JI and the listening composer

As we're debating the JI/ET business again, here's an observation. I was
listening somewhat inattentively to one of my ensemble players gently
improvising on a zither accurately tuned to 1/1 - 7/6 - 4/3 - 3/2 - 7/4
- 2/1. I began to hear, either in my head or as a result of combination
and difference tones, very beautiful and quite 'angular' tones, very
good possibilities for pedals, inverted pedals and inner voices.

The point is (in case all this sounds too romantic or poetic) that I've
never had these suggestions whilst listening to ETs and I work often
with several different ETs. I don't believe ETs will work in this way.

Without going too much into the whys and wherefores I've taken note of
something I didn't know before about Just Intonation and from a
composer's viewpoint this sets JI apart (not better, just different). I
feel very good about this. It's as if the music will write itself if I
can concentrate hard enough and listening deeply.

Anyone else had similar experiences?

Kind Regards

--- In tuning@y..., Alison Monteith <alison.monteith3@w...> wrote:

> The point is (in case all this sounds too romantic or poetic) that I've
> never had these suggestions whilst listening to ETs and I work often
> with several different ETs. I don't believe ETs will work in this way.

Would it matter to you if I pointed out that this is demonstrably wrong? Obviously, any et with tuning fine enough to be indistinguishable from JI will work this way.

--- In tuning@y..., "genewardsmith" <genewardsmith@j...> wrote:
> --- In tuning@y..., Alison Monteith <alison.monteith3@w...> wrote:
>
> > The point is (in case all this sounds too romantic or poetic)
that I've
> > never had these suggestions whilst listening to ETs and I work
often
> > with several different ETs. I don't believe ETs will work in this
way.
>
> Would it matter to you if I pointed out that this is demonstrably
>wrong? Obviously, any et with tuning fine enough to be
>indistinguishable from JI will work this way.

sounds snooty, right?

well, in this context, alison, i'm afraid gene's comment is perfectly
appropriate. no matter how well you tuned your zithers (which have
slightly inharmonic partials anyhow), you could find some et which
comes even closer to ji.

it may seem snooty, but that's not the point at all (at least not
*my* point). the point is that you should discover for yourself, for
your own ears, what it means to have 3 cents errors from ji, 2 cents
errors, 1 cent errors. then, when someone proposes something in this
or that temperament that can't be done in ji, you'll have a basis for
deciding whether, and how much, you'd be sacrificing the ji effects
you treasure.

romantic and poetic . . . the reasons you associate these with ji
rather than temperament are extra-musical. in another culture, in
another time, the associations would (and have been) reversed.

--- In tuning@y..., Alison Monteith <alison.monteith3@w...> wrote:

> As we're debating the JI/ET business again, here's an observation.
I was
> listening somewhat inattentively to one of my ensemble players
gently
> improvising on a zither accurately tuned to 1/1 - 7/6 - 4/3 - 3/2 -
7/4
> - 2/1. I began to hear, either in my head or as a result of
combination
> and difference tones, very beautiful and quite 'angular' tones, very
> good possibilities for pedals, inverted pedals and inner voices.
>
> The point is (in case all this sounds too romantic or poetic) that
I've
> never had these suggestions whilst listening to ETs and I work often
> with several different ETs.

i hear these all the time in 22. more to the point, have you tried
tuning the pentatonic scale above in 72 on your zither for
comparison? but do also try it in 22, where 4/3 will form a much more
consonant dyad with 7/4, and larger chords which include both notes
will benefit.

> I don't believe ETs will work in this way.

i can't blame you for wanting to tune a steel-string instrument very
justly. i've had the same experience which is leading to the
construction of the shrutar (which i've discussed quite a bit). but
you can only take this reasoning so far -- struck steel strings have
slightly inharmonic partials!

> Without going too much into the whys and wherefores I've taken note
of
> something I didn't know before about Just Intonation and from a
> composer's viewpoint this sets JI apart (not better, just
different). I
> feel very good about this. It's as if the music will write itself
if I
> can concentrate hard enough and listening deeply.
>
> Anyone else had similar experiences?

yes, i've had the same experience with 22. not on the classical
guitar though . . . have you tried 22-equal on any other instruments?

if you end up going with a ji philosophy and approach, i couldn't be
happier. i'd like to see you give 72 a fair chance, though, since it
will be far more comprehensible to western-trained musicians, in
addition to the "super-ji" (paraphrasing pehrson) possibilities which
have already been discussed to death here.

--- In tuning@y..., "genewardsmith" <genewardsmith@j...> wrote:
> Would it matter to you if I pointed out that this is demonstrably wrong? Obviously, any et with tuning fine enough to be indistinguishable from JI will work this way.

Just like drawing enough straight lines, at small enough angles, to end up with a curve.

Instead of just drawing a curve.

Cheers,
Jon

genewardsmith wrote:

> --- In tuning@y..., Alison Monteith <alison.monteith3@w...> wrote:
>
> > The point is (in case all this sounds too romantic or poetic) that I've
> > never had these suggestions whilst listening to ETs and I work often
> > with several different ETs. I don't believe ETs will work in this way.
>
> Would it matter to you if I pointed out that this is demonstrably wrong? Obviously, any et with tuning fine enough to be indistinguishable from JI will work this way.

It would matter indeed if my ears and brain were not wired up together and that I was therefore confused as to what I perceive. I'm not confused, except inasmuch as I
often confuse 'tuning' with 'music'.

I believe that I'm becoming more discriminating through exposure to accurate tuning. Anyone can do this, and some have offered their findings to the readers of this
list. But it requires direct experience to prove or disprove. I work every day with different tunings and can only report what I experience.

Obviously, as you rightly point out, there are ETs with tones that lie 0.1 or 0.2 of a cent off JI, thus indistinguishable to most ears. But their validity in this test
lies in their closeness to the just intervals. Why not just go the whole hog and catch the pure tone?

Kind Regards

emotionaljourney22 wrote:

> --- In tuning@y..., "genewardsmith" <genewardsmith@j...> wrote:
> > --- In tuning@y..., Alison Monteith <alison.monteith3@w...> wrote:
> >
> > > The point is (in case all this sounds too romantic or poetic)
> that I've
> > > never had these suggestions whilst listening to ETs and I work
> often
> > > with several different ETs. I don't believe ETs will work in this
> way.
> >
> > Would it matter to you if I pointed out that this is demonstrably
> >wrong? Obviously, any et with tuning fine enough to be
> >indistinguishable from JI will work this way.
>
> sounds snooty, right?
>
> well, in this context, alison, i'm afraid gene's comment is perfectly
> appropriate. no matter how well you tuned your zithers (which have
> slightly inharmonic partials anyhow), you could find some et which
> comes even closer to ji.
>
> it may seem snooty, but that's not the point at all (at least not
> *my* point). the point is that you should discover for yourself, for
> your own ears, what it means to have 3 cents errors from ji, 2 cents
> errors, 1 cent errors. then, when someone proposes something in this
> or that temperament that can't be done in ji, you'll have a basis for
> deciding whether, and how much, you'd be sacrificing the ji effects
> you treasure.

> romantic and poetic . . . the reasons you associate these with ji
> rather than temperament are extra-musical. in another culture, in
> another time, the associations would (and have been) reversed.

I didn't say that I associate JI with romantic and poetic or that temperaments are associated with
their opposites. I think it's more a case of assuming that that's what I mean because of the
inexplicable drift on this list to place someone in one or the other camp. The romantic and poetic
was probably flippant on my part - let's call it bloody-mindedness brought on by exasperation....

Let me put things straight. I work long and hard at the craft of inventing music, of putting tones
together into combinations, wherever they come from, JI or ET. In this case I'm putting out a
straight observation with an opinion based on my experience. I invite anyone to work intensively
with any tuning, JI or ET and discover useful properties through listening, and I mean
intensively, for hours and hours. Ask any experienced singer or player of raga. I haven't yet
experienced the "zoning in" with ETs that I do with JI or at least with the particular low number
ratios that I was working with recently.

If I follow this through conscientiously I will be building a pitch set (general term) by ear.

And, with respect, I do hail from a different culture to your good self, so, no assumptions there
please : - )

Best Wishes

--- In tuning@y..., Alison Monteith <alison.monteith3@w...> wrote:
> I didn't say that I associate JI with romantic and poetic or that
> temperaments are associated with their opposites. I think it's more
> a case of assuming that that's what I mean because of the
> inexplicable drift on this list to place someone in one or the
> other camp.

Alison, I can't believe you said that. I thought it was only me (and others who've exited) that felt this way.

> Let me put things straight. I work long and hard at the craft of
> inventing music, of putting tones together into combinations,
> wherever they come from, JI or ET. In this case I'm putting out a
> straight observation with an opinion based on my experience. I
> invite anyone to work intensively with any tuning, JI or ET and
> discover useful properties through listening, and I mean
> intensively, for hours and hours.

And you will be better at it than anyone else (and better for it). I can't imagine the amount of good music that will come our way in the years ahead!

> If I follow this through conscientiously I will be building a
> pitch set (general term) by ear.

Prepare to be burned at the stake, if they can find enough wood in Scotland...

Your humble servant,
Jon

--- In tuning@y..., Alison Monteith <alison.monteith3@w...> wrote:

> Why not just go the whole hog and catch the pure tone?

there's nothing wrong with adopting this as a philosophy and an
approach, and taking off from there. but we could pursue this
argument again, so here goes.

