See pictures
Shouldn't the first harmonic of cosine just be a 90 degrees out of phase sine instead of a constant ?
Message fro both sinesum and cosinesum

cosine and sinesum correspond to the 'real' and 'imaginary' parts of the 'real' fourier series respectively. since there is no imaginary part for frequency 0 (dc) I guess it's skipped for sinesum. see the help file of [rfft~] for some more info. (beyond that you'd have to start learning about dsp)

You will also notice that if N is the power-of-2 table size, the (N/2th) coefficient of sinesum is mostly noise, whereas the ((N/2)+1)th coefficient of cosinesum is Nyquist.

@seb-harmonik.ar said:

cosine and sinesum correspond to the 'real' and 'imaginary' parts of the 'real' fourier series respectively. since there is no imaginary part for frequency 0 (dc) I guess it's skipped for sinesum. see the help file of [rfft~] for some more info. (beyond that you'd have to start learning about dsp)

It's only skipped for cosinesum (lower table ) and not the sinesum (upper table) , the screesnhot shows the first partal for sinesum and a DC constant for cosinesum
( sinesum and cosinesum and their $1 $2 etc partials are combined in the same message )

@gentleclockdivider said:

It's only skipped for cosinesum (lower table ) and not the sinesum (upper table) , the screesnhot shows the first partal for sinesum and a DC constant for cosinesum

This means that the cosinesum preserves the zero-frequency component, while sinesum skips the zero-frequency component.

sin(0x) == 0, so there is no need to keep it.

cos(0x) == 1, so if it's skipped, then it becomes impossible to synthesize a wavetable that has a DC offset.

That's probably the reason for the different behavior. It's a bit surprising but not unreasonable.

hjh