K5synth

>As for the Atari, I was able run both Leslie's Wavemaker - again very
>  nice (I like the FM section, it looks very useful.  BTW, is there a
>way to "slow down" (i.e. step through) the wave drawer?)

Um... not sure. I'm embarrassed to say that I lost the source code to the 
program years ago (I wrote the program when I was just starting out as a 
programmer and was careless), and I haven't looked at programming the Atari 
in probably 5 years.

>Also, I have some spectrum/waveforms in hard copy from the PPG
>wavetables, the K1, and the Nord Lead.

Man, I would love to see those!

>It would be nice to resynth
>some of these forms "by-hand".  I read here that to translate linear
>spectra amplitude to the K5 you have to do a transformation.  Can
>anyone (i.e. Leslie)tell me what the exact equation is to do the
>transformation?

My formula is based on several assumptions:

First, that the K5's dynamic range is around 72db. This may be way off, btw. 
Once source I found puts the partials' dynamic range at around 37.5db 
(http://home.swipnet.se/~w-90557/20_k5.html).

Second, a 10db increase in sound pressure represents a doubling of the 
perceived loudness 
(http://www.audiovideo101.com/dictionary/dictionary.asp?dictionaryid=128).

Third, that the K5's scale is decibel based. This isn't hard to prove. Just 
program your standard sawtooth into the K5 using a linear scale, and you'll 
hear that it is way too dark.

And fourth, that a doubling in linear amplitude of a partial represents a 
doubling in its perceived loudness. In other words, using the linear scale, 
a partial with the amplitude of 10 is twice as loud as a partial with the 
amplitude of 5.

So I worked out a table (excuse the HTML tags if you are reading this in 
plain text) to illustrate the conversion:

<pre>
db         linear
0             1
10           2
20           4
30           8
40           16
50           32
60           64
70           128
72           147
</pre>

I assume that the K5 has 12 bit resolution (again, this could be off), so 
that gives me 72.24719896 decibel range. Dividing this by the number of 
steps the K5 has, 99, and I get 0.729769686db per step and a maximum linear 
amplitude of 149.5744446.

Say we have a set of partials we want to convert to the K5. To make this 
easy, we'll limit the range of the partials' amplitudes to [0, 1.0]. 
Converting this to the K5 gives us:

k5Amp = Log2(149.5744446 * partial) * 10 / step

There are a few assumptions that I've made that could be off. However, in 
practise, I've found that this formula works very well. So I'm satisfied 
that my formula is a good working approximation of what is needed to convert 
linear values to the K5, at least until someone with more knowledge can 
provide a better formula. :-)

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