingering patterns without aim, as long as they last, until superceded by some new motif... the stochastic, aleatoric innovations... Riley discounts the creative value of mind and deliberation and discounts it again, and again... the dollar-store of intellect... until the passion of meat is all that’s left, and animal instinct is restored...

O  nly connect the prose and the passion, and both will be exalted, and human love will be seen at its height. Live in fragments no longer. Only connect...”
  — E.M. Forster, ‘Howard’s End’, Ch. 22, 1910.

H ere’s a short MP3 clip.

T here is a ceremonial, magisterial, quasi-liturgical quality of ‘Aleph’ that reminds me of requiem forms. Or of chant, which can be heard as both archaic and contemporary. It is a mystical piece that unfolds at an implacable, glacial pace. The tone is largely meditative and serene, which provides space for contemplation and veneration. There are dozens-of-voices atmospheric Ligeti-like sound-fogs... fields of dissonance that convey an inhuman, infinite, primeval power—this surely is part of the Hebrew significance of Aleph; as is true also of the meaning of ‘א’ in mathematics—fitting as well in the context of requiem-writing.

I  t has been said that my ‘Requiem’ does not express the fear of death and someone has called it a lullaby of death. But it is thus that I see death: as a happy deliverance, an aspiration towards happiness above, rather than as a painful experience. The music of Gounod has been criticized for its over-inclination towards human tenderness. But his nature predisposed him to feel this way: religious emotion took this form inside him. Is it not necessary to accept the artist’s nature? As to my ‘Requiem’, perhaps I have also instinctively sought to escape from what is thought right and proper...”
  — Gabriel Fauré, 1902.

T hroughout, the piece is prodigiously inventive, with prolific layers upon layers of rhythmic and harmonic complexity, yet all presented with what appears on the surface to be minimalistic... it embodies the best of what minimalism can be: full of latent variety that captures and nourishes the listener’s awareness. (Which is why I find it helpful to listen to when I am tackling a hard problem, and why I am writing this blogpost you are reading. If you are interested in reading more about quantitative evidence concerning music listening and work productivity, have a look at the links below, esp. the book by Vikram Kiran.)

T he seamless, cluster-like blends fan out like a spilled liquid on a flat surface—part of the organic quality of just intonation, providing a support structure for the synth suona-like parts, a Toop-style “rawness” of intonation that sustains the emotional intensity of the piece.

M ost a cappella ensembles naturally gravitate to just intonation because its ‘stability’ or ‘target-pitch predictability’ is comfortable. In that regard, maybe the spectral flux and on-again-off-again frisson of this Terry Riley recording will be of special interest to people of a vocal bent, both amateur and professional singers alike.

T his sound of synth suonas keening, synth voices keening, choir of synth car horns keening... bears some resemblance to the György Ligeti piece in ‘2001 A Space Odyssey’, ‘Lux aeterna’... A friend who was overhearing my repeated playing of the 2 Riley ‘Aleph’ CDs wondered aloud “How can you stand that!? It’s driving me nuts!” So, to be truthful I should say that this is an acquired taste, or reveals a patience borne of equanimity. It is like being transported by William Kraft’s music in the walkway between terminals underneath Chicago’s O’Hare airport. It is like listening to a choir of chainsaws in the forest at a great and comfortable distance. Or like the persistent-but-beautiful bleating and tintinnabulation of sheep in a high alpine meadow in the Swiss alps, below the Jung Frau Joch in the late mornings of mid-summer. In other words, the bleating and tintinnabulation signify tolerant, salutary, and humane qualities that are implicit in our planet’s troubled story. Children of the Universe, you (every living creature) are here, hurray. Have a good life.

I  n short, these are qualities which make humans, the sum of which could be seen in love (esp. agape, which in turn can be seen as an embodiment of the ‘idea of One’). The musical gaze cast from this sphere upon the story world is distanced, more or less withdrawn, non-judgemental, calm, quiet, and slightly melancholic, yet non-sentimental. As film music, tintinnabuli music often qualifies as an ‘against all odds’ score capable of making the complicated plot-level matters more poignant.”
  — Kaire Maimets-Volt, p. 172.

I f you were in a foreign country and experiencing the local people performing on their native instruments, a long raga, for example—you would exhibit a tolerance toward such bleatings and tintinnabulations. But if instead, like my friend, you regard it as a choir of annoying car horns—multiple car alarms being set off repeatedly by marauding kids on a street a couple of blocks away—you just want it to stop.

I n summary, playing these 2 CDs consecutively without a break induces an awareness that can facilitate productive concentration at work and lift you into a realm beyond human understanding or hearing. The music requires an audience who must be willing to accept the spirit of the work and suspend their disbelief in order to receive its many rewards.


