re: defining just intonation

Just a few points,

o In my view, Dave has not demonstrated a need for such a precise
definition of a common term as he has attempted.

o Dave's definition of just scale is too strong, omitting scales where
only one pitch is not connected. Such examples point out the arbitrary
nature of such conditions -- changing the number of allowed un-connected
pitches causes only a smooth change it the properties of the tuning.

o One of Dave's central arguments that the current definition is
insufficient is the Hammond argument. But by his definition, too, the
Hammond organ is a just instrument.

o It seems obvious to me that there is already in common use both a
general and special definition for the term just intonation:

general - Any system of tuning which organizes sounds in such a
way that a human auditory system construes them, to some extent,
but not completely, as components of a single timbre. This is
usually done by appealing to one or both of the two known methods
of pitch resolution used by the auditory system: periodicity and
place.

This covers music like Mozart's, which uses a tempered scale but which
is clearly meant to imply just intonation in the sense above.

special - Any system of tuning which organizes pitches in such a
way that a human auditory system construes them, to a great extent,
as components of a single timbre, such that better fusion is
practically impossible given the pitches used... such that any
change in the intonation, greater than some slight and precise
amount, results in a noticable weakening of the fusion, even when
randomly applied.

This covers "just intonation", as it is used to distinguish between
pure JI, and general JI under temperament.

These definitions work in terms of a given listener, as they should.
The Hammond organ is an instrument capable of general, and probably of
special (although it is possible that, due to periodicity effects and
despite some beating, tuning a Hammond patch to small ratios would
result in greater fusion for some listeners) JI by these definitions.

-Carl

Carl wrote,

>o Dave's definition of just scale is too strong, omitting scales where
>only one pitch is not connected. Such examples point out the arbitrary
>nature of such conditions -- changing the number of allowed un-connected
>pitches causes only a smooth change it the properties of the tuning.

>o One of Dave's central arguments that the current definition is
>insufficient is the Hammond argument. But by his definition, too, the
>Hammond organ is a just instrument.

Whoa! In the Hammond tuning, _none_ of the pitches are connected to _any
others_! So it certainly seems that Dave would classify that as a non-just
tuning.

> general - Any system of tuning which organizes sounds in such a
> way that a human auditory system construes them, to some extent,
> but not completely, as components of a single timbre.

>This covers music like Mozart's, which uses a tempered scale but which
>is clearly meant to imply just intonation in the sense above.

This would be highly at odds with any use of the term JI in the literature,
since it would include all the usual tempered scales before it would include
utonal JI constructs.

> special - Any system of tuning which organizes pitches in such a
> way that a human auditory system construes them, to a great extent,
> as components of a single timbre, such that better fusion is
> practically impossible given the pitches used... such that any
> change in the intonation, greater than some slight and precise
> amount, results in a noticable weakening of the fusion, even when
> randomly applied.

Again, utonalities are JI constructs which couldn't be further from being
perceived as a single timbre, though beating between partials can be used to
tune them to great accuracy.

>The Hammond organ is an instrument capable of general, and probably of
>special (although it is possible that, due to periodicity effects and
>despite some beating, tuning a Hammond patch to small ratios would
>result in greater fusion for some listeners) JI by these definitions.

I don't understand the "probably of special" and "despite some beating"
part, but clearly your general definition of JI don't allow it to be
contrasted against all the things it's traditionally been contrasted
against. In particular, Mozart _doesn't_ work in JI, as normally understood.

On Thu, 07 Dec 2000 11:23:21 -0500, Carl Lumma <CLUMMA@NNI.COM> wrote:

>Just a few points,
>
>o In my view, Dave has not demonstrated a need for such a precise
>definition of a common term as he has attempted.

The problem is that tuning by integer ratios is a necessary but not
sufficient condition for just intonation.

>o Dave's definition of just scale is too strong, omitting scales where
>only one pitch is not connected. Such examples point out the arbitrary
>nature of such conditions -- changing the number of allowed un-connected
>pitches causes only a smooth change it the properties of the tuning.

Why would it be desirable to describe scales with unconnected pitches as
just scales? Quarter-comma meantone consists of a set of chains of just
major thirds that are unconnected from each other, yet it's not ordinarily
described as a just scale.

>o One of Dave's central arguments that the current definition is
>insufficient is the Hammond argument. But by his definition, too, the
>Hammond organ is a just instrument.

More precisely, the Hammond organ scale is "justly intoned for the Hammond
organ timbre". I think this is really a separate definition, not connected
with his definition of "just" per se, but it can be confusing because it
looks like it's part of the main definition.

The Hammond organ scale is a realistic illustration of the fact that, if
all rational scales are described as just, then all possible scales are
just for all practical purposes, and the word loses its meaning in all but
an abstract mathematical sense. In the extreme case, *any* scale can be
approximated so nearly by a rational scale that the lifetime of the
universe would be too short to detect any mistuning.

--
see my music page ---> ---<http://www.io.com/~hmiller/music/music.html>--
hmiller (Herman Miller) "If all Printers were determin'd not to print any
@io.com email password: thing till they were sure it would offend no body,
\ "Subject: teamouse" / there would be very little printed." -Ben Franklin

Herman Miller wrote,

>More precisely, the Hammond organ scale is "justly intoned for the Hammond
>organ timbre".

Not quite -- the "partials" of the Hammond "timbre" which have the
near-12-tET relationships of the Hammond tuning are not pure sine waves;
hence they will have some measure of the ordinary integer partials.

Besides, I think (I guess I'm back in this debate now) that the
Sethares-style matching of tuning to timbre shouldn't be considered JI (due
in part to factors like combination tones and virtual pitch); as you
yourself state:

>tuning by integer ratios is a necessary . . . condition for just
intonation.

--- In tuning@egroups.com, "Paul H. Erlich" <PERLICH@A...> wrote:

http://www.egroups.com/message/tuning/16339

> I don't understand the "probably of special" and "despite some
beating" part, but clearly your general definition of JI don't allow
it to be contrasted against all the things it's traditionally been
contrasted against. In particular, Mozart _doesn't_ work in JI, as
normally understood.

This seemed mighty peculiar to me, as well. Have you been resting
well, Carl??
_________ ___ __ _
Joseph Pehrson

>>o One of Dave's central arguments that the current definition is
>>insufficient is the Hammond argument. But by his definition, too, the
>>Hammond organ is a just instrument.
>
>Whoa! In the Hammond tuning, _none_ of the pitches are connected to _any
>others_! So it certainly seems that Dave would classify that as a non-just
>tuning.

I wasn't using Dave's definition of a just _scale_ here, but of a just
intonation. You were quoting across o's. I refer you to his Descriptive
and Injunctive definitions...

http://www.egroups.com/message/tuning/16287

>> general - Any system of tuning which organizes sounds in such a
>> way that a human auditory system construes them, to some extent,
>> but not completely, as components of a single timbre.
>>
>>This covers music like Mozart's, which uses a tempered scale but which
>>is clearly meant to imply just intonation in the sense above.
>
>This would be highly at odds with any use of the term JI in the literature,
>since it would include all the usual tempered scales before it would include
>utonal JI constructs.

It is my contention that the fusion I describe can be achieved not only
by appealing to the periodicity mechanism, but also the place mechanism.
Therefore, utonal constructs are included in the general definition. It
sounds like most of the uses of the term JI in the "literature" that you
mention are of the special type.

>> special - Any system of tuning which organizes pitches in such a
>> way that a human auditory system construes them, to a great extent,
>> as components of a single timbre, such that better fusion is
>> practically impossible given the pitches used... such that any
>> change in the intonation, greater than some slight and precise
>> amount, results in a noticable weakening of the fusion, even when
>> randomly applied.
>
>Again, utonalities are JI constructs which couldn't be further from being
>perceived as a single timbre, though beating between partials can be used to
>tune them to great accuracy.

Again, I disagree that utonal constructs don't fuse.

>>The Hammond organ is an instrument capable of general, and probably of
>>special (although it is possible that, due to periodicity effects and
>>despite some beating, tuning a Hammond patch to small ratios would
>>result in greater fusion for some listeners) JI by these definitions.
>
>I don't understand the "probably of special" and "despite some beating"
>part,

Tuning a Hammond patch to small integer ratios will result in more beating
than tuning them to 12-tET, but greater fusion by periodicity effects, at
least for higher-limit constructs which are approximated poorly in 12-tET.

>but clearly your general definition of JI don't allow it to be contrasted
>against all the things it's traditionally been contrasted against. In
>particular, Mozart _doesn't_ work in JI, as normally understood.

Let's not mix up definitions. When you say doesn't work in JI, you mean
a just _scale_. You have many times defended common practice music as
_approximating JI_. Well, approximating JI is what the general definition
is all about, and that is the definition to which this example clearly
referred.

-Carl

>>>o One of Dave's central arguments that the current definition is
>>>insufficient is the Hammond argument. But by his definition, too, the
>>>Hammond organ is a just instrument.
>>
>>Whoa! In the Hammond tuning, _none_ of the pitches are connected to _any
>>others_! So it certainly seems that Dave would classify that as a non-just
>>tuning.
>
>I wasn't using Dave's definition of a just _scale_ here, but of a just
>intonation. You were quoting across o's. I refer you to his Descriptive
>and Injunctive definitions...
>
>http://www.egroups.com/message/tuning/16287

...and even so, since Dave's definition of scale depends on his definition
of intervals, and all the perfect octaves and fifths on a Hamond organ
are just according to Dave, all the pitches on the organ _are_ connected.

-Carl

I wrote,

>>Whoa! In the Hammond tuning, _none_ of the pitches are connected to _any
>>others_! So it certainly seems that Dave would classify that as a non-just
>>tuning.

Carl wrote,

>I wasn't using Dave's definition of a just _scale_ here, but of a just
>intonation. You were quoting across o's. I refer you to his Descriptive
>and Injunctive definitions...

>http://www.egroups.com/message/tuning/16287

Still not seeing it . . . in his definition of a just intonation, Dave K
says,

>Just intonation is accuracy of one pitch in relation to another pitch, such
>that the resulting interval sounds harmonically pure; perfectly in tune;
>without beating. Such an interval is called a "just interval", "justly
>intoned interval", "JI interval" or "pure interval".

Especially if all the Hammond tone bars are on zero, I see no way of
justifying your claim.

>>> general - Any system of tuning which organizes sounds in such a
>>> way that a human auditory system construes them, to some extent,
>>> but not completely, as components of a single timbre.

>It is my contention that the fusion I describe can be achieved not only
>by appealing to the periodicity mechanism, but also the place mechanism.

Don't see how the mechanism matters . . . clearly the importance of the
place mechanism is incontrovertible.

Therefore, utonal constructs are included in the general definition.

Wha? I don't get it. A single timbre? Wouldn't _anything_ then qualify as a
single timbre?

>>> special - Any system of tuning which organizes pitches in such a
>>> way that a human auditory system construes them, to a great extent,
>>> as components of a single timbre, such that better fusion is
>>> practically impossible given the pitches used... such that any
>>> change in the intonation, greater than some slight and precise
>>> amount, results in a noticable weakening of the fusion, even when
>>> randomly applied.
>

>>Again, utonalities are JI constructs which couldn't be further from being
>>perceived as a single timbre, though beating between partials can be used
to
>>tune them to great accuracy.

>Again, I disagree that utonal constructs don't fuse.

I bet I could find a plethora of non-just chords that fuse into a single
timbre much better than an 11-limit, or even 9-limit, utonality. Observe the
rating that Joseph Pehrson, David Finnamore, and others have the 7-limit
utonality in our tetrad examples -- and that was in a context of
"consonance", which if anything should be more forgiving for utonalities
than a criterion of "fusing into a single timbre".

>Tuning a Hammond patch to small integer ratios will result in more beating
>than tuning them to 12-tET

Depends on the timbre you dial in with the tonebars, plus you've normally
got vibrato as well as Leslie effects to obscure any beating anyway . . .
but point taken. However, I agree with part of Herman Miller when he says
that integer ratios [representing themselves and not simpler integer
ratios], should be a necessary condition for calling something JI -- the
inharmonic case needs a different definition altogether. Tuning a piano to
JI is understood to mean (by La Monte Young and others) that you will get a
lot of beating due to the inharmonicity of the partials. La Monte uses the
longest-scale piano possible to minimize that inharmonicity, but the beating
is still there, and yet it's JI . . . right?

>but greater fusion by periodicity effects

It's not at all well established that the virtual pitch sensation, which
accounts for the perception of timbre with a single pitch (i.e., what you're
calling "fusion", I gather) is a result of periodicity effects. Terhardt and
Parncutt clearly feel that it is not.

>Let's not mix up definitions. When you say doesn't work in JI, you mean
>a just _scale_. You have many times defended common practice music as
>_approximating JI_.

Harmonically, yes. Melodically, no.

>Well, approximating JI is what the general definition
>is all about, and that is the definition to which this example clearly
>referred.

Uh . . . I'm getting a headache . . . more later . . .

Carl wrote,

>...and even so, since Dave's definition of scale depends on his definition
>of intervals, and all the perfect octaves and fifths on a Hamond organ
>are just according to Dave, all the pitches on the organ _are_ connected.

You must be misunderstanding something, since this would imply that 12-tET
is just intonation according to Dave, which it isn't. He may have used
something as large as a 0.5-cent tolerance for the connecting intervals in
one definition of JI at one point, but 12-tET has 2 cent errors in the
fifths . . . or is this a Setharian thing you're referring to?

>>I wasn't using Dave's definition of a just _scale_ here, but of a just
>>intonation. You were quoting across o's. I refer you to his Descriptive
>>and Injunctive definitions...
>>
>>http://www.egroups.com/message/tuning/16287
>
>Still not seeing it . . .

Try a find on the page for "injunctive".

>>Just intonation is accuracy of one pitch in relation to another pitch,
>>such that the resulting interval sounds harmonically pure; perfectly in
>>tune; without beating. Such an interval is called a "just interval",
>>"justly intoned interval", "JI interval" or "pure interval".
>
>Especially if all the Hammond tone bars are on zero, I see no way of
>justifying your claim.

Hammond intervals approximating the 5-limit are beatless, or at least
smoother than they would be with their "fundamentals" tuned to exact
5-limit ratios (ignoring Leslie and so forth).

>>It is my contention that the fusion I describe can be achieved not only
>>by appealing to the periodicity mechanism, but also the place mechanism.
>
>Don't see how the mechanism matters . . . clearly the importance of the
>place mechanism is incontrovertible.

It matters because it has to do with pitch discrimination, and it works
on a partial-matching principle, thus implicating utonal chords, which
you said my definition didn't include.

>Therefore, utonal constructs are included in the general definition.
>
>Wha? I don't get it. A single timbre? Wouldn't _anything_ then qualify as
>a single timbre?

Stimuli which are rough, beating, or have painfully ambiguous roots do not
tend to sound fused, as a single timbre.

>I bet I could find a plethora of non-just chords that fuse into a single
>timbre much better than an 11-limit, or even 9-limit, utonality. Observe
>the rating that Joseph Pehrson, David Finnamore, and others have the
>7-limit utonality in our tetrad examples -- and that was in a context of
>"consonance", which if anything should be more forgiving for utonalities
>than a criterion of "fusing into a single timbre".

I'm not sure I follow. How is the 7-limit utonality an example of a non-
just chord? Anyhow, this appears to be chicken and egg -- I'm claiming
that if it fuses in the way I describe, then it's just, so a non-just,
fusing chord is a misnomer.

>However, I agree with part of Herman Miller when he says that integer
>ratios [representing themselves and not simpler integer ratios], should be
>a necessary condition for calling something JI -- the inharmonic case needs
>a different definition altogether.

Okay. In that case, we'll need something different. So far, though, I've
worked hard to avoid integer ratios for the following reasons:

o Dave didn't want 'em.

o You wind up having to say something about timbre anyway, since not
every timbre produces an affect normally associated with JI when tuned to
integer ratios.

o As Dave points out, we need to specify "small" when using integer ratios
here. But the problem of how to define small is not yet worked out.

