Music

Musical robot composes, performs and teaches

I'm looking forward to seeing new music gear at the Audio Engineering Society (AES) convention in San Francisco this afternoon. However, I doubt I will see anything quite as innovative as this musical robot:

ATLANTA, Georgia (CNN) — A professor of musical technology at Georgia Tech, Gil Weinberg, enlisted the support of graduate student Scott Driscoll to create Haile — the first truly robotic musician…
…Think of Haile (pronounced Hi-lee) as a robotic partner in the percussion form of dueling banjos. Although it has numerous musical algorithms programmed into it, Haile's basic function is to “listen” to what musicians are playing and play along with them…
…The robotic drummer is not only programmed with specific pieces but also with an understanding of countless pitches, rhythms and patterns, which are used during performances. Like a concert drum solo, Haile never quite plays the same thing twice, but plays off the creations of those performing around it.

We'll know we have truly created robotic musicians when they show up late to gigs and step into the alley between sets for a smoking break and other recreational intakes.

Actually, I did some research into computer programs that can “listen” to music and generate new material that is similar but not identical, way back in high school in 1990. Basically, it recorded MIDI input, created a decision tree of sorts, and generated new music from it. I had good time working on that project, and while my teachers and a few computer-music faculty I talked to at MIT and elsewhere seemed impressed, other “distinguished scientists” brought in to review our research projects largely pooh-pooh'ed this work as “not being science.” True, it was not a science experimental per se, but I've always been bothered by those in academic science that don't value innovative engineering. This happened in graduate school as well, where the computer science faculty wanted “science.” I wonder how they would have reacted to Weinberg's musical-robot project? I have always been more interested in making things than taking measurents and analyzing data, and thus have been mostly turned off from pursuing a career in scientific research.




The Logistic Function and its Discontents

This article explores the mathematical and more specifically the musical products of a very simple equation. In that exploration, we touch not only mathematics and music, but art, architecture, nature and philosophy; so those who are usually squeamish about mathematics are encouraged to read on.

Most readers who made it through high school algebra should be familiar with quadratic functions and the parabolas described by these functions on the x-y plane. For those who have forgotten, a parabola looks like this:

Parabolas are seen not only in high-school math classes, but often in nature as well. Among the most exquisite uses of parabolae can be found in the architecture of Antoni Gaudí. I had the priveledge of seeing many of his buildings and spaces in Barcelona, including this magnificent example of parabolic architecture:

But (as usual), I digress. For the remainder of this article, we will focus on a particular class of these functions, called logistic functions:

f(x) = ax(x-1)

Logistic functions have roots and 0 and 1, and describe a downward facing parabola (or “water-shedding parabola” in the parlance of my high-school pre-calculus teacher). The peak of this parabola depends on the value of a, and as we will soon see, this is the least of the interesting properties dependent on a.

Now, instead of simply graphing the function on an x-y plane, apply the output of the function back as the next input value in a process known as iteration:

xn+1 = axn(xn–1)

This is a fancy way of saying “do the function over and over again.” What is interesting is that for different values of a, one will get different results. For low values (where a is less than one), repeated iterations get closer and closer to zero. If a is between 1 and 3, the it will end up at some value between zero and one. Above 3, things get more interesting. The first range bounces around between two values, as characterized below:

As a increases, eventually the results start bouncing among four values, and then eight, then sixteen, and so on. These “doubling periods” get closer and closer together (those interested in this part of the story are encouraged to look up the Feigenbaum constant). Beyond about 3.57 or so, things get a little crazy, and rather than settling into a period behavior around a few points, we obsserve what is best described as “chaotic behavior,” where the succession of points on the logistic function varies unpredictably.

It is not random in the same way that we usually think of (like rolling dice or using the random-number generators on our computers), but has rather intricate patterns within – those interested in learning more are encouraged to look up “chaos.” This chatoic behavior can be musically interesting, and I have used the chaotic range of the logistic function in compositions, such as the following except from my 2000 piece Spin Cycle/Control Freak.

