The Eat at Joe's Kawai K5000 Message Board Digest
Creating a Sawtooth Wave


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Those nonlinear rates and levels
Friday, 27-Feb-98 03:48:44 

     130.67.0.118 writes:

     At one time I believe I saw one of you - maybe it was Kenji - post information
     about the nonlinear nature of harmonics levels and how you had taken this into
     account in making a sawtooth wave. I cannot find that in the digest, so maybe
     the poster could point me to the right place or repeat the explanation, please?

     The thing is, the envelopes we get from books or PC sound tools need to be
     translated into K5000 terms, and for this purpose we need to know the precise
     nature of the rates and levels. The rates of the harmonic envelopes appear
     to be logarithmic. For a given level, the time needed to reach it seems to be
     proportional to 2^(-Rate/8). (Anyone know this for sure?) However, the level
     also needs to be part of this formula for the time, and it is obviously nonlinear.
     That's why I ask for that formula posted previously.

     Tore

     tl001@online.no 

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Re: Those nonlinear rates and levels
Friday, 27-Feb-98 04:36:09 

     194.172.230.108 writes:

     Hi Tore!
     It's here: (Let's see if the following becomes a link; otherwise, you will find
     it "by hand".)   Things that Should be in the Manual (Details!) 

     0.75 dB per step means, as formula:
     amplitude = max_amplitude * 2^((level_value-127)/8) 

     Or:
     level_value = 127 + 8 * log2(amplitude/max_amplitude) 

     To create a sawtooth wave, the amplitude spectrum must be inversely proportional
     to the harmonic number, that is: 
     level_value = 127 - 8 * log2(harmonic_number)

     For those who are missing the base-2 logarithm on their pocket calculator - use this:
     log2(...) = ln(...) / ln(2)

     Have fun with your additive sawtooth!

     Jens Groh 


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