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In his latest post, Dante Rosati yelped:

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From: "Dante Rosati" <dante@i...>
Date: Fri Apr 9, 2004 11:15 pm
Subject: RE: [metatuning] Let's clear up the confusion

"What have you got against integers?"

This is the well-known logical fallacy of the non sequitur accusation.
EXAMPLE: A white civil rights worker marches with Martin Luther King
in the early 1960s and Southern segregationists scream at him: "What
have you got against white people?"

The accusation is a non sequitur, since there is no evidence that the
civil rights worker has anything against white people. It's just an
inflammatory red herring designed to deter debate and raise blood
pressures.

Likewise, Dante Rosati's non sequitur accusation is just another red
herring designed to deflect debate. If your claim is not a classic
non sequitur accusation, Dante Rosati, then show us proof in my own
words where I denigrated integer ratios as a general class of pitches
and tunings.

Of course you can't, since I never said any such thing.

Note also that Dante Rosati has fallen into the obvious logical
fallacy of the excluded middle. If a person objects to element X of
argument Y, you conclude falsely that the person objects to argument Y
entirely. That might or might not be true. It is not necessarily true.
EXAMPLE: some people objected to the specific methodology of the
current war in Iraq )viz., not waiting for U.N. approval) but did not
object to the stated goal of removing Saddam Hussein from power.
Reasonable people can differ on methods while agreeing on goals.

"Do you deny that an octave is produced by dividing a string length by
2 or multiplying a frequency by the same integer?"

Yes. I deny that "an octave is produced by dividing a string length by
2 or multiplying a frequency by the same integer."

Your statement is provably false, Dante Rosati. The perceptual octave
exceeds 2:1 for harmonic series tones with many components, and
greatly exceeds the 2:1 for simple sine waves:

"It is quite remarkable that musicians seem to prefer too wide or
`stretched' inervals in many cases. Above we have seen several
examples of interval stretching: the barbershop singers' fifth and
just minor seventh; string trio players' melodic major and minor
thirds and fifths; music listeners preferred sizes of fifth and
octave; and a professional musician's settings of melodic intervals
that contain ascending fifths.
"In the case of octaves, the craving for stretching has been noticed
for both dyads and melodic intervals. The amount of stretching
preferred depends on the mid frequency of the interval, among other
things. THe average for synthetic, vibrato-free octave tones has been
found to be about 15 cents. Thus, subjects found a just octave too
flat but an octave of 1,215-cent just." [Sundberg, Johan, "The Science
Of Musical Sounds," Academic Press Inc., Harcourt Brace Jovanovich:
San Diego, 1991, pp. 103-104]

REFERENCES:
Agren, K. "Alto and tenor voice and harmonic intervals between them,"
Department of Speech Communications and Musical Acoustics, R. Inst.
Technoloyg, Stockholm, 1976.
Shackford, C, "Some Aspects of Perception" I, II and III in J. Music
Theory, Vol. 5, pp. 162-202, vol 6 pp. 66-90 and 2953, 1961-61

You may find revealing the drastically non-linear graphs showing how
the sizes of the octave and a fifth vary expressed as tone
heightdifferences, as shown as a function of frequency. This diagram
goes all the away back to Stevens and Davis in 1938. Yet while it's
old old 70-year-old news to scientists, the people on these tuning
forums are so far behind the times and so beclouded with superstitions
about small integers that the react with shock to such well-known
science and violently refuse to acknowledge the well-documented
experiments which prove it.

For low frequencies and single sine waves the perceptual octave
approaches 3:1:
"The mel scale is constructed such that a halving of the number of
mels corresponds to a halving of the pitch perceived. As shown in the
figure, a tone with the pitch of 1,000 mel sounds twice as high
another tone with the pitch of 500 mel. Examination of the figure
tells us that this correponds to a frequency shift from approximate
1,000 to 380 Hz." [Sundberg, Johan, "The Science Of Musical Sounds,"
Academic Press Inc., Harcourt Brace Jovanovich: San Diego, 1991, pp.
47]

The loudness of a single sine tone also affects its perceptual pitch:
"Rather substantial frequnecy changes are required to keep pitch
constant for the subject represnted in the figure. A 150-Hz tone
increasing from 45 to 90 dB drops in pitch to an extent coresponding
to a 12% frequency shift. This is close to two semitones in the
diatonic scale. (..) A funny consequence of this effect is that a soft
sine tone at 300 Hz may sound as a pure octave of a loud sine tone at
368 Hz. The tone that sounds as a pure octave is 12% too high. This
means that mathematically it is a minor seventh! This is a good
argument for avoiding confusion of perceptual and physical entities."
[Sundberg, Johan, "The Science Of Musical Sounds," Academic Press
Inc., Harcourt Brace Jovanovich: San Diego, 1991, pg. 46]

How about it, Dante Rosati? Can you provide us with references from
peer-reviewed psychoacoustics journals refuting these well-documented
facts? Of course you can't. You are pervasively uninformed about
psychoacoustics...which explains why you must resort to empty
name-calling. You have no facts and no logic to back up your claims,
thus your only alternative is to hurl invective ("baboon," "mentally
deranged," "asshole," ad nauseum).

"Do you deny that the octave is a component of some music?"

Of course not -- and here we get a classic example of your garbled
reasoning and scrambled logic, for you have now made the classic error
of selective evidence. The documented fact that the octave is a
component of *some* music does not prove that the octave is a
comopnent of all music -- in fact, in many non-Western musics, such as
the Banda Linda of central africa (where musicians strongly prefer an
interval of 1150 cents over 1200 cents) or Bali (where musicians
strongly prefer an interval between 1210 and 1230 cents, as opposed to
1200 cents) the 2:1 octave is not a component at all. However, your
statement is doubly false -- for even if it were true that the octave
is a component of all music, that does not mean it is the basis of
*all* music, or even of *most* music, or indeed even of *much* music
on our planet. Using the scrambled logic you employ here, we would
have to conclude that all integers are prime because some integers are
prime.
Even a small child recognizes the foolish logical fallacy you have
stumbled into here -- but Dante Rosati does not recognize this obvious
logical fallacy. Thus, your persistent name-calling.

"Do you deny that dividing a string into 3 parts or multiplying a
frequency by 3 produces an interval we call a fifth (12th)?"

Of course I deny it -- more to the point, the facts deny it, observed
reality denies it, and the physical universe denies it, as
psychoacoustic tests and the reality of the phsyical acoustics of
vibrating strings proves so clearly. The physical acoustics of even
the thinnest vibrating string require that all vibrating strings at
least slightly depart from strict integer ratios when the string is
plucked and divided into 3 parts (or n parts). If you played a string
instrument, Dante Rosati, you would know that 'cello players must make
allowances for this fact when playing very high pitches, as must
violinists and violists. The basic law of acoustics which requires
this is known as Weyl's Law of Acoustics. Can you explain Weyl's Law
Of acoustics in simple english?

Of course you can't. Dante Rosati is pervasively uninformed about
physical acoustics, just as he is pervasively uninformed about
psychoacoustics and about ethnomusicology. Speaking of which,
Shackford's 1961 paper in the Journal of Music Theory, together with
many other psychoacustic expeirments published in peer-reviewed
journals, prove conclusively that the perceptual perfect fifth is not
a 3:2 ratio. Naturally Dante Rosati is also unaware of these
well-documented facts, which explains his need to resort to empty
name-calling. People who have no facts and no logic to back up their
vacuous superstitious have no fallback position but name-calling.

For one reference proving the inharmonicity of vibrations of thin
wires and strings, see Schuck, O., H and Young, R. W. "Observations on
the vibrations of piano strings," J. Acoust. Soc Amer., Vol. 15, pg.
1, 1943. As the authors remark, "True harmonic series could not be
found..." [ibid.]

"Do you deny that the fifth is an important interval in music?"

