Supercolliding Space Music

| Music |

I have a sound programming application called Supercollider which, though it has a steep learning curve, is a brilliant coding application for programmatic and generative music and sound. This recording is my first #sc140 tweet: Creating something interesting in Supercollider in fewer than 140 characters. Here is my code:

{var a = LFNoise0.kr(12).exprange(110,880);Resonz.ar(LPF.ar(CombN.ar(SinOsc.ar([a,a],0,0.2),2,0.2,10),48,16),880,0.5,8)}.play;

To me, it resembles space music of the 1950s. Ambient space music like the kind of thing playing in the background as spacemonauts explored alien worlds.



Red-1

Red: A Song About Thursday

| Music

Tonight I downloaded MuseScore notation software. This is the first thing I wrote. Attempting to use phrygian mode, because I like it. (The image attached is not the complete score.)



Stockhausen’s Studie II

| Music

Stanley Kubrick’s decision to scrap the musical score originally written for 2001: A Space Odyssey and go with something different is what introduced me to the fantastic, creepy, and wonderful music of Gyorgy Ligeti. When I first signed on to Pandora internet radio, one of my first stations was seeded by Ligeti as an artist. Doing this introduced me to pioneers of early electronic music like Tod Dockstader, Morton Subotnick, John Cage, David Tudor. However, one name which was surprisingly overlooked was Karlheinz Stockhausen. It was only after I created my @mondayazura Twitter account and started connecting with other musicians that I was introduced to his works. Looking back, I now wonder how I managed to go so long without having discovered Stockhausen.

Stockhausen was the first person to publish a score for electronic music. I took it upon myself to recreate that score using the technology I have available to me, namely my computer and audio editing software. I wanted to understand the process Stockhausen used to create a seemingly simple and short piece of electronic music. The piece is only three minutes long, but it took me just over thirty days to realize those three minutes of sound. Here’s how I went about doing it.

Stockhausen created Studie II in 1954 using just a single electronic oscillator, a bit of reverb, and reel-to-reel tape. With only one oscillator, his method for creating chords was quite clever. He recorded a short length of each pure tone, then he cut these recordings into 4 cm strips and taped them end-to-end into a loop of five ascending tones. Then he played the loop through a ten-second reverb to produce each of the 193 chords. I wanted to try and reproduce the technique and sound to the best of my ability using digital technology, so my process for creating each chord was quite similar to Stockhausen’s despite the use of a computer.

Frequency
So pretty!

I began in Berna 1.0 by recording 1 s clips of each tone, 81 total from 100 Hz all the way up to 17200 Hz. Each tone is separated from the other by a ratio of a twenty-fifth root of five 5^(1/25), and rounded to the nearest whole number. Stockhausen was limited by the technology of his time, but Berna allows for more precision in tone generation. Nevertheless, I rounded my numbers to the nearest whole in order to stay true to Stockhausen’s technique. My numbers turned out to be different from his because of my rounding methods. I used the intervals listed on the score (100, 138, 190, 263, 362, 500, 690, 952, 1310, 1810, 2500, 3430, 4760, 6570, 9000, 12500, 17200) and calculated the in-between frequencies using the ratio above.

100 Hz
x 5^(1/25) =~ 106.649 Hz
x (5^(1/25)^2) =~ 113.741 Hz
x (5^(1/25)^3) =~ 121.304 Hz
x (5^(1/25)^4) =~ 129.370 Hz
x (5^(1/25)^5) =~ 137.973 Hz

Repeat this process for each interval listed in the parentheses above. The fifth tone in each sequence should be close to the next one listed in the parentheses, in this case, 138 Hz.

With all the tones generated, the next step was to cut them all into 4 cm lengths. Reel-to-reel tape speed is 30 inches per second or 76.2 cm/s, making 4 cm about 5 milliseconds. One file at a time, I cropped each 1000 ms clip to 5 ms using Adobe Audition. Then I lined up each tone sequentially in groups of five the same way Stockhausen did to create his initial loops. Each chord is created by tone intervals of 1, 2, 3, 4, or 5 apart, and grouped together by their base frequency. Hopefully the chart below clarifies what I mean by that.

Studie-II-Chord-Chart
Actually, these aren’t grouped by base frequency. But it’s cool to see the pattern.

I had a bit of trouble with pops appearing in between each 5 ms tone. When I tried running the poppy sequence through the reverb, I wound up with a lot of white noise overwhelming the chord. So I had to figure out how to get rid of the pops. Eventually I settled on applying a linear envelope to each tone, fading in, then fading out, to eliminate the pops in the sequence. Running the cleaned up sequence through the reverb then produced the clean chord I was looking for.

Berna Settings
Plate reverb: 10000 ms.

