From nwilson@morgan.com Tue Jan 17 13:35:38 1995 Date: Tue, 17 Jan 1995 12:17:11 -0500 From: Ab Wilson To: Analogue Heaven Subject: Ring Modulator Richard Klasic writes: > Excuse my totally dumb question. But can someone explain what a Ring > Modulator is to me? This will no doubt be one of many replies. A ring modulator has two inputs (lets call them x and y) and one output. The output is simply x multiplied by y. So if the inputs are two constant voltages the output will be their product. Also if either input is zero then the output will be zero. This is somewhat similar to a VCA except that a ring mod works in all four cases with (+ve x, +ve y), (+ve x, -ve y), (-ve x, +ve y), (-ve x, -ve y). To understand why a ring modulators are interesting you need to know one more thing - through some bizarre feet of mathmatics this multiplication has the following effects in the frequency domain. If x and y are fixed frequency sine waves then the output will be the sum and difference of these frequencies. eg for x=50Hz, y=50Hz, the output is a 100Hz sine wave with a 0Hz (dc) component. For x=50Hz, y=75Hz the output will be a mixture of a 25Hz sine and 100Hz sine. If the inputs are not pure sine waves then the output will consist of the sums and differences of all the frequency componts of each signal. So for x=3KHz sawwave, y=200Hz sine the output will be all the frequency components of the original saw shifted down 200Hz, plus all the components shifted up 200Hz. Since these shifts are additions in frequency and not multiplications the result will no longer sound harmonic because the partials of the sound will no longer be in tune with the fundamental. This is the first and probably most common applicatino of a ring modulator - creating disonant, clangy timbres. Now say x=1KHz sawwave and y=2KHz sawwave which has been passed though a low pass filter with the resonance set very high (but not self oscilating) so as to pick out a narror band of high harmonics. The output will now be the sum and product of each of the harmonics selected by the filter with each of the harmonics of the 1KHz saw. In this case the frequencies of the input signals where a simple ratio of each other so the output will still be harmonic. The actual result will sound similar to a formant filter since the original single peak in the response will have been replaces by multiple peaks - one for each of the sums and products. Like most interesting synthesis techniques ring mod takes quite a bit of tweaking to sound good. It's not just a case of turning it on, randomly moving a few sliders and then asking whether the trendy term is acid or hard trance this week. That's probably why it isn't included in more synths. I'm a recent convert having only discovered the prefiltering technique a few weeks ago. It came as one of those relevations. I now put ring mod up there with FM and waveshaping as a powerful non-subtractive synthesis technique (the term constructive seems appropriate). Ab. From PPilgrim@teleglobe.ca Tue Jan 17 13:41:17 1995 Date: 17 JAN 95 11:39:33 EST From: PPilgrim@teleglobe.ca To: analogue@magnus.acs.ohio-state.edu Subject: Re: Ring Modulator Rick, A ring modulator mixes two input signals and outputs two frequencies equal two the sum and difference of each input frequency. I believe the technical term for this is an intermodulation generator. For instance, if you input 100Hz and 80 Hz, the output would be 20Hz and 180 Hz. In human terms, the output sounds "bell like" thus the name "ring" modulator. On my CS-60 the ringmodulator uses the audio signal as one input so it must generate a second signal which it mixes with the audio signal (I never looked into this). It's a good tool to get metalic FMish sounds from an analog synth. Also you can get some great "weird" sounds for special percussive or theatrical needs.(especially B SciFi movies) Philip Pilgrim From media@pcnet.com Tue Jan 17 16:17:49 1995 Date: Tue, 17 Jan 1995 14:04:58 -0500 (EST) From: Machine Media To: Richard Klasic Cc: Analogue Heaven Subject: Re: Ring Modulator > Excuse my totally dumb question. But can someone explain what a Ring > Modulator is to me? When it comes to synths, I've asked even dumber questions. The last time I answered a question here, no one called me an asshole, so I'll continue :) OK, a ring modulator is pretty simple. If you take a waveform and cross-modulate (multiply) it with a another simple waveform, creating a new waveform that does not contain either original waveform, that's ring modulation. The new waveform only contains harmonics at the sum & difference of the two original frequencies eg. if a 300hz tone is ring modulated by an 1100hz tone, you would get a new signal with 1400hz & 300hz. This is assuming that the original waveforms are simple (contain only their fundamental harmonic). If you take more complex waveforms, every harmonic multiplies every other harmonic, & so on. Why is it called ring modulation?? Because it typically makes a "ringing" sound with all of these odd harmonics. Now lets add tubular bells: A bell is a cup until it is struck. A metal cup full of air has alot of mechanical resistance against oscillating at any frequency other than its own resonance. Try blowing across