general responses to Ray Tomes and Joe Monzo

Many of the opinions of Ray Tomes have been expressed by others in the past
and have garnered deep debates on this forum. Hopefully Joe Monzo will have
the complete archives up soon so anyone can look at how these discussions
evolved. I would like first of all to summarize some important physical and
psychophysical points, since these are not a matter of opinion as are the
points of musical theory (although the latter has a long history with which
I suggest Mr. Tomes begin to acquaint himself!)

First, subharmonics can be said to exist in natural sounds but the
subharmonic series can't. When a musical tone is accompanied by a
subharmonic, it is always a case of the subharmonic being the true
fundamental, over which a certain subset of the partials is so prominent
that one of the harmonics sounds like a fundamental. A true subharmonic
series would imply two or more relatively prime undertones of the
fundamental existing at the same time, and this does not occur in acoustic
sounds. Note: one should not draw _any_ conclusions directly from this about
the appropriateness of various chords in music. Music is a human construct,
so it is necessary (but not sufficient) that all known psychoacoustics (how
we perceive sound) _must_ be interposed between an analysis of sounds and
prescriptions for musical theory. There is much of primary importance here
that is being totally ignored in recent discussions (except Dave Keenan who
has kindly repeated some of my points). I refer you to my old postings.

Second, beating and difference tones ("ghost tones") are two completely
different phenomena. It is totally incorrect to treat them as one and the
same. (1) One is a rhythm and the other is a pitch. Although there are
certainly circumstances where a physical stimulus with a certain fundamental
frequency evokes both the pitch corresponding to that frequency and a rhythm
at that frequency, there is absolutely no evidence that this is musically
preferable to the hearing of a pitch corresponding to one frequency and a
rhythm at another. Absolutely none. (2) Beating arises in the ear due to
frequencies that are too close to be fully resolved -- so an average
frequency is heard with an amplitude modulation at a rate equal to the
difference between the frequencies (for a derivation of this, see, for
example, the Feynman Lectures on Physics). This modulation rate can be
within the (extreme lower part of the) range of audible frequencies but does
not evoke the slightest hint of the pitch corresponding to that frequency.
Difference tones arise due to non-linearities in the auditory system --
another section of the Feynman lectures shows how, in the case of a
quadratic (simplest possible) nonlinearity, two pitches will create the
impression of six: the two pitches themselves, the difference tone, the sum
tone, and the octave above each of the two original pitches. The human
ear-brain system is more complex so additional combination tones, such as
the difference between one tone and the octave above the other tone, are
important. Note: the existence of such combination tones gives a hint as to
one reason why otonal (harmonic-series based) chords are preferable to
utonal (subharmonic-series based) chords. All the combination tones of one
harmonic series belong to that same harmonic series, while the combination
tones of a subharmonic series will tend to fall outside that series and
densely fill frequency space.

Third, the relative masses of subatomic particles are neither integer ratios
nor constants. They are functions of energy. The experiments which determine
these ratios are designed, and their result interpreted, according to
quantum theory. It is fallacious to take these results out of that context
and interpret them according to a 19th century, classical mechanistic
mindset. Of course, this mindset continues to be promulgated by virtually
all academia and intelligensia (outside of physicists themselves and those
who would try to draw connections with Eastern philosophies) so it is hardly
surprising that this sort of thing goes on.

One musical point for Ray Tomes: You are incorrect in your assumptions about
composers' intentions and wandering tonics. Many classical pieces have been
analyzed in just intonation and almost invariably they have a net downward
drift in JI, sometimes by as much as half an octave. It is quite clear,
though, that the musical effect of the pieces depends on them returning to
the same actual pitch when the notation indicates a return to the home key
(which it does in perhaps 99% of Baroque, Classical, and Romantic pieces).
Although a solution involving a constant, upward, compensating drift could
certainly help in many situtations, it is difficult to see any grounds on
which this could be deemed preferable to the adaptive JI schemes that John
A. deLaubenfels (sp?) and I discussed.

There is so much more to reply to, but I just can't do the time anymore. One
point to Joe Monzo:

Your idea of tuning the ii chord in a major key as 27:32:40 is the worst
tuning idea I've heard in a long time. I think I speak for every composer
who's used the ii chord in a major key since the existence of major keys
(~400 years). In particular, composers in Mozart's time were fond of themes
which were (modally) transposed up a step, in which case the ii chord
functions a bit like the tonic of a temporary relative dorian. Actually, in
classical harmonic theory, it is not the ii chord but the iii chord that is
sometimes considered a non-functional triad in a major key and is often
analysed as an altered chord of some sort. As I am fond of pointing out,
your (and Schoenberg's) conception of the major scale has virtually no
support in the entire history of music.