The reverb I used was in Berna 1.0. Playing each sequence I’d created in a loop through a ten-second reverb in Berna, just as Stockhausen did with the tape loop, generated the chord I needed for the final realization of the piece. Since the longest note in the Studie II score is almost 5.5 seconds, I recorded each chord at 6 seconds. I could then shorten as needed using Adobe Audition.

While Stockhausen had to manually adjust the audio gain to produce the envelopes for each note, and play the tape in reverse to get increasing volume, I was able to use the faders and gain control for each clip to generate the necessary envelopes for each note in the score. This no doubt has an effect on the way my recording sounds compared to Stockhausen’s method. Considering how much time I put into this piece doing it digitally, I can only imagine how much longer it must have taken Stockhausen to create this piece. After a month of recording, fiddling, manipulating, editing, and tweaking, I finally had the finished three-minute piece completed. Including the extra day I took to write this blog post, I worked on this recording over 33 days, from 29 November 2013 to 2 January 2014. The original piece was written and performed in 1954, and my version comes nearly 60 full years later. Cool!

My previous seven audio pieces on my Soundcloud page were all generated live. None of them has a score to follow, though I did try to document the settings I used to create each piece. This is the first piece of music I made that was from a score. What I hope to do in the future with my sounds is to write scores for them in much the same way Stockhausen did with his Studie II so that others can perform my works if they choose, and not merely listen to them. What this creation and performance of Stockhausen’s score has taught me is that electronic music generated from oscillators and tape is just as complex and time consuming as scoring music on traditional staves for traditional instruments. I have a long way to go before I’m writing music of my own, but I’m one step closer to doing so.



Turanga-Leela

Futurama, French Composers, and Frequencies

| Music

The alluring cyclops pictured is Turanga Leela from Futurama. Leela’s name bears striking similarity to a musical work by French composer Olivier Messiaen called the Turangalîla-Symphonie, which features an rather unusual electronic instrument capable of producing sounds similar to the Theremin.

The same year Léon Theremin patented in America the electronic instrument bearing his name, the Ondes Martenot featured in the Turangalîla-Symphonie was invented in France by cellist Maurice Martenot. It is essentially an electronically enhanced piano capable of producing a variety of electronic tones either through the keys, or with a ring attached to a device which controls pitch, timbre, and glissando.

I absolutely love the frenetic intensity of the Turangalîla-Symphonie. It reminds me a lot of the dynamism of Igor Stravinsky’s The Rite of Spring. Then again, I’m partial to discordant tonalities in music.

It’s interesting that while the Theremin and the Ondes Martenot are both capable of producing similar sounds, the latter seems to have been taken more seriously as a proper symphonic instrument, while the former was relegated to campy b-movies of the 1950s and 1960s. Perhaps that’s simply because the Ondes Martenot has a more familiar interface with its piano keyboard. The Theremin is a difficult instrument, but when it’s played by an accomplished player, it too sounds simply amazing.

The video above is excelsior Theremin player Pamelia Kurstin speaking and performing at TED. She explains how a Theremin works and demonstrates to an awed audience just what it’s capable of doing beyond eerie science fiction sound effects.

I’m really glad the folks behind Futurama are such fantastic geeks. Without them, I probably would have never heard of Olivier Messiaen. And while I’m thanking folks for introducing me to French composers, a big shout-out to the band The Art of Noise for not only introducing me to the music of Claude Debussy, but also to Italian futurist Luigi Russolo.

Futurama TM and © Twentieth Century Fox


Space Music

| Music

The Juno spacecraft zipped by Earth recently on its way to Jupiter, and the people of Earth broadcast a collective “hi” at the passing probe in Morse code (**** **). NASA JPL processed the data from hundreds of ham radio operators broadcasting “hi” nearly simultaneously, to reveal the sound in the video above. The extra wooshing noise is the sound of our planet’s magnetosphere. Sounds like space!

One particular tool astronomers use to “look” up at the heavens is the radio telescope. As space itself expands, the energy waves traveling through it get stretched out into lower and lower frequencies, far lower than red or even infrared. The best way to observe these waves is with radio telescopes. These telescopes, such as the Arecibo Observatory in Puerto Rico or the Atacama Large Millimeter Array in Chile, are essentially giant “ears” pointed at the sky in order to “hear” what’s going on out in space.

In 1960, Bell Labs built a big antenna as a receiver for early satellite transmissions. Two employees, Arno Penzias and Robert Wilson, wanted to use the antenna to collect radio astronomy data from nearby galaxies. When they did so, they discovered a consistent and at the time inexplicable static coming from everywhere in the sky. No matter what direction the antenna was pointing, the same uniform static was found. It turned out to be the ancient birth pangs of the universe itself, the cosmic background radiation. NASA would launch satellites in later years, the Cosmic Background Explorer (COBE) in 1989 and the Wilkinson Microwave Anisotropy Probe (WMAP) in 2001, to collect data on the cosmic background radiation in order to better understand the origins of our universe. Some of this data has been sonified (made into sound), and the results are fascinating.

