strict rules of rational interpretation

[Ray Tomes, TD 175.4]
> I don't think that the chord C-E-G-Bb can possibly mean anything
> other than the ratios 4:5:6:7 in any system of music. It may be
> classically correct that Bb is 16/9 times C or whatever (which
> it would be if played with an F) but the raios would then be
> 36:45:54:64 which is impossibly complex to be "intentional".

I totally disagree. The classical 'dominant 7th' chord was
considered a dissonance that had to resolve, and 36:45:54:64
suits that purpose quite well. The complexity is an intrinsic
part of the harmonic movement, of tension and resolution.
In this same musical context, 4:5:6:7 doesn't sound right,
as it would in the blues.

That's exactly why I specified that in the blues
'these chords *do not* follow the type of...', etc. etc.

[Tomes]
> The problem is that apart from the main notes in the key the
> others have multiple possible different meanings and so a
> strict rule will often be wrong.

And here you contradict your first sentence and basically
agree with what I just said.

What criteria do you use to determine which notes are the
'main' ones and which are the 'others'? What method do you
use to determine the 'multiple possible different' rational
interpretations for those others? What method to determine
which is the interpretation that applies?

I know that you're guided largely by natural cycles in the
universe, but music provides **quite** a variety of different
contexts within which one may try to make a rational
interpretation of the harmonies or pitches, and the
subjectivity of the listener itself affects this too.

In many cases where irrational pitches are specified they carry
numerical significance of their own, which is (I think) a point
Dans Stearns tries to make repeatedly.

I believe Charles Lucy would agree with that too, although he
doesn't like me calling his scale 'irrational', but that's what
it is, by definition.

Actually, I'm not at all sure that a *strict* rule can't be
used, but it would most certainly have to be an extremely
*complex* rule if it were to be strict. The *simple* strict
rule is the one that 'will often be wrong'.

Much of the recent discussion in this forum (which you've missed)
has been precisely about how to measure exactly that complexity,
and that's the very word we've kicked around. No definite
consensus has been reached, but general trends have begun to
emerge and there's some agreement.

[afterthought]

I still really like that name 'quantum harmonics'... in a way,
the history of tuning and music theory can be characterized by
the history of mathematics that paralleled (or actually ran a
bit ahead of) it.

In the past there was a phase where rational mathematics was
seen as the ultimate, then later the logarithmic, now...
relative and quantum harmony, why not?

A lot of musicians have already made the leap to chaotic.

(music, that is...
I wasn't intending to refer to their lives.)

(hmmm... just realized that 'chaotic harmony' is an oxymoron.
interesting...)

-monz

Joseph L. Monzo monz@juno.com
http://www.ixpres.com/interval/monzo/homepage.html
|"...I had broken thru the lattice barrier..."|
| - Erv Wilson |
--------------------------------------------------

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[Ray Tomes, TD 175.4]
> I don't think that the chord C-E-G-Bb can possibly mean anything other
than the ratios 4:5:6:7 in any system of music. It may be classically
correct that Bb is 16/9 times C or whatever (which it would be if played
with an F) but the raios would then be 36:45:54:64 which is impossibly
complex to be "intentional".

[Joe Monzo:]
>I totally disagree. The classical 'dominant 7th' chord was considered a
dissonance that had to resolve, and 36:45:54:64 suits that purpose quite
well. The complexity is an intrinsic
part of the harmonic movement, of tension and resolution. In this same
musical context, 4:5:6:7 doesn't sound right, as it would in the blues.

Joseph Yasser wrote of the a cappella music of the Russian Church: "where
the 'bad influence' of instrumental intonation, to which acousticians
sometimes like to point, has manifestly to be ruled out," and: "the
age-long practice of composers who, when unambiguously using this system
invariably resolved the minor seventh..."

Dan

Monz wrote:
> ... The classical 'dominant 7th' chord was
> considered a dissonance that had to resolve, and 36:45:54:64
> suits that purpose quite well. The complexity is an intrinsic
> part of the harmonic movement, of tension and resolution.
> In this same musical context, 4:5:6:7 doesn't sound right,
> as it would in the blues.

> [Tomes]
>> The problem is that apart from the main notes in the key the
>> others have multiple possible different meanings and so a
>> strict rule will often be wrong.

