Re: [tuning] Digest Number 945

Hey gang-

Dave Keenan said
"Perhaps we can even agree that JI music using ratios of
integers greater
than say 50 is a very different kind of JI to that using
ratios of integers
less than say 20 (as consonances)."

I am inclined to call any music that relies solely on
integer ratios just intonation. Just because the human ear
cannot distinguish a 5/4 from its 53tet approximation in the
majority of practical settings does not contraindicate the
use of 5/4, and likewise a 341/247 is not another ET entity
because the ear cannot distinguish between them. Could we
perhaps use modifiers, for instance "practical JI" to
distinguish audible JI? In other words, let the simplest
definition stand, then make distinctions based on practical
considerations.

--
John Starrett
"We have nothing to fear but the scary stuff."
http://www-math.cudenver.edu/~jstarret/microtone.html

Paul Erlich wrote:

> In other words, multiplying two sine waves is the same as adding the
> difference tone and sum tone. And since our ears decompose what we
> hear into a _sum_ of sine waves, we hear the sum tone and difference
> tones; we can't hear the original two tones that we multiplied.

Is this the basis of Frequency Modulation synthesis?

--
David J. Finnamore
Nashville, TN, USA
http://personal.bna.bellsouth.net/bna/d/f/dfin/index.html
--

--- In tuning@egroups.com, "David J. Finnamore" <daeron@b...> wrote:

> > In other words, multiplying two sine waves is the same as adding the
> > difference tone and sum tone. And since our ears decompose what we
> > hear into a _sum_ of sine waves, we hear the sum tone and difference
> > tones; we can't hear the original two tones that we multiplied.
>
> Is this the basis of Frequency Modulation synthesis?

It's actually the basis of Amplitude Modulation -- FM is a bit more complicated.

>Paul Erlich wrote:
>
>> In other words, multiplying two sine waves is the same as adding the
>> difference tone and sum tone. And since our ears decompose what we
>> hear into a _sum_ of sine waves, we hear the sum tone and difference
>> tones; we can't hear the original two tones that we multiplied.
>
>Is this the basis of Frequency Modulation synthesis?
>
As Paul pointed out, frequency modulation does not come from multiplying
waves together. However, I would qualify his answer that this type of
modulation (multiplication) is sometimes more specifically refered to as
ring modulation. That is, amplitude modulation in which the modulator is
allowed to go below zero, creating phase reversal in the resultant wave. In
"classic" amplitude modulation, the modulation at maximum varies the
carrier from full amplitude to zero amplitude, i.e. no phase reversal. This
creates only one summation tone and one difference tone. By contrast, ring
modulation and frequency modulation create multiple combination tones:
frequency of the carrier +/- frequency of the modulator, frequency of the
carrier +/- 2 times the frequency of the modulator, etc. I should point out
that James Dashow has done computer music pieces in which the tuning system
was based on the combination tones resulting from the frequency modulation
used.

Bill

^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
^ Bill Alves email: alves@hmc.edu ^
^ Harvey Mudd College URL: http://www2.hmc.edu/~alves/ ^
^ 301 E. Twelfth St. (909)607-4170 (office) ^
^ Claremont CA 91711 USA (909)607-7600 (fax) ^
^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^

Bill Alves wrote,

>By contrast, ring
>modulation and frequency modulation create multiple combination tones:
>frequency of the carrier +/- frequency of the modulator, frequency of the
>carrier +/- 2 times the frequency of the modulator, etc.

That's not quite correct. Ring modulation is ideally only a quadratic
function, so cubic and higher-order combination tones would not in general
be produced. Frequency modulation, meanwhile, results, in general, in
_inharmonic_ relationships between the frequencies, generally involving
factors of pi, and not expressible as sum or difference tones of integer
multiples of the carrier or modulator.

Frequency modulation results in sidebands with a frequency of the carrier
plus or minus a multiple of the modulator:

.... c-3m c-2m c-m c c+m c+2m c+3m ....

The relative amplitude of these sidebands is determined by besselfunctions
of the modulation index (relative modulation depth).

Kees
www.kees.cc

> -----Original Message-----
> From: Paul H. Erlich [mailto:PERLICH@ACADIAN-ASSET.COM]
> Sent: Wednesday, November 22, 2000 2:12 PM
> To: 'tuning@egroups.com'
> Subject: RE: [tuning] Digest Number 945
>
>
> Frequency modulation, meanwhile, results, in general, in
> _inharmonic_ relationships between the frequencies, generally involving
> factors of pi, and not expressible as sum or difference tones of integer
> multiples of the carrier or modulator.
>

>Frequency modulation results in sidebands with a frequency of the carrier
>plus or minus a multiple of the modulator:

> .... c-3m c-2m c-m c c+m c+2m c+3m ....

Hmm . . . well I guess the pi comes in phase modulation rather than
frequency modulation . . . sorry.

--- In tuning@egroups.com, John Starrett <jstarret@c...> wrote:
> I am inclined to call any music that relies solely on
> integer ratios just intonation. Just because the human ear
> cannot distinguish a 5/4 from its 53tet approximation in the
> majority of practical settings does not contraindicate the
> use of 5/4, and likewise a 341/247 is not another ET entity
> because the ear cannot distinguish between them. Could we
> perhaps use modifiers, for instance "practical JI" to
> distinguish audible JI? In other words, let the simplest
> definition stand, then make distinctions based on practical
> considerations.

I realise this is a bit old and you may have "changed your tune" by
now, but others may still be thinking that way.

Isn't it a bit ridiculous to have a supposed distinction between
musical scales that is both inaudible and impractical?

We have a responsibility to the future, not to cut them off from the
past, by unnecessarily redefining terms. I think I have established
that the definition I am proposing is simply the original definition
that got lost for a while.

Just intonation is and always has been an audible property. Maybe not
always audible by untrained listeners, but audible nonetheless. In
case anyone missed it:

From The Shorter Oxford English Dictionary on Historical Principles.
Just
/Mus./ in /just interval/, etc. : Harmonically pure; sounding
perfectly in tune 1811.

Regards,
-- Dave Keenan