Turning data received from radio telescopes into sound is one way astronomers can better conceptualize the data. Listening to these sonifications of cosmic background radiation, it’s easy to hear how the energy from the early universe got stretched out as space itself expanded. In 1991, astronomer Dr. Fiorella Terenzi released an album of such space music titled Music from the Galaxies. This album is generated from real astronomical data, but it sounds like something out of a science fiction movie from the 1950s.

Speaking of science fiction movies from the 1950s… In 1956, the film Forbidden Planet was released. It was the first feature film to have its musical soundtrack generated entirely electronically. The pioneers behind this score, Louis and Bebe Barron, were electronic music enthusiasts who used oscilloscopes, patches, filters, reel-to-reel tape recorders, and other equipment to create a symphonic cacophony of electronic noise. The Barrons were credited on the film as the makers of “electronic tonalities” as opposed to a musical orchestration. While their sounds were remarkable, they were deemed too unusual to be considered “proper music”.

Léon Theremin was an inventor, a musician, a professor, and even a spy for the KGB. The instrument which bears his name, the Theremin, is a device which produces electrically generated tones. However, the Theremin is quite capable of more than just the eerie space sounds associated with science fiction, as the clip below of Theremin himself performing music with his invention will demonstrate.

Fiorella Terenzi, Louis and Bebe Barron, Léon Theremin, and more are all musicians who have made unusual music with unusual instruments. But the human fascination with unusual sounds isn’t merely an electronic phenomenon. Other unusual instruments include the musical saw, Luigi Russolo’s Intonarumori, or Benjamin Franklin’s Glass Armonica. It would be fascinating to hear a “space music” performance made with such non-electronic instruments.

The Space Age doesn’t have a monopoly on unusual sounds, though it has helped to establish the musical genre of “space music”. The noises of the world, and the cosmos, fascinate me and I’m happy that I’m finally creating “space music” of my own.



Pranayama

| Music

Pranayama is the practice of breath control in yoga. The pulsing white noise is reminiscent of breathing, and the slow crescendo of the tones is akin to the OM of the universe, or the vibration of a singing bowl. Made with Berna 1.0.





Phrygian Sea

| Music

I’m currently obsessed with phrygian mode, so I thought I’d try writing something that uses only the eight natural notes between (and including) E3 and E4. The texture of the repeating eighth notes pulsing throughout the piece was inspired by the works of Terry Riley and Steve Reich.



Klavierstuck IX

| Music

Six weeks ago I discovered the work of Karlheinz Stockhausen. In that six-week time, I have done very little subsequent investigation into the musical works of this composer because, life being what it is, I have been otherwise occupied. Today I was reading up on odd time signatures, and Stockhausen’s name came up with this particular piece of music. From what little I understand of it, it’s constructed using varying patterns of the Fibonacci sequence. (Watch the ‘Donald in Mathmagic Land for a bit about the Fibonacci sequence.)

Like the phased patterns Steve Reich uses in his compositions to create complex varying textures of sound, Stockhausen uses the Fibonacci sequence and varied time signatures throughout the piece to create a piece of music that is truly amazing to listen to. I realize that I have a long way to go before I’m composing piano pieces like Reich or Stockhausen (refer to my SoundCloud composition in the previous post), but with influences like these, I hope I will soon be composing much more complex experiments before too long.



Short Piano Composition

| Music

My first attempt to write a piece of music for piano. Written in Garageband using the on-screen piano and the notation editor.



It’s Just Equal Temperament

| Music

Over the last couple evenings, I have gotten a crash course on music theory. In my previous post I wrote about Donald Duck in Mathmagic Land, and how he was introduced to Pythagoras the math egghead who played music. This got me looking more into Pythagoras and how he developed his musical scale. At first I couldn’t figure out how he used the ratio 3:2 to get all the notes of the scale, and it kept me up for several hours scribbling math notes on sheets of paper (which turned out to be thoroughly engaging and mentally stimulating). Well after a few nights of further investigation, I’ve sussed out a couple of things which I’ll go over now.

I studied Greco-Roman history when I was at university, and I know that the ancient Greeks were very much into mathematical harmony with such things as the five perfect solids and the music of the spheres. Pythagoras was aware of the 2:1 ratio for octaves, and he used a 3:2 ratio to determine perfect fifths. I tried to reverse-engineer the numbers but couldn’t figure out how to do it. As it turned out, I couldn’t do it because “perfect” fifths aren’t perfect. The 3:2 ratio of fifths doesn’t fit within the 2:1 ratio of octaves.