(a) in tuning zither strings, you'll always have
(1) a certain imprecision in how you tune the fundamentals
(2) an inevitable tradeoff between getting the fundamentals in tune
and getting the overtones in tune (due to the inharmonicity of the
strings)

(b) if you know what imprecision you're willing to tolerate (even if
it's as small as 0.1 cent), you can "target" certain
microtemperaments (not necessarily equal), and you will be more
likely to end up with a larger number of intervals and chords that
pass your criterion for "justness", than if you simply "targeted" a
just scale.

dave keenan has discussed the latter quite a bit, so you might want
to contact him (i think he's still following the tuning-math list)

anyway, alison, did i miss something? did you end up doing some
direct comparisons and deciding that the intervals and chords in 72-
equal were too far from just for you? if so, i'd like to know that,
and you can rest assured that i'll never mention 72-equal to you
again!

--- In tuning@y..., Alison Monteith <alison.monteith3@w...> wrote:

> > romantic and poetic . . . the reasons you associate these with ji
> > rather than temperament are extra-musical. in another culture, in
> > another time, the associations would (and have been) reversed.
>
> I didn't say that I associate JI with romantic and poetic or that
temperaments are associated with
> their opposites.

oops -- i see now that that was my mistake! sorry!

--- In tuning@y..., "jonszanto" <JSZANTO@A...> wrote:
> --- In tuning@y..., Alison Monteith <alison.monteith3@w...> wrote:

> > Let me put things straight. I work long and hard at the craft of
> > inventing music, of putting tones together into combinations,
> > wherever they come from, JI or ET. In this case I'm putting out a
> > straight observation with an opinion based on my experience. I
> > invite anyone to work intensively with any tuning, JI or ET and
> > discover useful properties through listening, and I mean
> > intensively, for hours and hours.
>
> And you will be better at it than anyone else

huh?

> (and better for it). I can't imagine the amount of good music that
>will come our way in the years ahead!

i join you in that sentiment!

> > If I follow this through conscientiously I will be building a
> > pitch set (general term) by ear.

the above describes quite well my experiences and philosophies with
regard to the shrutar, for example.

> Prepare to be burned at the stake, if they can find enough wood in
> Scotland...

well, i guess we see this differently, and no need to go into this
again. i'd just like to remark, and hopefully leave it at that, that
the only 'heresies' i've seen declared have come from the other side.
all gene and dave keenan and i have done is to propose some related
and theoretically neglected approaches that may or may not be of
interest to any particular musician. they have obviously been of
interest to some and not to others. why this topic must always be
accompanied by this running commentary, i don't know. seems to tread
uncomfortably close to matters of 'religion' for certain readers. oh
well.

--- In tuning@y..., "emotionaljourney22" <paul@s...> wrote:
> --- In tuning@y..., "jonszanto" <JSZANTO@A...> wrote:
> > And you will be better at it than anyone else
>
> huh?

Sorry, unclear: I just meant that, knowing as I (we) do that Alison
is working on building an 'orchestra' and is doing all the design,
fabrication, and (most importantly) *tuning* for the instruments, she
is spending many, many hours explicitly listening to the tuning and
getting it how she likes it. This is not a dress rehearsal, this is
the real thing. What I meant is that when she is done with this, she
will know the tuning, and the sound, and the sound of the tuning, of
her resource/palette better than anyone else.

It is no wonder to me that no one else has been able to compose for
the Partch instruments as successfully as he did: from imagination to
concept to implementation to usage ... a direct line, and when you've
had a chance to perform his works you can almost see that line start
to appear at times.

"better than anyone else" was just meant that Alison would know her
own 'system' maximally.

Cheers,
Jon

>

Hello Alison!
This is wholly my experience. These intervals "feed" the composing process. There is no belief in it at all. To associate the word Poetry with this is more than appropriate, possibly mandatory!

>
> From: Alison Monteith <alison.monteith3@which.net>
> Subject: JI and the listening composer
>
> As we're debating the JI/ET business again, here's an observation. I was
> listening somewhat inattentively to one of my ensemble players gently
> improvising on a zither accurately tuned to 1/1 - 7/6 - 4/3 - 3/2 - 7/4
> - 2/1. I began to hear, either in my head or as a result of combination
> and difference tones, very beautiful and quite 'angular' tones, very
> good possibilities for pedals, inverted pedals and inner voices.
>
> The point is (in case all this sounds too romantic or poetic) that I've
> never had these suggestions whilst listening to ETs and I work often
> with several different ETs. I don't believe ETs will work in this way.
>
> Without going too much into the whys and wherefores I've taken note of
> something I didn't know before about Just Intonation and from a
> composer's viewpoint this sets JI apart (not better, just different). I
> feel very good about this. It's as if the music will write itself if I
> can concentrate hard enough and listening deeply.
>
> Anyone else had similar experiences?
>
> Kind Regards
>

-- Kraig Grady
North American Embassy of Anaphoria island
http://www.anaphoria.com

The Wandering Medicine Show
Wed. 8-9 KXLU 88.9 fm

> Hello Gene!

> Just because you can play with numbers on paper doesn't mean you are doing anything that any one would ever do! So we tune up 270+ tubes everytime we want to change ratios why. Yes Prose can say in 1000 pages what poetry can say in a few lines

>
> --- In tuning@y..., Alison Monteith <alison.monteith3@w...> wrote:
>
> > The point is (in case all this sounds too romantic or poetic) that I've
> > never had these suggestions whilst listening to ETs and I work often
> > with several different ETs. I don't believe ETs will work in this way.
>
> Would it matter to you if I pointed out that this is demonstrably wrong? Obviously, any et with tuning fine enough to be indistinguishable from JI will work this way.

-- Kraig Grady
North American Embassy of Anaphoria island
http://www.anaphoria.com

The Wandering Medicine Show
Wed. 8-9 KXLU 88.9 fm

--- In tuning@y..., Alison Monteith <alison.monteith3@w...> wrote:

> I began to hear, either in my head or as a result of combination
> and difference tones, very beautiful and quite 'angular' tones, very
> good possibilities for pedals, inverted pedals and inner voices.

> It's as if the music will write itself if I
> can concentrate hard enough and listening deeply.
>
> Anyone else had similar experiences?

though i've responded to this already, just thought i'd mention that
the pieces TIBIA and _rock thing_ in 22-equal originated in exactly
this manner. stepping downward 'chromatically' in parallel fourths in
conjunction with an inner pedal, or vice versa, and listening with
emotional receptivity, one hears the difference tones and implied
fundamentals, and the music writes itself. the melody, which occurs
in the bass line, is the inevitable result of completing the harmony,
which consists mostly of (approximate) harmonic series chords -- but
i find that having the 64:63 absorbed by the tuning is quite
liberating, both harmonically and melodically.

if the idea of a 'cage' bothers you, note that these pieces and
everything i've advocated about 22-equal would work fine in an open,
infinite pajara temperament.

--- In tuning@y..., Kraig Grady <kraiggrady@a...> wrote:

> So we tune up 270+ tubes everytime we want to change ratios why.

i don't understand this. where does the 270+ tubes come from?

--- In tuning@y..., "emotionaljourney22" <paul@s...> wrote:

/tuning/topicId_37425.html#37468

> --- In tuning@y..., Alison Monteith <alison.monteith3@w...> wrote:
>
> > Why not just go the whole hog and catch the pure tone?
>
> there's nothing wrong with adopting this as a philosophy and an
> approach, and taking off from there. but we could pursue this
> argument again, so here goes.
>
> (a) in tuning zither strings, you'll always have
> (1) a certain imprecision in how you tune the fundamentals
> (2) an inevitable tradeoff between getting the fundamentals in
tune
> and getting the overtones in tune (due to the inharmonicity of the
> strings)
>
> (b) if you know what imprecision you're willing to tolerate (even
if
> it's as small as 0.1 cent), you can "target" certain
> microtemperaments (not necessarily equal), and you will be more
> likely to end up with a larger number of intervals and chords that
> pass your criterion for "justness", than if you simply "targeted" a
> just scale.
>
> dave keenan has discussed the latter quite a bit, so you might want
> to contact him (i think he's still following the tuning-math list)
>
> anyway, alison, did i miss something? did you end up doing some
> direct comparisons and deciding that the intervals and chords in 72-
> equal were too far from just for you? if so, i'd like to know that,
> and you can rest assured that i'll never mention 72-equal to you
> again!

***I always get a "kick" out of what seems to be the demonstrable
fact that in some cases non-just, or approximating just scales can be
more just, all things considered, than the just ones!

JP

--- In tuning@y..., Alison Monteith <alison.monteith3@w...> wrote:

> Obviously, as you rightly point out, there are ETs with tones that lie 0.1 or 0.2 of a cent off JI, thus indistinguishable to most ears. But their validity in this test
> lies in their closeness to the just intervals. Why not just go the whole hog and catch the pure tone?

More possibilites present themselves if you don't. Why ignore them, unless for some extramusical and ideological reason?

>

Hello Paul!
This remark is snooty and avoids the fact that those who use ETs do not makes sounds like JI. This is extramusical speculation based on numerical games.

>
> > Would it matter to you if I pointed out that this is demonstrably
> >wrong? Obviously, any et with tuning fine enough to be
> >indistinguishable from JI will work this way.
>
> sounds snooty, right?
>
> well, in this context, alison, i'm afraid gene's comment is perfectly
> appropriate. no matter how well you tuned your zithers (which have
> slightly inharmonic partials anyhow), you could find some et which
> comes even closer to ji.
>
> it may seem snooty, but that's not the point at all (at least not
> *my* point). the point is that you should discover for yourself, for
> your own ears, what it means to have 3 cents errors from ji, 2 cents
> errors, 1 cent errors. then, when someone proposes something in this
> or that temperament that can't be done in ji, you'll have a basis for
> deciding whether, and how much, you'd be sacrificing the ji effects
> you treasure.
>
> romantic and poetic . . . the reasons you associate these with ji
> rather than temperament are extra-musical. in another culture, in
> another time, the associations would (and have been) reversed.
>
>

-- Kraig Grady
North American Embassy of Anaphoria island
http://www.anaphoria.com

The Wandering Medicine Show
Wed. 8-9 KXLU 88.9 fm

--- In tuning@y..., "jonszanto" <JSZANTO@A...> wrote:
> --- In tuning@y..., Alison Monteith <alison.monteith3@w...> wrote:

> > I didn't say that I associate JI with romantic and poetic or that
> > temperaments are associated with their opposites. I think it's more
> > a case of assuming that that's what I mean because of the
> > inexplicable drift on this list to place someone in one or the
> > other camp.
>
> Alison, I can't believe you said that. I thought it was only me (and others who've exited) that felt this way.

