Re: 12 eq (Paul)

>From: "Paul H. Erlich" <PErlich@Acadian-Asset.com>

>>Most ET intervals require
>>relatively high number ratio approximations
>
>I don't know what you mean by "require", but shouldn't the only
>requirement is that our ears can really make out the ratios you're
>using? I would say that under most circumstances, most 12-ET intervals
>require relatively low number ratio approximations: the minor third is
>6:5, the major third is 5:4, the perfect fourth is 4:3, their inversions
>similarly, and the tritone is quite often 7:5 or 10:7.
>

Surely it is easy to hear 5/4 and 400c as two different intervals. 400c is
closely approximated by 635/504 (399.99943c). This is a 127 limit(!) ratio.
Within a tonal context, we do read 400c as 5/4, but 400c still has a sound
of its own. Weather that sound fits within any discernable musical system
>as< itself is another question. I doubt if it could to any human ears (at
least at this stage of our aural evolution. Who knows what the next few
thousand years may bring!) But I would say that anyone who argues for an
independent function for et intervals (as opposed to their being read by
our ears as low number ratios) would have to answer this.

>>so the question of perception
>>of ET intervals can be considered as identical with that of the
>perception
>>of higher number ratios.
>
>Yes, both will tend to be heard in terms of simpler ratios (this is
>quite related to my last post!).
>

I think this has alot to do with context. To my ear, gamelan scales do not
sound like mistuned low integer ratios.

dante

On Wed, 24 Feb 1999 17:09:58 -0500, dante rosati <dante@pop.interport.net>
wrote:

>Surely it is easy to hear 5/4 and 400c as two different intervals. 400c is
>closely approximated by 635/504 (399.99943c). This is a 127 limit(!) ratio.

I agree that 5/4 and 400c sound different (13.7c apart), but the difference
between 63/50 (400.1c) and 635/504 is practically inaudible. The important
thing about 400c (as far as I'm concerned) is not that it's a good
approximation of 63/50, but that exactly three of them subdivide the octave
into equal parts, which allows for some interesting modulations in 12-tet
and 15-tet (or any other multiple of 3-tet) that can only be approximated
in just scales. (Just scales, on the other hand, have chords that are more
consonant than equal scales until you get up into the 41-tet and 53-tet
range, or unless you use custom timbres especially designed for the scale
you're using, like William Sethares.)

>I think this has alot to do with context. To my ear, gamelan scales do not
>sound like mistuned low integer ratios.

True. The metallophone spectra are non-harmonic, so scales with low integer
ratios have no special advantages.

I wrote:

>>But I would say that anyone who argues for an
>>independent function for et intervals (as opposed to their being read
>by
>>our ears as low number ratios) would have to answer this.
>
and Paul replied:

>I say most of them are read as low number ratios. Does that mean I don't
>have to answer? (Again, sorry if I sound rude, but I'm really concerned
>I'm not getting the jist of your arguments here.)
>

I think here I was commenting more on what Daniel Wolf had said in an
earlier post, after I suggested that et intervals are heard by our inner
ears as Ji ratios:

>I believe you are right, but I would like you to be wrong. One of my goals
>as a musician is to train myself to hear intervals with such precision that
>I can avoid these triggering mechanisms. I find absolutely nothing
>attractive in the idea that my listening is essentially a programmed
>response to such conditioning.

My point was that perhaps our brain/minds can only really respond to JI
intervals, and the et intervals that Daniel wants to hear for themselves,
and not as JI signifiers, are at best irrational approximations of high
number ratios. So I used 635/504 as an example (today in a post Herman
Miller pointed out 63/50 as a lower approximation) of the kind of JI ratio
that one would have to be able to hear to experience 400c as JI without it
being a signifier of 5/4. Since it seems that the point of contention as to
hearability is somwhere between 13 and 19, Id say that hearing even 63/50
as a ratio is beyond our ears at present, let alone 635/504. Given the
possibility of some kind of historical progressive exploration of higher
ratios (like Partch and others suggest), a whimsical possiblility is that
someday, in the far future, or maybe in a galaxy far far away, our remote
ancestors will have progressed up the series to the point where they can
hear these ratios as themselves. Now I am also aware that materialistic
Darwinism only uses the word "evolution" in a limited sense, hence Pauls
comment about survival of the fittest. Nevertheless, a more broad
definition of evolution can apply to the arts at least in the sense of
building upon what previous generations have accomplished.