Of course I deny that the fifth is an important interval in much
non-Western music. Examples include Japanese Noh music, Balinese
kacapi music, the music of the Are-Are peoples of the Solomon Islands,
the music of the Kwaiker indians of Guatama, the "weeping song" of the
Gisalo peoples of central Africa, the music of certain inhabitants of
Ghana who use harps tuned to 4 near-equal divisions of the octave,
etc.

Of course I deny that the fifth is an important interval in much
Western music composed after 1910 or so. Of course I deny that the
fifth is an important interval in much electroacoustic music and much
computer music and especially much modern tape music. Of course I deny
that the perfect fifth is an important component is most pop
industrial music composed after the mid-1970s. Once again, Dante
Rosati shows his lack of knowledge of ethnomusicology, as well as his
lack of knowledge of modern Western music post-1910.

"Now, 4 is just 2 x 2, so thats [sic] nothing new. But
divisions/multiplications by 5 gives [sic] after octave reduction)
what we call a major third."

Your statement is provably false. Many psychoacoustics experiments
show that the perceptual major third differs significantly from the
ratio 5:4. Western listeners overwhelmingly hear a 5:4 ratio as "out
of tune" and "too narrow" to qualify as a true major third, so once
again the facts disprove your laughably incorrent and foolishly false
claim.

REFRENCES:
from Shackford, C., 1961-2:
minor third dyads Mean Value (cents) Quartile Deviations

305 287-318

major third dyads Mean Value (cents) Quartile Deviations
410 402-418

"Do you say that the major third has had no part to play in music?"

Another example of Dante Rosati's garbled reasoning and scrambled
logic. The fact that X plays some part in Y does not mean that X
causes Y. This is the well-known logical fallacy of mistaking
correlation for causation. Example: the number of preachers in America
increased at the same rate as the number of drunks throughout the
1800s -- does this prove that preachers caused drunkenness? Obviously
not. Both populations increased because the population as a whole
increased. Correlation does not equal causation, as any high school
student in logic 101 knows...but Dante Rosati does not know it.
Another example: catnip plays a part in cats' lives, but catnip does
not cause cats. Morever, there is necessary connection twixt catnip
and cats. Plenty of places exist in which cats don't ever get catnip.

"Is it just a coincidence that these three interval types produced by
applying the smallest integers to pitches produces the major triad,
the most basic element of western music?'

Yes. Exactly. Just a coincidence. Here we arrive at an interesting
question: which integer ratios correspond to which musical intervals?
Is the 5/4 a major third? Or is the 81/54 a major third?
The question is meaningless and unanswerable, since they both do. In
fact an infinite range of different integer ratios are major thirds.
Ivor Darreg and Easley Blackwood both pioneered the use of equal
divisions of the octaves with perfect fifths radically different from
the 3/2, and the results sound vivid and memorable. Easley Blackwood
produced what seems to me the very best composition in 15 equal anyone
has composed in his 12 Microtonal Etudes For Electronic Media.
What's really interesting is that the number of choices is not
limited. In JI, the number of choices is *infinite.*
This is wonderful, because it gives JI composers an unlimited range of
integer ratios for any given musical interval -- the JI composer
can pitck and choose according to taste. For example, a JI composer
can choose the interval 24/19 as a major third...or the interval
8192/6561 as a as a major third...or the interval 651/512 as a major
third.
The number of choices is unlimited.
And this gives the composer a wide variety of different flavors of
major third and minor third and perfect fifth and perfect fourth and
major second and minor second and so on... Moreover, JI thirds need
not be major or minor -- they can be something in between, or larger
than major, or smaller than minor. There is no way to decide exactly
where the dividing line falls. And each of these different flavors of
JI thirds and seconds and fifths and fourths and sevenths and sixths
boast their own distinctive musical utility and their own uniquely
valuable musical character.
And as soon as we exit JI and move on to equal divisions of the
octave, we find a vast new range of options for each musical interval.
In the 15 tone equal tuning the perfect fifth is 720 cents. It
functions as a perfectly acceptable perfect fifth and produced triads
and harmonic progressions and cadences which sound entirely fuctional
and musically effective. In the 14 tone equal tuning, the perfect
fifth is 685.4 cents in width. It too sounds perfectly acceptable in
the context of hte 14 equal tuning, and it too produces enitrely
msuically effective cadences and triads and chord progressions.
In between these extremes we have a kaleidoscopic range of sizes of
perfect fifth, ranging from around 680 cents on the low side to
roughly 720 cents on the high side.
Many different equal divisions of the octave offer a dazzling range of
different sizes of perfect fifth, and as long as they fall in btween
roughly 680 cents and 720 cents, they prove musically effective and
harmonically functional.
Moreover, we can vary the size of the perfect fifth within just
intonation. Just as no law of nature requires that we use the 5/4
instead of the 81/64 or the 24/19 as a just major third, no law of
nature demands that we employ a 3/2 as a perfect fifth in a JI tuning
rather than a different ratio.
I have composed a variety of JI pieces, some with perfect fifths
ranging as low as 680 cents and some with perfect fifths ranigng as
high as 720 cents.
Here are some delicious-sounding flavors of perfect fifths I've used
in various JI compositions:
49/33 = 684 cetns
64/43 = 688 cents
55/37 = 687 cents
47/31 = 720 cents
If you build JI tunings in which these are the perfect fifths, they
will sound and function as musically acceptable perfect fifths.
Perfect fifths narrower than the 3/2 and pefect fifths wider than the
3/2 bth sound vibrant and rich, full of luscious beats which gives an
added inner life and wamrth to the tuning. For my part, I find just
3/2 perfect fifths bland and insipid.
Accordingly, rather than misnaming 5-limit diatonic tunings based on
4:5:6 chords as "just intonation," they ought more properly to be
called "bland insipid tuning."
Rather than misnaming 4:5:6 chords played with harmonic series tones
as "smooth triads," we ought more properly to describe them as
"lifeless-sounding dead triads."
Or, as Erv Wilson put it, "5-limit diatnonic JI sucks. It sounds so
insipid that if the word `insipid' did not exist, it would be
necessary to invent it to describe 5-limit diatonic JI."

If Dante Rosati would open his mind and compose music in some of these
tunings rather than blindly marching down the 5-limit diatonic 4:5:6
triad cul desac, he might open his eyes to a wider range of musical
possibiltiies. In that case he would no longer find it necessary to
scream insults and indulge in mindless name-calling, because he was
would have something of musical interest to cooupy himself
with...rather than the same-old same-old bland insipid dead-sounding
4;5:6 triads.

And if you *really* want to have your mind and your ears blown, Dante
Rosati, try composing in non-octave JI tunings. This is one of the
things I admire about both Kragi Grady and Erv Wilson -- they are
comlpetely open-minded in regard to microtnality. They have no
preconceptions about any imagined need to compose with triads, or
diatonic scales, or any of that stuff.

Moreover, Dante Rosati has also made the classic logical fallacy of
assuming a conclusion which he has not proven. For you have not
provided any objective verifiable hard evidence to prove that the
major triad is "the most basic leement of western music," Dante
Rosati. On the contrary, a wealth of historical evidence disproves
your claim. Even a cursory study of the history of Western music back
to circa 500 B.C. shows that the major triad was NOT "the most basic
element of western music" throughout most of Western music history.
From the time of the earliest Greek music of which we have written
records (viz., Aristonexos' treatise describing the enharmonic genus
as sound "old and rustic" to modern 5th-century Greek ears, which
strongly implies that the Greek enharmonic genus was the oldest of the
3 genera) to roughly the year 1400, there is no written record proving
that the major triad was used as a component in Western music, or that
tertian harmony was used in Western music, or that tertian harmonies
were ever used as chord progressions in Western music. That's a span
of 2000 years out of 2500 years in Western music WITHOUT the major
triad as a functional element. Only from circa 1400 to roughly 1900
did the major triad serve as "the basic element" in Western music --
and after 1900 the major triad gradually dropped out as "the most
basic element in western music" in favor of alternate vertical
constructions such as tone clusters (Iannis Xenakis, Kryzstof
Penderecki, Gyorgy Ligeti), quartal harmony (Paul Hindemith), secondal
harmony (Ravel, , and various other innovations.

