QM synthesis I invented


It’s hard to believe it’s still possible to invent something new and simple nowadays. It’s harder to believe it’s still possible to invent something simple and useful. What would you say if I say I’ve invented a new kind of sound synthesis? I guess you’d call me a liar or fool. Well, the thing I’m typing here is my experience, a small bit, a little flash in my head occurred something like a year or two ago. Maybe it’s already invented; maybe it’s a question of when. I’m typing my experience to leave my footsteps; to be able to look back at things shaped my life path. I don’t live for money, I don’t live for emotions nobody care of, I don’t collect stuff, I do collect my own thoughts before my personality is disappeared. The idea described below is my everyday challenge to the world – there are still simple things to discover.

Note: This post is not a claim the synthesis method described below is an invention that has been made by me. But I do not exclude that the described synthesis method is unknown or/and undeclared to the general public. I find possible to use a custom name for the sound synthesis method ("QM") and "invention" term within the post due to not scientific but cognitive kind of the information based on a pure practice.


When I was a 7 years old schoolboy I was basically usual kind of children. Basically. I was dreaming to become a machinery designer and an inventor. One of my brightest memories of those days when I was arguing my teacher that zero is not "nothing". Also I’ve been so sure I can invent a perpetual motion machine. I still remember my *design sketch* of it. The funny thing I’m still not sure it won’t work. Later I draw a couple of charts named "Bio-modem" and "Wireless Electricity" which based on "high-resonance module". If don’t read news both of devices exist for a while. But my imagination gave me them something like 15 years ago. I could say I had that *Leonardo Da Vinci* feeling made me draw stuff the world need so much. Honestly, I don’t know what Leonardo did feel. But I assume he loved life, he loved life within any nature, biology or machinery, art or chart. Love makes people see no frontiers. By the age 16 my Z-80 assembler coding adventures forced me to develop original graphic drawing algorithms. I’ve designed a few ones. They turned out to be fastest ever done. The *fastest* secret of the algorithms is in the nature, they’ve been designed within Z-80 assembler nature. They don’t operate with clear formulas of the graphical objects they draw. They treat the objects as bunches of bits. Most of the code is based on logical operations AND/OR/XOR which used to be fastest in any CPU ALU. The algorithms are so simple I’m not sure somebody else has invented them. And honestly I’m not bothered are things already invented or not. I don’t aim to be first. I do aim to set up a bidirectional connection with the world I live in. I’m not really interested in downloading gigabytes and reading megabytes for my own good. I put inspiration over pure knowledge. An inspiration is a true vectorized energy, some kind of heavily compressed information, superimposed information with dual nature make you do things should be born through your hands. It’s just like you’ve been asked by Universe. There are not so many of movies that inspire me. A couple of years ago a friend of mine suggested me to check out "Pi" movie by Darren Aronofsky, he said I’m just like the guy (Maximillian Cohen) from the movie. Indeed, it wasn’t hard to find a few similarities. But the main thing was the inspiration. Lets quote a small piece in the beginning of the movie:

Jenna (Max’s young neighbor): What’s 322 times 491?

Max: 158,102. Right?

Jenna: Right! OK, 73 divided by 22?

Max: 3.318181818181818..

—- Restate my assumptions. One: Mathematics is the language of nature. Two: Everything around us can be represented and understood through numbers. Three: If you graph the numbers of any system, patterns emerge. Therefore, there are patterns everywhere in nature. Evidence: The cycling of disease epidemics; the wax and wane of caribou populations; sun spot cycles; the rise and fall of the Nile. So, what about the stock market?

Maximillian Cohen, young and genius mathematician (according to the movie) has found true name of God by an accident – some kind of life form affected Euclid – his math computer. The name came up to Max as a number with 216 digits. An ultimate key of nature. I’ve been really inspired with the movie for awhile. The mystic behind the 216 digits and PI number really got my brain attention. But, honestly there is no direct connection between the movie and QM synthesis. I don’t want to fool you, the synthesis method was *invented* almost(!) by an accident – I connected wrong oscillator as a modulator. From time to time I do researches with very simple things, I try to get *more than expect*. It was an ordinary day under the *Pi attitude*, I sat down to Reaktor to build another monster ensemble, I started as I love to – start from zero, an empty ensemble, put a few modules, pressed a note, and damn, the sound came up wasn’t one I expected at all. The sound I heard was much more complex than a couple of oscillators could produce in any connection combinations. I should note it wouldn’t be fair to call my *invention spark* pure luck, I’ve been working a lot with a quantization and it’s side effects. It’s just like I worked the spark out. One of the main reasons I mentioned the PI movie is that QM synthesis make numbers *build* sounds. It makes possible to extract thousands sounds from the 3.318181818… and even PI (approx. to PI).