I see where I may seem to be contradicting myself: first I say that 400c is
distinguishable from 5/4 as an isolated interval (which of course it is),
but then I say that it cannot exist as anything but a signifier for 5/4 due
to our ear's inability to hear such high ratios. Now, 81/64 is alot closer
to 400c than is 5/4, and is of course a classic 3 (prime)limit ratio, so
why is it we dont read 400c as 81/64? I guess this is proof of Pauls
statements about odd limit being more important than prime limit when it
comes to consonance. In fact we read 81/64 as 5/4 too. (81/64 is closer to
9/7 than to 5/4. Can 81/64 be read as 9/7 under some circumstances?) So
maybe its not about how high you can hear, but how close is the ratio
you're trying to hear to a low (odd) limit ratio with its black hole
attractor? The closer it is, and the lower the odd limit of the ratio it's
near to, the harder it is to hear it "as itself" (81/64 may be closer to
9/7 but 5/4's attractor is stronger?)

If we hear 400c played on a piano within the context of tonal music, we
hear it as 5/4. But what is it we are hearing if we are played first 5/4,
then 400c, as isolated intervals, and we experience them as distinct?

just wondering...

dante

ps- Paul also said:

(Once again, I
>apologize if I seem like I'm being unnecessarily argumentative. But to
>be honest, I got the sense that your last post, which was a reply to me,
>had elements of changing the terms of the discussion to gain some sort
>of advantage. I had to defend myself, but if I totally misread you, I
>sincerely apologize.)

Rather than trying to gain an advantage (this is not a competition) any
changing of terms or inconsistancies on my part are simply the result of my
trying to get a handle on issues that are somewhat new to me. I can only
ask for your patience and try to formulate my thoughts more carefully in
future.

Message text written by INTERNET:tuning@onelist.com
>>I think this has alot to do with context. To my ear, gamelan scales do
not
>sound like mistuned low integer ratios.
<
<True. The metallophone spectra are non-harmonic, so scales with low
integer
<ratios have no special advantages.
<

Wait a minute! This is a constant fallacy on this list with little basis
in fact: the identification of gamelan tunings exclusively with the
metallophones. In Java, large gamelan groups also have instruments with
standard harmonic spectra and the repertoire is overwhelmingly dominated by
voices. The repertoire can also be played by ensembles composed
exclusively of voices and strings. Furthermore, the gender, which is the
instrument with which the gamelan smith sets the temperament, has 1/4 wave
tube resonators in the upper octaves, so that the ordinary odd-numbers
harmonics are part of the timbre. It is important to recall that a primary
function of the inharmonic spectra is to help individual instruments be
identifiable through the dense ensemble texture, and, in the repertoire
dominated by the least harmonic instruments (sarons and bonang), simply to
play louder.

I am only a novice rebab (spike fiddle) player, but it is striking how
helpful it is to orient my intonation with each ensemble I play by thinking
in terms of small rational intervals. The Javanese do not do this, but
they do talk in terms of acoustical octaves and fifths being in tune
('pleng'), or narrow or wide and sequences of melodic intervals in terms of
small, medium, or large (in slendro, these turn into something very close
to 9/8, 8/7, 7/6). It is my old contention that slendro, at least, is a
tempered pythagorean tuning in three keys, with the near-septimal melodic
intervals an accidental by-product of the tempering process, but in
practice they have become identifying features.

>True. The metallophone spectra are non-harmonic, so scales with low integer
>ratios have no special advantages.

I have to disagree. Though I haven't read William Sethares' book yet, I can
say with certainty from my own experience that just intonation definitely
does offer special advantages with many metallophone timbres, despite the
presence of some non-harmonic partials.

I myself have worked extensively with Javanese gender tuned to JI. For many
things I prefer JI with the subtle but slightly bittersweet effect of some
non-harmonic upper partials. It's a very different effect than playing on a
gender which is (like most in Java) not tuned to JI, but no less beautiful
than, say, JI with a synthesized timbre of all harmonics.

Having just this week heard Lou Harrison's beautiful suite for violin and
American gamelan (with his American gamelan shipped down from Aptos), I
remain all the more convinced of the success of JI metallophones.

With all respect to Sethares' work, I must say that I view with skepticism
the claim that tuning systems (or consonance/dissonance for that matter)
must be tied to timbre.

