Yahoo Tuning Groups Ultimate Backup metatuning an old post about 72-equal

http://members.tripod.com/~tuning_archive/Mills/html/s___3/msg_2800-
2999.html#2986

Date: Fri, 31 May 1996 10:40:20

Subject: Re: Boston Microtonal Society

From: PAULE

>The Boston Microtonal Society's mail address is 27
>Valentine Street, Cambridge, MA 02139. There doesn't seem to be
>a phone number or email address. They are trying to build up their
>membership so they can present more concerts, etc.

Gee, that's my zip code. Maybe I should pay them a visit. You have to
admit
that 72-tet is extremely convenient and comes extremely close to all
11-limit intervals, something Harry Partch seems to have overlooked
in his
glance at equal temperaments. For example, look at the
following "tones":

Ratio Degrees in 72-equal Conventional name
7:6 16 4/3-tone
8:7 14 7/6-tone
9:8 12 whole tone
10:9 11 11/12-tone
11:10 10 5/6-tone
12:11 9 3/4-tone

Of these, the greatest deviation from just intonation is for the
whole tone,
which, as is well known, is flat by 3.91000 cents. 72-tet seems like
a
perfect marriage between equal temperament and just intonation a la
Harry
Partch, with the added perk that everything is expressible in terms
of
conventionally used intervals. Additionally, it contains an excellent
representation of the golden ratio: 50/72 oct is only a quarter of a
cent
higher than the exact golden ratio. Since mathematicians consider the
golden
ratio "the most irrational number," it appears that 72-tet achieves
the
polar opposite of just intonation as well.

🔗Kraig Grady <kraiggrady@...>

🔗paulerlich <paul@...>

🔗Kraig Grady <kraiggrady@...>

Hello Paul!
Yes Paul this is an important observation that needed to be revived in
the resent post on 72. Glad you dug up your comment on this.
It was unclear how much of what you printed was from the previous post
so just wanted to clear this up. Just as the continuum can be "filled with
simple ratios, it is also possible to "fill" it with Noble ratios. It all
depends on how you wish to see the universe. I wonder if Julia is aware of
this feature of 72.
I don't know if anyone can be accused plagiarizing a "discovery" of a
property something, only when it entails "inventing".

paulerlich wrote:

> --- In metatuning@y..., Kraig Grady <kraiggrady@a...> wrote:
>
> > Paul!
> > this was just posted on last page of
> > http://www.anaphoria.com/tres.PDF
>
> cool! -- my post was 31 Mar 96, while Erv's article was 28 Jun 02. i
> hope therefore i won't be accused of plagiarizing these ideas -- i
> would certainly never dream of making any similar accusation. (i
> think it's your exclamation point, kraig, that got me nervous again.)
>
>
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-- Kraig Grady
North American Embassy of Anaphoria island
http://www.anaphoria.com

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

🔗paulerlich <paul@...>

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

> It was unclear how much of what you printed was from the
>previous post
> so just wanted to clear this up.

all of it was -- sorry!

> Just as the continuum can be "filled with
> simple ratios,

it can be filled with ratios (i.e. rational numbers), but only a few
of them will be simple -- unless i'm misunderstanding what you mean.

> it is also possible to "fill" it with Noble ratios.

true. any interval can be approximated more and more accurately by
more and more complex noble numbers. but again, only a few of them,
the "simple" ones, would seem to be relevant in a given context --
for example, the rings of saturn.

but what does erv think about phi? curiously, he writes that phi is
converged upon with "astonishing speed" by the fibonacci ratio
series. but this "astonishing speed" is in fact the *slowest possible
rate* of convergence -- no number is converged to more slowly than
phi. the latter (slowness of convergence) is the very raison d'etre
for phi's specialness in temes' paper. so erv's observation seems to
cast doubt upon the utility or importance of what temes points out. i
wonder if this was this conscious or unconscious on erv's part.

btw, i have my own views on "maximal harmonic mismatch" and how to
measure it in a perceptually relevant sense . . . i think such models
have a fundamental difference from circle maps or arnol'd tongues
where dynamicists tend to focus on the "golden-mean routes to
chaos" . . .

>It all
> depends on how you wish to see the universe. I wonder if Julia is
>aware of
> this feature of 72.

dollars to doughnuts she isn't and doesn't care. i'm planning to be
involved in the boston microtonal community for the forseeable
future, so hopefully she and i will have the opportunity to rub off
on one another.

> I don't know if anyone can be accused plagiarizing
>a "discovery" of a
> property something, only when it entails "inventing".

so plagiarism is impossible in, say, the field of chemistry, but is
possible in chemical engineering? hmm . . .

🔗Kraig Grady <kraiggrady@...>

Hello Paul!

paulerlich wrote:

>
>
> true. any interval can be approximated more and more accurately by
> more and more complex noble numbers. but again, only a few of them,
> the "simple" ones, would seem to be relevant in a given context --
> for example, the rings of saturn.

we keep an open mind that the more complex might have properties that the
simples don't or a meaningful variation can occur replacing a simpler with
a more complex.

