Re. Simple Ratio Theory

Tom Dent <stringph@...> wrote: "The author presents his own vision of just intervals, and points out the failure of simple ratios theory which marked the history of western music." Mysterious, eh?" Nothing mysterious. The simple ratios theory is wrong, I didn't speak so in my book, I was very polite. The simple ratio theory is the result of a huge confusion between : * ratios with small numbers : 2/1, 3/2, 4/3, 5/3, 5/4, 6/5, 7/3, 7/4,=20 7/5, 8/3, 7/6 * and harmonics (1, 2, 3, 4, 5, 7=85.) brought into the span of an octave by dividing several times by 2 : 2/1 (octave), 3/2 (dominant or fifth), 5/4 (natural third), 7/4 (harmonic seventh), 9/8 (tone or major second), 11/4 or 11/8 (middle of F and F*). Some of these both series are identical, others are not used in Music Theory, the only one which has paused a real problem for 15 centuries is the fourth 4/3. It has been considered as consonant by several ancient theorists, I have called this the "fourth paradox

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--- In tuning@yahoogroups.com, "serge donval" <s_donval@...> wrote:
>
> Tom Dent <stringph@> wrote: "The author presents his own vision of
just
> intervals, and points out the failure of simple ratios theory
which marked
> the history of western music." Mysterious, eh?" Nothing
mysterious. The
> simple ratios theory is wrong, I didn't speak so in my book, I was
very
> polite. The simple ratio theory is the result of a huge confusion
between :
> * ratios with small numbers : 2/1, 3/2, 4/3, 5/3, 5/4, 6/5, 7/3,
7/4,=20
> 7/5, 8/3, 7/6 * and harmonics (1, 2, 3, 4, 5, 7=85.) brought into
the span
> of an octave by dividing several times by 2 : 2/1 (octave), 3/2
(dominant or
> fifth), 5/4 (natural third), 7/4 (harmonic seventh), 9/8 (tone or
major
> second), 11/4 or 11/8 (middle of F and F*). Some of these both
series are
> identical, others are not used in Music Theory, the only one which
has
> paused a real problem for 15 centuries is the fourth 4/3. It has
been
> considered as consonant by several ancient theorists, I have
called this the
> "fourth paradox

Yeah, baby! This is going to be fun.

You'll find, however, that nothing will change religious convictions.

-Cameron Bobro

> You'll find, however, that nothing will change religious convictions.

The test of that is putting forth an alternate explanation, which
neither you nor Serge have done.

-Carl

Carl wrote : �The test of that is putting forth an alternate explanation, which neither you nor Serge have done.� Would you please give some details.

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>> The test of that is putting forth an alternate explanation,
>> which neither you nor Serge have done.
>
> Would you please give some details.

I use a (numerator * denominator) ranking for the discordance
of simple ratios, and Paul Erlich's harmonic entropy for
the disonance of irrational intervals, or rational intervals
where the above product is > 40.
Paul's model is based on simple ratios; it calculates the
dissonance of irrational intervals by their distance from
nearby simple ratios.

You made a claim that the simple ratios theory is flawed.
In that case I expect you to demonstrate how it is flawed,
and what you propose to use instead (for chores such as
ranking the discordance of intervals).

-Carl

--- In tuning@yahoogroups.com, "Carl Lumma" <clumma@...> wrote:
>
> >> The test of that is putting forth an alternate explanation,
> >> which neither you nor Serge have done.
> >
> > Would you please give some details.
>
> I use a (numerator * denominator) ranking for the discordance
> of simple ratios, and Paul Erlich's harmonic entropy for
> the disonance of irrational intervals, or rational intervals
> where the above product is > 40.
> Paul's model is based on simple ratios; it calculates the
> dissonance of irrational intervals by their distance from
> nearby simple ratios.
>
> You made a claim that the simple ratios theory is flawed.
> In that case I expect you to demonstrate how it is flawed,
> and what you propose to use instead (for chores such as
> ranking the discordance of intervals).
>
> -Carl

Amen.

On a relataed note, and this has been discussed before:

I think one of the strangest phenomenon that has never been explained
satisfactorally is why the brain hears pitches an octave aapart as
being members of the same pitch class. The best theory out there is
that all the members of the upper pitches harmonic series are present
in the lower's series, but that doesn't explain pitch class perception
in inharmonic spectra, unless we theorize that that must be 'learned'
by example and extrapolation from harmonic spectra....

This reminds me of seeing posts by Brian McLaren elsewhere where he
makes the claim that mathematics has nothing to tell us about music,
which is, of course, wrong. That guy has clearly 'gone over the edge'.

He was, it seems, was trying to make the point that the situation is
complicated by the human perceptual system, which is true (e.g. we
like sharp octaves sometimes, etc.), but he throws out the proverbial
baby with the bathwater, which is silly.