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

Message text written by Bill Alves

>With all respect to Sethares' work, I must say that I view with skepticism
the claim that tuning systems (or consonance/dissonance for that matter)
must be tied to timbre.<

One of the (many) qualities in Sethares' book is that he doesn't make such
a claim of a _necessary_ connection between tuning and timbre but rather
suggests a framework for making and discussing a possible connection. I
disagree myself with his analysis of Javanese tunings (much as one would
disagree with Kathleen Schlesinger about the Greek Aulos or Dr. Henesbry
about Sean Nos intonation), but find his ideas within the analysis to be
exciting ones for further research and compositional work.

Bill Alves also wrote:

<I can
<say with certainty from my own experience that just intonation definitely
<does offer special advantages with many metallophone timbres, despite the
<presence of some non-harmonic partials.

I recall a comment from a Javanese musician regarding one of the
Harrison/Colvig gamelans -- that the tuning was fine but that he couldn't
distinguish the instruments from one another. It is very important for the
ensemble that a kenong sounds different from a bonang and both sound
different from a saron or a gender. Beyond the distinctive envelopes, it
is the presence of non-harmonic partials in very roughly similar spectra
for each instrument type that contribute to making such distinctions. The
Harrison/Colvig instrument are aluminum, with a soft attack, and more of
the instruments are resonated than is typical in Java, both of these
dactors contribute to a general smoothing-out of timbral differences.

When I had my gambang (xylophone) keys made in Klaten, Java, the maker
first tuned the 2nd partial to an exact double octave and then tuned it
away from this interval, so that "it would be heard". This demonstrated
that the maker was aware of how the timbre could be manipulated, but
deliberately chose a non-harmonic timbre to bring out the distinctiveness
of the instrument.

Harry Partch, no stranger to distinctive instrumental timbres, writes a
bit about inharmonic partials in his description of Boo II and of the alto
flanks on the Quadrangularis Reversum in _Genesis_, and his remarks about
voicing Boo sections and harmonium reeds in his _Handbook_ are also worth
looking at. While not seeking a precise tunings for these partials,
Partch was interested in making sequence of tones that have similar
spectra.

Maybe Jonathan Szanto has a word or two to say about Boos I and II and the
notorious synthetic Boos...

dante rosati wrote:

>
>
> My point was that perhaps our brain/minds can only really respond to JI
> intervals, and the et intervals that Daniel wants to hear for themselves,
> and not as JI signifiers, are at best irrational approximations of high
> number ratios.

I feel this is a real underestimation of the human mind. Why would our
perceptions of intervals be any more limited than colour. There just hasn't
been enough research to completely except any conclusion. When we get to the
place of what happens in the mind in lets say a whole 40 min orchestral
compositions as far as pushes and pulls will we be able to say what it is we
are experiencing

> So I used 635/504 as an example (today in a post Herman
> Miller pointed out 63/50 as a lower approximation) of the kind of JI ratio
> that one would have to be able to hear to experience 400c as JI without it
> being a signifier of 5/4. Since it seems that the point of contention as to
> hearability is somwhere between 13 and 19, Id say that hearing even 63/50
> as a ratio is beyond our ears at present, let alone 635/504. Given the
> possibility of some kind of historical progressive exploration of higher
> ratios (like Partch and others suggest), a whimsical possiblility is that
> someday, in the far future, or maybe in a galaxy far far away, our remote
> ancestors will have progressed up the series to the point where they can
> hear these ratios as themselves. Now I am also aware that materialistic
> Darwinism only uses the word "evolution" in a limited sense, hence Pauls
> comment about survival of the fittest.

That which survives is not the "fittest" or "strongest" but those species that
maximize there interrelationships with other species. Look at plants as an
example

> Nevertheless, a more broad
> definition of evolution can apply to the arts at least in the sense of
> building upon what previous generations have accomplished.
>
> I see where I may seem to be contradicting myself: first I say that 400c is
> distinguishable from 5/4 as an isolated interval (which of course it is),
> but then I say that it cannot exist as anything but a signifier for 5/4 due
> to our ear's inability to hear such high ratios. Now, 81/64 is alot closer
> to 400c than is 5/4, and is of course a classic 3 (prime)limit ratio, so
> why is it we dont read 400c as 81/64? I guess this is proof of Pauls
> statements about odd limit being more important than prime limit when it
> comes to consonance. In fact we read 81/64 as 5/4 too. (81/64 is closer to
> 9/7 than to 5/4. Can 81/64 be read as 9/7 under some circumstances?) So
> maybe its not about how high you can hear, but how close is the ratio
> you're trying to hear to a low (odd) limit ratio with its black hole
> attractor? The closer it is, and the lower the odd limit of the ratio it's
> near to, the harder it is to hear it "as itself" (81/64 may be closer to
> 9/7 but 5/4's attractor is stronger?)
>
>
> dante
>