>
>
> but what does erv think about phi?

It is not fair for me to speak completely for him on this. so this is just
my take on this.
I think he finds it produces "consonances" all it own, albeit in a
different world than JI

> curiously, he writes that phi is
> converged upon with "astonishing speed" by the fibonacci ratio
> series.

i think he is just referring how close you get to within a few decimal
points using ratios.

> but this "astonishing speed" is in fact the *slowest possible
> rate* of convergence -- no number is converged to more slowly than
> phi.

like never really as i understand it.

> the latter (slowness of convergence) is the very raison d'etre
> for phi's specialness in temes' paper.so erv's observation seems to

> cast doubt upon the utility or importance of what temes points out. i
> wonder if this was this conscious or unconscious on erv's part.

he does not come to Temes conclusion. One such reason being that the
difference tones generated will often generate other tones of your scale.
How dissonant can that be?
the clash of difference tones being no less significant than harmonic so
what is the dissonant of one is the consonant of the other.
If entropy is (according to Arnheim) not the result of a singular
homogeneous like randomness but the result of conflicting and irreconcilable
orders then i guess maximum dissonance would exist in-between the two?
Empirically Some of the most dissonant music i have heard has been in
just where as in 12 ET the layers become ambiguous to the ear, it is quite
possible the stretch a chain out of simple ratios where the ear will still
hold it all together in its glorious tension. Kyle Gann has managed to do
this at time (or so it sounds).

>
>

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

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

🔗paulerlich <paul@...>

--- In metatuning@y..., Kraig Grady <kraiggrady@a...> wrote:
> Hello Paul!
>
> paulerlich wrote:
>
> >
> >
> > true. any interval can be approximated more and more accurately by
> > more and more complex noble numbers. but again, only a few of
them,
> > the "simple" ones, would seem to be relevant in a given context --
> > for example, the rings of saturn.
>
> we keep an open mind that the more complex might have properties
that the
> simples don't or a meaningful variation can occur replacing a
simpler with
> a more complex.

i'll keep my mind open to such a possibility as well. can you think
of any examples?

> > curiously, he writes that phi is
> > converged upon with "astonishing speed" by the fibonacci ratio
> > series.
>
> i think he is just referring how close you get to within a few
decimal
> points using ratios.

exactly! thus my point . . .

> > but this "astonishing speed" is in fact the *slowest possible
> > rate* of convergence -- no number is converged to more slowly than
> > phi.
>
> like never really as i understand it.

i'm sorry -- what are you saying here?

> > the latter (slowness of convergence) is the very raison d'etre
> > for phi's specialness in temes' paper.so erv's observation seems
to
>
> > cast doubt upon the utility or importance of what temes points
out. i
> > wonder if this was this conscious or unconscious on erv's part.
>
> he does not come to Temes conclusion. One such reason being that the
> difference tones generated will often generate other tones of your
>scale.

the context here (my article and erv's) is not a full scale generated
by phi but rather a single, isolated dyad, tuned perhaps as in 72-
equal.

> If entropy is (according to Arnheim)

who's arnheim?

> not the result of a singular
> homogeneous like randomness but the result of conflicting and
>irreconcilable
> orders

in this context, this quote may be very apt. the maximum dissonance
intervals appear to be the off-unison (~70 cents), the off-octave
(~1135 cents), the off-fifth (~760 cents), etc. -- the points at
which the simplicity and sureness of the nearby simple ratio is in
maximal conflict with the "homogeneous like randomness" due to the
predictable converging series of more complex ratios (e.g, 19/18,
20/19, 21/20, 22/21, 23/22, 24/23 . . .)

> then i guess maximum dissonance would exist in-between the two?

if you mean in-between total clear order and homogeneous like
randomness, then your guess would seem to be correct! near phi, for
example, one has a fairly "homogeneous" set of approximations, as erv
demonstrates, yet the entropy far from maximal . . .

> Empirically Some of the most dissonant music i have heard has
>been in
> just

any *open* tuning system would seem to be able to acheive arbitrary
dissonance, no?

> where as in 12 ET the layers become ambiguous to the ear,

hmm . . . 12-equal is of course quite limited in the dissonance it
can produce, but i'm not sure how "layers become ambiguous" relates
to this, or what you mean by it . . .

> it is quite
> possible the stretch a chain out of simple ratios where the ear
>will still
> hold it all together in its glorious tension. Kyle Gann has managed
>to do
> this at time (or so it sounds).

well this certainly accords well with his stated intent for using
just intonation . . . but as for how it relates to the above, i'm
completely lost . . .

wait, if i ignore punctuation, i realize that your last observation
above is related to the one above that, and together they make a
point . . . which is another can of worms . . . but i'm still
wondering what the last three quotes from you above have to do with
phi or 72-equal . . .

🔗Kraig Grady <kraiggrady@...>

paulerlich wrote:

>
>
> > If entropy is (according to Arnheim)

>
>
> who's arnheim?

