Sorry It’s been so long since i’ve been regularly posting! I’ve been tied up with a lot of crazy stuff. But I’m going to get back on the ball again, so, yes, I’m alive, and I’m here!
I’m going to start a new series here, where I post tracks and images together–music inspired by photos I’ve taken. Here is the first. This is a street about 2 blocks from where I live, that goes over the top of I-5.
the hill on 8th ave
and here is the track. ”Up 8th.”
It’s a beautiful sunday here in seattle, and moving is on my mind. My wife and I will be moving to new digs in the downtown Seattle area in the coming weeks, into our first real “home.” We’re buying a place! I don’t normally post about personal matters here, but it’s exciting, and, also, I’ll be getting my own studio space instead of having our living room be my studio.
won't be looking out this window much longer
Anyhow, with that in mind, I made a nice little lazy Sunday jam. A simple textural rhythmic drone kind of thing. Hope you enjoy!
Here is a new track I made, featuring more use of my harmonic ratio arpeggiator. I was also using my Pitch Bend Tuner to tune my hardware synths to the microtonal pitches the arpeggiator was generating. An interesting aspect of making tracks with the ratio arpeggiator is that there are no longer any “notes” in the traditional sense. They are notes just the same, but I’ve gotten to the point where I stop thinking about normal note names, and have started to get a sense of how different numbers will sound. For instance, higher numbers are generally more dissonant, and numbers with common divisors (or factors, or whatever you call it–i’m not a mathematician) generally sound good together. An interesting new world!
A diagram from Harry Partch's book, "Genesis of a Music" showing different ratios' correspondence to notes in an equal temperament scale
Here is the track:
I quite like how this track turned out–I will probably be including a longer, more structured version of this in an upcoming release.
Let me know if you like it, and enjoy!
On some previous blogs i’ve written on, I had a series of articles that I called “The God Chord” where I talked about tuning, the overtone series, and all the magical connections between numbers, math, frequencies, geometry and music. I think that the simplicity and beauty of the numbers behind music have been obscured behind arcane music theory systems that confuse the intuitiveness of the origin of the fundamental materials of sound and music.
I’ve talked to a lot of people and musicians who are intimidated by music theory. I think there is a reason for this–western music theory doesn’t make any sense! I consider all the words and ideas in old-school music theory to be the product of a centuries long cultural evolution that never gave a second thought to being clear or logical.
Sine waves (odd number harmonics) combing to create a square-wave shaped waveform.
Anyway, enough ranting. Let’s get down to the numbers. After familiarizing yourself with how musical frequencies are related, thinking about music from a mathematical standpoint is a lot more intuitive and direct. There are two basic materials that everything in music is based on: octaves, and the overtone series.
Musical notes are described numerically as frequencies, or in “cycles per second,” denoted by the term “hertz” or “hz.” The wonderful thing about frequencies is that they are also used to describe the electromagnetic spectrum, including visible light, radio, micro, gamma, and x-rays, or, if you want, the rotation and orbits of planets, anything that repeats periodically. The incredible thing about all of this, is that musical frequencies can be related to all kinds of phenomena–the light emitted by the sun, the resonances in minerals and atoms, with simple ratios. This begins to explain why I’ve titled this series “the god chord.” Because, I think, if God really exists somewhere, I think God is a frequency. Or a melody. Or, most likely, a CHORD.
If you need to catch up on your frequency theory, check WIKIPEDIA!
So, as I mentioned before, I wanted to describe octaves, and overtones. Let’s start with frequencies, and octaves.
Musical frequencies are Logarithmic. For instance, if we are in the key of A (440 hertz), the next octave up would be at 880 hz, and below, 220 hz, and so on. All of these frequencies, that are powers of 2 of the original frequency, are considered the same note, but just at different locations. This phenomenon is highly useful and fundamental to nearly all music in all cultures. If you were to describe this in ratios, with 440 hz being 1/1, then 880hz would be 2/1, 1760hz (the next octave up) would be 4/1, and so on. 220 hz would be 1/2, 110hz would be 1/4, etc. incidentally, 2/1 and 4/1 are both Overtones. Any frequency you can imagine has duplicates of itself in octaves going toward infinity both above and below, beyond the range of human hearing, and the scale of human perception.
OK. Now, let’s talk about the overtone series. The overtone series is also described by mathematicians as the Harmonic Series. Like the octaves I was just describing, the overtone series is infinite, only limited by the range of human hearing and the physical properties of whatever object is projecting the frequencies. When analyzing a musical tone, you can clearly see the overtone series in its frequency components:
Harmonic partials in a piano tone.