Tuesday, December 6, 2011

Tallis Scholars’ sound, or why 176 KHz/192 KHz HD sampling for choral chamber music is important

Tallis Scholars
I   t is known that energy in the 5-20 KHz range can be perceived even when it is 50 dB or more below the main voice spectrum peak. Also, these upper frequencies are conventionally emphasized in the production of popular vocal music. Yet very few studies of the acoustic content of this range have been made. High fidelity recordings were made of singers sustaining vowels at varying levels of vocal effort. A general characterization of the two highest octaves 5-20 KHz was sought. The prevalence of high-frequency energy, the variation of harmonics signal-to-noise ratio as a function of frequency, and the covariation with overall SPL were all highly variable, but several landmark features were identified... [including] clusters of resonances in the regions 7-10 KHz and 13-16 KHz. Harmonic energy was observed to over 16 KHz in strong female voices.”
  —  Sten Ternström, KTH Stockholm, 2008.
T he Tallis Scholars’ performance in Kansas City tonight was gorgeous. The concert was performed in the Cathedral of the Immaculate Conception, which has a central altar and a wide chancel such that there are myriad acoustic reflections that arrive at one’s ears from multiple directions. Unlike many performance venues where reflected sound for people seated in most locations is predominantly from one or two general directions, Immaculate Conception has quite high reflective efficiency from many of its interior surfaces.

I f you are seated close to the ensemble—not more than, say, 10 meters away from the sound source—the sound projects exaggerated cues of ‘spatiality’, accentuating the atmospheric qualities that are there in the music and the text. This was especially true tonight during the pieces by Arvo Pärt, which have considerable dissonance and frisson amongst the parts, with long sustained notes during which the spatial effects from the direct and indirect sounds arriving at our ears can be fully appreciated.

T    aking into account the speed of sound, we can convert energy defocusing in the time domain to “smear” in distance estimation by the ears. Energy spread over ±500 ms is the same as a distance smear of ±15 cm. 96 KS/s keeps almost all the energy within about ±50 ms, or ±1.5 cm. One of the observations people make about 96 KS/s material is that the spatial localisation of everything is very much better than 44.1 KS/s. 192 KS/s is better than this, although very dependent on amp and speaker performance to demonstrate it.”
  —  Mike Story, 1997.
Tallis Scholars
T he spectrum of frequencies and harmonics returning to your ears in this marble-and-plaster, highly-reflective cathedral has a surprising, pleasing amount of power in the range 4 KHz and up. In an age when noise and unpleasant/irrational/blurred stimuli bombard us every day, the Tallis Scholars’ sound in this sort of brightly reverberant performance space restores our belief in clarity—restores our belief in the fidelity of human communication across large distances in space and time. It is as though high signal-to-noise ratio becomes an aesthetic and cultural emblem of Civilization itself.

W hat I mean is, the sound (with its high S/N and high-end harmonics) not only embodies the enduring and transcendent meaning of the sacred music that Tallis performs and the human spirituality that caused this music to be written so long ago, but it asserts the very possibility of transcendence and persistence—of meaning that lasts beyond one’s own lifetime. After the concert, I go to Gimell Records’ website and download a couple of their 24-bit 176 KHz-sampled Studio Master high-def recordings, to get more of this. What I hear is truly thrilling—as good as the live performance.

C onventional wisdom doubts that humans can hear frequencies much higher than 20 KHz—frequencies higher than that are only perceptible to dogs and other animals. That is foolish—misinformation propagated uncritically since 50 years ago. In recent years, the misconception persists as a reflection of the fact that otolaryngologists’ and audiologists’ primary focus has been on “basic,” “practical” functions such as a person’s ability to hear and accurately understand speech. By contrast, research concerned with aesthetic and musical functioning has received much less attention or funding. [Measurement equipment for studying acoustics of bats in the 20 to 100 KHz part of the spectrum has existed for quite awhile—bat and bird and other animal communication is the subject of scholarly articles in acoustics society journals—but not many researchers studying humans have utilized it. Part of the reason why the freqency spectrum above 4 KHz for vocalizations has been under-studied is that high-speed video strobolaryngoscopy has been unable to detect the very small-amplitude (~0.1mm) vibrations in the larynx. Not surprisingly, if you can’t detect something, then you tend not to study what you can’t detect.]

T here is a common, mistaken notion that frequency response above 10 KHz is only relevant to sibilant “S” or fricative “F” type consonants in speech or singing. Well, that is most definitely not true, as evidenced by tonight’s Tallis Scholars performance! Recent research by Brian Monson, Andrew Lotto, and colleagues at the University of Arizona in Tucson (link below) shows that the frequency spectrum above 8 KHz figures prominently in singers’ sustained-vowel sound imaging—and figures also in listeners’ perception of open vowel sounds. The Pärt works in tonight’s program—and the effects of reverberation in these, in Immaculate’s chancel—especially emphasize intervallic and spatial relationships and transformations, and remind me of a workshop led by John Roeder at the 2003 Mannes Institute. That workshop examined expressive transformational representations for music by Pärt and others, and addressed how transformational representations relate to musical form, and to how musical forms are experienced. Varied repetition as in Pärt amounts to retracing similar transformational pathways among different sets of musical objects, and plumbing the extent and meaning of their similarities. Canon and contrapuntal cyclical spaces are frequent vehicles for enacting or showing transformations, of course, and—to the degree that each of these enactments is individually convincing—uncovering these unexpected connections becomes our primary mode of understanding and enjoying the music.

T onight’s performance and these HD Gimell/Tallis recordings reveal why it’s desirable to have a sampling frequency that is at least 4 times the desired system bandwidth, a process that is known as oversampling. If your goal is to maintain a “flat” response with 6 dB or less roll-off at the upper limit of the band, then a sampling frequency that is more than four times the desired bandwidth is needed—hence, the 176.4 KHz or 192 KHz sampling rates on these Gimell HD Studio Master files.