>Tuning a piano to JI is understood to mean (by La Monte Young and others)
>that you will get a lot of beating due to the inharmonicity of the partials.
>La Monte uses the longest-scale piano possible to minimize that
>inharmonicity, but the beating is still there, and yet it's JI . . . right?

Well, let's see:

o General - You bet.

o Special - Yep (notice the bit, 'such that better fusion is practically
impossible with the given tones'). [I said "pitches" there, but should have
said "tones".]

>>but greater fusion by periodicity effects
>
>It's not at all well established that the virtual pitch sensation, which
>accounts for the perception of timbre with a single pitch (i.e., what
>you're calling "fusion", I gather) is a result of periodicity effects.
>Terhardt and Parncutt clearly feel that it is not.

By "fusion", I simply mean the subjective experience of blend. But that's
interesting.

>>Let's not mix up definitions. When you say doesn't work in JI, you mean
>>a just _scale_. You have many times defended common practice music as
>>_approximating JI_.
>
>Harmonically, yes. Melodically, no.

I refer you to my earlier posts in this thread, where I argue against
a melodic definition of JI, and refuse to contribute to it. Thus,
everything in these posts has been either about harmonic JI, or about
Dave's definition of melodic JI.

>>...and even so, since Dave's definition of scale depends on his definition
>>of intervals, and all the perfect octaves and fifths on a Hamond organ
>>are just according to Dave, all the pitches on the organ _are_ connected.
>
>You must be misunderstanding something, since this would imply that 12-tET
>is just intonation according to Dave, which it isn't.

That's my point. His definition does not meet his own requirements.

>or is this a Setharian thing you're referring to?

I think so.

-Carl

Carl Lumma wrote,

>Stimuli which are rough, beating, or have painfully ambiguous roots do not
>tend to sound fused, as a single timbre.

Utonal chords have painfully ambiguous roots. I disagree with the other part
-- a 16:17:18:19 chord can sound very rough _and_ beating and yet sound much
more like a single timbre than a smooth utonal chord.

>>I bet I could find a plethora of non-just chords that fuse into a single
>>timbre much better than an 11-limit, or even 9-limit, utonality. Observe
>>the rating that Joseph Pehrson, David Finnamore, and others have the
>>7-limit utonality in our tetrad examples -- and that was in a context of
>>"consonance", which if anything should be more forgiving for utonalities
>>than a criterion of "fusing into a single timbre".

>I'm not sure I follow. How is the 7-limit utonality an example of a non-
>just chord?

It's a just chord!

>By "fusion", I simply mean the subjective experience of blend.

Well, you specifically brought up timbre, which would imply the virtual
pitch mechanism.

>>>Let's not mix up definitions. When you say doesn't work in JI, you mean
>>>a just _scale_. You have many times defended common practice music as
>>>_approximating JI_.
>
>>Harmonically, yes. Melodically, no.

>I refer you to my earlier posts in this thread, where I argue against
>a melodic definition of JI, and refuse to contribute to it. Thus,
>everything in these posts has been either about harmonic JI, or about
>Dave's definition of melodic JI.

uhh . . . if you're saying that the definition of JI shouldn't be applicable
to melody at all, then I'm afraid you're going to alienate a great many
self-professed JI composers . . . take a look at Blackwood's book for a
nice, authoritative usage of the term just intonation and then tell me
Mozart is in JI.

[Herman Miller wrote...]
>>o Dave's definition of just scale is too strong, omitting scales where
>>only one pitch is not connected. Such examples point out the arbitrary
>>nature of such conditions -- changing the number of allowed un-connected
>>pitches causes only a smooth change it the properties of the tuning.
>
>Why would it be desirable to describe scales with unconnected pitches as
>just scales?

Why should one note disqualify an otherwise connected scale? But to
answer your question, I can think of many instances where I have wanted
a few just chords, rooted at irrational intervals, to minimize the
shift of near-common tones (including several spots in my _Retrofit_).

[Paul Erlich wrote...]
>>Stimuli which are rough, beating, or have painfully ambiguous roots do not
>>tend to sound fused, as a single timbre.
>
>Utonal chords have painfully ambiguous roots.

That depends on the utonal chord, but many of them do, yes.

>I disagree with the other part -- a 16:17:18:19 chord can sound very
>rough _and_ beating and yet sound much more like a single timbre than
>a smooth utonal chord.

I have never experienced such a phenomenon.

>>>I bet I could find a plethora of non-just chords that fuse into a single
>>>timbre much better than an 11-limit, or even 9-limit, utonality. Observe
>>>the rating that Joseph Pehrson, David Finnamore, and others have the
>>>7-limit utonality in our tetrad examples -- and that was in a context of
>>>"consonance", which if anything should be more forgiving for utonalities
>>>than a criterion of "fusing into a single timbre".
>
>>I'm not sure I follow. How is the 7-limit utonality an example of a non-
>>just chord?
>
>It's a just chord!

Read your first sentence again.

>>By "fusion", I simply mean the subjective experience of blend.
>
>Well, you specifically brought up timbre, which would imply the virtual
>pitch mechanism.

Definitely.

>>I refer you to my earlier posts in this thread, where I argue against
>>a melodic definition of JI, and refuse to contribute to it. Thus,
>>everything in these posts has been either about harmonic JI, or about
>>Dave's definition of melodic JI.
>
>uhh . . . if you're saying that the definition of JI shouldn't be
>applicable to melody at all, then I'm afraid you're going to alienate a
>great many self-professed JI composers . . .

That I attempt a harmonic definition of JI alienates nothing.

>take a look at Blackwood's book for a nice, authoritative usage of the
>term just intonation and then tell me Mozart is in JI.

Looking at Blackwood's book means a trip to Manhattan, for me. I don't
have to tell you that Mozart's harmonies approximate JI -- you've said
it yourself.

-Carl

>>I disagree with the other part -- a 16:17:18:19 chord can sound very
>>rough _and_ beating and yet sound much more like a single timbre than
>>a smooth utonal chord.

>I have never experienced such a phenomenon.

Try it!

>>>>I bet I could find a plethora of non-just chords that fuse into a single
>>>>timbre much better than an 11-limit, or even 9-limit, utonality. Observe
>>>>the rating that Joseph Pehrson, David Finnamore, and others have the
>>>>7-limit utonality in our tetrad examples -- and that was in a context of
>>>>"consonance", which if anything should be more forgiving for utonalities
>>>>than a criterion of "fusing into a single timbre".
>
>>>I'm not sure I follow. How is the 7-limit utonality an example of a non-
>>>just chord?
>
>>It's a just chord!

>Read your first sentence again.

I don't see a problem with my first sentence.

>>take a look at Blackwood's book for a nice, authoritative usage of the
>>term just intonation and then tell me Mozart is in JI.

>Looking at Blackwood's book means a trip to Manhattan, for me. I don't
>have to tell you that Mozart's harmonies approximate JI -- you've said
>it yourself.

Well, the point is that a good definition of JI should both account for what
JI _is_ and what it is _not_ -- and part of that entails drawing out the
harmonic definition so that it has melodic implications as well.

>>>I disagree with the other part -- a 16:17:18:19 chord can sound very
>>>rough _and_ beating and yet sound much more like a single timbre than
>>>a smooth utonal chord.
>>
>>I have never experienced such a phenomenon.
>
>Try it!

I don't hear it that way, with the few patches at my disposal. But it's
difficult for me to play lines in these "timbres" with my current hardware
setup, so I feel a true test of this is not available to me right now.

>>>>>I bet I could find a plethora of non-just chords that fuse into a
>>>>>single timbre much better than an 11-limit, or even 9-limit, utonality.

If this is the case, then I am _calling_ those chords _just_! Your
argument is essentially that my definition is wrong because it conflicts
with integer-based definitions. It is the latter which we are trying to
avoid, at Dave's request. My definition may rank many traditionally just
chords below many chords which would traditionally be called tempered,
but I claim that it is more accurate language for common listeners, in a
greater range of circumstances (regardless of the timbres used).

>>>>>Observe the rating that Joseph Pehrson, David Finnamore, and others
>>>>>have the 7-limit utonality in our tetrad examples -- and that was in
>>>>>a context of "consonance", which if anything should be more forgiving
>>>>>for utonalities than a criterion of "fusing into a single timbre".

I'm not sure that "consonance" has a definition which doesn't rely on
"fusion" (if we actually meant "concordance"). In fact, I would say the
two terms are interchangeable.

>>Looking at Blackwood's book means a trip to Manhattan, for me. I don't
>>have to tell you that Mozart's harmonies approximate JI -- you've said
>>it yourself.
>
>Well, the point is that a good definition of JI should both account for what
>JI _is_ and what it is _not_ -- and part of that entails drawing out the
>harmonic definition so that it has melodic implications as well.

I'm not sure that JI has an accepted melodic definition. To me, "adaptive
JI" has always been simply "JI", and 400K of asci from me was insufficient
to get you to acknowledge the existence of the adaptive JI concept, before
John deLaubenfels came along... At any rate, I would like to develope the
harmonic definition first.

Are you saying that Blackwood's defintion is so good that you can't
remember it? Is it too long to post?

-Carl

--- In tuning@egroups.com, "Paul H. Erlich" <PERLICH@A...> wrote:

http://www.egroups.com/message/tuning/16376

I don't have to tell you that Mozart's harmonies approximate JI --
you've said it yourself.
>

I'm not getting this. Mozart initially seems almost entirely
antithetical to just intonation.... His work was mostly created and
performed in *meantone*, yes?? Why would it be considered just
intonation... simply because he uses 5-limit sonorities
consistently??
Those would be just in quarter-comma meantone, right?? Is that what
this is all about??

_______ ___ __ _ _
Joseph Pehrson

--- In tuning@egroups.com, Carl Lumma <CLUMMA@N...> wrote:
>
> If this is the case, then I am _calling_ those chords _just_! Your
> argument is essentially that my definition is wrong because it
conflicts
> with integer-based definitions. It is the latter which we are
trying to
> avoid, at Dave's request. My definition may rank many
traditionally just
> chords below many chords which would traditionally be called
tempered,
> but I claim that it is more accurate language for common listeners,
in a
> greater range of circumstances (regardless of the timbres used).

Then "fusing" or "blending" or something would be a better
word. "Just" is simply too tied up with integer ratios in the lexicon
of everyone who uses the term, to change that now . . . and I mean
everyone!
>
> >>>>>Observe the rating that Joseph Pehrson, David Finnamore, and
others
> >>>>>have the 7-limit utonality in our tetrad examples -- and that
was in
> >>>>>a context of "consonance", which if anything should be more
forgiving
> >>>>>for utonalities than a criterion of "fusing into a single
timbre".
>
> I'm not sure that "consonance" has a definition which doesn't rely
on
> "fusion" (if we actually meant "concordance"). In fact, I would
say the
> two terms are interchangeable.

Of course, they can be quite different -- observe Stumf vs. Sethares.
>
> I'm not sure that JI has an accepted melodic definition. To
me, "adaptive
> JI" has always been simply "JI", and 400K of asci from me was
insufficient
> to get you to acknowledge the existence of the adaptive JI concept,
before
> John deLaubenfels came along...

Whoa (cough) . . . I don't know what you mean here . . . I know that
the outspoken JI community today (Partchians, Doty . . .) use the
term JI to mean "strict JI", which is why we need a separate term
for "adaptive JI". And I really don't know what you're trying to say
regarding John deLaubenfels, as I came up with the roots-in-meantone
adaptive JI idea (which turned out to be Vicentino's second tuning of
1555) at the AFMM concert in late '94.

> Are you saying that Blackwood's defintion is so good that you can't
> remember it? Is it too long to post?

Blackwood's definition is essentially the same as the Doty
definition, as far as I know, as he is dealing specifically with 5-
limit diatonic concepts and their limited extension to 7-limit and/or
chromaticism.

--- In tuning@egroups.com, "Joseph Pehrson" <josephpehrson@c...>
wrote:
> --- In tuning@egroups.com, "Paul H. Erlich" <PERLICH@A...> wrote:
>
> http://www.egroups.com/message/tuning/16376
>
> I don't have to tell you that Mozart's harmonies approximate JI --
> you've said it yourself.
> >
>
> I'm not getting this. Mozart initially seems almost entirely
> antithetical to just intonation.... His work was mostly created
and
> performed in *meantone*, yes?? Why would it be considered just
> intonation... simply because he uses 5-limit sonorities
> consistently??
> Those would be just in quarter-comma meantone, right??

Well, no, the fifths and minor thirds would not be just.

> Is that what
> this is all about??

Well, a Vicentino or deLaubenfels adaptive JI rendition of Mozart
would do no audible disservice to the music, even though all major
and minor triads would be just 5-limit sonorities. In other words,
Mozart could be said to approximate JI _locally_ (as a given instant
in time) but _globally_, strict JI would lead to conflicts
melodically, motivically, and/or pitch-level-wise.

--- In tuning@egroups.com, "Paul Erlich" <PERLICH@A...> wrote:

http://www.egroups.com/message/tuning/16403

> >
> > I'm not getting this. Mozart initially seems almost entirely
> > antithetical to just intonation.... His work was mostly created
> and performed in *meantone*, yes?? Why would it be considered just
> > intonation... simply because he uses 5-limit sonorities
> > consistently??
> > Those would be just in quarter-comma meantone, right??
>
> Well, no, the fifths and minor thirds would not be just.

Oh sure... of course.

> Well, a Vicentino or deLaubenfels adaptive JI rendition of Mozart
> would do no audible disservice to the music, even though all major
> and minor triads would be just 5-limit sonorities. In other words,
> Mozart could be said to approximate JI _locally_ (as a given
instant
> in time) but _globally_, strict JI would lead to conflicts
> melodically, motivically, and/or pitch-level-wise.

Well, that makes sense, but then what is Carl talking about, if
anything, when he is trying to link Mozart to Just Intonation. (I
didn't mean to capitalize that, JI fans, it JUST happened!)

_________ ___ __ ___
Joseph Pehrson

Paul Erlich wrote,

<< Then "fusing" or "blending" or something would be a better word. >>

I remember Seashore scraping Stumpf's "fusion" from his order of merit
of the intervals in the consonance-dissonance series, as the results
were to conflicting and blurred the lines between logical and
affective judgement.

Carl Lumma wrote,

<< Are you saying that Blackwood's defintion is so good that you can't
remember it? Is it too long to post? >>

Blackwood's views, and he offers his analysis of a bunch of excerpts
(Machaut, di Lasso, Bach, Franck, Mozart, Beethoven) to flesh them
out, are a pretty extreme take on views that should not be strangers
to those that have frequented this list for any amount of time.

He states that the pursuit of perfection in tuning, and by that he
means "strict JI" as Paul says, is "the pursuit of an ignis fatuus"...
as he doesn't see any major composer "whose style conforms to the
inherent limitations and properties of just tuning", and believes that
"it must be concluded that at present, just tuning is of no practical
use with regard to the existing Western repertoire".

He offers these -- to my mind Keenanesque -- words to "composers of
the future" regarding "the style that might emerge from using
exclusively pure intervals in composition"...

"Such music would be harmonic rather than melodic, and generally in a
slow tempo. Owing to the presence of the syntonic and septimal commas,
the usual forces associated with the subdominant, dominant, and tonic
harmonies would be somewhat weakened, imparting a more static
character to all harmonies. Use of the discordant, higher-order basic
intervals would be desirable only if they were placed in the upper
voices, and then only in conjunction with the pure basic intervals in
the lower parts. It seems highly doubtful that such a style would be
expressive in the manner that Western ears have become accustomed to.
To appreciate such music would require a degree of infatuation with
sheer sound quality, and a disregard for harmonic progressions, that
does not presently charecterize our musical culture."

--Dan Stearns

Oh boy, "summing up" was a dumb thing for me to put in a title. I'm so glad
other folk have got more involved in this thread, since I've shut up. But I
can't help myself (definitely addicted). :-)

-------------------------------
Inaudible math is important too
-------------------------------

Bill Alves,

Yes we may want to know about the mathematical things the composer or scale
designer did that may not be audible, as in the case of serialism. But we
should also have a term for that purity of harmony that _is_ audible. I
think we are onto a winnner with RI for the former and JI for the latter.
If it must all be called JI, this would leave us without a term to describe
what has historically been an audible property (which includes the Dream
House even with its large integer ratios, and excludes Hammond organs
despite their medium integer ratios, and includes barbershop which only
closely _approximates_ small integer ratios and does not do so
"intentionally").