This is absurd--I'm one of those who works with *both* JI and temperament, both in theory and in practice, and you two seem to think I am a heretic against the One True Religion. Who exactly do you think is working to place people in one camp or the other?

--- In tuning@y..., Kraig Grady <kraiggrady@a...> wrote:

> > Just because you can play with numbers on paper doesn't mean you
are doing anything that any one would ever do! So we tune up 270+
tubes everytime we want to change ratios why. Yes Prose can say in
1000 pages what poetry can say in a few lines

This is the 21st century, and technology *now*, at its beginnings, is
already perfectly well able to deal with 270 tones to an octave; I
presume that will become ever more true as time passes.

Hello Alison and Jon!
Sorry to Alison If i put words in your mouth but I have noticed the "thinking about" ET as always a question "practicality and efficiency" and the "thinking about" JI a question of the beauty of these sounds. I do associate the latter with the poetic but
do not associate Poetic with the sentimental but with the basic language of the Archetypal.

> --- In tuning@y..., "jonszanto" <JSZANTO@A...> wrote:
> > --- In tuning@y..., Alison Monteith <alison.monteith3@w...> wrote:
>
> > > I didn't say that I associate JI with romantic and poetic or that
> > > temperaments are associated with their opposites. I think it's more
> > > a case of assuming that that's what I mean because of the
> > > inexplicable drift on this list to place someone in one or the
> > > other camp.
> >
> > Alison, I can't believe you said that. I thought it was only me (and others who've exited) that felt this way.
>

-- Kraig Grady
North American Embassy of Anaphoria island
http://www.anaphoria.com

The Wandering Medicine Show
Wed. 8-9 KXLU 88.9 fm

Gene!
Can you tune it by ear though! Yes technology has finally given Us 12 ET in all is
mathematical perfection never possible before, and we are abandoning it!

genewardsmith wrote:

> --- In tuning@y..., Kraig Grady <kraiggrady@a...> wrote:
>
> > > Just because you can play with numbers on paper doesn't mean you
> are doing anything that any one would ever do! So we tune up 270+
> tubes everytime we want to change ratios why. Yes Prose can say in
> 1000 pages what poetry can say in a few lines
>
> This is the 21st century, and technology *now*, at its beginnings, is
> already perfectly well able to deal with 270 tones to an octave; I
> presume that will become ever more true as time passes.
>
>

-- Kraig Grady
North American Embassy of Anaphoria island
http://www.anaphoria.com

The Wandering Medicine Show
Wed. 8-9 KXLU 88.9 fm

> --- In tuning@y..., Alison Monteith <alison.monteith3@w...> wrote:
>
> > If I follow this through conscientiously I will be building a
> > pitch set (general term) by ear.

> jonszanto wrote:

> Prepare to be burned at the stake, if they can find enough wood in Scotland...
>
> Your humble servant,
> Jon
>
> Ah yes, the old sin of relying on the ear - cut them off (and burn the witch)

Peace

Sorry to jump in an already much heated debate :-)

When I read about tuning to 0.1 cents I tought of a figure of style,
Then I read:

> some extent there's always an element of imprecision. But every
vibrating string or
> struck bar has a fundamental and I'm happy that my strobe tuner is
finding it and tuning it
> perfectly ( to 0.1 cent) on a zither or steel tube marimba.

Such a precision is neither any usefull, nor practically reachable.

It is not usefull because psycho-acoustic demontrates that ON AVERAGE
(for young auditors), the frequency resolution is 1.5 Hz up to 500 Hz
then roughly 0.3%: thus roughly 5 cents at best (Zwicker & al.).
Obviously those are average figures, taken in the best condition, but
not on a population of expert microtonalists.

Let's assume that through birth, learning, etc. microtonalist
musicians can do better than the average, let say 1 cent... that's my
best price :-)

Even for the conservative 5 cents average, we should consider
physiological facts: a pure tone, at the level where the frequency
discrimination is the best, excites about a dozen of ciliate cells on
the basiliary membrane of the cochlea. Making the (silly) hypothesis
that it is possible to discriminate a frequency using a SINGLE cell,
0.5 cents would be the absolute limit.

On a linear scale, 0.1 cents translate to 0.006 %. I do no know the
length of the strings on those zithers, but lets take a reasonable
50cm string. That means that the precision of the fret is 3 hundreths
of millimeters!! (not taking into account the unavoidable extra-stress
due to fingering).

The so called "classical uncertainty principle" DOES apply to an
electronic tuner (it is still a matter of debate if the human brain
can work-around it). This means that to reach such a precision at let
say 440 Hz, the tuner would have to integrate stable signal for nearly
40 seconds. I doubt that such precision exists beyond the mere display
of the tuner.

For those reasons, I would agree to say that if a JI and a ET notes
are within 1-2 cents they are practically impossible to differenciate.

yours truly

François Laferrière

This is why Charles Ives could use the 384 cent major third of a A-Db (the
ninth of the spiral of fifths) to achieve justness. Even minimal vibrato
will erase this schisma.

Oh, and we can hear better than the single cent, but only so. :)\

Johnny Reinhard
AFMM

In-Reply-To: <ae56g9+pbbk@eGroups.com>
francois_laferriere wrote:

> It is not usefull because psycho-acoustic demontrates that ON AVERAGE
> (for young auditors), the frequency resolution is 1.5 Hz up to 500 Hz
> then roughly 0.3%: thus roughly 5 cents at best (Zwicker & al.).
> Obviously those are average figures, taken in the best condition, but
> not on a population of expert microtonalists.

I've tuned perfect fifths by ear, with electronic timbres, to within 0.1
cents. Those figures must be for something different, probably melodic
pitch discrimination.

> Let's assume that through birth, learning, etc. microtonalist
> musicians can do better than the average, let say 1 cent... that's my
> best price :-)

You're wrong.

> Even for the conservative 5 cents average, we should consider
> physiological facts: a pure tone, at the level where the frequency
> discrimination is the best, excites about a dozen of ciliate cells on
> the basiliary membrane of the cochlea. Making the (silly) hypothesis
> that it is possible to discriminate a frequency using a SINGLE cell,
> 0.5 cents would be the absolute limit.

But this is irrelevant if you're considering notes sounding together. The
roughness perception is independent of pitch finding.

> On a linear scale, 0.1 cents translate to 0.006 %. I do no know the
> length of the strings on those zithers, but lets take a reasonable
> 50cm string. That means that the precision of the fret is 3 hundreths
> of millimeters!! (not taking into account the unavoidable extra-stress
> due to fingering).

I thought this was comparing open strings. It is still possible to
measure fractions of a millimetre, so 0.1 cents is comfortably beyond what
you need for that. As Alison said.

> The so called "classical uncertainty principle" DOES apply to an
> electronic tuner (it is still a matter of debate if the human brain
> can work-around it). This means that to reach such a precision at let
> say 440 Hz, the tuner would have to integrate stable signal for nearly
> 40 seconds. I doubt that such precision exists beyond the mere display
> of the tuner.

It may be a matter of debate that the human brain can work around it, but
we know electronics can. Robert Walker's got good results from a zero
point crossing algorithm. The tuner could be doing the same thing. The
important fact is that it's only guessing the pitch of one note. The
uncertainty principle you mention is for picking a frequency component out
against background noise, not a single note in isolation.

If the tuner is that precise, you can test its accuracy by seeing if it's
consistent.

40 seconds is still possible for a string decay.

> For those reasons, I would agree to say that if a JI and a ET notes
> are within 1-2 cents they are practically impossible to differenciate.

My ears disagree with you, and I trust my ears more than academic
journals. Have you ever tried tuning sawtooth wave dyads yourself?

Graham

Hello Francois!
I don't really care what psycho-acoustic demonstrates because there are so many loopholes in
these experiments that they are not only erroneous but often contradictory.
First we leave in a culture where we have been taught to ignore the comma. Hence our musical
language is based in part on not hearing. There is also a difference between what one can hear and
what one can feel. Second there is the question of how much time is involved. If one works with a
instrument constantly you begin to notice things you don't at the beginning. But if you have two
instruments tuned to the same tuning very slight mistunings will create beats sometimes two
seconds or more. It doesn't take much to hear such things. As someone who has heard absolute
tuning (tunings produced electronically where there is never a beat) the sound is very pronounced
and as identifiable as cinnamon. Those around La Monte can verify this i am sure.
Now if temperment cannot be tuned any better than Just, you have an even greater build up of
mistuning. Case in point is the yamaha standard, of what is it, 768. Now enough "experts" said
this was fine enough when in point of fact one cannot tune up a simple pythagorean chain up to a
pentatonic without running into problems. I could not even use instruments with this tuning
because i would get beats that have nothing to do with what i was tuning up.

you say

For those reasons, I would agree to say that if a JI and a ET notes
are within 1-2 cents they are practically impossible to differentiate.

