Microtemperament and scale structure

I understand that with microtemperament one can achieve greater
number of consonant intervals in a scale that is originally tuned in
strict Just Intonation.

This can be a great method for generating new and interesting scales
but doesn't it destroy the structure of the original scale?

For example I don't think that a microtempered Eikosany with greater
number of consonances is really an Eikosany at all. It's dissonances
are an integral part of it.

What do you think?

Kalle

--- In tuning@y..., kalleaho@m... wrote:
> I understand that with microtemperament one can achieve greater
> number of consonant intervals in a scale that is originally tuned
in
> strict Just Intonation.
>
> This can be a great method for generating new and interesting
scales
> but doesn't it destroy the structure of the original scale?
>
> For example I don't think that a microtempered Eikosany with
greater
> number of consonances is really an Eikosany at all. It's
dissonances
> are an integral part of it.
>
> What do you think?
>
> Kalle

Hi Kalle.

I defer to Dave Keenan on the details of the microtempered Eikosany.
However, it is purely an artistic decision whether one wishes to
microtemper it or not. In strict JI, some of the intervals will be
very close to consonant intervals . . . for example, a moderately
beating perfect fifth. Not necessarily what I'd call a dissonance,
despite its very complex ratio. What microtemperament does is to make
this, as well as the consonant (pure) perfect fifths, all identical
to one another, all beating very, very slowly. Same for other
consonant intervals. If you relish the differences, and present them
in a way that is likely to be meaningful to the listener, then
microtemperament is not for you! Kraig Grady is in complete agreement
with you about the Eikosany. However, someone else may enjoy the way
the consonant tetrads are connected to one another in the Eikosany,
and may not wish to make direct use of the "dissonances" that are
near-consonances. For such a person, working in a microtempered
system could be preferable, say, if they sought to modulate some of
the tetrad-connecting motifs, or work in some interesting
counterpoint with multiple harmonic implications, or . . . I could
think of various other things.

But I don't think temperament in any way necessarily "destroys the
original scale". For example take the diatonic scale. You'll see lots
of JI advocates saying that the "true" Western diatonic scale C D E F
G A B C is 1/1 9/8 5/4 4/3 3/2 5/3 15/8 2/1. As far as I am
concerned, this is hogwash. In 99.9% of the Western music written in
the diatonic scale, D-A is treated as a consonance just like any
other perfect fifth. Yet the JI ratios tell you that D-A is 40:27,
very rough in comparison will all those pure 3:2 fifths in the scale.
The musical reality is that, since the advent of triadic harmony,
virtually no instrument was ever tuned to the "JI diatonic" scale.
Temperament, adaptive JI, or various shadings in-between were
naturally and intuitively adopted as the desire for triadic harmony
began to dominate the Western musical style. So here is a case where,
I feel, strict JI "destroys the original scale".

Anyway, I'd keep my options open. Overall, temperament tends to
smooth out the melodies, reduce the number of interval sizes, and
(for me) make composing a lot easier, more direct, more natural, and
more fun. On the other hand, if you like to take a more cerebral
approach to composing, then the types of challenges the Eikosany
presents may be just the thing for you.

--- In tuning@y..., kalleaho@m... wrote:
> I understand that with microtemperament one can achieve greater
> number of consonant intervals in a scale that is originally tuned in
> strict Just Intonation.
>
> This can be a great method for generating new and interesting scales
> but doesn't it destroy the structure of the original scale?

This is a very good question. The short answer is: No.

> For example I don't think that a microtempered Eikosany with greater
> number of consonances is really an Eikosany at all. It's dissonances
> are an integral part of it.
>
> What do you think?

None of the real dissonances will be significantly affected by
microtempering. Any new consonance "introduced" by microtempering was
actually already present as a near-JI interval with an error typicaly
less than 8 cents (considerably less than that of the thirds and
sixths that most consider consonant in 12-EDO). In the case of a
guitar, it could as easily have been "introduced" (i.e. made
perceptibly just) by a tiny mistuning (of either open strings or fret
placement). I would expect that any composer seeking dissonance would
not have used one of these.

Dissonances tend to be on broad plateaux, unlike the sharp notches of
consonance. So microtempering alters the characteristic dissonances of
a scale even less than it affects the consonances.

But of course this will not really be proven until such guitars
are built and tried by experts.

-- Dave Keenan

> Dissonances tend to be on broad plateaux, unlike the sharp notches
> of consonance. So microtempering alters the characteristic
> dissonances of a scale even less than it affects the consonances.

Very good way of putting it, Dave.

-Carl

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

/tuning/topicId_26876.html#26898

>
> But I don't think temperament in any way necessarily "destroys the
> original scale". For example take the diatonic scale. You'll see
lots of JI advocates saying that the "true" Western diatonic scale C
D E F G A B C is 1/1 9/8 5/4 4/3 3/2 5/3 15/8 2/1. As far as I am
> concerned, this is hogwash. In 99.9% of the Western music written
in the diatonic scale, D-A is treated as a consonance just like any
> other perfect fifth. Yet the JI ratios tell you that D-A is 40:27,
> very rough in comparison will all those pure 3:2 fifths in the
scale. The musical reality is that, since the advent of triadic
harmony, virtually no instrument was ever tuned to the "JI diatonic"
scale. Temperament, adaptive JI, or various shadings in-between were
> naturally and intuitively adopted as the desire for triadic harmony
> began to dominate the Western musical style. So here is a case
where, I feel, strict JI "destroys the original scale".
>

Paul, this is such a clear explanation of this! This is the first
time I understood this so clearly... I don't know if we ever went
over this like this before, but if so, I don't remember it.

I suggest that any "silent lurkers" read this post very carefully, if
there are such out there...

It makes a *lot* of things quite clear...

_________ _______ _______
Joseph Pehrson

--- In tuning@y..., "Dave Keenan" <D.KEENAN@U...> wrote:
> --- In tuning@y..., kalleaho@m... wrote:
> > I understand that with microtemperament one can achieve greater
> > number of consonant intervals in a scale that is originally tuned
in
> > strict Just Intonation.
> >
> > This can be a great method for generating new and interesting
scales
> > but doesn't it destroy the structure of the original scale?
>
> This is a very good question. The short answer is: No.
>
> > For example I don't think that a microtempered Eikosany with
greater
> > number of consonances is really an Eikosany at all. It's
dissonances
> > are an integral part of it.
> >
> > What do you think?
>
> None of the real dissonances will be significantly affected by
> microtempering. Any new consonance "introduced" by microtempering
was
> actually already present as a near-JI interval with an error
typicaly
> less than 8 cents (considerably less than that of the thirds and
> sixths that most consider consonant in 12-EDO). In the case of a
> guitar, it could as easily have been "introduced" (i.e. made
> perceptibly just) by a tiny mistuning (of either open strings or
fret
> placement). I would expect that any composer seeking dissonance
would
> not have used one of these.
>
> Dissonances tend to be on broad plateaux, unlike the sharp notches
of
> consonance. So microtempering alters the characteristic dissonances
of
> a scale even less than it affects the consonances.

Great response Dave!

--- In tuning@y..., kalleaho@m... wrote:

> I understand that with microtemperament one can achieve greater
> number of consonant intervals in a scale that is originally tuned
in
> strict Just Intonation.

> This can be a great method for generating new and interesting
scales
> but doesn't it destroy the structure of the original scale?

When you finally get to the point where you can't tell the
difference, the question becomes moot. However, the answer is yes--
introducing approximations increases the flexibility of harmonic
relationships and thereby changes the structure. The question is
really best understood in terms of group theory.

The intervals of any form of just intonation are by definition
positive rational numbers, and so an element of the abelian group of
positive rationals under multiplication (since our hearing, and hence
musical structure, is multiplicative.) We are never really interested
in all rational numbers, but can content ourselves with a finitely
generated subgroup--for one easy example, the group G of all the
numbers of the form 2^a * 3^b * 5^c, where a, b and c are integers,
are the numbers generated by the first three primes, 2, 3 and 5.

An approximate tuning system can very often be seen as a (subset of
a) group homomorphism to a group of smaller rank, and most
significantly to a group of rank 1. For another easy example, the
rank 3 free group G can be sent to a rank 1 free group by a
homomorphism h12(2) = 12, h12(3) = 19, h12(5) = 28. A subset of 88
contiguous elements of this group associated to notes tuned as usual
by setting g12(1) = 440 hz, g12(2) = 2*440 hz, g12(3) = 2^19/12*440
hz, g12(5) = 2^28/12*440 hz is the standard keyboard.

Any such homomorphism is defined by its kernel, which are the
elements sent to the identity. In the case of h12, the kernel is
spanned by 81/80 (the diatonic comma) and 128/125 (the great diesis),
where we have h12(81/80) = h12(128/125) = 0. A tuning system which
does not contain the diatonic comma in its kernel (and this includes
just intonation!) will have a structure quite different that what
musicians normally expect. On the other hand one that does, such as
what we get from the 19 or 31 tone system, will seem more "normal".

Consider the system h72(2) = 72, h72(3) = 114, h72(5) = 167, h72(7) =
202, h72(11) = 249 (the last two values are irrelevant here, but they
do no harm and they cover the range which makes the 72 system
interesting.) This 72 system has a 12 system tuning embedded in it,
so we could suppose that structurally they are very similar. However,
intersecting the kernels shows they are remotely related; in
particular h72(81/80) = 1 and h72(128/125) = 3, the second is not so
important but the first shows that the 72 system is fundamentally
different in structure from the 12 system. In contrast, h31(2) = 31,
h31(3) = 49, h31(5) = 72, h31(7) = 87 and h31(11) = 107 *does* have
the property that h31(81/80) = 0; and while h31(128/125) = 1 we still
find h31 is much closer in structre to h12 than is h72.

--- In tuning@y..., genewardsmith@j... wrote:
> --- In tuning@y..., kalleaho@m... wrote:
>
> > I understand that with microtemperament one can achieve greater
> > number of consonant intervals in a scale that is originally tuned
> in
> > strict Just Intonation.
>
> > This can be a great method for generating new and interesting
> scales
> > but doesn't it destroy the structure of the original scale?
>
> When you finally get to the point where you can't tell the
> difference, the question becomes moot.

That's what a _micro_temperament is. A temperament where most people
can't tell the difference (from strict ratios). So isn't the rest of
your post is irrelevant to the actual question?

> The intervals of any form of just intonation are by definition
> positive rational numbers,

Not by my definition. This is a common misconception. They may only be
_very_close_to_ ratios of small whole numbers. Justness is
fundamentally a matter of human perception. When humans agree that a
harmony is just there is no finite measurement that can determine
whether the frequency ratio is rational or irrational. Do you agree?

Some of us use the term "rational intonation" (RI) for the thing you
are referring to.

Welcome to the list, Gene.

Regards,
-- Dave Keenan

--- In tuning@y..., "Dave Keenan" <D.KEENAN@U...> wrote:

Justness is
> fundamentally a matter of human perception. When humans agree that
a
> harmony is just there is no finite measurement that can determine
> whether the frequency ratio is rational or irrational. Do you agree?

Nope. I'm a mathematician and your definition makes hash out of the
mathematics. Can you come up with a version which is well-defined
mathematically?

> Some of us use the term "rational intonation" (RI) for the thing
you
> are referring to.

A rose by any other name would be a free abelian group. :)

--- In tuning@y..., "Dave Keenan" <D.KEENAN@U...> wrote:

> That's what a _micro_temperament is. A temperament where most
people
> can't tell the difference (from strict ratios). So isn't the rest
of
> your post is irrelevant to the actual question?

I'm not sure--he may have been asking about whether part of the
system was conceptual, actually.

When humans agree that a
> harmony is just there is no finite measurement that can determine
> whether the frequency ratio is rational or irrational. Do you agree?

My reply to this was a little cyptic--let me expand on it a bit by
pointing out that this would make every interval just, so it can't be
what you mean. That raises the question of what it is you *do* mean.

In case this is *still* crytic, the rational numbers are dense in the
reals, and therefore there are an infinity of rational numbers in any
neighborhood of any real number. Therefore your definition does not
seem to define anything.

--- In tuning@y..., genewardsmith@j... wrote:

> ...introducing approximations increases the flexibility of harmonic
> relationships and thereby changes the structure.

Thanks. I was thinking about the mathematical properties of scale
structures. Dave seems to be thinking more in terms of perception.

Your group theoretical considerations are solid but the other group
in your homomorphisms is always some equal temperament. What about
linear temperaments and more importantly microtemperaments? How much
do they preserve the properties of the original tuning?

--- In tuning@y..., jacky_ligon@y... wrote:

> I would like to respectfully toss in my two cents values here to
say
> that where there is discussion of what is *just* about intervals
> without some healthy inclusion of what this all means relative to
the
> infinity of possible timbres (acoustic and electronic), rhythm (or
> their use compositionally in time) and musical examples to show for
> final proofs, that much of this fails to have meaning in the real
> world of *music* and *music creation*.
>

Well, didn't Harry Partch use instruments with inharmonic timbres? At
the same time he tuned them in just intonation which he thought was
the same thing as rational intonation. So timbre is not included in
the definition of JI. I don't think we should revise the meaning
of "just intonation". It is a conceptual/mathematical model for
tuning. Real acoustic instruments can never be tuned to strict JI.
For them JI is an ideal like Galilei's pendulum. Strict ratios
between frequencies can only be attained by electronic means.

But as Sethares and others have shown, timbre and tuning are very
much related when it comes to *consonance* of intervals and chords.
And everybody knows you can't play melodies with white noise.

> Harmonic timbres are a minority in the world of acoustic timbres,
and
> in the world of analog and digital sound synthesis, about the most
> boring possible timbre that one can conceive of are ones with pure
> harmonic partials. Create a pure harmonic timbre and attempt to
write
> music with it, and the truth will be revealed. All this is to say,
> that what we may like to believe to be true for tuning with
harmonic
> timbres, fails to show the full picture for all of the other myriad
> timbral treasures, especially when one considers multi-part music
> with mixed timbres.

> To me, what is true of timbres can been shown in a musical setting
to
> be true of tunings; that many times scales which are intended to
> include as many possible consonances and are designed for harmonic
> timbres and harmonic music can be much less engaging in a
> compositional setting where inharmonic timbres, and melodic focus
are
> the rule. I find it generally too general to think that what works
> for tuning procedures of 5-7 limit JI with harmonic timbres, will
> have musical relevance on other timbre sets. The possbilities of
> scale design per composition are rarely discussed, as many seek to
> generalize tunings for all situations.

I'm sure that the spectral composition of a sound cannot alone make
it boring. A richly evolving harmonic timbre can be much more
interesting than a fairly static inharmonic one. Then again a tuning
that works with harmonic timbres works also with many timbres that
have slightly detuned harmonic partials.

Kalle

--- In tuning@y..., jacky_ligon@y... wrote:

> Harmonic timbres are a minority in the world of acoustic timbres,

Minority? How are you counting?

> and
> in the world of analog and digital sound synthesis, about the most
> boring possible timbre that one can conceive of are ones with pure
> harmonic partials.

Boring? So many variations are possible -- how
could you ever get bored?

But the harmonic timbres are the ones with the
clearest pitch.

> Create a pure harmonic timbre and attempt to write
> music with it, and the truth will be revealed.

Hmm . . . all music that has ever been written for
brass, reed, and bowed string instruments, and
human voices, is music with pure harmonic
timbres. I'd have to give it a thumbs-up!

> All this is to say,
> that what we may like to believe to be true for tuning with harmonic
> timbres, fails to show the full picture for all of the other myriad
> timbral treasures, especially when one considers multi-part music
> with mixed timbres.

This I agree with whole-heartedly.

--- In tuning@y..., kalleaho@m... wrote:
> --- In tuning@y..., genewardsmith@j... wrote:
>
> > ...introducing approximations increases the flexibility of harmonic
> > relationships and thereby changes the structure.
>
> Thanks. I was thinking about the mathematical properties of scale
> structures. Dave seems to be thinking more in terms of perception.

Though I may not agree with Dave on the
definition of JI, I have to agree with him that all
musical questions have to be dealt with in terms of
perception. If a mathematical framework seeks to
label something a discordance but it is perceptually
a concordance, then there are features of the
mathematical framework that don't correspond to
musical reality, and vice versa. So what your
question about the Eikosany really boils down to
is, are you going to hear, and use, concordances
detuned by less than 8 cents as discordances? If so,
then microtemperament is not for you. If not, then
you may benefit from microtemperament, to open
up musical possibilities and to reduce the number
of distinct pitches you need if you expand further
in the lattice.

--- In tuning@y..., kalleaho@m... wrote:

> I'm sure that the spectral composition of a sound cannot alone make
> it boring. A richly evolving harmonic timbre can be much more
> interesting than a fairly static inharmonic one. Then again a tuning
> that works with harmonic timbres works also with many timbres that
> have slightly detuned harmonic partials.

Or for many inharmonic timbres where the
fundamental is dominant, as Partch and Kraig
Grady have realized. An otonal chord played with
such inharmonic timbres with a fixed spectrum will
result in very stong, clear virtual pitch, i.e. root.
Combinational tones can only enhance this effect
when JI tunings are used. This kind of rootedness
is not possible to obtain with inharmonic tunings.
Although Sethares has done a great deal of
valuable work on the relationship between tuning
and timbre, his is only a piece of the puzzle.

--- In tuning@y..., jacky_ligon@y... wrote:
> I would like to respectfully toss in my two cents values here to
say
> that where there is discussion of what is *just* about intervals
> without some healthy inclusion of what this all means relative to
the
> infinity of possible timbres (acoustic and electronic), rhythm (or
> their use compositionally in time) and musical examples to show for
> final proofs, that much of this fails to have meaning in the real
> world of *music* and *music creation*.

Suppose you woke up one morning in a cranky mood and decided to make
music on a set of pitches chosen rather randomly, or according to
some clever method of your own. You could then go ahead and use
synthasized timbres whose partial tones only occurred among your
chosen pitch values. In terms of consonance/dissonance arising from
partial tones within critical bandwidths of each other, the results
could be quite consonant, depending on your choice of pitches and
assignment of energy to the partial tones of your timbres. Whether
the result would be any good as *music* I leave to the genius of
anyone who wants to try this!

--- In tuning@y..., genewardsmith@j... wrote:

> Suppose you woke up one morning in a cranky mood and decided to make
> music on a set of pitches chosen rather randomly, or according to
> some clever method of your own. You could then go ahead and use
> synthasized timbres whose partial tones only occurred among your
> chosen pitch values. In terms of consonance/dissonance arising from
> partial tones within critical bandwidths of each other, the results
> could be quite consonant, depending on your choice of pitches and
> assignment of energy to the partial tones of your timbres. Whether
> the result would be any good as *music* I leave to the genius of
> anyone who wants to try this!

Gene,

Jacky has been entertaining us recently with the
sounds of crickets and frogs, sampled and
"harmonized" with one another in just such a
"consonant" way, over on

MakeMicroMusic@yahoogroups.com

As a delightful organization of sound, I'd certainly
call it *good music*. Perhaps it's not the kind of
music I'm working on myself, or the kind of music
to which you'd like to turn your theoretical
attention, but let's be wary of dismissing another
human being's artistic expression -- especially now
that the entire 20th century has passed.

P.S. Jacky only wakes up in a cranky mood about
twice a year :) Mostly these "musical" endeavors,
should you agree to call it that, are an expression
of joy and deep spiritual searching.

-Paul

--- In tuning@y..., kalleaho@m... wrote:

> Your group theoretical considerations are solid but the other group
> in your homomorphisms is always some equal temperament.

If the image group is rank one then 2 has to be sent to some number n
of steps, and hence you get an n division system. How exactly this is
tuned is a separate question. If the image group has rank greater
than one you don't get an ET -- you could for instance have a two-
dimensional arragement of notes.

What about
> linear temperaments and more importantly microtemperaments? How
much
> do they preserve the properties of the original tuning?

The properties of the tuning are to some extent what you give them--
that is, they are conceptual as well as actual acoustic properties.
If you use a mean-tone temperment you *could* treat all keys alike.
On the other hand, it makes more sense to utilize the special
properties of the tuning, for instance when you use a Neapolitan
Sixth or avoid a wolf. The decision of what to do is not forced on
you by the tuning, however!

As for microtemperments, the only definition I've seen is that they
are tunings which differ only imperceptably from rational intonation.
If that is the case, why would you treat it any differently?

--- In tuning@y..., genewardsmith@j... wrote:
> --- In tuning@y..., "Dave Keenan" <D.KEENAN@U...> wrote:
>
> Justness is
> > fundamentally a matter of human perception. When humans agree that
> a
> > harmony is just there is no finite measurement that can determine
> > whether the frequency ratio is rational or irrational. Do you
agree?
>
> Nope. I'm a mathematician and your definition makes hash out of the
> mathematics. Can you come up with a version which is well-defined
> mathematically?

You are probably aware that it is very difficult to accurately model
human perception, for one reason because we're all different. Here is
a mathematicaly well-defined, but psychoacoustically very approximate,
definition of a just interval that I am currently using for very
practical purposes (designing guitars).

A justly intoned interval is (approximately) an interval within 2.8
cents of any ratio a:b in lowest terms, where a*b < 100.