Synthesis general information

Name: Quantized Modulator (QM)
Root-class: Frequency Modulation (FM)
Fundamental principle: spectral frequency interference of a modulated wave as result of sample-quantization of the modulator wave (conjectural description)
Synthesis potential: multi-harmonic sweeps, pseudo-vowel sweeps, drones, pseudo-sequenced harmonics, quantum and radio noise emulation, general special FX creating and experimental purposes
Technical minimum: 3 oscillators [2 waveforms + 1 clock] + sample&hold
Control minimum: 2 high resolution controllers
Advantages: high number of sounds can be created within a small amount of time, a big potential for further researches.
Disadvantages: not related to emulation of real instruments, relatively low sound quality (due to quantum-noise related nature), sensivity to the calculation accuracy Due to I’m not really skilled with physics and algebra official terminology the information above shouldn’t be treated as scientific. It’s a basic description for the post publication. With the "sample-quantization" term I want to note that it’s not a bit-depth quantization you might think, I meant sample clock timing (sampling rate) quantization, so the quantization goes within time scale. I could have used "resampling" term instead "quantization", but I prefer "quantization" as a general term as it’s related to quantum noise. Possible alternative names could be: [Q]uantum [M]odulator – another good name, [R]esampled [M]odulator (RM – conflict with Ring Modulation), [D]ownsampled [M]odulator (doesn’t really looks right). Maybe "FM side bands quantization" is also a quite fair name, but I’ve chosen "Quantized Modulator" because it describes fundamentals of the synthesis method pretty well/short=effective. Let’s use the name for the post at least. The synthesis method deserves having a name within the post.

Fundamental principle

QM synthesis principle

The picture is quite simplified, but the basics of the QM synthesis are very simple (unless you want to calculate the output wave). You take a simple wave (sin wave at the picture) with a frequency X (i.e. 1 / T), quantize by a frequency Y(1 / t) and use the result as FM modulator. It’s easy to see how it’s simple and *almost FM synthesis*. But the quantization makes an enormous and extraordinary difference between QM and FM synthesis. First, you can’t call it "fast vibrato" anymore. Second, say goodbye to real instruments simulation, QM won’t play a fancy electric piano. Third, forget about notes, QM synthesis loves wide modulation index values, "carrier" tone just doesn’t make any big practical sense. Four, QM synthesis don’t require any big modulation marix, LFO or envelopes to produce complex sounds. You just take X, Y, modulator waveform and tweak them until you find another sound-effective T/t ratio. Of course, you’re *locked* within the *FM sounding", but QM synthesis isn’t about the result, it’s about the method. QM sound creation process and it’s *speed*, it’s creative aspect is different to traditional FM synthesis programming. I hope you got me right on this. So, a simple QM synthesizer structure looks like this: simple QM synth Note that the frequency controllers (knob/faders) should have a very high resolution (1 hertz accuracy at least) to produce the full possible QM sound range (more or less). Generally, similar to the quantization side effect is well-known in a computer graphics sphere (IIRC), it’s kind of a digital interference. I did a graphical example with a small and a big number of gradients:

Round gradients

In all these cases the gradients are round, but the number of repeatings makes the visual difference. With the sound synthesis based on the quantization it looks (full spectrum sonograms) not so boring:

QM synthesis sonograms extra gallery you may find in previous post.