a top of a glass. (what am I?? Mr. Science? ;) Frequencies that do not create nodes inside the bell aren't going to last very long. So, we ring the bell, and it wags back and forth, gee, just like a fast pendulum -- doesn't a pendulum have a specific frencency? So, we have the frequency of the "pendulum" cross modulating the nodal frequencies inside the bell, so the resulting frequencies are the sum & difference of these original frequencies. That's ring modulation :) ************************* M A C H I N E M E D I A ************************* * CD Mastering & Digital Editing * * Personal attention, the finest quality, & the most competitive rates. * * Phone: (203) 223-6744 Fax: (203) 223-6743 Free Overnight Shipping * **APHEX*BEHRINGER*DBX*DIGIDESIGN*DRAWMER*LEXICON*MICROPOLIS*SONY*UREI*WAVES*** From don@till.com Wed Jan 18 12:42:27 1995 Date: Tue, 17 Jan 1995 22:31:29 -0800 From: Don Tillman To: analogue@magnus.acs.ohio-state.edu Subject: Re: Ring Modulator Date: Tue, 17 Jan 1995 12:17:11 -0500 From: nwilson@morgan.com (Ab Wilson) A ring modulator has two inputs (lets call them x and y) and one output. The output is simply x multiplied by y. So if the inputs are two constant voltages the output will be their product. Also if either input is zero then the output will be zero. Ahh, correct and succinct. To understand why a ring modulators are interesting you need to know one more thing - through some bizarre feet of mathmatics this multiplication has the following effects in the frequency domain. The math is actually quite simple. Remember in High School trigonometry, when you weren't hanging out by the industrial arts wing with the cool guys in those jackets, the equation for the cosine of the sum of two angles? cos(a + b) = cos(a)cos(b) + sin(a)sin(b) And since cos(x) = cos(-x): cos(a - b) = cos(a)cos(b) - sin(a)sin(b) Add them together: cos(a + b) + cos(a - b) = 2 cos(a)cos(b) The right half is multiplying to sine waves. The left half is a pair of sum and difference frequencies. Piece of cake. Like most interesting synthesis techniques ring mod takes quite a bit of tweaking to sound good. It's not just a case of turning it on, randomly moving a few sliders and then asking whether the trendy term is acid or hard trance this week. [Direct hit! Incoming, dive, dive.] That's probably why it isn't included in more synths. Another reason is that it requires a lot of routing flexibility -- it's not always obvious what the best sources for the inputs ought to be. So it's best on a modular. Date: Tue, 17 Jan 1995 14:04:58 -0500 (EST) From: Machine Media OK, a ring modulator is pretty simple. If you take a waveform and cross-modulate (multiply) it with a another simple waveform, creating a new waveform that does not contain either original waveform, that's ring modulation. The new waveform only contains harmonics at the sum & difference of the two original frequencies. This is a very mangled definition. "Cross modulation"? Why is it called ring modulation?? Because it typically makes a "ringing" sound with all of these odd harmonics. Uhhhhhhhhhhh, no. It was called ring modulation long before electronic music. The name came from the earliest implementations, consisting literally of a ring of diode tubes and three transformers. Now lets add tubular bells: A bell is a cup until it is struck. A metal cup full of air has alot of mechanical resistance against oscillating at any frequency other than its own resonance. Try blowing across a top of a glass. (what am I?? Mr. Science? ;) Frequencies that do not create nodes inside the bell aren't going to last very long. So, we ring the bell, and it wags back and forth, gee, just like a fast pendulum -- doesn't a pendulum have a specific frencency? So, we have the frequency of the "pendulum" cross modulating the nodal frequencies inside the bell, so the resulting frequencies are the sum & difference of these original frequencies. That's ring modulation :) Yuck, I count five blatent errors. Bells have oodles of resonant frequencies, pendulums have one, and the bell's frequencies are not harmonically related. In that way the sound of bells is similiar to the output of a ring modulator. There are very few other sources of sounds with those characteristics. -- Don From don@till.com Wed Jan 18 19:07:12 1995 Date: Wed, 18 Jan 1995 14:25:29 -0800 From: Don Tillman To: analogue@magnus.acs.ohio-state.edu Subject: Ring Modulator More ring modulator tidbits... Run a sine wave into both inputs of a ring modulator. The output will be a sine wave of twice the input frequency (sum frequency) with a dc bias (difference frequency). This only works with sine waves, for obvious reasons. Run a microphone into a ring modulator with an oscillator for the other input. Sing into the microphone. Notice anything? I mean besides the fact that your voice comes out real strange. It won't feed back even if you're holding the mic right next to the speaker and cranking it real loud. Maestro used to make a ring modulator effects box that was surprisingly popular with jazz electric pianists; both Jan Hammer (w/Mahavishnu) and George Duke (Zappa) used them on their Rhoades'. I'm pretty sure some member of the Don Ellis orchestra used one of these too. -- Don