One can more vividly observe the behavior I describe above as a graph called a bifurcation diagram. As the values is a increase (a is labelled as “r” in this graphic I shamelessly but legally ripped off from wikipedia), one can oberve vertically the period doubling where the logistic map converges on a single value, then bounces between two points, then four, then eight, and so on, until the onset of chaos at approximatley 3.57.

There are tons of books and online articles on chaos, the logistic function, and its bifurcation diagram. Thus, it’s probably best that interested readers simply google those phrases rather than suffer through more of my own writing on the topics. However, I do have more to say on my musical interpretations of these concepts.

Given my experience in additive synthesis and frequency-domain processing (if I have lost you, then skip to the musical excerpt at the end, it’s pretty cool), I of course viewed this map as a series of frequency spectra that grow more or less complex based on a. I implemented this idea in Open Sound World. using the logstic function and its bifurcation diagram to drive OSW’s additive synthesizer functions. The results were quite interesting, and have been used in several of my live performances. I use my graphics tablet to sweep through different values of a on the horizontal axis as in the bifurcation diagram:


Photo by Tiffany Worthington

The resulting sound is the synthesis of frequences based on the verticle slice through the diagram.

Click here to listen to an example.

In the periods of chaos, the sound is extremely complex and rich. Below 3.57 and in the observable “calm periods,” the sound is simpler, containing on a few components forming somethin akin to an inharmonic chord. In true chaotic fashion, small movements along the horizontal axis result in dramatic differences in the spectrum and the timbre. The leads to a certain “glitchy” quality in the sound – one can practice control over time to make smooth transitions and find interesting “islands of stability” within the timbral space.

I have used this simple but evocative computer instrument in several performances, including my 2006 Skronkathon performance as well as my work last year with the Electron SAlon series. I have really only scratched the surface the possibilities with this concept, and hope to have more examples int the future.

A tale of two CDs

I haven’t really followed contemporary popular music for the last few years. But two 2006-releases that I picked up recently are worth mentioning.


width=”1″ height=”1″ border=”0″ alt=”” style=”border:none !important;
margin:0px !important;” />First up is With Love and Squalor by New-York-based We Are Scientists. You might guess that I originally picked this CD because if its cover. I was at Streetlight Records in Santa Cruz to buy a gift for a friend and check whether any copies of my CD had sold. I also browsed for bargain experimental electronic or “contemporary classical” CDs, but instead came out with this one. Not only does the cover have three cute kittens, they have the markings/colorings of the three cats I have had, with Luna represented by the all-black center kitten. Musically, the band does decent indie-rock of the sort one can hear in clubs in downtown and Brooklyn.


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/>Next, we have the rather popular St. Elsewhere from hip-hop duo Gnarls Barkley. As the sticker on the CD case explains, “Gnarls Barkley = Cee-Lo + Danger Mouse,” both of whom have names in contemporary hip-hop. However, the album is a lot more ecclectic, with many tracks whose sound is more reminscent of old funk, soul and R&B from the 1960s/1970s – there is even one that sounds like British New Wave from the early 1980s. I think the retro quality is what appeals to me, tracks that sound more like funk and disco than the contemporary hip-hop sound, which frankly doesn’t resonate with me. The first three tracks, including “Crazy” which has become a hit as a single, form am amazing unit to listen to in tandem, and the final track of the album segues back into the beginning with something that sounds like an old movie projector. Those tracks have become part of my portable-player set, which I think qualifies as an aesthetic endorsement.

Well, you’re on your own now to check out these albums if you feel so inclined.

Fun with Emulator X: Bohlen 833 cents scale and harmonics

I have been experimenting lately with alternate tunings and scales. A couple that have particularly piqued my interest are the Bohlen-Pierce scale and the much-less-used Bohlen 833 cents scale. The latter is intriguing in that it is based on properties of the fibonacci sequence and the golden ratio (although Bohlen admits he did not have those concepts in mind when he stumbled upon this scale).