-- Kraig Grady
North American Embassy of Anaphoria Island
www.anaphoria.com

Bill Alves wrote:

>
> I must say that I view with skepticism
> the claim that tuning systems (or consonance/dissonance for that matter)
> must be tied to timbre.

I agree fully, look at the various timbres that work so well in ET! Or any
other tuning system in use in Large groups!

-- Kraig Grady
North American Embassy of Anaphoria Island
www.anaphoria.com

On Fri, 26 Feb 1999 06:13:57 -0500, Daniel Wolf
<DJWOLF_MATERIAL@compuserve.com> wrote:

>From: Daniel Wolf <DJWOLF_MATERIAL@compuserve.com>
>
>Message text written by INTERNET:tuning@onelist.com
>>>I think this has alot to do with context. To my ear, gamelan scales do
>not
>>sound like mistuned low integer ratios.
><
><True. The metallophone spectra are non-harmonic, so scales with low
>integer
><ratios have no special advantages.
><
>
>Wait a minute! This is a constant fallacy on this list with little basis
>in fact: the identification of gamelan tunings exclusively with the
>metallophones.

I know that gamelans include instruments and voices with harmonic spectra,
but I was specifically responding to the comment that traditional gamelan
scales don't sound like mistuned low integer ratios. Come to think of it,
some gamelans have instruments made of bamboo tubes rather than metal bars.
Still, the gamelans with metallophones are the ones I'm most familiar with,
and that's what came to mind when I wrote the reply. I've been thinking
about this, and I have what I think is a better explanation that doesn't
require any assumptions about timbre.

Low integer ratios are useful for explaining traditional Western harmony,
but they don't always make sense with other kinds of scales. If you take a
two-step interval from Wendy Carlos' alpha scale, for instance, I'd prefer
to call it half a minor third than an approximation to 12/11. Some pelog
scales have an interval size that has a similar impression to my ear,
splitting a (roughly) minor third into two parts that are (roughly) similar
in size. I'm not sure that it matters much whether it is closer to 11/10,
12/11, or 13/12, or somewhere in between. In general, my feeling is that
the pattern of small and large steps is more relevant to the character of a
pelog scale than the integer ratios that approximate those steps.
Blackwood's faux pelog in his 23-note etude is still recognizable as a
pelog scale. Similarly, the roughly equal size of the steps of a slendro
scale is what gives it its distinctive character.

On Fri, 26 Feb 1999 10:45:35 -0800, alves@orion.ac.hmc.edu (Bill Alves)
wrote:

>With all respect to Sethares' work, I must say that I view with skepticism
>the claim that tuning systems (or consonance/dissonance for that matter)
>must be tied to timbre.

I've been playing with the 16-tone scale recently, and I've noticed that
inharmonic timbres (resembling xylophones or bowed vibraphones, for
instance), as well as timbres with predominantly odd partials, sound better
than harpsichords or other instruments with a rich harmonic spectrum. I
retuned my kalimba today to a subset of the 16-note scale, with generally
pleasing results. But sustained harmonic sounds like accordions have a
tendency to sound unpleasant with that tuning.

On the other hand, I've also tried retuning instrument samples using the
methods described in Sethares' book. Timbres specifically tweaked for
15-tet do sound better in 15-tet than harmonic timbres, and they sound bad
in combination with harmonic timbres in the same tuning. One of my recent
experiments (http://www.io.com/~hmiller/music/yeequitch-keesha.ra) uses
these new 15-tet timbres.

(Incidentally, I recently ordered a copy of the score for Blackwood's
etudes, and it turns out that this instrumentation also sounds nice for his
15-note etude. I wonder if it would be much of a violation of the spirit of
Blackwood's project to construct timbres that specifically sound good for
those particular tunings?)