> And here you contradict your first sentence and basically
> agree with what I just said.

No I don't. I don't consider 36:45:54:64 is even one of the candidates
for being a reasonable 7th chord. Some examples where there is doubt is
when we play C-D which might be 8:9 but might be 9:10 and likewise for
some 3 and 4 note chords, but never 36:45:54:64.

Someone might speak unclearly in saying for example "I am not sure that
you are right" in that they could mean "I am unsure" or "I think you are
wrong" but they don't mean "Call on the Spannish Inquisition" if you see
what I mean.

> What criteria do you use to determine which notes are the
> 'main' ones and which are the 'others'?

I will post on the subject "Central Ratio of a Scale" in the near future
and answer this question in great detail, or at least gives a background
which allows this.

> What method do you
> use to determine the 'multiple possible different' rational
> interpretations for those others? What method to determine
> which is the interpretation that applies?

See the little slide rule device that I quoted in my post as being at
http://www.kcbbs.gen.nz/users/rtomes/aji-a.gif which I recommend that
you print out and cut in half horizontally. If you slide the halves
along you can answer all these questions. It basically recognises that
the ratios 1 2 3 4 5 6 7 8 etc occur at spacings in semitones in 12-tET
of 0 12 19 24 28 31 34 36 etc. By checking a set of notes against this
scale it is possible to find the simplest (and other nearly as simple)
arrangement that fits. Of course if music is not written in a 12
semitone scale then this does not apply. However the same principle can
be applied with a different table of numbers.

The question of which is the best choice is also addressed in my AJI
paper and a number of possible scoring schemes are considered. I think
that these need trying out and seeing what works in practice.

> I know that you're guided largely by natural cycles in the
> universe, but music provides **quite** a variety of different
> contexts within which one may try to make a rational
> interpretation of the harmonies or pitches, and the
> subjectivity of the listener itself affects this too.

The subjectivity of the listener is a part of the universe.
Our instincts, emotions, reactions are all built from aeons of existence
in the universe behaving as it does. However this is not important to
my argument - there is no reason to not use correct frequencies. I wish
that I hadn't mentioned "nature" at all because it is not really the key
point that I want to make which is "why not have correct frequencies?"

> In many cases where irrational pitches are specified they carry
> numerical significance of their own, which is (I think) a point
> Dans Stearns tries to make repeatedly.

> I believe Charles Lucy would agree with that too, although he
> doesn't like me calling his scale 'irrational', but that's what
> it is, by definition.

It is certainly possible that irrational ratios may be desired.
I am not saying that this should not be done. I am saying that we
should not get irrationality by default and no other option. That is
only chaos gone mad. I think that Charles may well be right that pi
does occur naturally in some cases.

> Actually, I'm not at all sure that a *strict* rule can't be
> used, but it would most certainly have to be an extremely
> *complex* rule if it were to be strict. The *simple* strict
> rule is the one that 'will often be wrong'.

This is true. However it is also true that even a simple rule will
produce more pleasant chords than any ET scale does, even if it
sometimes gets a wrong match on the ratios for a chord. From there on
it is all profits in the bank.

> Much of the recent discussion in this forum (which you've missed)
> has been precisely about how to measure exactly that complexity,
> and that's the very word we've kicked around. No definite
> consensus has been reached, but general trends have begun to
> emerge and there's some agreement.

I clearly need to have a look at some recent posts in the archives.
If you have any specific recommendations for me then please send me an
email with the date and subject or something. For the benefit of all I
just rejoined the list a few days ago after an absence of a couple of
years.

> [afterthought]

> I still really like that name 'quantum harmonics'... in a way,
> the history of tuning and music theory can be characterized by
> the history of mathematics that paralleled (or actually ran a
> bit ahead of) it.

> In the past there was a phase where rational mathematics was
> seen as the ultimate, then later the logarithmic, now...
> relative and quantum harmony, why not?

Interesting line of thought. I am of the opinion that the real universe
is much more ordered than present science thinks. Present scientific
theory is simply wrong in several of its interpretations and these have
lead it down a couple of blind alleys. Come to think of it this is just
the same with musical scales and tunings! Monz, you are on to a winner
here!

> A lot of musicians have already made the leap to chaotic.