>
> > Some of us use the term "rational intonation" (RI) for the thing
> you
> > are referring to.
>
> A rose by any other name would be a free abelian group. :)

Yes, but not as practically useful as the above approximate definition
of a justly intoned interval.

Regards,
-- Dave Keenan

--- In tuning@y..., "Paul Erlich" <paul@s...> wrote:
> So what your
> question about the Eikosany really boils down to
> is, are you going to hear, and use, concordances
> detuned by less than 8 cents as discordances? If so,
> then microtemperament is not for you. If not, then
> you may benefit from microtemperament, to open
> up musical possibilities and to reduce the number
> of distinct pitches you need if you expand further
> in the lattice.

And to make practical the construction of a guitar for the scale.

--- In tuning@y..., genewardsmith@j... wrote:
> --- In tuning@y..., kalleaho@m... wrote:
>
> > Your group theoretical considerations are solid but the other group
> > in your homomorphisms is always some equal temperament.
>
> If the image group is rank one then 2 has to be sent to some number n
> of steps, and hence you get an n division system. How exactly this is
> tuned is a separate question. If the image group has rank greater
> than one you don't get an ET -- you could for instance have a two-
> dimensional arragement of notes.

This is what we call a _planar temperament_ . . . the definition of _linear temperament_ should
be obvious now, with meantone an example of the latter.
>
> What about
> > linear temperaments and more importantly microtemperaments? How
> much
> > do they preserve the properties of the original tuning?
>
> The properties of the tuning are to some extent what you give them--
> that is, they are conceptual as well as actual acoustic properties.
> If you use a mean-tone temperment you *could* treat all keys alike.
> On the other hand, it makes more sense to utilize the special
> properties of the tuning, for instance when you use a Neapolitan
> Sixth or avoid a wolf. The decision of what to do is not forced on
> you by the tuning, however!
>
> As for microtemperments, the only definition I've seen is that they
> are tunings which differ only imperceptably from rational intonation.
> If that is the case, why would you treat it any differently?

They differ imperceptibly (1 or 2 cents) from rational intonation in their tuning of the
_consonances_ of the system (usually defined as ratios with no odd factor of either the
numerator or the denominator exceeding a predefined "limit"). For the "dissonances" (in JI terms)
of the system, i.e., notes not directly adjacent in the JI lattice of consonances, microtemperament
can make a larger difference, sometimes making such an interval identical to one of said
consonant ones, audibly changing its sound. Dave Keenan argued that, in the particular case
being asked about, these "dissonances" were less than 8 cents different from just consonances .
. . hence tempering them to within 1 or 2 cents of a just intonation consonance, while perhaps a
perceptable change, would be unlikely to be a musically important change. It's up to the
composer, of course, to decide whether the effect is musically important or not.

--- In tuning@y..., "Dave Keenan" <D.KEENAN@U...> wrote:
> --- In tuning@y..., "Paul Erlich" <paul@s...> wrote:
> > So what your
> > question about the Eikosany really boils down to
> > is, are you going to hear, and use, concordances
> > detuned by less than 8 cents as discordances? If so,
> > then microtemperament is not for you. If not, then
> > you may benefit from microtemperament, to open
> > up musical possibilities and to reduce the number
> > of distinct pitches you need if you expand further
> > in the lattice.
>
> And to make practical the construction of a guitar for the scale.

Yes -- if you want frets that go straight across, and you're using a good open string tuning.
Because then you really are expanding further in the lattice, and you might find two very close
pitches. Since you can't have two really close frets on a guitar, slicing the difference into tiny bits
and distributing these bits among the consonant intervals is a great solution. These bits are
smaller than the typical intonation vagaries of a well set-up guitar anyway.

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

/tuning/topicId_26876.html#27143

>
> But the harmonic timbres are the ones with the
> clearest pitch.
>
> > Create a pure harmonic timbre and attempt to write
> > music with it, and the truth will be revealed.
>
> Hmm . . . all music that has ever been written for
> brass, reed, and bowed string instruments, and
> human voices, is music with pure harmonic
> timbres. I'd have to give it a thumbs-up!
>

Is it not true that most of our "standard" orchestral instruments
involve harmonic timbres?? And is it also not true that still a
*majority* of listeners consider these sounds more "musical" than
inharmonic sounds?? In fact, it's the reason that so many synth
manufacturers still try to "ape" these sounds (and that's the word
for it) correct??

Yes?? Or am I "washed up" on this??

_________ ________ _______
Joseph Pehrson

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

/tuning/topicId_26876.html#27152

Blackjack is essentially a "microtemperament," correct??

_________ _______ ______
Joseph Pehrson

--- In tuning@y..., jpehrson@r... wrote:
> --- In tuning@y..., "Paul Erlich" <paul@s...> wrote:
>
> /tuning/topicId_26876.html#27152
>
> Blackjack is essentially a "microtemperament," correct??

To my way of thinking, "Miracle" temperament is a microtemperament
(and therefore just) for 7-limit purposes, but not 9-limit (and
therefore, not higher limits). There's definitely a grey area, but I'm
currently drawing the line at a max error of 2.8 cents.

I call it quasi-just to the 11-limit. In 72-tET it has a max error of
3.9c (in the 4:9). With the optimum generator that error goes down to
3.3c.

-- Dave Keenan

>> /tuning/topicId_26876.html#27152
>>
>> Blackjack is essentially a "microtemperament," correct??
>
>To my way of thinking, "Miracle" temperament is a microtemperament
>(and therefore just) for 7-limit purposes, but not 9-limit (and
>therefore, not higher limits). There's definitely a grey area, but
>I'm currently drawing the line at a max error of 2.8 cents.

How did you come up with this value?

A tolerance of 2.8 cents may be "just" on a guitar, but not
on a piano! It isn't even close by piano standards, where
tunings are typically accurate to 0.5, and often to 0.1 cents.

I'll grant that this is more accurate than any known objective
method for measuring the pitch of individual piano strings, so in
some sense a beatless tuning of this type is "beyond just", in
that frequency ratios are no longer truly the targets of such a
tuning. But what sense is there in evangelizing definitions?

-Carl

--- In tuning@y..., carl@l... wrote:
> >> /tuning/topicId_26876.html#27152
> >>
> >> Blackjack is essentially a "microtemperament," correct??
> >
> >To my way of thinking, "Miracle" temperament is a microtemperament
> >(and therefore just) for 7-limit purposes, but not 9-limit (and
> >therefore, not higher limits). There's definitely a grey area, but
> >I'm currently drawing the line at a max error of 2.8 cents.
>
> How did you come up with this value?

It's about half the error of 1/4-coma meantone.

I listened to such errors on my synth when we were fooling with that
12-tone scale of yours where the 224:225 vanished. It sounded just at
the 7-limit to me (beats you could count). It had 2.9 cent errors. In
one version there was a 6:8:11 where the 384:385 also vanished. I
agreed with you that it couldn't be considered just. I think it had
about 3.3 c errors. But my synth only has 1c accuracy anyway, so
that's more a function of needing to have a lower tolerance for more
complex ratios.

I learned from a URL that John Starrett posted, that even the most
carefully tuned guitar (including individually adjustable bridge for
each string) typically has intonation errors of +-3 cents and more,
(and that's when you don't move the guitar, and the temperature and
humidity don't change) but lots of people still say they are playing
JI guitar.

Most recently I settled on 2.8 c when I discovered that there were a
significant number of linear temperaments among those recently
generated by Graham Breed, that came in slightly under that figure.

However I'd be happy to see a definition that reduced the allowable
error below 2.8c as we go beyond the 7-limit, and possibly reduced the
allowable error for fifths to 2.0 c.

> A tolerance of 2.8 cents may be "just" on a guitar, but not
> on a piano! It isn't even close by piano standards, where
> tunings are typically accurate to 0.5, and often to 0.1 cents.

If 2.8 c is just on a guitar, why isn't it just on a piano (ignoring
inharmonicity), or any instrument? I don't see what relevance the
tuning accuracy of the instrument has. Electronic instruments can have
0c errors.

> But what sense is there in evangelizing definitions?

I don't see myself as "evangelising" the definition?

If I'm designing tunings and guitars and I say they are
"microtempered", meaning "tempered so slightly that the consonances
are indistinguishable from rational in normal use, i.e. just", then it
seems a good idea if I describe in an objective and reproducible way,
what that means to me.

-- Dave Keenan

>>>I'm currently drawing the line at a max error of 2.8 cents.
>>
>>How did you come up with this value?
/.../
>I learned from a URL that John Starrett posted, that even the most
>carefully tuned guitar (including individually adjustable bridge
>for each string) typically has intonation errors of +-3 cents and
>more, (and that's when you don't move the guitar, and the
>temperature and humidity don't change)

Well, guitars are usually tuned immediately before performance...

>but lots of people still say they are playing JI guitar.

A good reason to call a guitar tuning within 3 cents of just,
"just", I'd say.

>>A tolerance of 2.8 cents may be "just" on a guitar, but not
>>on a piano! It isn't even close by piano standards, where
>>tunings are typically accurate to 0.5, and often to 0.1 cents.
>
>If 2.8 c is just on a guitar, why isn't it just on a piano
>(ignoring inharmonicity), or any instrument? I don't see what
>relevance the tuning accuracy of the instrument has.

You listed it as one of your reasons.

>Electronic instruments can have 0c errors.

Well, not really. It all depends on the reproduction equipment,
and how the pitch of the timbre is measured. To pick a nit, I'd
argue that very few electronic instruments are as precisely
tuned as a good concert grand, unless the electronic instrument
had some sort of feedback system involved in its tuning.

I'm not trying to pick a fight here... I just wanted to say that
a tuning with a max error of 2.8 cents isn't necessarily the same
as just in all cases. Do you disagree?

-Carl

--- In tuning@y..., carl@l... wrote:
> Dave Keenan wrote:
> >I don't see what
> >relevance the tuning accuracy of the instrument has.
>
> You listed it as one of your reasons.

What is relevant is the instrument that has the largest unavoidable
random errors on which rationally specified tunings are still
considered just (e.g. the guitar). The fact that instruments exist
which have smaller such errors, is irrelevant.

> >Electronic instruments can have 0c errors.
>
> Well, not really. It all depends on the reproduction equipment,
> and how the pitch of the timbre is measured. To pick a nit, I'd
> argue that very few electronic instruments are as precisely
> tuned as a good concert grand, unless the electronic instrument
> had some sort of feedback system involved in its tuning.

Nah. If everything is derived by digital division from a single
crystal oscillator it will all be totally rational (but boring). But
of course you couldn't prove it rational by measurement, only by
logical deduction from the circuit.

> I'm not trying to pick a fight here... I just wanted to say that
> a tuning with a max error of 2.8 cents isn't necessarily the same
> as just in all cases. Do you disagree?

I don't necessarily disagree with this in general. But I disagree that
the exact same set of frequencies that we agree are just on one
instrument, can suddenly cease to be just, simply because they are
produced by a different instrument (with an equally harmonic timbre),
merely because that instrument has smaller unavoidable random errors.

Is that really what you want to say?

-- Dave Keenan

--- In tuning@y..., carl@l... wrote:
> >>>I'm currently drawing the line at a max error of 2.8 cents.
> >>
> >>How did you come up with this value?
> /.../
> >I learned from a URL that John Starrett posted, that even the most
> >carefully tuned guitar (including individually adjustable bridge
> >for each string) typically has intonation errors of +-3 cents and
> >more, (and that's when you don't move the guitar, and the
> >temperature and humidity don't change)
<snip>
>
> -Carl

Mostly due to finger pressure variation I would wager.

>> You listed it as one of your reasons.
>
>What is relevant is the instrument that has the largest unavoidable
>random errors on which rationally specified tunings are still
>considered just (e.g. the guitar). The fact that instruments exist
>which have smaller such errors, is irrelevant.

Irrelevant to the guitar, but not to the tuning in general. The
statement I was replying to was:

>To my way of thinking, "Miracle" temperament is a microtemperament
>(and therefore just) for 7-limit purposes /.../

>>>Electronic instruments can have 0c errors.
>>
>> Well, not really. It all depends on the reproduction equipment,
>> and how the pitch of the timbre is measured. To pick a nit, I'd
>> argue that very few electronic instruments are as precisely
>> tuned as a good concert grand, unless the electronic instrument
>> had some sort of feedback system involved in its tuning.
>
>Nah. If everything is derived by digital division from a single
>crystal oscillator it will all be totally rational (but boring). But
>of course you couldn't prove it rational by measurement, only by
>logical deduction from the circuit.

I was speaking of the electronic instruments in use by most
musicians.

In theory, one could have zero cents error if he had a such a
device and a way to reproduce sine tones without distortion.
Use a real timbre, and the issue is more complex. With perfectly
harmonic additive synthesis, I could see an argument for zero
cents error. . .

>>I'm not trying to pick a fight here... I just wanted to say that
>>a tuning with a max error of 2.8 cents isn't necessarily the same
>>as just in all cases. Do you disagree?
>
>I don't necessarily disagree with this in general. But I disagree
>that the exact same set of frequencies that we agree are just on one
>instrument, can suddenly cease to be just, simply because they are
>produced by a different instrument (with an equally harmonic
>timbre), merely because that instrument has smaller unavoidable
>random errors.

If the new intrument has smaller inherent errors, then they
aren't the same frequencies.

-Carl

--- In tuning@y..., jpehrson@r... wrote:
> --- In tuning@y..., "Paul Erlich" <paul@s...> wrote:
>
> /tuning/topicId_26876.html#27143
>
> >
> > But the harmonic timbres are the ones with the
> > clearest pitch.
> >
> > > Create a pure harmonic timbre and attempt to write
> > > music with it, and the truth will be revealed.
> >
> > Hmm . . . all music that has ever been written for
> > brass, reed, and bowed string instruments, and
> > human voices, is music with pure harmonic
> > timbres. I'd have to give it a thumbs-up!
> >
>
> Is it not true that most of our "standard" orchestral instruments
> involve harmonic timbres??

The above-mentioned ones are _exactly_ harmonic. Plucked strings are
_approximately_ harmonic. Tympani are inharmonic but have a prominent
lowest partial that is the "pitch". Flutes may be very slightly
inharmonic, certainly not more than very slightly. Any other
orchestral instruments?

--- In tuning@y..., carl@l... wrote:
> >> /tuning/topicId_26876.html#27152
> >>
> >> Blackjack is essentially a "microtemperament," correct??
> >
> >To my way of thinking, "Miracle" temperament is a microtemperament
> >(and therefore just) for 7-limit purposes, but not 9-limit (and
> >therefore, not higher limits). There's definitely a grey area, but
> >I'm currently drawing the line at a max error of 2.8 cents.
>
> How did you come up with this value?
>
> A tolerance of 2.8 cents may be "just" on a guitar, but not
> on a piano! It isn't even close by piano standards, where
> tunings are typically accurate to 0.5, and often to 0.1 cents.

You mean that's the tolerance for your own just tunings of the piano?

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

/tuning/topicId_26876.html#27240

> --- In tuning@y..., jpehrson@r... wrote:
> > --- In tuning@y..., "Paul Erlich" <paul@s...> wrote:
> >
> > /tuning/topicId_26876.html#27143
> >
> > >
> > > But the harmonic timbres are the ones with the
> > > clearest pitch.
> > >
> > > > Create a pure harmonic timbre and attempt to write
> > > > music with it, and the truth will be revealed.
> > >
> > > Hmm . . . all music that has ever been written for
> > > brass, reed, and bowed string instruments, and
> > > human voices, is music with pure harmonic
> > > timbres. I'd have to give it a thumbs-up!
> > >
> >
> > Is it not true that most of our "standard" orchestral instruments
> > involve harmonic timbres??
>
> The above-mentioned ones are _exactly_ harmonic. Plucked strings
are
> _approximately_ harmonic. Tympani are inharmonic but have a
prominent
> lowest partial that is the "pitch". Flutes may be very slightly
> inharmonic, certainly not more than very slightly. Any other
> orchestral instruments?

No... you've got them all... So, while we are *presently* fascinated
with inharmonic timbres and related tunings, the *harmonic* ones have
had and continue to have *more* than their place in the sun...

__________ _______ _______
Joseph Pehrson

>>>To my way of thinking, "Miracle" temperament is a microtemperament
>>>(and therefore just) for 7-limit purposes, but not 9-limit (and
>>>therefore, not higher limits). There's definitely a grey area, but
>>>I'm currently drawing the line at a max error of 2.8 cents.
>>
>>How did you come up with this value?
>>
>>A tolerance of 2.8 cents may be "just" on a guitar, but not
>>on a piano! It isn't even close by piano standards, where
>>tunings are typically accurate to 0.5, and often to 0.1 cents.
>
>You mean that's the tolerance for your own just tunings of the
>piano?

I mean that's a typical tolerance for 12-tone equal temperament
on pianos, at least in the middle octaves.

My Peterson strobe tuner is accurate to 0.1 cents, but it's up
to the human tuner to produce this accuracy. This involves a
practiced tuning hammer technique, a good ear for unisons, and
a lot of patience. I wouldn't say I got closer than 0.5 cents
on the tuning for wolves. I can do better by ear in JI, but
have not learned 12-equal. I learned Kinberger 3 for my
clavichord, but never practised this on a piano.

Sanderson Accutuner equipment is even better than a strobe
tuner, in that it actively considers the timbre of the
instrument.

-Carl

--- In tuning@y..., jpehrson@r... wrote:

> No... you've got them all... So, while we are *presently*
fascinated
> with inharmonic timbres and related tunings, the *harmonic* ones
have
> had and continue to have *more* than their place in the sun...

There are three things I can say about harmonic timbres right now:

1) It's been experimentally shown that we extract the sense of
_pitch_ from harmonic relationships among partials. Distort the
relationship between partials, and the pitch becomes more ambiguous.
This has been shown experimentally as well.

2) Though it's unknown whether this process is inborn or learned,
exposure to the mother's voice prenatally is a leading contender for
how it may be learned. Recent studies have shown (to my surprise)
that prenatal listening experience are remembered in a profound way
for months and even years (I think someone posted some links
recently).

3) Even if one could re-learn to orient one's sense of pitch around
some fixed inharmonic spectrum, playing such tones at loud volume
would cause combinational tones to ruin the sensation. Only with
harmonic spectra do combinational tones simply lead to reinforcement
of the same spectral peaks, rather than an introduction of new ones.

--- In tuning@y..., "Carl" <carl@l...> wrote:

> >>A tolerance of 2.8 cents may be "just" on a guitar, but not
> >>on a piano! It isn't even close by piano standards, where
> >>tunings are typically accurate to 0.5, and often to 0.1 cents.
> >
> >You mean that's the tolerance for your own just tunings of the
> >piano?
>
> I mean that's a typical tolerance for 12-tone equal temperament
> on pianos, at least in the middle octaves.

Well then that's hardly relevant for the "just/non-just" question!

>>>>A tolerance of 2.8 cents may be "just" on a guitar, but not
>>>>on a piano! It isn't even close by piano standards, where
>>>>tunings are typically accurate to 0.5, and often to 0.1 cents.
>>>
>>>You mean that's the tolerance for your own just tunings of the
>>>piano?
>>
>>I mean that's a typical tolerance for 12-tone equal temperament
>>on pianos, at least in the middle octaves.
>
>Well then that's hardly relevant for the "just/non-just" question!

It is, because we assume (and I have already claimed) that just
tunings would be possible with similar accuracy.

It is further relevant because Dave was basing his definition
of just on the tuning accuracy of 12-tone equal tempered
guitars.

-Carl

--- In tuning@y..., "John Starrett" <jstarret@c...> wrote:
> --- In tuning@y..., carl@l... wrote:
> > >>>I'm currently drawing the line at a max error of 2.8 cents.
> > >>
> > >>How did you come up with this value?
> > /.../
> > >I learned from a URL that John Starrett posted, that even the
most
> > >carefully tuned guitar (including individually adjustable bridge
> > >for each string) typically has intonation errors of +-3 cents and
> > >more, (and that's when you don't move the guitar, and the
> > >temperature and humidity don't change)
> <snip>
> >
> > -Carl
>
> Mostly due to finger pressure variation I would wager.

I understood that they attempted to eliminate finger pressure as a
variable, for those measurements. So in real use, finger pressure
_further_ increases the varability and further strengthens my case.
Can we have that URL again, John? I've just about given up trying to
find things in the archives with that useless search.

-- Dave Keenan

--- In tuning@y..., carl@l... wrote:
> >> You listed it as one of your reasons.
> >
> >What is relevant is the instrument that has the largest unavoidable
> >random errors on which rationally specified tunings are still
> >considered just (e.g. the guitar). The fact that instruments exist
> >which have smaller such errors, is irrelevant.
>
> Irrelevant to the guitar, but not to the tuning in general. The
> statement I was replying to was:
>
> >To my way of thinking, "Miracle" temperament is a microtemperament
> >(and therefore just) for 7-limit purposes /.../

Yes. I stand by that irrespective of what instrument it is played on,
provided that instrument does not have tuning errors worse than a
typical guitar.

> I was speaking of the electronic instruments in use by most
> musicians.