Let’s start with a frequency of 440 hertz.
The overtone series is simply the original frequency, multiplied by every integer, starting with the number one. so,
440*1 = 440
440*2 = 880
440*3 = 1320
440*4 = 1760
440*5 = 2200
and so on, until infinity.
In musical notation, the overtone series looks approximately like this, though most notes in the overtone series can’t be accurately represented in this kind of notation:
approximate representation of the overtone series on a musical staff
This very simple mathematical series is the root of all musical scales and harmonies.
It sounds like this:
It might sound vaguely familiar to you. If you’ve ever played the harmonics up and down a guitar string, those are the same frequencies. Periodic (repeating) musical tones are all built from these frequencies. In fact, here is a simple recording of me playing the harmonics up a guitar string, until the 8th harmonic in the harmonic series.
You can count along with the notes, and each number will be the corresponding harmonic: Just count:
The first harmonic is the “fundamental” and that is just the sound of me playing an open string. If you listen close, you can hear certain intervals. For instance, the 3rd harmonic is a perfect fifth, the 5th harmonic is a major third (doesnt’ make sense, right?). I personally love the sound of the seventh harmonic, which is a lot like a “minor seventh,” but is actually about 30% of a semitone flat from the interval you would play on a piano.
As opposed to an octave, this series is an Arithmetic Progression, not a logarithmic one. the octaves of the fundamental frequency, are the fundamental multiplied by 2, 4, 8, 16, 32, 64…. So, you can see that, between each octave further up the overtone series, the overtones become more closely spaced. At some point, the frequencies become so close together that it is difficult to for the human ear to distinguish them.
Allright. I hope you’re still with me! After these fundamentals, comes the interesting stuff. Now, we can combine the concept of the octave and harmonics to make all kinds of scales and harmonies. The trick is to take the frequencies in the overtone series and move them downwards (or upwards) with octave displacement to make the tones fit into a normal musical scale. For instance:
As described above, the fifth overtone of A 440 is 2200 hz. 2200 divided by 4 (this moves the note down two octaves) is 550 hertz. That is the exact frequency of a harmonically pure major third (the note C# in the key of A). On a well-tuned piano, the note would be about 554 hertz. A small but noticeable difference. And when you put more of these notes together in harmonies, you can really hear the beauty of the tones interlocking with their pure mathematical relationships!
Here is a demo I made just to show some very simple, overtone-based harmonies. Hopefully you can hear the quality of the overtone series, that I showed in the previous audio examples here, but applied in a looser context. Just a very simple improvisation, but I can’t get enough of those pure harmonies.
Hope you made it all the way through, and I hope I grabbed your interest! Check back, I will be writing more about this subject, with more illustrations and audio examples.
I had some time last week or two to sit down and work out some tracks, and thought I’d share them up here. I make a lot of tracks, of differing lengths, levels of detail, and spend more or less time on different ones. Many tracks are the kind that I put together in an evening after work or during a free afternoon on a weekend. I’ve been working on an album, but lately, have been busy buying a condo in downtown seattle! Anyhow, i’ve been feeling creative lately and here are a few tracks that I think turned out well.
Rat's nest behind the lab
As always, these tracks are free to share and listen for noncommercial purposes, but please let me know if you’re using them. Enjoy!
Kenny G In the Panama (dont’ ask)
Atonality Verge - This is a track that I made with the Harmonic Ratio arpeggiator that you can find here on this blog.
Moses - an experiment with making evolving melodies in Numerology
Let me know what you think :).
The most recent release of five12 Numerology included full support for the Novation Launchpad. It’s amazing! Here is a demo of myself using it to sequence a track. This track is a little bit long, but I am sequencing all the patterns and mixing everything live, so it takes a while, and I mess around with some of the different features of the launchpad support just to show some things.
There are a lot of different features hidden away in the launchpad support, and I didn’t get to all of them. But I hit on the main ones. You can completely sequence and arrange a track all from the launchpad without even touching numerology, after setting up your numerology patch!
For this track, I was using Reaktor for some sampling and effects, and my waldorf microwave and roland mks-70 for synthesis. Everything was sequenced and mixed in real time, no edits or overdubs.
