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The Eat at Joe's Kawai K5000 Message Board Digest Techniques and Formulae for Creating ADD Patches ------------------------------------------------------------------------------------------ ------------------------------------------------------------------------------------------ One harmonic from another Wednesday, 24-Jun-98 22:55:47 152.163.205.67 writes: I've made a lot of original additives patches that I have liked and used in my songs, but the creation of these patches has all been guess work by matter of chance. At least in Analog Subtractive synthesis I know what a certain parameter change is gonna do to the sound I have. In the K5000 I can't tell what one sine wave does from another, their seems to be very little difference in changing the harmonic levels. A more radical change comes when messing with the formant filter and useing LFOs on the FF. Can anyone give me tips on using additive synthesis to the fullest? David Beckman ------------------------------------------------------------------------------------------ Re: One harmonic from another Thursday, 25-Jun-98 12:17:50 192.28.2.16 writes: It works in mysterious ways . . . . Individual harmonics can seem like they're too low to hear, yet when you take out a bunch of them the whole character of the sound changes. I'd recomend wading through the message archive on this site. Maybe we could compile a list of methods to set the harmonics. Here's mine, in chrono order: a) copy from another patch b) use a sound diver template c) draw freehand (i.e. trial and error) d) select individual harmonics (and get a lot of bell patches) e) imitate harmonic profiles of real instruments, from books and the "sharc" website (difficult but rewarding) f) follow mathematical formulas (ditto) Another would be to use the sound diver "import" function; I haven't tried it much myself. leiter ------------------------------------------------------------------------------------------ ------------------------------------------------------------------------------------------ K5k Programing Made Easy Saturday, 27-Jun-98 14:15:26 199.86.33.51 writes: To program the harmonic levels, you need to find a way to reduce 64 numbers to a few meaningful decisions or a few meaningful numbers. One way to do this is to find a formula, A(n,a,b,c), that tells you an amplitude (A) for each harmonic number (n) after you plug in a few simple variables (a,b,c). A good formula should give you as much meaningful control as possible while using as few variables as possible. I've been using spreadsheets to try out different formulas and I've settled on one that seems to be optimal. Hopefully someone on this board, or at Kawai or Emagic, will write a utility that has "knobs" for the variables and a "transmit" button to send the harmonic profile to a selected ADD in the K5k. The best formula I've found uses between 1 and 7 variables. (That is, you don't have to use them all.) The variables are designated a, b, c, X%, d, e, Y%. Okay, here goes: A(n)=[1/n^a]*[(sin(n*Pi*X%))^b]*[(cos(n*Pi*X%))^c]*[(sin(n*Pi*Y%))^d]*[(cos(n*Pi*Y%))^e] Simplifies everything, right? :-) The formula can be broken down into three "modules". The first is simply [1/n^a]. The formula for a saw wave uses just this module; it's A(n) =1/n . You can get that by setting a=1 and b=c=d=e=0. The second and third "modules" are the same, excpt that one uses "X%" and the other uses "Y%". The "module" is: [(sin(n*Pi*X%))^b]*[(cos(n*Pi*X%))^c]. This lets you multiply in as many sine and cosine functions of X% as you want. (The sine is most useful, cosine sometimes; the other four trig fuctions go to infinity so they wouldn't be useful.) For example, the formula for a 20% pulse is: A(n)=[1/n]*[sin(n*Pi*20%)]. You can get that by setting a=b=1, c=d=e=0, and X%=20%. Here are some settings and the waveforms you get: a b c X% d e Y% Waveform 1 0 0 --- 0 0 --- saw 1 1 0 20% 0 0 --- 20% pulse 1 1 0 50% 0 0 --- square 2 1 0 50% 0 0 --- triangle 2 1 0 20% 0 0 --- 20% uneven triangle (plucked string) 2 2 0 10% 0 0 --- 10% triangular pulse (brassy) 3 1 0 48% 2 0 3.5% analog-style square 0.4 1 0 12% 0 1 47% oboe essence (roll off the high end) 2 1 0 4.5% 1 0 6.25% trombone essence (ditto) 2 1 0 9% 1 0 13% french horn essence (ditto) I'm sending in three patches (see below) that use some of these waveforms. There's one more step, which is to plug the amplitude values into Jen's formula to get K5k harmonic level values (L): L(n)=128+8*(log2(abs(A(n)/A(max)))). A(max) is