This tuning is well within this range and i can tell you , it is terrible sounding unless you like
garbled beating

francois_laferriere wrote:

> Sorry to jump in an already much heated debate :-)
>
> When I read about tuning to 0.1 cents I tought of a figure of style,
> Then I read:
>
> > some extent there's always an element of imprecision. But every
> vibrating string or
> > struck bar has a fundamental and I'm happy that my strobe tuner is
> finding it and tuning it
> > perfectly ( to 0.1 cent) on a zither or steel tube marimba.
>
> Such a precision is neither any usefull, nor practically reachable.
>
> It is not usefull because psycho-acoustic demontrates that ON AVERAGE
> (for young auditors), the frequency resolution is 1.5 Hz up to 500 Hz
> then roughly 0.3%: thus roughly 5 cents at best (Zwicker & al.).
> Obviously those are average figures, taken in the best condition, but
> not on a population of expert microtonalists.
>
> Let's assume that through birth, learning, etc. microtonalist
> musicians can do better than the average, let say 1 cent... that's my
> best price :-)
>
> Even for the conservative 5 cents average, we should consider
> physiological facts: a pure tone, at the level where the frequency
> discrimination is the best, excites about a dozen of ciliate cells on
> the basiliary membrane of the cochlea. Making the (silly) hypothesis
> that it is possible to discriminate a frequency using a SINGLE cell,
> 0.5 cents would be the absolute limit.
>
> On a linear scale, 0.1 cents translate to 0.006 %. I do no know the
> length of the strings on those zithers, but lets take a reasonable
> 50cm string. That means that the precision of the fret is 3 hundreths
> of millimeters!! (not taking into account the unavoidable extra-stress
> due to fingering).
>
> The so called "classical uncertainty principle" DOES apply to an
> electronic tuner (it is still a matter of debate if the human brain
> can work-around it). This means that to reach such a precision at let
> say 440 Hz, the tuner would have to integrate stable signal for nearly
> 40 seconds. I doubt that such precision exists beyond the mere display
> of the tuner.
>
> For those reasons, I would agree to say that if a JI and a ET notes
> are within 1-2 cents they are practically impossible to differenciate.
>
> yours truly
>
> Fran�ois Laferri�re

-- Kraig Grady
North American Embassy of Anaphoria island
http://www.anaphoria.com

The Wandering Medicine Show
Wed. 8-9 KXLU 88.9 fm

--- In tuning@y..., "francois_laferriere" <francois.laferriere@o...>
wrote:
> Sorry to jump in an already much heated debate :-)
>
> When I read about tuning to 0.1 cents I tought of a figure of style,
> Then I read:
>
> > some extent there's always an element of imprecision. But every
> vibrating string or
> > struck bar has a fundamental and I'm happy that my strobe tuner is
> finding it and tuning it
> > perfectly ( to 0.1 cent) on a zither or steel tube marimba.
>
> Such a precision is neither any usefull, nor practically reachable.
>
> It is not usefull because psycho-acoustic demontrates that ON
AVERAGE
> (for young auditors), the frequency resolution is 1.5 Hz up to 500
Hz
> then roughly 0.3%: thus roughly 5 cents at best (Zwicker & al.).

sorry, francois, that figure is not applicable here. that's the
*melodic* just noticeable difference. by eliminating beats, though,
one can tune *harmonic* intervals FAR more accurately than this. one
can easily reduce the rate of beating between high-order harmonics to
1 per 10 seconds, 1 per 15 seconds -- you do the math.

--- In tuning@y..., "francois_laferriere" <francois.laferriere@o...>
wrote:

> On a linear scale, 0.1 cents translate to 0.006 %. I do no know the
> length of the strings on those zithers, but lets take a reasonable
> 50cm string. That means that the precision of the fret is 3
hundreths
> of millimeters!!

zithers are not fretted instruments.

Alison,

>Certainly the possibility of working with the unique musical properties
>of well tuned low number ratios don't present themselves in ETs that I
>can practically use with acoustic instruments (we must have a context at
>some point in the debate)

This is the statement Gene's referring to.

>Well if you keep telling me that my experiences are not true there's not
>much I can say or do.

Are you saying you experienced every ET suitable for acoustic instruments?
Since the scale in discussion is a subset of an ET, you've experienced
every ET subset as well?

-Carl

I checked out the figures that I previously cited by memory. I was not
grossly inacurate but in fact the pitch discrimination is a bit worse
that what I said. It is 1.8 Hz up to 500 Hz, then 0.35%. In my
arguments, I tried to pull the figures as far as possible in the
"good" direction (in your sense) to show that even being very
optimistic, 0.1 cent is unrealistic.

The experiments described in "Das Ohr Als Nachrichetenempfänger" by
Zwicker and Feldtkeller (an extremely comprehensive book on
psychoaccoustic that I fortunately have in French translation) try to
explore the pitch discrimination in its most fundamental aspects. The
pitch discrimination experiment is made by modulating a frequency
between F and F+deltaF and determine the threshold for a noticeable
modulation. The threshold (deltaF) depends on many parameters:
- The frequency F.
- The modulation frequency Fm
- The accoustic level (in dB)
The pitch discrimination is best for Fm around 4Hz. The figures of
1.8Hz, 0.35% are measured for optimal level and Fm.
The experiment results are probably as near as it is possible of the
actual properties of the inner ear. I personnaly think that training
may improve pitch perception but certainly by less than an order of
magnitude, as we are here, bound to physiological limits.

I once tought that is was possible for the brain to take benefit of
higher harmonics to improve frequency resolution.
Rereading those figures, are must admit that I was wrong as long as
the RELATIVE frequency resolution (in % OR in cents) is fairly
constant above 500 Hz: thus if the resolution is N cents at 440 Hz, it
remains (at most) N cents at 880 Hz, 1320 Hz.

Obviously, those figures are for melodic pitch discrimination. But I
think that they are as near as possible as the physiological pitch
discrimination limits.

> Paul :
> zithers are not fretted instruments.

I must admit that I am totally ignorant of zithern that I confused
with cithern (an early fretted instrument). Are its strings plucked,
hit or bowed ?

> Paul:
> sorry, francois, that figure is not applicable here. that's the
> *melodic* just noticeable difference. by eliminating beats, though,
> one can tune *harmonic* intervals FAR more accurately than this. one
> can easily reduce the rate of beating between high-order harmonics
to
> 1 per 10 seconds, 1 per 15 seconds -- you do the math.

OK Paul I do the math:

In any cases, the harmonic aproximation cannot hold if we talk about
0.1 cents precision, so Paul is absolutely correct to question the
tuning of inharmonic string. The harmonic approximation supposes
(among other things) that the variation of the string length is
neglectible during its oscillation. Let say that that the rest string
length is L and the amplitude of vibration is A. In first
approximation, at maximum amplitude, the lenght of the string is
longer by some deltaL with deltaL/L ~= (A/L)**2. This is fairly
neglectible when reasonable precision is required. For reasonable L =
500mm, A = 5mm, we get deltaL/L = 0.01 %: which is above the claimed
precision of 0.006 % (0.1 cents). For elementary physic reasons, 0.1
cents does not make sense for string tuning.

Further, I doubt that if ever this precision could ever be reached,
any stringed instrument can hold it for more than a few minutes (or
more reasonably a few seconds) when played.

OK let's admit that I am all wrong because I am considering melodic
pitch. Let's now consider harmonic relationship of the simplest case:
slightly out of tune unison of two notes F and F + deltaF. It is
correct that the beat frequencies is increased as long is it is given
by the difference in frequency. for F0, beat is at deltaF, for F1, it
is 2*deltaF and so on. Overtone amplify the beat frequency, so that
0.006 % difference is made a 0.6 Hz beat at 10 KHz: that is not much
but that is something. But we are there at least on the 20th harmonics
for any note in mid range: that is faint (if perceptible) and masked.
Further the amplitude of 10th+ harmonics depends nearly ramdomly on
where the string is plucked, hit, bowed.

For 0.1 cents on unison, beat period vary from 40 seconds (~440 Hz) to
2 seconds (~10KHz) that is not much, If the string is hit or plucked,
that may affect very slightly the enveloppe of the note decay.

If the string is anything but bowed (to produce a stationary tone)
effect of the decay adds on with the long period harmonic beat and
various phase effects in a way that cannot be untangled. I hearsay
that the three strings of piano midrange notes may be slightly out of
tune to have a "rounder" decay (is that true??). At this level, taking
into account the inharmonicity, justness is no more a quantitative
measure, it is a matter of taste.

On one hand side I cannot honestly deny that those higher harmonics
effect exists (if tiny) and may be perceived (if only by gifted,
highly trained expert).

On the other hand side, I am totally convinced that those who sell
electronic tuners claiming 0.1 cent precision are incompetent crooks
and that such precision does not make sense for signal analysis theory
viewpoint, from an elementary physics viewpoint and from a
physiological viewpoint.

> Graham:
> My ears disagree with you, and I trust my ears more than academic
> journals. Have you ever tried tuning sawtooth wave dyads yourself?

I do not trust my ears, they were proven quite lousy with the
"jerries" :-(. No I never tried, but I can guess that sawtooth is
easier to tune to a given precision than accoustic instrument, because
its spectrum is nearly flat (little or no higher harmonics decay) and
because those pegs never get loose :-).

> Graham:
> It may be a matter of debate that the human brain can work around
it, but
> we know electronics can. Robert Walker's got good results from a
zero
> point crossing algorithm. The tuner could be doing the same thing.
The
> important fact is that it's only guessing the pitch of one note.
The
> uncertainty principle you mention is for picking a frequency
component out
> against background noise, not a single note in isolation.

I have discussed this point with Robert Walker on this list and
concluded that it was possible to take benefit of the higher harmonics
for enhanced pitch estimation, without anyhow contradict signal theory
or more specifically the "uncertainty principle". The latter hold for
isolated notes and ESPECIALLY for isolated notes. whenever there is
background noise, we hit many limits before hitting the uncertainty
principle limits.

> Kraig:
> I don't really care what psycho-acoustic demonstrates because there
are so many loopholes in
> these experiments that they are not only erroneous but often
contradictory.