So what exactly is a ‘fifth’ anyway? In some circles, it’s a measurement of alcohol. But that’s not the kind of fifth I’m talking about here. Once I plotted out the notes on a staff, I quickly realized that fifths are what I learned in my junior high and high school band classes as the order of flats and sharps: B E A D G C F. Suddenly everything became clear to me. Now that I grasped what the 3:2 ratio was generating, I could use a bit of math to determine the frequencies of the notes using Pythagorean tuning. What I discovered is exactly why 3:2 doesn’t go into 2:1.

In a similar regard that the cycle of the moon phases doesn’t sync up with the cycle of the solar year, the cycle of fifths doesn’t sync up with the cycle of octaves. Using the order of flats and sharps, I can show you what is meant by that.

Ab – Eb – Bb – F – C – G – D – A – E – B – F# – C# – G#

All these notes are adjacent to one another by fifths, so you’d expect the Ab at one end to be related by octaves to the G# at the other end. I mean when you play those notes on a piano, they’re the same key, right? Well as it turns out, because the ratios don’t sync up, that Ab is about half a semitone off from the G#. That means they are not the same note. In music theory, this is called the wolf interval because the dissonance from the different frequencies apparently sounds like a howling wolf. While chords played using this type of tuning sound sweeter to the ear because the frequencies have common factors and the waveforms don’t pulse, dissonance between upper and lower octaves increases the further away from the center note (in the case of the above chart, that would be D) the instrument goes. This is what is called “just temperament” or “just intonation”.

Now in the late 16th century, a prince in China named Zhu Zaiyu used math to figure out how to create “equal temperament”, which is equal distance between each semitone so that an instrument can play in any key without experiencing the wolf interval. About the same time in Europe (perhaps a little later), Galileo Galilei’s father Vincenzo was studying the very same thing. Mathematically, equal temperament is defined as the twelfth root of two (equal mathematical distance between twelve semitones) which works out to approximately 1.059463. (It actually goes on and on and on because it’s an irrational number.) The down side to equal temperament is that the frequencies of each note no longer have common factors, so chords will have some audible pulsing which can sour the music (particularly if you’re an audiophile).

Equal temperament is a compromise so that multiple instruments can play in multiple keys without experiencing any dissonance caused by the wolf interval. But typically small ensembles will tune to themselves using just intonation so that the integrity of the musical tones is preserved.



The Mathematics of Music

| Music

I never studied music theory when I was younger, though I did have tiny nibbles of it in my band classes at junior high and high school. The musical scale I learned beginning in grade five playing the recorder, notes A through G, were just black dots on sets of five lines: simple notation for a series of tones. Just to demonstrate how un-curious I was as a kid about the history of music, I never stopped to consider why we used this configuration of tones in music as opposed to other ones that might exist. Okay, I can understand octaves and how plucking a string divided at its midpoint produces the same tone one octave higher, but I never thought about how those middle notes came about.

When I was a child, one of my favorite Disney cartoons was “Donald in Mathmagic Land”. In it, Donald Duck is guided by the Spirit of Adventure through the fantastic realm of mathematics, and one of the first things Donald learns about is the mathematics of music. To show that math isn’t just for eggheads, the Spirit of Adventure explains how the ancient Greeks used math to create the musical scale we’re now most familiar with here in the West. Pythagoras and his fellow math and music geeks, the Pythagoreans, gathered together for a jam session, which Donald subsequently crashes with his best Richard Feynman impression.

In the video, octaves are shown with the ratio 2:1, and the arpeggio lengths between the end notes are shown as 8/5 and 4/3. Not having the slightest clue about music theory, I found myself asking the question “Why those fractions?” I spent about an hour trying to reverse-engineer the ratios of the arpeggios until I gave up and looked online. Turns out the ratio is 3:2, which makes sense given the ancient Greeks’ preference for rational numbers and mathematical harmony in nature. But when I did some further math, I couldn’t figure out how the ratio 3:2 resulted in the fractional string lengths of 8/5 and 4/3. But then I haven’t really used my brain for this kind of heavy fraction processing since 2007 when I took a term of calculus at uni. So another venture into the interwebs to investigate “perfect fifths” and the Pythagorean system of music revealed an absurd level of information which I kinda sorta knew was there but was ill-prepared for nonetheless. I am drinking from the fire hose.

While I don’t yet have a solid grip on how the musical scale developed, I do have an educated guess as to why there are so many different musical scales from around the world. Different cultures would no doubt have different approaches to sound and mathematics, and their musical scales would derive different ratios and different tones and semitones within the 2:1 octave. I’m not going to get into the vast diversity in world musical scales in this blog post as there is simply far too much to cover. But now that I know the method the ancient Greeks used to develop the musical scale used in much of Western music, I can start dissecting it and begin my studies of music theory.

Which is apparently all math.