usually, but not always, A(1). The spreadsheet I use takes seven variables as input and displays what the harmonic profile looks like, what the waveform should look like, and what the 64 (or 128) harmonic level values are. I'm getting pretty quick at entering the numbers into sounddiver from the keypad, but I bet a utility could be written to do all this and then send the harmonic levels to a selected ADD automatically. If it could do realtime modulation of these variables, that would really be something. There it is. If you've read this far and understand it, post a reply. copyright 1998 P.S. the patches: L7 Lead: Uses an analog-style square waveform, i.e. with sloping sides and tops. Obonus: Starts with an oboe-emulation waveform but adds synth-style filtering. FrchHorn: French Horn emulation. leiter ------------------------------------------------------------------------------------------ Re: K5k Programing Made Easy Monday, 29-Jun-98 09:55:37 194.172.230.108 writes: How did you get the idea to cascade two comb filters? Just creative inspiration? I like the idea with the power parameters acting as "filter influence faders", too. Another 7-parameter suggestion: A(n)=[1/n*[(sin(Pi*(n*X%+b)))^c]*[(sin(Pi*(n*Y%+d)))^e]^a] Here, a has become a global bright/mellow parameter. And b and d get a different meaning, similar to the well-known odd/even parameter. In fact, when X% resp. Y% are 50%, then b resp. d are odd/even parameters. How about that? Jens Groh ------------------------------------------------------------------------------------------ Re: Re: K5k Programing Made Easy Monday, 29-Jun-98 16:20:49 192.28.2.16 writes: > How did you get the idea to cascade two comb filters? Just creative inspiration? It was necessary to make trapezoidal pulses, which are a better brass emulation than triangular pulses (see the new French horn patch). >Another 7-parameter suggestion: > A(n)=[1/n*[(sin(Pi*(n*X%+b)))^c]*[(sin(Pi*(n*Y%+d)))^e]^a] If you move "a" to the end, you miss out on the ability to use fractional values for 1/n. You can uses fractional exponents for 1/n but not for the trig functions, because they go negative and then the result is imaginary. Unless there's a fix? I really like the idea of the "phase-shift" parameters b and d. You can change the sine to cosine by setting b or d = 1/2. But you also have the intermediate values--I'm not even sure what that will look like; I'll post again when I try it. leiter ------------------------------------------------------------------------------------------ Re: Re: Re: K5k Programing Made Easy Tuesday, 30-Jun-98 05:17:43 194.172.230.108 writes: [If you move "a" to the end, you miss out on the ability to use fractional values for 1/n. You can uses fractional exponents for 1/n but not for the trig functions, because they go negative and then the result is imaginary. Unless there's a fix?] Oh, I see. But you can take the absolute value of the sinusoids. Then the powers are always taken from positive numbers. This is no loss, as you need to make the amplitude positive anyway. Jens Groh ------------------------------------------------------------------------------------------ Re: Re: Re: Re: K5k Programing Made Easy Tuesday, 30-Jun-98 17:19:41 192.28.2.16 writes: >Oh, I see. But you can take the absolute value of the sinusoids. Then >the powers are always taken from positive >numbers. This is no loss, as you need to make the amplitude positive anyway. That's a good fix. The only catch is that you loose the ability to graph the waveform with the plus and minus signs in place, which you need if you want to see a triangle (e.g.); but, whatever. leiter ------------------------------------------------------------------------------------------ Re: Re: Re: K5k Programing Made Easy Tuesday, 30-Jun-98 17:15:49 192.28.2.16 writes: > I really like the idea of the "phase-shift" parameters b and d. You can change > the sine to cosine by setting b or d = 1/2. > But you also have the intermediate values--I'm not even sure what that > will look like; I'll post again when I try it. Okay, I found the right identity to use: sin(Pi*(n*X%+b)) = cos(Pi*b)*sin(Pi*n*X%) + sin(Pi*b)*cos(Pi*n*X%) So it's the _sum_ of a sin X% and a cos X%, with b as a kind of fader between them. (For b=0 it's all sine, for b=1/2 it's all cosine.) leiter ------------------------------------------------------------------------------------------ Re: K5k Programing Made Easy Monday, 06-Jul-98 21:15:46 209.160.126.117 writes: My Oberheim synth allows you