--------------------------
My Hammond organ ignorance
--------------------------

I honestly didn't realise that, apart from the all-tone-bars-on-zero case,
the "partials" of Hammond timbres are not harmonic, but match 12-tET. So it
_is_ a Setharian thing. That Hammond was one clever dude.

Thanks John Sprague (But I _was_ joking about building one as Paul Erlich
explained) and thanks Carl Lumma (but as Herman Miller pointed out, that
still doesn't make the Hammond unqualified just by my def.

------------------------------
Setharian not any kind of JI ?
------------------------------

I don't have a strong attachment to the "just for a particular timbre"
idea. So if folk object to saying that 12-tET is "Just for some Hammond
timbres" then lets drop it. My only problem with that is, how do we exclude
Hammond and other Setharian spectrum scales on a purely audible basis. If
there's enough 12-tET partials on the Hammond, doesn't it _sound_ beatless
(assuming you switch off the Leslie and any other source of vibrato)?

Maybe we have to make "Rational is necessary but insufficient", (i.e. "All
JI is rational but not all rational is JI) part of the def rather than a
derived consequence, but I'd rather not do so if we can avoid it. What's
different about how Setharia _sound_?

-------------------------
Top octave divider organs
-------------------------

Of course it is not important that the Hammond wasn't the clear-cut
counterexample to "All rational is JI", that I thought it was. Since the
Hammond ratios _could_ be used with harmonic partials. And there were also
the 70's top-octave-divider (also called top-octave-synthesizer) organs.

Here's the scale for one (using the S50240 chip).

1/1 478/451 239/213 239/201 478/379 239/179 239/169 478/319 478/301 239/142
239/134 478/253 2/1

It's a subset of the subharmonic series between 239 and 478.

Its worst interval deviation from 12-tET is 2.4 cents, and so the worst
pitch deviation from 12-tET is 1.2 cents (with the right master oscillator
frequency).

--------------
Partch's folly
--------------

Partch's folly sounds like, in some sense, exactly what I am trying to
avoid. It seems Wendy Carlos was saying that Partch's music might be Just
according to his _theories_, but you couldn't _hear_ whether they were Just
or not because he used rapidly decaying inharmonic timbres.

---------------------------------
Barbershop vs. playing in octaves
---------------------------------

Barbershop too is trickier than I thought, since in general, it does not
use a just _scale_ but definitely uses just
harmonies/interval/chords/sonorities. Certainly the harmony is the most
important thing as far as definitions of JI are concerned. But we now have
to work a bit harder to exclude Dan Stearns' "Happy Birthday in octaves".
Of course "Happy Birthday" here is irrelevant.

We could either say that playing in octaves is 2-limit JI (and therefore
only trivially JI) or simply say that octaves are so ubiquitous and so
rarely tempered that their presence or otherwise is irrelevant to the
question of whether or not something is JI.

A problem with the latter is that octaves are needed to fully connect most
JI scales when one looks at them in a non octave-equivalent way.

----------------------------------
Connectedness of scales and chords
----------------------------------

My proposed def is founded on first defining a JI interval (in harmonic
context) and then saying that the larger constructs of chords, scales and
tunings (but not pieces of music) need only have their pitches connected by
just intervals to qualify as just.

Carl Lumma, you seem to be saying that this condition is too strong for
scales and too weak for chords. I haven't seen any convincing examples of
either yet. Maybe I missed them. Wanna try again? I think I'd be more
easily convinced of the latter.

With scales, if we're gonna draw a line anywhere, this seems the obvious
place. If a scale fails this test, it means it has at least one remaining
interval that could be brought into just intonation without affecting any
others.

Note that I don't say that a piece has to be in a JI scale, to be JI.
That's only _one_ of the ways it can be in JI.

--------------------
Multiple definitions
--------------------

Multiple definitions are fine. But when a definition includes "All rational
is JI", with or without "provided the designer/composer intended it so",
the only thing I would hope, is that the consequences of such a definition
be clearly spelled out.

I'm sorry if folk feel defeated. I don't want to plant any flags in anyones
heart. If defeated, I'd rather it wasn't by me personally, but by the
logical consequences of previous definitions.

I love all you guys. You've all taught me so much. In a sense, what I'm
proposing isn't really "my" definition. I wouldn't have had a clue about a
definition of JI before I joined this list.

Even if we don't come up with a new generally acceptable definition, making
the effort has been a fabulous learning experience. I wish Kraig Grady had
been involved.

Regards,
-- Dave Keenan
http://dkeenan.com

On Sat, 09 Dec 2000 18:22:08 -0800, David C Keenan <D.KEENAN@UQ.NET.AU>
wrote:

>I don't have a strong attachment to the "just for a particular timbre"
>idea. So if folk object to saying that 12-tET is "Just for some Hammond
>timbres" then lets drop it. My only problem with that is, how do we exclude
>Hammond and other Setharian spectrum scales on a purely audible basis. If
>there's enough 12-tET partials on the Hammond, doesn't it _sound_ beatless
>(assuming you switch off the Leslie and any other source of vibrato)?

Well, let's see if I can pinpoint what seems to be a very subtle acoustic
effect that distinguishes the two kinds of scales. Beatlessness is one
consequence of both kinds of tunings (small integer ratios with harmonic
timbres and customized scales built to match inharmonic timbres), but there
are other effects of small integer ratio tuning that are audible in certain
musical contexts. With scales that follow the harmonic series, the
reinforcement of the fundamental by the combination tones is I'd guess one
of the major causes of this effect. But I've noticed it even in utonal
music like Prent Rodgers' _mino9_. Perhaps even in utonal scales, the
combination tones reinforce other notes of the scale to a degree that is
audible.

In some contexts this effect can sound like a buzz or drone, as Wendy
Carlos demonstrated in _Secrets of Synthesis_ with high-pitched synthesized
strings in the harmonic scale. Perhaps a similar effect could be achieved
with an inharmonic timbre and an appropriate irrational scale, but the
effect of William Sethares' music that uses inharmonic timbres isn't quite
the same as JI music. The inharmonic timbres lend a certain "roughness"
that's distinct from the "roughness" of discordance caused by beats. The
difference between these two kinds of beatless harmonies is vaguely similar
to one that I've noticed between sounds produced with the harmonics
perfectly in phase and sounds produced with random phase for each harmonic.
Theoretically we can't hear phase, but with certain artificial electronic
timbres, synthesized sounds with random phase seem to lack some of the
"hard-edged" purity of the same sounds with all the partials starting in
the same phase.

This can't be the whole story either, since I don't perceive this effect in
(e.g.) most of Harry Partch's music. But it's there in Ben Johnston's
_Suite for Microtonal Piano_, in Terry Riley's _Shri Camel_, in Wendy
Carlos' pieces that use the harmonic scale, and in much of the JI music of
Tuning List members.

>--------------
>Partch's folly
>--------------
>
>Partch's folly sounds like, in some sense, exactly what I am trying to
>avoid. It seems Wendy Carlos was saying that Partch's music might be Just
>according to his _theories_, but you couldn't _hear_ whether they were Just
>or not because he used rapidly decaying inharmonic timbres.

And much of it goes along at such a pace that the effects of JI aren't as
easily heard. In some cases it also makes use of tiny melodic intervals,
long glissandos, and other effects that in my perception at least tend to
obscure the just ratios. Certainly, Partch's music is a tour de force of
interesting and unusual sounds, but I've often wondered if it wouldn't
sound just as good in 41-TET.

--
see my music page ---> ---<http://www.io.com/~hmiller/music/music.html>--
hmiller (Herman Miller) "If all Printers were determin'd not to print any
@io.com email password: thing till they were sure it would offend no body,
\ "Subject: teamouse" / there would be very little printed." -Ben Franklin

Joeseph Pehrson...]
>I'm not getting this. Mozart initially seems almost entirely
>antithetical to just intonation.... His work was mostly created and
>performed in *meantone*, yes?? Why would it be considered just
>intonation... simply because he uses 5-limit sonorities consistently??

That's right.

>Those would be just in quarter-comma meantone, right?? Is that what
>this is all about??

I would say that the 5-limit triads in 1/4-comma meantone are, generally-
speaking, in just intonation, but speaking specially, tempered.

[Paul Erlich...]
>>I'm not sure that "consonance" has a definition which doesn't rely
>>on "fusion" (if we actually meant "concordance"). In fact, I would
>>say the two terms are interchangeable.
>
>Of course, they can be quite different -- observe Stumf vs. Sethares.

Don't know Stumf.

>>I'm not sure that JI has an accepted melodic definition. To me,
>>"adaptive JI" has always been simply "JI", and 400K of asci from me
>>was insufficient to get you to acknowledge the existence of the
>>adaptive JI concept, before John deLaubenfels came along...
>
>Whoa (cough) . . . I don't know what you mean here . . . I know that
>the outspoken JI community today (Partchians, Doty . . .) use the
>term JI to mean "strict JI", which is why we need a separate term
>for "adaptive JI".

I'm not sure what exactly the definition for "adaptive JI" is, but
Doty and many "Partchians" create or at least speak of music which...

o may not have irrational intervals, but which at least has an
incredibly large pitch set.

o if it doesn't adjust for comma shift, is at least written in such
a way that no shift is the least bit offensive.

>Blackwood's definition is essentially the same as the Doty definition,
>as far as I know, as he is dealing specifically with 5-limit diatonic
>concepts and their limited extension to 7-limit and/or chromaticism.

Likely a very specialized definition, then, as quotes provided by Dan
Stearns seem to illustrate quite well.

[Dave Keenan...]
>Thanks John Sprague (But I _was_ joking about building one as Paul Erlich
>explained) and thanks Carl Lumma (but as Herman Miller pointed out, that
>still doesn't make the Hammond unqualified just by my def.

How did he point that out? The closest I see is...

"More precisely, the Hammond organ scale is "justly intoned for the Hammond
organ timbre". I think this is really a separate definition, not connected
with his definition of "just" per se, but it can be confusing because it
looks like it's part of the main definition."

...and this doesn't seem to be accurate statement, given your injunctive
and descriptive definitions.

>Maybe we have to make "Rational is necessary but insufficient", (i.e.
>"All JI is rational but not all rational is JI) part of the def rather
>than a derived consequence, but I'd rather not do so if we can avoid it.
>What's different about how Setharia _sound_?

At what level of accuracy? At what point is a number rational, and at
what point is it irrational, and what does this have to do with what is
heard? I applaud you on your statements that the term "JI" should work
entirely on sound, and not be conditional to further 'knowledge' of the
music. I'd like not to get so beat up for attempting it.

The real issue, of course, is that I am discussing a timbre-specific
definition, while those resorting to "rational" are not. Chords can
sound rooted when tuned to integer ratios, despite beating from inharmonic
partials, and harmonic timbres are really the only ones tuned with
precision in any western music. These are good reasons for a definition
based on 'harmonic' timbres, and something like Miller's conditional
becomes useful. Such a definition is not exclusive of timbre-specific
ones like I'm expounding (why would you assume otherwise, Paul?), and
you when you say "harmonic", you may have to specify how much accuracy
will is required of the partials, etc. You're liable to wind back up in
timbre-specificsville, if you're not careful...

>My proposed def is founded on first defining a JI interval (in harmonic
>context) and then saying that the larger constructs of chords, scales and
>tunings (but not pieces of music) need only have their pitches connected
>by just intervals to qualify as just.

Exactly how I'm doing things.

>Carl Lumma, you seem to be saying that this condition is too strong for
>scales and too weak for chords.

Yes, but that's just my opinion. I'm also saying that you have failed to
demonstrate how drawing a line, as far as percentage of just connecting
intervals, is useful, and have failed to show that drawing the line in one
place is better than drawing it anywhere else, and failed to show how you
decided on the place you did pick.

>I haven't seen any convincing examples of either yet. Maybe I missed
>them. Wanna try again? I think I'd be more easily convinced of the latter.

Barbershop for the former, and cacophonies like {1/1, 9/7, 11/8} for
the latter.

-Carl

Paul Erlich wrote:

> Well, a Vicentino or deLaubenfels adaptive JI rendition of Mozart
> would do no audible disservice to the music, even though all major
> and minor triads would be just 5-limit sonorities. In other words,
> Mozart could be said to approximate JI _locally_ (as a given instant
> in time) but _globally_, strict JI would lead to conflicts
> melodically, motivically, and/or pitch-level-wise.

Would this not also be true of most barbershop singing, which has been recently heralded by
Dave Keenan as "the epitome of JI"?

--
David J. Finnamore
Nashville, TN, USA
http://personal.bna.bellsouth.net/bna/d/f/dfin/index.html
--

--- In tuning@egroups.com, "D.Stearns" <STEARNS@C...> wrote:

> Blackwood's views, and he offers his analysis of a bunch of excerpts
> (Machaut, di Lasso, Bach, Franck, Mozart, Beethoven) to flesh them
> out, are a pretty extreme

Extreme?

> take on views that should not be strangers
> to those that have frequented this list for any amount of time.
>
> He states that the pursuit of perfection in tuning, and by that he
> means "strict JI" as Paul says, is "the pursuit of an ignis
fatuus"...
> as he doesn't see any major composer "whose style conforms to the
> inherent limitations and properties of just tuning", and believes
that
> "it must be concluded that at present, just tuning is of no
practical
> use with regard to the existing Western repertoire".

Not too different from Woolhouse and most other theorists who have
really examined the issue.

--- In tuning@egroups.com, David C Keenan <D.KEENAN@U...> wrote

> What's
> different about how Setharia _sound_?

The greater the inharmonicity (if it's greater than a piano's in the
middle register), the less the timbre will evoke the sensation of a
single _pitch_.

> --------------
> Partch's folly
> --------------
>
> Partch's folly sounds like, in some sense, exactly what I am trying
to
> avoid. It seems Wendy Carlos was saying that Partch's music might
be Just
> according to his _theories_, but you couldn't _hear_ whether they
were Just
> or not because he used rapidly decaying inharmonic timbres.

Daniel Wolf quoted Erv Wilson that Partch couldn't hear any
deviations from his tuning on a 41-tET instrument Wilson built.

> But we now have
> to work a bit harder to exclude Dan Stearns' "Happy Birthday in
octaves".

Not really -- just say we are talking about _strict_ JI (aren't we?)

--- In tuning@egroups.com, Herman Miller <hmiller@I...> wrote:
>
> Well, let's see if I can pinpoint what seems to be a very subtle
acoustic
> effect that distinguishes the two kinds of scales. Beatlessness is
one
> consequence of both kinds of tunings (small integer ratios with
harmonic
> timbres and customized scales built to match inharmonic timbres),
but there
> are other effects of small integer ratio tuning that are audible in
certain
> musical contexts. With scales that follow the harmonic series, the
> reinforcement of the fundamental by the combination tones is I'd
guess one
> of the major causes of this effect.

> In some contexts this effect can sound like a buzz or drone, as
Wendy
> Carlos demonstrated in _Secrets of Synthesis_ with high-pitched
synthesized
> strings in the harmonic scale. Perhaps a similar effect could be
achieved
> with an inharmonic timbre and an appropriate irrational scale, but
the
> effect of William Sethares' music that uses inharmonic timbres
isn't quite
> the same as JI music. The inharmonic timbres lend a
certain "roughness"
> that's distinct from the "roughness" of discordance caused by
beats. The
> difference between these two kinds of beatless harmonies

This is of course something we've discussed a great deal on the
harmonic entropy list.

> is vaguely similar
> to one that I've noticed between sounds produced with the harmonics
> perfectly in phase and sounds produced with random phase for each
harmonic.
> Theoretically we can't hear phase, but with certain artificial
electronic
> timbres, synthesized sounds with random phase seem to lack some of
the
> "hard-edged" purity of the same sounds with all the partials
starting in
> the same phase.

