Re: [higher-prime translated out of academese]

I would like to add my comments to the following tutorial.

Joe Monzo <monz@juno.com> wrote:

> Someone on the Mahler List had a question about my reference
> to 'higher-prime', and my explanation to him ran to such
> depth that I thought tuning newbies could benefit, so I'm
> sending a copy here. As always, criticism is welcome.

> A sound which does not produce a specific pitch, for example,
> a cymbal crash or beating on a snare-drum, is one that does
> not vibrate air molecules at a specific frequency, but rather,
> vibrates the molecules in motions that are more-or-less
> random. This is referred to technically as 'white noise'.

Technically, white noise is *completely* random with a flat spectrum (every Hz
of bandwidth of the spectrum has the same amount of energy). I believe most
all listeners would be able to discriminate between a cymbal roll, snare drum
roll, and white noise. Another significant type of acoustical noise is called
"pink" noise, in which each *octave* has the same amount of energy (spectrum
falls off at 6 dB per octave). Pink noise is psychoacoustically perceived as
a more balanced spectrum - quite like the sound of a large waterfall.

> On the other hand, a sound which produces a specific pitch is
> one that vibrates air molecules at a *specific* frequency, as
> in our famous tuning-fork standard, A-440. This simply means
> that the note which we ordinarily call 'A' (above 'middle-C')
> vibrates air molecules back and forth at the rate of 440 cycles
> per second. A cycle is simply the waveform of that particular
> sound, which never varies (or varies so slightly that we
> don't perceive a change in pitch) during the course of the
> sound.

Periodic waveforms are only one class of sounds which have clearly discernable
pitch. Purely random noise processed through a narrow-band filter (the
subject of my master's degree psychoacoustic experiment) and very rapidly
decaying transient waveforms (such as woodblocks) have readily perceived pitch
properties. I think this just points out that the ear is much more of a
*spectrum* analyzer than a *time-domain* analyzer.

> but the important point is that the numerical relationships
> *always* exist, as long as the sound source is periodic.

or has a clearly perceived pitch (see above).

> The 'perfect 5th' in rational tuning theories is 3:2.
> The 'perfect 4th', its inverse or 'complement', is 4:3.

No! 3:2 is a *pure* or *just* 5th, 4:3 is a *pure* or *just* 4th. A *perfect*
5th or 4th is one which is neither chromatically diminished or augmented.

> I simply use the term 'sonance' to describe the whole
> continuum, with the understanding that absolute consonance
> means the 1:1 (unison) ratio, absolute dissonance is an
> undefinable ratio which is too complex to comprehend
> (perhaps it is 'white noise'), and the sonance of all
> other musical ratios falls somewhere in between.

I believe that consonance is defined as the subjective perception of
"blending" of a pair of tones (which may or may not be pure), and is
quantified by pair ranking of all possible intervals (Is interval A more or
less consonant than interval B?).

> PYTHAGOREAN TUNING
> ------------------
>
> Pythagorean tuning (named after the ancient Greek philosopher)
> is based on a series of 'perfect 5ths' or 'perfect 4ths'.

Change 'perfect' to 'pure' or 'just'(see above).

> This is because the 12th pitch in the series is very close
> to the original starting pitch, about 23 cents (or approximately
> 1/4 of a semitone, or 1/8-tone) ....

Actually much closer to 1/9 of a Pythagorean tone (9/8).

> What this means acoustically is that the waveforms of the
> two pitches will coincide at every 64th cycle of the lower
> pitch and every 81st cycle of the higher pitch.

The waveforms *never* completely coincide because they have different time
periods, and probably different shapes.
Again, modeling the ear as a spectrum analyzer, it is more pertinent to say
that the 64th harmonic of the upper tone coincides with the 81st harmonic of
the lower tone.

> As these
> numbers are too high for the brain to comprehend their
> relationship during listening, this is not a very consonant
> sound.

Using the spectrum analyzer model, one would say that these harmonics (for
tones around middle-C) are above the frequency limit of human hearing.
Perhaps more importantly, the subjective difference tone is not a subharmonic
or near-subharmonic of either incident tone.

Fred Reinagel

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Get your own FREE, personal Netscape WebMail account today at http://webmail.netscape.com.

Fred Reinagel wrote,

>Perhaps more importantly, the subjective difference tone is not a
subharmonic
>or near-subharmonic of either incident tone.

This is a poor criterion for consonance. For example, most of us would agree
that 5:2 (just major tenth) is a consonant interval, yet the difference
tone, 3, is not a subharmonic of either 5 or of 2.

and I always thought that white noise was a playback of an audio signal with
the peaks and troughs of the waves inverted... when added to the original
signal it creates silence. Popular Mechanics/Science were talking about
"white noise mufflers" to reduce sound without affecting the exhaust system
like standard mufflers do. Have I messed up the terminology, or is this too
called "white noise".

Thanks,
Alex

----Original Message Follows----
From: Fred Reinagel <freinagel@netscape.net>
Reply-To: tuning@onelist.com
To: tuning@onelist.com
Subject: Re: [[tuning] higher-prime translated out of academese]
Date: 4 Nov 99 15:59:24 EST
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I would like to add my comments to the following tutorial.

Joe Monzo <monz@juno.com> wrote:

> Someone on the Mahler List had a question about my reference
> to 'higher-prime', and my explanation to him ran to such
> depth that I thought tuning newbies could benefit, so I'm
> sending a copy here. As always, criticism is welcome.

> A sound which does not produce a specific pitch, for example,
> a cymbal crash or beating on a snare-drum, is one that does
> not vibrate air molecules at a specific frequency, but rather,
> vibrates the molecules in motions that are more-or-less
> random. This is referred to technically as 'white noise'.