Obviously, there are loophole in psychoacoustics, but is not reason to
trow away the baby with the water of the bath, like creationists who
reject Darwin in block because there are some loophole in evolution
theory.

By the way, it is a pity that big company like Yamaha filled their
hardware with cheap tuning features. If there was no people like those
on this list to make things advance, there would be no tuning
capability at all in electronic keyboards.

yours truly

François

Hello francois!
I see it as more of throwing out pseudo science especially since to contradicts my own
personal experience. I often tune to a pitch an them check how accurate i am. better than this
science says i can do.

francois_laferriere wrote:

>
>
> > Kraig:
> > I don't really care what psycho-acoustic demonstrates because there
> are so many loopholes in
> > these experiments that they are not only erroneous but often
> contradictory.
>
> Obviously, there are loophole in psychoacoustics, but is not reason to
> trow away the baby with the water of the bath, like creationists who
> reject Darwin in block because there are some loophole in evolution
> theory.
>
> By the way, it is a pity that big company like Yamaha filled their
> hardware with cheap tuning features. If there was no people like those
> on this list to make things advance, there would be no tuning
> capability at all in electronic keyboards.
>
> yours truly
>
> Fran�ois
>

-- Kraig Grady
North American Embassy of Anaphoria island
http://www.anaphoria.com

The Wandering Medicine Show
Wed. 8-9 KXLU 88.9 fm

--- In tuning@y..., "francois_laferriere" <francois.laferriere@o...>
wrote:

> > Paul:
> > sorry, francois, that figure is not applicable here. that's the
> > *melodic* just noticeable difference. by eliminating beats,
though,
> > one can tune *harmonic* intervals FAR more accurately than this.
one
> > can easily reduce the rate of beating between high-order harmonics
> to
> > 1 per 10 seconds, 1 per 15 seconds -- you do the math.
>
> OK Paul I do the math:
>
> In any cases, the harmonic aproximation cannot hold if we talk about
> 0.1 cents precision, so Paul is absolutely correct to question the
> tuning of inharmonic string.

excuse me, francois, but how about we consider one thing at a time.
many sustained instruments have perfectly harmonic partials. let's
take two notes from such an instrument (or two of them) and ask how
small a deviation from a simple ji interval we can recognize. is your
original statement about human hearing resolution applicable?

> The harmonic approximation supposes
> (among other things) that the variation of the string length is
> neglectible during its oscillation. Let say that that the rest
string
> length is L and the amplitude of vibration is A. In first
> approximation, at maximum amplitude, the lenght of the string is
> longer by some deltaL with deltaL/L ~= (A/L)**2. This is fairly
> neglectible when reasonable precision is required. For reasonable L
=
> 500mm, A = 5mm, we get deltaL/L = 0.01 %: which is above the claimed
> precision of 0.006 % (0.1 cents). For elementary physic reasons, 0.1
> cents does not make sense for string tuning.

it makes sense if the target is some comprimise between what the
harmonics suggest (as tuning for *virtual pitch* would require) . . .

> On the other hand side, I am totally convinced that those who sell
> electronic tuners claiming 0.1 cent precision are incompetent crooks
> and that such precision does not make sense for signal analysis
theory
> viewpoint, from an elementary physics viewpoint and from a
> physiological viewpoint.

robert walker has presented his wave-counting method. is he an
incompetent crook?

> I have discussed this point with Robert Walker on this list and
> concluded that it was possible to take benefit of the higher
harmonics
> for enhanced pitch estimation, without anyhow contradict signal
theory
> or more specifically the "uncertainty principle". The latter hold
for
> isolated notes and ESPECIALLY for isolated notes. whenever there is
> background noise, we hit many limits before hitting the uncertainty
> principle limits.

but electronic instrument tuners are *meant* to be used for isolated
notes, with low background noise. so your statement about incompetent
crooks above puzzles me.

--- In tuning@y..., "jpehrson2" <jpehrson@r...> wrote:
> ***I always get a "kick" out of what seems to be the demonstrable
> fact that in some cases non-just, or approximating just scales can
be
> more just, all things considered, than the just ones!

Yeah. That's fun, but its really using two different meanings of
"just". The not-so-useful one that means "whole-number ratios" and can
be replaced by the word "rational". And the other which relates to how
it _sounds_ and turns out to mean "within a cent or two(-point-eight)
:-) of small whole number ratios".

So, to spoil your fun ;-) I'd rewrite that as: "It is a demonstrable
fact that in some cases non-rational, or only approximately rational
scales can be more just, all things considered, than the rational
ones."

And that's an excellent way to put it. Thanks.

These are the microtemperaments. They are usually not equal
temperaments, but are more typically linear or planar. The "Middle
Path". However, I consider 72-equal to (just barely) be a 7-limit
microtemperament, and therefore a just tuning. I do not consider it
so, for 9-limit intervals or higher, but the synergistic effect of
large otonalities may mean that the 9 and 11 limit complete otonal
chords sound just.

--- In tuning@y..., "emotionaljourney22" <paul@s...> wrote:
> (b) if you know what imprecision you're willing to tolerate (even if
> it's as small as 0.1 cent), you can "target" certain
> microtemperaments (not necessarily equal), and you will be more
> likely to end up with a larger number of intervals and chords that
> pass your criterion for "justness", than if you simply "targeted" a
> just scale.

Yes. And although it's possible, there's absolutely no point in being
as strict as +-0.1 cents. What I call the Reinhard principle is that
even the best microtonal human ear/brain on the planet, doesn't
experience a +-0.5 cents deviation from an exact ratio as a mistuning.

And we know from careful measurements of the best tuned guitars with
individually adjustable bridgepieces for each string, that +- 3 cent
intonation errors are commonplace and practically unavoidable. These
are apparently unnoticed by guitarists who still (correctly in my
opinion) consider their Guitars to be tuned in JI.

--- In tuning@y..., "dkeenanuqnetau" <d.keenan@u...> wrote:
> --- In tuning@y..., "emotionaljourney22" <paul@s...> wrote:

> Yes. And although it's possible, there's absolutely no point in
being
> as strict as +-0.1 cents.

"absolutely"?

> What I call the Reinhard principle is that
> even the best microtonal human ear/brain on the planet, doesn't
> experience a +-0.5 cents deviation from an exact ratio as a
>mistuning.

experience? what experience are you referring to?

this kind of thinking is beneath you, dave.

let's say someone wrote a piece, 78 minutes long, a single chord of
six notes, with sustained harmonic tones whose fundamentals were all
multiples of 0.125 Hz. clearly this is a just intonation tuning.
there are many beating patterns, but they will all be synchronized
(in time with one another), as the entire waveform inevitably repeats
itself every 8 seconds.

how much deviation from ji would it take to cause a noticeable
departure from the rhythmic synchronization over the course of the 78
minutes?

> And we know from careful measurements of the best tuned guitars
with
> individually adjustable bridgepieces for each string, that +- 3
cent
> intonation errors are commonplace and practically unavoidable.
These
> are apparently unnoticed by guitarists who still (correctly in my
> opinion) consider their Guitars to be tuned in JI.

how much time have you spent tuning your guitar to ji?

--- In tuning@y..., "dkeenanuqnetau" <d.keenan@u...> wrote:

/tuning/topicId_37425.html#37658
>
> So, to spoil your fun ;-) I'd rewrite that as: "It is a
demonstrable fact that in some cases non-rational, or only
approximately rational scales can be more just, all things
considered, than the rational ones."
>
> And that's an excellent way to put it. Thanks.

***Thanks, Dave! That's a *lot* clearer...

>
> These are the microtemperaments. They are usually not equal
> temperaments, but are more typically linear or planar. The "Middle
> Path". However, I consider 72-equal to (just barely) be a 7-limit
> microtemperament, and therefore a just tuning. I do not consider it
> so, for 9-limit intervals or higher, but the synergistic effect of
> large otonalities may mean that the 9 and 11 limit complete otonal
> chords sound just.

***Quite frankly, my emphasis in Blackjack rarely focuses on anything
higher than 7-limit. I use *those* all the time, though. However, I
*do* use some of the "crunch chords" that you helped me find which, I
believe sound just at the 9 or 11 limit.

But, what do you mean exactly by "synergistic effect" and how is it
that Blackjack can *sometimes* create 9 and 11-limit just otonalities
when it really isn't "microtempered" to tune that limit??

??

Thanks, Dave!

Joseph

--- In tuning@y..., "emotionaljourney22" <paul@s...> wrote:
> --- In tuning@y..., "dkeenanuqnetau" <d.keenan@u...> wrote:
> > --- In tuning@y..., "emotionaljourney22" <paul@s...> wrote:
>
> > Yes. And although it's possible, there's absolutely no point in
> being
> > as strict as +-0.1 cents.
>
> "absolutely"?

OK. You got me there. I expect LaMonte Young's Dreamhouse wouldn't be
the same with 0.5 cent errors. But we _were_ talking about a zither.

> > What I call the Reinhard principle is that
> > even the best microtonal human ear/brain on the planet, doesn't
> > experience a +-0.5 cents deviation from an exact ratio as a
> >mistuning.
>
> experience? what experience are you referring to?
>
> this kind of thinking is beneath you, dave.

Correct me if I'm wrong, but Johnny Reinhard claims that notating JI
to within +-0.5 cents is not only necessary, but sufficient.
Presumably he has in mind the 99% of JI pieces, that don't involve
intervals sustained for more than a few seconds.

I may be remembering the numbers wrong, but haven't we also heard that
piano tuners experience deviations less than about half a cent, more
as variations in timbre than as mistunings.

> let's say someone wrote a piece, 78 minutes long, a single chord of
> six notes, with sustained harmonic tones whose fundamentals were all
> multiples of 0.125 Hz. clearly this is a just intonation tuning.
> there are many beating patterns, but they will all be synchronized
> (in time with one another), as the entire waveform inevitably
repeats
> itself every 8 seconds.
>
> how much deviation from ji would it take to cause a noticeable
> departure from the rhythmic synchronization over the course of the
78
> minutes?