That's a different phenomenon -- we are sensitive to phase to a very
small degree, and this particular example will give sharp spikes in
the waveform when the sawtooth or pulse, etc. waves are in phase, and
is thus more likely to excite combination tones, which are of course
reinforcing in this case.

> Certainly, Partch's music is a tour de force of
> interesting and unusual sounds, but I've often wondered if it
wouldn't
> sound just as good in 41-TET.

q.v. the anecdote I just posted. Since it is a 43-tone scale, and due
to the importance of the 11-limit diamond, I'd go to 72-tET to be
safe.

--- In tuning@egroups.com, "David J. Finnamore" <daeron@b...> wrote:
> Paul Erlich wrote:
>
> > Well, a Vicentino or deLaubenfels adaptive JI rendition of Mozart
> > would do no audible disservice to the music, even though all major
> > and minor triads would be just 5-limit sonorities. In other words,
> > Mozart could be said to approximate JI _locally_ (as a given
instant
> > in time) but _globally_, strict JI would lead to conflicts
> > melodically, motivically, and/or pitch-level-wise.
>
> Would this not also be true of most barbershop singing, which has
been recently heralded by
> Dave Keenan as "the epitome of JI"?

I guess Dave Keenan is not talking about _strict JI_, while I was.
Barbershop singing may often approach a version of _adaptive JI_,
though it's often not JI at all.

Paul Erlich wrote,

<< Not too different from Woolhouse and most other theorists who have
really examined the issue. >>

No, but I think he overstates the case.

--Dan Stearns

Dave Keenan wrote:
>
>Yes we may want to know about the mathematical things the composer or scale
>designer did that may not be audible, as in the case of serialism. But we
>should also have a term for that purity of harmony that _is_ audible. I
>think we are onto a winnner with RI for the former and JI for the latter.
>If it must all be called JI, this would leave us without a term to describe
>what has historically been an audible property

I have no problem with you coming up with a term to describe a particular
kind of harmonic sound, but to me you've got it backwards. I don't think
that the term "just intonation" has historically been an audible property.
Writers have long described tuning systems as instructions and ratios, i.e.
from the tuning/composing side of the equation. Distinguishing them as RI
and JI is not, to me, making a too broad definition more precise, it's
taking away a term as I (and many others) have used it (JI) and replacing
it with another (RI).

I am also suspicious of any definition that depends on harmonic factors,
even on the audible side of the equation. Harmony is a European
preoccupation, and using it as a metric would be foreign to other cultures
that have created JI systems without primary regard to harmony (ancient
Greeks, Chinese).

Bill

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

--- In tuning@egroups.com, Bill Alves <ALVES@O...> wrote:

> http://www.egroups.com/message/tuning/16440
>
> I am also suspicious of any definition that depends on
> harmonic factors, even on the audible side of the equation.
> Harmony is a European preoccupation, and using it as a metric
> would be foreign to other cultures that have created JI
> systems without primary regard to harmony (ancient Greeks,
> Chinese).

Ah, yes, Bill... but who was it who *labelled* ancient Greek
and Chinese music-theory as "JI"? It *wasn't* the Greeks
and Chinese themselves; it was later Europeans and
Americans.

While I can't speak with authority on Chinese music-theory,
I do know a thing or two about ancient Greek treatises...

The Greeks employed the term _'armonia_ ("harmony")
to refer to several concepts which many of us (including
you and I) would put under the broad definition of "JI".
But their idea of "harmony" was far broader than ours
(or at least most of us today, excluding perhaps Denny
Genovese and his followers), and almost always also
included ideas about the "proper" (that is, "just")
relationships between non-musical objects or events
as well.

At the same time, it must also be pointed out that the
Greek concept of _'armonia_ very often *did* refer
specifically to mathematical properties... not necessarily
low-integer ratios, but certainly superparticularity
(for newbies: that means that successive string-lengths
of certain pitches in a scale were to be successive
integer proportions).

But perhaps the most important point to make in regard
to ancient Greek music-theory is that the most influential
one by far was that of Aristoxenus, and his theory
had absolutely *nothing* to do with ratios; it was based
entirely on audible principles. He sought to create
a unique science of music with a metaphysical basis
that was divorced from cosmology, mathematics, and
other domains which theorists were fond of associating
with music, and which was based instead entirely on
consideration of audible properties at many different
structural levels.

As I've posted before in support of Dave K's argument,
the etymology of the word "just" must be given a promenint
place in debating the defintion of the term. It refers
to "correct" intonation, and that correctness is not
to be determined solely by frequency-numbers and such,
but rather by what listeners's ears *hear* as correct.
(What exactly is meant by "correct" provides much scope
for further debate...)

It's important to remember that use of the term "just
intonation" originated in Europe, and did not begin until
European musical practice concerned itself primarily with
triadic *harmony*.

Intonation was never described as "just" before c.1500,
and this was the period when melodic/contrapuntal considerations
were pre-eminent. The only exception I'd admit to this
is that the Greeks did indeed mean "correctness of proportion"
in their employment of the term _'armonia_ specifically
as it referred to intonation.

I realize that much of what I've written in this post
may be seen as self-contradictory, but I'm "calling it
as I see it". Further debate is encouraged. :)

-monz
http://www.ixpres.com/interval/monzo/homepage.html
'All roads lead to n^0;

Bill Alves wrote,

>Harmony is a European
>preoccupation, and using it as a metric would be foreign to other cultures
>that have created JI systems without primary regard to harmony (ancient
>Greeks, Chinese).

Traditional Chinese music is essentially based on dyadic, 3-limit harmony
(thus the Pythagorean tuning). I recently went to a concert of the top
Chinese musicians from China -- they'll be playing again at Harvard's
Sanders Theater on January 6th.

>Bill Alves wrote,
>
>>Harmony is a European
>>preoccupation, and using it as a metric would be foreign to other cultures
>>that have created JI systems without primary regard to harmony (ancient
>>Greeks, Chinese).
>
Paul H. Erlich replied:
>Traditional Chinese music is essentially based on dyadic, 3-limit harmony
>(thus the Pythagorean tuning). I recently went to a concert of the top
>Chinese musicians from China -- they'll be playing again at Harvard's
>Sanders Theater on January 6th.
>
Despite what Yasser claims, the basis of traditional Chinese music is not
harmonic, Pythagorean or otherwise. Though "harmony of fifths" may show up
very occasionally, usually through heterophonic variations, that is not the
basis for their tuning systems. It is true that instruments such as the
zheng and guqin are tuned by successive 3/2s, but whole sections of pieces
on the qin are also played in harmonics. Chinese writers have written
extensively on tuning systems and why they are adopted, but have never, to
my knowledge, invoked harmony in musical pieces as a justification for
tuning systems.

I might as well respond to Joe while I'm at it. If I understand him, it
would seem that because Europeans came up with the term just intonation,
and in particular at a time when harmonic music was standard, that defining
the term with specific reference to sounds of harmony is therefore
justified. He also invokes the original meaning of "just" as "correct" or
"precise."

And yet I haven't seen any information that would suggest that these terms
originally refered to a subjective quality of a sonority rather than a
method of tuning -- that is, "justness" meaning rational ratios, in the
sense that you say that the Greeks used the term harmonia, rather than
"locking-in" harmonies.

In this sense (tuning by integer ratios), I feel justified in applying the
European term of just intonation to other cultures, because that is what
they do or did. But if the term is a description of harmony, then it seems
misplaced in describing these other musical systems.

Bill

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

>>Bill Alves wrote,
>
>>>Harmony is a European
>>>preoccupation, and using it as a metric would be foreign to other
cultures
>>>that have created JI systems without primary regard to harmony (ancient
>>>Greeks, Chinese).
>
>Paul H. Erlich replied:
>>Traditional Chinese music is essentially based on dyadic, 3-limit harmony
>>(thus the Pythagorean tuning). I recently went to a concert of the top
>>Chinese musicians from China -- they'll be playing again at Harvard's
>>Sanders Theater on January 6th.
>
>Despite what Yasser claims, the basis of traditional Chinese music is not
>harmonic, Pythagorean or otherwise. Though "harmony of fifths" may show up
>very occasionally

Forget Yasser! All I can tell you for sure is that I went to this very
wonderful concert and the vast majority of the music was characterized by
dyadic, 3-limit harmony. Many pieces were almost rigorously constructed in
this manner -- and these are supposedly the great traditional pieces as
played by the masters from the Shanghai and Beijing conservatories. A
flexible pentatonicism, that frequently employed "altered" degrees that
could be siad to come from a heptatonic "master mode", was also evident.
I'll see if I can get a CD at the Jan. 6th concert -- they didn't have any
available at the last one.

>Chinese writers have written
>extensively on tuning systems and why they are adopted, but have never, to
>my knowledge, invoked harmony in musical pieces as a justification for
>tuning systems.

They may have a more mystical set of justifications . . . please elaborate.

>And yet I haven't seen any information that would suggest that these terms
>originally refered to a subjective quality of a sonority rather than a
>method of tuning -- that is, "justness" meaning rational ratios, in the
>sense that you say that the Greeks used the term harmonia, rather than
>"locking-in" harmonies.

The evidence was Dave Keenan's reference to a dictionary entry from 1811.

Bill, I also just want to point out that I don't disagree or agree with you
on the issue of defining JI . . . I'm just acting as a neutral observer on
that one.

Bill Alves wrote:

> I have no problem with you coming up with a term to describe a particular
> kind of harmonic sound, but to me you've got it backwards. I don't think
> that the term "just intonation" has historically been an audible property.
> Writers have long described tuning systems as instructions and ratios, i.e.
> from the tuning/composing side of the equation. Distinguishing them as RI
> and JI is not, to me, making a too broad definition more precise, it's
> taking away a term as I (and many others) have used it (JI) and replacing
> it with another (RI).

As Paul Erlich mentioned, the killer here is the following entry in The
'Shorter Oxford English Dictionary on Historical Principles'.

--------------------------------------------------------------------------
Just
/Mus./ in /just interval/, etc. : Harmonically pure; sounding perfectly in
tune 1811.
--------------------------------------------------------------------------

This means that the earliest known appearance of this musical usage (in
English) was in 1811. No alternative musical meanings are given and nothing
indicates that this usage is obsolete or has changed in any way since 1811
(this would have been indicated if it was so). There is no mention of
ratios, and a clear indication that it is an audible property.

The edition I have is 'Third edition, revised with addenda', 1959. It is
quarto size with 2,500 pages in two volumes. It is an officially authorised
abridgement of the 15,000 page 'A New English Dictionary on Historical
Principles', now known as 'The Oxford English Dictionary'.

I wonder what a more recent edition, or the 'Oxford English Dictionary'
says on the matter? But none of us have so far suggested that the
definition ought to have changed since 1959.

I think we'd need some pretty serious evidence to convince the Delegates of
the Oxford University Press and the Philological Society that they screwed up.

Regards,
-- Dave Keenan
http://dkeenan.com

On Mon, 11 Dec 2000 02:03:14 -0000, "Paul Erlich"
<PERLICH@ACADIAN-ASSET.COM> wrote:

>> Certainly, Partch's music is a tour de force of
>> interesting and unusual sounds, but I've often wondered if it
>wouldn't
>> sound just as good in 41-TET.
>
>q.v. the anecdote I just posted. Since it is a 43-tone scale, and due
>to the importance of the 11-limit diamond, I'd go to 72-tET to be
>safe.

72-TET would be a better approximation, certainly, especially considering
the relatively poor 5/3 and 5/4 approximations of 41-TET. You'd lose the
11/10 and 20/11 by going to 41-TET, and I think the 11/10 in particular is
a nice interval to have. But I haven't heard anything in Partch's music per
se that requires those features. That these features can have audible
results is demonstrated more clearly by Prent Rodgers' music, among others.

--
see my music page ---> ---<http://www.io.com/~hmiller/music/music.html>--
hmiller (Herman Miller) "If all Printers were determin'd not to print any
@io.com email password: thing till they were sure it would offend no body,
\ "Subject: teamouse" / there would be very little printed." -Ben Franklin

--- In tuning@egroups.com, Bill Alves <ALVES@O...> wrote:

> http://www.egroups.com/message/tuning/16451
>
> ...
>
> I might as well respond to Joe while I'm at it. If I
> understand him, it would seem that because Europeans came
> up with the term just intonation, and in particular at
> a time when harmonic music was standard, that defining
> the term with specific reference to sounds of harmony
> is therefore justified. He also invokes the original
> meaning of "just" as "correct" or "precise."
>
> And yet I haven't seen any information that would suggest
> that these terms originally refered to a subjective quality
> of a sonority rather than a method of tuning -- that is,
> "justness" meaning rational ratios, in the sense that you
> say that the Greeks used the term harmonia, rather than
> "locking-in" harmonies.

Hi Bill,

I'd say that the original employment of the term "just
intonation" in Europe (c.1500?) did indeed refer to a
"subjective quality".

The reason the word "just" was invoked in the first place
was because the retuning of the "3rds" and "6ths" from
Pythagorean to 5-limit ratios was seen as a mathematical
justification for the increased "sweetness" or "purity"
of those intervals as their classification by theorists and
their stylistic manipulation by composers was changed from
"imperfect consonances" to simply plain old "consonances".

Something else to bear in mind: I did say in a previous post
that while the earliest use of this word "just" in regard to
musical tuning in English appears to date from 1811 (according
to the Oxford Dictionary), I suspect that an Italian or German
equivalent was employed probably a couple of centuries earlier.
BUT... no one has as yet responded to my challenge to find an
actual earlier occurence.

Therefore, until an earlier citation surfaces, I think we'd
do well to accept 1811 as date of the emergence of the term
"just intonation", and if we do accept this, then we must
absolutely understand the term to refer to musical practice
during an era when triadic harmony was the prevalent norm
in composition... at least, in its *original* meaning.

Of course, this is not to say that the term cannot have
accumulated various other shades of meaning or different
meanings altogether since that time. Even taking 1811 as
the earliest date, that's nearly two centuries of use during
which the meanings could evolve, and certainly there are
many other instances of changing definitions in English
over much shorter periods of time. I think right away of
the way the word "bad" during the 1980s acquired a secondary
definition meaning exactly the opposite of the original one.

So....

>
> In this sense (tuning by integer ratios), I feel justified
> in applying the European term of just intonation to other
> cultures, because that is what they do or did.

Fair enough. But in *technical* discourse, it would be
appropriate at this stage of the game (i.e., since the handful
of us on this list have argued about it) to be extremely
clear about which definition of JI is intended when it's
invoked.

I personally favor the idea of using a qualifier in every
case which means something other than Renaissance-era
(or Renaissance-style, if concerning a later era) 5-limit
tuning, which would be the only instance I'd be willing
to describe as plain "just intonation".

-monz
http://www.ixpres.com/interval/monzo/homepage.html
'All roads lead to n^0'

--- In tuning@egroups.com, " Monz" <MONZ@J...> wrote:

> http://www.egroups.com/message/tuning/16460
>
> I personally favor the idea of using a qualifier in every
> case which means something other than Renaissance-era
> (or Renaissance-style, if concerning a later era) 5-limit
> tuning, which would be the only instance I'd be willing
> to describe as plain "just intonation".

I was just reflecting on where this might lead, and realized
that we could end up with Bill Alves writing in "Alvesian JI",
Partch's music being in "Partchian JI", etc.

Is that comedy or tragedy?

...perhaps Jacky Ligon (cf. "Microtonal Hamlet") should
comment... ;-)

-monz
http://www.ixpres.com/interval/monzo/homepage.html
'All roads lead to n^0'

--- In tuning@egroups.com, " Monz" <MONZ@J...> wrote:
>
> Is that comedy or tragedy?
>
> ...perhaps Jacky Ligon (cf. "Microtonal Hamlet") should
> comment... ;-)
>
> -monz

Rightly to be great
Is not to stir without great argument,
But greatly to find quarrel in a straw
When honour's at the stake.

Johann Gottleib Walther defines the term "just" in his Lexicon of 1732. I'll
have to uncover it later on if it is not available to others. His cousin,
Johann Sebastian Bach, was the agent for the Lexicon in Leipzig.