Technically, white noise is *completely* random with a flat spectrum (every
Hz
of bandwidth of the spectrum has the same amount of energy). I believe most
all listeners would be able to discriminate between a cymbal roll, snare
drum
roll, and white noise. Another significant type of acoustical noise is
called
"pink" noise, in which each *octave* has the same amount of energy (spectrum
falls off at 6 dB per octave). Pink noise is psychoacoustically perceived
as
a more balanced spectrum - quite like the sound of a large waterfall.

> On the other hand, a sound which produces a specific pitch is
> one that vibrates air molecules at a *specific* frequency, as
> in our famous tuning-fork standard, A-440. This simply means
> that the note which we ordinarily call 'A' (above 'middle-C')
> vibrates air molecules back and forth at the rate of 440 cycles
> per second. A cycle is simply the waveform of that particular
> sound, which never varies (or varies so slightly that we
> don't perceive a change in pitch) during the course of the
> sound.

Periodic waveforms are only one class of sounds which have clearly
discernable
pitch. Purely random noise processed through a narrow-band filter (the
subject of my master's degree psychoacoustic experiment) and very rapidly
decaying transient waveforms (such as woodblocks) have readily perceived
pitch
properties. I think this just points out that the ear is much more of a
*spectrum* analyzer than a *time-domain* analyzer.

> but the important point is that the numerical relationships
> *always* exist, as long as the sound source is periodic.

or has a clearly perceived pitch (see above).

> The 'perfect 5th' in rational tuning theories is 3:2.
> The 'perfect 4th', its inverse or 'complement', is 4:3.

No! 3:2 is a *pure* or *just* 5th, 4:3 is a *pure* or *just* 4th. A
*perfect*
5th or 4th is one which is neither chromatically diminished or augmented.

> I simply use the term 'sonance' to describe the whole
> continuum, with the understanding that absolute consonance
> means the 1:1 (unison) ratio, absolute dissonance is an
> undefinable ratio which is too complex to comprehend
> (perhaps it is 'white noise'), and the sonance of all
> other musical ratios falls somewhere in between.

I believe that consonance is defined as the subjective perception of
"blending" of a pair of tones (which may or may not be pure), and is
quantified by pair ranking of all possible intervals (Is interval A more or
less consonant than interval B?).

> PYTHAGOREAN TUNING
> ------------------
>
> Pythagorean tuning (named after the ancient Greek philosopher)
> is based on a series of 'perfect 5ths' or 'perfect 4ths'.

Change 'perfect' to 'pure' or 'just'(see above).

> This is because the 12th pitch in the series is very close
> to the original starting pitch, about 23 cents (or approximately
> 1/4 of a semitone, or 1/8-tone) ....

Actually much closer to 1/9 of a Pythagorean tone (9/8).

> What this means acoustically is that the waveforms of the
> two pitches will coincide at every 64th cycle of the lower
> pitch and every 81st cycle of the higher pitch.

The waveforms *never* completely coincide because they have different time
periods, and probably different shapes.
Again, modeling the ear as a spectrum analyzer, it is more pertinent to say
that the 64th harmonic of the upper tone coincides with the 81st harmonic of
the lower tone.

> As these
> numbers are too high for the brain to comprehend their
> relationship during listening, this is not a very consonant
> sound.

Using the spectrum analyzer model, one would say that these harmonics (for
tones around middle-C) are above the frequency limit of human hearing.
Perhaps more importantly, the subjective difference tone is not a
subharmonic
or near-subharmonic of either incident tone.

Fred Reinagel

____________________________________________________________________
Get your own FREE, personal Netscape WebMail account today at
http://webmail.netscape.com.

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<< text3.html >>

>Popular Mechanics/Science were talking about
>"white noise mufflers" to reduce sound without affecting the exhaust system

>like standard mufflers do. Have I messed up the terminology, or is this
too
>called "white noise".

There is only one definition of white noise. A "white noise muffler" would
invert the peaks and troughs of an incoming white noise signal, so its
output would cancel out the noise.

There may be more to it than the consonance between harmonics. Your ear is
a non-linear device and it has both harmonic and intermodulation distortion.

Have you ever heard the demonstration of what happens when you play two
pure sing waves that are sepaarated by a perfect, 2:3 ratio fifth? You
"hear" the fundamental. There is a demo of this on a Wenday Carlos disk
(secrets of syntheis??) and it was mind blowing to me. I don't know if
this is psychological or physiological or both.

Bob G.

At 03:59 PM 11/4/99 EST, you wrote:
>From: Fred Reinagel <freinagel@netscape.net>
>
>I would like to add my comments to the following tutorial.
>

___deleted stuff---

>Using the spectrum analyzer model, one would say that these harmonics (for
>tones around middle-C) are above the frequency limit of human hearing.
>Perhaps more importantly, the subjective difference tone is not a subharmonic
>or near-subharmonic of either incident tone.
>
>Fred Reinagel
>
>
>____________________________________________________________________
>Get your own FREE, personal Netscape WebMail account today at
http://webmail.netscape.com.
>
>>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.
>
>

Bob G. wrote,

>There may be more to it than the consonance between harmonics. Your ear is
>a non-linear device and it has both harmonic and intermodulation
distortion.

>Have you ever heard the demonstration of what happens when you play two
>pure sing waves that are sepaarated by a perfect, 2:3 ratio fifth? You
>"hear" the fundamental. There is a demo of this on a Wenday Carlos disk
>(secrets of syntheis??) and it was mind blowing to me. I don't know if
>this is psychological or physiological or both.

Both. There is the difference tone, which is physiological, and the virtual
fundamental, which is psychological. There is a good body of research on
both in the psychoacoustical literature. The two don't necessarily agree in
pitch.