Well, for all you poor bastards who don’t own a G2 modular, and can’t use the VOSIM patch I made for mine, I have put together a VOSIM patch in Reaktor. Actually, part of the reason I made it was just to implement some features I couldn’t get in the G2, and because I thought it might sound different in reaktor.
part of the GUI for the vosim synth
It does sound different, and, actually, I think it sounds better in Reaktor! Part of the reason (geek speak here) is that the ramp oscillator in Reaktor allows more precision for syncing the waveforms and there are less jitter artifacts. Also, reaktor just sounds good :). I was also able to mess around with a couple tricks that are easier in reaktor than on the nord.
another snap of the GUI
The architecture of this synth: It is a 3 OP VOSIM/FM hybrid. The 3 oscillators can frequency modulate each other, and are all fed into the same VOSIM “burst envelope” which creates the fundamental frequency, and the 3 operator/oscillators are what create the formants.
I found that using a little frequency modulation can add a lot of texture to the vocal sound, or just help in creating a lot of crazy textures.
I’ve also included a fairly comprehensive modulation section. There are only a few presets, but there is really a lot of possibilities in this synth, so enjoy!
I made a simple track to show some sounds from this Reaktor patch. It was just a fun quick demo, but there’s some good textures in there, anyhow. The pad/abstraction sounds are from the VOSIM synth. The “techno” sounding synth and the drums are from the nord g2 modular.
unsavory Associations Mp3 audio
and here is the reaktor patch:
A track I made recently. Doesn’t really fit in with the album I’m working on, but I liked how it turned out. So here it is!
floating ship!!!
The technical details: The synth bass sound was Roland MKS-70, Vocal sampling done in Reaktor, Drums done in the Nord G2, and I believe that digital sounding pad (if I remember right) was done with my waldorf microwave. That crusty digital percussion sound in the background was G2 as well, I think.
My partner in crime, John Farrell, of Bagger288 has an upcoming website, which I will be designing. Look out for it!
Proto-Minotaurs Interrogate Tolteck Differentials
He’s a great artist and his writing will blow your mind. Also expect more activity on the bagger288 front. Stay tuned! Above: a painting-collage of his, titled “Mobile Birthrights”
I’m always on the lookout for interesting new ways to get sounds, or new synthesis methods. Especially ones that don’t take a degree an DSP engineering to figure out. VOSIM fits the bill. VOSIM is a kind of formant synthesis where you can control the formant (louder peaks in the frequency spectrum, like in vocals) and fundamental frequency of a tone completely independently, without using any subtractive filters.
Some VOSIM waveforms
Above are some VOSIM waveforms. It’s hard to glean exactly what VOSIM is from the Csound patches and weird academic descriptions online, so I am just giving my approximate definitions and explanations here (please correct me if I’m wrong here, inter-nerds). Basically, VOSIM is a chain of Parabol (or sine) pulses that are “windowed” or enveloped into bursts. There can be a delay between these bursts, or they can immediately follow one another. I found that the delay between bursts did not affect the sound as much as the frequency of the pulse trains, and it was tricky to implement (I did have a working version of a delayed-burst version of VOSIM working to get the waveforms in the image above) so I just made a version with continuous bursts (where one follows immediately after the preceding burst).
Breaking it down...
The diagram above explains the Signal flow of my patch. A sine wave is multiplied by itself to give sine^2. This makes the waveform completely positive instead of bipolar. A sawtooth wave that has only positive values is multiplied with the Sin^2 pulses to give continuous Bursts of pulses. The length of these bursts, determined by the frequency of the sawtooth wave, gives the fundamental frequency of the tone, and the frequency of the sine^2 pulses gives the formant frequency.
sawtooth wave (orange) provides the envelope for the pulses (yellow)
There is one other trick to getting this all working–the sine^2 pulses must be phase-synced with the sawtooth wave so there are no ugly clicking sounds. Any synthesis system with oscillators that can be synced should do this just fine. Make sure that the sawtooth wave is ramping downwards, not upwards, as is often the case in synthesizers.
This is a very interesting synthesis method that can be implemented in just about any digital modular system! I think more people should give it a try. And I think there should be more dialogue online about doing cool stuff like this instead of gazillions of rehashings of classic analogue sounds and “how did so and so get this sound in such and such track.” So, anyone else have some cool ideas?
Here is a video I made to illustrate what the VOSIM waveform looks like, and some of the sounds that can be achieved with a simple VOSIM patch:
Here is my nord G2 modular VOSIM patch:
I got my idea for this stuff from the fantastic “Advanced programming Techniques for Modular Synthesizers” website.
Here’s a quick track I made with the VOSIM sounds (needed my 2nd beer for this one):