Johnny Reinhard

--- In tuning@egroups.com, Afmmjr@a... wrote:

> http://www.egroups.com/message/tuning/16471
>
> Johann Gottleib Walther defines the term "just" in his
> Lexicon of 1732. I'll have to uncover it later on if it
> is not available to others. His cousin, Johann Sebastian
> Bach, was the agent for the Lexicon in Leipzig.

Cool! Thanks, Johnny.

Did Walther use the German term 'reinen Stimmung',
which is translated literally as 'pure tendency' but
in music-theory is usually rendered as 'just intonation'?

If not, what is the actual German term used by Walther?
A little quote would be most appreciated.

(For those who might want to search the web for more
info on Walther, be forewarned that a search for
"Johann Walther" will turn up pages that refer to the
musician who assisted Martin Luther in the composition
of the first German mass, a couple of centuries before
*this* J. G. Walther, as he's usually known.)

The actual German title of the document to which Johnny
refers is the _Musikalisches Lexikon_ (the full title is
very long and is given below); Walther is usually given
credit as the editor. The frontispiece is reproduced here:

http://www.islandnet.com/~arton/barvlnbo.html

A copy of the original _Lexikon_ on microfilm is housed at
Harvard University; here's their catalog info:

AUTHOR: Walther, Johann Gottfried, 1684-1748.
TITLE: Musicalisches lexicon; oder, Musicalische Bibliothec,
darinnen nicht allein die Musici, welche so wol in alten
als neuern Zeiten, ingleichen bey verschiedenen Nationen,
durch Theorie und Praxin sich hervor gethan, und was von
jedem bekannt worden, oder er in schrifften hinterlassen,
mit allem Fleisse und nach den vornehmsten umstanden
angefuhret, sondern auch die in griechischer, lateinischer,
italianischer und frantzosischer Sprache gebrauchliche
musicalische Kunst- oder sonst dahin gehorige Worter,
nach alphabetischer Ordnung vorgetragen und erklaret,
und zugleiche die meisten vorkommende Signaturen erlautert
werden von Johann Gottfried Walthern.
PUB. INFO: Leipzig, W. Deer, 1732.
DESCRIPTION: 659, [7] p. XXII fold. pl. (music) 22 cm.
LOCATION: Loeb Music: Merritt Room Mus 45.104.2
Loeb Music: Isham Lib. 3874.533.66.4
Microfilm (negative).
Microfilm
Bound together with pages containing annotations for
a second edition.
Loeb Music: Isham Lib. 3830.364.78.206 (5)
Microfilm

A rough English translation of the long full title is:

Musical Lexicon, or, Musical Library, containing not
only the musicians of old and newer times, of different
nations, both theorists and performers, but also classic
writings from Greek, Latin, Italian, and French,
arranged in alphabetical order and explained, by
Johann Gottfried Walther.

There have been two reprint facsimile editions, issued
in 1953 and 1986; both are also available at Harvard.
(And - lucky for me! - both of these reprints are also
available at the U. of Penn. What a great library...)

Here's the Library of Congress entry for the 1953 edition:

LC Control Number: 64000859
Type of Material: Book (Print, Microform, Electronic, etc.)
Personal Name: Walther, Johann Gottfried, 1684-1748.
Main Title: Musikalisches Lexikon; oder, Musikalische
Bibliothek, 1732. Faksimile-Nachdruck hrsg.
von Richard Schaal.
Published/Created: Kassel, Bärenreiter-Verlag, 1953.
Related Names: Schaal, Richard, ed.
International Association of Music Libraries.
International Musicological Society.
Description: 659 p. front., 22 fold. plates (music) 22 cm.
Notes: At head of title: Association international
des bibliothèques musicales; Internationale Gesellschaft
für Musikwissenschaft.
Subjects: Music--Dictionaries--German.
Music--Bio-bibliography.
Series: Documenta musicologica, 1.
Reihe: Druckschriften-Faksimiles, 3
LC Classification: ML100 .W21 1953
Other System No.: (OCoLC)399901
Request in: Performing Arts Reading Room (Madison, LM113)

A short bio of Walther is here:
http://jan.ucc.nau.edu/~tas3/walther.html

-monz
http://www.ixpres.com/interval/monzo/homepage.html
'All roads lead to n&0'

>Just
>/Mus./ in /just interval/, etc. : Harmonically pure; sounding perfectly in
>tune 1811.

>I think we'd need some pretty serious evidence to convince the Delegates of
>the Oxford University Press and the Philological Society that they screwed up.

OK, I see that evidence now, but it seems to me that the problem is that
the musicians from this period could consider that "integer ratios" and
"harmonically pure" were synonymous. They had no reason to include
possibilities of higher limits (indeed, 7 was rare and controversial),
non-harmonic timbres, non-Western use, or any of the other cases that have
arisen in our discussion. Barbour, Apel, and others concerned primarily
with European historical use define JI only as a tuning with pure fifths
and thirds. I'm not saying that they "screwed up," only that their
perspective is not what ours is.

And yet, a closer look at the OED provides some clues. "Just" was applied
to weights and other measurements by the 15th century whose numbers were
exact and "right in proportion": c1430 LYDG. Min. Poems (Percy Soc.) 60
Iuste weight halte justly the balaunce. 1588 W. SMITH Brief Descr. Lond.
(Harl. MS. 6363 lf. 13) If they ffynd [the weights] not Iust: they breake
them.

I'm no etymologist, but it would seem that "just" in this sense could have
easily arisen from the more common meaning as "fair." That is, a "just"
weight is one that is *exactly* a pound or an exact fraction, so that when
buying your food, you could be certain that the price was fair. I would
submit that this same concept of just as an exact measurement or proportion
was then applied to the monochord to distinguish those tunings from
temperaments.

Writers from Ramis onward defined JI tunings via the monochord or some
other measurement, though they often justified them both by the simplicity
of the fractions as well as the sound which results. Barbour quotes Ramis'
(1482) defence against advocates of Pythagorean ratios: "So therefore we
have made all our divisions very easy, because the fractions are common and
are not difficult." Though he does not call this "just" yet, neither does
he define the tuning system by the sound which results -- he defines it by
measurements on the monochord.

The person whom I think is most responsible for expanding the Western
conception of JI beyond the 5-limit 12-tone scale was Harry Partch, who
defined it as "a system in which interval- and scale-building is based on
the criterion of the ear and consequently a system and procedure limited to
small-number ratios." Though he, like Ramis, assumes that the system will
appeal to the ear, it is the "consequently" that is the crucial word here.
One cannot assume from this definition that any scale built on "the
criterion of the ear" is JI, only that small-number ratios are JI and those
thereby appeal to the ear.

David Doty's definition for some time has been, "Just Intonation is any
system of tuning in which all of the intervals can be represented by
whole-number frequency ratios, with a strongly implied preference for the
simplest ratios compatible with a given musical purpose."

So if faced with tunings that are based on whole-number ratios but don't
sound "harmonically pure" what do we do? Or conversely, sonorities that
sound harmonically pure but aren't based on whole number ratios? Should we
accept uncritically the non-technical definition of a dictionary written in
the period when 5-limit, 12-tone scales with harmonic timbres were assumed
and therefore "harmonically pure" was synonymous with 3/2 and 5/4? Or do we
accept Partch's and others' extension of the term to higher limits, the
non-West, and the ancient Greeks by giving primacy to the composer's use of
exactly-proportional relationships (the original meaning of just as a
measurement)? To me the latter is much more useful and consistent with use
by composers in this century, though it does not contradict the use of the
term in earlier times.

Bill

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

Monz wrote,

>I personally favor the idea of using a qualifier in every
>case which means something other than Renaissance-era
>(or Renaissance-style, if concerning a later era) 5-limit
>tuning, which would be the only instance I'd be willing
>to describe as plain "just intonation".

By Renaissance-era or Renaissance-style I presume you mean the strict JI
systems considered by theorists such as Fogliano, and not systems that were
actually practicable to Renaissance music, such as the adaptive JI of
Vicentino . . . correct?

--- In tuning@egroups.com, "Paul H. Erlich" <PERLICH@A...> wrote:

> http://www.egroups.com/message/tuning/16481
>
> Monz wrote,
>
> > I personally favor the idea of using a qualifier in every
> > case which means something other than Renaissance-era
> > (or Renaissance-style, if concerning a later era) 5-limit
> > tuning, which would be the only instance I'd be willing
> > to describe as plain "just intonation".
>
> By Renaissance-era or Renaissance-style I presume you mean
> the strict JI systems considered by theorists such as Fogliano,
> and not systems that were actually practicable to Renaissance
> music, such as the adaptive JI of Vicentino . . . correct?

Right. (I thought it was already evident that I would use
the qualified term "adaptive JI" to refer to a tuning such
as Vicentino's.)

Based mainly on corrections you've pointed out to me in the
past, Paul, I try hard these days to be careful not to apply
the unqualified label "JI" to historical musical usages except
in a general theoretical sense, unless it was specifically
advocated by someone such as Fogliano.

Please be aware, on the other hand, that there is quite a
tradition of _a cappella_ singing which *is* intended to be
in more-or-less "strict" 5-limit JI. It carried on well
beyond the Renaissance, especially in England. John Curwen
was a singing teacher who was one of its principle advocates.

-monz
http://www.ixpres.com/interval/monzo/homepage.html
'All roads lead to n^0'

Monz wrote,

>Please be aware, on the other hand, that there is quite a
>tradition of _a cappella_ singing which *is* intended to be
>in more-or-less "strict" 5-limit JI. It carried on well
>beyond the Renaissance, especially in England. John Curwen
>was a singing teacher who was one of its principle advocates.

I'd like to learn more, particularly on how the problems of comma shifts and
drifts, chords of three or more stacked fourths/fifths, and symmetrical
chords would be handled by this tradition.

--- In tuning@egroups.com, "Paul H. Erlich" <PERLICH@A...> wrote:

> http://www.egroups.com/message/tuning/16489
>
> Monz wrote,
>
> > Please be aware, on the other hand, that there is quite a
> > tradition of _a cappella_ singing which *is* intended to be
> > in more-or-less "strict" 5-limit JI. It carried on well
> > beyond the Renaissance, especially in England. John Curwen
> > was a singing teacher who was one of its principle advocates.
>
> I'd like to learn more, particularly on how the problems of
> comma shifts and drifts, chords of three or more stacked
> fourths/fifths, and symmetrical chords would be handled by
> this tradition.

I'll note first of all that, living before the 20th century,
Curwen et al did not concern themselves with such "modern"
practices as "stacked 4ths/5ths" or "symmetrical chords".
The problem of "comma shifts and drifts", however, was
indeed their primary area of investigation.

It's been at least a couple of years since I ran across a
quite lengthly article about Curwen. I can't remember now
where I found it, but what I do recall is that he expanded
the set of solfege syllables so as to accomodate various
shades of 5-limit intonation, carefully differentiating
commatic and diesis differences with slightly different
syllables (i.e., "ma, me, mi, mo, mu", etc., for various
versions of "3rds").

This is not unlike some of the proposals found in Helhmoltz's
book, by either Helmholtz himself or Ellis. In fact, I do
believe it's Ellis's appendix to _On the Sensations of Tone_
which has the info about Curwen.

Curwen published his "Tonic sol-fa" system in 1863, according to:
http://www.freechurch.org/crown4.html

There's a quote from Curwen's _Teachers' Manual_ here:
http://ubmail.ubalt.edu/~pfitz/play/ref/notation.htm

You will see references in these pages to the terms
"shape note" and "fasola" (fa-sol-la... get it?).
These are related topics having to do with singing
in correct 5-limit JI. "Shape note" notation was
invented here in Philly, about 21 years before the
O.E.D. citation for "just intonation".

This page has a lot of info on these topics and is quite good:
http://www.mcsr.olemiss.edu/~mudws/faq/

This page has a bit to say about the difference between
"doremi" (7-syllable) and "fasola" (4-syllable) solfege.
It's worth pointing out that the reason "fasola" works
is because of tetrachordal similarity in the heptatonic
scale, and that this is something that was noted as a
*practical* structural characteristic by Guido d'Arezzo,
c.1000 AD, in his fantastic success with teaching monks
how to sing at sight.

Hope that gives you bit of a lead... be sure to look also
in Helmholtz. I'd bet that _Groves_ probably also has a
pretty in-depth treatment of Curwen and all of these topics.

-monz
http://www.ixpres.com/interval/monzo/homepage.html
'All roads lead to n^0'

Dear Bill Alves and Jacky Ligon,

Your recent posts in this thread suggest a misunderstanding of what the
Oxford English Dictionary project actually is (and has always been). It's
entries do not contain "frozen definitions" they show the evolution of
meanings through time and in all English-speaking countries. Please read

http://dictionary.oed.com/public/inside/

Bill Alves wrote:

> OK, I see that evidence now, but it seems to me that the problem is that
> the musicians from this period could consider that "integer ratios" and
> "harmonically pure" were synonymous.

No. They may have considered that "harmonically pure" was synonomous with
"small whole-number ratios". They may even have considered it synonomous
with "ratios of whole-numbers no larger than 6". But never "all
whole-number ratios". I think you will agree that musical theorists of this
era were aware of the existence of whole numbers beyond six :-) and had
ample opportunity to try ratios of 7 on monochords.

[Note: I say "whole number" rather than "integer" because I don't think
anyone really intends to include negative numbers or zero.]

If someone, soon after 1811, played a bare 64:81 interval, (e.g. on a pair
of monochords), and claimed that it was a just interval or an example of
just intonation, they would have been laughed at by anyone cognisant with
the musical usage of the term "just". Their subsequent proof that it was an
integer ratio of 64:81 would have been considered irrelevant. Do you agree?

I see no reason to believe that has changed, or ever should.

If we allow the definition to change in this manner now, future students of
music theory are going to find it rather confusing that no one back then
considered a Pythagorean major third to be just, when the property of it
being a whole number ratio was known to the ancients and hasn't changed.

> They had no reason to include
> possibilities of higher limits (indeed, 7 was rare and controversial),
> non-harmonic timbres, non-Western use, or any of the other cases that have
> arisen in our discussion. Barbour, Apel, and others concerned primarily
> with European historical use define JI only as a tuning with pure fifths
> and thirds. I'm not saying that they "screwed up," only that their
> perspective is not what ours is.

I agree that they had little reason to consider higher limits. But the fact
that 7 was controversial strongly suggests that their definition of just
was based on how the intervals sounded, not on "whole number ratios".
Surely you are not claiming that they found it controversial as to whether
7 was a whole number or not. :-)

> And yet, a closer look at the OED provides some clues. "Just" was applied
> to weights and other measurements by the 15th century whose numbers were
> exact and "right in proportion": c1430 LYDG. Min. Poems (Percy Soc.) 60
> Iuste weight halte justly the balaunce. 1588 W. SMITH Brief Descr. Lond.
> (Harl. MS. 6363 lf. 13) If they ffynd [the weights] not Iust: they breake
> them.

You are here assuming that "proportion" refers to a ratio. It could however
mean simply size, magnitude, dimension.

I take it you have access to the complete OED and a more recent version
than my 1959 Shorter OED. What year was it published? Could you please post
(at least) the full numbered entry for the meaning that includes the
musical use of "just" with the corresponding quotes, or if you feel
generous, the full entry for "just" as an adjective.

Also please post the full entry for "jazz" as a noun, so folk can see that
the OED _does_ follow the evolution of meanings. They simply do not
consider that the musical meaning of "just" has changed.

> I'm no etymologist, but it would seem that "just" in this sense could have
> easily arisen from the more common meaning as "fair." That is, a "just"
> weight is one that is *exactly* a pound or an exact fraction, so that when
> buying your food, you could be certain that the price was fair. I would
> submit that this same concept of just as an exact measurement or proportion
> was then applied to the monochord to distinguish those tunings from
> temperaments.