I wish to indicate my general agreement with Paul Erlich's excellent recent
posting. The physics and mathematics sufficient for the description of
music are classical (with perhaps, following Penrose, some allowance for
the issue of timing in perception). As the old saw goes, for all intents
and purposes, music is reckoned in terms of flat earth coordinates. Any
venture to invoke the post-classical needs to be held to a high standard of
necessity.

Two small points of objection, though. First, concerning subharmonics.
There is some evidence that the spectra of the attack portions of idiophone
sounds are simultaneously subharmonic. This is clearly an exceptional and
transient phenomenon, but one that does violate the notion that there are
no subharmonic series in nature. Second, concerning Joe Monzo's tuning of
the minor triad on ii as 27:32:40. While I agree that this is highly
unlikely in Major, I find it to be quite possible in minor. Terry Riley has
used this triad to good effect.

Daniel Wolf wrote,

>I wish to indicate my general agreement with Paul Erlich's excellent recent
>posting. The physics and mathematics sufficient for the description of
>music are classical (with perhaps, following Penrose, some allowance for
>the issue of timing in perception). As the old saw goes, for all intents
>and purposes, music is reckoned in terms of flat earth coordinates. Any
>venture to invoke the post-classical needs to be held to a high standard of
>necessity.

I agree with this but said nothing to that effect in my original posting. While I am gratified that you found my posting excellent, your statement above does not corroborate any of its points. Perhaps you misunderstood me?

>Two small points of objection, though. First, concerning subharmonics.
>There is some evidence that the spectra of the attack portions of idiophone
>sounds are simultaneously subharmonic. This is clearly an exceptional and
>transient phenomenon, but one that does violate the notion that there are
>no subharmonic series in nature.

Mildly interesting; more info would be appreciated.

>Second, concerning Joe Monzo's tuning of
>the minor triad on ii as 27:32:40. While I agree that this is highly
>unlikely in Major, I find it to be quite >possible in minor. Terry Riley has
>used this triad to good effect.

Where would this triad occur in the minor scale? Certainly not the tonic, I would hope!

Message text written by INTERNET:tuning@onelist.com
<>
<I agree with this but said nothing to that effect in my original posting.
While I am gratified <that you found my posting excellent, your statement
above does not corroborate any of its <points. Perhaps you misunderstood
me?

I did not misunderstand you, I simply added some remarks of my own spurred
on by recent frustration at encountering terms like 'quantum' in the tuning
list.

<>Two small points of objection, though. First, concerning subharmonics.
<>There is some evidence that the spectra of the attack portions of
idiophone
<>sounds are simultaneously subharmonic. This is clearly an exceptional and
<>transient phenomenon, but one that does violate the notion that there are
<>no subharmonic series in nature.
<
<Mildly interesting; more info would be appreciated.

This is more than mildly interesting to those of us working with
idiophones! I posted an extended review last summer of a recent book with
very detailed spectrographic analyses.

<>Second, concerning Joe Monzo's tuning of
<>the minor triad on ii as 27:32:40. While I agree that this is highly
<>unlikely in Major, I find it to be quite >possible in minor. Terry Riley
has
<>used this triad to good effect.
<
<Where would this triad occur in the minor scale? Certainly not the tonic,
I would hope!

I wrote: 'the minor triad on ii'. Could that have been any clearer?

The triad on the second degree of the minor mode, especially in the context
of the ascending 'melodic' minor scale, has a composite, almost bitonal
character which one hears to good effect in this tuning.

Sorry for the delay in replying. I have been away for 2 weeks.
Expect a flood of posts as I catch up.

Paul H. Erlich [TD188.8]
>the relative masses of subatomic particles are neither integer ratios

Neither are the masses of isotopes integer ratios and yet they are
considered to be made up of an integer number of nucleons. The reason
is the same, that there are ever more subtle energies (other waves)
which are called "binding energy".

>nor constants.

I am not sure what you mean by this. Please explain?