Based on the golden ratio (1.618034…), one can construct a harmonic series as multiples of 833 cents that has a very distinct timbre. This can be easily implemented in Emulator X as a series of sinewave voices (or voices of any other harmonic single-wave sample) tuned multiples of 833 cents above the fundamental:

The series above consists of a fundamental, three golden-ratio harmonics, followed by the octave above the fundamental (traditional first harmonic 2:1 ratio), and the three-golden-ratio sub-harmonics of the octave.

Using these and other harmonics, Bohlen was able to construct the following seven-step scale between the tonic and the tone 833 above.

Step
Ratio (dec.)
Ratio (cents)

Diff. to previous step (cents)
0
1.0000
0
–
1
1.0590
99.27
99.27
2
1.1459
235.77
136.50
3
1.2361
366.91
131.14
4
1.3090
466.18
99.27
5
1.4120
597.32
131.14
6
1.5279
733.82
136.50
7
1.6180
833.09
99.27

Emulator X does not have editable tuning tables, although it does have a 36ET tuning (36 divisions of the octave). Bohlen suggests that playing specific steps out of the 36ET scale yields a good appoximation of the 833 scale:

Step (just)
Cents (just)
Step (36/octave)
Cents (36/octave)
0
0
0
0
1
99.27
3
100.00
2
235.77
7
233.33
3
366.91
11
366.67
4
466.18
14
466.67
5
597.32
18
600.00
6
733.82
22
733.33
7
833.09
25
833.33

Combining the Bohlen 833 scale and harmonic series, which are both based on the golden ratio yields a new tonality. Although it is quite different from the traditional Western tonality based on integer ratios, it is nonetheless “harmonic” with respect to its own overtone series. This is perhaps a simple counter-example to to the Monk's Musical Musings from an earlier article.

But how does it sound? To that end, I provide the following audio example consisting of the scale played on the 833-timbre in Emulator X, along with some additional intervals. Because this is only an approximation using 36ET, things aren't perfectly “harmonic,” but I think one can get a feel for the tonality. I particularly like the “tri-tone” (600 cents above fundamental) here.

The next steps are to come up with a more musical timbre based on the harmonic series, as well as short composition using the scale…

Listen to audio from headphone festival

I'm taking a short break out of cat blogging to post the audio from my recent performance at the headphone festival. You listen to it here.

This will be the first in my podcast series, though getting that set up is taking longer than planned, all these pesky details setting up the RSS feed, populating the content, collateral, etc. So for now, just enjoy the music on its own…






Thoughts on last night's performance

In this article I review my performance last night at the plug:dos headphone festival in San Francisco.

First, the venue itself. 5lowershop is in a warehouse near the junction of highways 280 and 101 in San Francisco. It’s at the edge of the Bernal Heights neighborhood.


The venue and its surroundings have that seedy edge-of-the-city feel that I probably wouldn’t want to live in but nonetheless often find intriguing and romantic. It’s just another part of the quintessentially “modern” world.

The interior matches the exterior, a jumble of areas within the warehouse, including the main performance area. The space is quite porous with the outside, and I noticed several cats wander though, including the grey fellow and a small black-and-white kitten. They were presumably feral cats attracted by the warmth, activity and possibility of food. Feral cats are an inevitable part of urban environments, but it’s still heartbreaking to see them this way. I was also concerned for them because of the dogs that were present, fortunately the dogs seemed to be pets and quite mellow.

The atmosphere of people crowded in a warehouse listening to headphones was quite unusual to say the least. Some of the performances were quite interesting, including a serinate for voice and hammer-dulcimer, and of course several acts mixing guitar, analog synthesizers and turntable. The analog synths didn’t strike me as a good fit for headphone performance, and thus avoided them myself (as described in my article on the preparation), but they did a good job of keeping the sound within a reasonable range.