I think this is a long-shot. You used the word "fraction", but it doesn't
appear in the OED entry. Right? I simply claim that your reading of
"proportion" as "fraction" or "ratio" is unwarranted. In my Shorter OED the
musical meaning of "just" is given as sub-meaning "b" of meaning "5" as
follows:

-----------------------------------------------------------------------------
5. Conformable to the standard; right; proper; correct ME. b. /Mus./ in
/just interval/, etc. : Harmonically pure; sounding perfectly in tune 1811.
-----------------------------------------------------------------------------

Exactly what Carl Lumma said a while back.

ME stands for Middle-English and means somewhere between about 1150 and
1500 CE.

> Writers from Ramis onward defined JI tunings via the monochord or some
> other measurement, though they often justified them both by the simplicity
> of the fractions as well as the sound which results. Barbour quotes Ramis'
> (1482) defence against advocates of Pythagorean ratios: "So therefore we
> have made all our divisions very easy, because the fractions are common and
> are not difficult." Though he does not call this "just" yet, neither does
> he define the tuning system by the sound which results -- he defines it by
> measurements on the monochord.

This paragraph appears to beg the question. You begin by saying he defined
"JI tunings" and end by saying he did not call them "just". I suppose you
mean he defined "tunings that we now call just". But if he didn't call them
"just", what bearing can this have on our discussion?

There is no argument that ratios of small enough whole-numbers are
guaranteed to be just and that such ratios are a very convenient and
unambiguous way of describing such intervals. I argue only that not all
whole-number ratios are just and that the sound comes first and the
mathematical model second.

> The person whom I think is most responsible for expanding the Western
> conception of JI beyond the 5-limit 12-tone scale was Harry Partch,

Are you maybe being a little USA-centric here?

Does anyone have an early quote where a 4:7 (or other non-5-limit) ratio is
referred to as "just" (or the arguable equivalent in a language other than
English). Presumably the relative purity of the 1/4-comma-meantone
augmented sixth did not go unnoticed until Partch.

One can certainly understand, based on an audible definition, that
acceptance of such ratios as "just" was gradual, since their justness is
not as obvious as for those of 5-limit ratios, particularly if harmony is
limited to triads. But surely their integer-ratio-ness (even
small-integer-ratio-ness) was blatantly obvious to anyone who cared to
apply a monochord to the question.

> [Harry Partch] who
> defined it as "a system in which interval- and scale-building is based on
> the criterion of the ear and consequently a system and procedure limited to
> small-number ratios."

I read this as, "the criterion of the ear is primary and 'it just so
happens' that this corresponds to small-number ratios". And clearly he
still wants to limit the size of the numbers, he isn't proposing that _all_
whole-number ratios are just.

> Though he, like Ramis, assumes that the system will
> appeal to the ear, it is the "consequently" that is the crucial word here.

Yes indeed.

> One cannot assume from this definition that any scale built on "the
> criterion of the ear" is JI, only that small-number ratios are JI and those
> thereby appeal to the ear.

I respectfully suggest you look up "consequently" (or "consequentially") in
a dictionary. "[by ear] and consequently [by numbers]" means that [by
numbers] follow from [by ear], not the other way 'round.

> David Doty's definition for some time has been, "Just Intonation is any
> system of tuning in which all of the intervals can be represented by
> whole-number frequency ratios, with a strongly implied preference for the
> simplest ratios compatible with a given musical purpose."

I fully understand why it is so tempting, especially in this day of readily
available computers and digitally tunable instruments, to try to make a
definition like this, based on the numbers. But with its "strongly implied"
it tries to sit on the fence about whether there is a limit to the size of
the numbers or not, perhaps in recognition that it is as much a mistake to
limit the numbers (to less than some particular value) as it is not to
limit them at all. The way out is to go back to the audible property.

Doty gets close with his "compatible with a given musical purpose", but
this is too vague. It looks too much like the "intent" idea. i.e. "If it's
in ratios and I, the composer (decider of musical purpose), intend it to be
just, then it _is_ just, no matter how big the numbers are." Even if it is
indistinguishable from 12-tET?

> So if faced with tunings that are based on whole-number ratios but don't
> sound "harmonically pure" what do we do?

Remember that a just tuning doesn't have to have all just intervals. But if
an interval is based on a whole-number ratio but doesn't sound harmonically
pure (in any harmonic context that the tuning can provide) the answer is
simple. We call it a non-just interval (possibly within a just tuning).

> Or conversely, sonorities that
> sound harmonically pure but aren't based on whole number ratios?

I would call them "just for that particular (inharmonic) timbre".

> Should we
> accept uncritically the non-technical definition of a dictionary written in
> the period when 5-limit, 12-tone scales with harmonic timbres were assumed
> and therefore "harmonically pure" was synonymous with 3/2 and 5/4?

The dictionary wasn't written in 1811! My copy was written in 1959 and
takes account of changes of meaning over time. Have a look at that web
site, there are an enormous number of people, including specialists in
various fields of the arts and sciences working continually to keep it up
to date. It is simply the case that that definition of "just" has stood the
test of time. If it had been based on ratios it would have needed an extra
entry every few years with a new upper limit on the numbers.

> Or do we
> accept Partch's and others' extension of the term to higher limits, the
> non-West, and the ancient Greeks by giving primacy to the composer's use of
> exactly-proportional relationships (the original meaning of just as a
> measurement)?

As far as I know, the audible-property definition does not exclude any of
these. Partch's tunings are audibly just (due to the presence of large
otonalities). Pythagorean is 3-limit just.

Which non-western did you have in mind, as just by your def but not mine?
Indeed some non-western tunings may only be just for certain inharmonic
timbres and not based on ratios.

> To me the latter is much more useful and consistent with use
> by composers in this century, though it does not contradict the use of the
> term in earlier times.

This isn't where the conflict exists. The conflict is between an
audible-property-based definition that would
(a) include LaMonte Young's dreamhouse, and at the same time
(b) exclude tunings indistiguishable from 12-tET,
and other definitions which would either include both (all ratios) or
exclude both (small ratios).

Regards,
-- Dave Keenan
http://dkeenan.com

--- In tuning@egroups.com, David C Keenan <D.KEENAN@U...> wrote:
> Dear Bill Alves and Jacky Ligon,
>
> Your recent posts in this thread suggest a misunderstanding of what
the
> Oxford English Dictionary project actually is (and has always
been). It's
> entries do not contain "frozen definitions" they show the evolution
of
> meanings through time and in all English-speaking countries. Please
read
>
> http://dictionary.oed.com/public/inside/
>
>

The Oxford English Dictionary is the accepted authority on the
evolution of the English language over the last millennium. It is an
unsurpassed guide to the meaning, history, and pronunciation of over
half a million words, both present and past. It traces the usage of
words through 2.5 million quotations from a wide range of
international English language sources, from classic literature and
specialist periodicals to film scripts and cookery books.

Dave and all,

Good Morning!

If "It is an unsurpassed guide to the meaning, history, and
pronunciation of over half a million words, both present and past.",
and "It's entries do not contain "frozen definitions" they show the
evolution of meanings through time and in all English-speaking
countries.", then naturally it makes one question if they may have
somehow missed the evolution of this term. Seems logical to me that
their delegates aren't researching this down in the
modern "microtonal trenches", if they have neglected (perhaps because
of the obscurity of contemporary meaning and practice) to make even a
footnote about the contemporary meaning this word has assumed for
many. With this doubt in mind, and the fact that their mission is to
track the evolution of meanings, I find it difficult to conclude that
the door of the Oxford English Dictionary must slam shut in the face
of the contemporary meaning of JI.

The above is not to further perpetuate needless clarification about
the Oxford English Dictionary meaning - I got this weeks ago, but is
to invite the possibility that this term is in serious need of being
updated to match the view of contemporary composers.

Really - what mechanisms do the fine delegates at the Oxford English
Dictionary have at their disposal to tap into this popularly
transformed word? The answer could be that they have absolutely no
direct connection to the current "JI" (contemporary meaning)
practices, so how would they know of it's contemporary
transformation? Doubtful they would, since it's sort of in the
underground, relative to many other popular musics. It makes me
wonder if they were to become aware of their own omission, would they
be interested in making note of it.

Maybe I'll just have to give them a call about all this!

: )

Thanks!

Jacky Ligon

Dave Keenan wrote,

>I think you will agree that musical theorists of this
>era were aware of the existence of whole numbers beyond six :-) and had
>ample opportunity to try ratios of 7 on monochords.

Yes, and though the reactions were mainly negative, there were a few
theorists (Huygens, Euler, Tartini) who saw a place for 7 in music.

>Presumably the relative purity of the 1/4-comma-meantone
>augmented sixth did not go unnoticed until Partch.

Did Partch even notice that himself??? Huygens noticed it -- although in his
day, string lengths were used instead of frequency ratios, so the chord he
analyzed as "4:5:7" is what we today call "1/7:1/5:1/4" -- an incomplete
French augmented sixth chord in meantone.

>I read this as, "the criterion of the ear is primary and 'it just so
>happens' that this corresponds to small-number ratios". And clearly he
>still wants to limit the size of the numbers, he isn't proposing that _all_
>whole-number ratios are just.

True -- as a matter of fact, Partch points out that at no point near the
interval of 25:24 does one hear any stability or consonance -- changing the
tuning of this ratio slightly simply makes the beats faster or slower. The
implication, in the context of the rest of Partch's philosophy, is that he
puts the "odd-limit for justness" somewhere between 11 and 23 -- and stuck
to 11 in his own music simply because he felt the step to 11 was already a
large enough one for one man to take.

Jacky wrote,

>With this doubt in mind, and the fact that their mission is to
>track the evolution of meanings, I find it difficult to conclude that
>the door of the Oxford English Dictionary must slam shut in the face
>of the contemporary meaning of JI.

Jacky, I don't know what you mean. Dave Keenan's interpretation of the OED
definition would include the music of contemporary composers like Partch,
Johnston, and LaMonte Young. Who's having a door slammed in their face?

--- In tuning@egroups.com, David C Keenan <D.KEENAN@U...> wrote:

> http://www.egroups.com/message/tuning/16505
>
> [Note: I say "whole number" rather than "integer" because
> I don't think anyone really intends to include negative numbers
> or zero.]

Good point which I've overlooked, Dave. I'll have to update
my definitions to reflect this.

>
> Does anyone have an early quote where a 4:7 (or other
> non-5-limit) ratio is referred to as "just" (or the
> arguable equivalent in a language other than English).
> Presumably the relative purity of the 1/4-comma-meantone
> augmented sixth did not go unnoticed until Partch.

I don't have references handy, but several centuries ago
(1700s, IIRC) Tartini described the 4:7 as "consonant" or
something similar. Partch includes this info in his book.

> > [Bill Alves:]
> > [Harry Partch] who defined it as "a system in which
> > interval- and scale-building is based on the criterion
> > of the ear and consequently a system and procedure limited
> > to small-number ratios."
>
>
> I read this as, "the criterion of the ear is primary and 'it
> just so happens' that this corresponds to small-number ratios".
> And clearly he still wants to limit the size of the numbers,
> he isn't proposing that _all_ whole-number ratios are just.
>
> ...
>
> > [Bill Alves:]
> > David Doty's definition for some time has been, "Just
> > Intonation is any system of tuning in which all of the
> > intervals can be represented by whole-number frequency
> > ratios, with a strongly implied preference for the
> > simplest ratios compatible with a given musical purpose."
>
>
> I fully understand why it is so tempting, especially in this
> day of readily available computers and digitally tunable
> instruments, to try to make a definition like this, based
> on the numbers. But with its "strongly implied" it tries
> to sit on the fence about whether there is a limit to the
> size of the numbers or not, perhaps in recognition that it
> is as much a mistake to limit the numbers (to less than some
> particular value) as it is not to limit them at all. The
> way out is to go back to the audible property.

This Doty definition is pretty darn close to Partch's.
I'd say that the "sitting on the fence" aspect stemmed
directly from Partch's desire to include larger numbers
in his ratios (specifically, to increase the prime- and
odd-limits).

And I reiterate, note that Partch chose to label his
tuning system as "Monophony", a subheading under the
broader label "just intonation".

> This isn't where the conflict exists. The conflict is
> between an audible-property-based definition that would
> (a) include LaMonte Young's dreamhouse, and at the same
> time (b) exclude tunings indistiguishable from 12-tET,
> and other definitions which would either include both
> (all ratios) or exclude both (small ratios).

A very good summary of the argument, Dave.

-monz
http://www.ixpres.com/interval/monzo/homepage.html
'All roads lead to n^0'

--- In tuning@egroups.com, ligonj@n... wrote:

> http://www.egroups.com/message/tuning/16509
>
>
>

> If "It [the Oxford English Dictionary] is an unsurpassed
> guide to the meaning, history, and pronunciation of over
> half a million words, both present and past.", and "It's
> entries do not contain "frozen definitions" they show the
> evolution of meanings through time and in all English-speaking
> countries.", then naturally it makes one question if they
> may have somehow missed the evolution of this term. Seems
> logical to me that their delegates aren't researching this
> down in the modern "microtonal trenches", if they have
> neglected (perhaps because of the obscurity of contemporary
> meaning and practice) to make even a footnote about the
> contemporary meaning this word has assumed for many.

Jacky, please *do* call them about this! I agree with you
that it's very likely that the Oxford experts may have missed
out on some of the more recent nuances of meaning in the
definition of "just intonation". Send them an email with
the URL to this list, and some links to various posts in
the debate! I'd bet that they *would* consider adding a
few more sub-definitions, or at least a footnote.

-monz
http://www.ixpres.com/interval/monzo/homepage.html
'All roads lead to n^0'

--- In tuning@egroups.com, "Paul H. Erlich" <PERLICH@A...> wrote:
> Jacky wrote,
>
> >With this doubt in mind, and the fact that their mission is to
> >track the evolution of meanings, I find it difficult to conclude
that
> >the door of the Oxford English Dictionary must slam shut in the
face
> >of the contemporary meaning of JI.
>
> Jacky, I don't know what you mean. Dave Keenan's interpretation of
the OED
> definition would include the music of contemporary composers like
Partch,
> Johnston, and LaMonte Young. Who's having a door slammed in their
face?

Paul and all,

Hello!

If one is to conclude from this that every chord of every single
composition by these composers can be qualified as Just Intonation in
the OED sense, then I totally fail to see the significant difference,
between that which would truly differentiate or disqualify a system
such as Margo Schulter's, Bill Alves', or mine for that matter, from
fitting into this category. An especially difficult stretch, is to
infer that one is or isn't using a similar aesthetic, without first
hearing their music (since it is an audible quality we want to
perceive after all).

I find it exceedingly difficult to believe that it could be shown to
be true, that these composers you listed here have produced music
which is totally beatless. I think just one listen to "The World of
Harry Partch" would reveal beating in the simultaneities of his
music. If it's an audible quality of beatlessness which is always and
perpetually present in a composition that makes it "JI", then perhaps
we need to continue to rethink this whole thing.

I would enjoy and hugely benefit from seeing and hearing proof that
all of these composers do not, and perhaps have never had chords in
there music which deviate from the OED meaning. I just find this
nearly impossible to believe! So Partch had no beats in his music? I
perceive something "unusual" in this inference.

If I'm still missing something here please do take the liberty of
correction, as I stand to be further instructed.

Gratefully,

Jacky Ligon

It's interesting to go here (Encyclopedia Britannica online) and do a
search on "just intonation".
http://www.eb.com/limited_search.html

You only get the first x words of the definition but it is clearly only
referring to 5-limit. "pure natural thirds and fifths". You can sign up for
a 14 day free trial to read more (but there isn't much more in that entry).
I can only legally reproduce here 15% of any entry/article, or 1000 words,
whichever is less.

I signed up for the 14 day trial and followed many links where just
intonation is referred to in other parts of the Britannica and found the
following which appears to contradict the above.

From the Britannica article on 'Tuning and temperament':
-----------------------------------------------------------------------
"Ptolemaic tuning, often misleadingly named just intonation, sacrifices
one of the fifths (D-A), which is altered to 40:27 from the simpler
ratio 3:2, making it flat (too narrow) by a comma. The advantage of
this system is that all the major thirds are true, or "in tune," as are all
the major sixths except F-D, which is tuned to the ratio 27:16, as in
the Pythagorean tuning (instead of to 5:3)."
-----------------------------------------------------------------------

Even if what we are discussing _is_ "extended JI", as Monz has been saying,
it seems inevitable that the "extended" will be dropped and we will refer
to the other as "5-limit-JI".