For your edification, here are the actual basic elements in music time
period by time period:

circa 500 B.C. to circa 800 A.D.: tetrachord
circa 800 A.D. to roughly 1300 A.D.: vertical perfect fifth
circa 1300 A.D. to roughly 1900 A.D - some form of major triad
(meantone, Pythagorean, 12 equal, well tempered, etc.)
circa 1900 A.D. to the present: a wide variety of vertical and
horizontal structures including (but not
restricted to) quartal harmonies, secondal harmonies, tone clusters,
klangfarbenmelodie, tone rows,
tonal matrices, computer-generated inharmonic tone-complexes, rhythmic
cells, melodic motifs, etc., etc., etc.

Examples of music from 1900 A.D. to the present which eschew the major
triad as the basic element:
Ionisation by Edgard Varese
Threnody For the Victims of Hiroshima by Krysztof Penderecki
Songes by Jean-Claude Risset
de Snelheid by Louis Andriessen
Solar Ellipse by Barry Truax
Ku-Ka Ilimoku by Christopher Rouse
Symphony Number 2 by Henri Dutilleux
Kraanerg by Iannis Xenakis
Disclosures by James Dashow
Silver Apples of the Moon by Morton Subotnik
Beyond the Valley of A Day In the Life by The Residents
Phosphones by Emmanuel Ghent
Incantation (from "Beauty In the Beast") by Wendy Carlos
Cuttlefish Fantasies by Warren Burt
Borrowing and Stealing by The Hub (John Bischoff, Tim Perkis, Chris
Brown, Scot Gresham-Lancaster, Mark Trayle)
Quatermass by Tod Dockstader
Piano Phase by Steve Reich
Wait For Me! by William Schottstaedt
Mortuos Plango Vivo Voco by Jonathan Harvey
Drifting Island by Maki Ishii

These came from my recent listening stack of CDs. They represent only
a microscopic cross section of the vast quantities of post 1950 music
which abandons the major tirad (or any triads) as the basic element.

"Of course there are infinite musics possible using all kinds of
tunings and transformations. Who ever said otherwise? But to say that
small integers have nothing to do with music is crankism at its worst.
Surely this is not your position?"

Thank you for admitting that you have fallen into another classic
logical fallcy, the well-known fallacy of the straw man argument. As
you point out, I did N*O*T say that "small integers have nothing to do
with music."

🔗Dante Rosati <dante@...>

What up dude-

You can hurl all the citations you want. I trust my ears. A 3:2 fifth sounds
way more consonant than fifths that deviate from it. A 5:4 third sounds way
more in consonant than a 12edo third or a pythagorean third. Consonance
graphs for harmonic timbres clearly show the reason for this. This is not to
say that JI triads are "better" than tempered ones, simply that they are
more consonant. So you dont like perfectly tuned intervals- fine. a chacon a
son gout. But you cant seriously contend that there is nothing linking the
shape of consonance graphs, the harmonic series, and the development of our
scales and triads. Of course its not completely simple, one to one, but
close enough for me to have no doubts that they are linked.

Yes I know that many non-western musics do not use triads at all or even
remotely JI intervals in their scales. However, the two richest musical
traditions- western music and musics of India - are perfectly aware of the
contours of the consonance graph (as "ear knowledge") and that the intervals
that coincide with its valleys have a distinctive and compelling sound.

Sine waves may be a different story but no acoustic instruments I know of,
unless you include the tuning fork (and even then not really) produce single
sine tones. Since the phenomena of consonance and dissonance that shaped
western (and Indian) music is based on complex harmonic tones that exhibit
these phenomenab of consonance and dissonance, the perception (or
mis-perception) of intervals between single sine waves is not relevant.

So, if you reject the theory that the major triad became (and remains to
this day, 20th c. avant garde notwithstanding) the fundamental unit of
western music (and of course I'm talking about the last 500 years or so, not
2500) due to the presence of its components in the lower reaches of the
harmonic series, and coincident with the significant consonances marked by
the consonance graph, then where, pray tell, did it come from?

And how come I don't get a fun "middle name" in quotes any more!!! I feel
deprived!