Herman Miller wrote:

>
>
> I've been playing with the 16-tone scale recently, and I've noticed that
> inharmonic timbres (resembling xylophones or bowed vibraphones, for
> instance), as well as timbres with predominantly odd partials, sound better
> than harpsichords or other instruments with a rich harmonic spectrum. I
> retuned my kalimba today to a subset of the 16-note scale, with generally
> pleasing results. But sustained harmonic sounds like accordions have a
> tendency to sound unpleasant with that tuning.

As it so happens the Chopi in S.E. Africa have a tuning that falls somewhere
in between 7 equal and 16 equal although they never use equal anything. The
Mbira of Zimbabwe is tuned to these same tunings. In all here are the timbre
you mentioned. In Anaphoria there is a 20 min. piece called COURT MUSIC OF THE
MESA transcribed for pump organ (very accordion like) that works amazing well.
A CD recording Exist on From the Interiors of Anaphoria.
-- Kraig Grady
North American Embassy of Anaphoria Island
www.anaphoria.com

On Fri, 26 Feb 1999, Kraig Grady wrote
>
> dante rosati wrote:
>
> > My point was that perhaps our brain/minds can only really respond to JI
> > intervals, and the et intervals that Daniel wants to hear for themselves,
> > and not as JI signifiers, are at best irrational approximations of high
> > number ratios.
>
> I feel this is a real underestimation of the human mind. Why would our
> perceptions of intervals be any more limited than colour.

Indeed, why not? There's a whole range of wavelengths which are just plain
'blue'. They're completely different on a mass spectrometer, and if you
had different filters which only let through narrow bands of blue there
would be some interesting effects with pairs of them making black, but to
the normal human eye they're all just plain blue.

Not to mention our total lack of perception of polarity, or any
wavelengths in the infrared or ultraviolet ...

-Bram

bram wrote:

> From: bram <bram@gawth.com>
>
> On Fri, 26 Feb 1999, Kraig Grady wrote
> >
> > dante rosati wrote:
> >
> > > My point was that perhaps our brain/minds can only really respond to JI
> > > intervals, and the et intervals that Daniel wants to hear for themselves,
> > > and not as JI signifiers, are at best irrational approximations of high
> > > number ratios.
> >
> > I feel this is a real underestimation of the human mind. Why would our
> > perceptions of intervals be any more limited than colour.
>
> Indeed, why not? There's a whole range of wavelengths which are just plain
> 'blue'. They're completely different on a mass spectrometer, and if you
> had different filters which only let through narrow bands of blue there
> would be some interesting effects with pairs of them making black, but to
> the normal human eye they're all just plain blue.
>
> Not to mention our total lack of perception of polarity, or any
> wavelengths in the infrared or ultraviolet ...

The human eye is best in the yellow green range and under optimum conditions can
detect a single photon. I would see the blue and violet and the infa reds as
analogous to the high and low of our hearing range. In the middle It does
uncannily well!
-- Kraig Grady
North American Embassy of Anaphoria Island
www.anaphoria.com

Message text written by Herman Miller

>Blackwood's faux pelog in his 23-note etude is still recognizable as a
pelog scale.<

By whom?

Dante Rosati wrote,

>>I think this has alot to do with context. To my ear, gamelan scales do
not
>>sound like mistuned low integer ratios.

Daniel Wolf wrote,

>Furthermore, the gender, which is the
>instrument with which the gamelan smith sets the temperament, has 1/4
wave
>tube resonators in the upper octaves, so that the ordinary odd-numbers
>harmonics are part of the timbre.

This is a common fallacy. The resonator can do nothing but selectively
amplify partials already contained in the source of the vibration.
What's a gender? If it is a struck metallophone, it won't have any
integer partials, resonantor or not.

>I am only a novice rebab (spike fiddle) player, but it is striking how
>helpful it is to orient my intonation with each ensemble I play by
thinking
>in terms of small rational intervals. The Javanese do not do this, but
>they do talk in terms of acoustical octaves and fifths being in tune
>('pleng'), or narrow or wide and sequences of melodic intervals in
terms of
>small, medium, or large (in slendro, these turn into something very
close
>to 9/8, 8/7, 7/6).

I think nearly every musical culture can perceive octaves and fifths and
bases their scales upon them. So in that sense, I do hear gamelan scales
as containing (mistuned) low integer ratios, regardless of overtone
spectrum considerations.