--- In tuning@yahoogroups.com, "Carl Lumma" <clumma@...> wrote:
>
> >> The test of that is putting forth an alternate explanation,
> >> which neither you nor Serge have done.
> >
> > Would you please give some details.
>
> I use a (numerator * denominator) ranking for the discordance
> of simple ratios, and Paul Erlich's harmonic entropy for
> the disonance of irrational intervals, or rational intervals
> where the above product is > 40.
> Paul's model is based on simple ratios; it calculates the
> dissonance of irrational intervals by their distance from
> nearby simple ratios.
>
> You made a claim that the simple ratios theory is flawed.
> In that case I expect you to demonstrate how it is flawed,
> and what you propose to use instead (for chores such as
> ranking the discordance of intervals).
>
> -Carl
>

Why, the question seems simple enough. We recognize geometric series to
sound the same, and arithemetic series to sound different.

SNIP

>
> I think one of the strangest phenomenon that has never been explained
> satisfactorally is why the brain hears pitches an octave aapart as
> being members of the same pitch class. The best theory out there is
> that all the members of the upper pitches harmonic series are present
> in the lower's series, but that doesn't explain pitch class perception
> in inharmonic spectra, unless we theorize that that must be 'learned'
> by example and extrapolation from harmonic spectra....
>
>
>

--- In tuning@yahoogroups.com, "Cameron Bobro" <misterbobro@...> wrote:

> You'll find, however, that nothing will change religious convictions.

Including yours and his?

--- In tuning@yahoogroups.com, "Carl Lumma" <clumma@...> wrote:
>
> > You'll find, however, that nothing will change religious
convictions.
>
> The test of that is putting forth an alternate explanation, which
> neither you nor Serge have done.

Explanation? Serge is not talking about the science of hearing, as far
as I can make out. I await clarification of what, exactly, he *is*
talking about because his comments on musical history don't seem to
make much sense.

--- In tuning@yahoogroups.com, "Aaron Krister Johnson" <aaron@...>
wrote:

> The best theory out there is
> that all the members of the upper pitches harmonic series are present
> in the lower's series, but that doesn't explain pitch class perception
> in inharmonic spectra, unless we theorize that that must be 'learned'
> by example and extrapolation from harmonic spectra....

It seems to me that theory simply fails because 3, the so-
called "tritave", is a counter-example.

Aaron wrote:

> I think one of the strangest phenomenon that has never been explained satisfactorally is why the brain hears pitches an octave aapart as being members of

> the same pitch class. The best theory out there is that all the members of the upper pitches harmonic series are present in the lower's series, but that doesn't

> explain pitch class perception in inharmonic spectra, unless we theorize that that must be 'learned' by example and extrapolation from harmonic spectra....

I definitely don't know how to explain this in terms of why our ears are translating octave intervals this way but I have a "speculative" oppinion why the strong acoustical similarity in two tones an octave apart is occurring. The number 2 is somewhat special in such a way that it meets two important conditions at the same time: A) It's a prime, B) It's an even number. This "evenness" gives it some kind of symmetry which no other prime can have (whatever you frame in chunks of two, it gives you the option to find the opposite meaning or value of the matter in question -- people must have been aware of this very long ago, concidering the fact that there's a translation for "even" and "odd" in perhaps all the languages I can think of). Should this symmetry occur in sounds, there should be an audible similarity between 100Hz and 200Hz which is remarcably stronger than in case of other intervals than 2/1. To explain my meaning of the "opposite value", let's suppose mixing frequencies of 200-400-600-800Hz and so on and so on. This gives a harmonic spectrum with a fundamental of 200Hz. Shifting the entire frequency band 100Hz down, you get a different harmonic spectrum with a fundamental of 100Hz which is symmetrical in its shape since the even harmonics are missing. And, to get a "happy ending", shifting the entire frequency band another 100Hz down gives the same spectrum as the original since the frequency of 0Hz is silent. Are you asking why the tones on an overtone flute are complementing so well? The answer is the same: When the flute is tuned to 200-400-600-800-...Hz when its opposite end is open, closing it shifts all the overtones approximately 100Hz down. -- BTW: When I was about 12, I realized that the even harmonics played alone can also produce a regular part of the series with the sole exception that it's an octave lower. This was one of the rarest surprises for me at that time.

Petr

> I think one of the strangest phenomenon that has never been
> explained satisfactorally is why the brain hears pitches an
> octave aapar as being members of the same pitch class. The
> best theory out there is that all the members of the upper
> pitches harmonic series are present in the lower's series,
> but that doesn't explain pitch class perception in inharmonic
> spectra, unless we theorize that that must be 'learned'
> by example and extrapolation from harmonic spectra....