Of course you are right. But it gets a little tedious having to put in
all these caveats every time, to cater for less than 1% of cases. I am
happy to leave it to you to add these, but I'd prefer if you didn't
imply that I'd forgotten about them. Or that it was "beneath me". I
notice you have taken to writing "etc. etc." in similar cases, perhaps
I'll adopt thatin future.

> > And we know from careful measurements of the best tuned guitars
> with
> > individually adjustable bridgepieces for each string, that +- 3
> cent
> > intonation errors are commonplace and practically unavoidable.
> These
> > are apparently unnoticed by guitarists who still (correctly in my
> > opinion) consider their Guitars to be tuned in JI.
>
> how much time have you spent tuning your guitar to ji?

Very little. What's your point?

--- In tuning@y..., "dkeenanuqnetau" <d.keenan@u...> wrote:

> > > And we know from careful measurements of the best tuned guitars
> > with
> > > individually adjustable bridgepieces for each string, that +- 3
> > cent
> > > intonation errors are commonplace and practically unavoidable.
> > These
> > > are apparently unnoticed by guitarists who still (correctly in
my
> > > opinion) consider their Guitars to be tuned in JI.
> >
> > how much time have you spent tuning your guitar to ji?
>
> Very little. What's your point?

the point is that any guitarist with a good ear can compensate for
intonation difficulties with the fingers, and that in discussions
like these, we should be concerned with the most discerning
musicians, not the least. if you delved into the (guitar) area
yourself i suspect you'd end up demanding, and acheiving, better than
3 cent accuracy on long, sustained ji harmonies.

--- In tuning@y..., "jpehrson2" <jpehrson@r...> wrote:
> ***Quite frankly, my emphasis in Blackjack rarely focuses on
anything
> higher than 7-limit. I use *those* all the time, though. However,
I
> *do* use some of the "crunch chords" that you helped me find which,
I
> believe sound just at the 9 or 11 limit.
>
> But, what do you mean exactly by "synergistic effect" and how is it
> that Blackjack can *sometimes* create 9 and 11-limit just
otonalities
> when it really isn't "microtempered" to tune that limit??

Joseph,

you are a teacher's dream! You always ask the _best_ questions. :-)

Of course there's no sharp boundary between just and not-just, it's
all fairly arbitrary, but there is definitely an effect whereby the
more notes you have sounding simultaneously, with their fundamental
frequencies forming a subset of the harmonic series (otonal), the more
deviation you can tolerate in any one of them.

--- In tuning@y..., "dkeenanuqnetau" <d.keenan@u...> wrote:

/tuning/topicId_37425.html#37677

> --- In tuning@y..., "jpehrson2" <jpehrson@r...> wrote:
> > ***Quite frankly, my emphasis in Blackjack rarely focuses on
> anything
> > higher than 7-limit. I use *those* all the time, though.
However,
> I
> > *do* use some of the "crunch chords" that you helped me find
which,
> I
> > believe sound just at the 9 or 11 limit.
> >
> > But, what do you mean exactly by "synergistic effect" and how is
it
> > that Blackjack can *sometimes* create 9 and 11-limit just
> otonalities
> > when it really isn't "microtempered" to tune that limit??
>
> Joseph,
>
> you are a teacher's dream! You always ask the _best_ questions. :-)
>
> Of course there's no sharp boundary between just and not-just, it's
> all fairly arbitrary, but there is definitely an effect whereby the
> more notes you have sounding simultaneously, with their fundamental
> frequencies forming a subset of the harmonic series (otonal), the
more
> deviation you can tolerate in any one of them.

***Got it! Thanks, Dave! I'm glad we *have* these 9 and 11-limit
chords, they really add "spice" to the entire!

Joseph

--- In tuning@y..., "emotionaljourney22" <paul@s...> wrote:
> --- In tuning@y..., "dkeenanuqnetau" <d.keenan@u...> wrote:
>
> > > > And we know from careful measurements of the best tuned
guitars
> > > with
> > > > individually adjustable bridgepieces for each string, that +-
3
> > > cent
> > > > intonation errors are commonplace and practically unavoidable.
> > > These
> > > > are apparently unnoticed by guitarists who still (correctly in
> my
> > > > opinion) consider their Guitars to be tuned in JI.
> > >
> > > how much time have you spent tuning your guitar to ji?
> >
> > Very little. What's your point?
>
> the point is that any guitarist with a good ear can compensate for
> intonation difficulties with the fingers, and that in discussions
> like these, we should be concerned with the
> musicians, not the least. if you delved into the (guitar) area
> yourself i suspect you'd end up demanding, and acheiving, better
than
> 3 cent accuracy on long, sustained ji harmonies.

I expect that's all true, and I certainly agree that we should
consider the experience of the most _discerning_ musicians. But I
don't see that it argues _against_ my appeal for the acceptance of
microtemperaments _as_ JI. If anything, it argues _for_ it.

I understood the +-3 cent errors in those measurements were
independent of anything a player might do. The guitar was carefully
set up in some kind of jig that supported the neck and so on. They
were purely a property of the guitar.

If one can compensate for _accidental_ mistunings due to bridge
position, relative fret placement, machine-head slip, nut friction,
neck bending, and changes in temperature and humidity etc., then
surely one can just as easily compensate for _deliberate_ "mistunings"
of a similar size, introduced by microtempering.

Does your lack of further comment on the "Reinhard Principle" (+-0.5
cent) imply 99% acceptance, (with the caveat you noted)?

--- I wrote:
> I expect that's all true, and I certainly agree that we should
> consider the experience of the most _discerning_ musicians. But I
> don't see that it argues _against_ my appeal for the acceptance of
> microtemperaments _as_ JI. If anything, it argues _for_ it.

Oops! Lets change that second-last sentence to "... the acceptance of
microtemperaments.(period)". I know the "_as_ JI" part is too much of
a leap for many people, and it isn't essential.

--- In tuning@y..., "dkeenanuqnetau" <d.keenan@u...> wrote:

> But I
> don't see that it argues _against_ my appeal for the acceptance of
> microtemperaments _as_ JI.

no -- i wasn't addressing that.

> I understood the +-3 cent errors in those measurements were
> independent of anything a player might do.

isn't that inherently nonsensical?

> The guitar was carefully
> set up in some kind of jig that supported the neck and so on. They
> were purely a property of the guitar.

as played by a non-listening machine!

> If one can compensate for _accidental_ mistunings due to bridge
> position, relative fret placement, machine-head slip, nut friction,
> neck bending, and changes in temperature and humidity etc., then
> surely one can just as easily compensate for
_deliberate_ "mistunings"
> of a similar size, introduced by microtempering.

you bet! but that would result in *adaptive ji*, which does not agree
with what most ji advocates advocate.

> Does your lack of further comment on the "Reinhard Principle" (+-
0.5
> cent) imply 99% acceptance, (with the caveat you noted)?

if johnny were to voice this principle, then you could call it
that . . . but mainly, if you advocate it, i'd hope it would be
something you had actually gone through the trouble of investigating
with your own ears, for a wide variety of timbres, registers,
amplitudes, and durations . . . it seems like you did something like
that for sensitivity of various intervals to mistuning, but that was
in whole cents, and fractions of cents (required here) are
harder . . .

99% acceptance? maybe the other 1% is poised to be the future of
music. maybe not. let's let the future of music decide.

i have no interest in the "what is ji" debate.

i've got some cds to send out to the few of you who requested
them . . . be prepared for further lack of further comment . . .

--- In tuning@y..., "emotionaljourney22" <paul@s...> wrote:
> > I understood the +-3 cent errors in those measurements were
> > independent of anything a player might do.
>
> isn't that inherently nonsensical?

No. Why? All you have to do is to support the guitar and have some
means of applying a constant pressure to the strings via the
recently severed finger of a famous guitarist (only joking). A piece
of rubber might do. Or maybe some other phyically measurable variable
would be chosen to be kept constant.

> > The guitar was carefully
> > set up in some kind of jig that supported the neck and so on. They
> > were purely a property of the guitar.
>
> as played by a non-listening machine!

Yes. I think so. But the article wasn't clear on that. But what's the
problem if it was. I have already agreed that a guitarist can
compensate, but I'm interested in how much they must routinely
compensate for, and whether there is much point in trying very hard,
when building a custom instrument, to acheive better than 1 c accuracy
in fret placement. The sky is not the limit.

> > If one can compensate for _accidental_ mistunings due to bridge
> > position, relative fret placement, machine-head slip, nut
friction,
> > neck bending, and changes in temperature and humidity etc., then
> > surely one can just as easily compensate for
> _deliberate_ "mistunings"
> > of a similar size, introduced by microtempering.
>
> you bet! but that would result in *adaptive ji*, which does not
agree
> with what most ji advocates advocate.

Hmm. I think maybe I unwittingly came into the middle of something
here, and you felt I was arguing against your position on something
else.

> > Does your lack of further comment on the "Reinhard Principle" (+-
> 0.5
> > cent) imply 99% acceptance, (with the caveat you noted)?
>
> if johnny were to voice this principle, then you could call it
> that . . .

I can't find it now, but remember the post where he described how he
could split the difference between a rational fifth and a 12-tET
fifth, but couldn't hear to go any further.

> but mainly, if you advocate it, i'd hope it would be
> something you had actually gone through the trouble of investigating
> with your own ears, for a wide variety of timbres, registers,
> amplitudes, and durations . . . it seems like you did something like
> that for sensitivity of various intervals to mistuning,

That was finding at what ratios I could hear anything that _was_
sensitive to mistuning (not by how much)

> but that was
> in whole cents, and fractions of cents (required here) are
> harder . . .