Despite the best efforts of the organizers, whom I liked and thought did a good job overall, things tended to run rather late, and I ended up going on 9:40PM, two hours after my scheduled performance. But I think it went well musically, pretty much meeting my expectations for mixing ambient and rhythmic/punctuated material while keeping things mellow for the headphones. I did bounce around and repeat elements more than I expected, but such is the nature of improvisation, reacting as things unfold.

The equipment (Dell Laptop, Emulator X, E-MU 1616m, E-MU Xboard 25) performed flawlessly. I did make a direct recording on the laptop, and will be posting that shortly. I am also planning to make that the first release in my planned podcast series.

UPDATE: you can now listen to the audio from this performance. Enjoy!

Preparing for tomorrow's performance

My upcoming performance at the the plug.dos headphone festival provides some special challenges. Because the audience, both at the venue and online, will be using headphones, I need make sure my sounds and processes are headphone-safe, i.e., low volume with no clipping, glitching or large volume-spikes. More positively, I can take advantage of a uniform stereo listening environment with deliberate pan and positioning effects.

The need for steady volume and stability rules out the use of feedback and high-resonance filtering that I use in a lot of my recent music. Thus, the Evolver is out. Many of my Open Sound World patches are probably not approrpriate, though stable-volume patches are certainly doable.

I am focusing on Emulator X controlled with a MIDI keyboard (E-MU Xboard25). Thus, my preparations have focused on selecting existing sounds from the E-MU sound library that meet my technical and aesthetic requirements, and creating some new sounds. One preset that I spent a lot of time building is a modification of my additive synthesizer for Emulator X, consisting of eight independently controllable sinewaves. In addition to MIDI control of amplitude and frequency, I use a function generator to add amplitude modulations do the sinewave components of the timbre. Additionally, each “note” played has an independent pan position, spreading the sound across in the stereo field. I have also modified some existing sounds to include stable amplitude-modulation effects. The end result is a highly-controllable pallete of sounds from which I plan to make an ambient but punctuated sound scape, with a few rhythmic elements for good measure.

Logistically, this will be a very simple performance to travel and set up, just my laptop, the E-MU 1616m sound module, and the keyboard. I am looking forward to a relaxed, simple and enjoyable experience.

I'm not posting any advance examples, so you'll have to listen online to the show to hear what I'm describing. Hopefully I will be able to post a recording after the fact.








performance

Amar @ plug:dos headphone festival in SF, Saturday 9/9, 7:40PM

I will be performing live at 992 Paralta St. in San Francisco at 7:40PM on Saturday. Mostly experimental, “lowercase” (i.e., soft) electronic music. This is intriguing because it is a “headphone” event where people live at the venue as well as those listening online will be using headphones.

For those who are interested, you can also listen live online on Saturday. visit http://www.deletist.info/plugdose.html or
http://www.leplacard.org for more info.

Official press release below:

SAN FRANCISCO'S 2ND ANNUAL HEADPHONE FESTIVAL
AUG 5-6 2006
5LOWERSHOP COLLECTIVE WAREHOUSE
992 PERALTA AVE., SF
http://www.deletist.info

a festival within a festival, transmitting 48 live performances for 48 hours in participation with the worldwide interaural experiment known as LE PLACARD #9 – a self-organized nonstop streaming festival that migrates from city to city broadcasting headphone conterts to headphone people around the world from june-october 2006.
http://leplacard.org

admission is free
B.Y.O. HEADPHONES

[:] p l u g [:] 2005
last year, a constant flow of over 300 people plugged their headphones in at the 5lowershop warehouse on peralta ave to hear 48 headphone-only performances from the likes of beth custer, swoondoll, bunnyphonic, jeff ray, justino, neighborhood bass coalition, skullcaster, nullspace, sky sosa, toshio hirano, 666 gangsta, dj crackhouse, heartworm, members of subarachnoid space, ryan of slidecamp, mono, halcyon high, things falling apart, aaron x of the quiet american, viola-cello improv victor lowrie, sodium channel, useless unknown facts, tina butcher, the deletist, and many more..
a simultaneous pirate radio broadcast was heard at 104.1 fm, and untold numbers of listeners were plugged in at various listening rooms in LE PLACARD's global network. a live irc chat also allowed listeners to communicate during the event.
Wired magazine praised the festival, and LE PLACARD organizers in paris
dubbed [:] p l u g [:] “the best transmission of the year”