When first starting ear training, people often confuse fifths
and octaves, according to David L. Burge.
Paul E. points out that when singing songs in unison, some
non-musicians will enter a fifth away.
So I posit that the notion of pitch class is simply a good
stopping point for periodicity in note naming.
Maybe a very good one, as 1/x (the number of partials shared
by successive harmonics with a fundamental) decays quickly.
Octave equivalence becomes more clear through exposure to music.
Therefore the perception of octave equivalence may not have
any adaptive significance in and of itself, other than for
musical activities of course (which do provide a living for
some :). However the underlying mechanism is probably a
consequence of the brain's pitch detector.
As for inharmonic specctra, many still resemble harmonic
spectra, or have a single loudest partial which the brain
"hears out". Completely inharmonic spectra have no pitch,
and therefore no octave equivalence.

-Carl

Hi Aaron,

--- In tuning@yahoogroups.com, "Aaron Krister Johnson" <aaron@...> wrote:
>

> On a relataed note, and this has been discussed before:
>
> I think one of the strangest phenomenon that has never
> been explained satisfactorally is why the brain hears
> pitches an octave aapart as being members of the same
> pitch class. The best theory out there is that all the
> members of the upper pitches harmonic series are present
> in the lower's series, but that doesn't explain pitch
> class perception in inharmonic spectra, unless we theorize
> that that must be 'learned' by example and extrapolation
> from harmonic spectra....

You're right, we have discussed this many times before,
but again i'll offer my explanation: i think it's simply
that "equivalence" (or "pitch class perception" if you
prefer) is the affect of prime-factor 2.

According to the ideas i subscribe to, the lowest prime-factors
(definitely 2, 3, 5, 7, 11, possibly also 13, 17, 19 and 23,
and possibly several more beyond that in the prime series)
each manifest a distinctive affect. We've tried to classify
them before, but there's no real agreement beyond the idea
that:

2 = equivalence
3 = power / "hollowness"
5 = sweetness
7 = "bluesiness"

But one of the important things to remember about this
theory, at least in my formulation of it, is that the
perception of prime affect diminishes rapidly as one
progresses up the prime series.

I hold that the perception of affect only holds true
for particular intervals under auditory testing, in
relation to an "origin" or 1/1 "fundamental". IOW,
the distinct affect appears as intervals are related
to a harmonic series.

If you try to test affect for other types of chords,
or take an actual sample and try to include musical
context, it becomes far too complicated to isolate
perceptions of affect.

-monz
http://tonalsoft.com
Tonescape microtonal music software

Hi Petr and Aaron,

I think what Petr writes here supports the post that i
just sent concerning prime-affect.

The "evenness" of 2 is nothing special, it's simply a
mathematical property of numbers which have 2 as a factor.

It's no different from numbers divisible by 3 having
a certain kind of property, namely that they are divisible
by 3. And so on for each successive prime factor.

It is generally true that a harmonic timbre will have
more overtones divisible by 2, and then a smaller number
divisible by 3, and then a smaller divisible by 5, etc.,
with the count diminishing for each successive prime factor.

The difference is that long ago humans decided to classify
numbers as "even" or "odd" depending on whether or not
they are divisible by 2. The only reason we see this as
something special is because names were not given to the
properties of divisibility by the other primes.

Which, again, supports my theory in that 2 would have the
strongest affect simply because it is the lowest prime.

-monz
http://tonalsoft.com
Tonescape microtonal music software

--- In tuning@yahoogroups.com, Petr Parízek <p.parizek@...> wrote:
>
> Aaron wrote:
>
> > I think one of the strangest phenomenon that has never been
explained satisfactorally is why the brain hears pitches an octave
aapart as being members of
>
> > the same pitch class. The best theory out there is that all the
members of the upper pitches harmonic series are present in the
lower's series, but that doesn't
>
> > explain pitch class perception in inharmonic spectra, unless we
theorize that that must be 'learned' by example and extrapolation from
harmonic spectra....
>
> I definitely don't know how to explain this in terms of why our ears
are translating octave intervals this way but I have a "speculative"
oppinion why the strong acoustical similarity in two tones an octave
apart is occurring. The number 2 is somewhat special in such a way
that it meets two important conditions at the same time: A) It's a
prime, B) It's an even number. This "evenness" gives it some kind of
symmetry which no other prime can have (whatever you frame in chunks
of two, it gives you the option to find the opposite meaning or value
of the matter in question -- people must have been aware of this very
long ago, concidering the fact that there's a translation for "even"
and "odd" in perhaps all the languages I can think of). Should this
symmetry occur in sounds, there should be an audible similarity
between 100Hz and 200Hz which is remarcably stronger than in case of
other intervals than 2/1. To explain my meaning of the "opposite
value", let's suppose mixing frequencies of 200-400-600-800Hz and so
on and so on. This gives a harmonic spectrum with a fundamental of
200Hz. Shifting the entire frequency band 100Hz down, you get a
different harmonic spectrum with a fundamental of 100Hz which is
symmetrical in its shape since the even harmonics are missing. And, to
get a "happy ending", shifting the entire frequency band another 100Hz
down gives the same spectrum as the original since the frequency of
0Hz is silent. Are you asking why the tones on an overtone flute are
complementing so well? The answer is the same: When the flute is tuned
to 200-400-600-800-...Hz when its opposite end is open, closing it
shifts all the overtones approximately 100Hz down. -- BTW: When I was
about 12, I realized that the even harmonics played alone can also
produce a regular part of the series with the sole exception that it's
an octave lower. This was one of the rarest surprises for me at that time.
>
> Petr
>

