re: recent sine tone stuff

>Yes, and the value of the parameter I like to use (1%) was based on the
>performance in the optimal frequency range, a narrow one in the
middle-upper >register. The parameter rapidly increases outside that range.
Most musical >instuments produce harmonic partials in this range, so the 1%
can be assumed >to apply across a wide range of frequencies. But for sine
tones, one gets no >help from harmonic partials, so the relevant parameter
value will usually be >quite a bit higher.

Sounds wishy-washy to me. Maybe partials in a complex tone do not help, or
maybe they help a great deal more than simply allowing us to extend the
measurements made in the optimal frequency range to all frequency ranges.
Paul, this sounds very strange to me. I would expect that if partials
helped, they would increase resolution but leave the relative resolution at
different frequencies more or less unchanged. In other words, I would
expect that data about individual partials is thrown out at an early stage
in the listening system; the frequency-resolver probably only gets one
wave, which would carry the extra resolution provided by the partials from
an earlier stage.

We need to repeat Goldstein's experiment with complex tones.

-C.

>Or try tuning two sine generators, alternating so that you can't hear the
>interval harmonically, to a familiar interval. I think you'll be
astonished >as to how far off you'll be.

Malinowski once double-dared me to tune dyads on his science fair sine tone
generator box. Which I did with ease, thanks to distortion from the amp.
So, I had to try to tune the dyads with the volume real low, and then we
would try to check by turning up the volume and listening for beating.
This procedure wasn't conclusive, but again I did well, thanks to sum
tones, which is what I listen to when I tune pianos (which I should stop
doing, since it turns out horrible tunings).

-C.

Could someone please explain the science of sum and difference tones, and
how they relate to tuning of sine tones? I did use Csound to generate some
sine tone dyads. It was quite easy to tell the out of tune 3/2, even as
little as .1 hertz off (if the sample was long enough)

Darren

Carl Lumma wrote,

>I would expect that if partials
>helped, they would increase resolution but leave the relative resolution at
>different frequencies more or less unchanged. In other words, I would
>expect that data about individual partials is thrown out at an early stage
>in the listening system; the frequency-resolver probably only gets one
>wave, which would carry the extra resolution provided by the partials from
>an earlier stage. [. . .] We need to repeat Goldstein's experiment with
complex tones.

I would say go read Parncutt's book (_Harmony: A Psychoacoustical
Approach_). I don't think you're viewing these processes correctly. All the
partials are brought to bear on the central pitch processor. Parncutt's
models and experiments are not flawless but his book should give you a
recent view of the scientific understanding of these processes. Dichoic
experiments have been especially illuminating. It is essential to keep this
knowledge in mind when speculating like this. I need to look at this stuff
again too, it's been a really long time (well over five years).

I wrote,

>>Or try tuning two sine generators, alternating so that you can't hear the
>>interval harmonically, to a familiar interval. I think you'll be
>astonished >as to how far off you'll be.

Carl wrote,

>Malinowski once double-dared me to tune dyads on his science fair sine tone
>generator box. Which I did with ease, thanks to distortion from the amp.
>So, I had to try to tune the dyads with the volume real low, and then we
>would try to check by turning up the volume and listening for beating.
>This procedure wasn't conclusive, but again I did well, thanks to sum
>tones, which is what I listen to when I tune pianos (which I should stop
>doing, since it turns out horrible tunings).

I don't know what you mean about summation tones. But anyway, what if you
try tuning only the melodic interval, as I suggested?

Darren Burgess wrote,

>Could someone please explain the science of sum and difference tones, and
>how they relate to tuning of sine tones? I did use Csound to generate some
>sine tone dyads. It was quite easy to tell the out of tune 3/2, even as
>little as .1 hertz off (if the sample was long enough)

Unless you were listing through ultra-hi-fi equipment, it is unlikely you
were really listening to sine tone dyads. Sum and difference tones would be
created by the equipment. Even in the hi-fi case, your ear would create them
unless you turn down the sound to a very low level.

The Feynman Lectures on Physics give the best scientific (i.e., complete
with math) explanation of sum and difference tones. Read that if you can get
a hold of it.