Yes. I don't have the equipment for that, but even if I did, I
wouldn't trust _my_ ears. I've noticed that others can hear stuff that
I can't. I must instead rely on what I hope are reliable reports from
others such as Johny Reinhard and yourself.

So instead I'll adopt the 0.5 c cutoff for practical purposes, and
wait for someone to convincingly refute it.

You wont beleive this but ... in the middle of this discussion today,
a woman came to the door doing market research on bread, she happened
to mention that she just lives down the street a bit and apologised
for all the construction going on, as it sometimes spills onto the
street. She said she and her husband are building a guitar workshop
out the back of their house. I said "Did you say a _GUITAR_ workshop!"
and one thing led to another ... She actually knows what meantone and
well temperament are ...

Isn't life funny sometimes.

--- In tuning@y..., "dkeenanuqnetau" <d.keenan@u...> wrote:

> whether there is much point in trying very hard,
> when building a custom instrument, to acheive better than 1 c
accuracy
> in fret placement.

oh, of course. many noted ji guitarists and luthiers don't even
correct for the bending of the string induced by fretting.

> I can't find it now, but remember the post where he described how
he
> could split the difference between a rational fifth and a 12-tET
> fifth, but couldn't hear to go any further.

there are a lot of places in the intervallic continuum where it's
harder to hear a 1 cent difference than others.

>
> > but mainly, if you advocate it, i'd hope it would be
> > something you had actually gone through the trouble of
investigating
> > with your own ears, for a wide variety of timbres, registers,
> > amplitudes, and durations . . . it seems like you did something
like
> > that for sensitivity of various intervals to mistuning,
>
> That was finding at what ratios I could hear anything that _was_
> sensitive to mistuning (not by how much)

no, no, i'm talking about your whole deal where you found that ratios
about as complex as 6:5 were _most_ forgiving of mistuning . . .
remember all that?

> I must instead rely on what I hope are reliable reports from
> others such as Johny Reinhard and yourself.

bad idea :)

> She actually knows what meantone and
> well temperament are ...

that is truly incredible. i've never met anyone at a guitar workshop
who knows anything about alternate tunings, just some misconceptions
about indian music using quartertones. mostly they look at my
microtonal guitars funny and ask if that band has any groupies. at
that point, my modesty takes over ;)

--- In tuning@y..., "emotionaljourney22" <paul@s...> wrote:
> --- In tuning@y..., "dkeenanuqnetau" <d.keenan@u...> wrote:
>
> > whether there is much point in trying very hard,
> > when building a custom instrument, to acheive better than 1 c
> accuracy
> > in fret placement.
>
> oh, of course. many noted ji guitarists and luthiers don't even
> correct for the bending of the string induced by fretting.
>
> > I can't find it now, but remember the post where he described how
> he
> > could split the difference between a rational fifth and a 12-tET
> > fifth, but couldn't hear to go any further.
>
> there are a lot of places in the intervallic continuum where it's
> harder to hear a 1 cent difference than others.

Good point. Let me know when you find those places where a 0.5 c error
is objectionable when it lasts for less than 10 seconds.

> > > but mainly, if you advocate it, i'd hope it would be
> > > something you had actually gone through the trouble of
> investigating
> > > with your own ears, for a wide variety of timbres, registers,
> > > amplitudes, and durations . . . it seems like you did something
> like
> > > that for sensitivity of various intervals to mistuning,
> >
> > That was finding at what ratios I could hear anything that _was_
> > sensitive to mistuning (not by how much)
>
> no, no, i'm talking about your whole deal where you found that
ratios
> about as complex as 6:5 were _most_ forgiving of mistuning . . .
> remember all that?

As I explained before when you suggested that, (maybe you missed that
post), that I never systematically investigated that. It was mostly an
opinion cobbled together from years of reading of other people's
experiences.

> that is truly incredible. i've never met anyone at a guitar workshop
> who knows anything about alternate tunings, just some misconceptions
> about indian music using quartertones. mostly they look at my
> microtonal guitars funny and ask if that band has any groupies. at
> that point, my modesty takes over ;)

Tee hee.

I think she'd have trouble grasping anything like Blackjack, but yes,
it's amazing to just bump into someone in my own neighbourhood who
understands at least those historical western tunings, let alone
builds guitars.

First, I want to apologiged if I have been anyhow vexing anybody.

I meant no harm to Robert Wendell with whom I discussed on this group
to eventally conclude that his use of harmonics to improve pitch
estimation is clever if (in my sense) a little over-optimistic. I now
use Robert's idea for my own personal measures on singing voices and
it is really an improvement (even though I could not expect extremely
accurate pitch measurement on voice).

I had a look at the web site of Peterson and found no technical
information justifying their claim for 0.1 cents accuracy beside a
claim that "A tuner can only be accurate if its display is
accurate"... that is a little light. It is said that its adjust
instantaneously, which is clear nonsense. I agree that they should be
suited for falacious claim :-).

I still believe that 0.1 cents does not make sense on the tuning, as
long as I perhaps rely on a quite (too) strict acceptance of "tuning".
In my mind, mere concept of tuning is based on the assumption that the
instrument we tune has evenly distributed harmonics. This is true for
strings, bells, pipes etc. this is true, yes, but up to a certain
limits, limits in string tension, air flow and pressure and precision
required. As I stated in previous post requiring 0.1 ~ 0.006 % places
us way out of the harmonicity limit for a physical string:

I wrote :
> In any cases, the harmonic aproximation cannot hold if we talk about
> 0.1 cents precision, so Paul is absolutely correct to question the
tuning
> of inharmonic string. The harmonic approximation supposes (among
other
> things) that the variation of the string length is neglectible
during its
> oscillation. Let say that that the rest string length is L and the
amplitude
> of vibration is A. In first approximation, at maximum amplitude, the
lenght
> of the string is longer by some deltaL with deltaL/L ~= (A/L)**2.
This is
> fairly neglectible when reasonable precision is required. For
reasonable
> L = 500mm, A = 5mm, we get deltaL/L = 0.01 %: which is above the
claimed
> precision of 0.006 % (0.1 cents). For elementary physic reasons, 0.1
cents
> does not make sense for string tuning.

being out of the harmonic limit, this means that

- Harmonic F(N) is not accurately N * F0 (it is slightly smaller that
an amount probably more than 0.006 %)
- F0 depends on the amplitute of vibration with a variation which is
more than 0.006 %

This is like the period of pendulum that is fairly constant given that
amplitude is small and that you are not too much demanding on
accuracy.

We can make a tought experiment in which measurement accuracy is not a
problem. For instance, instead of dumbly recording the sound we will
use an ultra rapid camera to take a movie of the string with one
million images per second plugged to a microscope that can record
string position with a precision of one atom.

We pluck the string in such a clever way that we are not bothered by
upper harmonics, and see what happen. At the begining, the string
moves at, let say 439.95 Hz, then, as amplitude goes down, frequency
goes to an asymptotic limit of 440.00 Hz. The pitch goes up during the
decay. In fact, this is quite common sense to think that a longer
trajectory takes more time than shorter ones.

This is a tought experiment, but give an insight on what occurs in
"reality".

Some other acoustic devices may be more linear than string but I doubt
so. Further 0.006 % implies more than five digits (linear) precision
that is hardly reached for any kind of commonplace measurement or
mecanical device.

So even if we admit that 0.1 cent measurable (I don't), that is way
out of the harmonicity limits where precision of the tuning has any
meaning for acoustical musical instruments.

It is not impossible a 0.006% "detuning" of a dyad may be audible. But
as the beat period of higher harmonics is (at best) of the same order
of magnitude as the decay period, it is not, strictly speaking
"tuning", but more "enveloppe shaping".

I must admit that this distinction between "tuning" and "enveloppe
shaping" is of no musical relevance. As I must admit that
psycoaccoustic is absolutely not necessary to any musical creation or
experience. I just personaly think that it is fun to try to understand
relationship between what is perceived and what exists, and try to
understand the limits of applicability of ANY theory or system.

yours truly

François Laferrière

--- In tuning@y..., "francois_laferriere" <francois.laferriere@o...>
wrote:
> First, I want to apologiged if I have been anyhow vexing anybody.
>
> I meant no harm to Robert Wendell with whom I discussed on this
group
> to eventally conclude that his use of harmonics to improve pitch
> estimation is clever if (in my sense) a little over-optimistic. I
now
> use Robert's idea for my own personal measures on singing voices and
> it is really an improvement (even though I could not expect
extremely
> accurate pitch measurement on voice).

you must mean robert walker?

> As I stated in previous post requiring 0.1 ~ 0.006 % places
> us way out of the harmonicity limit for a physical string:

not true for bowed strings!

> This is a tought experiment, but give an insight on what occurs in
> "reality".

yes, for the plucked string this is relevant, but don't
overgeneralize into overarching "principles".

> I just personaly think that it is fun to try to understand
> relationship between what is perceived and what exists, and try to
> understand the limits of applicability of ANY theory or system.

i share that feeling with you.

I am TERRIBLY SORRY, what can be worse than making such a gross
mistake in an apology....

me :
> First, I want to apologised if I have been anyhow vexing anybody.
>
> I meant no harm to Robert Wendell with whom I discussed on this
group
> to eventYally conclude that his use of harmonics to improve pitch
> estimation is clever if (in my sense) a little over-optimistic. I
now
> use Robert's idea for my own personal measures on singing voices and
> it is really an improvement (even though I could not expect
extremely
> accurate pitch measurement on voice).

> paul:
> you must mean robert walker?

of course

please excuse my stupidity

François Laferrière

> me:
> As I stated in previous post requiring 0.1 ~ 0.006 % places
> us way out of the harmonicity limit for a physical string:

> Paul:
> not true for bowed strings!