Oh sure. They typically have +- 0.5 c errors or thereabouts.

> >>I'm not trying to pick a fight here... I just wanted to say that
> >>a tuning with a max error of 2.8 cents isn't necessarily the same
> >>as just in all cases. Do you disagree?
> >
> >I don't necessarily disagree with this in general. But I disagree
> >that the exact same set of frequencies that we agree are just on
one
> >instrument, can suddenly cease to be just, simply because they are
> >produced by a different instrument (with an equally harmonic
> >timbre), merely because that instrument has smaller unavoidable
> >random errors.
>
> If the new intrument has smaller inherent errors, then they
> aren't the same frequencies.

I'm asking you to do the following thought experiment: Suppose we tune
up Blackjack on a guitar and we listen and we agree it is 7-limit just
and then we take a synth with very fine resolution and accuracy and we
tune it until it reproduces the tuning of that specific guitar (with
all its flaws) to within say 0.01c. We can even use a reproduction of
that guitar's timbre if you wish. I see no reason not to call the
synth tuning 7-limit just too.

-- Dave Keenan

>>Irrelevant to the guitar, but not to the tuning in general. The
>>statement I was replying to was:
>>
>>>To my way of thinking, "Miracle" temperament is a microtemperament
>>>(and therefore just) for 7-limit purposes /.../
>
>Yes. I stand by that irrespective of what instrument it is played
>on, provided that instrument does not have tuning errors worse
>than a typical guitar.

The point I was trying to make is that instruments with tuning
errors _smaller_ than a typical guitar can also bear on this
definition. Do you disagree?

>> I was speaking of the electronic instruments in use by most
>> musicians.
>
> Oh sure. They typically have +- 0.5 c errors or thereabouts.

Most synths aren't that accurate, even ignoring the wavetable
problem.

>>>/.../I disagree that the exact same set of frequencies that we
>>>agree are just on one instrument, can suddenly cease to be just,
>>>simply because they are produced by a different instrument (with
>>>an equally harmonic timbre), merely because that instrument has
>>>smaller unavoidable random errors.
>>
>>If the new intrument has smaller inherent errors, then they
>>aren't the same frequencies.
>
>I'm asking you to do the following thought experiment: Suppose we
>tune up Blackjack on a guitar and we listen and we agree it is 7-
>limit just and then we take a synth with very fine resolution and
>accuracy and we tune it until it reproduces the tuning of that
>specific guitar (with all its flaws) to within say 0.01c. We can
>even use a reproduction of that guitar's timbre if you wish. I see
>no reason not to call the synth tuning 7-limit just too.

The tuning is just on the guitar because it can't be improved on
the guitar. In this thought experiment, we simply tune the synth
directly in JI and compare it with blackjack, and notice a
difference. You can't call something just if you can retune it by
ear and take out beats. Three cents is substantial in many
contexts, as Herman Miller's warped canons showed!

You can't have your cake and eat it too. If we want tuning to be
considered relative to the instrument, then we must stick to it.
By your thought experiment, if 12-tET is as good as just on a bass
drum then it must be as good as just everywhere.

-Carl

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

/tuning/topicId_26876.html#27254

> --- In tuning@y..., jpehrson@r... wrote:
>
> > No... you've got them all... So, while we are *presently*
> fascinated
> > with inharmonic timbres and related tunings, the *harmonic* ones
> have
> > had and continue to have *more* than their place in the sun...
>
> There are three things I can say about harmonic timbres right now:
>
> 1) It's been experimentally shown that we extract the sense of
> _pitch_ from harmonic relationships among partials. Distort the
> relationship between partials, and the pitch becomes more
ambiguous.
> This has been shown experimentally as well.
>
> 2) Though it's unknown whether this process is inborn or learned,
> exposure to the mother's voice prenatally is a leading contender
for
> how it may be learned. Recent studies have shown (to my surprise)
> that prenatal listening experience are remembered in a profound way
> for months and even years (I think someone posted some links
> recently).
>
> 3) Even if one could re-learn to orient one's sense of pitch around
> some fixed inharmonic spectrum, playing such tones at loud volume
> would cause combinational tones to ruin the sensation. Only with
> harmonic spectra do combinational tones simply lead to
reinforcement
> of the same spectral peaks, rather than an introduction of new ones.

Well, what impresses me about all this is the fact that these kinds
of sounds, out of all the possibilities, are considered "musical."
Imagine all the time our ancestors human and pre-human had to bang
and scrape on things. After all these centuries... millenia and
more, we have "musical" sounds which seem, for the most part to have
harmonic spectra.

Of course, that's primarily *Western* music, so there's a bias in
that sense. However, I find it humorous that these timbres are so
*ingrained* that synth manufacturers will always "ape" them as
essential sounds.

To the Western ear, such sounds are actually "synonymous" with
music... it seems... ??

_________ _________ ______
Joseph Pehrson

Dave Keenan wrote:

>Nah. If everything is derived by digital division from a single
>crystal oscillator it will all be totally rational (but boring). But
>of course you couldn't prove it rational by measurement, only by
>logical deduction from the circuit.

Dave has mentioned many times that he considers exactly just timbres and tunings
"boring". I think this point needs some clarification. "Boring" is a totally
subjective description as is interesting etc. I think what Dave means [please
correct me if I am wrong] is that he equates interest to movement. I.e slow
beats or whatever are interesting because they are not static.

Jacky Lignon also made a similar statement regarding harmonic timbres recently.

A tuning or an isolated timbre cannot be considered interesting or boring unless
it is compared to somthing which is it's opposite. Even when looking at
something in [supposed] isolation the beholder who declares something to be
interesting or boring is using some criteria to base this judgement on.

If I had the choice between a synth with 0.0 cents resolution and once with
1cent resolution I would choose the former. Tunings can easily be made non just.
To make something perfectly just is quite difficult.

In compositions I like to vary between the incredibly complex timbres and
tunings and very simple harmonic timbres and just tunings. This way the complex
aspects actually mean something because they are compared to simple just
harmonies and harmonic timbres.

I once made a piece that used only one timbre. This was a sample of a plucked
string instrument that I had fiddled with so that it had infinite sustain. I
then used a harmonic series tuning and had each tone divided into rhythms based
on the prime number associated with that harmonic. This way none of the attack
portions of the sound would line up. At the beginning of the piece I sustained a
note for the duration of one bar and then an octave above it I played two notes
per bar and so on. At first it seemed just like one timbre until the attack
portion of the sound interrupted the blending of the sounds. The interruptions
came more frequently as I introduced more harmonics into the piece. At this
point there was no mistaking it as one sound. Also "interest" was provided by
the dropping out of the sound and the resulting simplification of the
chord/timbre.

I think Dave's microtempering is a good idea and will provide good musical
results. But I think because Dave is a theorist rather than a composer he is
trying to create "interesting" tunings. Leave this part up to the composers !
It does not have any meaning when applied to a tuning or timbre without any
music.

There is no such thing as an boring/interesting tuning or interesting timbre.
It's simply how you use it.

Justin White

DAVID JONES LIMITED ACN 000 074 573

--- In tuning@y..., "Carl" <carl@l...> wrote:
> The point I was trying to make is that instruments with tuning
> errors _smaller_ than a typical guitar can also bear on this
> definition. Do you disagree?

Yes. I disagree. That is, unless you are going to say that
typical guitars are incapable of just tunings. That would seem the
only way for you to be consistent here.

> >I'm asking you to do the following thought experiment: Suppose we
> >tune up Blackjack on a guitar and we listen and we agree it is 7-
> >limit just and then we take a synth with very fine resolution and
> >accuracy and we tune it until it reproduces the tuning of that
> >specific guitar (with all its flaws) to within say 0.01c. We can
> >even use a reproduction of that guitar's timbre if you wish. I see
> >no reason not to call the synth tuning 7-limit just too.
>
> The tuning is just on the guitar because it can't be improved on
> the guitar.

No, it's just on the guitar because people who should know listen to
it and pronounce it so.

> In this thought experiment, we simply tune the synth
> directly in JI and compare it with blackjack, and notice a
> difference. You can't call something just if you can retune it by
> ear and take out beats.

Nonsense. In practice people may stop tuning when they find the beats
are slow enough, without considering whether they _could_ make them
even slower. This alone would not be sufficient to prevent the tuning
from being called just.

> Three cents is substantial in many
> contexts, as Herman Miller's warped canons showed!
>
> You can't have your cake and eat it too. If we want tuning to be
> considered relative to the instrument, then we must stick to it.

> By your thought experiment, if 12-tET is as good as just on a bass
> drum then it must be as good as just everywhere.

First it would have to be a _set_ of bass drums to fit 12-tET.
Secondly it would have to play it in the same octaves as we are
interested in elsewhere. And thirdly it would have to have an
approximately harmonic timbre. Then sure, if 12-tET is as good as just
on that, then it is as good as just on anything that fits those same
criteria. But of course the thing is that no-one _would_ consider
12-tET to be as good as just on such an instrument.

By your argument, I could claim that my 12-tET guitar is really just.
It's merely that I can't get the beats any slower. :-)

-- Dave Keenan

--- In tuning@y..., "Justin White" <justin.white@d...> wrote:
> Dave has mentioned many times that he considers exactly just timbres
and tunings
> "boring". I think this point needs some clarification. "Boring" is a
totally
> subjective description as is interesting etc.

Yes. I assumed everyone would take it as such.

> I think what Dave means [please
> correct me if I am wrong] is that he equates interest to movement.
I.e slow
> beats or whatever are interesting because they are not static.

Yes indeed. That's how I find it.

> Jacky Lignon also made a similar statement regarding harmonic
timbres recently.
>
> A tuning or an isolated timbre cannot be considered interesting or
boring unless
> it is compared to somthing which is it's opposite. Even when looking
at
> something in [supposed] isolation the beholder who declares
something to be
> interesting or boring is using some criteria to base this judgement
on.

Yes, although possibly unconsciously.

> If I had the choice between a synth with 0.0 cents resolution and
once with
> 1cent resolution

Resolution and accuracy are different things. I assume you mean 0 cent
accuracy with very fine resolution. 0 cent resolution would mean you
can't change it at all.

> I would choose the former.

If my interpretation of your statement is correct, so would I.

> Tunings can easily be made non just.

I agree.

> To make something perfectly just is quite difficult.

No it isn't. I just described how to do it with digital dividers
(incidentally this would be 0 cent accuracy with rather coarse
resolution). But I agree that, to make acoustic instruments (and most
electronic instruments designed primarily for 12-tET) perfectly tuned
in rational ratios is quite difficult (in fact impossible). But it's
also quite unnecessary.

> In compositions I like to vary between the incredibly complex
timbres and
> tunings and very simple harmonic timbres and just tunings. This way
the complex
> aspects actually mean something because they are compared to simple
just
> harmonies and harmonic timbres.

Sounds great. But I hope you will agree that it wouldn't matter if all
your just harmonies were 0.5c away from rational. And even in any
rational scale of more than 6 notes per octave there will be non-just
intervals available (due to their ratios being too complex). Of course
harmonic series segments have the fewest.

> I once made a piece that used only one timbre. This was a sample of
a plucked
> string instrument that I had fiddled with so that it had infinite
sustain. I
> then used a harmonic series tuning and had each tone divided into
rhythms based
> on the prime number associated with that harmonic. This way none of
the attack
> portions of the sound would line up. At the beginning of the piece I
sustained a
> note for the duration of one bar and then an octave above it I
played two notes
> per bar and so on. At first it seemed just like one timbre until the
attack
> portion of the sound interrupted the blending of the sounds. The
interruptions
> came more frequently as I introduced more harmonics into the piece.
At this
> point there was no mistaking it as one sound. Also "interest" was
provided by
> the dropping out of the sound and the resulting simplification of
the
> chord/timbre.

Brilliant. Yes, some genius can always make the best of anything
s/he's given, but for obvious reasons I'm interested in designing
scales (and instruments) that lots of non genii (and some genii) might
find possibilities within, and that lots of performers might be able
to use to render the compositions of lots of different microtonal
composers.

> I think Dave's microtempering is a good idea and will provide good
musical
> results. But I think because Dave is a theorist rather than a
composer he is
> trying to create "interesting" tunings.
>
> Leave this part up to the composers !
> It does not have any meaning when applied to a tuning or timbre
without any
> music.

Huh. You mean spew out thousands of tunings at random and let
composers decide between them??? I beg to differ. Certain properties
of tunings are known to be of more interest to more microtonal
composers (and listeners). If I'm getting those wrong, then I hope
people will tell me how. That's the whole point of me engaging in
dialogue on tuning.

> There is no such thing as an boring/interesting tuning or
interesting timbre.
> It's simply how you use it.

Sure. But some tunings allow for more possibilities that have been
shown to be of interest to more composers, in fewer notes, than others
do. I understand Just intonation as one such property that is
difficult to do in few notes. Microtemperament greatly improves the
odds. But just how much tempering is tolerable to most people, is
something I am still exploring.

I'd love to know which 11-limit Blackjack harmonies (as a 72-tET
subset) are considered just by how many people.

I think maybe I missed your point. What is it you would have me stop
doing, or do differently?

Aren't I allowed to use the words "interesting" or "boring". Surely
everyone either knows what I mean by that by now, or if not, will
assume that it is simply my personal preference.

Or has peoples' perception of my expertise stepped over some line,
such that I can't have (fallible) personal opinions any more, and must
now spell this out every time?

Regards,
-- Dave Keenan

> Yes. I disagree. That is, unless you are going to say that
> typical guitars are incapable of just tunings. That would seem the
> only way for you to be consistent here.

No, I'm only following your idea out consistently, which is to
consider the justness of a tuning relative to the instrument it's
on.

> No, it's just on the guitar because people who should know listen
> to it and pronounce it so.

In that case I will listen to your synthesizer with 2.8-cent errors
and pronounce it non-just.

If you like, you may consider the fact that I may be unable to do
this for a pair of guitars. [Though not necessarily -- if the JI
guitar's 3-cent errors are random they will be centered on JI
intervals, whereas the Blackjack guitar will have errors centered
on Blackjack, and this difference may be audible.]

> Nonsense. In practice people may stop tuning when they find the
> beats are slow enough, without considering whether they _could_
> make them even slower. This alone would not be sufficient to
> prevent the tuning from being called just.

You seem to be refusing my version of your "guitars have that much
error anyway" point, and implying that you would like to go ahead
and call 2.8-cent-error temperaments just tunings in general. In
so doing, you will be going against hundreds of years of usage of
the term "just" -- a term used specifically to distinguish between
tunings as accurate as can be made, and tunings featuring deliberate
and purposeful errors. This historic use includes quarter-comma
meantone tuning, whose max error from 5-limit JI is 6 cents -- also
within the random error of the guitar, by some accounts. And today,
we have found unanimously (as far as I know) that even 3-cent errors
are musically important!

Get the error down to 1 cent, and I will join you in calling these
tunings truly just in all circumstances (even though this would
not be true for pianos, it takes a trained ear to hear errors less
than a cent on a piano -- such errors are reported only as subtle
differences in the instrument's timbre).

-Carl

--- In tuning@y..., "Carl" <carl@l...> wrote:
> > Yes. I disagree. That is, unless you are going to say that
> > typical guitars are incapable of just tunings. That would seem the
> > only way for you to be consistent here.
>
> No, I'm only following your idea out consistently, which is to
> consider the justness of a tuning relative to the instrument it's
> on.

That isn't what I'm doing at all! I'm merely using the fact that
people consider that just guitar tunings are possible, to place a
lower bound on the errors that a rational tuning can sustain (on any
instrument) and still be considered just.

> > No, it's just on the guitar because people who should know listen
> > to it and pronounce it so.
>
> In that case I will listen to your synthesizer with 2.8-cent errors
> and pronounce it non-just.

That's fine, but I don't understand why you would then consider it
just on a typical guitar. What if you didn't know whether you were
hearing a guitar or a synth?

> If you like, you may consider the fact that I may be unable to do
> this for a pair of guitars. [Though not necessarily -- if the JI
> guitar's 3-cent errors are random they will be centered on JI
> intervals, whereas the Blackjack guitar will have errors centered
> on Blackjack, and this difference may be audible.]

Yes. That's a good point. We have to tolerate the systematic Blackjack
errors _plus_ the guitars unsystematic errors. But because the guitars
errors are unsystematic they are as likely to improve Blackjack
consonances as to make them worse. If we go by the MA (max absolute)
error, then yes it will be twice as bad. If we go by the RMS error it
will only be 1.4 times (or something like that).

So the conclusion I should draw from the guitar accuracy data is that
folks should consider Blackjack just (at least at the 7-limit) when
tuned accurately (say on a good synth), but not necessarily on a
guitar.

> You seem to be refusing my version of your "guitars have that much
> error anyway" point,

Yes. I think you are drawing a different conclusion from that and
considering it mine.

> and implying that you would like to go ahead
> and call 2.8-cent-error temperaments just tunings in general.

Yes (at least 7-limit). If justness is decided by _listening_, then if
it's just when such errors are accidental on a guitar, why isn't it
just when they are deliberate, on a more accurate instrument?

You say justness occurs when the beats cannot be further reduced. But
that would allow 12-tET to be considered just, on a suitable
instrument (You didn't address this from last time). And many (most?)
people don't want their JI to be phase-locked, they actually prefer
slow beating.

> In
> so doing, you will be going against hundreds of years of usage of
> the term "just" -- a term used specifically to distinguish between
> tunings as accurate as can be made, and tunings featuring deliberate
> and purposeful errors.

I don't believe so. Until the last 50 years or so there has been no
difference between "as accurate as can be made" and "within 2 cents
either way". The distinction never had to be faced. Now that it does,
I'm coming down on the side that says it's about how it sounds on the
day, not what accuracy the instrument is capable of. If 2 cent errors
were Just a hundred years ago, then they still are today (no matter
what instrument they are on).

And when did people start to consider temperaments that had errors
less than 2 cents, _as_ temperaments. I'd guess schismic would have
been the first (as used on the Dinarra).

The sharp distinction you are trying to make between just tuning and
temperament is a purely mathematical one, one that can be revealed by
no listening and no measurement. I'll allow that the definition of
temperament is a mathematical one. But since justness is defined
perceptually, we must allow that a sufficiently gentle temperament can
be just. The two concepts have a small overlap. As I say, the
development of musical instruments and musical mathematics has meant
that we are only having to face this now.

> This historic use includes quarter-comma
> meantone tuning, whose max error from 5-limit JI is 6 cents -- also
> within the random error of the guitar, by some accounts. And today,
> we have found unanimously (as far as I know) that even 3-cent errors
> are musically important!

Can you give me more info on that.

> Get the error down to 1 cent, and I will join you in calling these
> tunings truly just in all circumstances (even though this would
> not be true for pianos, it takes a trained ear to hear errors less
> than a cent on a piano -- such errors are reported only as subtle
> differences in the instrument's timbre).

But you're not talking here about playing music. You're talking about
maximally sustained dyads specifically for tuning it. In actual music
much larger errors in 7-limit intervals are undetectable by most
listeners. I'd prefer to keep ratios of 9 below about 2.2 c and ratios
of 11 below 1.8 c. Which is one reason why I'm pretty skeptical about
the idea of a guitar that's 13-limit or higher. But then we have got
the effect of otonal context masking large errors at higher limits.

I'm happy to refine the number downwards (and even to make it
different for different consonances), but I can't understand this
business of wanting to make it smaller the better the accuracy of the
instrument. If anything, it should go the other way, the less accurate
the instrument, the smaller the errors permissible in the intended
tuning (e.g. microtemperament).

I really value this discussion. Thanks Carl.

-- Dave Keenan

<snip>
> >
> > Mostly due to finger pressure variation I would wager.
>
> I understood that they attempted to eliminate finger pressure as a
> variable, for those measurements. So in real use, finger pressure
> _further_ increases the varability and further strengthens my case.
> Can we have that URL again, John? I've just about given up trying to
> find things in the archives with that useless search.
>
> -- Dave Keenan

Dave, I can't seem to locate it at the moment. It should be
here: http://www-math.cudenver.edu/~jstarret/notes.html but it could
be in someone else's links here:
http://www-math.cudenver.edu/~jstarret/resources.html
Sorry I can't help at the moment.

John Starrett

--- In tuning@y..., "Dave Keenan" <D.KEENAN@U...> wrote:

> I don't believe so. Until the last 50 years or so there has been no
> difference between "as accurate as can be made" and "within 2 cents
> either way".

Very untrue. Until early in this century, people actually attempted
to tune 12-tET by tempering the _fifths_. This, of course, means that
the fifths were deliberately tuned 2 cents flat.

>>No, I'm only following your idea out consistently, which is to
>>consider the justness of a tuning relative to the instrument it's
>>on.
>
>That isn't what I'm doing at all! I'm merely using the fact that
>people consider that just guitar tunings are possible, to place a
>lower bound on the errors that a rational tuning can sustain (on any
>instrument) and still be considered just.

Ah, okay. Maybe that was my idea, all along. I'll stick to my
bass drum argument, then... of course, you're right about the
particulars of that example. But my point is that you're only
getting a reasonable result because you're choice of 'reference'
instruments is loaded.