Future QM synthesis researches/development:

– Sound-effective frequencies (auto)search (compute) (FFT lookup, prime numbers tables, etc) – Sound-effective modulator waveform distortion research – Source modulator signal FX-processing – Frequency tweak improving – Quantizer clock oscillator modulation – Expanding oscillators frequency range – Use samples as modulator source Basically, these are just example ways to research. There are probably many more ones. Now, let me introduce my first QM synthesis experimental achievement:

Quantum Radio v1.0

ensemble idea

The idea behind the ensemble is very natural for QM synthesis – free Modulator and Quantization frequencies surfing. Basically, it’s just like you’re tuning a radio with 2 very big frequency scales. The ensemble was born with thousands small improvements out of 2 frequency faders. I started something like January 5th, and finished the ensemble a week ago. So, it was a quite smooth developing process full of *basic features* ideas.

ensemble general information

version 1.0 include: – 3 oscillators QM synthesis engine (multi-wave modulator > quantizer clock > sin-wave) – multi-wave XY-controlled source modulator OSC (modified Jericho OSC) – frequencies joystick with adapted MIDI control support – advanced frequency modify functions – frequencies keyboard scaling module No automated elements (LFO, envelopes, step-sequencers and etc) are included. No FX-processing is chained.

ensemble controls

As you can have seen at the general ensemble panel view there are not so many of controls available, but basically, it’s because it’s first QM synth. Though I’ve made it to show QM synthesis basics it does produce thousands of interesting sounds. It was a quite fun to get 128 snapshots out of the synth. I’ve put some serious effort to two main control elements of QM synthesis: modulator waveform distorting and modulator/quantization frequencies *surfing*. That made the synth tweaking extremely simple and fast. Most features were created during practical experiments. Also I spent another week to improve general usability and n_of_controls/effectiveness ratio. And one more day to draw controls description pictures. I’ve tried to put an optimal amount of information to the pictures. Unrelated control elements are faded to the background. Additional notes go below pictures.

frequencies controls:

The joystick is basically QM sound "surfing" and fine-tuning tool. General usage is quite simple: you drag the bar and move it away from the centre. The bigger offset you produce the bigger frequency increments occurs every 1/25 second. Shorts click are also allowed (with small smoothing amounts). Axis X affects source modulator frequency (S), Y – modulator quantization frequency (Q). When S/Q ratio lock is on any moment affects both frequencies to keep the ratio constant. "Midi" button enables midi-control support for the joystick. Pitch-bend wheel becomes an accelerator pedal, and modulation wheel becomes a steering-wheel which controls a surfing direction within -90…+90 degrees, opposite directions set by pitch-bend sign. Different surfing degrees produce different increments for Source and Quantization frequencies. The button is off by default to prevent wrong pitch-bend centre values and other unexpected things. Basically, it’s quite experimental kind of control and I decided to put an off button for the first public release. I hope you’ll enjoy the feature.

Modifiers are useful to get a *completely* new frequency (sound). Upper buttons row adds or multiplies, bottom – subtracts or divides. Note that theta, 3/4, 5/7 are smaller than 1. You should divide by them to get a higher frequency. As theta I’ve used 144/233 (0,618025..), if you don’t know why you’ve to check out the Π’«PIΠ’» movie to get the answer πŸ™‚ As PI I used 3.14153, basically because Reaktor has a pretty brutal constant value keyboard input. But since the modifiers are designed for the sound research the accuracy isn’t the goal. Note that S/Q ratio lock works with the modifiers as well, any frequency modification affects the opposite frequency, it will be rescaled to keep the ratio constant. Note that, the octave increment is equal to x2 multiplier. Also note the frequency display is red when you go out of master_sampling_rate / 2, i.e. oscillators are unavailable produce a wave with the frequency.

General functions are useful to get certain ratios, i.e. PI, theta, x2, and etc, To set a certain S/Q ratio you need to set a basic frequency with the frequency joystick, then copy the frequency to the opposite frequency and rescale it with a modifier(s) you need. Make sure S/Q ratio lock is off during the rescaling. Then you can turn the lock back on and search sounds within the ratio.

The frequency scaling is another creative mechanism I designed to find new sounds within seconds. Since QM synthesis doesn’t like notes it would be logically to throw (midi) keyboard away. Logically doesn’t mean wise. It turned out damn effective to use keyboard to rescale the frequencies. Some of S/Q ratios produce a new sound under any log-scaled (or lin-scaled) frequencies, you just push another keyboard key and get a new one. Funny to admit that it was basically a problem to me during the ensemble snapshots creating, I just wanted to save all the sounds under such sound-effective ratio.. Just imagine, it’s possible to fill a full 128 snapshots bank within a few minutes, how do you like it?

