Re: [tuning] Digest Number 3541

Reply to Dave Keenan:

I had hoped that by using the term "constructive" in connection with my idea that Just Intonation is more process than product, you would've picked up on some relationship to intutionism (Brouwer held that the initial perception ("twoity") was bound up with the perception of time passing). I'm not equipped well enough mathematically to pursue this much farther, but I certainly did not intend that my "constructive" approach had nothing to do with sound. Indeed, I find it has everything to do with the process of making sounds, even if the intended ideal is not (or never) physically realized.

In my opinion, composers have always wrestled with musical arrangements of sounds that were generally understood at the time to be incomprehensible, and the best composers have had the invention to find ways of making these sounds even more than simply comprehensible: Beethoven's Grosse Fuge was considered both unplayable and inaudible, but playing technique evolved to meet the challenge, while listeners discovered unused capacities. Sometimes crossing barriers of perception will require drastically changing the circumstances of music making: Conlon Nancarrow's complex canons demanded an alternative instrumentation (the player piano, although a number of these pieces are now played bu human pianists), La Monte Young's complexes of sines in higher rational relationship depends upon electronics, extended durations, and perhaps perception of sounds through senses more spatial than acoustic. And Alvin Lucier has discovered a number of elegant ways to make music from phenomena (brain waves, interference beating, room and object resonances) that were generally assumed to be too subtle for musical use. I agree that there is a defineable extent and limit to our musical perception, but I believe that (a) it is not yet defined, and (b) that definition has to be a dynamic one (and yeah -- our hearing could get worse as well: I recently received a sample of music as heard with a cochlear implant. Pitch discrimation reduced to a band of about a major third in width. Sarah Vaughan sounded like she was rapping. In fact, with an implant, everything sounds like rap...)

Finally, I appreciate your appeal for attempting to define Just Intonation by extrapolating from the sound itself. However, and reiterating my point about process instead of product, there is simply no single "sound of just intonation" from which to begin. When it comes to real musical materials, I am neither willing to play interval policeman with someone elese's music nor let someone else play interval policeman with my music. And I'm afraid that your idea about starting from a determination about which intervals are Just and which are not, is, absent from a real compositional context, let alone any of the potential contexts in which music might be made, not musically meaningful.

DJW

--- In tuning@yahoogroups.com, Daniel Wolf <djwolf@s...> wrote:
> Reply to Dave Keenan:
>
> I had hoped that by using the term "constructive" in connection with my
> idea that Just Intonation is more process than product, you would've
> picked up on some relationship to intutionism
...

OK. Sorry about that. Perhaps I would have got it if you had said
"constructivist" or "constructionist".

> In my opinion, composers have always wrestled with musical arrangements
> of sounds that were generally understood at the time to be
> incomprehensible,
...
> And I'm afraid that your idea about starting
> from a determination about which intervals are Just and which are not,

And those which we can't (and don't need to) decide on. I'm not
claiming it's a black-and-white kind of distinction.

> is, absent from a real compositional context, let alone any of the
> potential contexts in which music might be made, not musically
meaningful.
>

Maybe so, but can you understand that it's very relevant to me as a
listener. And can you believe that there _is_ a particular audible
quality of harmony that I have no other name for than justness?

And can you at least admit that the simple "tuning by ratios"
definition of JI is useless in helping a listener predict anything
about what they might hear, including that it could sound exactly like
it's in 12-equal?

Surely you use terms like "just major third" as contrasted with
"equal-tempered major third"?

-- Dave Keenan

In a message dated 6/6/2005 11:35:57 AM Eastern Standard Time,
d.keenan@bigpond.net.au writes:

Surely you use terms like "just major third" as contrasted with
"equal-tempered major third"?

-- Dave Keenan
Hi Dave,

Though I prefer the term polymicrotonalist, I consider myself a JI composer
as well. Accordingly, I have to set my own limits on what is to be considered
JI.

First, I would like to ask if there is an audible difference between rational
beatings in a complex dissonance formed determinidly by JI informance, and
irrational beatings formed by temperament-driven decisions. I feel there is
such a difference.

Second, regarding "And can you believe that there _is_ a particular audible
quality of harmony that I have no other name for than justness?," I think the
term may well be "lock." It is the lock of beatless JI intervals that is the
"particular audible quality of harmony" you may be seeking.

Third, I must disagree with the following:

"And can you at least admit that the simple "tuning by ratios"
definition of JI is useless in helping a listener predict anything
about what they might hear, including that it could sound exactly like
it's in 12-equal?"

Although, you make some good points about the Venn Diagramming of tunings,
each with common properties, you may have gone too far. Math is full of
different ways to say the same thing. The differences are from the different
semantic realms or perspectives which they are drawn from. Maybe this is a case of
multiple choice and we are to pick the "best" answer for the choices given.

In my head there is much to predict based on the idea of tuning by ratios,
only I'd like to exactly know how it is to be tuned.

Ivor Darreg spoke about the "immigration" of one tuning to another, rather
than the transposition of key to key. Each tuning had a gut level feel. 12-tET
has a restless quality to it that may well be indicative of the anxieties of
the past and present century.