>>>No, it's just on the guitar because people who should know listen
>>>to it and pronounce it so.
>>
>>In that case I will listen to your synthesizer with 2.8-cent errors
>>and pronounce it non-just.
>
>That's fine, but I don't understand why you would then consider it
>just on a typical guitar. What if you didn't know whether you were
>hearing a guitar or a synth?

I'm claiming I can hear if intonation is very accurate, or if it's
blurred by 3 cents. A just guitar is defined as tuned as well as I
can expect guitar technology to be tuned. The same goes for pianos,
and bass drums.

>Yes. That's a good point. We have to tolerate the systematic
>Blackjack errors _plus_ the guitars unsystematic errors. But
>because the guitars errors are unsystematic they are as likely
>to improve Blackjack consonances as to make them worse.

Right.

>If we go by the MA (max absolute) error, then yes it will be
>twice as bad.

Half of the time.

>If we go by the RMS error it will only be 1.4 times (or something
>like that).

Where did you get that number? If Blackjack was off just in random
directions by random amounts up to the same max random error as the
guitar introduced, RMS should be the same with or without the guitar
error, right? Blackjack _doesn't_ do that, so how could you tell
without doing the calculation?

I prefer RMS for judging how well harmony approximates JI, but for
a group of sonorities (a tuning), max error may be better. Which
is why I didn't bring it up. Hmm- maybe max RMS for the group would
be best. . .

>So the conclusion I should draw from the guitar accuracy data is
>that folks should consider Blackjack just (at least at the 7-limit)
>when tuned accurately (say on a good synth), but not necessarily
>on a guitar.

That's exactly the opposite conclusion I would draw!

>>You seem to be refusing my version of your "guitars have that much
>>error anyway" point,
>
>Yes. I think you are drawing a different conclusion from that and
>considering it mine.

Guilty.

>You say justness occurs when the beats cannot be further reduced.
>But that would allow 12-tET to be considered just, on a suitable
>instrument (You didn't address this from last time).

What type of instrument? In the case of a 12-tET guitar, errors
can (and are everyday) reduced by bending notes [by my experience],
tweaking the open-string tuning [I have been told], and choosing
certain positions over others [Don Slepian demonstrated this to
me].

>And many (most?) people don't want their JI to be phase-locked, they
>actually prefer slow beating.

I don't think either of us have any data here at all. Besides,
phase-locking is a purely theoretical concern at this point, since
it requires beyond-run-of-the-mill electronic instruments to
produce.

>>In so doing, you will be going against hundreds of years of usage
>>of the term "just" -- a term used specifically to distinguish
>>between tunings as accurate as can be made, and tunings featuring
>>deliberate and purposeful errors.
>
>I don't believe so. Until the last 50 years or so there has been no
>difference between "as accurate as can be made" and "within 2 cents
>either way". The distinction never had to be faced.

Oh, Dave! Bosanquet's 53-tET harmonium in 1875? A whole genre of
accurate meantone fifths not by counting beats, but by getting very
accurate just thirds in 1575? The idea that only modern man can
distinguish 2-cent errors??

>Now that it does, I'm coming down on the side that says it's about
>how it sounds on the day, not what accuracy the instrument is
>capable of. If 2 cent errors were Just a hundred years ago, then
>they still are today (no matter what instrument they are on).

Take a step back! We're making wonderful discoveries, but we're not
privileged to any manifest destiny! Ears have always been ears, and
they will always be the highest court in music, and they ear can
hear errors of 2 cents!

>The sharp distinction you are trying to make between just tuning and
>temperament is a purely mathematical one, one that can be revealed
>by no listening and no measurement.

To the contrary, my opinion is that the difference between just and
tempered is entirely perceptual, and I don't claim to have any model
of it that allows me to tell without listening.

I also believe that the perceptual difference between temperament and
JI goes beyond one of psychoacoustics. Even if a bare sonority cannot
be distinguished from just, if we want to claim that "puns" are
interesting, we have to claim that the brain has some sort of access
to the lattice, and by using an un-connected structure as a harmony
we are tempering. Fortunately, I don't think there are any sonorities
which are psychoacoustically just _and_ severe enough, or in a
sequence short enough to be heard as a pun.

>>This historic use includes quarter-comma
>>meantone tuning, whose max error from 5-limit JI is 6 cents -- also
>>within the random error of the guitar, by some accounts. And today,
>>we have found unanimously (as far as I know) that even 3-cent errors
>>are musically important!
>
>Can you give me more info on that.

In one of Graham Breed's early posts, he listed his findings to that
time. Included was that differences of down to a cent were musically
significant. I've done several listening tests involving these sorts
of differences. Others have certainly chimed in, but I don't want
speak for anyone else from memory.

>>Get the error down to 1 cent, and I will join you in calling these
>>tunings truly just in all circumstances (even though this would
>>not be true for pianos, it takes a trained ear to hear errors less
>>than a cent on a piano -- such errors are reported only as subtle
>>differences in the instrument's timbre).
>
>But you're not talking here about playing music. You're talking
>about maximally sustained dyads specifically for tuning it.

I am most definitely talking about music. What makes a good piano
tuning "good"?

>In actual music much larger errors in 7-limit intervals are
>undetectable by most listeners.

They are? Maybe the difference between 12-tET and 5-limit JI is
undetectable to the man on the street, without training.

I think the best Barbershop quartets tune complete chords to an
accuracy of about a cent... a finding supported by an FFT I once
did on a typical professional Barbershop performance.

>I'd prefer to keep ratios of 9 below about 2.2 c and ratios
>of 11 below 1.8 c. Which is one reason why I'm pretty skeptical
>about the idea of a guitar that's 13-limit or higher. But then we
>have got the effect of otonal context masking large errors at
>higher limits.

Above the 7-limit, I think we start to get into the situation where
not all bare dyads have low-enough harmonic entropy to be accurately
tuned.

.x? Significant digits, man!

Jon Catler's music is proof positive of the 13-limit guitar.

>I'm happy to refine the number downwards (and even to make it
>different for different consonances), but I can't understand this
>business of wanting to make it smaller the better the accuracy of
>the instrument.

Sounds like you want the laws of nature to hold for all reference
frames! The speed of light may, but the length of your error yard
stick does not, I say.

> I really value this discussion. Thanks Carl.

Ditto.

-Carl

--- In tuning@y..., "Carl" <carl@l...> wrote:

> I also believe that the perceptual difference between temperament
and
> JI goes beyond one of psychoacoustics. Even if a bare sonority
cannot
> be distinguished from just, if we want to claim that "puns" are
> interesting, we have to claim that the brain has some sort of access
> to the lattice, and by using an un-connected structure as a harmony
> we are tempering. Fortunately, I don't think there are any
sonorities
> which are psychoacoustically just _and_ severe enough, or in a
> sequence short enough to be heard as a pun.

I don't understand what you're saying, Carl. I do believe that the
ability to make "puns" perceptually distinguishes microtemperaments
from JI even if their individual consonant sonorities are
indistinguishable. Not sure if this has anything to do with what
you're saying.
>
> Jon Catler's music is proof positive of the 13-limit guitar.

13-limit, yes. 2 or 3 cent errors due to variations in finger
pressure, etc . . . almost certainly.

>>I also believe that the perceptual difference between temperament
>>and JI goes beyond one of psychoacoustics. Even if a bare sonority
>>cannot be distinguished from just, if we want to claim that "puns"
>>are interesting, we have to claim that the brain has some sort of
>>access to the lattice, and by using an un-connected structure as a
>>harmony we are tempering. Fortunately, I don't think there are any
>>sonorities which are psychoacoustically just _and_ severe enough,
>>or in a sequence short enough to be heard as a pun.
>
>I don't understand what you're saying, Carl. I do believe that the
>ability to make "puns" perceptually distinguishes microtemperaments
>from JI even if their individual consonant sonorities are
>indistinguishable. Not sure if this has anything to do with what
>you're saying.

That's _exactly_ what I'm saying.

The last sentence adds that there probably aren't any intervals
psychoacoustically confounded with just (under ideal conditions)
that are part of a usable pun. For example, will anybody hear
a sequence of 53, 53-tET fifths as a pun? How many people hear
Grahams Miracle pump as a pun (and in this case the tempered
intervals are distinguishable from just)?

-Carl

--- In tuning@y..., "Carl" <carl@l...> wrote:

> The last sentence adds that there probably aren't any intervals
> psychoacoustically confounded with just (under ideal conditions)
> that are part of a usable pun. For example, will anybody hear
> a sequence of 53, 53-tET fifths as a pun?

The point isn't that you directly hear it "as" a pun in the sense
you're trying to get at -- I don't think that's possible, for any
progression, no matter how simple, since I don't believe we "keep
track" of ratios or our position in the ratio lattice -- the point is
that the microtemperament allows you to do something you can't do in
strict (non-adaptive) JI. I think a perceptually-based definition of
JI should take into account what a mathematically defined JI _can't_
do, as well as what it can. This has been my disagreement with Dave
from the start.

> since I don't believe we "keep track" of ratios or our position
> in the ratio lattice

I can't, at least. But then what is a pun? Taking one pitch
in two senses, literally, right? But if we're ignorant of
the senses...

> -- the point is that the microtemperament allows you to do
>something you can't do in strict (non-adaptive) JI.

Which is what, exactly?

-Carl

--- In tuning@y..., "Paul Erlich" <paul@s...> wrote:
> --- In tuning@y..., "Dave Keenan" <D.KEENAN@U...> wrote:
>
> > I don't believe so. Until the last 50 years or so there has been
no
> > difference between "as accurate as can be made" and "within 2
cents
> > either way".
>
> Very untrue. Until early in this century, people actually attempted
> to tune 12-tET by tempering the _fifths_. This, of course, means
that
> the fifths were deliberately tuned 2 cents flat.

I'm quite prepared to be corrected. But this doesn't seem to do it,
because you are saying nothing about how _sucessful_ they were. I
don't remember where I read it (it might have been Llewellyn S.
Lloyd, 1937, "Music and sound"), but I read that piano tuners
typically didn't do better than +-2 c. Any piano tuners out there who
know this history of their art? And how long did a piano tuning
typically _stay_ accurate to +-2 c, 50 or 100 years ago?

-- Dave Keenan

>I'm quite prepared to be corrected. But this doesn't seem to do it,
>because you are saying nothing about how _sucessful_ they were.

There are tuning procedures that address this much accuracy, and
a record of 300 years of pedagogy that supports their use.

>I don't remember where I read it (it might have been Llewellyn S.
>Lloyd, 1937, "Music and sound"), but I read that piano tuners
>typically didn't do better than +-2 c.

Quite frankly, I'd be surprised to learn of anyone who's ever
tuned or played these instruments to any extent entertaining
such a statement.

>Any piano tuners out there who know this history of their art? And
>how long did a piano tuning typically _stay_ accurate to +-2 c, 50
>or 100 years ago?

Before there were pianos, there were harpischords. Harpsichords
today are built largely the same way as they were in the past, and
tuned with the same methods as they were in the past. As someone
who's tuned with these procedures, I can tell you I've followed
them to a greater accuracy than 2 cents!

Harpsichords and fortepianos are usually, and were usually, tuned
on a daily basis.

2 cents is around the JND for non-simultaneous melodic sine tones
in the middle of the musical range. Do you really believe that
harmonic intervals on a large stringed instrument would be tuned
with that much error?

-Carl

--- In tuning@y..., "Carl" <carl@l...> wrote:
> > since I don't believe we "keep track" of ratios or our position
> > in the ratio lattice
>
> I can't, at least. But then what is a pun? Taking one pitch
> in two senses, literally, right? But if we're ignorant of
> the senses...

It's a pun only if you insist on pinning JI ratios on all the pitches.
>
> > -- the point is that the microtemperament allows you to do
> >something you can't do in strict (non-adaptive) JI.
>
> Which is what, exactly?
>
Play certain progressions, observing all common tones, without
experiencing pitch drift, for example.

--- In tuning@y..., "Dave Keenan" <D.KEENAN@U...> wrote:

/tuning/topicId_26876.html#27274

>
> Huh. You mean spew out thousands of tunings at random and let
> composers decide between them??? I beg to differ. Certain
properties
> of tunings are known to be of more interest to more microtonal
> composers (and listeners). If I'm getting those wrong, then I hope
> people will tell me how. That's the whole point of me engaging in
> dialogue on tuning.
>

It's a bit hard for me to believe the line that "all tunings are
equal..." Sure, probably a good composer can make pretty good music
out of virtually *anything* and there are some fascinating
*anomalies* in even "poorly constructed" scales... but, for example,
the great abilities of 12-tET to replicate consonances practically up
to the 9th limit... well, with error, but still, doing this with only
12 notes as evidenced on Paul Erlich's "famous" chart, and the fact
that this tuning became so widespread *can't* only be coincidental.
That would be a bit hard to believe...

This is why I believe composers should *work* with theoriticians...
sure, sometimes theoriticians will be wrong, but other times they
really will come up with more fascinating "building materials" than
composers might stumble across otherwise....

Well, that's *my* take as of this moment...

________ ________ ______
Joseph Pehrson

In-Reply-To: <9m3q4p+9dbv@eGroups.com>
In article <9m3q4p+9dbv@eGroups.com>, carl@lumma.org (Carl) wrote:

> In one of Graham Breed's early posts, he listed his findings to that
> time. Included was that differences of down to a cent were musically
> significant. I've done several listening tests involving these sorts
> of differences. Others have certainly chimed in, but I don't want
> speak for anyone else from memory.

I've found audible differences, I don't know if they count as musically
significant. One was where I tested meantones to see how far I could
narrow the fifth before 4:6:9 chords sounded wrong. I found a small
change made a big difference, and upon investigation found I was hitting
the cent-resolution of the synthesizer.

Another is the sensitivity of 7-limit schismic tuning. For some reason I
still don't have an explanation for (but may have something to do with the
critical band) the Pythagorean region is soured, but this improves
dramatically when you get close to a just 7:4 and remains okay until you
get to 41-equal, which is theoretically much more out of tune. This still
seems to be the case in Kyma, and so not an artifact of the tuning
resolution.

I did try tuning fifths once on Kyma with sawtooth waves. This would be a
half-blind experiment, because I could see the number that described the
tuning, but it took a bit of calculation to tell if it was right or not.
Once I hit on the right local minimum, I tuned it to 0.1 cents accuracy by
minimizing the roughness. To go beyond that, you'd have to listen for the
beats.

For general, musical significance I don't think you need to worry about
better than 1 cent precision. So long as you tune by ear to avoid these
special cases. Most timbres are less sensitive than sawtooths, along with
the effects being too subtle to worry about as they drift past in real
time.

Another thing is that I found quarter-comma meantone was too bland with my
Korg's piano setting. Retuning to a 50-equal subset, or 1/6-comma
meantone, improved it. It didn't matter much which. The difference
between 50 and 31 is only a few cents in the 5-limit, and the RMS optimum
is actually closer to 50.

Then again, I've played melodies in magic temperament with the tuning
varying beyond 19 and 22, or in miracle between 10 and 21, and found it
made surprisingly little difference.

Graham

--- In tuning@y..., "Carl" <carl@l...> wrote:

/tuning/topicId_26876.html#27304

>
> The last sentence adds that there probably aren't any intervals
> psychoacoustically confounded with just (under ideal conditions)
> that are part of a usable pun. For example, will anybody hear
> a sequence of 53, 53-tET fifths as a pun? How many people hear
> Grahams Miracle pump as a pun (and in this case the tempered
> intervals are distinguishable from just)?
>
> -Carl

Could someone please refresh my memory about what would be meant
by "hearing Graham's Miracle pump" as a pun?? Then I will comment
whether I am doing that.... :)

_________ ________ _______
Joseph Pehrson

--- In tuning@y..., "Carl" <carl@l...> wrote:

/tuning/topicId_26876.html#27306

> > since I don't believe we "keep track" of ratios or our position
> > in the ratio lattice
>
> I can't, at least. But then what is a pun? Taking one pitch
> in two senses, literally, right? But if we're ignorant of
> the senses...
>

If there is any "pun" in Graham's Blackjack progression I believe it
would be the attempt of the ear to relate it to progressions in 12-
tET and, as Paul has commented before, the ear's attempt to due this
combined with the fact that it is only 7 chords rather than the usual
8 of a progression is what makes this progression so mystifying...
like a perceptual mobius strip.... At least it was for me...

___________ ______ ______
Joseph Pehrson

--- In tuning@y..., jpehrson@r... wrote:
> --- In tuning@y..., "Carl" <carl@l...> wrote:
>
> /tuning/topicId_26876.html#27304
>
> >
> > The last sentence adds that there probably aren't any intervals
> > psychoacoustically confounded with just (under ideal conditions)
> > that are part of a usable pun. For example, will anybody hear
> > a sequence of 53, 53-tET fifths as a pun? How many people hear
> > Grahams Miracle pump as a pun (and in this case the tempered
> > intervals are distinguishable from just)?
> >
> > -Carl
>
> Could someone please refresh my memory about what would be meant
> by "hearing Graham's Miracle pump" as a pun??

I believe it's meaningless. W. A. Mathieu would disagree (have you
read his book)?

If you have two progressions, one of which is a "pump" in a
temperament where drift doesn't occur, and one which simply moves
around the lattice and comes back to where it started (tuned, say, in
the same temperament), I don't think there's a qualitative difference
between the two (speaking in terms of musical effect here).

But I could be wrong. Maybe Mathieu is right. Maybe we hear something
special when we've moved in one direction in the lattice, without
coming back in the other direction, and yet we somehow return to our
starting point. That's what he claims.

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

/tuning/topicId_26876.html#27349

> --- In tuning@y..., jpehrson@r... wrote:
> > --- In tuning@y..., "Carl" <carl@l...> wrote:
> >
> > /tuning/topicId_26876.html#27304
> >
> > >
> > > The last sentence adds that there probably aren't any intervals
> > > psychoacoustically confounded with just (under ideal conditions)
> > > that are part of a usable pun. For example, will anybody hear
> > > a sequence of 53, 53-tET fifths as a pun? How many people hear
> > > Grahams Miracle pump as a pun (and in this case the tempered
> > > intervals are distinguishable from just)?
> > >
> > > -Carl
> >
> > Could someone please refresh my memory about what would be meant
> > by "hearing Graham's Miracle pump" as a pun??
>
> I believe it's meaningless. W. A. Mathieu would disagree (have you
> read his book)?
>
> If you have two progressions, one of which is a "pump" in a
> temperament where drift doesn't occur, and one which simply moves
> around the lattice and comes back to where it started (tuned, say,
in
> the same temperament), I don't think there's a qualitative
difference
> between the two (speaking in terms of musical effect here).
>
> But I could be wrong. Maybe Mathieu is right. Maybe we hear
something
> special when we've moved in one direction in the lattice, without
> coming back in the other direction, and yet we somehow return to
our
> starting point. That's what he claims.

Thanks, Paul, for the clarification. No, I haven't read the Mathieu
yet, but it is sitting on my shelf, and I have a pretty good record
of *eventually* getting to stuff there...

__________ _________ ________
Joseph Pehrson

--- In tuning@y..., jpehrson@r... wrote:
> --- In tuning@y..., "Carl" <carl@l...> wrote:
>
> /tuning/topicId_26876.html#27306
>
> > > since I don't believe we "keep track" of ratios or our position
> > > in the ratio lattice
> >
> > I can't, at least. But then what is a pun? Taking one pitch
> > in two senses, literally, right? But if we're ignorant of
> > the senses...
> >
>
> If there is any "pun" in Graham's Blackjack progression I believe
it
> would be the attempt of the ear to relate it to progressions in 12-
> tET
> and, as Paul has commented before, the ear's attempt to due this

To clarify, the progression would "drift" by a full semitone in 12-
tET, each time it goes around the 7 chords. I think an ear that's
been trained to follow 12-tET all its life ends up being very
confused by this progression, initially. This is an additional issue,
having to do with categorical perception, and the question
of "punning" remains separate.

> combined with the fact that it is only 7 chords rather than the
usual
> 8 of a progression is what makes this progression so mystifying...
> like a perceptual mobius strip.... At least it was for me...

Yes. "Punning" occurs any time you have any kind of "pump" --
including the typical I-vi-ii-V-I and I-IV-ii-V-I progressions. Do
these have a qualitatively different effect then a progression like
that of Pachelbel's Canon, which has no "punning" or "pumping"?

--- In tuning@y..., jpehrson@r... wrote:
>
> Thanks, Paul, for the clarification. No, I haven't read the
Mathieu
> yet, but it is sitting on my shelf, and I have a pretty good record
> of *eventually* getting to stuff there...
>
Well how about the simple progressions I mentioned. I-IV-ii-V-I and I-
vi-ii-V-I are "pumps" which involve "punning", while the progression
of Pachelbel's Canon (I-iii-vi-I-IV-I-IV-V-I) doesn't. Is there a
qualitative musical difference between the two cases, to your ear,
when both are played in the same tuning (say 12-tET or meantone)?