p l u g [:] dos 2006
this year, we return with 2 days of sound experimentation, continuing the diverse mix of acoustic, experimental, electronic, and non-genresfrom underground artists all across california. again, we will transmit a simulltaneous pirate radio broadcast at 104.1 fm, include the live chat for listeners, stream live audio through LE PLACARD's global network, and
due to popular demand, a live video stream will be added to this year's festival.

everyone is invited to listen, participate and experience this unforgettable event.

there will be food, drinks, merchandise, and more!




Professors, Monks, Imbalance, Pattern, Harmony and Noise

A fun, far-reaching flight of fancy for this evening's post.

I opted to enjoy a quiet day off in my yard rather than fight the inevitably nasty Santa-Cruz-area traffic. It's actually been quite productive, a lot of cleaning in the garden as well as some much needed maintenance work on the outdoor sculptures. In particular, rust management on the metalworks, and cleaning off the accumulated grime from my own fountain sculpture entitled Imbalance. I don't use a lot of chemical treatments in the water because a lot of local critters wander through and drink from the surface, notably neighborhood cats and the hummingbird that is flittering about the fountain as I write this – or rather, was around the fountain until I pulled out the camera. Anyhow, here is a post-cleaning photo (I do need to figure out something to hide that electrical cord):

In keeping with the work's title, the various columns have shifted and tilted in relation to the ground below and the weight of the stone elements.

After a mid-afternoon's hard work, I settled down to relax, enjoy a refreshing beverage and read for a bit. I am currently reading Metamagical Themas: Questing for the Essence of Mind and Pattern by Douglas Hofstadter, who is best known for his earlier book Gödel, Escher, Bach. It's actually not as heavy as the name implies. It's a series of pieces Hofstadter did for Scientific American in the early 80s, covering a wide variety of issues including patterns, creativity, language, etc. The two articles a read this afternoon dealt with the pattern and aesthetics of the music of Chopin, and transformations on simple “parquet floor” patterns as a form of visual music, respectively. While the latter was more interesting to me personally, it is the former that I wish to write about. While I admire the musicality and technical skill of Chopin as both a composer and pianist, I can't say that I've ever been a “fan.” Indeed, his music is about 180 degrees from my own aesthetically. However, I was struck in particular by one passage Hofstadter wrote:

That there are semantic patterns in music is as undeniable as that there are courses in the theory of harmony. Yet harmony theory has no more succeeded in explaining such patterns than any set of rules has yet succeeded in capturing the essence of artistic crfeativity. To be sure, there are words to decribe well-formed patterns and progressions, but no theory yet invented has even come close to creating a semantic sieve so fine as to let all bad compositions fall through and to retain all good ones. Theories of musical quality are still descriptive and not generative; to some extent, they can explain in hindsight why a piece seems goodm, but they are not sufficient to allow someone to create new peices of quality and interest.

I was reminded of an article that I read last week entitled A Monk's Musical Musings: Musical Philosophy. The author, Huchbald, attempts to argue (with all the style and sophistication usually found in right-wing political bloggers) that everything right and good in music derives from the “god-given” harmonic series, and anything that eschews baroque-era diatonic voice leading rules is somehow not music at all. In the process, he dismisses atonal music (and probably a lot of other music) as “noise.”