--- In tuning@yahoogroups.com, "Carl Lumma" <clumma@...> wrote:
>
> > You'll find, however, that nothing will change religious
convictions.
>
> The test of that is putting forth an alternate explanation, which
> neither you nor Serge have done.
>
> -Carl

Been doing so for months now, you simply ignore or sidetrack.
Infinitely more important, I exercise my "alternate explanations"
in music making, and they work.

--- In tuning@yahoogroups.com, "Gene Ward Smith" <genewardsmith@...>
wrote:
>
> --- In tuning@yahoogroups.com, "Cameron Bobro" <misterbobro@> wrote:
>
> > You'll find, however, that nothing will change religious
convictions.
>
> Including yours and his?
>

In your Internet browser, you'll find a menu, "View/Encoding". Make
sure it's set to "Unicode (UTF-8)" or "Western European (ISO)",
something along those lines, not to "George Orwell" or "Louis Carroll".

Just hours ago I posted a comment on how I'm re-evaluating my take on
81/64 because of this test, did you not see it or do you have trouble
putting two and two together?

My religious conviction here is to believe my ears, with a grain of
salt because I know I imagine things sometimes. That religious
conviction won't change.

-Cameron Bobro

Monz wrote:

> The difference is that long ago humans decided to classify numbers as "even" or "odd" depending on whether or not they are divisible by 2. The only

> reason we see this as something special is because names were not given to the properties of divisibility by the other primes.

I'm not sure if I can agree about this. As far as higher primes are concerned, I still miss the symmetry given by the option of an exact contra-value (or how to call that). If you have a unit and want to find its "mid-position", you split it in two parts to be able to get half the way. If you take any other prime and want to find a "simple mean", you always end up with units split into halves -- provided that the arithmetic mean was the oldest kind of mean I can think of.

Petr

--- In tuning@yahoogroups.com, "Cameron Bobro" <misterbobro@...> wrote:

> Been doing so for months now, you simply ignore or sidetrack.

I've not noticed any theorizing coming from you. I *have* noticed some
claims about rational intervals which you don't seem to be able to
support in terms of anyone else's hearing.

> > > You'll find, however, that nothing will change religious
> > > convictions.
> >
> > The test of that is putting forth an alternate explanation, which
> > neither you nor Serge have done.
> >
> > -Carl
>
> Been doing so for months now, you simply ignore or sidetrack.

You told me you have nothing, but asked me to wait, which I
am doing.

> Infinitely more important, I exercise my "alternate explanations"
> in music making, and they work.

Can you demonstrate how your music is a test of your music
theories?

-Carl

> I definitely don't know how to explain this in terms of why our
> ears are translating octave intervals this way but I have
> a "speculative" oppinion why the strong acoustical similarity
> in two tones an octave apart is occurring. The number 2 is
> somewhat special in such a way that it meets two important
> conditions at the same time: A) It's a prime,

Why is that important?

> B) It's an even number. This "evenness" gives it some kind of
> symmetry which no other prime can have (whatever you frame in
> chunks of two, it gives you the option to find the opposite
> meaning or value of the matter in question -- people must have
> been aware of this very long ago, concidering the fact that
> there's a translation for "even" and "odd" in perhaps all the
> languages I can think of).

How does this relate to the perception of consonance?

>Should this symmetry occur in sounds, there should be a
>n audible similarity between 100Hz and 200Hz which is remarcably
>stronger than in case of other intervals than 2/1.

You're assuming the conclusion.

>To explain my meaning of the "opposite value", let's suppose
>mixing frequencies of 200-400-600-800Hz and so on and so on.
>This gives a harmonic spectrum with a fundamental of 200Hz.
>Shifting the entire frequency band 100Hz down, you get a
>different harmonic spectrum with a fundamental of 100Hz
>which is symmetrical in its shape since the even harmonics
>are missing.

What do you mean by "symmetrical in shape"?

>And, to get a "happy ending", shifting the entire frequency
>band another 100Hz down gives the same spectrum as the original
>since the frequency of 0Hz is silent. Are you asking why the
>tones on an overtone flute are complementing so well? The
>answer is the same: When the flute is tuned to 200-400-600-800-
>...Hz when its opposite end is open, closing it shifts all the
>overtones approximately 100Hz down. -- BTW: When I was about 12,
>I realized that the even harmonics played alone can also produce
>a regular part of the series with the sole exception that it's
>an octave lower. This was one of the rarest surprises for me at
>that time.