Tallis Scholars
A  problem (for me, at least) with off-the-shelf HD audio equipment is that the sound reproduction chain (player, preamps, EQ, power amps, speakers) can sometimes have too much high-frequency power. It can sound too sibilant—even for vowel sounds—somewhere between 12 KHz and 20 KHz. The spectrum EQ sliders on your playback equipment may not have center frequencies that correspond to wherever that objectionable tweeter “break-up frequency” peak is—so the adjustments you make to cope with it end up impairing the quality of the sound around that peak, essentially leaving you with a sound that's far less than HD. But Bowers & Wilkins speakers are one example of a product that doesn’t have this issue. They’re clear above 8 KHz, and give smooth mid-range and ample bass. Put two 800 Diamonds in front of you, two 802s behind you, plus a couple of DB1s somewhere in the room to cover the bottom bass frequencies. HD music recordings—such as those produced by Tallis and Gimell—have frequencies that exceed 20 KHz and we need speakers (and other components in the reproduction chain) that can accurately render these. The response of the 800Ds is essentially flat between 25 Hz and 33 KHz. Their tweeter “break-up” frequency is way, way out of harm’s way—at about 70 KHz.

R eproducing high frequencies has everything to do with recreating the sensation of sharpness and immediacy—the experience of being near the sound-source, in or near the front row (see Beranek, p. 511). There is not just the issue of rapid attenuation of high-frequency portions of the spectrum as a function of distance, but also the matter of inter-aural time-difference cues.

W    e found that robust pitch perception can be elicited by harmonic complex tones with fundamental frequencies below 2 KHz, even when all of the individual harmonics are above 6 KHz—well above the currently-accepted ‘existence region’ of pitch and above the currently-accepted limits of neural phase-locking. The results suggest that perception of musical pitch at high frequencies is not constrained by temporal phase-locking in the auditory nerve but may instead stem from higher-level constraints shaped by [immediately] prior exposure to harmonic sounds.”
  —  Andrew Oxenham, Christophe Micheyl, Michael Keebler, Adam Loper & Sébastien Santurette, Dept of Psychology, Univ Minnesota, 2011.
I n other words, our ability to perceive (a) spatial relationships—relative locations of different singers or depth and breadth of other sound-sources—and (b) overtones/harmonics generated by the blending of all of the lower frequencies in ensemble (Fourier spectra of mixed signals) ... depends primarily on the high-frequency (short-wavelength) components and on phase-angle relationships between the frequencies as they mingle with each other in the performance space (or the playback environment, for a recording). If the sound-sources are moving (as in an opera; or even for singers who are shifting or rotating slightly on-stage), then the high-frequency components contribute most to our ability to perceive that motion. It’s part of how our brain sorts out “signal” from “noise” in noisy environments.

A nd we get special pleasure from successfully doing this. Clarity that facilitates the listener’s own brain’s processing—which is what the HD 176 KHz/192 KHz-sampled media does for us (see Vorländer, pp. 222ff).
  • Jan Pieterszoon Sweelinck - Hodie Christus Natus Est
  • John Taverner - Magnificat (A5)
  • Robert White - Tota Pulchra Es
  • Arvo Pärt - Magnificat
  • Arvo Pärt - Nunc Dimittis
  • Hieronymous Praetorius - Magnificat IV
  • Robert White - Regina Caeli
  • Morales - Regina Caeli
  • Benjamin Britten: Hymn to the Virgin
  • Giovanni Pierluigi Da Palestrina - Magnificat for Double Choir
  • Giovanni Pierluigi Da Palestrina - Nunc Dimittis for Double Choir
I  very much hope that Phillips and colleagues continue to add aggressively to their HD DVD-Audio recording downloads. There are many of us out here who crave the immersive psychoacoustic experience that only very high sample-rate HD can deliver. The Tallis Scholars’ recordings are [one of the types of—] music that powerfully motivates and intensely satisfies the “immersive HD” desire.

B efore you place an order, Gimell recommmends to try the Test Files they provide for free download, to insure compatibility with your system.

T allis and Gimell recommend using an audiophile-quality Network Music Player to listen to the HD download files. If you own a DVD-Audio player and your PC has a DVD burner, then you can create your own DVD-Audio discs by importing the HD download files into Cirlinca’s DVD-Audio Solo® or other similar software apps. The files are 15 to 18 times larger than the equivalent track with MP3 compression. The Gimell offerings also include multichannel Quadraphonic/Surround Sound formats. Cirlinca’s HD-Audio Solo Ultra® v4.1 software costs just USD$75 for a single-user license— HD-Audio Solo Ultra® is the product that I use. Cirlinca has relationships with record labels including Gimmel, Deutsche Grammophon, and Hyperion, plus orchestras and ensembles including Boston Symphony Orchestra, Philadelphia Orchestra, and many others.

M arketing-wise, when HD recordings such as these from Tallis/Gimell are coupled with correspondingly good playback chain equipment it opens up a promising (and to-date under-developed) market segment for serious music: tech-avid audiences and software developers and gamers whose primary passion is virtual reality (VR) and who have a strong but decidedly secondary interest in music. Many in this segment or niche market may not be musicians per se, and they may not be people who regularly attend ‘conventional’ live concerts. But they crave excellent VR and immersive “worlds” that can capture the heart and mind—as good music can do so effectively. And such people spend quite a lot of money each year on personal “world-building”. Their sort of passionate “sonic-experience-first-music-second” amateurism is, I suppose, not unlike serious HiFi audiophiles of the 1960s or late 50s.

