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If we look at the harmonic content of complex waveforms, and compare them to the tricks used to create 'analog synth' waveforms on the DX7, there are some ways to work around the differences.? Disclaimer:? this will NOT perfectly duplicate the results; but it might get close enough on some sounds.

-? A sawtooth wave is the fundamental, plus 1/n * each harmonic (1/2 of the 2nd, harmonic, 1/3 of the 3rd, etc.)

- A square wave is the fundamental plus 1/n * the odd harmonics only.

- A triangle wave is similar to the square, but only 1/n^2 * the odd harmonics.

- A pulse wave is similar to the square, but the magnitude of the harmonics is more complicated; and every so often, a harmonic is missing.? As an example, a 20% pulse is 1/5 of the length of each waveform, so the 5th harmonic is missing.

So, we need to find waves in the complex table whose harmonics match these waveforms; then simulate them with two or more sine operators:

-? A 1x modulator will approximate a sawtooth wave, with care taken to keep the modulation level to a reasonable amount.? This is similar to the effect of W4, or W2+W3.

A 2x modulator will make a reasonable square or triangle wave, similar to W2.

A 3x modulator will simulate a 20-30% pulse, along the lines of W5 or W6.

One can use these relations to substitute two (or three) sines on a 6-op synth for one complex wave on a 4-op 'deluxe' like the DX100 or TX81z.? The results may not be exactly the same, but might be 'good enough.'

What I've always wondered is if there's a way to create those additional
waveforms using a carrier/modulator pair so straight sine wave instruments
could get in the neighborhood.

Sent from my HAL 9000 in transit to Jupiter


-----Original Message-----
From: [email protected] [mailto:[email protected]] On Behalf Of Martin
Tarenskeen
Sent: Tuesday, June 15, 2021 6:32 AM
To: Jeremy Bernstein <jeremy.d.bernstein@...>
Cc: YamahaDX <[email protected]>
Subject: Re: [YamahaDX] The 4OP to DX7 Conversion Project



On Tue, 15 Jun 2021, Jeremy Bernstein wrote:

Thanks so much for your work on this!

A naive question: how, if at all, have you handled the additional

waveforms on the TX81Z/DX11?

Hi,

The additional waveforms that were introduced with the TX81Z are ignored. 
In general not everyting could be converted faithfully. There are quite some
bigger and smaller differences between the DX7 and the 4-op FM family of
synths. But I hereby invite everyone to do something useful and interesting
with the 2 unused operators that are left :-)