I'm afraid you lost me here.

-Carl

--- In tuning@yahoogroups.com, "Gene Ward Smith" <genewardsmith@...>
wrote:

> I've not noticed any theorizing coming from you. I *have* noticed
>some
> claims about rational intervals which you don't seem to be able to
> support in terms of anyone else's hearing.

You didn't notice my theory that proximity to a simple interval
isn't the only explanation for perception of consonance? 8 people
have taken the high-fifths test, last time I checked. 4 prefered the
lower fith (708 IIRC), 4 thought the higher (710 IIRC) fifth more
consonant. (Both were complex ratios.)

There you go: a concrete theoretical statement backed up by
"someone else's" hearing.

Carl would rather state that I "poisoned" his judgement somehow
than admit that he heard a triad with 19/15 as the third as more
consonant than a triad with 81/64.

Did you download the Scala file I posted and check if it sounds
cohesive to you, or just a hodge-podge of intervals?

> --- In tuning@yahoogroups.com, "Aaron Krister Johnson" <aaron@>
wrote:

> > I think one of the strangest phenomenon that has never
> > been explained satisfactorally is why the brain hears
> > pitches an octave aapart as being members of the same
> > pitch class. The best theory out there is that all the
> > members of the upper pitches harmonic series are present
> > in the lower's series, but that doesn't explain pitch
> > class perception in inharmonic spectra, unless we theorize
> > that that must be 'learned' by example and extrapolation
> > from harmonic spectra....

At eight months of age my son would sing in perfect octaves
with me, often two octaves above. Whether octaves
are the first harmonies, or "equivalent", and whether that's
learned or "natural", at this point I don't know and actually
don't care,to be honest- they're just there. .

--- In tuning@yahoogroups.com, "monz" <monz@...> wrote:

> You're right, we have discussed this many times before,
> but again i'll offer my explanation: i think it's simply
> that "equivalence" (or "pitch class perception" if you
> prefer) is the affect of prime-factor 2.

Whether or not this is true, it's definitely backwards, seems
to me.

Number is adjective. In other words, we'd use "prime factor 2" as
one of the descriptions of "equivalence". The number 2, a
description, doesn't create anything.

> According to the ideas i subscribe to, the lowest prime-factors
> (definitely 2, 3, 5, 7, 11, possibly also 13, 17, 19 and 23,
> and possibly several more beyond that in the prime series)
> each manifest a distinctive affect.

The partials of a harmonic series cetainly manifest
distinctive "affects", that's part and parcel of timbre. The prime-
factors just name things, they don't create anything at all.

I've mentioned before that I think of a tuning as a giant timbre.

All of this can be demonstrated very easily with an additive
synthesizer. Just start with a sine fundamental and start
rasing and lowering specific partials. You'll find affects but you'll
find that they change in context with other partials, as in real
life sounds.

Really you guys, please get ZynAddSubFx, it's free (in a way, see
below) and the additive synth is perfect for this, I've got it
running as I type this, idly boosting and dropping partials.

Try raising just the 11th partial, a strong character. Then raise
the 12 along with it.... hoho, pretty mean! But the 10th and 11th
together is more the cry of a tragic mallard. The 6th partial with
the eleventh... well that sounds very different in character than
with the 12th, I'm digging "affect" but definitely disagree
with "prime" affect.

We've tried to classify
> them before, but there's no real agreement beyond the idea
> that:
>
> 2 = equivalence
> 3 = power / "hollowness"
> 5 = sweetness
> 7 = "bluesiness"

Well, in terms of partials effecting timbre, that doesn't conflict
at all with my additive synthesis experiences.

> But one of the important things to remember about this
> theory, at least in my formulation of it, is that the
> perception of prime affect diminishes rapidly as one
> progresses up the prime series.

The partials in most timbres diminish rapidly in amplitude
as you go higher.

> I hold that the perception of affect only holds true
> for particular intervals under auditory testing, in
> relation to an "origin" or 1/1 "fundamental".

I think it permeates everything

>IOW,
> the distinct affect appears as intervals are related
> to a harmonic series.

...but this I agree with.
>
> If you try to test affect for other types of chords,
> or take an actual sample and try to include musical
> context, it becomes far too complicated to isolate
> perceptions of affect.

Isolate yes, but cathing the vibe is easy as pie, no
harder than, say, seeing that painting is all in
cold blues and greens or warm yellows and oranges or
whatever.

-Cameron Bobro

--- In tuning@yahoogroups.com, "Cameron Bobro" <misterbobro@...>
wrote:

> You didn't notice my theory that proximity to a simple interval
> isn't the only explanation for perception of consonance?

I wouldn't call that a theory. A theory would be what does account
for the percepti0on of consonance.