Dante

> -----Original Message-----
> From: xenharmonic [mailto:xed@...]
> Sent: Saturday, April 10, 2004 10:02 PM
> To: metatuning@yahoogroups.com
> Subject: [metatuning] The usual rebuttal
>
>
> In his latest post, Dante Rosati yelped:
>
> Message 7055 of 7057 | Previous | Next [ Up Thread ] Message
> Index
> Msg #
> From: "Dante Rosati" <dante@i...>
> Date: Fri Apr 9, 2004 11:15 pm
> Subject: RE: [metatuning] Let's clear up the confusion
>
> "What have you got against integers?"
>
> This is the well-known logical fallacy of the non sequitur accusation.
> EXAMPLE: A white civil rights worker marches with Martin Luther King
> in the early 1960s and Southern segregationists scream at him: "What
> have you got against white people?"
>
> The accusation is a non sequitur, since there is no evidence that the
> civil rights worker has anything against white people. It's just an
> inflammatory red herring designed to deter debate and raise blood
> pressures.
>
> Likewise, Dante Rosati's non sequitur accusation is just another red
> herring designed to deflect debate. If your claim is not a classic
> non sequitur accusation, Dante Rosati, then show us proof in my own
> words where I denigrated integer ratios as a general class of pitches
> and tunings.
>
> Of course you can't, since I never said any such thing.
>
> Note also that Dante Rosati has fallen into the obvious logical
> fallacy of the excluded middle. If a person objects to element X of
> argument Y, you conclude falsely that the person objects to argument Y
> entirely. That might or might not be true. It is not necessarily true.
> EXAMPLE: some people objected to the specific methodology of the
> current war in Iraq )viz., not waiting for U.N. approval) but did not
> object to the stated goal of removing Saddam Hussein from power.
> Reasonable people can differ on methods while agreeing on goals.
>
> "Do you deny that an octave is produced by dividing a string length by
> 2 or multiplying a frequency by the same integer?"
>
> Yes. I deny that "an octave is produced by dividing a string length by
> 2 or multiplying a frequency by the same integer."
>
> Your statement is provably false, Dante Rosati. The perceptual octave
> exceeds 2:1 for harmonic series tones with many components, and
> greatly exceeds the 2:1 for simple sine waves:
>
> "It is quite remarkable that musicians seem to prefer too wide or
> `stretched' inervals in many cases. Above we have seen several
> examples of interval stretching: the barbershop singers' fifth and
> just minor seventh; string trio players' melodic major and minor
> thirds and fifths; music listeners preferred sizes of fifth and
> octave; and a professional musician's settings of melodic intervals
> that contain ascending fifths.
> "In the case of octaves, the craving for stretching has been noticed
> for both dyads and melodic intervals. The amount of stretching
> preferred depends on the mid frequency of the interval, among other
> things. THe average for synthetic, vibrato-free octave tones has been
> found to be about 15 cents. Thus, subjects found a just octave too
> flat but an octave of 1,215-cent just." [Sundberg, Johan, "The Science
> Of Musical Sounds," Academic Press Inc., Harcourt Brace Jovanovich:
> San Diego, 1991, pp. 103-104]
>
> REFERENCES:
> Agren, K. "Alto and tenor voice and harmonic intervals between them,"
> Department of Speech Communications and Musical Acoustics, R. Inst.
> Technoloyg, Stockholm, 1976.
> Shackford, C, "Some Aspects of Perception" I, II and III in J. Music
> Theory, Vol. 5, pp. 162-202, vol 6 pp. 66-90 and 2953, 1961-61
>
> You may find revealing the drastically non-linear graphs showing how
> the sizes of the octave and a fifth vary expressed as tone
> heightdifferences, as shown as a function of frequency. This diagram
> goes all the away back to Stevens and Davis in 1938. Yet while it's
> old old 70-year-old news to scientists, the people on these tuning
> forums are so far behind the times and so beclouded with superstitions
> about small integers that the react with shock to such well-known
> science and violently refuse to acknowledge the well-documented
> experiments which prove it.
>
> For low frequencies and single sine waves the perceptual octave
> approaches 3:1:
> "The mel scale is constructed such that a halving of the number of
> mels corresponds to a halving of the pitch perceived. As shown in the
> figure, a tone with the pitch of 1,000 mel sounds twice as high
> another tone with the pitch of 500 mel. Examination of the figure
> tells us that this correponds to a frequency shift from approximate
> 1,000 to 380 Hz." [Sundberg, Johan, "The Science Of Musical Sounds,"
> Academic Press Inc., Harcourt Brace Jovanovich: San Diego, 1991, pp.
> 47]
>
> The loudness of a single sine tone also affects its perceptual pitch:
> "Rather substantial frequnecy changes are required to keep pitch
> constant for the subject represnted in the figure. A 150-Hz tone
> increasing from 45 to 90 dB drops in pitch to an extent coresponding
> to a 12% frequency shift. This is close to two semitones in the
> diatonic scale. (..) A funny consequence of this effect is that a soft
> sine tone at 300 Hz may sound as a pure octave of a loud sine tone at
> 368 Hz. The tone that sounds as a pure octave is 12% too high. This
> means that mathematically it is a minor seventh! This is a good
> argument for avoiding confusion of perceptual and physical entities."
> [Sundberg, Johan, "The Science Of Musical Sounds," Academic Press
> Inc., Harcourt Brace Jovanovich: San Diego, 1991, pg. 46]
>
> How about it, Dante Rosati? Can you provide us with references from
> peer-reviewed psychoacoustics journals refuting these well-documented
> facts? Of course you can't. You are pervasively uninformed about
> psychoacoustics...which explains why you must resort to empty
> name-calling. You have no facts and no logic to back up your claims,
> thus your only alternative is to hurl invective ("baboon," "mentally
> deranged," "asshole," ad nauseum).
>
> "Do you deny that the octave is a component of some music?"
>
> Of course not -- and here we get a classic example of your garbled
> reasoning and scrambled logic, for you have now made the classic error
> of selective evidence. The documented fact that the octave is a
> component of *some* music does not prove that the octave is a
> comopnent of all music -- in fact, in many non-Western musics, such as
> the Banda Linda of central africa (where musicians strongly prefer an
> interval of 1150 cents over 1200 cents) or Bali (where musicians
> strongly prefer an interval between 1210 and 1230 cents, as opposed to
> 1200 cents) the 2:1 octave is not a component at all. However, your
> statement is doubly false -- for even if it were true that the octave
> is a component of all music, that does not mean it is the basis of
> *all* music, or even of *most* music, or indeed even of *much* music
> on our planet. Using the scrambled logic you employ here, we would
> have to conclude that all integers are prime because some integers are
> prime.
> Even a small child recognizes the foolish logical fallacy you have
> stumbled into here -- but Dante Rosati does not recognize this obvious
> logical fallacy. Thus, your persistent name-calling.
>
> "Do you deny that dividing a string into 3 parts or multiplying a
> frequency by 3 produces an interval we call a fifth (12th)?"
>
> Of course I deny it -- more to the point, the facts deny it, observed
> reality denies it, and the physical universe denies it, as
> psychoacoustic tests and the reality of the phsyical acoustics of
> vibrating strings proves so clearly. The physical acoustics of even
> the thinnest vibrating string require that all vibrating strings at
> least slightly depart from strict integer ratios when the string is
> plucked and divided into 3 parts (or n parts). If you played a string
> instrument, Dante Rosati, you would know that 'cello players must make
> allowances for this fact when playing very high pitches, as must
> violinists and violists. The basic law of acoustics which requires
> this is known as Weyl's Law of Acoustics. Can you explain Weyl's Law
> Of acoustics in simple english?
>
> Of course you can't. Dante Rosati is pervasively uninformed about
> physical acoustics, just as he is pervasively uninformed about
> psychoacoustics and about ethnomusicology. Speaking of which,
> Shackford's 1961 paper in the Journal of Music Theory, together with
> many other psychoacustic expeirments published in peer-reviewed
> journals, prove conclusively that the perceptual perfect fifth is not
> a 3:2 ratio. Naturally Dante Rosati is also unaware of these
> well-documented facts, which explains his need to resort to empty
> name-calling. People who have no facts and no logic to back up their
> vacuous superstitious have no fallback position but name-calling.
>
> For one reference proving the inharmonicity of vibrations of thin
> wires and strings, see Schuck, O., H and Young, R. W. "Observations on
> the vibrations of piano strings," J. Acoust. Soc Amer., Vol. 15, pg.
> 1, 1943. As the authors remark, "True harmonic series could not be
> found..." [ibid.]
>
> "Do you deny that the fifth is an important interval in music?"
>
> Of course I deny that the fifth is an important interval in much
> non-Western music. Examples include Japanese Noh music, Balinese
> kacapi music, the music of the Are-Are peoples of the Solomon Islands,
> the music of the Kwaiker indians of Guatama, the "weeping song" of the
> Gisalo peoples of central Africa, the music of certain inhabitants of
> Ghana who use harps tuned to 4 near-equal divisions of the octave,
> etc.
>
> Of course I deny that the fifth is an important interval in much
> Western music composed after 1910 or so. Of course I deny that the
> fifth is an important interval in much electroacoustic music and much
> computer music and especially much modern tape music. Of course I deny
> that the perfect fifth is an important component is most pop
> industrial music composed after the mid-1970s. Once again, Dante
> Rosati shows his lack of knowledge of ethnomusicology, as well as his
> lack of knowledge of modern Western music post-1910.
>
> "Now, 4 is just 2 x 2, so thats [sic] nothing new. But
> divisions/multiplications by 5 gives [sic] after octave reduction)
> what we call a major third."
>
> Your statement is provably false. Many psychoacoustics experiments
> show that the perceptual major third differs significantly from the
> ratio 5:4. Western listeners overwhelmingly hear a 5:4 ratio as "out
> of tune" and "too narrow" to qualify as a true major third, so once
> again the facts disprove your laughably incorrent and foolishly false
> claim.
>
> REFRENCES:
> from Shackford, C., 1961-2:
> minor third dyads Mean Value (cents) Quartile Deviations
>
> 305 287-318
>
>
> major third dyads Mean Value (cents) Quartile Deviations
> 410 402-418
>
> "Do you say that the major third has had no part to play in music?"
>
> Another example of Dante Rosati's garbled reasoning and scrambled
> logic. The fact that X plays some part in Y does not mean that X
> causes Y. This is the well-known logical fallacy of mistaking
> correlation for causation. Example: the number of preachers in America
> increased at the same rate as the number of drunks throughout the
> 1800s -- does this prove that preachers caused drunkenness? Obviously
> not. Both populations increased because the population as a whole
> increased. Correlation does not equal causation, as any high school
> student in logic 101 knows...but Dante Rosati does not know it.
> Another example: catnip plays a part in cats' lives, but catnip does
> not cause cats. Morever, there is necessary connection twixt catnip
> and cats. Plenty of places exist in which cats don't ever get catnip.
>
> "Is it just a coincidence that these three interval types produced by
> applying the smallest integers to pitches produces the major triad,
> the most basic element of western music?'
>
> Yes. Exactly. Just a coincidence. Here we arrive at an interesting
> question: which integer ratios correspond to which musical intervals?
> Is the 5/4 a major third? Or is the 81/54 a major third?
> The question is meaningless and unanswerable, since they both do. In
> fact an infinite range of different integer ratios are major thirds.
> Ivor Darreg and Easley Blackwood both pioneered the use of equal
> divisions of the octaves with perfect fifths radically different from
> the 3/2, and the results sound vivid and memorable. Easley Blackwood
> produced what seems to me the very best composition in 15 equal anyone
> has composed in his 12 Microtonal Etudes For Electronic Media.
> What's really interesting is that the number of choices is not
> limited. In JI, the number of choices is *infinite.*
> This is wonderful, because it gives JI composers an unlimited range of
> integer ratios for any given musical interval -- the JI composer
> can pitck and choose according to taste. For example, a JI composer
> can choose the interval 24/19 as a major third...or the interval
> 8192/6561 as a as a major third...or the interval 651/512 as a major
> third.
> The number of choices is unlimited.
> And this gives the composer a wide variety of different flavors of
> major third and minor third and perfect fifth and perfect fourth and
> major second and minor second and so on... Moreover, JI thirds need
> not be major or minor -- they can be something in between, or larger
> than major, or smaller than minor. There is no way to decide exactly
> where the dividing line falls. And each of these different flavors of
> JI thirds and seconds and fifths and fourths and sevenths and sixths
> boast their own distinctive musical utility and their own uniquely
> valuable musical character.
> And as soon as we exit JI and move on to equal divisions of the
> octave, we find a vast new range of options for each musical interval.
> In the 15 tone equal tuning the perfect fifth is 720 cents. It
> functions as a perfectly acceptable perfect fifth and produced triads
> and harmonic progressions and cadences which sound entirely fuctional
> and musically effective. In the 14 tone equal tuning, the perfect
> fifth is 685.4 cents in width. It too sounds perfectly acceptable in
> the context of hte 14 equal tuning, and it too produces enitrely
> msuically effective cadences and triads and chord progressions.
> In between these extremes we have a kaleidoscopic range of sizes of
> perfect fifth, ranging from around 680 cents on the low side to
> roughly 720 cents on the high side.
> Many different equal divisions of the octave offer a dazzling range of
> different sizes of perfect fifth, and as long as they fall in btween
> roughly 680 cents and 720 cents, they prove musically effective and
> harmonically functional.
> Moreover, we can vary the size of the perfect fifth within just
> intonation. Just as no law of nature requires that we use the 5/4
> instead of the 81/64 or the 24/19 as a just major third, no law of
> nature demands that we employ a 3/2 as a perfect fifth in a JI tuning
> rather than a different ratio.
> I have composed a variety of JI pieces, some with perfect fifths
> ranging as low as 680 cents and some with perfect fifths ranigng as
> high as 720 cents.
> Here are some delicious-sounding flavors of perfect fifths I've used
> in various JI compositions:
> 49/33 = 684 cetns
> 64/43 = 688 cents
> 55/37 = 687 cents
> 47/31 = 720 cents
> If you build JI tunings in which these are the perfect fifths, they
> will sound and function as musically acceptable perfect fifths.
> Perfect fifths narrower than the 3/2 and pefect fifths wider than the
> 3/2 bth sound vibrant and rich, full of luscious beats which gives an
> added inner life and wamrth to the tuning. For my part, I find just
> 3/2 perfect fifths bland and insipid.
> Accordingly, rather than misnaming 5-limit diatonic tunings based on
> 4:5:6 chords as "just intonation," they ought more properly to be
> called "bland insipid tuning."
> Rather than misnaming 4:5:6 chords played with harmonic series tones
> as "smooth triads," we ought more properly to describe them as
> "lifeless-sounding dead triads."
> Or, as Erv Wilson put it, "5-limit diatnonic JI sucks. It sounds so
> insipid that if the word `insipid' did not exist, it would be
> necessary to invent it to describe 5-limit diatonic JI."
>
> If Dante Rosati would open his mind and compose music in some of these
> tunings rather than blindly marching down the 5-limit diatonic 4:5:6
> triad cul desac, he might open his eyes to a wider range of musical
> possibiltiies. In that case he would no longer find it necessary to
> scream insults and indulge in mindless name-calling, because he was
> would have something of musical interest to cooupy himself
> with...rather than the same-old same-old bland insipid dead-sounding
> 4;5:6 triads.
>
> And if you *really* want to have your mind and your ears blown, Dante
> Rosati, try composing in non-octave JI tunings. This is one of the
> things I admire about both Kragi Grady and Erv Wilson -- they are
> comlpetely open-minded in regard to microtnality. They have no
> preconceptions about any imagined need to compose with triads, or
> diatonic scales, or any of that stuff.
>
> Moreover, Dante Rosati has also made the classic logical fallacy of
> assuming a conclusion which he has not proven. For you have not
> provided any objective verifiable hard evidence to prove that the
> major triad is "the most basic leement of western music," Dante
> Rosati. On the contrary, a wealth of historical evidence disproves
> your claim. Even a cursory study of the history of Western music back
> to circa 500 B.C. shows that the major triad was NOT "the most basic
> element of western music" throughout most of Western music history.
> From the time of the earliest Greek music of which we have written
> records (viz., Aristonexos' treatise describing the enharmonic genus
> as sound "old and rustic" to modern 5th-century Greek ears, which
> strongly implies that the Greek enharmonic genus was the oldest of the
> 3 genera) to roughly the year 1400, there is no written record proving
> that the major triad was used as a component in Western music, or that
> tertian harmony was used in Western music, or that tertian harmonies
> were ever used as chord progressions in Western music. That's a span
> of 2000 years out of 2500 years in Western music WITHOUT the major
> triad as a functional element. Only from circa 1400 to roughly 1900
> did the major triad serve as "the basic element" in Western music --
> and after 1900 the major triad gradually dropped out as "the most
> basic element in western music" in favor of alternate vertical
> constructions such as tone clusters (Iannis Xenakis, Kryzstof
> Penderecki, Gyorgy Ligeti), quartal harmony (Paul Hindemith), secondal
> harmony (Ravel, , and various other innovations.
>
> For your edification, here are the actual basic elements in music time
> period by time period:
>
> circa 500 B.C. to circa 800 A.D.: tetrachord
> circa 800 A.D. to roughly 1300 A.D.: vertical perfect fifth
> circa 1300 A.D. to roughly 1900 A.D - some form of major triad
> (meantone, Pythagorean, 12 equal, well tempered, etc.)
> circa 1900 A.D. to the present: a wide variety of vertical and
> horizontal structures including (but not
> restricted to) quartal harmonies, secondal harmonies, tone clusters,
> klangfarbenmelodie, tone rows,
> tonal matrices, computer-generated inharmonic tone-complexes, rhythmic
> cells, melodic motifs, etc., etc., etc.
>
> Examples of music from 1900 A.D. to the present which eschew the major
> triad as the basic element:
> Ionisation by Edgard Varese
> Threnody For the Victims of Hiroshima by Krysztof Penderecki
> Songes by Jean-Claude Risset
> de Snelheid by Louis Andriessen
> Solar Ellipse by Barry Truax
> Ku-Ka Ilimoku by Christopher Rouse
> Symphony Number 2 by Henri Dutilleux
> Kraanerg by Iannis Xenakis
> Disclosures by James Dashow
> Silver Apples of the Moon by Morton Subotnik
> Beyond the Valley of A Day In the Life by The Residents
> Phosphones by Emmanuel Ghent
> Incantation (from "Beauty In the Beast") by Wendy Carlos
> Cuttlefish Fantasies by Warren Burt
> Borrowing and Stealing by The Hub (John Bischoff, Tim Perkis, Chris
> Brown, Scot Gresham-Lancaster, Mark Trayle)
> Quatermass by Tod Dockstader
> Piano Phase by Steve Reich
> Wait For Me! by William Schottstaedt
> Mortuos Plango Vivo Voco by Jonathan Harvey
> Drifting Island by Maki Ishii
>
> These came from my recent listening stack of CDs. They represent only
> a microscopic cross section of the vast quantities of post 1950 music
> which abandons the major tirad (or any triads) as the basic element.
>
> "Of course there are infinite musics possible using all kinds of
> tunings and transformations. Who ever said otherwise? But to say that
> small integers have nothing to do with music is crankism at its worst.
> Surely this is not your position?"
>
> Thank you for admitting that you have fallen into another classic
> logical fallcy, the well-known fallacy of the straw man argument. As
> you point out, I did N*O*T say that "small integers have nothing to do
> with music."
>
>
>
>
> Meta Tuning meta-info:
>
> To unsubscribe, send an email to:
> metatuning-unsubscribe@yahoogroups.com
>
> Web page is http://groups.yahoo.com/groups/metatuning/
>
> To post to the list, send to
> metatuning@yahoogroups.com
>
> You don't have to be a member to post.
>
>
> Yahoo! Groups Links
>
>
>
>
>