I n summary, Tallis Scholars and Gimell are creating the right kinds of HD content to grow a VR audio market. Maybe more and different marketing, including social media, will be needed to really drive its growth. For now, I’m delighted to have experienced these wonderful recordings that prove once and for all that very high sampling-rates of 176.4 KHz and 192 KHz are actually necessary, to accurately reproduce the nuances that we hear up-close in live performance. The freshness and lightness and clarity of the sound invite the listener “inside” the world that the music conjures—the Studio Master HD files enable listeners to inhabit that world via interactive replay evoking “live” sensations and realism, most vividly when the listener/file-downloader can freely explore and re-explore again and again ad lib. We avid listeners want to rehearse our neurons—not only to re-experience the shivers up our spines, but (through practice) to train our bodies to optimally respond to the aural cues that are in these beautiful HD recordings, and in the next live performance we’re able to attend. Bravo!

Tallis Scholars

Sunday, November 2, 2008

Weilerstein & Barnatan: Prepared Cello, Unexpected Microtonality

 Alisa Weilerstein Inon Barnatan
W    eilerstein showed that she certainly has the technique to emerge as one of the leading cellists of the next generation. She produced a consistently lavish tone and demonstrated remarkably assured technical facility... With nearly flawless passagework and intonation, the cellist provided some pretty thrilling playing.”
  —  Chicago Tribune.
B    arnatan … has an instinctive understanding of Schubert’s fragile, deep world... he obtained a hypnotic tone from the piano... he made sounds that might have won the approval of Schnabel himself.”
  —  The New Yorker.
Cellist Alisa Weilerstein and pianist Inon Barnatan performed a program of Kodály, Golijov, Chopin, and Beethoven on Saturday evening in Kansas City in a Friends of Chamber Music concert at the Folly Theater. The program allowed the audience a wonderful opportunity to experience each of the artists as soloists, as well as their special chemistry together. Each is a tremendously passionate, emotional interpreter; together, their responsiveness to each other was magical.

  • Beethoven: Sonata No. 5 in D Major, Op. 102, No. 2
  • Kodály: Sonata for solo cello, Op. 8
  • Chopin: Barcarolle in F-Sharp Major, Op. 60
  • Golijov: Omaramor
  • Chopin: Sonata for cello and piano, Op. 65
Alisa Weilerstein is the daughter of Donald Weilerstein, the founding first violinist of the Cleveland String Quartet. At 26, she has performed with top U.S. and European orchestras and has given recitals throughout the U.S. and Europe. Her festival performances (Spoleto, Aspen, Caramoor, Schleswig-Holstein,Verbier) have been well-received. Alisa is the recipient of an Avery Fisher Career Grant. (She is also a 2004 graduate in Russian History (Columbia University). This is something of a unique path for an artist of her caliber, one made accessible for her by the stature and acclaim that her parents have as musicians, in addition to her own performance ability from an early age. How many people have the option to pursue studies in another field—liberal arts, engineering, whatever—and not have the door to a career in music shut on them? Not many. It is wonderful to see Alisa make this dream happen!)

Inon Barnatan is an artist of the Chamber Music Society of Lincoln Center. He has performed with the San Francisco Symphony, the Aspen Music Festival, the Mostly Mozart Festival at Lincoln Center, Carnegie Hall, the Concertgebouw, Salla Verdi in Milan, the Royal Festival, and Wigmore Hall in London. In past seasons Barnatan has made his debut with the Israel Philharmonic, Netherlands Chamber Orchestra, Orchestre de las Suisse Romande, Jerusalem Symphony, and numerous other ensembles. He trained with Maria Curcio with additional coaching from Leon Fleisher, Radu Lupu, Richard Goode, Murray Perahia, Claude Frank, Menahem Pressler, and Christoph Eschenbach.

The performance last night was engaging throughout. But the Kodály sonata especially intrigued me. Not the ubiquitous Kodály Eastern-European folk music elements, nor the fact that this sonata is imbued with the milieu of 1915, composed as it was in the early days of WWI. Yes, it’s a very passionate piece, and is therefore a perfect vehicle to illustrate the range of Ms. Weilerstein’s extraordinary expressiveness. Alisa’s use of rubato and rhythmic flexibility renders the improvisatory character of Hungarian elements with style, energy, and elegance. Yes. But those are not the aspects that really intrigued me.

What intrigued me—Alisa revealing this piece to us as though we were hearing it for the first time—was to grasp Kodály’s use of classical sonata form here and—oh, what does it amount to?—to figure out whether our own expectations have any force or moral standing? whether we’re fated to struggle and struggle and eventually lose? What I mean is, sonata form is conventionally an epitome of Enlightenment rationality. But, in this piece, our expectations keep getting dashed. Struggle and lose. How does this happen? Why? I think it’s not enough to think in terms of Epstein’s concept of ‘structural downbeat’ or ‘structural accent’, or, say, E. T. Cone’s concept of ‘frame’. I think the ‘How’ goes well beyond the notes on the page and the nominal structural features that are there. Our anticipation—and how it gets dashed repeatedly—is bound up with the timbral changes and the scordatura and the metrical displacements that keep happening.