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

/tuning/topicId_26876.html#27359

> --- In tuning@y..., jpehrson@r... wrote:
> >
> > Thanks, Paul, for the clarification. No, I haven't read the
> Mathieu
> > yet, but it is sitting on my shelf, and I have a pretty good
record
> > of *eventually* getting to stuff there...
> >
> Well how about the simple progressions I mentioned. I-IV-ii-V-I and
I-
> vi-ii-V-I are "pumps" which involve "punning", while the
progression
> of Pachelbel's Canon (I-iii-vi-I-IV-I-IV-V-I) doesn't. Is there a
> qualitative musical difference between the two cases, to your ear,
> when both are played in the same tuning (say 12-tET or meantone)?

Well, I would think not, regardless of what Mathieu believes. That
sounds a little like "hokus pokus" of which there appears to be at
least a little in his book....

_________ _______ _______
Joseph Pehrson

--- In tuning@y..., jpehrson@r... wrote:
> This is why I believe composers should *work* with theoriticians...
> sure, sometimes theoriticians will be wrong,

No? Really?

Do you mean that, in theory, theory and practice are the same, but in
practice they are not?

:-) Sorry. I couldn't resist.

> but other times they
> really will come up with more fascinating "building materials" than
> composers might stumble across otherwise....
>
> Well, that's *my* take as of this moment...

Mine too.

-- Dave Keenan

--- In tuning@y..., jpehrson@r... wrote:
> If there is any "pun" in Graham's Blackjack progression I believe it
> would be the attempt of the ear to relate it to progressions in 12-
> tET and, as Paul has commented before, the ear's attempt to due this
> combined with the fact that it is only 7 chords rather than the
usual
> 8 of a progression is what makes this progression so mystifying...

Yes, that sure explains what I hear too.

-- Dave Keenan

--- In tuning@y..., "Dave Keenan" <D.KEENAN@U...> wrote:

/tuning/topicId_26876.html#27399

> --- In tuning@y..., jpehrson@r... wrote:
> > This is why I believe composers should *work* with
theoriticians... sure, sometimes theoriticians will be wrong,
>
> No? Really?
>
> Do you mean that, in theory, theory and practice are the same, but
in practice they are not?
>
> :-) Sorry. I couldn't resist.
>

Ha... That *did* sound a little dumb.

Well, if we are to think about some of the concepts that the "nutty
professor" rambles on and on about... I guess sometimes things that
*should* be interesting may not always be, due to our acculturation,
etc., etc., etc.,... you know all the "nutty professor" stuff....
(I'm sure you've been reading some of his stuff.. although I pity
anybody in some ways who does...)

Oh... and I should have said simply, "theorists"
not "theoriticians"...

The latter *is* a word, but since the former is shorter it saves
energy or something of the like that physicists or engineers might
know about! :)

________ ________ ________
Joseph Pehrson

--- In tuning@y..., "Carl" <carl@l...> wrote:
> A just guitar is defined as tuned as well as I
> can expect guitar technology to be tuned.

I'm sorry, but that just seems like a crazy definition to me. If a
new method of guitar construction and playing was invented tomorrow,
that cost no more to build and was accurate to 0.5 cent, would that
suddenly make all other guitars non-just? Of course not.

As you know, I believe that justness should be perceptually defined.

> >If we go by the RMS error it will only be 1.4 times (or something
> >like that).
>
> Where did you get that number?

Basic statistics and measurement theory. Only I was wrong. The sqrt(2)
factor is as true of the max absolute error as it is of the RMS. You
can try the experiment for yourself in a spreadsheet or whatever.
Generate two parallel lists of random numbers (say 100) in a normal
(bell curve) distribution with a mean of zero and a standard deviation
(i.e. RMS error) of 1. Add corresponding numbers from each list and
then find the MA and RMS errors of the original lists and those of the
list of sums. In general it's pythagoras, total_err ~= sqrt(err1^2 +
err2^2).

> If Blackjack was off just in random
> directions by random amounts ... Blackjack _doesn't_ do that, so
how could you tell
> without doing the calculation?

You're right. I'm guessing that the errors in Blackjack are roughly
normally distributed.

> >You say justness occurs when the beats cannot be further reduced.
> >But that would allow 12-tET to be considered just, on a suitable
> >instrument (You didn't address this from last time).
>
> What type of instrument?

Any instrument with fixed 12-tET tuning.

> In the case of a 12-tET guitar, errors
> can (and are everyday) reduced by bending notes [by my experience],
> tweaking the open-string tuning [I have been told], and choosing
> certain positions over others [Don Slepian demonstrated this to
> me].

This is another matter, outside of what we are discussing. If you can
bend 12-TET to just, you can bend anything.

> >And many (most?) people don't want their JI to be phase-locked,
they
> >actually prefer slow beating.
>
> I don't think either of us have any data here at all. Besides,
> phase-locking is a purely theoretical concern at this point, since
> it requires beyond-run-of-the-mill electronic instruments to
> produce.

During the era of top-octave-divider organs, phase locking at small
whole-number ratios was very easy to do, and I suspect that designers
took pains to avoid it. Of course that might simply be because they
were trying to approximate 12-tET. They certainly didn't bother tuning
12-TET any closer than +- 1c, when they easily could have done.

> >>In so doing, you will be going against hundreds of years of usage
> >>of the term "just" -- a term used specifically to distinguish
> >>between tunings as accurate as can be made, and tunings featuring
> >>deliberate and purposeful errors.

I would change that to -- a term used specifically to distinguish
between tunings as accurate as can be _heard_, and tunings featuring
deliberate and purposeful errors.

> >I don't believe so. Until the last 50 years or so there has been no
> >difference between "as accurate as can be made" and "within 2 cents
> >either way". The distinction never had to be faced.
>
> Oh, Dave! Bosanquet's 53-tET harmonium in 1875? A whole genre of
> accurate meantone fifths not by counting beats, but by getting very
> accurate just thirds in 1575?

But do we know how sucessful these methods actually were, and how long
the tunings lasted, on the instruments of the day.

> The idea that only modern man can
> distinguish 2-cent errors??

Huh? I didn't say that. It was the accuracy of the instruments I was
referring to. But I'll accept that I was wrong about that. How
accurate were they in actual use?

See folks, don't assume I'm a "noted authority". There are huge gaps
in my knowledge. A noted authority? What a frightening idea! (but of
course my ego just laps it up :-)

As Robin said to the ever-modest Batman after some particularly clever
explanation: "Gosh Batman, what _don't_ you know?". His reply:
"Oh several things Robin".

> Take a step back! We're making wonderful discoveries, but we're not
> privileged to any manifest destiny! Ears have always been ears, and
> they will always be the highest court in music, and they ear can
> hear errors of 2 cents!

Sure. Again, I was talking about the accuracy of the instruments. And
this when in actual use (not 10 seconds after they were tuned by an
expert). Read the note at the end of
http://www.izzy.net/~jc/PSTInfo/fretbd.html

> >The sharp distinction you are trying to make between just tuning
and
> >temperament is a purely mathematical one, one that can be revealed
> >by no listening and no measurement.
>
> To the contrary, my opinion is that the difference between just and
> tempered is entirely perceptual, and I don't claim to have any model
> of it that allows me to tell without listening.

Your [paraphrased] "as accurately as the instrument technology will
allow" has absolutely nothing to do with hearing, and yet you have
said it will affect your judgement of what is just. So you seem to
contradict yourself when you say that the difference is _entirely_
perceptual.

> I also believe that the perceptual difference between temperament
and
> JI goes beyond one of psychoacoustics. Even if a bare sonority
cannot
> be distinguished from just, if we want to claim that "puns" are
> interesting, we have to claim that the brain has some sort of access
> to the lattice, and by using an un-connected structure as a harmony
> we are tempering.

Oh sure. Whether you call them "puns" or not, and whether or not we
keep track of the lattice in any sense (which I doubt), I think I know
what you mean. I understand Paul Erlich agrees with you here, and
thinks he is disagreeing with me.

But all I am claiming about microtemperament is that most listeners on
hearing most music created for the original rational scale will be
none the wiser when it is played in a microtemperament. As you say,
the person in the street can't tell the difference between Pachelbel's
canon played in 5-limit JI or 12-tET (with 16 cent errors!).

But as Paul points out, it doesn't work in the other direction. If you
compose for the microtemperament, it may not work in the rational
scale.

> >>This historic use includes quarter-comma
> >>meantone tuning, whose max error from 5-limit JI is 6 cents --
also
> >>within the random error of the guitar, by some accounts. And
today,
> >>we have found unanimously (as far as I know) that even 3-cent
errors
> >>are musically important!
> >
> >Can you give me more info on that.
>
> In one of Graham Breed's early posts, he listed his findings to that
> time.

Grahams reply in
/tuning/topicId_26876.html#27331
doesn't cause me to alter my position. But it was very interesting.
Thanks Graham. I'll push my schismic temperaments closer to precise
4:7s and further from precise 2:3s. What's the most accurate fourth
you find acceptable as the generator?

> >>Get the error down to 1 cent, and I will join you in calling these
> >>tunings truly just in all circumstances.

I'll settle for 90% of circumstances, and await further evidence
before I shift from my 2 to 3 cents stance. There certainly wouldn't
be much to be gained in guitar design, from a microtemperament with
only 1 cent errors, except perhaps with schismic at the 5-limit.

> I think the best Barbershop quartets tune complete chords to an
> accuracy of about a cent... a finding supported by an FFT I once
> did on a typical professional Barbershop performance.

I severely doubt it. Unless you really know what you're doing, an FFT
can easily exagerate the harmonicity of a waveform. At 250 Hz you'd
need a sample 7 seconds long to have a resolution of 1 cent. Can
someone else confirm or deny?

> .x? Significant digits, man!

To describe this guitar design process mathematically, I need to draw
sharp boundaries somewhere and so the decimal place _is_ significant.
Also, some folks complain about 2 decimal places of cents when
specifying optimum generators, but they should understand that the
generator might need to be iterated 20 times to produce an
approximation to some SWNR. In this case a 0.05 cent change in the
generator will produce a 1 cent change in the approximate SWNR.

> Jon Catler's music is proof positive of the 13-limit guitar.

And as Paul said, almost certainly has 2 or 3 cent variations due to
finger pressure.

But these variations do not detract from the music. And, I claim, nor
would a microtemperament with similar errors.

> Sounds like you want the laws of nature to hold for all reference
> frames!

Why not?

> The speed of light may, but the length of your error yard
> stick does not, I say.

I don't understand what this means when translated to the topic of our
discussion. My apologies if it is intended only as rhetoric.

-- Dave Keenan

--- In tuning@y..., jpehrson@r... wrote:
> .,... you know all the "nutty professor" stuff....
> (I'm sure you've been reading some of his stuff.. although I pity
> anybody in some ways who does...)

Then you have no need to pity me. I have read none of it, nor anything
else on those lists apart from Jacky Ligon's Blackjack composition.
Thanks Jacky.

-- Dave Keenan

--- In tuning@y..., "Dave Keenan" <D.KEENAN@U...> wrote:

/tuning/topicId_26876.html#27412

> --- In tuning@y..., jpehrson@r... wrote:
> > .,... you know all the "nutty professor" stuff....
> > (I'm sure you've been reading some of his stuff.. although I pity
> > anybody in some ways who does...)
>
> Then you have no need to pity me. I have read none of it, nor
anything
> else on those lists apart from Jacky Ligon's Blackjack composition.
> Thanks Jacky.
>
> -- Dave Keenan

Smart. Although, "nutty professor" is a good springboard to ideas
sometimes, if he doesn't drive us yelping to the looney bin right
after him...

_________ _______ _______
Joseph Pehrson

--- In tuning@y..., "Dave Keenan" <D.KEENAN@U...> wrote:
> --- In tuning@y..., "Carl" <carl@l...> wrote:

> > A just guitar is defined as tuned as well as I
> > can expect guitar technology to be tuned.

> I'm sorry, but that just seems like a crazy definition to me.

It seems to me that justness is a sort of Platonic ideal, which can
only be completely true of conceptual objects and not of actual ones.
To say a tuning is just is exactly like saying an object is
triangular. Whether or not an object is triangular depends on context-
-for instance, we would have different standards for a cheese cracker
than for a diagram in a geometry textbook. In the same way, we might
very well want to call a guitar justly tuned--for a guitar. To ask
how many cents out of tune something must be before it is no longer
just is like asking how bumpy a cheese craker must be before it is no
longer triangular.

--- In tuning@y..., genewardsmith@j... wrote:
> It seems to me that justness is a sort of Platonic ideal, which can
> only be completely true of conceptual objects and not of actual
ones.

No. Substitute the word "rationalness" for "justness" and I'll agree.

> To say a tuning is just is exactly like saying an object is
> triangular. Whether or not an object is triangular depends on
context-
> -for instance, we would have different standards for a cheese
cracker
> than for a diagram in a geometry textbook.

Yes. I agree with this so far ...

> In the same way, we might
> very well want to call a guitar justly tuned--for a guitar. To ask
> how many cents out of tune something must be before it is no longer
> just is like asking how bumpy a cheese craker must be before it is
> no longer triangular.

... and if your analogy mapped correctly I'd agree with the rest. But
your mapping is wrong.

It should be
sight --> sound
sight maker --> sound maker
i.e.
cheese cracker, textbook diagram --> played chord
cracker maker, printing press --> musical instrument

Instead you have mapped
sight -> sound maker
i.e.
cheese cracker, textbook diagram --> musical instrument

Now consider that we have two identically shaped cheese crackers (as
best even the experts can tell, their corners are equally rounded
etc. etc.) but one of them was made by a machine and the other was
made by hand. Are you going to claim that one is more triangular than
the other?

If your analogy mapped the different contexts (crackers, textbooks) to
different types of chord or different timbres or different durations,
then I'd say yes, different maximum deviations from rational may be
heard as Just in these different contexts.

With triangularity we can distinguish mathematical-triangularity,
which is a property posessed only by Platonic objects,
from visual-triangularity which is a property of how humans perceive
shapes. In the case of musical sonorities we already have a perfectly
good word for what you might call mathematical-justness, and that is
rationalness (rationality?).

The Oxford English Dictionary defines "just" to mean "Harmonically
pure, sounding perfectly in tune".

So clearly justness is a matter of perception, not mathematics. There
is no need to confuse the issue by using the word "just" for the
purely mathematical concept as well.

-- Dave Keenan

--- In tuning@y..., "Dave Keenan" <D.KEENAN@U...> wrote:

> Now consider that we have two identically shaped cheese crackers
(as
> best even the experts can tell, their corners are equally rounded
> etc. etc.) but one of them was made by a machine and the other was
> made by hand. Are you going to claim that one is more triangular
than
> the other?

No, but I don't see your point. Neither cracker will be as nearly
triangular as a diagram in a geometry book, because that is the
nature of cheese crackers, and how they are produced is irrelevant.

> With triangularity we can distinguish mathematical-triangularity,
> which is a property posessed only by Platonic objects,
> from visual-triangularity which is a property of how humans
perceive
> shapes. In the case of musical sonorities we already have a
perfectly
> good word for what you might call mathematical-justness, and that
is
> rationalness (rationality?).

It's obviously not that good a word if you don't know what it is,
but "rational intonation" would do though it has an obvious double
sense.

> The Oxford English Dictionary defines "just" to mean "Harmonically
> pure, sounding perfectly in tune".

I was just listening to something in 1/4 comma meantone, and it
sounded pretty good to me. Does that mean it was just?

If it comes down to dictionary wars, chew on this:

Just intonation (Mus.) (a) The correct sounding of notes or
intervals; true pitch. (b) The giving all chords and intervals in
their purity or their exact mathematical ratio, or without
temperament; a process in which the number of notes and intervals
required in the various keys is much greater than the twelve to the
octave used in systems of temperament. --H. W. Poole.

Source <http://www.dictionary.com/cgi-bin/dict.pl?
config=about&term=00-database-info&db=web1913>: Webster's Revised
Unabridged Dictionary, © 1996, 1998 MICRA, Inc.

This is all over the map, which means it's probably a pretty good
dictionary entry because that's the way language works.

> If your analogy mapped the different contexts (crackers, textbooks)
to
> different types of chord or different timbres or different
durations,
> then I'd say yes, different maximum deviations from rational may be
> heard as Just in these different contexts.

Such was my intent--more specifically, just as we might not expect a
cracker to be so nearly triangular as a geometric diagram, we might
not expect a guitar to be so nearly in tune as some other instrument.
Therefore, the claim that "just" might mean something different in
the case of guitars as it does in some other context makes sense to
me, just as "triangular" might mean something different in the
context of cheese crackers than in some other context.

> So clearly justness is a matter of perception, not mathematics.

If being a triangular cheese cracker is not a question of mathematics
nor entirely of perception, being a justly tuned guitar need not be
either.

> There
> is no need to confuse the issue by using the word "just" for the
> purely mathematical concept as well.

I think the issue is pretty well confused as it is, and if it becomes
a matter of deciding how many cents (from where?) counts as "just",
it will be more confused yet.

--- In tuning@y..., genewardsmith@j... wrote:
> --- In tuning@y..., "Dave Keenan" <D.KEENAN@U...> wrote:
>
> > Now consider that we have two identically shaped cheese crackers
> (as
> > best even the experts can tell, their corners are equally rounded
> > etc. etc.) but one of them was made by a machine and the other was
> > made by hand. Are you going to claim that one is more triangular
> than
> > the other?
>
> No,

I'm gald.

> but I don't see your point.

I already tried my hardest to explain where your analogy goes wrong,
and how it should work. Try reading it again slowly.

> Neither cracker will be as nearly
> triangular as a diagram in a geometry book, because that is the
> nature of cheese crackers, and how they are produced is irrelevant.

Indeed! For me, this corresponds to saying that neither of two chords
with identical large tuning errors (from rational) will be nearly as
just as a chord with much smaller tuning errors, and what instrument
they are played on is irrelevant.

> > rationalness (rationality?).
>
> It's obviously not that good a word if you don't know what it is,

Tee hee. But I've never wanted a noun for it in normal usage, only
now that I'm talking about the word. The adjective is clearly
"rational".

> but "rational intonation" would do

Sure.

> though it has an obvious double sense.

But it should be clear from the context.

> If it comes down to dictionary wars, chew on this:
>
> Just intonation (Mus.) (a) The correct sounding of notes or
> intervals; true pitch. (b) The giving all chords and intervals in
> their purity or their exact mathematical ratio, or without
> temperament; a process in which the number of notes and intervals
> required in the various keys is much greater than the twelve to the
> octave used in systems of temperament. --H. W. Poole.
>
> Source <http://www.dictionary.com/cgi-bin/dict.pl?
> config=about&term=00-database-info&db=web1913>: Webster's Revised
> Unabridged Dictionary, © 1996, 1998 MICRA, Inc.
>
> This is all over the map, which means it's probably a pretty good
> dictionary entry because that's the way language works.

It's a lousy dictionary entry. "The giving all chords and intervals
..."? What does that mean? It isn't even English grammar. I guess it
has to mean "the _playing_of_ all chords and intervals ...".

We know that exact mathematical ratios are only available from digital
instruments, so that certainly can't be a necessary condition and the
"or" in "purity or ..." must be allowing alternatives rather than
equating the two.

I'm not saying that rational isn't just (for simple enough ratios),
only that just isn't necessarily rational. Most of the time it's
merely close to rational.

> > If your analogy mapped the different contexts (crackers,
textbooks)
> to
> > different types of chord or different timbres or different
> durations,
> > then I'd say yes, different maximum deviations from rational may
be
> > heard as Just in these different contexts.
>
> Such was my intent--more specifically, just as we might not expect a
> cracker to be so nearly triangular as a geometric diagram, we might
> not expect a guitar to be so nearly in tune as some other
instrument.

No. You just don't seem to be getting my objection to your analogy.

The crackers or diagrams and the chords or intervals are the perceived
objects. The guitar is merely a means of making a chord or interval.
The justness of a chord or interval does not depend on how it is made.

You are equating crackers to guitars. You see a cracker but you don't
hear a guitar, except in a loose usage where you really mean that you
hear the sounds that occur when a guitar is used to make them.

> > So clearly justness is a matter of perception, not mathematics.
>
> If being a triangular cheese cracker is not a question of
mathematics
> nor entirely of perception, being a justly tuned guitar need not be
> either.

But being a triangular cheese cracker _is_ entirely a question of
perception. My 3 year old doesn't know anything about geometry or
mathematics, but she can tell me if something is triangular. She just
learnt by absorbing the ways that other people use the word.

> > There
> > is no need to confuse the issue by using the word "just" for the
> > purely mathematical concept as well.
>
> I think the issue is pretty well confused as it is,

Well yes. And I'm doing my damndest to try to clear it up.

> and if it becomes
> a matter of deciding how many cents (from where?) counts as "just",
> it will be more confused yet.

From small whole number ratios (SWNRs) of frequency.

Oh dear! That's not what I'm trying to do here. You've come in on this
part way thru. I would not be so foolish as to try to lay down for
everybody and for all time and for every kind of sonority in every
timbre and for every duration, how many cents from rational is still
just. Obviously it's a very fuzzy thing to model. The first thing to
establish is that _some_ deviation is acceptable. Some folks even deny
that! But most folks seem happy that a 1 cent error doesn't matter
much.

