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The Eat at Joe's Kawai K5000 Message Board Digest
Multiple Source Harmonics


non-series harmonics
 Thursday, 20-Nov-97 04:54:06

      Message: writes:

      Just a thought (I saw somebody talking about it in the newsgroups some time ago)
      - you could get all kinds of wierd harmonics into the series by just using
      more than one ADD sound. The example I saw explained was a harmonic detuning made
      by using three different ADD sources, staggering the harmonics
      between them (each source has only every third harmonic, all starting on a different
      harmonic), and then detuning the different sets of harmonics (eg: source 1
      has harmonics 1, 4, 7, 10, etc. Source 2 has harmonics 2, 5, 8, 11, etc. Source 
      3 has harmonics 3, 6, 9, 12, etc. Source 2 has fine tuning -7, Source 3 has
      fine tuning +7). The original post said that this technique creates a really *FAT*
      sound, but I haven't tried it yet. Theoretically, this type of detuning should be
      something you can ONLY do on an additive synthesizer shouldn't it?

      Further exploring this technique, couldn't you also generate all kinds of strange
      out-of-series harmonics by adding more sources starting at different notes,
      but not low enough to interfere with the fundamental (and thus your perception of
      the pitch of the note and make you hear a chord instead of a harmonic).

      Hopefully I'll be able to make some interesting sounds this weekend and put them
      up on the site. 


Re: non-series harmonics
Thursday, 20-Nov-97 20:12:50 writes:

     I wrote that. The second patch I did that way didn't turn out fat, but it did have
     a kind of "real" instrument sound. The detuned harmonics seem to break the
     sweet, clean sound of the K5k.

     I like your idea of mixing a note with harmonics of another note. I'll try to post
     something too. 


Re: non-series harmonics
Friday, 21-Nov-97 04:52:18 writes:

     Well, I made my first sound with this technique. I noticed that the basic sawtooth
     wave comprised of three parts (three sources with staggered harmonic
     series'), while it should sound the same before detuning, does seem to have a
     bit of a sharper edge, and a more metallic quality to it. I really like that tone
     better to start from. It's a shame it eats up three times the polyphony.

     I'll put a basic patch with the three staggered ADD sources up on my site so people
     can play with this without having to edit the harmonic levels from scratch.
     Won't have any modulation or filtering, and only a little chorus and reverb.

     Anyway. The new sound is fun. The different overtone series' are wiggling around
     with resonance and creating lots of space sounds. All of the knobs except
     velocity and decay effect the sound in some way, so this one is fun to tweak
     with......enjoy the new patch (it is definately much more sonically complex than
     the old patches). 


Some Rambling Theory About the Fifth Interval
 Thursday, 08-Jan-98 22:44:30

      Message: writes:

      I've sent in another patch, "fifth", which is more of an experiment than a patch
      for playing. The patch is essentially two saw waves a fifth apart, but it uses
      only one ADD generator to make two apparent notes.

      Here's the theory: When you play an interval of a fifth, for example a C3 and a
      G3, all of the harmonics that appear coincide with the harmonics of another
      note, the note an octave below the tonic, or C2 in this example. The C3 contains
      every second harmonic of the C2, starting with number two. The G3
      contains every third harmonic of the C2, starting with number three. So the C3
      and G3 can be constructed from one ADD generator playing just the C2
      note: Take out the odds and you have the C3, now put back (or boost) every
      third harmonic and you've added the G3.

      So, when you play a fifth interval at C3, (that's a "power chord" if you play
      it on a guitar), it "suggests" a note an octave below, the C2. 

      However, it does more than just suggest the C2, it can generate the fundamental
      frequency of the C2. Any two notes played together will interfere with each
      other and generate a third perceived note. The frequency of the third note is
      the difference between the frequencies of the first two notes. This is what causes
      the "beating" when two notes are out of tune with each other; if they're out of
      tune by 3 hertz they generate a "beat" with a frequency of three hertz. When
      you're talking about tones in the harmonic series, the difference in frequency
      between any two adjacent harmonics is the frequency of the fundamental. So
      every pair of adjacent harmonics creates a beat that supports the fundamental.
      When the fundamental is missing, these beats still occur at the frequency of
      the fundamental and seem to "recreate" the fundamental. (For example, I have a
      patch on an analog synth with three saws tuned to the 7th, 9th and 10th
      harmonic of a low note, the note three octaves below the note you play. It can
      send a pretty strong 4 hertz beat thru 6 ½ inch speakers; the speakers only
      have to be able to carry the harmonics. Sounds like an engine idling. Big engine.)