Op. 8 requires scordatura tuning, borrowing an instrumental practice of the 16th and 17th centuries. The timbral characteristics of the cello are altered by the detuning of strings, and the cello’s resonance takes on a mysterious, hollow, melancholy quality. The scordatura is indicated at the beginning of the movement, above the first bar. The notes are performed ‘as-written’, as if the instrument were tuned normally.

 Kodály Op. 8, I, mm. 21-25
The other characteristic element of this sonata is what I referred to as ‘metric displacements’, through which the repositioning of the beat continually generates a sensation of ever-present alternatives. Although written in 3/4, the beginning of the first movement up to m. 31 is marked by metric ambiguity caused by variable positioning of accents in each measure, so that our anxiety is heightened. The emphatic 4-note chords are a major source of the metric ambiguity—quasi-boundaries or pseudo downbeats. The metric slippage and preemption—the displacements—create a sense of pulse in a different part of the successive measures. It’s like structural accents, as discussed by Epstein (1995, p. 23-6). Even when we achieve a ‘stable’ measure, whose downbeat is strong enough to be believed, it cannot be trusted for long. The ‘exceptionalism’ is recurrent, pernicious … so emphatic that it’s inescapable. The exceptions become the rule rather than the exception. The metric ambiguity is one of the main elements lending (or permitting the performer to give—) an improvisatory feel to this sonata.

The first movement begins with two chords that are repeated emphatically as a feature of the first theme. Things progress in mm. 21-25 (the bars pictured above), but, dashing our expectations, a transition surprisingly drives instead in measure 31, to the beginning of a new thematic group. Once we get here, we naturally feel things should move toward some new harmonic center of this new (second) thematic group. But, again, our expectations are thwarted.

The slow, lamenting phrases have these rich ornamentations—offering some emotional solace, I suppose. But instead of solace, these make us feel still more ‘on-edge’.

The metric displacements can preoccupy a performer, but not Alisa. She preserves a ‘speaking’ style in each phrase—to which the paroxysmal rhythmic gestures are incidental, not dominant. I imagine Kodaly’s rhythms and phrasing are somehow descended from the inflections of the Hungarian language. Weilerstein ably contours her phrasing, through agogic and rubato embellishments—in the lamenting sections especially. While Alisa may not be Hungarian, her sense of these inflections is admirable.

Beyond the interesting metric displacements, the scordatura intrigued me even more—how it sounds in the rapid technical passage work; and how it sounds in the context of the impressive Weilersteinian ardor.

It feels weird to place your fingers when the string(s) is (are) de-tuned, the scordatura does. This wasn’t written in C minor—in which case Kodaly could’ve either (a) left the lower two strings normally tuned and the fingerings on the upper two strings would’ve been higher by a half-step or (b) called for raised-tenor scordatura up-tuning of the D string and the A string, to E-flat and B-flat. No, he wrote it in B minor. And the open strings have a dramatically different timbre compared to stopped strings. The sound the bow produces at a given pressure and bowstick velocity is different from normal. (The hollow, scary quality of scordatura is why Saint-Saëns scored it in ‘Danse Macabre’—the discordant double, unstopped bowing in the scordatura-detuned first violins evokes a far-gone, unstoppable, decomposing, pell-mell ride to oblivion. Also, the departure from conventional tuning suggests some sort of irrevocable departure from the community of the living.)

Scordatura’s an aggressively soloistic thing—it cannot help but draw attention to the otherness of the scordatura-detuned instrument, in much the way that prepared piano draws extraordinary attention to the pianist. This is noticeable even in a solo piece like the Kodály sonata Op. 8…

Oh, the scordatura changes things—easy to say, but what does it mean really? Well, when you tune the string(s) down to lower pitch, the upper partials of the lower-pitched strings now become significantly lower in amplitude than the neighboring partials of the normally-tuned strings. And, if you do Fourier Transform analysis of a digital recording of it you see that, since the acoustic spectral energy tends to decrease with successive partials, the higher-pitched tones now tend to ‘mask’ the partials of the lower-pitched tones more than the reverse. So the lower-pitched strings now sound … long-dead. Cool effect, directly related to the acoustic physics of the harmonics/partials—and how (and anatomically where, in millimeters from the cochlear apex!) these superimposed sounds register in the nerve cells of the inner ear.

Have a look at the graph below, showing the frequencies of the harmonic spectrum for a bowed cello’s top string, A220 (solid lines), and as detuned to G196 (dashed lines)—and showing too the anatomical positions within the inner ear where those frequencies are sensed. A relatively large change in millimeters on the x-axis, this—especially for the higher partials. Look how much those shift downward (to the left in the plot), compared to the big spike, the fundamental frequency of the note, off to the far left. It doesn’t shift nearly so far when it’s detuned down to G196. We could do a similar graph for the cello’s detuned C and G strings, as called-for in the first movement of this sonata…

 Scordatura changes which haircells in cochlea of ear are affected by sound
And it’s not just the string by itself. It’s the change in the Chladni-plate resonances of the body—the radiation of the sound of the instrument. It’s the change in what the fingers are doing—the scordatura stopped string sounds muted (in general) compared to what the conventionally-tuned stopped string would sound like at the same pitch, because of the altered finger placement, the altered fingerboard coupling and the altered resonance acoustics. And it’s what the strings do in reaction to the bowhair, under the lesser tension after the strings have been scordatura-detuned. More weight of bow against the detuned string digs deeper than normal, starts up bigger amplitude vibrations quicker than normal. Bow speed that you are accustomed to now microtonally ‘pitch-bends’ on the detuned string many cents different than you expect. The note on the page, that’s not the half of it!