🔗Aaron K. Johnson <akjmicro@...>

Brian,

I'm wondering what you think of the Benade (I hope I'm spelling that right)
'special relationship' experiment with JI, where the subjects apparantly found
2/1, 3/2, 5/4, 7/4, etc by tuning oscillators?

Also, just curious what you hope you're trying to gain through what you surely
must know is 'ad hominem' (e.g. Gene "Wooley Headed Numerology" Smith, etc).

It's clear that no one here questions your considerable expertise on the
subject of microtonality. I for one have read and enjoyed and learned
countless interesting facts that I would not have otherwise known by reading
your articles (e.g. "Brief History of Microtonality in the US"), and I think
your compilation of CD titles is a remarkably helpful resource for those of
us scanning the landscape of recorded microtonal literature. I've read all of
your CPS articles in the archives, and found them inspiring. Your greatest
enemies value you. When did you start to feel that you were undervallued or
unwelcome for your considerable expertise? Perhaps if anyone were guilty of
that, you might make peace with those parties in a direct way, by confronting
the moment in time when that happened, and working it through.

What else can be done? Do you really enjoy spending your hours typing
invective? Does it thrill you to hurt others feelings, or attempt to hurt
others feelings? What do you really hope to gain? More attention to your
music? Do you really think human nature will work that way, that you can
insult your way into being respected/admired? Neither am I suggesting that you
kiss up to anyone, the opposite wrong. But, if you have no respect and
admiration for anyone in this community, why do you waste your time trying to
make them feel miserable? Or communicating at all? There must be some deeper
mechanism at work. Some basic need you have to reach out, in spite of your
resentments.

Here's a fact for you: people enjoy feeling that they are part of a supportive
community, and they don't enjoy feeling that they are alienated and alone.
Microtonalists come in all flavors--some compose intuitively and prolifically,
others less so, some not at all, but express interest nontheless. Some like
the math involved and it's contemplation is almost an end in itself, an
almost Greek quality when you think about it. There's no harm done. Let it
be. Why does that have to threaten you? Why must that be attacked? They are
not Fundamentalist Christians trying to convert the sheep masses, or Bush
voters, but thinking people, connected to you in that they share in interest
with you of something that surely less than 1% of the world population does.
If they present false facts or argument, let them be found wanting by rational
discourse, not heated and superfluous, inelegant and unseemly ad hominem
attacks !!!

To attack and alienate yourself from the few members of that community that
shares with you an uncommon interest seems like the height of illogic to me,
and certainly you know the effects of negativity, of bile, of active hate, on
the health of the whole human being. High blood pressure alone will kill you.

Perhaps you might try an experiment, and try a different tenor of
communicating, and see what changes about how welcome you perceive yourself
to be. Ask yourself what the common denominator is in the countless
contentious relationships you find yourself in the middle of.

Or, don't, and be content to be ignored, which would be tragic given how the
community could be benefit from your presence. You have the choice, whether
you choose to acknowledge it or not.

Most respectfully,
Aaron.