There are numerous ways to refute his claims (other than simply celebrating noise as music), perhaps the simplest being the rather casual way he dismisses everything other than his voice-leading rules as “simply rules based on taste which can be left to the discresson [sic] of the composer.” Well, as Hofstadter eloquently points out, this discretion and not the rules is precisely what makes for the best music. It was what separates a genius like J.S. Bach (admired by both authors discussed here) from a typical student in a first-year class on music theory. The sieve is simply too coarse, and “accepts” both the good and bad equally. One need only consider what Bach was able to do contrapuntally with the chromatic theme of A Musical Offering to see how much more there is to even baroque music than basic harmony. There is something in Bach's music that can be described and informed by harmonic theory, but it doesn't tell nearly the whole story, nor explain how he can work with both harmonicity and chromaticism with such ease.

But back to the god-given harmonic series. Simply put, the harmonic series as a set of frequencies that are all integer multiples of the lowest, or fundamental frequency. That is, for fundamental f, the harmonic series is (1)f, 2f, 3f, 4f and so on. Starting on a really low C, i.e., the bottom C of a piano, one can approximate the corresponding harmonic series as follows:

Note the use of “approximate”, we'll get back to that in a moment. The harmonic series does indeed play an important role in acoustics, the timbre of musical instruments and are perception of musical harmonies. For those who would like play with the harmonic series, a good example can be found in the “additive_synthesis” tutorial of Open Sound World – in OSW, simply go to Help:Browse Tutorials, select the “audio” subfolder and open “additive_synthesis.osw”. You can increase or decrease the contribution of different harmonics and hear the effect on the timbre of a sound. The low harmonics (2,3,4, etc.) do indeed contribute to a constant timbre, though some of the higher harmonics start to get a little “squirrelly.” As one gets into harmonics that are not simple powers of two or multiples of three and a power of two (e.g., 6, 12, etc.), the harmonics appear to play less of a role, even when they can be approximated by notes in the western diatonic scale. Moreover, these are approximates that differ from the standard note degrees in western music, the divergence is illustrated in in this chart and elsewhere. One can preserve harmonic relationships using so-called “just intonation”, which is easily to do on electronic instruments, but would require our friend to retune his guitar whenever he changed keys.

Even if one accepts the harmonic series as central to making music, there are numerous ways to use it besides diatonic voice leading. Consider the first few harmonics, which form octaves and perfect fifths. Octaves and perfect fifths are the most consonant intervals – any popular or contemporary musician will immediately recognize them as “power chords.” Prior to the baroque era, such power chords were used quite often in western music, both serious and popular, as the consonances and cadences. In serious music, there were also the Greek modes, which initially did not include the Ionic mode corresponding to our modern notion of a major scale. Indeed, one of the more common modes was the Dorian mode, which can be found on the piano by playing the white keys starting on D. It is a minor mode that can be found in some of my favorite pre-baroque music such as Josquin Des Prez's Missa Mater Patris, and is the foundation for the blues scale that informs American jazz and popular music. Despite violating most of the rules Huchbald puts forth as inherent in music, minor modes sound quite “natural” and moving to most people.

And what of music beyond the harmonic series? Many (most?) acoustic instrument timbres have overtones outside the harmonic series, and indeed some instruments (e.g., bells) can be very inharmonic. Such inharmonicity can lend itself to different ideal tunings and scales than western just intonation, and indeed we see different tunings in other musical traditiions, such as Middle Eastern, South Asian and Southeast Asian (i.e., gamelan) music. Even where we don't hear the western diatonic scale and direct allusions to the harmonic series, we can nonetheless recognize the music as music, and appreciate it in many levels, from simple enjoyment to deep spiritual understanding.

As modern composers and musicians, we often work to subvert these traditions, and indeed I found myself experimental with alternate tunings, such as 19-tone and Bohlen 833 (Golden Ratio). They have tonicities that can be quite different from what we are used to, but a good composer should be able to immerse himself or herself in them and use knowledge from other musical experiences to produce something interesting.

Well, that's enough on the Monk's philosophy and my opinions to the contrary. In subsequent articles, I would like to touch more upon alternative tunings as well as some more of Hofstadter's writings, which certainly deserve more time.