sine waves baaaaaad

Upon consultation with my personal trainer... or rather personal
tuning trainer, who happens to also have the name Paul Erlich, I will
state with temerity that sine waves are, indeed, not the optimal
waveform for tuning experiments.

My own personal experience is that they are so soft one can't really
hear what pitch they are, to begin with... Try to tune any other
instrument with these, and one will soon see what I mean.

My trainer says this has something to do with the Classical
Uncertainty Principle, but I am a little uncertain about this myself,
so I will say no more about it at present...

JP

Joseph Pehrson wrote:

>Upon consultation with my personal trainer... or rather personal >tuning trainer, who happens to also have the name Paul Erlich, I will >state with temerity that sine waves are, indeed, not the optimal >waveform for tuning experiments.
>
>My own personal experience is that they are so soft one can't really >hear what pitch they are, to begin with... Try to tune any other >instrument with these, and one will soon see what I mean.
>
>My trainer says this has something to do with the Classical >Uncertainty Principle, but I am a little uncertain about this myself, >so I will say no more about it at present...
>

Pure sine waves have no overtones so you can hear the exact relationship
of the intervals. No overtones to distort the results!

--
* David Beardsley
* microtonal guitar
* http://biink.com/db

On Sunday 21 December 2003 04:09 pm, Joseph Pehrson wrote:
> Upon consultation with my personal trainer... or rather personal
> tuning trainer, who happens to also have the name Paul Erlich, I will
> state with temerity that sine waves are, indeed, not the optimal
> waveform for tuning experiments.
>
> My own personal experience is that they are so soft one can't really
> hear what pitch they are, to begin with... Try to tune any other
> instrument with these, and one will soon see what I mean.
>

What would be better than pure sine waves then? I've been using CSound to
generate fixed pitch sine waves, then burn them to CD to make a "tuning
reference" CD for some of my instruments. I have noticed it can be difficult
to know exactly when the pitches match up when trying to tune instruments to
it. Would putting a few odd and even harmonics on it help?

Jay

--- In tuning@yahoogroups.com, Jay Rinkel <jrinkel@h...> wrote:
>>>>
> What would be better than pure sine waves then? I've been using CSound to
> generate fixed pitch sine waves, then burn them to CD to make a "tuning
> reference" CD for some of my instruments. I have noticed it can be difficult
> to know exactly when the pitches match up when trying to tune instruments to
> it. Would putting a few odd and even harmonics on it help?
>
> Jay >>>>

Often, to tune the 4th string -- which is C3 when the tonic is C4 -- of the tanpura, we use the self-generated 5th partial (and/or the 10th?), the major third, to tune C3.

Regards,
Haresh.

>What would be better than pure sine waves then? I've been using
>CSound to generate fixed pitch sine waves, then burn them to CD to
>make a "tuning reference" CD for some of my instruments. I have
>noticed it can be difficult to know exactly when the pitches match
>up when trying to tune instruments to it. Would putting a few odd
>and even harmonics on it help?

Sine waves are great for tuning to for precisely the reason you
mention. Note that the context of this thread was completely
different. We were looking for timbres that would make it easy
to hear pitches of isolated *melodic* (as opposed to harmonic)
tones. For this complex tones with natural harmonics are best,
because the ear/brain uses all the partials to help it determine
the pitch. That's the theory anyway.

-Carl

on 12/25/03 12:16 PM, Carl Lumma <ekin@lumma.org> wrote:

>> What would be better than pure sine waves then? I've been using
>> CSound to generate fixed pitch sine waves, then burn them to CD to
>> make a "tuning reference" CD for some of my instruments. I have
>> noticed it can be difficult to know exactly when the pitches match
>> up when trying to tune instruments to it. Would putting a few odd
>> and even harmonics on it help?
>
> Sine waves are great for tuning to for precisely the reason you
> mention.

Not in my experience. For tuning my pipe organ I found that tuning with a
timbre that is somewhere in the same ballpark as the timbre of the pipe made
it much easier to hear the beats. In fact it was possible to distinguish
sharp from flat based on the harmonic pattern of the beats, which is a real
boon. The waveforms were not symmetrical in +/- time and so neither was the
beat. Thus I could hear whether the beat was going forward or backward,
once I got the hang of it. But at the point I discovered this my organ was
almost tuned already, so I don't have a lot more to say about it.