8 people
> have taken the high-fifths test, last time I checked. 4 prefered
the
> lower fith (708 IIRC), 4 thought the higher (710 IIRC) fifth more
> consonant. (Both were complex ratios.)
>
> There you go: a concrete theoretical statement backed up by
> "someone else's" hearing.

Without any concrete theoretical statement.

> Did you download the Scala file I posted and check if it sounds
> cohesive to you, or just a hodge-podge of intervals?

This is too vague to pass jugment on. What the heck is meant by a
hodge podge of intervals?

Aaron Krister Johnson wrote:

> > On a relataed note, and this has been discussed before:
> > I think one of the strangest phenomenon that has never been explained
> satisfactorally is why the brain hears pitches an octave aapart as
> being members of the same pitch class. The best theory out there is
> that all the members of the upper pitches harmonic series are present
> in the lower's series, but that doesn't explain pitch class perception
> in inharmonic spectra, unless we theorize that that must be 'learned'
> by example and extrapolation from harmonic spectra....

One point that may be of interest is that (at least in my case) somewhere above the range of the piano, while I still have a perception of pitch, notes start sounding lower than their "actual" pitch class (if transposed down an octave). I first noticed this years ago listening to bird songs at half speed, which should have sounded the same pitch an octave lower. I haven't done this test in a long time, but it would be interesting to see if the results are the same (or if it's possible for perception of pitch to change over time).

Hi Petr,

--- In tuning@yahoogroups.com, Petr Parízek <p.parizek@...> wrote:
>
> Monz wrote:
>
> > The difference is that long ago humans decided to
> > classify numbers as "even" or "odd" depending on
> > whether or not they are divisible by 2. The only
> > reason we see this as something special is because
> > names were not given to the properties of divisibility
> > by the other primes.
>
> I'm not sure if I can agree about this. As far as higher
> primes are concerned, I still miss the symmetry given by
> the option of an exact contra-value (or how to call that).
> If you have a unit and want to find its "mid-position",
> you split it in two parts to be able to get half the way.
> If you take any other prime and want to find a "simple mean",
> you always end up with units split into halves -- provided
> that the arithmetic mean was the oldest kind of mean I can
> think of.

But don't you see that this is a circular argument?
The only reason you find a midpoint by invoking division
by 2 is because: it is the mathematical property of
division by 2 that you find a midpoint.

The only reason why you think there's something special
about being able to use division by 2 to find a midpoint
is because you decided it's important.

Of course if you try to find a mean with any other prime,
you'll end up with units split into halves, because all
primes are by definition incommensurable, and
"finding a mean" invokes division by 2, and "one half"
by definition invokes division by 2.

You can find an analogy of a mean by dividing by 3 ...
i don't know what it would be called, but the process
is the same except that you use 3 instead of 2. And the
same for all the other primes.

Again, i will not argue that there is not something
special and important about 2: as i've already said,
it's my theory that the prime affect property diminishes
rapidly as you progress thru the prime series, so 2 as
the lowest prime will have the strongest affect. This
goes not only for "equivalence" in music, but also
"evenness" in numbers and math, etc.

-monz
http://tonalsoft.com
Tonescape microtonal music software

Youse guys might appreciate having a look at the late
James Tenney's book Consonance and Dissonance.

--- Gene Ward Smith <genewardsmith@coolgoose.com>
wrote:

> --- In tuning@yahoogroups.com, "Aaron Krister
> Johnson" <aaron@...>
> wrote:
>
> > The best theory out there is
> > that all the members of the upper pitches harmonic
> series are present
> > in the lower's series, but that doesn't explain
> pitch class perception
> > in inharmonic spectra, unless we theorize that
> that must be 'learned'
> > by example and extrapolation from harmonic
> spectra....
>
> It seems to me that theory simply fails because 3,
> the so-
> called "tritave", is a counter-example.
>
>
>

____________________________________________________________________________________
Need Mail bonding?
Go to the Yahoo! Mail Q&A for great tips from Yahoo! Answers users.
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> Youse guys might appreciate having a look at the late
> James Tenney's book Consonance and Dissonance.

We do. In fact we use a formula therein for what we
call "Tenney weighting". But we should probably go to
the libary and get ourselves a full copy to puruse.

-Carl

Carlos, Hermano Mio,

U put tu many u's in peruse! Pero, no importa, and
"importa" isn't in my spanish-english dictionary!

-- Marko

--- Carl Lumma <clumma@yahoo.com> wrote:

> > Youse guys might appreciate having a look at the
> late
> > James Tenney's book Consonance and Dissonance.
>
> We do. In fact we use a formula therein for what we
> call "Tenney weighting". But we should probably go
> to
> the libary and get ourselves a full copy to puruse.
>
> -Carl
>
>

____________________________________________________________________________________
Don't pick lemons.
See all the new 2007 cars at Yahoo! Autos.
http://autos.yahoo.com/new_cars.html

--- In tuning@yahoogroups.com, "Gene Ward Smith" <genewardsmith@...>
wrote:
>
> --- In tuning@yahoogroups.com, "Cameron Bobro" <misterbobro@>
> wrote:
>
> > You didn't notice my theory that proximity to a simple interval
> > isn't the only explanation for perception of consonance?
>
> I wouldn't call that a theory.