The plucking or hitting a string is the excitation scheme that can be
easilly an quite reliably by linear modeling.

Obviously, bowing a string can produce a sustained sound.

You certainly know that bowing a string is an awfully complex
mechanism that relies on the difference between the difference between
the static and dynamic friction between the horsehairs and the string.
The result is a relatively important inharmonicity of bowed strings.
There is a good web page on violin at
http://www.zainea.com/Oscilationsofbowedstring.html. It seems that a
string sound sharper when bowed than plucked. Further inharmonicity
(if those figures given on this page is correct, but bibliography look
sound) is much worse than I taught. For a A string on a "good violin",
it is given inharmonicity figures

...mode number ..1 ...2 ...3 ...4 ...5 ...6 ...7 ...8
freq shift(Hz) 0.0 +1.0 +2.0 -1.0 +1.0 +5.0 +2.0 +8.0
freq shift (¢) 0.0 +2.0 +2.6 -1.0 +0.8 +3.3 +1.0 +3.9

(cents computation are mine, eventual errors are mine :-))

Note that inharmonicity goes the other way than inharmocity of piano
strings (where higher harmonics are flat)

That should be cross checked with other sources, but that looks
reasonable to me.

And to me it makes the 0.1 cents precise tuning less and less likely.

When I have some spare time, I will try to check this from a recording
of some artist playing something better than a "good violin" (let say
an Amati or a Stradivarius) if I can find a single note without
vibrato!!.

If somebody have time to send me or post on the list some zithern
notes recording I would be pleased to checked (when I have some time)
if the violin results apply to zithern as well.

yours truly.

François Laferrière

--- In tuning@y..., "francois_laferriere" <francois.laferriere@o...>
wrote:

> The result is a relatively important inharmonicity of bowed strings.
> There is a good web page on violin at
> http://www.zainea.com/Oscilationsofbowedstring.html.

this didn't work for me -- did you spell it right?

--- In tuning@y..., "emotionaljourney22" <paul@s...> wrote:
> --- In tuning@y..., "francois_laferriere" <francois.laferriere@o...>
> wrote:
>
> > The result is a relatively important inharmonicity of bowed strings.
> > There is a good web page on violin at
> > http://www.zainea.com/Oscilationsofbowedstring.html.
>
> this didn't work for me -- did you spell it right?

http://www.zainea.com/Oscilationsofbowedstring.htm

(htm not html)
sorry.

This site looks like a compendium of more or less classical articles
"taken" her and there. There are some articles by Johan Sundberg on
accoustics of singing voice that I recognise as "classic".

François Laferrière

--- In tuning@y..., "francois_laferriere" <francois.laferriere@o...>
wrote:
> --- In tuning@y..., "emotionaljourney22" <paul@s...> wrote:
> > --- In tuning@y..., "francois_laferriere"
<francois.laferriere@o...>
> > wrote:
> >
> > > The result is a relatively important inharmonicity of bowed
strings.
> > > There is a good web page on violin at
> > > http://www.zainea.com/Oscilationsofbowedstring.html.
> >
> > this didn't work for me -- did you spell it right?
>
> http://www.zainea.com/Oscilationsofbowedstring.htm
>
> (htm not html)
> sorry.
>
> This site looks like a compendium of more or less classical
articles
> "taken" her and there. There are some articles by Johan Sundberg on
> accoustics of singing voice that I recognise as "classic".

i'll have to take a look at this later. please remind me if i forget!

--- In tuning@y..., "francois_laferriere" <francois.laferriere@o...>
wrote:

> There is a good web page on violin at
> http://www.zainea.com/Oscilationsofbowedstring.html. It seems that a
> string sound sharper when bowed than plucked. Further inharmonicity
> (if those figures given on this page is correct, but bibliography
look
> sound) is much worse than I taught. For a A string on a "good
violin",
> it is given inharmonicity figures
>
> ...mode number ..1 ...2 ...3 ...4 ...5 ...6 ...7 ...8
> freq shift(Hz) 0.0 +1.0 +2.0 -1.0 +1.0 +5.0 +2.0 +8.0
> freq shift (¢) 0.0 +2.0 +2.6 -1.0 +0.8 +3.3 +1.0 +3.9
>
> (cents computation are mine, eventual errors are mine :-))
>
> Note that inharmonicity goes the other way than inharmocity of piano
> strings (where higher harmonics are flat)

francois, as i read the article, these numbers are for the
*resonances* of a freely vibrating string, not the harmonics of a
bowed string.

as far as i can tell from anything in this article, bowed strings,
played correctly, are harmonic.

an analogy to all this is brass instruments and reed instruments --
though the resonant peaks form a noticeably inharmonic series, the
instrument tone itself is harmonic.

note the assertion toward the end that a string whose resonances are
too far removed from harmonicity is *unplayable* with a bow. the
article shows how this, again, is analogous to wind instruments.

i fear you may have been reading benade with a fundamental
misunderstanding on these basic issues . . .

> Paul:
> francois, as i read the article, these numbers are for the
> *resonances* of a freely vibrating string, not the harmonics of a
> bowed string.

> as far as i can tell from anything in this article, bowed strings,
> played correctly, are harmonic.

correct.

That was not really clear from the text, so I assumed (wrongly) that
it was bowed. I was mislead by the tiltle of the article, and maybe by
some prejudices of my own: I never suspect that pizzicati where that
inharmonic, given that harpsichord notes I personally analysed shows
no significant inharmonicity. Obviously (I say obviously now that I
was proven wrong, it was not that obvious to me 3 days ago), as the
string is much shorter and (I think) less tense than on an
harpsichord. As the inharmonicity factor is proportional to
(L**-2)*(T**-1) it goes up quickly when string length goes down.

Further, it seems, from the text, that inharmonicity depends heavily
on the environment on which the string is set. That suggest a strong
coupling between the modes of the string and the resonnant modes of
the rest of the instrument; no trivial matter.

> Paul:
> i fear you may have been reading benade with a fundamental
> misunderstanding on these basic issues . . .

Do not despair about me, I eventually understood the very basic. What
has been misleading, is that the free modes of a string that can be
easilly modeled (including basic inharmonicity aspects) are less
harmonic than bowed modes which can be only crudely modeled as far as
it imply awfully complex and tremendously non-linear mechanisms.

I understood that in the bowing mechanism, there is a phase lock mode
that reinitialize the initial boundary condition each time the string
is stopped by static friction with the horsehairs. I didn't knew that
before, I should never miss an opportunity to get instructed :-)

Thanks for sharing your knowledge.

Nevertheless the phase lock harmonicity model of bowed string has
necessarilly a limit and I wonder what is it. I found no other
references on this topic. Physicists have probably little interest in
this problem because its complexity makes it probably way out the
reach of analytical solutions. Richard Feynman stated with humour that
"there are two kind of problems in physics: those that we know how to
solve using simple harmonic-oscillators approximation and those that
we do no know how to solve".

We drifted far away from the original concerns (does 0.1 cent makes
sense?) and the discussion raises more question than it provided
answers. For instance assuming infinite precision in tuning and
hearing, but dealing with material objects that have no infinite
harmonicity.

- What is pitch when the accuracy required is beyond the harmonic
approximation limit? i.e. when f(N) is not reliably equal to N*f(1).

- When tuning an interval, with those extreme accuracy requirements,
do we tune the "pitch" (whatever that means) or the most prominent
beating harmonics?

- If we tune two notes by the most prominent beating harmonics, the
overall tuning may not be transitive (be sensitive to the order of the
tuning). If it not transitive, does the concept of temperament still
makes sense?

If we stay within an admitted audibility limit of 2-3 cents, none of
those are real issues, but if we admit that 0.1 cents make sense, a
lot of other things stop to make sense.

yours truly

François Laferrière

--- In tuning@y..., "francois_laferriere" <francois.laferriere@o...>
wrote:

> Nevertheless the phase lock harmonicity model of bowed string has
> necessarilly a limit and I wonder what is it. I found no other
> references on this topic.

did you see the link i posted to a (probably undergraduate-oriented)
university website?

> If we stay within an admitted audibility limit of 2-3 cents, none of
> those are real issues, but if we admit that 0.1 cents make sense, a
> lot of other things stop to make sense.

i'm glad you're thinking along these lines. please stay with us and
continue to share your insights, especially where they relate (such
as in the tuning of a piano to "just intonation") . . .

--- In tuning@y..., "emotionaljourney22" <paul@s...> wrote:

> did you see the link i posted to a (probably undergraduate-oriented)
> university website?

Yes, interresting, but cope with, let say, first order phenomena,
without realy exploring its limits

> > If we stay within an admitted audibility limit of 2-3 cents, none
of
> > those are real issues, but if we admit that 0.1 cents make sense,
a
> > lot of other things stop to make sense.
>
> i'm glad you're thinking along these lines. please stay with us and
> continue to share your insights, especially where they relate (such
> as in the tuning of a piano to "just intonation") . . .

It is heartwarming to know that you share some of my interests.

yours truly

François Laferrière

--- In tuning@y..., "francois_laferriere" <francois.laferriere@o...>
wrote:
> --- In tuning@y..., "emotionaljourney22" <paul@s...> wrote:
>
> > did you see the link i posted to a (probably undergraduate-
oriented)
> > university website?
>
> Yes, interresting, but cope with, let say, first order phenomena,
> without realy exploring its limits

true, but how rare it is to find any information that is so correct
and straightforward in the first-order phenomena!

what are the limits of this description? torsional motion of the
string and other phenomena such as player unsteadiness make the slip-
stick cycle of bowing fail to repeat exactly the same waveform every
period. result? some 'bandwidth' in the partials. a systematic
deviation from harmonicity? i don't think so, and haven't seen any
evidence that would lead me to believe otherwise . . .