Using sine waves didn't work well at all, particularly when tuning timbres
that have little fundamental in them.

But of course this whole approach assumes no inharmonicity in the instrument
being tuned.

-Kurt

> Note that the context of this thread was completely
> different. We were looking for timbres that would make it easy
> to hear pitches of isolated *melodic* (as opposed to harmonic)
> tones. For this complex tones with natural harmonics are best,
> because the ear/brain uses all the partials to help it determine
> the pitch. That's the theory anyway.
>
> -Carl

>>> What would be better than pure sine waves then? I've been using
>>> CSound to generate fixed pitch sine waves, then burn them to CD to
>>> make a "tuning reference" CD for some of my instruments. I have
>>> noticed it can be difficult to know exactly when the pitches match
>>> up when trying to tune instruments to it. Would putting a few odd
>>> and even harmonics on it help?
>>
>> Sine waves are great for tuning to for precisely the reason you
>> mention.
>
>Not in my experience. For tuning my pipe organ I found that tuning
>with a timbre that is somewhere in the same ballpark as the timbre of
>the pipe made it much easier to hear the beats. In fact it was
>possible to distinguish sharp from flat based on the harmonic pattern
>of the beats, which is a real boon.

Wow that is a boon. You'll have to show me how to do that.

>The waveforms were not symmetrical in +/- time

The waveform of an organ pipe must be...

>But of course this whole approach assumes no inharmonicity in the
>instrument being tuned.

Tuning forks produce a sine wave I'm told (it sure sounds like it),
but usually they are sounded against a resonator like a table.
Here I would expect the (driven) resonator to contribute some
partials, but IIRC Paul says they don't really (I may remember
incorrectly -- time to look up that bit with Daniel Wolf about
gamelan resonators...).

-Carl

on 12/25/03 10:39 PM, Carl Lumma <ekin@lumma.org> wrote:

>>>> What would be better than pure sine waves then? I've been using
>>>> CSound to generate fixed pitch sine waves, then burn them to CD to
>>>> make a "tuning reference" CD for some of my instruments. I have
>>>> noticed it can be difficult to know exactly when the pitches match
>>>> up when trying to tune instruments to it. Would putting a few odd
>>>> and even harmonics on it help?
>>>
>>> Sine waves are great for tuning to for precisely the reason you
>>> mention.
>>
>> Not in my experience. For tuning my pipe organ I found that tuning
>> with a timbre that is somewhere in the same ballpark as the timbre of
>> the pipe made it much easier to hear the beats. In fact it was
>> possible to distinguish sharp from flat based on the harmonic pattern
>> of the beats, which is a real boon.
>
> Wow that is a boon. You'll have to show me how to do that.

Just try it. Tune against a synth patch with a lot of harmonics. Or tune
one synth patch against another. Listen to the dynamic timbre changes of
the beat as you adjust the pitch on the + and - sides.

It may not work well with just *any* timbre. I can't remember whether it
worked on all types of pipes or not. Come visit and find out.

>> The waveforms were not symmetrical in +/- time
>
> The waveform of an organ pipe must be...

I'm not sure what you are saying. But I was saying that the waveform of the
organ pipes in question is not such that

f(t - t0) = f(t0 - t)

no matter how you choose t0.

But it is possible that this does not actually matter. I *think* the
combination waveform (loosely speaking here) will not be symmetric unless
both the pipe and the tuning waveform are symmetric. I can tell you that
the tuning waveform I used was not.

-Kurt

>>> The waveforms were not symmetrical in +/- time
>>
>> The waveform of an organ pipe must be...
>
>I'm not sure what you are saying. But I was saying that the waveform
>of the organ pipes in question is not such that
>
> f(t - t0) = f(t0 - t)
>
>no matter how you choose t0.

Right, but organ pipes are harmonic, excluding attack and decay
transients. If they are harmonic, they're periodic. If they're
periodic, musn't they obey the above equality? I guess it depends
on what f() is.

>But it is possible that this does not actually matter. I *think* the
>combination waveform (loosely speaking here) will not be symmetric
>unless both the pipe and the tuning waveform are symmetric. I can
>tell you that the tuning waveform I used was not.

What kind of waveform was that?