The scordatura-perturbed fine motor control of the hand muscles—and the disruption of the mind-body imaging of the fingerboard and its relation to the pitches—add yet another dimension (for the performer; not for a listener). The note on the page and the placement of your fingers no longer produce the note that your mind expects to hear. It’s tremendously disturbing to people with perfect pitch. But it’s disorienting to almost every performer. In fact, a friend of mine in Minnesota once said she couldn’t possibly play scordatura—it was too ‘painful’.

Conventional wisdom has it that the Kodály sonata in B-minor has the cellist de-tune the two lower strings by a half-step from C to B and G to F#, respectively, to enable open-string sonority for the recurring 4-note B-minor chords (bottom three notes are then open strings, with the scordatura arranged this way; only one finger down on top A-string) and to put the hand in first-position and make some of the passages easier to play. This ‘lowered-bass’ tuning, B-F#-D-A, down a half-step on each of the two lower strings is very different from the ‘raised-base’ tuning (up whole-step) that’s occasionally used with violin.

To hear Alisa Weilerstein play this is to realize that there are other timbral and gestural reasons to do the scordatura. The breadth of the 4-note chords forces you to attack the detuned low (B) string and quickly roll to the F# and D string together. The bowstick speed over that bottom string gives a forlorn, microtonally-bending B. This effect would be there, had Kodaly written it in C minor, but the effect would not be as pronounced as it is with the low B.

And besides that, with the open F#, etc., the string players among us just sense the different double-stops that are available, even if the composition turns out not to call for them. Sense where vibrato will not be. You don’t have to be up there performing it; you sense these things just sitting in your seat in the audience listening. It’s this pervasive, latent intuition of ‘possibilities’ now opened, of possibilities foreclosed—of unhingedness, of all bets now being ‘off’. And it seems implausible that Kodály would not have found all of those effects and rationales interesting and supportive—not just the nominal ‘detune the lower two strings, to enable open-string, tonic B-minor’ one. On the eve of WWI, all bets were definitely off…

Scordatura does appear in Bach’s ‘Six Suites’ for solo cello; many other Baroque pieces, too. In the Bach Suite No. 5, the discant string is tuned down one whole tone, from A to G. The cello in George Crumb’s ‘Vox Balaenae’ (for electric flute, electric cello, and electric piano) calls for detuning from C-G-D-A to B-F#-D#-A, which makes the B major last movement that much more sonorous, much like the Kodály.

Probably the weirdest and most symbolically over-the-top is Biber’s Sonata XI (The Resurrection of Christ), calling for detuning the G-D-A-E violin strings to G-G-D-D octaves and switching the two inner strings between the bridge and tailpiece, to make the sign of the cross. The D string moves into the position of the A string and vice versa! I don’t know of anything quite this strange in the cello literature, though.

 Biber, Scordatura Gone Wild
The ‘other-worldly’ impact of scordatura on the performer is both visual as well as registral/timbral/aural. As mentioned above, the ‘normal’ sight-sound intuitions are thrown out-of-kilter by detuning the string(s). Since the notated music you see now bears only a tenuous relationship to what you hear, you experience a profound loss—a sense of alienation. I try it on my violin, and the psychological effect can be hypnotic … if you take it further, do we get a detachment from the self; a sort of ‘dissociation’ experience? Very weird anyhow, the visual disorientation and eyes and ears ‘lying’ to each other. I wonder whether scordatura matters to folk fiddlers who don’t read music…

Curiously, out of the detuning and disrupted sight-sound relationships come these beautiful pitch-bent microtonal pitch anomalies. The fingers go where they’re told, but not quite. We get circumstantial microtonal pitch shifts, not just the different timbre associated with the detuned strings. And we get big differences from performer to performer, owing to underlying neurophysiologic differences between individuals maybe?

 Kodály Op. 8, I, mm. 1 - 22
    [50-sec clip, Janoš Starker, Kodály Op. 8, ‘Allegro maestoso ma appassionato’, 1.2MB MP3]


    [50-sec clip, Xavier Phillips, Kodály Op. 8, ‘Allegro maestoso ma appassionato’, 1.2MB MP3]


    [50-sec clip, Roel Dieltiens, Kodály Op. 8, ‘Allegro maestoso ma appassionato’, 1.2MB MP3]

How did I get on this peculiar path—microtonality via scordatura—with Weilerstein and cello and Kodály? Well, Ted Mook’s concert of microtonal cello compositions by Ezra Sims and Daniel Rothman occurred a couple of weeks ago (16-OCT-2008) at Roulette in New York. ‘Sensitized’ to microtonality in this way, it’s not much of a ‘stretch’ to start hearing interesting microtonal features in cello pieces that are not, on the face of them, overtly microtonal—like Weilerstein’s Kodály. Not actively looking for microtonal features, but nonetheless finding some. Thanks for your interest in this topic. Please feel free to comment or email me about microtonality caused by circumstantial or biomechanical/technic pragmatics that you happen to notice in compositions that are not explicitly scored as ‘microtonal’ pieces per se. And please go and attend Alisa’s and Inon’s concerts whenever you get a chance.