What I'm trying to do is to establish the _reasonableness_ of
considering temperaments with errors of around 2.8 cents to be Just
for most listeners with most sonorities in most timbres and durations.

I want to do this because several such microtemperaments are known
(some were only discovered a few weeks ago by Graham Breed), and their
use makes the design of playable JI guitars possible with a minimum
number of full width frets. We're talking 20 or 30 frets versus 60 or
70 fretlets.

-- Dave Keenan
That's all.

>I'm sorry, but that just seems like a crazy definition to me. If a
>new method of guitar construction and playing was invented tomorrow,
>that cost no more to build and was accurate to 0.5 cent, would that
>suddenly make all other guitars non-just? Of course not.
>
>As you know, I believe that justness should be perceptually defined.

Me too! In fact, I'm taking this farther than you. You want to sum
over all the different instruments to get some kind of abstraction...
the tuning is just or not. Except you're just arbitrarily picking
the guitar, and a number, and using that. You haven't shown any
elegant way to get your abstraction.

I say tuning is relative to the instrument. I haven't shown any
elegant way to get numbers either. But if you want to ignore
instruments entirely... the worst case is the bass drum... if you
want to use the best case, then there isn't any such thing as a
just guitar at all!

>>>If we go by the RMS error it will only be 1.4 times (or something
>>>like that).
>>
>>Where did you get that number?
>
>Basic statistics and measurement theory. Only I was wrong. The
>sqrt(2) factor is as true of the max absolute error as it is of the
>RMS. You can try the experiment for yourself in a spreadsheet or
>whatever. Generate two parallel lists of random numbers (say 100)
>in a normal (bell curve) distribution with a mean of zero and a
>standard deviation (i.e. RMS error) of 1. Add corresponding numbers
>from each list and then find the MA and RMS errors of the original
>lists and those of the list of sums. In general it's pythagoras,
>total_err ~= sqrt(err1^2 + err2^2).

Cool.

>>In the case of a 12-tET guitar, errors can (and are everyday)
>>reduced by bending notes [by my experience], tweaking the open-
>>string tuning [I have been told], and choosing certain positions
>>over others [Don Slepian demonstrated this to me].
>
>This is another matter, outside of what we are discussing. If
>you can bend 12-TET to just, you can bend anything.

I think it addresses the reality of 12-tET guitars not being
considered just by my definition quite well.

>>>And many (most?) people don't want their JI to be phase-locked,
>>>they actually prefer slow beating.
>>
>>I don't think either of us have any data here at all. Besides,
>>phase-locking is a purely theoretical concern at this point, since
>>it requires beyond-run-of-the-mill electronic instruments to
>>produce.
>
>During the era of top-octave-divider organs, phase locking at small
>whole-number ratios was very easy to do, and I suspect that
>designers took pains to avoid it.

Baldwin must have; I've recorded several hours of music in 7-limit
JI on a Baldwin octave-divider organ without any problems.

>Of course that might simply be because they were trying to
>approximate 12-tET. They certainly didn't bother tuning 12-TET any
>closer than +- 1c, when they easily could have done.

The octave divider organ I used was tuned by means of 12 tiny
screws. Are you thinking of a specific example?

>I would change that to -- a term used specifically to distinguish
>between tunings as accurate as can be _heard_, and tunings featuring
>deliberate and purposeful errors.

I'll agree to that.

>>>I don't believe so. Until the last 50 years or so there has been
>>>no difference between "as accurate as can be made" and "within 2
>>>cents either way". The distinction never had to be faced.
>>
>>Oh, Dave! Bosanquet's 53-tET harmonium in 1875? A whole genre of
>>accurate meantone fifths not by counting beats, but by getting very
>>accurate just thirds in 1575?
>
>But do we know how sucessful these methods actually were, and how
>long the tunings lasted, on the instruments of the day.

No tuning lasts more than a few days on historical keyboard
instruments. That's why they tuned them every day!!

The success of the method depends on the tuner. I guess we'll
never know how those people did. But we have a direct line to
them through people alive today, still working the same procedures,
and working them to fractions of a cent.

>See folks, don't assume I'm a "noted authority". There are huge
>gaps in my knowledge. A noted authority? What a frightening idea!
>(but of course my ego just laps it up :-)

I wouldn't have it any other way! I'm not a noted authority either.
But, I have spent a lot of time with various acoustic keyboard
instruments. OTOH, I have absolutely no knowledge of the guitar.

>Sure. Again, I was talking about the accuracy of the instruments.
>And this when in actual use (not 10 seconds after they were tuned
>by an expert). Read the note at the end of
>http://www.izzy.net/~jc/PSTInfo/fretbd.html

Great link! The furnace would affect all notes equally, though,
I would think... I wonder how rotating the neck was causing a
change?

Now we just need a corresponding site for intervals, and we'll
have something useful for our discussion. I have a strobe tuner,
but no guitar. :(

>>>The sharp distinction you are trying to make between just tuning
>>>and temperament is a purely mathematical one, one that can be
>>>revealed by no listening and no measurement.
>>
>>To the contrary, my opinion is that the difference between just and
>>tempered is entirely perceptual, and I don't claim to have any model
>>of it that allows me to tell without listening.
>
>Your [paraphrased] "as accurately as the instrument technology will
>allow" has absolutely nothing to do with hearing,

It does when the instrument must be tuned by a human!

>and yet you have said it will affect your judgement of what is just.
>So you seem to contradict yourself when you say that the difference
>is _entirely_ perceptual.

The confusion may result from a step I'm taking tacitly here.
Actually, we did discuss it... the human ear is the final judge of
pitch. My point is that people already tune their instruments to
a greater level of accuracy than our best algoritms have at guessing
the pitch of complex tones with some degree of inharmonicity. The
idea of getting strange results from my definition by setting
up a synth with a just tuning to a greater degree of accuracy than
we can hear... is a fallacy, since I define accuracy by what we
can hear -- not by what a computer says the accuracy is.

>Oh sure. Whether you call them "puns" or not, and whether or not we
>keep track of the lattice in any sense (which I doubt),

At least we all (myself, Paul, Pehrson, you) agree on this doubt.

>But all I am claiming about microtemperament is that most listeners
>on hearing most music created for the original rational scale will
>be none the wiser when it is played in a microtemperament.

Agreed!

>But as Paul points out, it doesn't work in the other direction. If
>you compose for the microtemperament, it may not work in the
>rational scale.

Yeah. . . . I doubt puns will be a problem for our definition of
just intonation. Forget I mentioned it!

>Grahams reply in /tuning/topicId_26876.html#27331
>doesn't cause me to alter my position.

Even though he said he could tune to .1 cents without counting
beats?

>>I think the best Barbershop quartets tune complete chords to an
>>accuracy of about a cent... a finding supported by an FFT I once
>>did on a typical professional Barbershop performance.
>
>I severely doubt it. Unless you really know what you're doing, an
>FFT can easily exagerate the harmonicity of a waveform.

I don't, though I am aware of this.

>At 250 Hz you'd need a sample 7 seconds long to have a resolution
>of 1 cent. Can someone else confirm or deny?

Would like to know more about this.

>>Jon Catler's music is proof positive of the 13-limit guitar.
>
>And as Paul said, almost certainly has 2 or 3 cent variations due to
>finger pressure.

Def! I'm not denying the 3 (Denny said 6) cent fudge factor on
guitars.

>But these variations do not detract from the music. And, I claim,
>nor would a microtemperament with similar errors.

Maybe so, maybe not. Try it on a piano.

>>The speed of light may, but the length of your error yard
>>stick does not, I say.
>
>I don't understand what this means when translated to the topic of
>our discussion. My apologies if it is intended only as rhetoric.

I'm simply saying that though you can't hear a 3-cent error on
a guitar, you can hear it on a piano! The guitar's timbre has
something invested in 3 cents of blur, whereas the piano's timbre
has something invested in a cent of accuracy.

-Carl

--- In tuning@y..., "Carl" <carl@l...> wrote:

/tuning/topicId_26876.html#27444

>
> I say tuning is relative to the instrument. I haven't shown any
> elegant way to get numbers either. But if you want to ignore
> instruments entirely... the worst case is the bass drum... if you
> want to use the best case, then there isn't any such thing as a
> just guitar at all!
>

What a hoot! I'm waiting to hear a justly intoned bass drum!

_________ ________ _______ _
Joseph Pehrson

BTW-- I'm getting a message that the tuning list is not currently available... I'll try
again.
===
> >Are there any extant cultures that accept the 7-limit in theory
> >and/or practice?
>
> Only Barbershop, so far as I know.

That's all I've heard of too, but there *must* be some culture somewhere that has
septimal consonances...it would seem weird if it isn't so since they're such salient
consonances. I've heard that blue notes in jazz are septimal, but it varies from singer
to singer. Jazz seems to be founded on tensions that can't be easily analyzed in any
tuning system.

>
> >What about the 11-limit?
>
> None that I know of.

It wouldn't surprise me if there were none, since there are no practical 11-limit
consonaces, unless people like singing 3 1/2 octaves apart! - higher limits just don't
seem practical for 'people-generated' musics (I'll explain that later). Twining's
composition is in some sense a theoretical work that admits limits higher than what
might emerge culturally.

>
> >There's probably a cut-off point where the music becomes
> >incomprehensible in a folk tradition,
>
> What's a folk tradition?

A folk musical tradition is, in my definition, any tradition whose theoretical
comprehensibility does not exceed the intuitive knowledge of anyone raised in the
culture in which it occurs. Art music is not usually a folk tradition, although it can be.
You don't find people whistling catchy Boulez tunes or chanting in 19-limit JI. I wish I
could understand where the cutoff point is for 'comprehensibility', but I'm betting it
isn't universal and probably can't be intellectually fathomed. I don't find 7edo
particularly 'comprehensible' from an intuitive perspective, and yet that tuning system
does exist and on more than one continent...of couse, I'm not sure where the notes
are in practice vs. theory.

>
> >especially when the system begins generating numerous intervals
> >that could potentially compete for the same function (e.g.,
> >subminor vs. minor third).
>
> This assumes the diatonic scale.

Most music around the world is based in scales of some form or another; but you're
right, I could construct two separate non-diatonic scales, one which uses 6/5 and one
which uses 7/6 and these could theoretically co-occur in the same musical
tradition--but I don't think they do. Even Turkish music with its famed microdivisions
of the tone never uses all those divisions in the same scale-- and they aren't tuned
according to theory anyway. Why? Because the folk tradition has rationalized the
theoretical tradition to make it more comprehensible.

>
> >If the 'people' can't find the notes intuitively, the tradition
> >will always remain hyperspecialized and won't infiltrate the
> >general artistic culture.
>
> That's why recordings help. A microtonal *keyboard instrument*,
> or other suitably-powerful polyphonic instrument would be a great
> help.

Yes, I'm sure that if you played a melody in 13-limit JI over and over on the radio, that
people would ultimately start singing it in perfect intonation--if it were catchy and
sung by Britney Spears... But the questions remain: Why didn't the culture poop out
13-limit JI in the first place? and why has no extant culture ever done so? I think it's
because people don't start singing music because a theorist told them to do it; they
sing (and play instruments) because they enjoy it. Any tuning structure that requires
extensive theory to explain will never catch on in practice, even if the culture buys
into the explanatory nature of the theory. Theory is usually (always?) rationalized by
practice.

>> Only Barbershop, so far as I know.
>
>That's all I've heard of too, but there *must* be some culture
>somewhere that has septimal consonances...it would seem weird
>if it isn't so since they're such salient consonances.

Yep, it is weird, but I'm not aware of any systematic use of
accurately-tuned septimal harmony outside of Barbershop.

>>>What about the 11-limit?
>>
>>None that I know of.
>
>It wouldn't surprise me if there were none, since there are no
>practical 11-limit consonances, unless people like singing 3
>1/2 octaves apart!

11:4 is a perfectly practical consonance, as Twining proves.

>Twining's composition is in some sense a theoretical work that
>admits limits higher than what might emerge culturally.

A similar argument could have been (and certainly was) made
about the 7-limit before the emergence of Barbershop (from the
most unassuming of places)!

I think Twining's showed this is quite practical. In the
Amsterdam and New York concerts, some singers were able to go
for short periods without their headphones. And these concerts
were given with very little rehearsal.

>> >There's probably a cut-off point where the music becomes
>> >incomprehensible in a folk tradition,
>>
>> What's a folk tradition?
>
>A folk musical tradition is, in my definition, any tradition
>whose theoretical comprehensibility does not exceed the intuitive
>knowledge of anyone raised in the culture in which it occurs.

That certainly rules out jazz, and probably all music, since
music theory isn't very powerful at explaining music.

>You don't find people whistling catchy Boulez tunes or chanting
>in 19-limit JI.

I've never heard any Boulez, but you actually *do* find people
*chanting* in higher-limit JI!

>> >especially when the system begins generating numerous intervals
>> >that could potentially compete for the same function (e.g.,
>> >subminor vs. minor third).
>>
>> This assumes the diatonic scale.
>
>Most music around the world is based in scales of some form or
>another; but you're right, I could construct two separate
>non-diatonic scales, one which uses 6/5 and one which uses 7/6 and
>these could theoretically co-occur in the same musical tradition --
>but I don't think they do.

What I meant was, we can expand the number of basic intervals, so
that the new intervals coming from our harmonies are less likely
to be confounded. See, for example, Paul Erlich's decatonic scales.

>the questions remain: Why didn't the culture poop out 13-limit JI
>in the first place?

Why ask why?

>why has no extant culture ever done so?

Why did some cultures evolve technologically faster than others?
Why did jazz wait until the 20th century to be invented? Who knows?

>I think it's because people don't start singing music because a
>theorist told them to do it; they sing (and play instruments)
>because they enjoy it.

And maybe one day the higher limits will evolve.

>Any tuning structure that requires extensive theory to explain will
>never catch on in practice,

Why? I see no reason it can't go both ways. On this list we have
seen excellent examples of theory informing practice. Also in
Messiaen we have unfathomably-cool music in the octatonic scale,
which came from the composer's theoretical investigations IIRC
(maybe someone here can confirm this).

>Theory is usually (always?) rationalized by practice.

No, I think practice comes first (including in the case of Turkish
music you mention). Theory either sits there and does nothing, or
feeds back into practice.

-Carl

on 7/31/03 2:58 PM, Justin Weaver <improvist@usa.net> wrote:

>>> Are there any extant cultures that accept the 7-limit in theory
>>> and/or practice?
>>
>> Only Barbershop, so far as I know.
>
> That's all I've heard of too, but there *must* be some culture somewhere that
> has septimal consonances...it would seem weird if it isn't so since they're
> such salient consonances. I've heard that blue notes in jazz are septimal, but
> it varies from singer to singer. Jazz seems to be founded on tensions that
> can't be easily analyzed in any tuning system.

I had mostly written this before Justin's message came through, and decided
to paste my response right here, since it has more meaning in this context
than it had before...

After some recent exposure to JI (perhaps it was after listening to the
twining) I sat down and did some jazz improv on the piano (tuned to 12et),
and I felt a growing awareness of the important of harmonics in the
structure of the jazz which I was never conscious of before. I described
this at the time as the sense that the harmonics were floating over my
fingers, guiding them. This was definitely a new experience of the
potential available in 12et. And I would say that jazz has never been so
available to me before.

It occurred to me since then that such an awareness might guide the choice
of what notes are left out of jazz chords: perhaps those notes which, if
left in, would do the most damage to underlying harmonic sensibilities which
might be behind the jazz chords.

So this sounds to me like something that might be called "reverse adaptive
JI", a process by which a (perhaps unconscious) conception with a purely
harmonic aspect is mapped onto the scale at hand. Like adaptive JI as I
understand it, the horizontal direction would be free, but since the scale
is fixed, what is actually "free" would then be the JI "conception" that is
guiding the improvisation/composition. So with successive chords, the
"underlying" JI might find ways to shift so that more notes are close to the
fixed scale, taking into account what might be improved by dropping various
notes from a chord.

Or stated another way, the improvising hand/mind might be searching
(solving) for a horizontal positionining of the "internal" JI which puts
(for example) the most harmonics near enough to notes in the available
scale, probably guided also by current hand position and momentary melodic
tendencies, all this together being synthesized into a choice of which
harmonics can be played as notes at a given moment.

I say "harmonics" and I don't know whether subharmonics might also be
involved, or possibly a more complex structure. But in the case of jazz my
_impression_ was that harmonics "is where its at" when it comes to
generating the big (and probably incomplete) chords.

I say this because I momentarily became conscious of it. Such an
interpretations of experience is of course very tentative, since it is a
momentary analysis of a largely unconscious process.

... And regarding tensions in jazz, I would state it this way: My
impression is that jazz is constantly seeking resolution in a very
high-dimensional space of interactions. Tensions are just fodder for
resolution. Resolution is always incomplete. Nonetheless the affirmation
of that such a process can occur is a kind of an affirmation of a life that
embraces many dimensions without hesitation.

-Kurt

--- In tuning@yahoogroups.com, "Justin Weaver" <improvist@u...>
wrote:
> BTW-- I'm getting a message that the tuning list is not currently
available... I'll try
> again.
> ===
> > >Are there any extant cultures that accept the 7-limit in theory
> > >and/or practice?
> >
> > Only Barbershop, so far as I know.
>
> That's all I've heard of too, but there *must* be some culture
somewhere that has
> septimal consonances...

in melody, the tuvan throat-singers make use of the 7th, 11th, even
occasionally all the way up to the 41st harmonics, by the nature of
what they're doing.

i've heard some african vocal ensemble stuff that sounded like it was
approximating a 4:5:6:7:9 chord. clearly removed from any western
influence.

>it would seem weird if it isn't so since
they're such salient
> consonances. I've heard that blue notes in jazz are septimal,

more often they're bent in the opposite direction!

> >
> > >What about the 11-limit?
> >
> > None that I know of.
>
> It wouldn't surprise me if there were none, since there are no
practical 11-limit
> consonaces, unless people like singing 3 1/2 octaves apart! -

people often do sing 3 1/2 octaves apart, and i don't know what you
mean by "practical". if you play me a 4:5:6:9 chord, i can easily
lock in on the 11 with my voice to make a 4:5:6:9:11 chord.

since it's so close to the equal-tempered tuning of the minor triad,
there is an attraction to 16:19:24 chords often mentioned by players
of higher-pitched orchestral instruments. the combinational tones
make this practical to "lock in" and strengthen the conventional,
classical conception of the "root" of this chord, octave-equivalent
to the '16' of course.

> isn't universal and probably can't be intellectually fathomed. I
don't find 7edo
> particularly 'comprehensible' from an intuitive perspective, and
yet that tuning system
> does exist and on more than one continent...of couse, I'm not sure
where the notes
> are in practice vs. theory.

tuning systems *evolve*. is the human organism comprehensible from an
intuitive perspective?

> Why? Because the folk tradition has
>rationalized the
> theoretical tradition to make it more comprehensible.

you mean the theoretical tradition has rationalized the folk
tradition to make it more comprehensible? that would seem more
comprehensible :)

>Why didn't the
culture poop out
> 13-limit JI in the first place? and why has no extant culture ever
done so? I think it's
> because people don't start singing music because a theorist told
them to do it; they
> sing (and play instruments) because they enjoy it. Any tuning
structure that requires
> extensive theory to explain will never catch on in practice,

i don't know about that. meantone tuning causes most beginners
difficulty in the theory department, yet we know that it evolved as
the standard tuning in the west before any theorist was even able to
explain it!

----- Original Message -----
From: "Carl Lumma" <ekin@lumma.org>

> >You don't find people whistling catchy Boulez tunes or chanting
> >in 19-limit JI.
>
> I've never heard any Boulez, but you actually *do* find people
> *chanting* in higher-limit JI!

!!!

You should.

* David Beardsley
* microtonal guitar
* http://biink.com/db

>> >You don't find people whistling catchy Boulez tunes or chanting
>> >in 19-limit JI.
>>
>> I've never heard any Boulez, but you actually *do* find people
>> *chanting* in higher-limit JI!
>
>!!!
>
>You should.

Hear Boulez?

-Carl

on 7/31/03 3:35 PM, Carl Lumma <ekin@lumma.org> wrote:

>>>> There's probably a cut-off point where the music becomes
>>>> incomprehensible in a folk tradition,
>>>
>>> What's a folk tradition?
>>
>> A folk musical tradition is, in my definition, any tradition
>> whose theoretical comprehensibility does not exceed the intuitive
>> knowledge of anyone raised in the culture in which it occurs.
>
> That certainly rules out jazz, and probably all music, since
> music theory isn't very powerful at explaining music.

You heard me doing jazz improv the other day, and I think you know that I
have very little theory. I have essentially no jazz theory, except for tiny
bits that I have picked up, and I don't consciously use any theoretical
knowledge until I find it somehow already coming out of me anyway. So I
have learned, essentially by listening, with very little theory available to
me.

So I guess I think theory follows practice, for the most part.

Now it may be that theory enters into the process by the presence of an
"elite" within a culture who are aware of theory, and that awareness may
expand the expressiveness available to the whole culture, even though the
culture as a whole never learned theory. My guess is such a process might
be self-sustaining to a large degree even after all those with theoretical
knowledge have died.