-Carl

on 12/26/03 5:25 PM, Carl Lumma <ekin@lumma.org> wrote:

>>>> The waveforms were not symmetrical in +/- time
>>>
>>> The waveform of an organ pipe must be...
>>
>> I'm not sure what you are saying. But I was saying that the waveform
>> of the organ pipes in question is not such that
>>
>> f(t - t0) = f(t0 - t)
>>
>> no matter how you choose t0.
>
> Right, but organ pipes are harmonic, excluding attack and decay
> transients. If they are harmonic, they're periodic. If they're
> periodic, musn't they obey the above equality? I guess it depends
> on what f() is.

Periodic means they have what you might call "periodic symmetry" which is
something that repeats from "left to right" so to speak, whereas I am
talking about something that has left-right mirror symmetry, like a sine
wave or a square wave or a (symmetrical) triangle wave. A sawtooth wave
does *not* have such symmetry.

-Kurt

--- In tuning@yahoogroups.com, Kurt Bigler <kkb@b...> wrote:

> I *think* the
> combination waveform (loosely speaking here) will not be symmetric
unless
> both the pipe and the tuning waveform are symmetric.

But it sort of seems that if *either* waveform is symmetric, the beat
pattern will be symmetric, as it's a 'convolution' of sorts. Remind
me to investigate this more fully when I get a chance -- plotting a
few examples should suffice to move this issue from the speculative
to the concrete realm.

> Pure sine waves have no overtones so you can hear the exact
relationship
> of the intervals. No overtones to distort the results!

If the exact relationship of the intervals one wishes to hear is a
Just relationship, then harmonic overtones would seem to be helpful
if not absolutely necessary. For harmonies, one reason is that one
can use beats to judge whether the Just relationship is exact or not.
For another example, when two sine waves are tuned to a melodic
octave so that it sounds most 'in tune', most like an 'equivalence',
the octave will not be a Just 2:1 ratio, but will be stretched by
more than a couple of cents -- especially in the extreme registers.
Try it! This effect is greatly attenuated when you use timbres with
harmonic overtones.

Paul,

on 12/30/03 11:59 AM, Paul Erlich <paul@stretch-music.com> wrote:

> --- In tuning@yahoogroups.com, Kurt Bigler <kkb@b...> wrote:
>
>> I *think* the
>> combination waveform (loosely speaking here) will not be symmetric
> unless
>> both the pipe and the tuning waveform are symmetric.
>
> But it sort of seems that if *either* waveform is symmetric, the beat
> pattern will be symmetric, as it's a 'convolution' of sorts. Remind
> me to investigate this more fully when I get a chance -- plotting a
> few examples should suffice to move this issue from the speculative
> to the concrete realm.

Since waveforms are harder to type, I will use three examples in which a
couple of integer "waveforms" with frequencies 1/5 and 1/4 are mixed to
create a beat waveform with a frequency of 1/20:

example 1:
12341234123412341234 waveform 1 (5 cycles) - not symmetric (sawtooth)
12345123451234512345 waveform 2 (4 cycles) - not symmetric (sawtooth)
24686357574646853579 sum (1 cycle) - not symmetric

example 2:
12321232123212321232 waveform 1 (5 cycles) - symmetric (triangle)
12345123451234512345 waveform 2 (4 cycles) - not symmetric (sawtooth)
24666355574446833577 sum (1 cycle) - not symmetric

example 3:
12321232123212321232 waveform 1 (5 cycles) - symmetric (triangle)
12321123211232112321 waveform 2 (4 cycles) - symmetric (near triangle)
24642355334444433553 sum (1 cycle) - symmetric

Only in the third case with both inputs symmetric does a symmetric sum
result. The center of symmetry is either around the 6 or around the middle
4 in the series of five 4's.

While this is not a proof, the fact that the example includes a full range
of representative phase relationships, it is to me pretty close to an
intuitive proof.

Also, what the above proves is that in an exact-ratio scenario in which
there is such a thing as a *full* waveform period in the beat, that the
*entire* beat waveform is symmetrical. This at least explains my original
thinking, but perhaps does not directly address the real question of whether
the momentarily perceived beat pattern will be symmetric or not. I believed
there was a connection between the two questions, but perhaps I am wrong,
and I think it is too late for me to do the full analysis.

Now I see your point about convolution. The real issue here is harmonic
cancellation and perhaps that is another way to address the question. When
will there be a symmetric pattern of harmonic cancellation?

I might be tuning the organ again soon, so I will have more real info to
share. Chances are Carl will also hear it.

-Kurt