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I found a Puredata patch that calculates Chebyshev Polynomials!

I first tried using the output of the array to quickly get 1024 plot points but it totally failed.

The waveform represented in the GUI for the array isn't the same as the output. I did get a really awesome ramp waveform that I'm going to use.

Next, I recorded the each polynomial at 46.87hz to get exactly 1024 samples and the waveforms sound amazing!

As you suspected the aliasing is greatly diminished. I'll post user waveform txt files tomorrow. In the meantime poke around the Pd file.

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Great stuff!

I'm doing a bunch of Chebyshev tables in Mathematica + the ones in Daniel Arfib's paper. Here are some quick tests at 1024 samples => T2 to T13 with graphic plots of the table function. I'll try a few at smaller sizes at some point too. Note that T11 has a big click [which I like of course!] as interpreted by Preen, and I think this is something to do with how the import works. ?? It will be interesting to hear the differences in table sizes too.

EDIT

Refs to Arfib's paper =>

this is a free pdf, but is an early version with lot of handwritten bits =>

https://quod.lib.umich.edu/i/icmc/bbp2372.1978.009/1/--digital-synthesis-of-complex-spectra?page=root;size=100;view=textand an even earlier one here =>

https://quod.lib.umich.edu/i/icmc/bbp2372.1977.001/--digital-synthesis-of-complex-spectra?rgn=main;view=fulltextthe full paper ended up in AES, but its behind the dreaded academic paywall =>

http://www.aes.org/e-lib/browse.cfm?elib=3178with a slim chance of being able to maybe view online here for free? =>

https://www.researchgate.net/publication/243764314_Digital_Synthesis_of_Complex_Spectra_by_means_of_Multiplication_of_Non-linear_Distorted_Sine_Waves+

I just spotted in my little example preset that OP1 is set to keybd, which would also normally be set to fixed for classic waveshaping. Having it track the keyboard will push it more or less away from zero hertz, depending on tuning table.

Which also reminded me that there is a little section on low frequency carriers in Chowning & Bristow, FM Theory and Applications: By Musicians for Musicians p97 - 102.

EDIT 2

Marc Le Brun's classic AES paper Digital Waveshaping Synthesis is also behind paywall, have not located a readable version of this online =>

http://www.aes.org/e-lib/browse.cfm?elib=3212I've got copies of both Arfib and Le Brun's papers, from photocopies I made in the 90s, but as they are copyrighted I obviously can't scan & upload them..