An intelligent and educated resonse would be, "that's a colloquial
use of the word "theory".

Better yet, "most of what you've been saying is more like
hypothesis than theory". You fail to grasp such easily inferred
things such as: Bobro has hammered out his ideas related to the
physics of sound past a physicist upon whose practical work the
lives of millions depend, long before flaunting them on the
Internet.

>A theory would be what does account
> for the perception of consonance.

Which I propose again and again, and which you ignore or are
incapable of comprehending. Our perceptions of consonance are in the
first place related to the harmonic series, how many times do I have
to say it? Secondly, in the light of function or the context of the
Uebertimre that is tuning, they are related to coherencies and
patterns within the the tuning, are you so dense that you have
failed to catch that in what I've been ceasely saying?

> 8 people
> > have taken the high-fifths test, last time I checked. 4 prefered
> the
> > lower fith (708 IIRC), 4 thought the higher (710 IIRC) fifth >
>more
> > consonant. (Both were complex ratios.)
> >
> > There you go: a concrete theoretical statement backed up by
> > "someone else's" hearing.
>
> Without any concrete theoretical statement.

Anything to avoid confroting something that doesn't fit in your
religious beliefs, eh?

Now stop squirming around and explain to me why four of eight would
percieve a ~710 cent fifth as more "fifth" and consonant than a ~708
fifth.

> > Did you download the Scala file I posted and check if it sounds
> > cohesive to you, or just a hodge-podge of intervals?
>
> This is too vague to pass jugment on.

Yet grasped immediately by all kinds of practicing musicians.

>What the heck is meant by a
> hodge podge of intervals?

I asked my secretary to dig up my job description. I see "raging
stallion", "loving father" "occaisionally inebriated
buffoon", "bastion of questionable odors" and all kinds of things,
but I fail to find "instructor of American English to Gene". Look it
up, man.

-Cameron Bobro

--- In tuning@yahoogroups.com, "Cameron Bobro" <misterbobro@...>
wrote:
> --- In tuning@yahoogroups.com, "Gene Ward Smith" <genewardsmith@>
> wrote:

> Better yet, "most of what you've been saying is more like
> hypothesis than theory". You fail to grasp such easily inferred
> things such as: Bobro has hammered out his ideas related to the
> physics of sound past a physicist upon whose practical work the
> lives of millions depend, long before flaunting them on the
> Internet.

Argument by anonymous authority just won't work.

Your alleged theory is that intervals like 196/169 are harmonious
because they involve small rations, meaning three-digit number ratios.
The trouble with that "theory" is that between 196/169 we find this:

29/25, 181/156, 152/131, 123/106, 94/81, 159/137, 65/56, 166/143,
101/87, 137/118, 173/149, 36/31, 187/161, 151/130, 115/99, 194/167,
79/68, 122/105, 165/142, 43/37, 179/154, 136/117, 93/80, 143/123,
193/166, 50/43, 157/135, 107/92, 164/141, 57/49, 178/153, 121/104,
185/159, 64/55, 135/116, 71/61, 149/128, 78/67, 163/140, 85/73,
177/152, 92/79, 191/164, 99/85, 106/91, 113/97, 120/103, 127/109,
134/115, 141/121, 148/127, 155/133, 162/139, 169/145, 176/151,
183/157, 190/163, 197/169

The 29/25 is a real problem for your "theory". It's 256.95 cents,
whereas 196/169 is 256.60 cents. We have been given no reason to
think 196/169 is especially consonant sounding, and no reason to
imagine that if it is, it has anything to do with the particular
ratio of 196/169 rather thsn being a feature of anything of about
256.5 cents or so. We certainly have been given no reason to think
that if intervals of about this size have some special woo-woo
quality, it's not attributable to 29/25 instead.

> Which I propose again and again, and which you ignore or are
> incapable of comprehending.

Rather than _ad hominem_ to the effect that your interlocutors are
stupid, try dealing with their criticisms.

> Secondly, in the light of function or the context of the
> Uebertimre that is tuning, they are related to coherencies and
> patterns within the the tuning, are you so dense that you have
> failed to catch that in what I've been ceasely saying?

I do not deal well with vague mush.

> Now stop squirming around and explain to me why four of eight would
> percieve a ~710 cent fifth as more "fifth" and consonant than a
~708
> fifth.

Small sample size, possibly. Also, studies seem to show that some
people prefer intervals mistuned by about 10 cents or so, and other
people like them near-just.

> > > Did you download the Scala file I posted and check if it sounds
> > > cohesive to you, or just a hodge-podge of intervals?
> >
> > This is too vague to pass jugment on.
>
> Yet grasped immediately by all kinds of practicing musicians.