      There's more interesting stuff in that direction -- like the fact that, because
      square and triangle waves have only the odd harmonics, the distance between any
      two harmonics is an even multiple of the fundamental, so all of the beat
      frequencies fall only on the even harmonics, which are the missing harmonics. I
      think this gives those waveforms more of a "hollow," "dead" or "wooden" sound. I'm
      putting some patches together that use this.

      Back to the fifth -- besides missing the fundamental of the C2, the fifth interval
      is also missing other harmonics; 5, 7, 11, 13, etc. These happen to include the
      three strongest dissonant harmonics: 7, 11 and 13, which makes the C3+G3 interval
      a kind of "non-dissonant" C2.

      Guess that's enough . . . my brain feels lighter now. 


Re: Some Rambling Theory About the Fifth Interval
Friday, 09-Jan-98 10:26:35 writes:

     Try searching the WWW for the phrase "missing fundamental", for example:

     I can't promise that your brain won't feel heavy again then, but maybe you'll
     learn something useful from the scientists...

     Jens Groh 


Re: Some Rambling Theory About the Fifth Interval
Friday, 16-Jan-98 07:20:11 writes:

     Hey, Leiter, drowned in theory? 
     Did you try to introduce a nonlinearity? This actually generates the difference
     frequencies in the spectrum (not only as an envelope). Introduce an overdrive or
     distortion in the effect chain and listen how the subharmonic appears.

     Jens Groh 


Re: Re: Some Rambling Theory About the Fifth Interval
Friday, 16-Jan-98 13:53:59 writes:

     A couple questions about energy:

     If you have the sum of a sine wave at frequency 2x and another at 3x, there is
     no energy at 1x, but there is a beat frequency there. So if it hits something that
     resonates at 1x, like the appropriate part of your inner ear, it causes vibration
     at 1x. The energy must come out of the two frequencies that are "really"
     there--how is it distributed?

     Same question if you run the wave through a non-linear circuit, like a passive
     clipper. How is the energy in the original wave distributed in the end product,
     which now includes the fundamental that was missing before?

     Also, a math question: Whats the difference between A) the sum of 2x and 3x, and
     B) 3x amplitude-modulated by 1x? On inspection, the amplitude profile is
     similar, it looks like the maxima and minima are in the same places, but the zero
     crossings are shifted. 


Re: Re: Re: Some Rambling Theory About the Fifth Interval
Monday, 19-Jan-98 10:31:20 writes:

     Maybe our auditory system contains a sort of "envelope follower". This would be a
     nonlinear system! 

     Any (time-independent) nonlinearity can be expressed as: 

     A + Bx + Cx^2 + Dx^3 + ... 

     For easier understanding of what happens, take only the quadratic ( x^2 ) part
     and apply it to a sum-of-sinusoids signal ( sin(a) + sin(b) ): 

     (sin(a) + sin(b))^2 = sin(a)*sin(a) + 2*sin(a)*sin(b) + sin(b)*sin(b) .

     Now you have some product-of-sinusoids signals. They can be transformed again
     into sum-of-sinusoids signals: 

     sin(a) * sin(b) = 0.5*cos(a-b) - 0.5*cos(a+b) .

     and so on. Here are the new frequencies! That is, the difference and the sum. 
     You can use the product formula to answer your third question. Recall (see
     board digest: "AM"): Amplitude modulation is: 

     sin(a) * (1 + m*sin(b)) . (m=0...1)

     Here you have again: sin(a)*sin(b) . Thus, if a = 3x and b = 1x, the result
     will contain 3x and 2x _and_4x_! 

     Jens Groh