Anyway, here's an example. Let's say you're comparing 660Hz and 660.1 Hz
against a 440Hz drone. The 660.1 will produce a 220.1 Hz first-order
difference tone against the 440. That will produce a second-order difference
tone of 219.9 Hz against the 440, so one would hear a .2 Hz beat at 220Hz.
Other beats would be produced at other frequencies. With the 660, no beating
is produced, as all sum and difference tones form an exact overtone series
over 220Hz, no matter what order you go up to.

Darren B:
>>Could someone please explain the science of sum and difference tones, and
>>how they relate to tuning of sine tones? I did use Csound to generate
some
>>sine tone dyads. It was quite easy to tell the out of tune 3/2, even as
>>little as .1 hertz off (if the sample was long enough)

Paul E:
>Unless you were listing through ultra-hi-fi equipment, it is unlikely you
>were really listening to sine tone dyads. Sum and difference tones would be
>created by the equipment. Even in the hi-fi case, your ear would create
them
>unless you turn down the sound to a very low level.

Actually they are middle of the road PC speakers with a sub woofer, so I was
expecting that they would distort the tones.

>
>Anyway, here's an example. Let's say you're comparing 660Hz and 660.1 Hz
>against a 440Hz drone. The 660.1 will produce a 220.1 Hz first-order
>difference tone against the 440. That will produce a second-order
difference
>tone of 219.9 Hz against the 440, so one would hear a .2 Hz beat at 220Hz.
>Other beats would be produced at other frequencies. With the 660, no
beating
>is produced, as all sum and difference tones form an exact overtone series
>over 220Hz, no matter what order you go up to.

So, said another way, a first order difference tone results from a
subtraction of the two primary frequencies (660.1-440=220.1) and a second
order difference tone results from subtraction of a difference tone from the
primary tone (440-220.1=219.9).

Summation tones would also be possible:

440+220.1 = 660.1 (resulting in a .1 Hz beat, and 2 Hz beat)
440+219.9 = 559.9 (resulting in a .1 Hz beat, and 2 Hz beat)
440+660.1 = 1100.1 (no near invertal conflicts, no beating?)

Is it possible to continue in this way through third and higher orders,
producing an exact harmonic series as you described above?

What are the practical limits of continuing to add a subtract multiple order
sum and difference tones?
How far would human perception take this? Human perception combined with
sub-"ultra hifi" audio equipment? Under what conditions? What about in an
outdoor environment? (The carillon will be amplified through outdoor PA's)
This is another way of asking: How far I should go when examining and
composing for the aural effects that will be created by the Carillon? (of
course actual experience, when the instrument is complete, will prevail)

>From: Carl Lumma <clumma@nni.com>
>
>>Or try tuning two sine generators, alternating so that you can't hear the
>>interval harmonically, to a familiar interval. I think you'll be
>astonished >as to how far off you'll be.
>
>Malinowski once double-dared me to tune dyads on his science fair sine tone
>generator box. Which I did with ease, thanks to distortion from the amp.
>So, I had to try to tune the dyads with the volume real low, and then we
>would try to check by turning up the volume and listening for beating.
>This procedure wasn't conclusive, but again I did well, thanks to sum
>tones, which is what I listen to when I tune pianos (which I should stop
>doing, since it turns out horrible tunings).
>
What tunings were you tuning with sum tones, and why are they horrible?

George
>
>>You do not need web access to participate. You may subscribe through
>email. Send an empty email to one of these addresses:
> tuning-subscribe@onelist.com - subscribe to the tuning list.
> tuning-unsubscribe@onelist.com - unsubscribe from the tuning list.
> tuning-digest@onelist.com - switch your subscription to digest mode.
> tuning-normal@onelist.com - switch your subscription to normal mode.

>Is it possible to continue in this way through third and higher orders,
>producing an exact harmonic series as you described above?

Exactly, but . . .

>What are the practical limits of continuing to add a subtract multiple
order
>sum and difference tones?
>How far would human perception take this? Human perception combined with
>sub-"ultra hifi" audio equipment? Under what conditions?

Basically, the human ear tends to mostly create first- and second-order
combination tones, although at loud volumes fifth or sixth order combination
tones (of which there are many) can be heard. A transistor amp with
distortion will essentially create combination tones up to order infinity,
since the clipping function would require an infinite-order polynomial to
describe (this would make sense to you if you've read the Feynman). A tube
amp responds more smoothly so fewer orders of combination tones come into
the picture, but they can do so quite strongly. There's much more to this
subject, ask an audio engineer . . .