Jacky Ligon wrote:

> If one is to conclude from this that every chord of every single
> composition by these composers can be qualified as Just Intonation in
> the OED sense ... An especially difficult stretch, is to
> infer that one is or isn't using a similar aesthetic, without first
> hearing their music (since it is an audible quality we want to
> perceive after all).

As I said before, I am not very concerned about defining what is JI music.
My main concerns are JI interval, chord, scale and tuning. I also said I'd
be happy to call a piece of music JI if more than 50% of its harmonies were
just or more than 50% of it was in a just scale.

The OED only clearly defines what "just" means when applied to an interval,
and with its "etc." leaves open the question of what other musical objects
it might apply to.

> I find it exceedingly difficult to believe that it could be shown to
> be true, that these composers you listed here have produced music
> which is totally beatless. I think just one listen to "The World of
> Harry Partch" would reveal beating in the simultaneities of his
> music.

I have only ever heard one very short piece by Partch (I forget its name,
something about a waterfall? Carl Lumma?) and I certainly couldn't tell if
it contained Just simultaneities or not, due to the previously mentioned
rapidly decaying inharmonic timbres and rapid progress. I have however
examined some of Partch's tunings (reproduced from his mathematical
description of them), and given the freedom to sustain their chords and use
harmonic timbres, I am quite prepared to agree that they are just.

One might wish to say that some Partch piece is non-just although it is in
a just scale (sort of the opposite of Barbershop, which is just but in a
non-just scale) but I'm prepared to grudgingly give the benefit of the
doubt and allow that such a piece may be called just. At least it doesn't
particularly sound non-just.

> Show me any Barbershop Quartet singer, or any singer that can
> deliberately sing "within +-0.5 cents" of Just Intonation ...

I realise I said that Barbershop was the epitome of just intonation. I am
happy to retract that, but if it is allowed to stand, I must qualify it by
saying that it is not _accuracy_ of just harmony that it epitomises, but
_quantity_.

I only proposed +-0.5 cent as a deviation from small whole-number ratios
that (almost?) everyone can agree is still just, despite not actually
corresponding to a small whole-number ratio. I also proposed +-5 cents as a
deviation that (almost?) everyone would find too large to still be
considered just (based on 1/4 comma meantone not being considered just). In
between those limits I expect much disagreement, and as you point out,
major and minor thirds can tolerate greater mistuning than fifths. But
these were only proposed as rough rules-of-thumb say for ratios up to an
a*b complexity of 99 (or 11-odd-limit) as bare dyads.

> In light of the above challenge, can it truly be shown that
> Barbershop Quartet singing is really the ironclad and unshakeable
> proof we need of the definition of JI? To clarify my point here: If
> indeed a "beatlessness" is perceived in the chords of this music, and
> yet we are saying also that there must be "within +-0.5 cents"
> accuracy for it to truly be considered JI, then which am I to
> understand is correct; an audible quality of beatlessness, or
> the "within +-0.5 cents" rendered accuracy of the performance?

The audible quality.

We can forget the +-0.5 cents. The reason I brought it up was that even
folks who say JI is strictly ratios, routinely tolerate _at_least_ +-0.5
cent mistunings, which are not strictly ratios.

Whatever deviation barbershop competition winners (or merely competitors)
do have (after the initial adaptation period for each chord) could well be
taken as defining the upper limit for what is considered JI (for those
particular chords in that timbre and register).

> And to illustrate the problem in
> front of us all in pursuance of this topic, when a singer deviates
> "+-5 cents" whilst singing a 3/2 or 2/1 in a harmony, what do you get?
> Beats showering down like raindrops in a hurricane! Although with
> thirds (or other intervals, according to the chord voicing) this
> might be less perceptible.

Yes indeed. That's a good point, and serves to remind us that it's the
perception that matters. The actual number of cents deviation that is
perceptible will depend on many factors.

> To
> clarify: If certain chord tones are slightly distuned to where there
> is only very slow beating, would we not generally tend to perceive
> this as also being justly intoned? Especially if one were to hear it
> without having first tuned the interval themselves. Would this slight
> phasing make any difference in qualifying a chord as being justly
> intoned?

It wouldn't disqualify it for me.

> To answer your question, in light of the Keenanian/OED definition,
> being an audible quality, likely it would be construed as "true
> JI".

Quite correct. If JdL's vertical tunings deviate from simple ratios by no
more than does barbershop, then I would call it JI. Adaptive-JI is still
JI, but quasi-JI isn't. Others may not be so generous, and may wish to also
disqualify barbershop from being just.

Here's the home page of the Society for the Preservation and Encouragement
of Barber Shop Quartet Singing in America (SPEBSQSA, Inc.)
http://www.spebsqsa.org/

See particularly:
http://www.spebsqsa.org/Music/definition.htm
which contains the following sentence:

-----------------------------------------------------------------------
"Barbershop singers adjust pitches to achieve perfectly tuned chords in
just intonation while remaining true to the established tonal center."
-----------------------------------------------------------------------

Jacky, sorry for the confusion. Thanks for helping me clean up my act.

Regards,
-- Dave Keenan
http://dkeenan.com

In-Reply-To: <918s5v+v3rt@eGroups.com>
Jacky Ligon wrote:

> I find it exceedingly difficult to believe that it could be shown to
> be true, that these composers you listed here have produced music
> which is totally beatless. I think just one listen to "The World of
> Harry Partch" would reveal beating in the simultaneities of his
> music. If it's an audible quality of beatlessness which is always and
> perpetually present in a composition that makes it "JI", then perhaps
> we need to continue to rethink this whole thing.

I don't think this word "beatless" is a good charactarisation of JI. I'm
surprised it's still being used this late into the discussion.

Say you have two notes 0.5 cents apart, fulfilling the strictest criterion
so far of JI. The difference tone can be approximated as a ratio of
ln(2)*0.5/1200 from the original pitch. Say the notes or partials are at
440 Hz, that puts the beats at 440*ln(2)*0.5/1200 = ln(2)*220/1200 =
ln(2)*11/60 = 0.055 Hz. So there's a beat at something like 18 seconds
(probably a factor of 2 out). You're going to hear that, if the notes are
sustained long enough for their "JI-ness" to be apparent. If they get out
of tune to 5 cents, the upper limit mentioned for JI, the beating will be
every 1.8 seconds. And that'll mix in with the beats of other notes and
partials thereof in the chord. So much more out of tune, and you won't
hear beats, you'll hear roughness.

Really, beating is precisely the sound of JI. Theoretically perfect JI
would phase lock, but that's almost impossible to achieve without
electronics. You don't hear beating with 12-equal, at least not with
thirds. You hear a mush of chorusing. If the chords (especially in the
11-limit) are well enough tuned that you can hear beats between
non-unisons, you can call it JI.

(after lighting blue touch paper, retreat to a safe distance)

Graham

--- In tuning@egroups.com, David C Keenan <D.KEENAN@U...> wrote:
>
> As I said before, I am not very concerned about defining what is JI
music.
> My main concerns are JI interval, chord, scale and tuning. I also
said I'd
> be happy to call a piece of music JI if more than 50% of its
harmonies were
> just or more than 50% of it was in a just scale.
>
> The OED only clearly defines what "just" means when applied to an
interval,
> and with its "etc." leaves open the question of what other musical
objects
> it might apply to.

Dave and all,

It occurred to me this morning that the popularized and transformed
meaning of the term JI, could better be stated as:

Just Intonation: A facet of musical style, built upon an integer
ratio based tuning system, in which chords are capable of being
justly intoned as an important and predominantly used feature of a
composition.

I really think it's the "A facet of musical style", that we have not
considered in the light of the contemporary meaning of this term. And
it is the very thing that I think we must consider as a footnote to
the OED definition.

>
> I have only ever heard one very short piece by Partch (I forget its
name,
> something about a waterfall? Carl Lumma?) and I certainly couldn't
tell if
> it contained Just simultaneities or not, due to the previously
mentioned
> rapidly decaying inharmonic timbres and rapid progress. I have
however
> examined some of Partch's tunings (reproduced from his mathematical
> description of them), and given the freedom to sustain their chords
and use
> harmonic timbres, I am quite prepared to agree that they are just.

And I think this is the really tricky part for all of us; is that
when we are discussing the mathematical "bare ratio" without
considering the timbres being used, then we are indeed dealing with a
mathematically abstracted analysis of a musical system, which might
look one way on paper, and behave in another when perceived as an
audible quality. Truly challenging, is to agree that inharmonic
timbres are being "justly intoned" or not (more on this later today).

>
> One might wish to say that some Partch piece is non-just although
it is in
> a just scale (sort of the opposite of Barbershop, which is just but
in a
> non-just scale) but I'm prepared to grudgingly give the benefit of
the
> doubt and allow that such a piece may be called just. At least it
doesn't
> particularly sound non-just.

Again this references the above idea of justly intoning as a "facet
of style". Surely there is little interesting music written which is
totally beatless - it would likely be a bland sound with out the
needed tensions of complexity. It would be a rather subjective call
in my mind, to attempt to define percentages of justly intoning in
compositional settings, which would qualify one's style or individual
compositions as JI, and might just be easier to say that JI is a
facet of one's style. Perhaps this could be truer to the OED
definition, while embracing its popular meaning as a stylistic
reference.

Kind Thanks,

Jacky Ligon

--- In tuning@egroups.com, graham@m... wrote:
> In-Reply-To: <918s5v+v3rt@e...>
> Jacky Ligon wrote:
>
> > I find it exceedingly difficult to believe that it could be shown
to
> > be true, that these composers you listed here have produced music
> > which is totally beatless. I think just one listen to "The World
of
> > Harry Partch" would reveal beating in the simultaneities of his
> > music. If it's an audible quality of beatlessness which is always
and
> > perpetually present in a composition that makes it "JI", then
perhaps
> > we need to continue to rethink this whole thing.
>
> I don't think this word "beatless" is a good charactarisation of
JI. I'm
> surprised it's still being used this late into the discussion.
>

Graham,

Hello!

I would tend to agree that it is not an appropriate word to use when
referring to Just Intonation as a facet of one's musical style, but I
have been using in relation to the OED definition for clarification.

> Say you have two notes 0.5 cents apart, fulfilling the strictest
criterion
> so far of JI. The difference tone can be approximated as a ratio
of
> ln(2)*0.5/1200 from the original pitch. Say the notes or partials
are at
> 440 Hz, that puts the beats at 440*ln(2)*0.5/1200 = ln(2)*220/1200
=
> ln(2)*11/60 = 0.055 Hz. So there's a beat at something like 18
seconds
> (probably a factor of 2 out). You're going to hear that, if the
notes are
> sustained long enough for their "JI-ness" to be apparent. If they
get out
> of tune to 5 cents, the upper limit mentioned for JI, the beating
will be
> every 1.8 seconds. And that'll mix in with the beats of other
notes and
> partials thereof in the chord. So much more out of tune, and you
won't
> hear beats, you'll hear roughness.
>
> Really, beating is precisely the sound of JI. Theoretically
perfect JI
> would phase lock, but that's almost impossible to achieve without
> electronics. You don't hear beating with 12-equal, at least not
with
> thirds. You hear a mush of chorusing. If the chords (especially
in the
> 11-limit) are well enough tuned that you can hear beats between
> non-unisons, you can call it JI.
>

I think that when you say "beating is precisely the sound of JI", you
are in direct accord with what I'm saying about the contemporary
meaning of this word, which again, can perhaps be best described as
a "facet of style", where the integer based tuning system is capable
of justly intoning chords as a prominent feature of the style of a
composition.

Thanks,

Jacky Ligon

Jacky wrote,

>If one is to conclude from this that every chord of every single
>composition by these composers can be qualified as Just Intonation in
>the OED sense, then . . .

>I find it exceedingly difficult to believe that it could be shown to
>be true, that these composers you listed here have produced music
>which is totally beatless.

Jacky, you're missing an essential part of Dave Keenan's definition of "just
intonation" as a tuning system: You're allowed to have plenty of dissonant
chords and beating sonorities, as long as each note in the tuning system is
connected to at least one other by a "just" (OED) relationship, and the
connections can potentially extend from any note to any other note -- and
therefore no note in the tuning can be changed without sacrificing at least
one "just" (OED) relationship. Perhaps Dave K. extended beyond the OED here,
but since he's the one you're having this argument against, perhaps you
should take the time to understand his definition better.

Jacky wrote,

>Surely there is little interesting music written which is
>totally beatless

The only example that comes to mind is the "panconsonant" (Margo's term)
Renaissance repertoire, if performed in adaptive JI. But I think that the
term JI, if not synonymous with RI, does (in the literature) include those
cases where the _pitches_ derived from beatless sonorities are potentially
combined in dissonant ways. Also, I don't think adaptive JI can be
considered "JI" without further qualification (namely, that the ratios will
apply to the harmonic, but not melodic, intervals) -- otherwise the
distinctions made in the literature fall apart.

--- In tuning@egroups.com, "Paul H. Erlich" <PERLICH@A...> wrote:
> Jacky wrote,
>
> >If one is to conclude from this that every chord of every single
> >composition by these composers can be qualified as Just Intonation
in
> >the OED sense, then . . .
>
> >I find it exceedingly difficult to believe that it could be shown
to
> >be true, that these composers you listed here have produced music
> >which is totally beatless.
>
> Jacky, you're missing an essential part of Dave Keenan's definition
of "just
> intonation" as a tuning system: You're allowed to have plenty of
dissonant
> chords and beating sonorities, as long as each note in the tuning
system is
> connected to at least one other by a "just" (OED) relationship, and
the
> connections can potentially extend from any note to any other note -
- and
> therefore no note in the tuning can be changed without sacrificing
at least
> one "just" (OED) relationship. Perhaps Dave K. extended beyond the
OED here,
> but since he's the one you're having this argument against, perhaps
you
> should take the time to understand his definition better.

Paul,

Hello!

No, actually I do get his meaning (and the OED one as well), and was
just merely questioning the degree to which one must be using the
audible quality of JI (OED) to consider JI a dominant facet of a
composer's style - or to further probe what we will allow to be
called a "JI Style". Please read my following posts and related
replies for clarification of my points on this (including Dave's last
reply).

Thanks,

Jacky Ligon

Jacky wrote,

>No, actually I do get his meaning (and the OED one as well), and was
>just merely questioning the degree to which one must be using the
>audible quality of JI (OED) to consider JI a dominant facet of a
>composer's style - or to further probe what we will allow to be
>called a "JI Style". Please read my following posts and related
>replies for clarification of my points on this (including Dave's last
>reply).

Hmm . . . not sure if I'm missing something, but my interpretation of Dave
K.'s interpretation would be that the pitches should be derivable from one
another using the audible quality of JI, and that the composer is then free
to do whatever he or she wants with them. Of course, we're treading on thin
ice here, since Partch shows a near-12tET major scale in his system . . . I
guess there will always be a gray area . . .

--- In tuning@egroups.com, graham@m... wrote:
> I don't think this word "beatless" is a good charactarisation of JI.
I'm
> surprised it's still being used this late into the discussion.
...
> much more out of tune, and you won't
> hear beats, you'll hear roughness.
>
> Really, beating is precisely the sound of JI.
...
> If the chords (especially in the
> 11-limit) are well enough tuned that you can hear beats between
> non-unisons, you can call it JI.
>
> (after lighting blue touch paper, retreat to a safe distance)

You won't get any explosions from me.

Strike the word "beatless" from my definitions.

However, I think that beats are still perceptible _as_ beats up to
at least 10 Hz and I don't think many people will accept a 10 Hz beat
as just.

And I think we can include phase-locked as just, however undesirable
phase-locking might be.

So replace "beatless" with "slowly beating" in my attempted
definitions.