As you might read in one of previous posts I created an experimental multi-wave oscillator Jericho. Originally it’s been designed specially for Quantum Radio. I didn’t bother about it’s audio quality or it’s classic additive synthesis usage. Modulator waveform shape is the thing SQ synthesis cares about. I’ve tried to build the most effective multi-wave oscillator within a few wave-forming controls and the time window I had. And I should say I’m quite happy I didn’t go with the classic multi-wave mixed oscillator. There are some basic example waves the Jericho OSC generate: Jericho OSC (modified)

ensemble usage

Typical Quantum Radio usage strategy may look like this: frequency surfing >> find sound-effective S/Q ratio >> make snapshot find sound-effective S/Q ratio >> find interesting sound with keyboard-scaling (waveforming) >> render the sound Basically, there are a few QM synthesis peculiarities that I found out by the late practice: – high S/Q (or Q/S) ratios produce more complex sounds – inversely proportional S/Q ratios (when you swap Q and S) produce similar sounds in some cases – typical sound-effective S/Q (and Q/S) ratios are 0.1666, 0.3333, 0.5, 0.6, 1.1666, 2, 2.1666, etc. If you’ve read the post above you should be quite ready to work out new sounds with the ensemble. For a start, load the ensemble, try to produce sound with the snapshots, to do this you need to select a snapshot and press c-3 ("Q" key for PC keyboard), other notes will alter the sound with the keyboard scaling. Make sure you’re running the ensemble at 44100 hz sampling rate. If the sound you hear is similar to the sound I’ve rendered in the post then the magic worked and you can try swap Q and S (S <> Q button) and get another 128 sounds out of the snapshots πŸ™‚ And then you may realize what’s the QM synthesis about πŸ™‚ I suggest you to render sounds you’ll find with Quantum Radio. For worse or better there is no guarantee it will sound the same on another machine under the same conditions. Reaktor’s QM synthesis realization seems to be very sensitive to internal digital signal processing accuracy and master sampling rate which is no surprise. The thing about Quantum Radio is that you may lose a certain sound you’ve found *forever* if you didn’t render it or didn’t memorize the source modulator and it’s quantization frequencies at least. Of course I don’t think you may lose a very unique sound, most of QM synthesized sounds are quite similar, but I remember a couple of moments when I was quite surprised with the sounds Quantum Radio is able to produce. And last note – I don’t recommend Quantum Radio for real-time VSTi usage; render the sound you need for your music.

visualization notes

There is another interesting thing to share. When I sat to add some visualization to the parabolic shaper XY background display I thought it would be cool to make some 3d thing people used to create. But then I realized I’m quite newbie in the visualization programming. And I decided to build some more practical visualization for the ensemble. I made a simple circumference scope with a sync to quantization frequency and scaled Jericho OSC output wave.

Quantum Radio visualization structure

This made possible to find sound-effective S/Q ratios with the visualization only (with no sound). I wasn’t really sure what exactly I’ll see in the XY scope. But then I found out that some of Jericho waveforms and S/Q ratios (sound-effective) create these pictures:

Quatum Radio visual

Do you need any comments on it? Well, I’d say I saw spirals, flowers, molecules/atoms, snowflakes – all the basic shapes of the world. I’m not really sure should I look for any meaning more in the pictures I’ve discovered.. But I really felt something magical for a second when I realized how it’s really simple to get the shapes out. Maximillian Cohen was right, they are everywhere.


Quantum Radio v1.0 ensemble Quantum Radio 15 mins tweak session – how the tweaking process sounds like, joystick surfing, keyboard scaling, waveform distorting. 128 rendered snapshots:

Snap 001
Snap 002
Snap 003
Snap 004
Snap 005
Snap 006
Snap 007
Snap 008
Snap 009
Snap 010
Snap 011
Snap 012
Snap 013
Snap 014
Snap 015
Snap 016
Snap 017
Snap 018
Snap 019
Snap 020
Snap 021
Snap 022
Snap 023
Snap 024
Snap 025
Snap 026
Snap 027
Snap 028
Snap 029
Snap 030
Snap 031
Snap 032
Snap 033
Snap 034
Snap 035
Snap 036
Snap 037
Snap 038
Snap 039
Snap 040
Snap 041
Snap 042
Snap 043
Snap 044
Snap 045
Snap 046
Snap 047
Snap 048
Snap 049
Snap 050
Snap 051
Snap 052
Snap 053
Snap 054
Snap 055
Snap 056
Snap 057
Snap 058
Snap 059
Snap 060
Snap 061
Snap 062
Snap 063
Snap 064
Snap 065
Snap 066
Snap 067
Snap 068
Snap 069
Snap 070
Snap 071
Snap 072
Snap 073
Snap 074
Snap 075
Snap 076
Snap 077
Snap 078
Snap 079
Snap 080
Snap 081
Snap 082
Snap 083
Snap 084
Snap 085
Snap 086
Snap 087
Snap 088
Snap 089
Snap 090
Snap 091
Snap 092
Snap 093
Snap 094
Snap 095
Snap 096
Snap 097
Snap 098
Snap 099
Snap 100
Snap 101
Snap 102
Snap 103
Snap 104
Snap 105
Snap 106
Snap 107
Snap 108
Snap 109
Snap 110
Snap 111
Snap 112
Snap 113
Snap 114
Snap 115
Snap 116
Snap 117
Snap 118
Snap 119
Snap 120
Snap 121
Snap 122
Snap 123
Snap 124
Snap 125
Snap 126
Snap 127
Snap 128

Note: the snapshots have been created under 44100hz master sampling rate. Different sampling rates produce different sounds! Also a different CPU-ALU is a cause to get different sounds.


A practical side of QM synthesis is very specific. The sounds have pure numerical nature. But it’s as specific as wide. QM synthesis opens another wide door between two worlds – numbers and sounds. The door makes audible thousands sounds from a couple of numbers within 3 oscillators and 2 faders structure. Something more than just a discord. Something more than just a harmonic sweep. Something more than just a noise. Something more than you got used to tweak. I assume there are millions and millions of sounds behind the synthesis. I assume there are more simple things to discover. Have a nice QM synthesis. Stick to nature while being creative.

22 Responses to “QM synthesis I invented

  • 1
    March 2nd, 2007 05:13

    WOW great post & great ensemble. I’ve been waiting for a long time to see what you had up your sleeve and was very excited for it to finally be posted. I really appreciate your site and look forward to your future projects.

    Another long time silent visitor

  • 2
    Synth Of Mine’s QM synthesis at FlightDynamics
    March 2nd, 2007 23:27

    […] Must go… download… drone! Synthesis general informationName: Quantized Modulator (QM) […]

  • 3
    March 3rd, 2007 01:01

    Fantastic piece of work!

  • 4
    ethan mahmeinntow
    March 3rd, 2007 01:27

    In my opinion, Quantum Radio v1.0 has a lifetime’s worth of musical output & then some. Just flirting with the instrument produced percussion, fx layering, melodies, drones, & could probably produce phonemes from the neuropsychodynamics of a predator. Hats off to your finely sharpened ensemble.

  • 5
    March 4th, 2007 20:32

    Thanks for the comments, guys! I hope nobody is disappointed with the post I promised for such a long time. But there are more and more things to share. Synthofmine.com is a part of my life now, I’ll try to be wide and detailed in the publishing. I hope you’ll enjoy it.

  • 6
    March 4th, 2007 20:37

    Btw, nice description, Ethan! QR produce quite a different range of sounds indeed. But note, it’s just 1.0, there is no pre/post fx processing, there is nothing except simple QM engine with Jericho OSC. There are loads of ways to experiment. But I think it’s a subject for the future posts.

  • 7
    March 6th, 2007 14:14

    All I can say is wow, this will be one long read. I hope I can grasp this stuff hehe.
    Thanks for the effort you put into this blogpost, really great stuff.

    Ps. please stay away from a boring machine, if you know what I mean

  • 8
    March 7th, 2007 05:46

    Hehe… It’s seems quite a lot of people read the post and most of them have nothing to add to “wow” πŸ™‚
    I should say I didn’t know what’s gonna be exact feedback for the post. But now I realized the feedback corresponds to the post. It’s basically my “fault” that I’ve closed most probable questions in the post with the notes and details, I just put too much effort πŸ™‚
    But I promised the interesting stuff, the post had no other way to be published. And there’s a lot of synthesis/sampling routine to be published as well.

  • 9
    April 11th, 2007 03:15

    Do you know anything about Smith charts? That might be a really great way to visualize your S/Q ratio. Just a thought.