>> You don't find people whistling catchy Boulez tunes or chanting
>> in 19-limit JI.
>
> I've never heard any Boulez, but you actually *do* find people
> *chanting* in higher-limit JI!

Yes, I was going to say: chanting of harmonics *as* harmonics has emerged
culturally. The question is whether this might lead to chanting of
harmonics via added fundamentals. I suspect this is highly likely. Simple
indigenous cultures may have felt little pressure to expand their musical
possibilities. But individuals of "indigenous origin" being integrated into
"civilization" may experience such pressure. And likewise "civilized
people" growing to appreciate a growing range of possibilities of various
ethnic origins also are likely to generate some new kinds of synthesis.
*Now* of course it may all hinge on what the pop music industry decides to
do with it, at least until some apocalypse occurs.

-Kurt

--- In tuning@yahoogroups.com, Kurt Bigler <kkb@b...> wrote:

> It occurred to me since then that such an awareness might guide the
choice
> of what notes are left out of jazz chords: perhaps those notes
which, if
> left in, would do the most damage to underlying harmonic
sensibilities which
> might be behind the jazz chords.

hmm . . . it's usually the fifth above the bass/root which is left
out -- leaving it in does the most damage how?

> So this sounds to me like something that might be called "reverse
adaptive
> JI", a process by which a (perhaps unconscious) conception with a
purely
> harmonic aspect is mapped onto the scale at hand. Like adaptive JI
as I
> understand it, the horizontal direction would be free, but since
the scale
> is fixed, what is actually "free" would then be the JI "conception"
that is
> guiding the improvisation/composition. So with successive chords,
the
> "underlying" JI might find ways to shift so that more notes are
close to the
> fixed scale, taking into account what might be improved by dropping
various
> notes from a chord.

hmm . . . can you give an example?

>
> Or stated another way, the improvising hand/mind might be searching
> (solving) for a horizontal positionining of the "internal" JI which
puts
> (for example) the most harmonics near enough to notes in the
available
> scale, probably guided also by current hand position and momentary
melodic
> tendencies, all this together being synthesized into a choice of
which
> harmonics can be played as notes at a given moment.
>
> I say "harmonics" and I don't know whether subharmonics might also
be
> involved, or possibly a more complex structure. But in the case of
jazz my
> _impression_ was that harmonics "is where its at" when it comes to
> generating the big (and probably incomplete) chords.

well i certainly can sympathize in that there is some tendency to
hear dom9#11 chords as 4:5:6:7:9:11 chords, and m9b5 chords as
5:6:7:9:11 chords . . .
>
> I say this because I momentarily became conscious of it. Such an
> interpretations of experience is of course very tentative, since it
is a
> momentary analysis of a largely unconscious process.
>
> ... And regarding tensions in jazz, I would state it this way: My
> impression is that jazz is constantly seeking resolution in a very
> high-dimensional space of interactions. Tensions are just fodder
for
> resolution. Resolution is always incomplete. Nonetheless the
affirmation
> of that such a process can occur is a kind of an affirmation of a
life that
> embraces many dimensions without hesitation.

yup. and this includes melodic, as well as harmonic, dimensions . . .

> > ===
> > > >Are there any extant cultures that accept the 7-limit in theory
> > > >and/or practice?
> > >
> > > Only Barbershop, so far as I know.
> >
> > That's all I've heard of too, but there *must* be some culture
> somewhere that has
> > septimal consonances...
>
> in melody, the tuvan throat-singers make use of the 7th, 11th, even
> occasionally all the way up to the 41st harmonics, by the nature of
> what they're doing.

True, but that's more a pure acoustic phenomenon than an element of structure.

>
> i've heard some african vocal ensemble stuff that sounded like it was
> approximating a 4:5:6:7:9 chord. clearly removed from any western
> influence.

Yes, thanks for pointing that out-- now that you mention it I think Africa may be the
home of the elusive 7-limit....anyone have any more info on this?

> > >
> > > >What about the 11-limit?
> > >
> > > None that I know of.
> >
> > It wouldn't surprise me if there were none, since there are no
> practical 11-limit
> > consonaces, unless people like singing 3 1/2 octaves apart! -
>
> people often do sing 3 1/2 octaves apart, and i don't know what you
> mean by "practical". if you play me a 4:5:6:9 chord, i can easily
> lock in on the 11 with my voice to make a 4:5:6:9:11 chord.

This is a missing point that I failed tot ake into account--if the chord is 'stacked up'
enough, I think the 11-limit can be admitted as well as any limit beyond it, depending
on how high the stack piles up... huge chordal piles are rare outside the Western art
music tradition though and vanishingly rare in folk traditions.

>
> > isn't universal and probably can't be intellectually fathomed. I
> don't find 7edo
> > particularly 'comprehensible' from an intuitive perspective, and
> yet that tuning system
> > does exist and on more than one continent...of couse, I'm not sure
> where the notes
> > are in practice vs. theory.
>
> tuning systems *evolve*. is the human organism comprehensible from an
> intuitive perspective?

I'd say the human organism can only be comprehended through intuition, but I say
that as something of an existentialist, not with any scientific meaning. I think what
does happen in a culture is driven exclusively by intuition (vs. what *could* happen);
even what theory the culture chooses to engage is driven by human intuition-- choice
is existential, not theoretical.

>
> > Why? Because the folk tradition has
> >rationalized the
> > theoretical tradition to make it more comprehensible.
>
> you mean the theoretical tradition has rationalized the folk
> tradition to make it more comprehensible? that would seem more
> comprehensible :)

That depends on what you mean by 'rationalize'. I meant that when a theory crops up
to explain a folk tradition or when a new theory comes into vogue and is adopted by
a folk tradition, then the folk tradition turns the theory into something more
intuitively comprehensible. Of course, theory very often comes *after* practice and
just as often has nothing at all to do with practice.

>
> >Why didn't the
> culture poop out
> > 13-limit JI in the first place? and why has no extant culture ever
> done so? I think it's
> > because people don't start singing music because a theorist told
> them to do it; they
> > sing (and play instruments) because they enjoy it. Any tuning
> structure that requires
> > extensive theory to explain will never catch on in practice,
>
> i don't know about that. meantone tuning causes most beginners
> difficulty in the theory department, yet we know that it evolved as
> the standard tuning in the west before any theorist was even able to
> explain it!

I think that's because theorists didn't *want* to explain it--they were hung up on 3-
limit thinking. Sometimes theoretical tradition makes it hard to see what's right in
front of you. -Justin

>> in melody, the tuvan throat-singers make use of the 7th, 11th, even
>> occasionally all the way up to the 41st harmonics, by the nature of
>> what they're doing.
>
>True, but that's more a pure acoustic phenomenon than an element of structure.

Uh...

>Yes, thanks for pointing that out-- now that you mention it I think
>Africa may be the home of the elusive 7-limit....anyone have any more
>info on this?

I've listened to a bit of Southern-African vocal stuff and I've yet
to hear any repeated use of 7-limit harmony.

>huge chordal piles are rare outside the Western art
>music tradition though and vanishingly rare in folk traditions.

Isn't barbershop a folk tradition?

-Carl

>
> You heard me doing jazz improv the other day, and I think you know that I
> have very little theory. I have essentially no jazz theory, except for tiny
> bits that I have picked up, and I don't consciously use any theoretical
> knowledge until I find it somehow already coming out of me anyway. So I
> have learned, essentially by listening, with very little theory available to
> me.
>
> So I guess I think theory follows practice, for the most part.
>

That's my "background" in jazz too-- no background :) -- and yet somehow I seem to
be able to pull it off intuitively. I actually *agree* that theory follows practice-- before
I was only suggesting that folk culture IS (in its essence) a more intuitively rational
version of whatever theory says (if that). -Justin

--- In tuning@yahoogroups.com, Carl Lumma <ekin@l...> wrote:
> >> in melody, the tuvan throat-singers make use of the 7th, 11th, even
> >> occasionally all the way up to the 41st harmonics, by the nature of
> >> what they're doing.
> >
> >True, but that's more a pure acoustic phenomenon than an element of structure.
>
> Uh...

You know what I meant. :) Of course acoustic phenomena are in and of themselves
elements of structure--but their spontaneous occurence in nature is only given
structure in our minds.

>
> >Yes, thanks for pointing that out-- now that you mention it I think
> >Africa may be the home of the elusive 7-limit....anyone have any more
> >info on this?
>
> I've listened to a bit of Southern-African vocal stuff and I've yet
> to hear any repeated use of 7-limit harmony.

I don't think you'd hear it there. I know mbube music fairly well and it's pretty much
5-limit -- actually, it's the "ideal" simple 5-limit system because it denies any
utonalities and also denies any chord progression that might lead to drift (no II-->V
progressions in mbube).

>
> >huge chordal piles are rare outside the Western art
> >music tradition though and vanishingly rare in folk traditions.
>
> Isn't barbershop a folk tradition?

I'd say it's a folk tradition heavily informed by Western harmony, even as it breaks the
rules. But yes, I'd say it's an emergent folk tradition...and the 7-limit chordal piles in
it are vanishingly rare outside of Barbershop. -Justin

----- Original Message -----
From: "Carl Lumma" <ekin@lumma.org>

> >> >You don't find people whistling catchy Boulez tunes or chanting
> >> >in 19-limit JI.
> >>
> >> I've never heard any Boulez, but you actually *do* find people
> >> *chanting* in higher-limit JI!
> >
> >!!!
> >
> >You should.
>
> Hear Boulez?

Yep. I think he's one of the more interesting 20th century composers.

* David Beardsley
* microtonal guitar
* http://biink.com/db

In a message dated 7/31/03 7:42:00 PM Eastern Daylight Time,
improvist@usa.net writes:

> Yes, thanks for pointing that out-- now that you mention it I think Africa
> may be the
> home of the elusive 7-limit....anyone have any more info on this?
>
>

The Kung! (in South Africa) use 7-, up to 11-limit. Johnny

In a message dated 7/31/03 7:46:19 PM Eastern Daylight Time, ekin@lumma.org
writes:

> Isn't barbershop a folk tradition?

According to the latest President of the American Musicological Society, if
you know the name of a composer for a music, it is not folk music. I don't
agree, however.

Johnny

I think Boulez is against everything the alternative tuning movement stands for. -
Justin

--- In tuning@yahoogroups.com, "David Beardsley" <db@b...> wrote:
> ----- Original Message -----
> From: "Carl Lumma" <ekin@l...>
>
> > >> >You don't find people whistling catchy Boulez tunes or chanting
> > >> >in 19-limit JI.
> > >>
> > >> I've never heard any Boulez, but you actually *do* find people
> > >> *chanting* in higher-limit JI!
> > >
> > >!!!
> > >
> > >You should.
> >
> > Hear Boulez?
>
> Yep. I think he's one of the more interesting 20th century composers.
>
>
> * David Beardsley
> * microtonal guitar
> * http://biink.com/db

That wouldn't surprise me; the !kung are on the fringes of just about everything from
language to religion to you-name-it. They are also one of the most pacifistic cultures
known.

What is !kung music like? Is it just chant with some 7- and 11-limit intervals? -Justin

--- In tuning@yahoogroups.com, Afmmjr@a... wrote:
> In a message dated 7/31/03 7:42:00 PM Eastern Daylight Time,
> improvist@u... writes:
>
>
> > Yes, thanks for pointing that out-- now that you mention it I think Africa
> > may be the
> > home of the elusive 7-limit....anyone have any more info on this?
> >
> >
>
> The Kung! (in South Africa) use 7-, up to 11-limit. Johnny

>> >> >You don't find people whistling catchy Boulez tunes or chanting
>> >> >in 19-limit JI.
>> >>
>> >> I've never heard any Boulez, but you actually *do* find people
>> >> *chanting* in higher-limit JI!
>> >
>> >!!!
>> >
>> >You should.
>>
>> Hear Boulez?
>
>Yep. I think he's one of the more interesting 20th century composers.

I'll check it out. I tend to like his conducting. What do you think
of Berio?

-Carl

--- In tuning@yahoogroups.com, "Justin Weaver" <improvist@u...>
wrote:
> > > ===
> > > > >Are there any extant cultures that accept the 7-limit in
theory
> > > > >and/or practice?
> > > >
> > > > Only Barbershop, so far as I know.
> > >
> > > That's all I've heard of too, but there *must* be some culture
> > somewhere that has
> > > septimal consonances...
> >
> > in melody, the tuvan throat-singers make use of the 7th, 11th,
even
> > occasionally all the way up to the 41st harmonics, by the nature
of
> > what they're doing.
>
> True, but that's more a pure acoustic phenomenon than an element of
>structure.

the melodies are structured, though, using these pitches . . .

> >
> > i've heard some african vocal ensemble stuff that sounded like it
was
> > approximating a 4:5:6:7:9 chord. clearly removed from any western
> > influence.
>
> Yes, thanks for pointing that out-- now that you mention it I think
Africa may be the
> home of the elusive [7-limit] . . .
> This is a missing point that I failed tot ake into account--if the
chord is 'stacked up'
> enough, I think the 11-limit can be admitted as well as any limit
beyond it, depending
> on how high the stack piles up... huge chordal piles are rare
outside the Western art
> music tradition though and vanishingly rare in folk traditions.

the 4:5:6:7:9 that occurs in remote african music -- isn't this just
as 'stacked up' as a 4:5:6:11 chord? and what resemblance does the
latter have to anything in the western art music tradition?

> > > isn't universal and probably can't be intellectually fathomed.
I
> > don't find 7edo
> > > particularly 'comprehensible' from an intuitive perspective,
and
> > yet that tuning system
> > > does exist and on more than one continent...of couse, I'm not
sure
> > where the notes
> > > are in practice vs. theory.
> >
> > tuning systems *evolve*. is the human organism comprehensible
from an
> > intuitive perspective?
>
> I'd say the human organism can only be comprehended through
intuition, but I say
> that as something of an existentialist, not with any scientific
meaning. I think what
> does happen in a culture is driven exclusively by intuition (vs.
what *could* happen);
> even what theory the culture chooses to engage is driven by human
intuition-- choice
> is existential, not theoretical.

what if i had said "the fruit fly" instead of the "human organism"? i
think i should have . . .

> > > Why? Because the folk tradition has
> > >rationalized the
> > > theoretical tradition to make it more comprehensible.
> >
> > you mean the theoretical tradition has rationalized the folk
> > tradition to make it more comprehensible? that would seem more
> > comprehensible :)
>
> That depends on what you mean by 'rationalize'. I meant that when a
theory crops up
> to explain a folk tradition or when a new theory comes into vogue
and is adopted by
> a folk tradition, then the folk tradition turns the theory into
something more
> intuitively comprehensible.

you mean like nashville chords or something?

>
> >
> > >Why didn't the
> > culture poop out
> > > 13-limit JI in the first place? and why has no extant culture
ever
> > done so? I think it's
> > > because people don't start singing music because a theorist
told
> > them to do it; they
> > > sing (and play instruments) because they enjoy it. Any tuning
> > structure that requires
> > > extensive theory to explain will never catch on in practice,
> >
> > i don't know about that. meantone tuning causes most beginners
> > difficulty in the theory department, yet we know that it evolved
as
> > the standard tuning in the west before any theorist was even able
to
> > explain it!
>
> I think that's because theorists didn't *want* to explain it--they
were hung up on 3-
> limit thinking. Sometimes theoretical tradition makes it hard to
see what's right in
> front of you. -Justin

well, it was still a darn long time (well longer than my lifespan so
far) between ramos, who was explicitly talking 5-limit, and the first
accurate description of what we call "meantone" today.

--- In tuning@yahoogroups.com, Carl Lumma <ekin@l...> wrote:

> >Yes, thanks for pointing that out-- now that you mention it I
think
> >Africa may be the home of the elusive 7-limit....anyone have any
more
> >info on this?
>
> I've listened to a bit of Southern-African vocal stuff and I've yet
> to hear any repeated use of 7-limit harmony.

this was central african, if i recall correctly. just one chord.

--- In tuning@yahoogroups.com, "Paul Erlich" <perlich@a...> wrote:
> --- In tuning@yahoogroups.com, Carl Lumma <ekin@l...> wrote:
>
> > >Yes, thanks for pointing that out-- now that you mention it I
> think
> > >Africa may be the home of the elusive 7-limit....anyone have any
> more
> > >info on this?
> >
> > I've listened to a bit of Southern-African vocal stuff and I've
yet
> > to hear any repeated use of 7-limit harmony.
>
> this was central african, if i recall correctly. just one chord.

central african Pygmy polyphony, yes. Have a look at

http://www-math.cudenver.edu/~jstarret/pygmies.html

If this is correct, pygmy polyphonies rely on septimal interval and
not at all on any 5 based interval. could not be more remote from
european tradition. Those polyphonies are really extraordinary.

yours truly

François Laferrière

Where can we *hear* this? -Justin

--- In tuning@yahoogroups.com, "francois_laferriere" <francois.laferriere@o=
...>
wrote:
> --- In tuning@yahoogroups.com, "Paul Erlich" <perlich@a...> wrote:
> > --- In tuning@yahoogroups.com, Carl Lumma <ekin@l...> wrote:
> >
> > > >Yes, thanks for pointing that out-- now that you mention it I
> > think
> > > >Africa may be the home of the elusive 7-limit....anyone have any
> > more
> > > >info on this?
> > >
> > > I've listened to a bit of Southern-African vocal stuff and I've
> yet
> > > to hear any repeated use of 7-limit harmony.
> >
> > this was central african, if i recall correctly. just one chord.
>
> central african Pygmy polyphony, yes. Have a look at
>
> http://www-math.cudenver.edu/~jstarret/pygmies.html
>
> If this is correct, pygmy polyphonies rely on septimal interval and
> not at all on any 5 based interval. could not be more remote from
> european tradition. Those polyphonies are really extraordinary.
>
> yours truly
>
> François Laferrière

on 7/31/03 4:47 PM, Justin Weaver <improvist@usa.net> wrote:

Kurt (to Carl):
>> You heard me doing jazz improv the other day, and I think you know that I
>> have very little theory. I have essentially no jazz theory, except for tiny
>> bits that I have picked up, and I don't consciously use any theoretical
>> knowledge until I find it somehow already coming out of me anyway. So I
>> have learned, essentially by listening, with very little theory available to
>> me.
>>
>> So I guess I think theory follows practice, for the most part.
Justin:
> That's my "background" in jazz too-- no background :) -- and yet somehow I
> seem to be able to pull it off intuitively.
> I actually *agree* that theory follows practice-- before
> I was only suggesting that folk culture IS (in its essence) a more intuitively
> rational version of whatever theory says (if that). -Justin

Oh, yes, I always felt we were in agreement.

And when Paul chided you about having it reversed:

Justin:
>> Why? Because the folk tradition has rationalized the
>> theoretical tradition to make it more comprehensible.
Paul:
> you mean the theoretical tradition has rationalized the folk
> tradition to make it more comprehensible? that would seem more
> comprehensible :)

it brought up some interesting questions about uses of the words "rational"
and "comprehensible". And perhaps "comprehensive" might be clearer in a
way.

The meaning of the word "rational" it seems to me might be divided along
intellectual-political lines. Rational is commonly used to mean something
like "analytical" and those who acuse others of being irrational are often
acusing a thought process that can not be analyzed, "does not compute". And
in fact rational does seem to have its origins in computation, according to
Joseph T. Shipley, Dictionary of Word Origins:

L. ratio to calculate, to figure; hence to figure out, to reason;
whence Eng. ratio; rational;

so maybe that is even correct usage. However experience with near-just
intervals being more easily assimilable leads me to think of rational as
referring to thought process that fall together in good ratios, i.e. things
that mesh. What meshes in a culture is a different thing from what meshes
in a theoretical analysis.

So perhaps it is open to question whether folk tradition or theory
rationalizes. I would perhaps accuse "theory" of rationalizing folk
tradition, and perhaps sometimes that happens in the worst (e.g.
psychoanalytic) sense of rationalize, which as I see it involves making
rational at the expense of something like "truth". So I might agree with
Paul that it is theory that rationalizes. But you may be onto another
meaning of rationalize, which may be something that cultures do in order to
assimilate.

Theory is sometimes too skeletal and over-focused, tending toward isolating
things more than integrating them. The musician's cultural function is
partly to integrate. That which is integral is complete, comprehensive.
What has been comprehended becomes thus comprehensive, and what is
comprehensive will be more comprehensible to another with a similar
background.

from Shipley again:

comprehend, to take together, may mean to understand or to include;
the second sense is dominant in _comprehensive_

and so this is relating comprehensiveness to inclusiveness. Comprehension
likewise involves an assimilation of knowledge, which involves an inclusion
within oneself and one's structures. It is not an analytic thing.