to sum square and saw waves. I was wondering if the following adaption of your equation would do the same: A(n)=((1/n)+abs((1/n)*(sin(n*Pi*0.50))))/2 Leslie ------------------------------------------------------------------------------------------ Re: Re: K5k Programing Made Easy Tuesday, 07-Jul-98 13:43:30 199.86.33.68 writes: I think that's right. But it may not sound the same: In the K5k case, all of the harmonics of the two waves would always be perfectly in phase, always adding and never cancelling. That probably isn't true in the OB. leiter ------------------------------------------------------------------------------------------ Re: K5k Programing Made Easy Tuesday, 07-Jul-98 15:59:12 209.160.126.70 writes: Another question (doubt if it will be the last). When I calculate a pulse wave of less than 50%, the max amplitude is less than 1. I have a software program that does additive synthesis using a linear scale instead of a decibel one. Can I normalize the results of the equation be adding a fixed number to all the harmonics with amplitudes greater than zero? Leslie ------------------------------------------------------------------------------------------ Re: Re: K5k Programing Made Easy Tuesday, 07-Jul-98 20:56:36 199.86.33.50 writes: Jen's formula for harmonic levels (above) does it a good way--divide every value by the maximum value, so the max is always 1 and the rest are relative. leiter ------------------------------------------------------------------------------------------ Re: Re: Re: K5k Programing Made Easy Tuesday, 07-Jul-98 22:39:00 209.160.126.77 writes: I use Jen's formula for my K5 because it uses a decibel scale for the harmonic's amplitude. For a linear scale, like my software program, I was just wondering if there was some other way. I wonder if we can get more cool waveforms from your equations by summing up some of them. I mentioned the saw and square my OB uses --what about summing up different pulse widths? I may mess around with my Oberheim to see if any useful ones come up. Leslie ------------------------------------------------------------------------------------------ Re: Re: Re: K5k Programing Made Easy Tuesday, 07-Jul-98 23:09:35 209.160.126.158 writes: Whoops! You answered my question and I didn't even realize it. Just divide the number by the maximum value; Got it! Thanks. Leslie ------------------------------------------------------------------------------------------ Re: K5k Programing Made Easy Sunday, 12-Jul-98 22:40:27 209.160.126.89 writes: Since I've been using your equations, I have tried to think of a way to combine them with what I know about calculating FM sidebands. This is what I've come up with so far: A(c+(m*n))=1/(c+(m*n)) A(abs(c-(m*n)))=1/(abs(c-(m*n))) Where A is the amplitude, c is the carrier, m is the modulator, and n is the number the modulator is multiplied by (n starts at 0 and increases by one each time the equations are used). There is two formulas because FM always generates sidebands in pairs. If you had the ratio 7:1, where 7 is the modulator and 1 is the carrier, you would get the following: A(1)=127 A(6)=106 A(8)=103 A(13)=97 A(15)=95 A(20)=92 A(22)=91 This is like a saw with many of its harmonics missing. It sounds like a bell. A ratio of 3:1 produces a hollow guitar like sound. Another variation of the formula could be: A(c+(m*n))=1/n A(abs(c-(m*n)))=1/n Here the carrier would be elimanated. A ratio of 2:5 might sound interesting. What would really be cool would be a formula for calculating a ratio like 22:3:1. This would be kinda hard because each sideband generated by 22:3 would become a modulator for 1. These formulas are not meant to calculate the amplitudes of the harmonics as they would be generated by FM, but rather make the FM spectra easier to use. Leslie ------------------------------------------------------------------------------------------ ------------------------------------------------------------------------------------------ Parametric Formant Filter Tool Friday, 03-Jul-98 07:57:14 194.172.230.108 writes: Hi all! Leiter's seven-knobs-for-all-real-life-waveforms formula is a cool idea. It can be called a parametric approach, the only way to really morph sounds, not to just cross-fade them. I am working on a similar thing for the Formant Filter. I have written a program (for Atari - sorry!) that calculates a resonator bank and transmits the data to the K5000. It has still a lot of parameters, but resonators are already somewhat closer to 'real life' than FF levels. Each resonator