  • 10
    April 11th, 2007 03:21

    I would really love to see you tackle “scanned” synthesis next. Do you think Reaktor’s up to it? Not talking about wavetables either.

  • 11
    April 11th, 2007 03:26

    It’s refreshing to see Reaktor being used differently for a change. Wonder what would happen if you modulated your modulator. If you click my name it will take you to my “myspace” blog, where I describe a strikingly similar technique I use for sequencing. I really think you should turn your structure into a sequencer to drive what you’ve already created. Then you’d really be “surfing”!

  • 12
    April 13th, 2007 19:17

    No, I don’t know Smith Chart, but yeah, a good visualization is a good way for visual controllers development.

    About the scanned synthesis. I’m quite newbie to the synthesis. It seems like it’s based on advanced controllers for to scan down waveforms. I know some people use beam-based wireless controllers with Reaktor. So, I think it’s possible to recreate some of the elements of the synthesis at least. But actually, I’d like to stick to simple and fresh ideas in Reaktor.

    I’ll continue the QM synthesis development. I’m not really sure how much of effort I’ll put to it, but it’s definitely worth to add some ideas. I think there are quite a lot of things besides sequencing.

  • 13
    April 13th, 2007 23:21

    Why am I not able to comment? Is there a way to reach you directly?

  • 14
    April 14th, 2007 00:00

    Hmm… weird.. actually, there is a simple anti-spam filter, but it’s should work ok.

    Anyway, you can reach me by email, zed.tsd AT gmail.com should be fine

  • 15
    June 22nd, 2007 18:18

    Sweet looking ensemble, and great post.

  • 16
    QM-Synth at K.M.Krebs 833-45
    October 5th, 2007 02:01

    […] A while back I designed a synth implementing quantized modulator (QM) synthesis as described/discovered by the fellow who runs the Synth of Mine blog. It’s made in SynthEdit, and probably has numerous bugs, so be warned. […]

  • 17
    October 6th, 2007 01:30

    The correct term would be “decimated modulator”.

    And the correct name for the noise you get from it would be “aliasing”.

    The reason that “QM” as you call it makes so much difference is because aliasing is generaly inharmonic, and inharmonic frequencys + FM = madness πŸ˜€

    And the rythmic timbral patterns you get are from detune between carrier and modulator as they drift and and out of phase.

  • 18
    October 6th, 2007 21:07

    Hey, Hoohar.

    It’s a quite true I’ve ruined a big amount of time to find some proper terms for the publication. I’ve not found the 100% correct ones, I knew it, but I just couldn’t wait anymore. I was sure it’s not gonna get into wikipedia anyhow, so, I’ve used some decent terms for the general description. I think I need some real help for a proper documentation for the synthesis. Though it’s gonna ruin the magic part of it πŸ™‚

  • 19
    QM-Synth by K.M. Krebs, a SynthEdit implementation of Quantized Modulator synthesis
    November 22nd, 2007 13:43

    […] Zed @ Synth Of Mine explains Quantized Modulator synthesis: You take a simple wave (sin wave at the picture) with a frequency X (i.e. 1 / T), quantize by a frequency Y(1 / t) and use the result as FM modulator. ItΠ²Π‚β„’s easy to see how itΠ²Π‚β„’s simple and *almost FM synthesis*. But the quantization makes an enormous and extraordinary difference between QM and FM synthesis. […]

  • 20
    qm patch for the nord modular g2
    December 18th, 2007 00:08

    first a big thank you for sharing this with the rest of the world. now it is so easy to make electro sounds. based on your idea, i created a nord modular g2 patch (freely downloadable at http://www.electro-music.com/forum/viewtopic.php?p=158902). i hope i did it right – at least it sounds so to me :o)

    finn anklam
    hamburg, germany

  • 21
    December 20th, 2007 01:01

    That’s great, Beatretreat! I guess QM is now in hardware πŸ™‚ Would be great to hear how does that patch sounds like. The important things are source modulator waveform and an accuracy (and range) of the frequency knobs, then it’s gonna get the right sound I think.

  • 22
    qm patch for the g2 demo application
    January 12th, 2008 15:29

    at the bottom of http://electro-music.com/forum/viewtopic.php?p=163083#163083 you find a modified patch which should run under the g2 demo application. you will also find a link for downloading the freeware demo application.

    finn anklam