question re: eliminating beats

Hi Gene, or anyone else who can help,

I'm in the process of creating a piano sound using
additive synthesis.

Today i've been working on C1, the lowest C on the piano.
My synthesized sound is very good, except that it has
beats that a real piano timbre doesn't have.

The sound i created for this note uses many sine-wave
partials, and all of them are tuned somewhat sharper
than integer overtones. The beating is coming from this
mistuning, but there are so many partials that i have
no idea how to find it and fix it.

Here's the data:

frequency of C1 = ~32.70319566 Hz

one wavelength = ~0.030578051 second

beat time = ~0.37147375 second

# beats per second = ~2.691980254

# waves per beat = ~12.14837873

Hopefully from that you can help me find which sets
of partials are causing the beating, and hopefully
if i retune them slightly i'll get rid of it.

-monz
http://tonalsoft.com
Tonescape microtonal music software

--- In tuning-math@yahoogroups.com, "monz" <monz@t...> wrote:

> Here's the data:
>
> frequency of C1 = ~32.70319566 Hz
>
> one wavelength = ~0.030578051 second
>
> beat time = ~0.37147375 second
>
> # beats per second = ~2.691980254
>
> # waves per beat = ~12.14837873

I thought i should mention that that's pretty close
to 8 beats in 3 seconds ... in case that helps.

It's exactly 8 beats in 2.97179 seconds.

-monz
http://tonalsoft.com
Tonescape microtonal music software

Hi Monz,

I'd love to help . . .

--- In tuning-math@yahoogroups.com, "monz" <monz@t...> wrote:
>
> Hi Gene, or anyone else who can help,
>
>
> I'm in the process of creating a piano sound using
> additive synthesis.
>
> Today i've been working on C1, the lowest C on the piano.
> My synthesized sound is very good, except that it has
> beats that a real piano timbre doesn't have.
>
> The sound i created for this note uses many sine-wave
> partials, and all of them are tuned somewhat sharper
> than integer overtones. The beating is coming from this
> mistuning, but there are so many partials that i have
> no idea how to find it

Find it? What are you trying to find?

> and fix it.
>
>
> Here's the data:
>
> frequency of C1 = ~32.70319566 Hz
>
> one wavelength = ~0.030578051 second
>
> beat time = ~0.37147375 second
>
> # beats per second = ~2.691980254
>
> # waves per beat = ~12.14837873

How did you get such accurate data on what you claim you can hear but
not explain?

> Hopefully from that you can help me find which sets
> of partials are causing the beating, and hopefully
> if i retune them slightly i'll get rid of it.

It's not likely this data by itself could be of any help for the
question, though I may be missing something. Why don't you even say
how you stretched the partials, other than "somewhat"? Don't you have
any data on that?

Most likely you're hearing a second-order beat of some kind. Real
pianos will do this too, as will any spectrum distorted a bit from
harmonicity. Also, real piano strings can produce *first-order*
beating, when the string vibrates with slightly different frequencies
in two orthogonal planes of vibration.

Hi Paul,

--- In tuning-math@yahoogroups.com, "wallyesterpaulrus" <perlich@a...>
wrote:

> > The sound i created for this note uses many sine-wave
> > partials, and all of them are tuned somewhat sharper
> > than integer overtones. The beating is coming from this
> > mistuning, but there are so many partials that i have
> > no idea how to find it
>
> Find it? What are you trying to find?

The the tuning of the partials which is causing the beating.

-monz
http://tonalsoft.com
Tonescape microtonal music software

--- In tuning-math@yahoogroups.com, "monz" <monz@t...> wrote:
>
> Hi Paul,
>
> --- In tuning-math@yahoogroups.com, "wallyesterpaulrus" <perlich@a...>
> wrote:
>
> > > The sound i created for this note uses many sine-wave
> > > partials, and all of them are tuned somewhat sharper
> > > than integer overtones. The beating is coming from this
> > > mistuning, but there are so many partials that i have
> > > no idea how to find it
> >
> > Find it? What are you trying to find?
>
>
> The the tuning of the partials which is causing the beating.

Replied offlist.

>> The the tuning of the partials which is causing the beating.
>
>Replied offlist.

Can you guys post the result back here?

-Carl

--- In tuning-math@yahoogroups.com, Carl Lumma <ekin@l...> wrote:
>
> >> The the tuning of the partials which is causing the beating.
> >
> >Replied offlist.
>
> Can you guys post the result back here?
>
> -Carl

Turned out the frequency resolution with which the analysis was done
was only equal to, well, that beat frequency that was so prominently
audible.

>> >> The the tuning of the partials which is causing the beating.
>> >
>> >Replied offlist.
>>
>> Can you guys post the result back here?
>
>Turned out the frequency resolution with which the analysis was done
>was only equal to, well, that beat frequency that was so prominently
>audible.

Analysis? I thought this was a digital additive synth, where
the input frequencies are precisely known...?

-Carl

--- In tuning-math@yahoogroups.com, Carl Lumma <ekin@l...> wrote:
>
> >> >> The the tuning of the partials which is causing the beating.
> >> >
> >> >Replied offlist.
> >>
> >> Can you guys post the result back here?
> >
> >Turned out the frequency resolution with which the analysis was done
> >was only equal to, well, that beat frequency that was so prominently
> >audible.
>
> Analysis? I thought this was a digital additive synth, where
> the input frequencies are precisely known...?

Exactly. They're precisely known because they can be chosen freely. How
were they chosen? They were copied from a (poor) analysis of a real
piano sound.

At 06:49 PM 12/24/2005, you wrote:
>--- In tuning-math@yahoogroups.com, Carl Lumma <ekin@l...> wrote:
>>
>> >> >> The the tuning of the partials which is causing the beating.
>> >> >
>> >> >Replied offlist.
>> >>
>> >> Can you guys post the result back here?
>> >
>> >Turned out the frequency resolution with which the analysis was done
>> >was only equal to, well, that beat frequency that was so prominently
>> >audible.
>>
>> Analysis? I thought this was a digital additive synth, where
>> the input frequencies are precisely known...?
>
>Exactly. They're precisely known because they can be chosen freely. How
>were they chosen? They were copied from a (poor) analysis of a real
>piano sound.

Ah! Thanks! I've got three of those on my Kawai additive synth.
They don't beat, but they do sound poor. :)

-Carl