On Saturday 10 April 2004 09:02 pm, xenharmonic wrote:
> In his latest post, Dante Rosati yelped:
>
> Message 7055 of 7057 | Previous | Next [ Up Thread ] Message
> Index
> Msg #
> From: "Dante Rosati" <dante@i...>
> Date: Fri Apr 9, 2004 11:15 pm
> Subject: RE: [metatuning] Let's clear up the confusion
>
> "What have you got against integers?"
>
> This is the well-known logical fallacy of the non sequitur accusation.
> EXAMPLE: A white civil rights worker marches with Martin Luther King
> in the early 1960s and Southern segregationists scream at him: "What
> have you got against white people?"
>
> The accusation is a non sequitur, since there is no evidence that the
> civil rights worker has anything against white people. It's just an
> inflammatory red herring designed to deter debate and raise blood
> pressures.
>
> Likewise, Dante Rosati's non sequitur accusation is just another red
> herring designed to deflect debate. If your claim is not a classic
> non sequitur accusation, Dante Rosati, then show us proof in my own
> words where I denigrated integer ratios as a general class of pitches
> and tunings.
>
> Of course you can't, since I never said any such thing.
>
> Note also that Dante Rosati has fallen into the obvious logical
> fallacy of the excluded middle. If a person objects to element X of
> argument Y, you conclude falsely that the person objects to argument Y
> entirely. That might or might not be true. It is not necessarily true.
> EXAMPLE: some people objected to the specific methodology of the
> current war in Iraq )viz., not waiting for U.N. approval) but did not
> object to the stated goal of removing Saddam Hussein from power.
> Reasonable people can differ on methods while agreeing on goals.
>
> "Do you deny that an octave is produced by dividing a string length by
> 2 or multiplying a frequency by the same integer?"
>
> Yes. I deny that "an octave is produced by dividing a string length by
> 2 or multiplying a frequency by the same integer."
>
> Your statement is provably false, Dante Rosati. The perceptual octave
> exceeds 2:1 for harmonic series tones with many components, and
> greatly exceeds the 2:1 for simple sine waves:
>
> "It is quite remarkable that musicians seem to prefer too wide or
> `stretched' inervals in many cases. Above we have seen several
> examples of interval stretching: the barbershop singers' fifth and
> just minor seventh; string trio players' melodic major and minor
> thirds and fifths; music listeners preferred sizes of fifth and
> octave; and a professional musician's settings of melodic intervals
> that contain ascending fifths.
> "In the case of octaves, the craving for stretching has been noticed
> for both dyads and melodic intervals. The amount of stretching
> preferred depends on the mid frequency of the interval, among other
> things. THe average for synthetic, vibrato-free octave tones has been
> found to be about 15 cents. Thus, subjects found a just octave too
> flat but an octave of 1,215-cent just." [Sundberg, Johan, "The Science
> Of Musical Sounds," Academic Press Inc., Harcourt Brace Jovanovich:
> San Diego, 1991, pp. 103-104]
>
> REFERENCES:
> Agren, K. "Alto and tenor voice and harmonic intervals between them,"
> Department of Speech Communications and Musical Acoustics, R. Inst.
> Technoloyg, Stockholm, 1976.
> Shackford, C, "Some Aspects of Perception" I, II and III in J. Music
> Theory, Vol. 5, pp. 162-202, vol 6 pp. 66-90 and 2953, 1961-61
>
> You may find revealing the drastically non-linear graphs showing how
> the sizes of the octave and a fifth vary expressed as tone
> heightdifferences, as shown as a function of frequency. This diagram
> goes all the away back to Stevens and Davis in 1938. Yet while it's
> old old 70-year-old news to scientists, the people on these tuning
> forums are so far behind the times and so beclouded with superstitions
> about small integers that the react with shock to such well-known
> science and violently refuse to acknowledge the well-documented
> experiments which prove it.
>
> For low frequencies and single sine waves the perceptual octave
> approaches 3:1:
> "The mel scale is constructed such that a halving of the number of
> mels corresponds to a halving of the pitch perceived. As shown in the
> figure, a tone with the pitch of 1,000 mel sounds twice as high
> another tone with the pitch of 500 mel. Examination of the figure
> tells us that this correponds to a frequency shift from approximate
> 1,000 to 380 Hz." [Sundberg, Johan, "The Science Of Musical Sounds,"
> Academic Press Inc., Harcourt Brace Jovanovich: San Diego, 1991, pp.
> 47]
>
> The loudness of a single sine tone also affects its perceptual pitch:
> "Rather substantial frequnecy changes are required to keep pitch
> constant for the subject represnted in the figure. A 150-Hz tone
> increasing from 45 to 90 dB drops in pitch to an extent coresponding
> to a 12% frequency shift. This is close to two semitones in the
> diatonic scale. (..) A funny consequence of this effect is that a soft
> sine tone at 300 Hz may sound as a pure octave of a loud sine tone at
> 368 Hz. The tone that sounds as a pure octave is 12% too high. This
> means that mathematically it is a minor seventh! This is a good
> argument for avoiding confusion of perceptual and physical entities."
> [Sundberg, Johan, "The Science Of Musical Sounds," Academic Press
> Inc., Harcourt Brace Jovanovich: San Diego, 1991, pg. 46]
>
> How about it, Dante Rosati? Can you provide us with references from
> peer-reviewed psychoacoustics journals refuting these well-documented
> facts? Of course you can't. You are pervasively uninformed about
> psychoacoustics...which explains why you must resort to empty
> name-calling. You have no facts and no logic to back up your claims,
> thus your only alternative is to hurl invective ("baboon," "mentally
> deranged," "asshole," ad nauseum).
>
> "Do you deny that the octave is a component of some music?"
>
> Of course not -- and here we get a classic example of your garbled
> reasoning and scrambled logic, for you have now made the classic error
> of selective evidence. The documented fact that the octave is a
> component of *some* music does not prove that the octave is a
> comopnent of all music -- in fact, in many non-Western musics, such as
> the Banda Linda of central africa (where musicians strongly prefer an
> interval of 1150 cents over 1200 cents) or Bali (where musicians
> strongly prefer an interval between 1210 and 1230 cents, as opposed to
> 1200 cents) the 2:1 octave is not a component at all. However, your
> statement is doubly false -- for even if it were true that the octave
> is a component of all music, that does not mean it is the basis of
> *all* music, or even of *most* music, or indeed even of *much* music
> on our planet. Using the scrambled logic you employ here, we would
> have to conclude that all integers are prime because some integers are
> prime.
> Even a small child recognizes the foolish logical fallacy you have
> stumbled into here -- but Dante Rosati does not recognize this obvious
> logical fallacy. Thus, your persistent name-calling.
>
> "Do you deny that dividing a string into 3 parts or multiplying a
> frequency by 3 produces an interval we call a fifth (12th)?"
>
> Of course I deny it -- more to the point, the facts deny it, observed
> reality denies it, and the physical universe denies it, as
> psychoacoustic tests and the reality of the phsyical acoustics of
> vibrating strings proves so clearly. The physical acoustics of even
> the thinnest vibrating string require that all vibrating strings at
> least slightly depart from strict integer ratios when the string is
> plucked and divided into 3 parts (or n parts). If you played a string
> instrument, Dante Rosati, you would know that 'cello players must make
> allowances for this fact when playing very high pitches, as must
> violinists and violists. The basic law of acoustics which requires
> this is known as Weyl's Law of Acoustics. Can you explain Weyl's Law
> Of acoustics in simple english?
>
> Of course you can't. Dante Rosati is pervasively uninformed about
> physical acoustics, just as he is pervasively uninformed about
> psychoacoustics and about ethnomusicology. Speaking of which,
> Shackford's 1961 paper in the Journal of Music Theory, together with
> many other psychoacustic expeirments published in peer-reviewed
> journals, prove conclusively that the perceptual perfect fifth is not
> a 3:2 ratio. Naturally Dante Rosati is also unaware of these
> well-documented facts, which explains his need to resort to empty
> name-calling. People who have no facts and no logic to back up their
> vacuous superstitious have no fallback position but name-calling.
>
> For one reference proving the inharmonicity of vibrations of thin
> wires and strings, see Schuck, O., H and Young, R. W. "Observations on
> the vibrations of piano strings," J. Acoust. Soc Amer., Vol. 15, pg.
> 1, 1943. As the authors remark, "True harmonic series could not be
> found..." [ibid.]
>
> "Do you deny that the fifth is an important interval in music?"
>
> Of course I deny that the fifth is an important interval in much
> non-Western music. Examples include Japanese Noh music, Balinese
> kacapi music, the music of the Are-Are peoples of the Solomon Islands,
> the music of the Kwaiker indians of Guatama, the "weeping song" of the
> Gisalo peoples of central Africa, the music of certain inhabitants of
> Ghana who use harps tuned to 4 near-equal divisions of the octave,
> etc.
>
> Of course I deny that the fifth is an important interval in much
> Western music composed after 1910 or so. Of course I deny that the
> fifth is an important interval in much electroacoustic music and much
> computer music and especially much modern tape music. Of course I deny
> that the perfect fifth is an important component is most pop
> industrial music composed after the mid-1970s. Once again, Dante
> Rosati shows his lack of knowledge of ethnomusicology, as well as his
> lack of knowledge of modern Western music post-1910.
>
> "Now, 4 is just 2 x 2, so thats [sic] nothing new. But
> divisions/multiplications by 5 gives [sic] after octave reduction)
> what we call a major third."
>
> Your statement is provably false. Many psychoacoustics experiments
> show that the perceptual major third differs significantly from the
> ratio 5:4. Western listeners overwhelmingly hear a 5:4 ratio as "out
> of tune" and "too narrow" to qualify as a true major third, so once
> again the facts disprove your laughably incorrent and foolishly false
> claim.
>
> REFRENCES:
> from Shackford, C., 1961-2:
> minor third dyads Mean Value (cents) Quartile Deviations
>
> 305 287-318
>
> major third dyads Mean Value (cents) Quartile Deviations