In contradistinction, JI is delimited by its level of prime number activity.
The spiraling of numbers as with Pythagorean 3-limit and the 19-tET
culmination of 6/5 minor thirds are a different "take" on JI. It must be seen as such.
There are other takes to be explored, as well. I am glad that your notation
accounts for every such take.

all best, Johnny Reinhard

--- In tuning@yahoogroups.com, Daniel Wolf <djwolf@s...> wrote:

> And I'm afraid that your idea about starting
> from a determination about which intervals are Just and which are not,
> is, absent from a real compositional context, let alone any of the
> potential contexts in which music might be made, not musically
meaningful.

It sounds as if you are saying "JI" has no specific meaning now and
one should not be assigned. Is that it?

--- In tuning@yahoogroups.com, Afmmjr@a... wrote:
> In a message dated 6/6/2005 11:35:57 AM Eastern Standard Time,
> d.keenan@b... writes:
>
>
> Surely you use terms like "just major third" as contrasted with
> "equal-tempered major third"?
>
> -- Dave Keenan
> Hi Dave,
>
> Though I prefer the term polymicrotonalist, I consider myself a JI
composer
> as well. Accordingly, I have to set my own limits on what is to be
considered
> JI.
>
> First, I would like to ask if there is an audible difference between
rational
> beatings in a complex dissonance formed determinidly by JI
informance, and
> irrational beatings formed by temperament-driven decisions. I feel
there is
> such a difference.

If the numbers in the ratios are small enough then I expect there is.

It is also possible to design irrational temperaments so that the beat
rates of different intervals within a chord are equal (or in small
whole number ratios) which gives a more "Just" quality to these
tempered chords. So once again I would not say that it was
rational-ness per se that gives rise to the audible differences.

>
> Second, regarding "And can you believe that there _is_ a particular
audible
> quality of harmony that I have no other name for than justness?," I
think the
> term may well be "lock." It is the lock of beatless JI intervals
that is the
> "particular audible quality of harmony" you may be seeking.

Yes. But I don't insist on total "lock" before I will call an interval
"just". In fact I prefer slow beating.

> Third, I must disagree with the following:
>
> "And can you at least admit that the simple "tuning by ratios"
> definition of JI is useless in helping a listener predict anything
> about what they might hear, including that it could sound exactly like
> it's in 12-equal?"
>
> Although, you make some good points about the Venn Diagramming of
tunings,
> each with common properties, you may have gone too far. Math is
full of
> different ways to say the same thing. The differences are from the
different
> semantic realms or perspectives which they are drawn from. Maybe
this is a case of
> multiple choice and we are to pick the "best" answer for the choices
given.
>
> In my head there is much to predict based on the idea of tuning by
ratios,
> only I'd like to exactly know how it is to be tuned.
>
> Ivor Darreg spoke about the "immigration" of one tuning to another,
rather
> than the transposition of key to key. Each tuning had a gut level
feel. 12-tET
> has a restless quality to it that may well be indicative of the
anxieties of
> the past and present century.
>
> In contradistinction, JI is delimited by its level of prime number
activity.

Right. But in going to larger and larger whole-numbers in your ratios
there comes a point where absolutely anything is within 1/3 of a cent
(or whatever threshold you choose) of such a ratio. e.g. 51/50 and
52/51 are only 2/3 of a cent apart.

If someone tells me that a piece is in 7-limit JI then I know
something about what I am about to hear, but if they tell me it is in
19-limit JI I may well be about to hear something I can't tell from
12-equal (which isn't to say that a clever composer couldn't make the
distinction between 12-equal and its best 19-limit approximation
audible, however I don't think that anyone can make the difference
between 12-equal and its best 1001-limit approximation audible).

> The spiraling of numbers as with Pythagorean 3-limit and the 19-tET
> culmination of 6/5 minor thirds are a different "take" on JI. It
must be seen as such.

But they are certainly not _typical_ JI. I'd be happy to define them
out of JI.

> There are other takes to be explored, as well.

Sure.

> I am glad that your notation
> accounts for every such take.

Thanks.

-- Dave Keenan

--- In tuning@yahoogroups.com, "Dave Keenan" <d.keenan@b...> wrote:
have no other name for than justness?," I
> think the
> > term may well be "lock." It is the lock of beatless JI intervals
> that is the
> > "particular audible quality of harmony" you may be seeking.
>
> Yes. But I don't insist on total "lock" before I will call an interval
> "just". In fact I prefer slow beating.

Do we always get lock? It seems to me the opposite is true; if you
produce sounds with a system like Csound, it seems to me you'd get
increasingly slow beats, until you'd have to sustain the chord for a
ridiculous time to tell there was a beat, yet beat there will be. In
any case, asking for complete absence of slow beats in sustained
intervals does get you awfully close to rational intervals. Just
listening to the soundcard product of a midi file seems to allow for
very slow beats also, actually. Yet in a normal musical passage, you
can't hear them.