T    he notes and groups you ornament ... are, I think, best always performed with a glissando or portamento. This applies even when some notes will be detached clearly from the group.”
  —  Kodály Zoltán, Pentatonicism 1970, p. 239.

Y    ou have to figure out what string players can do. It’s interesting when the instrumentality has been radically shifted. I love collisions. I hate cross-over, multi-culti—I prefer a colossal smash, where you get sparks that actually deliver something else, something surprising that the players could never have premeditated. The notion of musical possibilities defined by the instrument and by the playing—scordatura, for example—that’s of interest. But when the instrumentalist tells the composer what’s possible and what’s not, you usually don’t get the best results. An improviser is going to actually deliver that stuff all the time they play. That’s in the nature of music practice.”
  —  Jon Rose, The Relative Violins, ‘Johannes Rosenberg: Violin Music in the Age of Shopping’.


Wednesday, April 2, 2008

Was Dallapiccola’s Piano Microtonal or Just-Tuned?

 Dallapiccola, Simbolo, mm. 1-4
W  hy are D-sharp, F-sharp, and G-sharp so horrible?”
  —  Anonymous.
M  any recent composers have come to feel that the compromise of Equal Temperament was a mistake. They feel that the musical logic of moving from any key to any other key became a priority at the expense of music’s sonic sensuousness. Equal temperament chords do have a kind of active ‘buzz’ to them—a level of harmonic excitement and intensity. Equal Temperament could be described as the musical equivalent to eating a lot of red meat and watching violent action films. By contrast, Just intonation intervals are much calmer, more passive. You literally have to slow down to listen to them.”
  —  Kyle Gann.
After my recent CMT blog post on Dallapiccola’s ‘Quaderno di Annalibera’ I have continued to explore these pieces, especially ‘Simbolo’. The dissonances in them are peculiar, unsettling. And the consonances in them are also peculiar—unsettling in their ‘tentativeness’, a quality that’s hard to put your finger on.

I revisited the late David Lewin’s excellent analysis of Quaderno, in hopes of finding a persuasive explanation of these pieces’ effects on me. But, rather than feeling convinced or reassured, I instead began to feel that Lewin’s erudite analysis may manifest certain ‘assumptions’ that were not acknowledged, namely, the assumption that Dallapiccola’s piano was tuned in the standard, modern way—with Equal Temperament (ET). Lewin’s analysis presumes that the piano was equal-tempered. It’s a natural assumption to make, but is it necessarily true? After all, Quaderno was composed during a period that was for Dallapiccola full of intensive exploring and discovery.

How would the tensions and dramatic consonances and dissonances in Quaderno work if the instrument had been tuned in Just Intonation (JI), I wondered? To find out, I downloaded a script to my MIDI keyboard / synthesizer, to change it to JI tuning.

The result was fascinating. The effective tonal dissonance is markedly different when Simbolo is played in JI tension structure instead of ET. In fact, Dallapiccola’s choice of register for the several lines or voices seems especially congenial in JI. The consonances in JI generally fall in Dallapiccola’s relatively long passages and very often dwell on long, now only mildly dissonant stases. In ET, the consonances are transient, and the stases are pretty strongly dissonant. ‘Violent’, to use Gann’s phrase. In my opinion, the contemplative quality of Dallapiccola’s Quadernos di Annalibera is far better in Just Intonation than in Equal Temperament. The JI has a primitive, crunchy-but-laconic, ‘communitarian’ feel. By contrast, the spectra and timbre of the ET—for the intervals in Simbolo, say—are, to my ear, too urgent.

In ET, it’s hard to keep Simbolo from sounding hurried, judgmental, aspiring, and self-referential. In JI, however, Simbolo exhorts the listener (and the pianist) to a zen-like composure, a stop-and-smell-the-roses alertness, a non-judgmental satisfaction with what one has. The former matches what we know of Dallapiccola’s politics; the latter matches what a father (Luigi) might reasonably express to his young daughter (Annalibera).

Modern composers using Just Temperament include Carola Anderson, Bill Alves, David Canright, Jon Catler, John Chalmers, David Doty, Tom Doughterty, Dean Drummond, Dudley Duncan, Adriaan Fokker, Glenn Frantz, Kyle Gann, Denny Genovese, Philip Glass, Eivind Groven, Lou Harrison and Michael Harrison, Norman Henry, Ralph Hill, Jim Horton, Ben Johnston, Joan LaBarbara, Anne LeBaron, Janis Mattox, David Mitros, Norbert Oldani, Harry Partch, P.Q. Phan, Larry Polansky, James Pugiliese, Robert Rich, Eric Ridgway, Terry Riley, Gino Robair, Daniel Schmidt, Carter Scholz, Bill Sethares, Jules Siegel, James Tenney, Toby Twining, Erling Wold, and La Monte Young.

But, so far as I can tell, there’s no documentation that Luigi Dallapiccola used JI when composing Quaderno. Nonetheless, the emotionally coherent effect that JI imparts to these pieces makes the JI conjecture at least plausible.