>They are functions of energy. The experiments which determine
>these ratios are designed, and their result interpreted, according to
>quantum theory. It is fallacious to take these results out of that context
>and interpret them according to a 19th century, classical mechanistic
>mindset. Of course, this mindset continues to be promulgated by virtually
>all academia and intelligensia (outside of physicists themselves and those
>who would try to draw connections with Eastern philosophies) so it is hardly
>surprising that this sort of thing goes on.

The masses of particles are nothing other than their energies (as
expressed in E=mc^2) and energy in quantum physics is directly
proportional to frequency (E=hf in Planck's law). Therefore any
comparison of the masses of particles is actually a comparison of
frequencies. Steven Weinberg has said that frequency should be
considered the fundamental unit. There is nothing eastern of non-QM
about this, it is quite standard physics as measured in x-ray
diffraction patterns etc.

>One musical point for Ray Tomes: You are incorrect in your assumptions about
>composers' intentions and wandering tonics. Many classical pieces have been
>analyzed in just intonation and almost invariably they have a net downward
>drift in JI, sometimes by as much as half an octave.

I am unsure as to what you are saying here. Are you saying that turning
a piece into JI commonly (and wrongly) causes this drift in many pieces?
If so, I suggest that this depends very strongly on the algorithm used
in the process. I dealt with some considerations in this regard a
couple of weeks ago and it is clear that slightly different algorithms
can jump to different notes under the same circumstances and introduce
ratios such as 80/81 etc.

>It is quite clear,
>though, that the musical effect of the pieces depends on them returning to
>the same actual pitch when the notation indicates a return to the home key
>(which it does in perhaps 99% of Baroque, Classical, and Romantic pieces).

Agreed.

>Although a solution involving a constant, upward, compensating drift could
>certainly help in many situtations, it is difficult to see any grounds on
>which this could be deemed preferable to the adaptive JI schemes that John
>A. deLaubenfels (sp?) and I discussed.

Where is this information?

-- Ray Tomes -- http://www.kcbbs.gen.nz/users/rtomes/rt-home.htm --
Cycles email list -- http://www.kcbbs.gen.nz/users/af/cyc.htm
Alexandria eGroup list -- http://www.kcbbs.gen.nz/users/af/alex.htm
Boundaries of Science http://www.kcbbs.gen.nz/users/af/scienceb.htm

Paul H. Erlich [TD188.8]
>>One musical point for Ray Tomes: You are incorrect in your assumptions about
>>composers' intentions and wandering tonics. Many classical pieces have been
>>analyzed in just intonation and almost invariably they have a net downward
>>drift in JI, sometimes by as much as half an octave.

Ray Tomes [TD201.11]
>I am unsure as to what you are saying here. Are you saying that turning
>a piece into JI commonly (and wrongly) causes this drift in many pieces?
>If so, I suggest that this depends very strongly on the algorithm used
>in the process. I dealt with some considerations in this regard a
>couple of weeks ago and it is clear that slightly different algorithms
>can jump to different notes under the same circumstances and introduce
>ratios such as 80/81 etc.

I should make a bolder statement in regard to this to Paul. If the
large playing ground idea is used (which shows what I called C and C-
etc) then we are in agreement that the piece should end on C and not C--
or some such if it started on C. This can be achieved by keeping track
of the CoG (centre of gravity) as we go along and not letting it get too
far from the starting place. This method will ensure that the "breaks"
will happen at the most correct places where there is considerable
ambiguity. Of course this is easier to do well with the whole piece of
music available than to do in real time where retrospect can play no
part.

For example, in the big playing field ...

D-- A- E- B- F#- C#- G#- D#- A# E# B#
F- C- G- D- A E B F# C# G# D#
Ab Eb Bb F C G D A+ E+ B+
Fb Cb Gb Db Ab+ Eb+ Bb+ F+ C+ G+ D+

... if we have wandered from D to E to D- and E- we would not want to go
to D-- but would have a bias built in to pull back to D- instead. Maybe
even the first time (E to D-) would have pulled back unless the music
very powerfully made this move. Paul, I'm not sure that we can fully
resolve this without worked examples.

-- Ray Tomes -- http://www.kcbbs.gen.nz/users/rtomes/rt-home.htm --
Cycles email list -- http://www.kcbbs.gen.nz/users/af/cyc.htm
Alexandria eGroup list -- http://www.kcbbs.gen.nz/users/af/alex.htm
Boundaries of Science http://www.kcbbs.gen.nz/users/af/scienceb.htm