[sdiy] Generating acyclic waveforms?

[cheater cheater]

I consulted a fellow composer and he says that pretty much all western
instruments have different tuning starting the 6th harmonic of their
central pitch. So the harmonic series looks like this:

C C G C E G (Bb) C...

but the Bb is out of tune with the ieal equal temperatment tuning (and
I assume the following C too, but not sure). I didn't get to know
which way it's out of tune (sharp or flat), because he's busy dumping
MIDI. Those composers, sheesh.. ;-)

Also according to Wikipedia the Gamelan has a very stretched harmonic series.

I think it might be the same situation that causes gongs and other
such stuff to have such a very inharmonic sound, but I'm very far out
of my expertise here.

D.

On Sun, Mar 21, 2010 at 22:23, cheater cheater <cheater00 at gmail.com> wrote:
> It happens in all accoustic instruments to some degree. No accoustic
> instrument adheres to the ideal string and generally ideal resonator
> equations. Even wind instruments have that, because even if the air
> can generate a perfect resonator, the instrument's body will have that
> effect and, by leeching the accoustic power from the resonator, will
> generate even more anharmonic content.
>
> D.
>
> On Sun, Mar 21, 2010 at 22:19, Tom Wiltshire <tom at electricdruid.net> wrote:
>> Does anyone (physicists?) on the list know whether this harmonic stretching
>> occurs only with strings, or do similar things happen in wind instruments?
>> reeds?
>>
>> What I'm really asking is whether this is a 'string' effect or an 'acoustic'
>> effect.
>>
>> Thanks,
>> Tom
>>
>>
>>
>> On 21 Mar 2010, at 16:58, cheater cheater wrote:
>>
>>> Most people here know that in piano timbre the partials are sine waves
>>> that are not spaced like in synth waveforms. That is, in the
>>> synthesizer, if the note's fundamental frequency is F, then harmonics
>>> will be at 1F, 2F, 3F, 4F etc. In a stretched-harmonic waveform, the
>>> frequencies will for example be of the form 1sF, 2sF, 3sF, 4sF, and so
>>> on, where s is the stretching factor. For s=1 we have the usual
>>> harmonic series. For s which is not an integer and not a specially
>>> chosen rational number, we have a probability of 100% of generating an
>>> acyclic waveform. Of course, the spacing of harmonics in the piano is
>>> more complex than that, but this is the first approximation.
>>
>>
>