We have no way of knowing in mm. 2-3 whether the G-flat—A-flat—D is an order-segment of an emerging tone-row. We don’t know in ET, and we don’t know in JI. So we don’t hear the trichord { G-flat, A-flat, D } in mm. 2-3 as yet bound to an intervallic ‘context’ when we hear { G, D-flat, F } in m. 4. We are only ‘situated’ in-context later on. And yet… and yet in JI the ‘context’ looms in a more immediate, more rapidly apprehended, more hospitable and inviting way.

The sense of tension in this music is, I suggest, fundamentally linked to the temperament (and its timbre and spectrum, to use Sethares’s language) in which the music is played. The JI tuning is far less tense overall. Most of the tritones in Simbolo are less disturbing in JI than they are in ET. Often these JI tritones are more consonant than the thirds and the sixths—because of the particular positions of the intervals [see spreadsheet, below] used in Simbolo. (But, conversely, in JI some of the Major sixths are off by a whopping 32 cents. Even some of the Perfect fifths are as much as 24 cents out of tune.)

In other words, JI neutralizes some of the tensions that were present when the pieces that comprise Quaderno are performed in ET and simultaneously gives wolfish dissonances in intervals that would otherwise be warm and consonant. Rather than feeling disoriented, we are oriented in new and dramatically different ways. It is as though I am hearing Simbolo for the first time—and maybe understanding it for the first time? Did David Lewin ever think about this?

Dallapiccola, Simbolo, mm. 31-35
Lewin once wrote that the marking ‘oscuro’ in m. 33 is a hint that ‘something large’ should happen in mm. 34-36: a tone-row might appear; a new configuration may appear, or a new variation; or the piece may just end (which it does, soon afterward). Lewin maintained that the enigmatic effect of the writing here is not just due to a ‘stimmung’ but rather is due to an ‘incompleteness’—a withdrawing or withholding of the hoped-for tone-row.

Instead, I now think it plausible that Simbolo may have been intended to be played on a JI-tuned piano. Why? In part, I think this because then nothing ‘large’ is expected and frustrated in mm. 34-36; nothing so red-meatlike happens earlier in the piece as occurs in ET. Some of the gestural ‘questions’ and ‘problems’ that Lewin worries about are, in JI, not so puzzling or enigmatic. Instead, in JI we get the calm equanimity that Kyle Gann alludes to. It is a seductive conceit. It may be right or it may be wrong. But based on these little MIDI keyboard experiments it is now intriguing enough to make me want to look for evidence, talk to Annalibera.

And, while JI may be the best possibility, it is not necessarily the only alternative. For example, I think I will also try the temperament put forward by Giuseppe Zarlino, the Maetre de Chapelle of San Marco in Venice. In 1560 Zarlino proposed inverting the Major and Minor tones of the upper group in Aristoxenus’s classical scale. This gave him these intervals:

CDEFGABC 
0  20438649870288410881200 cents

He then reduced every fifth by 2/7ths of a comma to minimize the comma between the rest of the intervals. This was basically a Meantone (MT) temperament. The MT scheme redistributes the intervals such that the principal ones, such as fourths and fifths are uniformly near-perfect in most keys and other intervals are re-tuned so that they still fulfill their traditional intervallic role within the scale. The most common way of doing this involves flatting the first four fifths (C-G, G-D, D-A, and A-E), reducing them enough to give a true third.

This also eliminates the difference between the Major and Minor tones, producing a ‘Mean’ whole tone between the two, hence, the MT name. The major thirds and the minor sixths are then true, but most of the fifths are slightly flat. It enabled safe modulation from key to key but it left problematic intervals like the fifth G#-D# (viz, the Anonymous remark at the top of this post). The interval’s way too sharp, and its inversion (the perfect fourth) is severely flat.

This is known historically as a wolf tone, so called because the effect is like howling of wolves. There are other wolf tones, but this one is the worst. Apart from readability, the wolf tones are one reason why composers historically have tended to avoid using keys with a large number of sharps or flats.

Here is a spreadsheet you can download by clicking on the screenshot. The spreadsheet enables you to see the sensitivity of deviations from ET to scale position, for JI and for a variety of other historical temperaments, including Zarlino.


Spreadsheet with Temperaments and Intervals calculated

Interestingly, Mozart avoided C# (D-flat), F# (G-flat), G# (A-flat), and B Major. Correspondingly, he also avoided A# (D-flat) minor, D# (E-flat) minor, F minor, and G# (A-flat) minor, respectively. These keys display prominent wolf tones. Mozart also avoided F# (G-flat) minor and B minor. The latter is odd when you consider that one of his favorite keys was the relative D Major. And if you totalize across the various historical temperaments, both D Major and B minor are about as ‘wolfish’ as the more famously wolfish keys.

MajorMinor
C-sharp (D-flat)A-sharp (B-flat)
D-sharp (E-flat)C
F-sharp (G-flat)D-sharp (E-flat)
G-sharp (A-flat)F
A-sharp (B-flat)G
BG-sharp (A-flat)

Here is a spreadsheet you can download by clicking on the screenshot.


Spreadsheet tabulating Mozart keyboards works’ keys

I think I should take an inventory of Dallapiccola’s works, to see what patterns appear and to see whether any of it sheds light on the Quaderno, either corroborating or discorroborating the ideas about JI vs. ET. I’d be very grateful for comments from any of you Dallapiccola scholars out there ...