Then they need saving. :-) I am here now to do that. :-)

By way of a hint at things to come I will simply suggest that irrational
frequency ratios can result from rational ratios that are disturbed by
harmonically related longer term modulations. An example of this in
"nature" is the 3.39 year cycle in the US stock market. This is
modulated by a 23.72 (3.39*7) year cycle so that it gets longer and
shorter by about half a year over the 23.72 year cycle.

Saying that chaos exists in some particular case can be just a failure
to see a big enough picture.

-- Ray Tomes -- http://www.kcbbs.gen.nz/users/rtomes/rt-home.htm --
Cycles email list -- http://www.kcbbs.gen.nz/users/af/cyc.htm
Alexandria eGroup list -- http://www.kcbbs.gen.nz/users/af/alex.htm
Boundaries of Science http://www.kcbbs.gen.nz/users/af/scienceb.htm

[Ray Tomes:]
>I am saying that we should not get irrationality by default and no other
option.

If only that were all that you say... (!)

[Tomes:]
>Present scientific theory is simply wrong in several of its
interpretations and these have lead it down a couple of blind alleys. Come
to think of it this is just the same with musical scales and tunings!

[Monzo:]
> A lot of musicians have already made the leap to chaotic.

[Tomes:]
>Then they need saving. :-) I am here now to do that. :-)

Hi Ray. When I said you 'agreed with me', I meant that
*you* said 'a strict rule will often be wrong', which was
exactly what I illustrated with my example.

I'm skipping responding to the big middle chunk of your
post because, in fairness, I want to visit your website first
and see exactly where you're coming from, and I won't have
time for that until later. But...

[Ray Tomes, TD 177.25]
>
> I am saying that we should not get irrationality by default
> and no other option.

Well, finally, something on which I can agree with you
wholeheartedly.

But you're talking about replacing it with another 'default
and no other option', and that's exactly what so many of us
on this list are against.

[Ray]
> ...the key point that I want to make which is "why not have
> correct frequencies?"

I think everyone on this list is interested in having the
'correct frequencies'. The problem is, what are they?

I know you have an answer ready, but I'm afraid it's just
not that simple.

As I said, music generally is full of dynamics of tension
and resolution, and the numbers involved in this interplay
don't have to be, but certainly *can* be, quite complex.

Music based on simple JI ratios usually lacks tension,
which is great if that's what you're aiming for; but if
it's not... We live in a world full of tension, and rather
than escape from that in their music, some composers like
to reflect it, and even wallow in it.
(do you hear me Dan Stearns?) :)

Also, you can't just assume that because digital electronics
is a JI panacaea for you (and it is for me too), that other
musicians want to give up playing instruments with strings
and holes and keyboard levers.

For those instruments, it's imperative to conscientiously design
a tuning system beforehand, and there are a lot of other factors
that go into that design besides mere rational or otherwise
'in tune with nature' correctness.

36:45:54:64 can be, is, and was, either used or implied for
the 'dominant 7th' chord on keyboards and other instruments for
maybe a couple of centuries. Just because you don't consider
it 'even one of the candidates for being a reasonable 7th chord'
doesn't mean other people don't.

As I said, in 'classical' music, it's very effective in a typical
cadential formula, and I am prepared to argue that it would be
the proper tuning of the chord in, say, a Beethoven string quartet
(altho string players probably wouldn't agree because they
like Pythagorean intervals).

This is the major criticism I have of Easley Blackwood's
otherwise excellent book _The Structure of Recognizable Diatonic
Tunings_. He consistently wants to use the simplest rational
interpretation for diatonic music, and it unfortunately just
doesn't work that way.

[Ray]
> I clearly need to have a look at some recent posts in the
> archives. If you have any specific recommendations for me...

I began archiving Tuning Digests at my site last November,
but haven't kept up with that for a while. I'll eventually
get around to putting all of my own postings on my site.
The ten or so that are there are worth looking at, because
they're linked into my dictionary and some have diagrams
I added to supplement the text discussion.

Since January 1 of this year, when the List migrated to Onelist,
there has been an archive which is searchable. The URL is:

http://www.onelist.com/arcindex.cgi?listname=tuning

Most of the really interesting discussion on 'complexity measures'
has been since about the middle of February. I suggest just
reading thru them all one by one since that date. Or you
could try searches on 'complexity' and 'lattice'.