> 410 402-418
>
> "Do you say that the major third has had no part to play in music?"
>
> Another example of Dante Rosati's garbled reasoning and scrambled
> logic. The fact that X plays some part in Y does not mean that X
> causes Y. This is the well-known logical fallacy of mistaking
> correlation for causation. Example: the number of preachers in America
> increased at the same rate as the number of drunks throughout the
> 1800s -- does this prove that preachers caused drunkenness? Obviously
> not. Both populations increased because the population as a whole
> increased. Correlation does not equal causation, as any high school
> student in logic 101 knows...but Dante Rosati does not know it.
> Another example: catnip plays a part in cats' lives, but catnip does
> not cause cats. Morever, there is necessary connection twixt catnip
> and cats. Plenty of places exist in which cats don't ever get catnip.
>
> "Is it just a coincidence that these three interval types produced by
> applying the smallest integers to pitches produces the major triad,
> the most basic element of western music?'
>
> Yes. Exactly. Just a coincidence. Here we arrive at an interesting
> question: which integer ratios correspond to which musical intervals?
> Is the 5/4 a major third? Or is the 81/54 a major third?
> The question is meaningless and unanswerable, since they both do. In
> fact an infinite range of different integer ratios are major thirds.
> Ivor Darreg and Easley Blackwood both pioneered the use of equal
> divisions of the octaves with perfect fifths radically different from
> the 3/2, and the results sound vivid and memorable. Easley Blackwood
> produced what seems to me the very best composition in 15 equal anyone
> has composed in his 12 Microtonal Etudes For Electronic Media.
> What's really interesting is that the number of choices is not
> limited. In JI, the number of choices is *infinite.*
> This is wonderful, because it gives JI composers an unlimited range of
> integer ratios for any given musical interval -- the JI composer
> can pitck and choose according to taste. For example, a JI composer
> can choose the interval 24/19 as a major third...or the interval
> 8192/6561 as a as a major third...or the interval 651/512 as a major
> third.
> The number of choices is unlimited.
> And this gives the composer a wide variety of different flavors of
> major third and minor third and perfect fifth and perfect fourth and
> major second and minor second and so on... Moreover, JI thirds need
> not be major or minor -- they can be something in between, or larger
> than major, or smaller than minor. There is no way to decide exactly
> where the dividing line falls. And each of these different flavors of
> JI thirds and seconds and fifths and fourths and sevenths and sixths
> boast their own distinctive musical utility and their own uniquely
> valuable musical character.
> And as soon as we exit JI and move on to equal divisions of the
> octave, we find a vast new range of options for each musical interval.
> In the 15 tone equal tuning the perfect fifth is 720 cents. It
> functions as a perfectly acceptable perfect fifth and produced triads
> and harmonic progressions and cadences which sound entirely fuctional
> and musically effective. In the 14 tone equal tuning, the perfect
> fifth is 685.4 cents in width. It too sounds perfectly acceptable in
> the context of hte 14 equal tuning, and it too produces enitrely
> msuically effective cadences and triads and chord progressions.
> In between these extremes we have a kaleidoscopic range of sizes of
> perfect fifth, ranging from around 680 cents on the low side to
> roughly 720 cents on the high side.
> Many different equal divisions of the octave offer a dazzling range of
> different sizes of perfect fifth, and as long as they fall in btween
> roughly 680 cents and 720 cents, they prove musically effective and
> harmonically functional.
> Moreover, we can vary the size of the perfect fifth within just
> intonation. Just as no law of nature requires that we use the 5/4
> instead of the 81/64 or the 24/19 as a just major third, no law of
> nature demands that we employ a 3/2 as a perfect fifth in a JI tuning
> rather than a different ratio.
> I have composed a variety of JI pieces, some with perfect fifths
> ranging as low as 680 cents and some with perfect fifths ranigng as
> high as 720 cents.
> Here are some delicious-sounding flavors of perfect fifths I've used
> in various JI compositions:
> 49/33 = 684 cetns
> 64/43 = 688 cents
> 55/37 = 687 cents
> 47/31 = 720 cents
> If you build JI tunings in which these are the perfect fifths, they
> will sound and function as musically acceptable perfect fifths.
> Perfect fifths narrower than the 3/2 and pefect fifths wider than the
> 3/2 bth sound vibrant and rich, full of luscious beats which gives an
> added inner life and wamrth to the tuning. For my part, I find just
> 3/2 perfect fifths bland and insipid.
> Accordingly, rather than misnaming 5-limit diatonic tunings based on
> 4:5:6 chords as "just intonation," they ought more properly to be
> called "bland insipid tuning."
> Rather than misnaming 4:5:6 chords played with harmonic series tones
> as "smooth triads," we ought more properly to describe them as
> "lifeless-sounding dead triads."
> Or, as Erv Wilson put it, "5-limit diatnonic JI sucks. It sounds so
> insipid that if the word `insipid' did not exist, it would be
> necessary to invent it to describe 5-limit diatonic JI."
>
> If Dante Rosati would open his mind and compose music in some of these
> tunings rather than blindly marching down the 5-limit diatonic 4:5:6
> triad cul desac, he might open his eyes to a wider range of musical
> possibiltiies. In that case he would no longer find it necessary to
> scream insults and indulge in mindless name-calling, because he was
> would have something of musical interest to cooupy himself
> with...rather than the same-old same-old bland insipid dead-sounding
> 4;5:6 triads.
>
> And if you *really* want to have your mind and your ears blown, Dante
> Rosati, try composing in non-octave JI tunings. This is one of the
> things I admire about both Kragi Grady and Erv Wilson -- they are
> comlpetely open-minded in regard to microtnality. They have no
> preconceptions about any imagined need to compose with triads, or
> diatonic scales, or any of that stuff.
>
> Moreover, Dante Rosati has also made the classic logical fallacy of
> assuming a conclusion which he has not proven. For you have not
> provided any objective verifiable hard evidence to prove that the
> major triad is "the most basic leement of western music," Dante
> Rosati. On the contrary, a wealth of historical evidence disproves
> your claim. Even a cursory study of the history of Western music back
> to circa 500 B.C. shows that the major triad was NOT "the most basic
> element of western music" throughout most of Western music history.
> From the time of the earliest Greek music of which we have written
> records (viz., Aristonexos' treatise describing the enharmonic genus
> as sound "old and rustic" to modern 5th-century Greek ears, which
> strongly implies that the Greek enharmonic genus was the oldest of the
> 3 genera) to roughly the year 1400, there is no written record proving
> that the major triad was used as a component in Western music, or that
> tertian harmony was used in Western music, or that tertian harmonies
> were ever used as chord progressions in Western music. That's a span
> of 2000 years out of 2500 years in Western music WITHOUT the major
> triad as a functional element. Only from circa 1400 to roughly 1900
> did the major triad serve as "the basic element" in Western music --
> and after 1900 the major triad gradually dropped out as "the most
> basic element in western music" in favor of alternate vertical
> constructions such as tone clusters (Iannis Xenakis, Kryzstof
> Penderecki, Gyorgy Ligeti), quartal harmony (Paul Hindemith), secondal
> harmony (Ravel, , and various other innovations.
>
> For your edification, here are the actual basic elements in music time
> period by time period:
>
> circa 500 B.C. to circa 800 A.D.: tetrachord
> circa 800 A.D. to roughly 1300 A.D.: vertical perfect fifth
> circa 1300 A.D. to roughly 1900 A.D - some form of major triad
> (meantone, Pythagorean, 12 equal, well tempered, etc.)
> circa 1900 A.D. to the present: a wide variety of vertical and
> horizontal structures including (but not
> restricted to) quartal harmonies, secondal harmonies, tone clusters,
> klangfarbenmelodie, tone rows,
> tonal matrices, computer-generated inharmonic tone-complexes, rhythmic
> cells, melodic motifs, etc., etc., etc.
>
> Examples of music from 1900 A.D. to the present which eschew the major
> triad as the basic element:
> Ionisation by Edgard Varese
> Threnody For the Victims of Hiroshima by Krysztof Penderecki
> Songes by Jean-Claude Risset
> de Snelheid by Louis Andriessen
> Solar Ellipse by Barry Truax
> Ku-Ka Ilimoku by Christopher Rouse
> Symphony Number 2 by Henri Dutilleux
> Kraanerg by Iannis Xenakis
> Disclosures by James Dashow
> Silver Apples of the Moon by Morton Subotnik
> Beyond the Valley of A Day In the Life by The Residents
> Phosphones by Emmanuel Ghent
> Incantation (from "Beauty In the Beast") by Wendy Carlos
> Cuttlefish Fantasies by Warren Burt
> Borrowing and Stealing by The Hub (John Bischoff, Tim Perkis, Chris
> Brown, Scot Gresham-Lancaster, Mark Trayle)
> Quatermass by Tod Dockstader
> Piano Phase by Steve Reich
> Wait For Me! by William Schottstaedt
> Mortuos Plango Vivo Voco by Jonathan Harvey
> Drifting Island by Maki Ishii
>
> These came from my recent listening stack of CDs. They represent only
> a microscopic cross section of the vast quantities of post 1950 music
> which abandons the major tirad (or any triads) as the basic element.
>
> "Of course there are infinite musics possible using all kinds of
> tunings and transformations. Who ever said otherwise? But to say that
> small integers have nothing to do with music is crankism at its worst.
> Surely this is not your position?"
>
> Thank you for admitting that you have fallen into another classic
> logical fallcy, the well-known fallacy of the straw man argument. As
> you point out, I did N*O*T say that "small integers have nothing to do
> with music."
>
>
>
>
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--
Aaron Krister Johnson
http://www.akjmusic.com
http://www.dividebypi.com

OCEAN, n. A body of water occupying about two-thirds of a world made
for man -- who has no gills. -Ambrose Bierce 'The Devils Dictionary'

The usual rebuttal

🔗xenharmonic <xed@...>

🔗Dante Rosati <dante@...>

🔗Aaron K. Johnson <akjmicro@...>

🔗Gene Ward Smith <gwsmith@...>

🔗Graham Breed <graham@...>