has an amplitude, a center frequency, and a bandwidth. There is an additional delay parameter in order to make the PWM emulation stuff we were talking about a while ago. A universal filter is connected in series with the resonator bank, with a few (not yet parametric) lowpass templates I have made. It is all in a very early state. The software does not even have a user interface. (Who wants to make it for me? :-) A demo patch will follow soon. Jens Groh ------------------------------------------------------------------------------------------ Re: Parametric Formant Filter Tool Saturday, 04-Jul-98 23:16:21 199.86.40.89 writes: That sounds good--what's the math? leiter ------------------------------------------------------------------------------------------ Re: Re: Parametric Formant Filter Tool Sunday, 05-Jul-98 10:50:47 195.232.55.162 writes: The resonator bank consists of a number of band-pass filters. I calculate the frequency responses of these filters and sum them up. A single band-pass filter with the resonance frequency fR , the resonance amplitude AR and the relative bandwidth D has the following frequency response: AR * D * i * (f / fR) / ( 1 + D * i * (f / fR) + (f / fR)2 ) Attention - this formula uses complex-numbers arithmetic! (Complex numbers represent both amplitude and phase - I refer to the literature.) I realize the delays T by additionally multiplying each resonator's frequency response with a "rotation factor": exp( i * T * f ) In order to get a real-valued result I take the absolute value of the complex amplitude after the summation. The frequencies are taken from the table in the K5000 manual. That's it, in principle. Jens Groh ------------------------------------------------------------------------------------------ ------------------------------------------------------------------------------------------ Site Update: Leiter's patch available now Tuesday, 27-Oct-98 00:06:52 208.254.230.161 writes: At long last I uploaded the patch that Leiter sent in. You can get it in the Patch Archive right here. Here is a description: SolinaPd: An analog string-synth style pad. The waveforms come from: A(n)=1/n + (1/n)(cos(Pi*n*X%)^21) where X is 34% for one and 25.5% for another. This came out of trial and error, looking for waveforms with the right "sawteeth". Kenji ------------------------------------------------------------------------------------------ ------------------------------------------------------------------------------------------ Is the K5000s capable of complex functions? Wednesday, 04-Nov-98 02:38:57 152.171.44.48 writes: Hello K5ker's! I too have noticed the sam ash sale. Being that I'm a comp sci student, I'm no stranger to math. I'm currently thinking of adding this synth to my Yamaha EX5, Alesis QSR, and Ensoniq ESQ1. Question is: can it do complex functions? say(This might not even be possible, just an arbitrary function out of my head)something to the effect of: f(x)=(cos x^2)*(tan x)/(PI/4)*(e^x) I do have one of those neat TI-85 calculators to see all the waves before I actually do them. And also, are a good bit of these kind of functions musical, or will only all but carefuly engineered ones sound like garbage? Thanx in advance. Btw, I'm part of the non-techno/not dance crowd, doing prog rock. Figure this might be something for that "different" sound, any thoughts? How does it do the non-dance stuff? Thanx in advance Wes ------------------------------------------------------------------------------------------ Re: Is the K5000s capable of complex functions? Wednesday, 04-Nov-98 03:01:45 209.160.126.113 writes: You should look a leiter's formula in the Message Board Digest under "Techniques and Formulae for Creating ADD Patches". My specialty has been to adapt FM synthesis to additive synthesis. I'm currently rewriting my Wavemaker program for the Atari to include more FM algorithms this time using feedback. You can find some discusssion in the digest on this subject as well. Leslie ------------------------------------------------------------------------------------------ Re: Is the K5000s capable of complex functions? Wednesday, 04-Nov-98 15:48:55 192.28.2.16 writes: >Question is: can it do complex functions? A perfect additive synth would be able make a Fourier reconstruction of any repeating waveform. The K5k has two shortcomings from this ideal. First, the partials all come out in the same phase. This is not a big problem musically, since the difference is usually inaudible. Second, each additive source (ADD) creates