You can also search by author. Some of the main contributors
in that discussion were Paul Erlich, Dave Keenan, Paul Hahn,
Carl Lumma, John Chalmers, Daniel Wolf and myself. Long and
interesting contributions on other subjects by Dave Hill and
Margo Schulter (and me - look at TD 132) are also well worth
reading. Apologies for leaving anyone out; speak up!

I also suggest [plug alert] looking up some of the terms in
my Tuning Dictionary which pertain to some of the more recent
concepts in tuning theory, or at least stuff that will make
you more familiar with my viewpoint: finity, bridging,
periodicity block, affect, prime, lattice, consistency, unique,
and of course, complexity and its related links.

http://www.ixpres.com/interval/dict/index.htm

I have links all over it that will lead you anywhere else you
need to go.

>> [me, monz]
>> I still really like that name 'quantum harmonics'...<snip>
>
> [Ray]
> Interesting line of thought. I am of the opinion that the real
> universe is much more ordered than present science thinks.
> Present scientific theory is simply wrong in several of its
> interpretations and these have lead it down a couple of blind
> alleys. Come to think of it this is just the same with musical
> scales and tunings! Monz, you are on to a winner here!

ooh - I just *love* biting sarcasm!

(Yet another reason why I miss Zappa so much!)

I really think it would be a good thing to think of harmony
and tuning in relativistic terms, especially given that
the listener's subjectivity can be such a widely variable
dimension in the 'algorithm', so to speak. It's interesting
that you choose to ignore this aspect.

I recommend, as I have before, a great book by Richard Norton
called _Tonality In Western Culture_ [1984], wherein Norton
takes the stance (correctly, IMO) that subjectivity has been
largely side-stepped in past theories of tonality, and he seeks
to restore it to its proper place in the scheme of things.

The bottom line with me, Ray, is that I've already been where
you are now, and the more research I do and the more interaction
I have here with others who hold different views, the more
mine change.

Paul Erlich, in particular, is a theorist worth coming to terms
with.

It may seem at first like he's just another tuning theorist
with his own pet theories (partly because he can get quite
aggressive when he *knows* he's right), but his opinions have
been formed after much *extremely careful* thought, and
usually, he *is* right!

He's the chief of the 'harmony police' around here
(and Paul Hahn's his deputy). :)

-monz

Joseph L. Monzo monz@juno.com
http://www.ixpres.com/interval/monzo/homepage.html
|"...I had broken thru the lattice barrier..."|
| - Erv Wilson |
--------------------------------------------------

___________________________________________________________________
You don't need to buy Internet access to use free Internet e-mail.
Get completely free e-mail from Juno at http://www.juno.com/getjuno.html
or call Juno at (800) 654-JUNO [654-5866]

[Ray Tomes, TD 175.4]
>> I don't think that the chord C-E-G-Bb can possibly mean anything
>> other than the ratios 4:5:6:7 in any system of music. It may be
>> classically correct that Bb is 16/9 times C or whatever (which
>> it would be if played with an F) but the raios would then be
>> 36:45:54:64 which is impossibly complex to be "intentional".

[Joseph Monzo, TD 176.6]
> I totally disagree. The classical 'dominant 7th' chord was
> considered a dissonance that had to resolve, and 36:45:54:64
> suits that purpose quite well. The complexity is an intrinsic
> part of the harmonic movement, of tension and resolution.
> In this same musical context, 4:5:6:7 doesn't sound right,
> as it would in the blues.

I wouldn't state it as categorically as Tomes, but to my ear, 4:5:6:7
is by far the best tuning for the V7 -> I transition (In this example,
C-E-G-Bb would resolve to F-A-C or some inversion thereof). The very
flat Bb falling to A has, to my ear, all the more sense of resolution
than the larger step implied by Monzo's tuning. To say that dissonance
must be added to the V7 in order to enhance the feeling of resolution is
incorrect, I believe.

Note that Mark Nowitzky talks about this issue, with tuning charts, at

http://www.pacificnet.net/~nowitzky/justint/dom7.htm

He adds a third tuning, in which the Bb is 9/5 of C, but, like Monzo
chooses 16/9 rather than 7/4.

It took me a while to like 4:5:6:7, but now anything else sounds nasty.
There is a longing in the sound that begs for resolution, yet there is
also a sweetness which comes from the 6 JI intervals.

JdL