Listen to your favourite barbershop and start timing those beats guys.
:-)

Regards,
-- Dave Keenan

[JdL]
>>See my post, "Barbershop Spectrogram", circa Dec. '98 (the files for
>>the post are temp. off line, but I will provide them upon request).
>
>I would very much like to see this!

[Dave Keenan]
>I can't find this post in the archive. Please post a copy or the URL.
>I'm not sure I need the files. I only want the method, results and
>conclusions, not the data.

I ran a short excerpt of a barbershop sonority from a 1970's recording
through Spectrogram (Windows freeware). No deviation from 7-limit JI
greater than the resolution of the fft was found, even at the highest
resolution that produced usable results, given the performance of the
software and the sample rate of the recording.

Here's the post:

[CKL]
>The other day Dan Wolf recommended a freeware spectrogram program and
>I downloaded it. It works really well.
>
>To test the program, I thought I'd try some Barbershop. For the test,
>I picked a brief excerpt of song by the Happiness Emporium. This
>group did most of their recordings (including this one, from their
>album "That's Entertainment!") back in the 70's, when Barbershop
>technique wasn't a shadow of what it is today. However, they have a
>nice sound, and I thought I'd give them a try.
>
>Using Cool Edit, I extracted the CD audio to 16-bit 44.1 WAV format,
>and mixed it down from stereo to mono. I then ran it thru
>Spectrogram, fiddling with the settings until I got a clear picture.
>The values used to produce the image full.bmp are:
>
>Attenuation = 0
>Palette = CB
>Freq Scale = Log
>FFT Size (points) = 8192
>Freq Resolution (hertz) = 5.4
>Band (hertz) = 10-22050
>Time Scale (ms) = 12
>Spectrum Average (ms) = 1
>Toggle Grid = off
>
>This example contains a nice C7 chord, and I cropped it with Cool Edit
>and spectrogrized it with the same options as above, except with a time
>scale of 4 miliseconds.
>
>Then, I opened Notepad with the idea that I'd write down the frequencies
>of the first 9 peaks (starting at the bottom of the graph) in this chord
>that I could get a signal strength of greater than -40 dbs out of. I
>picked the number 9 arbitrarily. I started at the bottom because I knew
>that's where most of the parts would be.
>
>I didn't take the readings from the same time on the graph. Rather, I
>took each reading at the strongest point in each peak (it happened that
>all of these fell very near each other, in third quarter or so of the
>total time). The crosshairs have a resolution of 1cps, and I did some
>careful work with the mouse. If there was a range of frequencies that
>shared the same strength, I took the one closest to the middle of the
>range, taking the higher frequency if the range was odd.
>
>After I had done all that and closed Spectrogram, I turned the text
>file into the chart in up.txt. I am at a loss to explain the results.
>With the transform limited to a frequency resolution worse than 5 hertz,
>I should not have gotten anywhere as close to JI as I did -- yet a
>coincidence here seems unlikely.
>
>It may be noticed that I do not have the Lead part labeled in the up.txt
>chart. At first I thought that maybe the Baritone was at peak3 and the
>Lead at peak4, with peak2 being 5-3. However, this would be an unusual
>voicing, and listening reveals that the chord is in standard Barbershop
>voicing -- the Baritone is singing peak2, and the Lead is singing a 5/2
>above the bass. This Lead pitch has a peak in the spectrogram (up.bmp)
>but doesn't appear in the chart because I couldn't get more than -40
>db's out of it.

Here's the chart:

[CKL]
>------------------------------------------------------------------------
>Peak Frequency Strength decimal cents possible ratio possible
> # (Hertz) (db) (peak#1=1) (raw) (w/cents error) origin
>------------------------------------------------------------------------
> 9 906 -29 7.0233 3374.6 7/4 (+5.8)
>------------------------------------------------------------------------
> 8 772 -27 5.9845 3097.5 3/2 (-4.5)
>------------------------------------------------------------------------
> 7 644 -26 4.9922 2783.6 5/4 (-2.7)
>------------------------------------------------------------------------
> 6 579 -25 4.4884 2599.4 9/8 (-4.5) #1+5?
>------------------------------------------------------------------------
> 5 452 -34 3.5039 2170.7 7/4 (+1.9) Tenor
>------------------------------------------------------------------------
> 4 387 -30 3.0000 1902.0 3/2 (0.0)
>------------------------------------------------------------------------
> 3 258 -39 2.0000 1200.0 1/1 (0.0)
>------------------------------------------------------------------------
> 2 193 -34 1.4961 697.5 3/2 (-4.5) Baritone
>------------------------------------------------------------------------
> 1 129 -37 1.0000 0.0 1/1 (0.0) Bass
>========================================================================

-Carl

On Fri, 15 Dec 2000 04:24:36 -0000, "Dave Keenan" <D.KEENAN@UQ.NET.AU>
wrote:

>--- In tuning@egroups.com, graham@m... wrote:
>> Really, beating is precisely the sound of JI.
>...
>> If the chords (especially in the
>> 11-limit) are well enough tuned that you can hear beats between
>> non-unisons, you can call it JI.
>>
>> (after lighting blue touch paper, retreat to a safe distance)
>
>You won't get any explosions from me.
>
>Strike the word "beatless" from my definitions.
>
>However, I think that beats are still perceptible _as_ beats up to
>at least 10 Hz and I don't think many people will accept a 10 Hz beat
>as just.
>
>And I think we can include phase-locked as just, however undesirable
>phase-locking might be.
>
>So replace "beatless" with "slowly beating" in my attempted
>definitions.

Hmm.... Naturally, some amount of beating is expected in any real-world
implementation of JI that doesn't involve digital synthesis, oscillators
tied together mechanically by gear ratios, or the equivalent. But I would
think it's a goal of JI to minimize beating of consonant intervals. I've
taken JI scales and added 3 Hz to every pitch, with the result that the
scale beats at a uniform rate for any given type of interval no matter
where it occurs in the range of the keyboard. Is that JI? Or is 3 Hz per
octave enough beating to put it in the tempered category? I think when the
beating is deliberately introduced, it makes more sense to consider it a
tempered scale, while if the beating is a natural result of trying to
approximate beatless combinations of notes imprecisely, it's JI.

Of course, examples like this "JI + n Hz" scale only show that there isn't
a sharp delineation of the boundaries of JI, which is true of just about
any definition of any word you can think of, outside of mathematics.
Perhaps the definition could read something like "beatless or nearly so".
Personally, I'd probably add "or as nearly so as possible", but I'm not
entirely opposed to including "nearly beatless" tuning as JI even if the
beating is intentional. I wouldn't use the word that way, but I don't think
it would be too inaccurate.

--
see my music page ---> ---<http://www.io.com/~hmiller/music/music.html>--
hmiller (Herman Miller) "If all Printers were determin'd not to print any
@io.com email password: thing till they were sure it would offend no body,
\ "Subject: teamouse" / there would be very little printed." -Ben Franklin

Graham wrote,

> Really, beating is precisely the sound of JI.

???A 12-tET major third in the middle of the piano beats 7 times a second.

Joseph Pehrson wrote in
http://www.egroups.com/message/tuning/16597

>Oh... while I'm on this topic. I would like to "weigh in" with what
>I believe is a slight caveat to using general dictionary sources to
>describe specific tuning terms which are evolving in the "tuning
>community."

Joseph,

You make a good point. However I'd like to point out that the idea that "JI
is tuning by any whole-number ratios" is not an _evolution_ of earlier
meanings, it is a radical departure, since it would include tunings which
were known to the ancients and which have never before been considered to
be JI. e.g. tunings indistinguishable from 12-tET.

The idea that "JI is tuning by small whole-number ratios" is not quite so
radical but unfortunately
(a) we don't have the maths worked out to say how small is small and under
what circumstances. Invoking the composer or scale designers _intention_
here is not merely too subjective it is narcissistic.
(b) it disallows tunings that have the same audible quality of justness but
are not based on whole-number ratios at all. e.g. barbershop singing,
tunings with deliberate slight offsets to introduce slow beats, stretched
just tunings to match piano inharmonicity.

The historical meaning, based on an audible criterion, has none of these
limitations.

>We have a bunch of "specialists" here on this list, and,
>yet, we can't come to a lexacographic concensus. How can we expect a
>general dictionary, even an authoritative one, to do similarly??

Because they can, in effect, "apply a low-pass filter" to eliminate the
very short term variations in meaning that arise in particular places.

>I, personally, would put more credence in the definition of tuning
>terms as they might appear in a specialized source, such as 1/1 or
>Xenharmonicon... These are evolving terms in action.

Or they may be momentary abberations, whose consequences have not yet been
fully appreciated.

Do you think 1/1 or XH would publish my proposed definition, and my
criticisms of currently popular definitions?

>We might only
>expect the "general" dictionaries to keep up later... (??)

Yes. And to ignore temporary abberations.

It seems to me that Partch, with his "criterion of the ear" would have been
quite happy with the OED definition.

Jack Ligon wrote
in http://www.egroups.com/message/tuning/16563

>Just Intonation: A facet of musical style, built upon an integer
>ratio based tuning system, in which chords are capable of being
>justly intoned as an important and predominantly used feature of a
>composition.
>
>I really think it's the "A facet of musical style", that we have not
>considered in the light of the contemporary meaning of this term. And
>it is the very thing that I think we must consider as a footnote to
>the OED definition.

Jacky,

I think your idea that "just intonation" has one contemporary meaning as "a
facet of musical style" is just fine. But the phrase "built upon an integer
ratio based tuning system," is unnecessary and I believe, simply wrong. How
about:

Just Intonation (2): A facet of musical style in which the tuning system
allows chords to be justly intoned as an important and predominantly used
feature of a composition. Such a tuning system is typically based on small
whole-number ratios.

Carl Lumma,

Why can't 1/1 : 9/7 : 11/8 be considered a just chord (with appropriate
timbre)? I haven't tried it, but wouldn't one hear new slow beats start up
if any note was slightly mistuned? Of course one must first establish that
the 8:11 can be heard as just, or the chord would be disqualified on that
ground, even by _my_ definition.

Regards,
-- Dave Keenan
http://dkeenan.com

--- In tuning@egroups.com, David C Keenan <D.KEENAN@U...> wrote:
>
> Jacky,
>
> I think your idea that "just intonation" has one contemporary
meaning as "a
> facet of musical style" is just fine. But the phrase "built upon an
integer
> ratio based tuning system," is unnecessary and I believe, simply
wrong. How
> about:
>
> Just Intonation (2): A facet of musical style in which the tuning
system
> allows chords to be justly intoned as an important and
predominantly used
> feature of a composition. Such a tuning system is typically based
on small
> whole-number ratios.
>

Dave,

Hello!

Agreed, and I understand your logic with this subtle modification. My
stated variation/interpretation of the popularized meaning was an
attempt to come to some sort of concensus about JI being an integral
part of a compositional system. And I think we are in agreement about
it being - by definition - an audible quality, whether ratio derived
or not. My main point with the "facet of style" spin, was to address
the fact that we had spoken little about this as a stylistic element
of music creation, as we were focused on the definition itself.

Thanks,

Jacky Ligon

[Dave Keenan]
>Why can't 1/1 : 9/7 : 11/8 be considered a just chord (with appropriate
>timbre)? I haven't tried it, but wouldn't one hear new slow beats start
>up if any note was slightly mistuned?

The chord is already too dissonant to hear slow beats.

>Of course one must first establish that the 8:11 can be heard as just,
>or the chord would be disqualified on that ground, even by _my_
>definition.

11:8 can be heard as just, but not in the above chord.

-Carl

--- In tuning@egroups.com, David C Keenan <D.KEENAN@U...> wrote:

http://www.egroups.com/message/tuning/16638

>
> You make a good point. However I'd like to point out that the idea
that "JI is tuning by any whole-number ratios" is not an _evolution_
of earlier meanings, it is a radical departure, since it would
include tunings which were known to the ancients and which have never
before been considered to be JI. e.g. tunings indistinguishable from
12-tET.
>

Well, this makes sense... but has the definition of "JI is tuning by
any whole-number ratios" ever been seriously considered as a
dictionary entry (without the "small number" caveat) in anything but
informal discussion??

>
> >I, personally, would put more credence in the definition of tuning
> >terms as they might appear in a specialized source, such as 1/1 or
> >Xenharmonicon... These are evolving terms in action.
>
>
> Or they may be momentary abberations, whose consequences have not
yet been fully appreciated.
>
> Do you think 1/1 or XH would publish my proposed definition, and my
> criticisms of currently popular definitions?
>

Well, that certainly is something to think about. Specialized
journals could have a "faddish" angle which would skew what they
would print.

Thanks for the commentary, Dave.... certainly more to think about
concerning this subject!

_________ ___ __
Joseph Pehrson

Herman Miller,

Thanks for your post
http://www.egroups.com/message/tuning/16413

I agree with your descriptions of the subtle difference in sound between
harmonic and inharmonic spectrum-based tunings, but the difference still
seems to me to be too subtle to disqualify the inharmonic from being
described as "just for that timbre", particularly with the piano being a
borderline case as Carl Lumma pointed out.

Thanks also for
http://www.egroups.com/message/tuning/16612

I'd like to say "beatless or nearly so" but there's another problem with
describing JI as beatless. Maximally rough dyads like 1:phi (833 cents) may
also be beatless but I don't think anyone wants to call them just. Of
course we know that roughness and beats are the same phenomenon at
different frequencies (as Carl Lumma said), but if we're after a definition
based on audible qualities we must distinguish beating from roughness.

So I'm still inclined to say "slowly beating" and let folks assume that
beatless is included by virtue of being "maximally slow beating" and avoid
the possibile assumption of being beatless by being maximally fast beating.

I think the injuctive definition avoids all these problems and is the
fundamental definition, but we'd still like the descriptive definition to
be as good as possible. Any other suggestions?

Just as we can't yet put cents values on deviations as a boundary between
just and non-just, I don't think we can put frequencies on beats. But we
can probably describe upper and lower bounds in common situations.

Regards,

-- Dave Keenan
http://dkeenan.com

P.S. to Herman Miller

Of course if we are going for a definition based on audible qualities we
must consider it irrelevant whether any beating is intentional or not, and
consider only how it sounds.

-- Dave Keenan
http://dkeenan.com

On Sun, 17 Dec 2000 16:44:10 -0800, David C Keenan <D.KEENAN@UQ.NET.AU>
wrote:

>I'd like to say "beatless or nearly so" but there's another problem with
>describing JI as beatless. Maximally rough dyads like 1:phi (833 cents) may
>also be beatless but I don't think anyone wants to call them just. Of
>course we know that roughness and beats are the same phenomenon at
>different frequencies (as Carl Lumma said), but if we're after a definition
>based on audible qualities we must distinguish beating from roughness.
>
>So I'm still inclined to say "slowly beating" and let folks assume that
>beatless is included by virtue of being "maximally slow beating" and avoid
>the possibile assumption of being beatless by being maximally fast beating.

Hmm... okay, how about taking the limit of slowly beating as the beat
frequency approaches zero? That would also work for slightly inharmonic
timbres such as the piano. I'm starting to agree that we need a definition
of JI based on the acoustic properties of instruments. "Small whole number
ratios" would be a first approximation for "mathematically ideal" timbres.

But I wonder if this new definition would include the Hammond organ scale
as just? For the Hammond organ timbre, it represents a scale with
"maximally slow beating". The same goes for 15-tet and my synthetic
Mizarian instrument samples (designed to have partials that approximate
15-TET). In this case it might be more useful to reverse the definition and
say that "The Hammond organ timbre is just for a scale that approximates
12-TET" and "The Mizarian trumpet timbre is (nearly) just in 15-TET".

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Dave Keenan wrote,

>Maximally rough

Not!

>dyads like 1:phi (833 cents) may
>also be beatless

It beats clearly and multiply in most timbres. Listen!

Just a reminder that the deadline for composition and paper submissions to
the MicroFest 2001 conference is, appropriately enough, 1/1 (i.e. Jan. 1,
2001). The full call for papers and compositions is at:

http://www2.hmc.edu/~alves/microfest2001.html

I look forward to seeing you all out here April 6-8!

Bill

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