only partials that are in a harmonic series. Natural instruments generally have overtones that are near the harmonic series, but not always. Since you can use up to six ADDs in a patch, independently tuned, you can still combine a significant number of non-harmonic partials. But there are things you can't do, like stretch tuning. Still, it's the limitations that make the character of a synth; I think this one has a sweet sound because the overtones are often more in tune than in a natural instrument. >And also, are a good bit of these kind of functions musical, or will only all but carefuly engineered ones sound like garbage? "Careful" helps but "persistent" is better! Many elegant functions and beautiful looking waveforms sound like crap. Just keep throwing out the cheeze organs, irritating bells, and Simon game sounds and you'll find a lot of very musical functions. > Figure this might be something for that "different" sound, any thoughts? You're right! leiter ------------------------------------------------------------------------------------------ Re: Is the K5000s capable of complex functions? Wednesday, 04-Nov-98 23:19:09 209.207.189.165 writes: "A convergent Fourier series may be found for any bounded periodic function, f(x), that contains a finite number of maximum points, minimum points, and points of discontinuity within a given period a convergent Fourier. The series will be convergent at each point of x were f(x) is continuous and to the average of the left and right hand limits of f(x) at those points where f(x) is discontinuous." -Theorem attributed to PG Dirichlet I can't reproduce the proof for that but I think that in a word it means yes is the answer to your question. Basically, most periodic mathematical functions that can be defined in closed form will have a Fourier series representation that is suitable for use with the K5000. So yeah, if the TI-85 will graph it (watch out for jumps to infinity though: like when x= +- pi/2 for your function), then if you're clever enough you'll probably be able to persuade the K5000 to "sound" it. Actual acoustic signals introduce a new dimension of difficulty since they don't have a steady state (not in real life anyway), may not be strictly periodic and definitely aren't expressable in closed form. The best you can hope for here is probably a good approximation, if you're very clever. I'm not brave enough to tread this territory, not yet anyway! I'm not sure about the enharmonics, but I suspect that this results from applying the actual Fourier transform to a non-periodic signal and examining each value of the resulting continuous frequency spectrum. BTW, the actual transform isn't necessary for a strictly periodic signal. Although, non-periodicity is going to be a problem for the K5000, as well as any instrument that depends on strictly periodic harmonic oscillators to generate waveforms. Funny you should bring up the TI-85, mine spent the weekend on top of my K5000 (& it was on most of the time too!). jon ------------------------------------------------------------------------------------------ Re: Re: Is the K5000s capable of complex functions? Thursday, 05-Nov-98 08:11:01 164.107.171.51 writes: >Although, non-periodicity is going to be a problem for the K5000, as well as any instrument that depends on strictly periodic harmonic oscillators to generate waveforms. I believe you can get around this through clever use of un-looped envelopes, since you can apparently have a different envelope for each tone, or at least voice/band in the FF. Haven't tried it yet though--I just got my K5000s yesterday. Bob ------------------------------------------------------------------------------------------ Re: Re: Re: Is the K5000s capable of complex functions? Thursday, 05-Nov-98 12:22:21 209.207.189.209 writes: I agree, up to a point. The envelopes will help alleviate this to an extent, but their limited number of stages will quickly cause non-periodicity to become a problem again. I really love the K5000 but I'm kind of hoping that since they cancelled the K5000X they will produce a K6000 with 127 freely assignable env stages for each osc. With envelopes like that we might get alot further alot easier with replicating acoustic signals. jon ------------------------------------------------------------------------------------------ Re: Re: Re: Re: Is the K5000s capable of complex functions? Thursday, 05-Nov-98 13:52:42 192.86.155.91 writes: And while your at it make the machine such that the large numbers of sine