Evidence? They grasped what, exactly? How do you know that unlike me,
they are not inclined to call you on your claims because they know it
will lead to all kinds of unpleasantness?

Agreeing with someone that a scale "sounds cohesive" is easy,
especially if you don't know what that means. But no, I didn't check
it, and don't know what scale you are referring to. If someone tells
me something "sounds cohesive", however, the first thing I *would*
check is whether it is proper and CS. Is it?

> >What the heck is meant by a
> > hodge podge of intervals?
>
> I asked my secretary to dig up my job description. I see "raging
> stallion", "loving father" "occaisionally inebriated
> buffoon", "bastion of questionable odors" and all kinds of things,
> but I fail to find "instructor of American English to Gene". Look
it
> up, man.

In other words, you don't know.

--- In tuning@yahoogroups.com, "Gene Ward Smith" <genewardsmith@...>
wrote:

> The trouble with that "theory" is that between 196/169 we find this:

Between 196/169 and 7/6, sorry.

Greetings,

Perhaps of interest to some:

http://icking-music-archive.org/ByComposer/Valls.php

All best wishes,

Gordon Rumson

Gene Ward Smith, I wrote a long response then thought, pfui, I'm
wasting my time. Instead of us bickering, why don't you just
explain, with some examples, what epimorphic is all about, because
somehow I'm getting this kind of thing:

Scale is JI-epimorphic in non-monotonic order with mapping: 2: 17 3:
27 5: 37 7: 48 11: 59 13: 63 17: 70 19: 70 71: 108
Scale is JI-epimorphic in non-monotonic order with mapping: 2: 17 3:
27 5: 37 7: 48 11: 59 13: 63 17: 70 19: 71 71: 107
Scale is JI-epimorphic in non-monotonic order with mapping: 2: 17 3:
27 5: 39 7: 48 11: 59 13: 63 17: 68 19: 69 71: 105
Scale is JI-epimorphic in non-monotonic order with mapping: 2: 17 3:
27 5: 39 7: 48 11: 61 13: 63 17: 66 19: 69 71: 103
Scale is JI-epimorphic in non-monotonic order with mapping: 2: 17 3:
28 5: 37 7: 49 11: 59 13: 64 17: 71 19: 75 71: 102
Scale is JI-epimorphic in non-monotonic order with mapping: 2: 17 3:
28 5: 39 7: 49 11: 57 13: 64 17: 67 19: 75 71: 104
Scale is JI-epimorphic in non-monotonic order with mapping: 2: 17 3:
28 5: 39 7: 49 11: 57 13: 64 17: 69 19: 73 71: 104

in all the tunings I hear as cohesive and of well-related character
families.

It's the only consistent thing in Scala's analysis- the scales are
not proper, sometimes they're CS, sometimes not, etc.

-Cameron Bobro

--- In tuning@yahoogroups.com, "Cameron Bobro" <misterbobro@...> wrote:
>
> Gene Ward Smith, I wrote a long response then thought, pfui, I'm
> wasting my time. Instead of us bickering, why don't you just
> explain, with some examples, what epimorphic is all about, because
> somehow I'm getting this kind of thing:

The numbers followed by colons are primes, followed by how many steps
the prime is mapped to. So 2:17 3:27 5:37 says 2 is mapped to 17 steps,
3 to 27, and 5 to 37. A JI scale is epimorphic in monotonic order, or
simply epimorphic, if any interval in the nth interval class is mapped
by this to n. It is non-monotonically epimorphic if
each interval class gets a unique number by such a mapping, but the nth
interval above 1/1 does not neceesarily get mapped to n. Hence, there
is some kind of rhyme and reason here, but not from a very strong
condition on the scale. It's a fairly weak condition, and hence happens
a lot, so you see it a lot.

--- In tuning@yahoogroups.com, Gordon Rumson <rumsong@...> wrote:
>
> Greetings,
>
> Perhaps of interest to some:
>
> http://icking-music-archive.org/ByComposer/Valls.php
>
> All best wishes,
>
> Gordon Rumson
>

From the composer's notes:

"This is the enharmonic composition which I
have offered. I repeat that except with these
instruments, played with great care, its use is
very difficult. There are, however, some
voices and instrumental performers who are
so tone deaf that they ordinarily play or sing
enharmonically. It is unbearable to listen to
them."

Ha!

... This composition is also cited in Barbieri's article on Violin
Intonation.

~~~T~~~

17th-century enharmonic music with scores and
MIDI? Pinch me.

Wow, this dude lived to be old.

-Carl

--- In tuning@yahoogroups.com, Gordon Rumson <rumsong@...> wrote:
>
> Greetings,
>
> Perhaps of interest to some:
>
> http://icking-music-archive.org/ByComposer/Valls.php
>
> All best wishes,
>
> Gordon Rumson
>