<Message text written by INTERNET:tuning@onelist.com
<>
<>Furthermore, the gender, which is the
<>instrument with which the gamelan smith sets the temperament, has 1/4
<wave
<>tube resonators in the upper octaves, so that the ordinary odd-numbers
<>harmonics are part of the timbre.
<
<This is a common fallacy. The resonator can do nothing but selectively
<amplify partials already contained in the source of the vibration.
<What's a gender? If it is a struck metallophone, it won't have any
<integer partials, resonantor or not.<
<
<Paul Erlich:

Aside from the well-known fact that idiophone partials can be tuned to
interger harmonics , you're simply wrong about the gender. In the lowest
tones of the gender barung, the resonators have smaller openings, so behave
more like Helmholtz resonators and only the fundamental is storngly
amplified, but above this, the resonators are straight tubes closed at one
end, and once excited at the fundamental will also sound, albeit
attenuated, at odd harmonics. Gamelan makers tune the resonators and keys
simultaneously to the same fundamental. Suspend the keys over the
resonators and take a spectrogram; you'll find a mixture of the integer
harmonics and bar harmonics. A spectrogram of the key alone does not show
these integer harmonics. The resonators on the gender (which is right next
to me as I speak) were tuned with probably more care than is usual --
since the maker knew I was fussy about it -- and the 3rd, 5th and 7th
harmonic partials are ALL stronger than the upper bar partials.

I wrote,

>>This is a common fallacy. The resonator can do nothing but selectively
>>amplify partials already contained in the source of the vibration.

Daniel Wolf wrote,

>Suspend the keys over the
>resonators and take a spectrogram; you'll find a mixture of the integer
>harmonics and bar harmonics. A spectrogram of the key alone does not
show
>these integer harmonics. The resonators on the gender (which is right
next
>to me as I speak) were tuned with probably more care than is usual --
>since the maker knew I was fussy about it -- and the 3rd, 5th and 7th
>harmonic partials are ALL stronger than the upper bar partials.

There has to be some explanation for this -- I stand by the physical
validity of my original statement.

>From: "Paul H. Erlich" <PErlich@Acadian-Asset.com>
>
>I wrote,
>
>>>This is a common fallacy. The resonator can do nothing but selectively
>>>amplify partials already contained in the source of the vibration.
>
>Daniel Wolf wrote,
>
>>Suspend the keys over the
>>resonators and take a spectrogram; you'll find a mixture of the integer
>>harmonics and bar harmonics. A spectrogram of the key alone does not
>show
>>these integer harmonics. The resonators on the gender (which is right
>next
>>to me as I speak) were tuned with probably more care than is usual --
>>since the maker knew I was fussy about it -- and the 3rd, 5th and 7th
>>harmonic partials are ALL stronger than the upper bar partials.
>
>There has to be some explanation for this -- I stand by the physical
>validity of my original statement.
>

On guitar you can play multiphonics because higher harmonics played in the
vicinity of a major node like 1/2 will exite that node without having to be
exactly on it. Perhaps resonators may resonate if the bar's partials are in
the vicinity of its frequency?

dante

>From: "Paul H. Erlich" <PErlich@Acadian-Asset.com>
>
>I wrote,
>
>>>This is a common fallacy. The resonator can do nothing but selectively
>>>amplify partials already contained in the source of the vibration.
>
>Daniel Wolf wrote,
>
>>Suspend the keys over the
>>resonators and take a spectrogram;...the 3rd, 5th and 7th
>>harmonic partials are ALL stronger than the upper bar partials.
>
Paul H. Erlich:
>There has to be some explanation for this -- I stand by the physical
>validity of my original statement.

One possible explanation is that the "bars" of a gender are certainly not
regular rectangular shapes like those of a vibraphone. They are very thin
and have two prominent ridges ("blimbingan" or "star-fruit") running down
their length. I have been told that the shape of these ridges affects the
timbre and tuning, but I don't have any details. Daniel?