waves it produces can be tuned however you want - with templates you can use to set them up in the harmonic series when desired. Now combine that with the 127 env stages.....mmmmmmm...... You would almost never need to make another synth again! Kenji ------------------------------------------------------------------------------------------ Re: Re: Re: Re: Re: Is the K5000s capable of complex functions? Thursday, 05-Nov-98 14:42:05 209.207.189.216 writes: Amen! Thats the right idea. This weekend, while I was tinkering with my K5000, I also decided to try additive techniques out with my Casio VZ synth. This turned out to be somewhat worthwhile since it gives you tunable oscillators (up to about 6 octaves) with eight stage envelopes (just like the CZ's envelopes). You only get eight oscs per sound but by layering you can get up to 32 oscs(4 note polyphony though). Maybe Casio and Kawai should collaborate and produce the KZ-6000, I'd buy one! jon ------------------------------------------------------------------------------------------ Re: Re: Re: Re: Re: Is the K5000s capable of complex functions? Thursday, 05-Nov-98 16:05:41 192.28.2.16 writes: You could implement non-harmonic overtones without getting too complicated by allowing "stretching", i.e. allowing the interval between harmonics to be greater than (or less than) the fundamental. That would make just one more number to set. I don't know what I'd do with 64 completely arbitrary harmonics! leiter ------------------------------------------------------------------------------------------ Re: Re: Re: Re: Re: Re: Is the K5000s capable of complex functions? Thursday, 05-Nov-98 16:41:09 209.160.126.140 writes: What would also be nice is the ability to use other waveforms besides sine. I have an old Digidesign program for my Atari. It allows you to use other waves like triangle, square, filtered noise, and white noise. What I've found is assigning white noise to one of the partials giving it a very short decay can help the attack of many sounds. Of course, some of the attack transients of the K5000 may do this trick for you. I also like the idea of stretch tuning the harmonics. From what I understand, the harmonics of an acoustic instrument like the guitar have harmonics which are sharp compared to the fundamental. For example, the first harmonic could be 440hz, the second 883hz, and the third 1326 and so on. Leslie ------------------------------------------------------------------------------------------ Re: Re: Re: Re: Re: Re: Re: Is the K5000s capable of complex functions? Thursday, 05-Nov-98 17:41:49 192.28.2.16 writes: Oh yeah--for stretched harmonics, you'd also have to stretch tune the keyboard. The stretch in the harmonics of strings is supposed to be due to string stiffness. Maybe that's why the K5K emulates a classical guitar better than a steel string guitar. Also, it's more important with shorter strings than longer strings. It is possible to do a stretch by taking, e.g., the fourth harmonic to be the fundamental, the 9th as the second, the 14th as the third, etc. I haven't gotten many good results yet, though, partly because you can't stretch tune the keyboard. Also, it's too much stretch. It tends to sound like a tubular bell--which is, I suppose, just a very stiff string. leiter ------------------------------------------------------------------------------------------ Re: Re: Re: Re: Re: Re: Is the K5000s capable of complex functions? Thursday, 05-Nov-98 21:43:56 209.207.189.217 writes: I'm afraid that I don't really understand stretch tuning, but it seems to me that it would be possible with tunable oscs. I would interested in hearing more about it, are there any resources about this (online or otherwise)? 64 tunable oscs would be a headache in alot of ways, I think that you would probably need a computer based helper app to assist with the programming chores. Come to think of it the K5000 could really use such an app. I don't think that programming the K5000 is unintuitive (it's as elegant as possible for an instrument that can generate any periodic waveform), but it is very time consuming. One other thing, the Casio VZ allows for using non-sine waveforms as building blocks(5 saws each with increasing harmonic content & noise). The VZ wasn't primarily designed to be an additive synth, but it's cool that you can do it. jon ------------------------------------------------------------------------------------------ ------------------------------------------------------------------------------------------