-Kurt

>
> L. ratio to calculate, to figure; hence to figure out, to reason;
> whence Eng. ratio; rational;
>
>
> comprehend, to take together, may mean to understand or to include;
> the second sense is dominant in _comprehensive_
>

Since I wasted three years of my life getting an MA in functional linguistics, I feel
obliged to throw in here that the meaning of words can't be found in the dictionary,
since meaning is constructed through use in discourse and is indeed constantly
reconstructed. Sometimes when we hear a word used in a novel way it can tweak the
way we ourselves use the word--this is called a 'dialogic' theory of meaning. (I don't
expect that to be interesting to anyone but me, but there it is!) :) -- At any rate, I'm
sure that there are many different vectors of emergent meaning for 'rational' and
'comprehensive' in use and these will be slightly different from person to person and
different for even the same person from day to day.
-Justin

on 7/31/03 4:09 PM, Paul Erlich <perlich@aya.yale.edu> wrote:

> --- In tuning@yahoogroups.com, Kurt Bigler <kkb@b...> wrote:
>
>> It occurred to me since then that such an awareness might guide the
>> choice
>> of what notes are left out of jazz chords: perhaps those notes
>> which, if
>> left in, would do the most damage to underlying harmonic
>> sensibilities which
>> might be behind the jazz chords.
>
> hmm . . . it's usually the fifth above the bass/root which is left
> out -- leaving it in does the most damage how?

Ok, well, I'm glad I said "perhaps". Maybe I should even be so bold as to
substitute "sometimes".

For myself, I leave out the 5th because it is something like "too boring",
and detracts from the other higher-numbered ratios with its blandness. But
in any case this makes it obvious that nearness to just does not stand alone
as a criteria for jazz chord choice.

>> So this sounds to me like something that might be called "reverse
>> adaptive
>> JI", a process by which a (perhaps unconscious) conception with a
>> purely
>> harmonic aspect is mapped onto the scale at hand. Like adaptive JI
>> as I
>> understand it, the horizontal direction would be free, but since
>> the scale
>> is fixed, what is actually "free" would then be the JI "conception"
>> that is
>> guiding the improvisation/composition. So with successive chords,
>> the
>> "underlying" JI might find ways to shift so that more notes are
>> close to the
>> fixed scale, taking into account what might be improved by dropping
>> various
>> notes from a chord.
>
> hmm . . . can you give an example?

Well, ok, but to given an example I have to become more "theoretically
conscious" than I have been. So I have started to work on this, and should
get back to you sometime in the next year. ;)

Meanwhile it seems to me that what I am saying breaks down into two aspects:
(1) that the harmonic series may directly inform jazz chord choice,
including choice of which notes to include and which to omit
(2) that comma-sized or perhaps smaller shifts in the pitch of an
"underlying" harmonic series (i.e. relative to the imposed 12et) might make
different harmonics closer to 12et notes, and if so, some "adaptive" process
might "adjust" this shift in order to make different chord possibilities
available for "consideration".

So if this breakdown is correct, then which is it that you wanted an example
of?

I suspect that (1) is probably nothing new to people on this list, perhaps
all too obvious, although of course there might be subtleties to work out.

Meanwhile, preliminary theoretical investigation of (2) seems to indicate
that there is very little shifting available that helps bring alternate
harmonics closer to 12et. And chances are that most people on this list
already know this too. But I'll go ahead and continue anyway.

Using my old 12-inch slide rule, for the heck of it (something I have always
wondered about doing, and taking advantage of the fact that log10 of 2 is
almost exactly .3), I was able to make visible the relation between the
harmonic series up to 35 or so and the 12et scale. This approach had its
limitations however, and next time I'll try to learn how to use scala first.
With a fairly "strict" definition of what is "close" to 12et (which I didn't
quantify precisely, because it was a visual judgement, but roughtly speaking
I was throwing out harmonics that were 4 cents off or more), I found only 2
different harmonic series subsets that are of much interest, those being:

1 2 3 4 6 8 9 12 15 16 18 19 24 27 30 32

1 2 3 4 6 8 9 12 16 17 18 19 24 27 32 34

and these are only distinct by the inclusion of multiples of 15 versus 17,
and the shift required to bring one series versus the other very close to
12et is slightly larger than what would be needed to bring harmonic 5 (and
multiples) into the picture.

Meanwhile, looking for other subsets that would include the missing numbers
5, 7, 11, 13 had the following results. By creating the shift that allows
multiples of 5 to be included, nothing else *besides* multiples of 5 is
included. For 7, 11, and 13 there were 3 distinct but very short
close-to-12et harmonic series subsets:

7 14 21 25 28 (no surprise here except for the 25)

11 22 31? 33 35 (31 is more "off" than what I have been including)

13 26 31

These additional sequences don't offer much in the way of big chords, though
I suppose it might turn out these can be useful for sparse chords, and might
also be useful if it turns out that having *one* note a little "off" is
admissable, as a way of adding tension while preserving a sense of harmonic
structure (in a strict sense).

I tried working on a chord progression, at first entirely by ear, and then
reworked it with the help of the knowledge of the first 2 harmonic series
subsets I listed above. The final result was the following, wherein I made
the base line be the 2nd harmonic because of the octaves I wanted to play in
on the piano. The chords are situated in the first two octaves above middle
C.

base chord approximate ratios
C G/B/D/E 2:12:15:16:18
dn to F# G/B/C#/D# 2:17:21:24:27 (the 21 is "off" in 12et)
up to D A/C#/E/F 2:12:15:18:19
dn to E G#/C#/F/A 2:20:27:34:42 (20 and 42 are "off" in 12et)

The 2nd and 4th chords above have one or two tones that are not as stricly
close to 12et as all the rest, as noted above. However, the net result has
a surprising amount of consonance (though my piano needs a tune, so I hope
this is accurate), and perhaps the consonance even worked well with the
exceptional dissonant tones, in that the beating pattern itself you could
say was fairly consonant, i.e. had some complexity but not too much. In any
case the knowledge of the harmonic series clearly helped me become conscious
of more possible choices that might work, which I had somehow missed based
on the knowledge already "in my hand" (and ears). (There's a case of theory
feeding into practice.)

In trying to make some sense out of the choices I was making in order to
"compose" this short progression, I came up with the following:

try to have a lot of fairly exact ratios
but avoid octaves and fifths
avoid minor 2nds by relocating one of the notes by an octave
prefer more motion in chord notes over less
(not necessarily further movements, but more notes moving)
allow in one or two inexact ratios in order to create tension

Curious, this experience gives me the impression that in a certain jazz
aesthetic, what functions as "resolution" actually involves more tension,
i.e. transitional chords should be milder, and final chords of a phrase
should be more dissonant. If my memory serves me this is a fairly common
pattern.

So that's my research so far. And this process has consumed me for an
entire day (actually it is 25 hours since I started), so I need to give it a
break!

-Kurt

on 8/1/03 4:41 PM, Justin Weaver <improvist@usa.net> wrote:

>
>>
>> L. ratio to calculate, to figure; hence to figure out, to reason;
>> whence Eng. ratio; rational;
>>
>>
>> comprehend, to take together, may mean to understand or to include;
>> the second sense is dominant in _comprehensive_
>>
>
> Since I wasted three years of my life getting an MA in functional linguistics,
> I feel
> obliged to throw in here that the meaning of words can't be found in the
> dictionary,
> since meaning is constructed through use in discourse and is indeed constantly
> reconstructed. Sometimes when we hear a word used in a novel way it can tweak
> the
> way we ourselves use the word--this is called a 'dialogic' theory of meaning.
> (I don't
> expect that to be interesting to anyone but me, but there it is!) :) -- At any
> rate, I'm
> sure that there are many different vectors of emergent meaning for 'rational'
> and
> 'comprehensive' in use and these will be slightly different from person to
> person and
> different for even the same person from day to day.
> -Justin

Yes, yes, that's the way I love it! (Apologies for continuing off-topic.)

Part of the process is also an "archaelogical" one: digging for depth of
meaning that may have been lost in "modern" usage. In this regard I think
Shipley is more useful than most dictionary etymologies. However, I take
pleasure and a sense of responsibility for the reformation of meanings, so
that language can be enriched rather than flattenned. (Not unlike what is
going on in relation to music on this list.) Reference to the past is one
resource in this process, as we all know.

-Kurt

--- In tuning@yahoogroups.com, Kurt Bigler <kkb@b...> wrote:

> Well, ok, but to given an example I have to become
more "theoretically
> conscious" than I have been. So I have started to work on this,
and should
> get back to you sometime in the next year. ;)
>
> Meanwhile it seems to me that what I am saying breaks down into two
aspects:
> (1) that the harmonic series may directly inform jazz chord choice,
> including choice of which notes to include and which to omit
> (2) that comma-sized or perhaps smaller shifts in the pitch of an
> "underlying" harmonic series (i.e. relative to the imposed 12et)
might make
> different harmonics closer to 12et notes, and if so,
some "adaptive" process
> might "adjust" this shift in order to make different chord
possibilities
> available for "consideration".
>
> So if this breakdown is correct, then which is it that you wanted
an example
> of?

both, but the second in particular, since it seems more difficult to
understand without examples.

>In any
> case the knowledge of the harmonic series clearly helped me become
conscious
> of more possible choices that might work, which I had somehow
missed based
> on the knowledge already "in my hand" (and ears). (There's a case
of theory
> feeding into practice.)

hey, that's terrific! any way to add to what's in your hands and ears
will make you a better musician . . .

>
> In trying to make some sense out of the choices I was making in
order to
> "compose" this short progression, I came up with the following:
>
> try to have a lot of fairly exact ratios
> but avoid octaves and fifths
> avoid minor 2nds by relocating one of the notes by an octave

in jazz, many of the minor 2nds that occur in various chords (that
between the root and b9 would be an exception) are voiced typically
as minor 2nds, or as major 7ths, but not as minor 9ths. in fact, you
can often imply the whole chord with a single minor 2nd, a favorite
trick of john scofield and thelonious monk. typical examples would be
the dom13th chord (6 and b7) and the 7#9 chord (#2 and 3).

> prefer more motion in chord notes over less
> (not necessarily further movements, but more notes moving)
> allow in one or two inexact ratios in order to create tension
>
> Curious, this experience gives me the impression that in a certain
jazz
> aesthetic, what functions as "resolution" actually involves more
tension,
> i.e. transitional chords should be milder, and final chords of a
phrase
> should be more dissonant. If my memory serves me this is a fairly
common
> pattern.

doesn't sound right to me at all. any examples you can come up with?

> So that's my research so far. And this process has consumed me for
an
> entire day (actually it is 25 hours since I started), so I need to
give it a
> break!

well, it sounds like this is feeding into your own musical
development, and even if (or especially if) you're following your ear
rather than any particular musical tradition, this is valuable effort!

on 8/2/03 11:52 AM, Paul Erlich <perlich@aya.yale.edu> wrote:

>> prefer more motion in chord notes over less
>> (not necessarily further movements, but more notes moving)
>> allow in one or two inexact ratios in order to create tension
>>
>> Curious, this experience gives me the impression that in a certain
> jazz
>> aesthetic, what functions as "resolution" actually involves more
> tension,
>> i.e. transitional chords should be milder, and final chords of a
> phrase
>> should be more dissonant. If my memory serves me this is a fairly
> common
>> pattern.
>
> doesn't sound right to me at all. any examples you can come up with?

The progression I gave is a very clear example of what I mean, and I think
it should sound a little familiar. No? Though I played it on the piano I
was thinking in terms of alto/soprano jazz vocals. Maybe if you play it and
think that way you will realize the kind of stuff I am referring to. I
certainly can't tell you what particular music it reminds me of, although I
suspect it might have come from easy-listening jazz stations 20-some years
ago. Mind you it was stuff I never particularly liked, but my appreciation
is now growing.

-Kurt

on 8/2/03 11:52 AM, Paul Erlich <perlich@aya.yale.edu> wrote:

> --- In tuning@yahoogroups.com, Kurt Bigler <kkb@b...> wrote:
>
>> Well, ok, but to given an example I have to become
> more "theoretically
>> conscious" than I have been. So I have started to work on this,
> and should
>> get back to you sometime in the next year. ;)
>>
>> Meanwhile it seems to me that what I am saying breaks down into two
> aspects:
>> (1) that the harmonic series may directly inform jazz chord choice,
>> including choice of which notes to include and which to omit
>> (2) that comma-sized or perhaps smaller shifts in the pitch of an
>> "underlying" harmonic series (i.e. relative to the imposed 12et)
> might make
>> different harmonics closer to 12et notes, and if so,
> some "adaptive" process
>> might "adjust" this shift in order to make different chord
> possibilities
>> available for "consideration".
>>
>> So if this breakdown is correct, then which is it that you wanted
> an example
>> of?
>
> both, but the second in particular, since it seems more difficult to
> understand without examples.

But based on the other stuff I wrote, you know what I am referring to now,
right? The problem is that (as I said) such relative motion may not have
much chance of actually existing. The fact that the mind would take
advantage of that degree of freedom would turn out to be rather unimportant
if the degree of freedom wasn't really there. That is, so much of the
harmonic series overlays 12et at approximately a single "offset", as I
showed in the numbers, and as presumably (I'm assuming) you already know.

I was hoping for a little more input in this regard. So actual musical
examples aside, if you aren't getting what I'm looking for, please let me
know so I can clarify it.

-Kurt

--- In tuning@yahoogroups.com, Kurt Bigler <kkb@b...> wrote:
> on 8/2/03 11:52 AM, Paul Erlich <perlich@a...> wrote:
>
> > --- In tuning@yahoogroups.com, Kurt Bigler <kkb@b...> wrote:
> >
> >> Well, ok, but to given an example I have to become
> > more "theoretically
> >> conscious" than I have been. So I have started to work on this,
> > and should
> >> get back to you sometime in the next year. ;)
> >>
> >> Meanwhile it seems to me that what I am saying breaks down into
two
> > aspects:
> >> (1) that the harmonic series may directly inform jazz chord
choice,
> >> including choice of which notes to include and which to omit
> >> (2) that comma-sized or perhaps smaller shifts in the pitch of an
> >> "underlying" harmonic series (i.e. relative to the imposed 12et)
> > might make
> >> different harmonics closer to 12et notes, and if so,
> > some "adaptive" process
> >> might "adjust" this shift in order to make different chord
> > possibilities
> >> available for "consideration".
> >>
> >> So if this breakdown is correct, then which is it that you wanted
> > an example
> >> of?
> >
> > both, but the second in particular, since it seems more difficult
to
> > understand without examples.
>
> But based on the other stuff I wrote, you know what I am referring
to now,
> right?

i think so -- i think it could be explained equivalently, and perhaps
more clearly, by simply saying that you're trying to match a harmonic
series in the measurements of *all* the intervals in the chord, not
merely the intervals from the fundamental. i naturally think this way
anyhow, so what you did seems quite natural to me (except
quantitatively, for example how can both of the notes in 2:15 be less
than 4 cents off if 15/8 is 1088? you probably meant 6 cents or
something . . . and don't forget that the piano's overtones are
noticeably stretched relative to the natural harmonic series, so that
an "equal-tempered" major third expanded by enough octaves actually
becomes beatless . . .)

> The problem is that (as I said) such relative motion may not have
> much chance of actually existing.

well, perhaps there's more leeway than you think when it comes to
approximating a harmonic series and projecting a fundamental? that
avenue at least seems worth considering given that the inharmonicity
of the piano makes "just intonation" a bit of a will-o-wisp on that
instrument anyway. can you hear a m9b5 chord as a "cloudy"
5:6:7:9:11, for example?

on 8/3/03 9:58 AM, Paul Erlich <perlich@aya.yale.edu> wrote:

> --- In tuning@yahoogroups.com, Kurt Bigler <kkb@b...> wrote:
>> on 8/2/03 11:52 AM, Paul Erlich <perlich@a...> wrote:
>>
>>> --- In tuning@yahoogroups.com, Kurt Bigler <kkb@b...> wrote:
>>>
>>>> Well, ok, but to given an example I have to become
>>> more "theoretically
>>>> conscious" than I have been. So I have started to work on this,
>>> and should
>>>> get back to you sometime in the next year. ;)
>>>>
>>>> Meanwhile it seems to me that what I am saying breaks down into
> two
>>> aspects:
>>>> (1) that the harmonic series may directly inform jazz chord
> choice,
>>>> including choice of which notes to include and which to omit
>>>> (2) that comma-sized or perhaps smaller shifts in the pitch of an
>>>> "underlying" harmonic series (i.e. relative to the imposed 12et)
>>> might make
>>>> different harmonics closer to 12et notes, and if so,
>>> some "adaptive" process
>>>> might "adjust" this shift in order to make different chord
>>> possibilities
>>>> available for "consideration".
>>>>
>>>> So if this breakdown is correct, then which is it that you wanted
>>> an example
>>>> of?
>>>
>>> both, but the second in particular, since it seems more difficult
> to
>>> understand without examples.
>>
>> But based on the other stuff I wrote, you know what I am referring
> to now,
>> right?
>
> i think so -- i think it could be explained equivalently, and perhaps
> more clearly, by simply saying that you're trying to match a harmonic
> series in the measurements of *all* the intervals in the chord,

Not quite, but effect yes. I was not measuring the chord intervals
directly, but instead measuring the chord "pitches". Yes the entire chord
is free to slide together as a unit, so although I mean pitches rather than
intervals, pitch is really the wrong word because I mean something that is
relative. The error in an intervals will be the sum of the two errors in
the two "pitches" involved.

So maybe I had not framed this in the clearest way, admittedly. The slide
rule analogy is the best way to describe what I was *thinking*. The fixed
rule represents the fixed scale of the instrument, 12et in this case. The
moving scale represents the harmonic series. The chord "finding" process
involves sliding the moving scale relative to the fixed scale and finding
the strengths/weaknesses of any given placement.

> not
> merely the intervals from the fundamental. i naturally think this way
> anyhow, so what you did seems quite natural to me (except
> quantitatively, for example how can both of the notes in 2:15 be less
> than 4 cents off if 15/8 is 1088? you probably meant 6 cents or
> something

Yes, in your terms I realize now it would have been 8 cents as an
upperbound. And so to analyze intervals per-se I was not really analyzing
the right thing. Thanks for the clarification - I will have to rethink.

> . . . and don't forget that the piano's overtones are
> noticeably stretched relative to the natural harmonic series, so that
> an "equal-tempered" major third expanded by enough octaves actually
> becomes beatless . . .)

I better try the whole thing over on the organ. For some reason I was
preferring the piano, but your point makes me realize it was the wrong
choice for this kind of discrimination. Of course in reality it is a valid
choice, but the analysis would have to be much more complex, and probably
not the best place to start.

>> The problem is that (as I said) such relative motion may not have
>> much chance of actually existing.
>
> well, perhaps there's more leeway than you think when it comes to
> approximating a harmonic series and projecting a fundamental? that
> avenue at least seems worth considering given that the inharmonicity
> of the piano makes "just intonation" a bit of a will-o-wisp on that
> instrument anyway. can you hear a m9b5 chord as a "cloudy"
> 5:6:7:9:11, for example?

I'll get back to you on this. Thanks.

-Kurt

--- In tuning@yahoogroups.com, Kurt Bigler <kkb@b...> wrote:
> on 8/3/03 9:58 AM, Paul Erlich <perlich@a...> wrote:
>
> > --- In tuning@yahoogroups.com, Kurt Bigler <kkb@b...> wrote:
> >> on 8/2/03 11:52 AM, Paul Erlich <perlich@a...> wrote:
> >>
> >>> --- In tuning@yahoogroups.com, Kurt Bigler <kkb@b...> wrote:
> >>>
> >>>> Well, ok, but to given an example I have to become
> >>> more "theoretically
> >>>> conscious" than I have been. So I have started to work on
this,
> >>> and should
> >>>> get back to you sometime in the next year. ;)
> >>>>
> >>>> Meanwhile it seems to me that what I am saying breaks down into
> > two
> >>> aspects:
> >>>> (1) that the harmonic series may directly inform jazz chord
> > choice,
> >>>> including choice of which notes to include and which to omit
> >>>> (2) that comma-sized or perhaps smaller shifts in the pitch of
an
> >>>> "underlying" harmonic series (i.e. relative to the imposed
12et)
> >>> might make
> >>>> different harmonics closer to 12et notes, and if so,
> >>> some "adaptive" process
> >>>> might "adjust" this shift in order to make different chord
> >>> possibilities
> >>>> available for "consideration".
> >>>>
> >>>> So if this breakdown is correct, then which is it that you
wanted
> >>> an example
> >>>> of?
> >>>
> >>> both, but the second in particular, since it seems more
difficult
> > to
> >>> understand without examples.
> >>
> >> But based on the other stuff I wrote, you know what I am
referring
> > to now,
> >> right?
> >
> > i think so -- i think it could be explained equivalently, and
perhaps
> > more clearly, by simply saying that you're trying to match a
harmonic
> > series in the measurements of *all* the intervals in the chord,
>
> Not quite, but effect yes.

in effect yes? that's what i meant.

> So maybe I had not framed this in the clearest way, admittedly. The
slide
> rule analogy is the best way to describe what I was *thinking*. The
fixed
> rule represents the fixed scale of the instrument, 12et in this
case. The
> moving scale represents the harmonic series. The chord "finding"
process
> involves sliding the moving scale relative to the fixed scale and
finding
> the strengths/weaknesses of any given placement.

not inconsistent with an interval-based philosophy, which is what i
typically follow and what seems to be the norm on the tuning-math
list.