Bill

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

Message text written by Bill Alves
>
One possible explanation is that the "bars" of a gender are certainly not
regular rectangular shapes like those of a vibraphone. They are very thin
and have two prominent ridges ("blimbingan" or "star-fruit") running down
their length. I have been told that the shape of these ridges affects the
timbre and tuning, but I don't have any details. Daniel?<
>

Bill Alves has brass keys on his gender, which are much thinner than my
bronze keys. The effect of the scalloping is greater on thinner keys, in
that the deeper the scallop the higher the fundamental, thus reducing the
interval between the fundamental and the upper partial. (Brass keys are in
fact tuned by bending them, along the scallop to raise, and lengthwise to
lower, while bronze keys are tuned by filing away metal.) I'm not aware
of any makers tuning the partials of gender keys, as my gambang keys were
tuned

Perhaps to close the discussion, the fact is -- perhaps either through the
noise of the attack or near resonances between the partials of the bar and
the harmonics of the resonator -- the odd integer harmonics are prominent
in the tone of the gender as the gamelan smith tunes.

> > I must say that I view with skepticism
> > the claim that tuning systems (or consonance/dissonance for that matter)
> > must be tied to timbre.
> I agree fully, look at the various timbres that work so well in ET! Or any
> other tuning system in use in Large groups!

Well, I don't think it's as simplistic a matter as "whether" they work in
a particular tuning, as much as how they affect each other. It's had to deny
that timbre affects the perception of tuning, but it rarely comes down to a
pass or fail sort of effect.

Here's an example effect: If you wanted to demonstrate that a 400-cent M3
doesn't sound as clean as a 5:4, would you use a clarinet or violin timbre?
Answer: Clarinet. It will much raunchier on a clarinet than on a violin.

Now as for how many timbres sound good on 12TET and several other equal
temperaments. I think that that's a meaningful point, but there's another
partial explanation to consider too: The spectrum of timbral possibilities
sound good in realizing 5-limit harmony partly because those timbres were
developed simultaneously with tunings designed around 5-limit harmonies.

Anybody who listens to the demonstrations in Bill's book can hear that, as
he put it, "these are not subtle effects". Now it's certainly true that the
book deals, at first anyway, with extreme cases (like extremely widely
stretched octaves for example) to illustrate the concepts more clearly. But
it's pretty obvious that the same processes that produce these extreme effects
can produce significant effects under more subtle conditions.

Dante Rosati wrote,

>On guitar you can play multiphonics because higher harmonics played in
the
>vicinity of a major node like 1/2 will exite that node without having
to be
>exactly on it.

Unlike multiphonics on a wind instrument, what you are describing is all
just part of a single harmonic series (that with the open string's
frequency as the fundamental).

>Perhaps resonators may resonate if the bar's partials are in
>the vicinity of its frequency?

Yes, but they will resonate at the bar's frequencies, not the
resonator's frequencies (this is undergrad physics: have you ever seen a
graph of vibrational amplitude versus driving frequency (=vibrational
frequency) for a harmonic oscillator? It's a roughly bell-shaped curve
that reaches its maximum at the resonant frequency. If there is no
damping in the system, the maximum is infinitely high, as the energy
pumped in to the system doesn't dissipate, it just accumulates).

Message text written by INTERNET:tuning@onelist.com
>Yes, but they will resonate at the bar's frequencies, not the
resonator's frequencies (this is undergrad physics: have you ever seen a
graph of vibrational amplitude versus driving frequency (=vibrational
frequency) for a harmonic oscillator? It's a roughly bell-shaped curve
that reaches its maximum at the resonant frequency. If there is no
damping in the system, the maximum is infinitely high, as the energy
pumped in to the system doesn't dissipate, it just accumulates).<

When the resonator and the bar are not exactly in tune -- but rather on
sides of the bell curve -- striking the bar and quickly damping will cause
a slight portamento from the pitch of the bar to that of the resonator.
This is one way the maker checks the tuning.

An important point to be made about the non-harmonic
partials on those metallophones: they're all bunched up near the onset of the
sound,
then the sustaining tone is much smoother.
Rick Sanford
manhattan

Bill Alves wrote:

> From: alves@orion.ac.hmc.edu (Bill Alves)
>
> >True. The metallophone spectra are non-harmonic, so scales with low integer
> >ratios have no special advantages.

>From: Rick Sanford <rsanf@pais.org>
>
>An important point to be made about the non-harmonic
>partials on those metallophones: they're all bunched up near the onset of the
>sound, then the sustaining tone is much smoother.
>
>Bill Alves wrote:
>
>> >True. The metallophone spectra are non-harmonic, so scales with low integer
>> >ratios have no special advantages.

By the way, I didn't write this part. I wouldn't bring up a mistaken
attribution, except that I don't agree with what was quoted. (In fact I
commissioned and own JI gender -- Javanese metallophones.)

Bill

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