He wrote a little book Entropy and Art. Univ. of California press. 1971
I remember getting into an argument about Entropy and we both saying, well
you have to read this book, in the end we discovered we were referring to
this same book :-)

>
> > Empirically Some of the most dissonant music i have heard has
> >been in
> > just
>
> any *open* tuning system would seem to be able to acheive arbitrary
> dissonance, no?
>
> > where as in 12 ET the layers become ambiguous to the ear,
>
> hmm . . . 12-equal is of course quite limited in the dissonance it
> can produce, but i'm not sure how "layers become ambiguous" relates
> to this, or what you mean by it . . .

Sorry i wasn't clear on this, This ambiguousness leads to the dissonance
being limited

>
>
> > it is quite
> > possible the stretch a chain out of simple ratios where the ear
> >will still
> > hold it all together in its glorious tension. Kyle Gann has managed
> >to do
> > this at time (or so it sounds).
>
> well this certainly accords well with his stated intent for using
> just intonation . . . but as for how it relates to the above, i'm
> completely lost . . .

It creates something that is unambiguous and hence makes more remote ratio
less ambiguous

> but i'm still
> wondering what the last three quotes from you above have to do with
> phi or 72-equal . . .

it has to do with Temes concept of maximum dissonance- which relates to
PHI.

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

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

🔗paulerlich <paul@...>

🔗Kraig Grady <kraiggrady@...>

Paul!
i tend to think and experience dissonance and ambiguousness as not the same
thing.
In tonal harmony dominants are dissonant. often Mozart to my ear can be very
dissonant (yet still "polite'). On the other hand you can have real enriched
chords in say the hands of a Stevie Wonder which are ambiguous but really
not that dissonant at all. sweet if anything.

paulerlich wrote:

> --- In metatuning@y..., Kraig Grady <kraiggrady@a...> wrote:
>
> > This ambiguousness leads to the dissonance
> > being limited
>
> how so?
>
> > > but i'm still
> > > wondering what the last three quotes from you above have to do
> with
> > > phi or 72-equal . . .
> >
> > it has to do with Temes concept of maximum dissonance
>
> because it deals with ambiguity?
>
>

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

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

🔗paulerlich <paul@...>

--- In metatuning@y..., Kraig Grady <kraiggrady@a...> wrote:
> Paul!
> i tend to think and experience dissonance and ambiguousness as not
the same
> thing.
> In tonal harmony dominants are dissonant. often Mozart to my ear
can be very
> dissonant (yet still "polite'). On the other hand you can have real
enriched
> chords in say the hands of a Stevie Wonder which are ambiguous but
really
> not that dissonant at all. sweet if anything.

ok . . . but my questions below remain . . . i guess i can try to
rephrase them in light of the above

(1) in an ambiguous scale or tuning, dissonance is limited because
there isn't as much of a stable, firm consonance to contrast it
against? or because it's possible to project unambiguously a very
long journey away from a tonic in the lattice?

(2) if your answer to the second question is yes, could i then not
respond that while phi may somehow convey maximal ambiguity if
interloping in a just context, a phi-generated tuning like you and
lorne mention would use it as an unambiguous, basic lattice rung?

> paulerlich wrote:
>
> > --- In metatuning@y..., Kraig Grady <kraiggrady@a...> wrote:
> >
> > > This ambiguousness leads to the dissonance
> > > being limited
> >
> > how so?
> >
> > > > but i'm still
> > > > wondering what the last three quotes from you above have to do
> > with
> > > > phi or 72-equal . . .
> > >
> > > it has to do with Temes concept of maximum dissonance
> >
> > because it deals with ambiguity?
> >
> >
>
> -- Kraig Grady
> North American Embassy of Anaphoria island
> http://www.anaphoria.com
>
> The Wandering Medicine Show
> Wed. 8-9 KXLU 88.9 fm

🔗Kraig Grady <kraiggrady@...>

Hello Paul!
First let me state that is as far as i know this is subjective, unless
others hear likewise. It might be something that evolves as music evolves
and might always remain an elusive. slipping through our hands.

paulerlich wrote:

>
>
> ok . . . but my questions below remain . . . i guess i can try to
> rephrase them in light of the above
>
> (1) in an ambiguous scale or tuning, dissonance is limited because
> there isn't as much of a stable, firm consonance to contrast it
> against?

I believe this would be true or that

> or because it's possible to project unambiguously a very
> long journey away from a tonic in the lattice?

and this can be heard. How far i do not know. Ben Johnson i think likewise
creates some dissonances this way. It gets very tricky cause it is the
context that defines alot of this. If you just played two intervals it might
not sound this way, but to build it up in the music compositionally , it can
be quite striking.

>
>
> (2) if your answer to the second question is yes, could i then not
> respond that while phi may somehow convey maximal ambiguity if
> interloping in a just context, a phi-generated tuning like you and
> lorne mention would use it as an unambiguous, basic lattice rung?

If you us phi your difference tones will generate other tones in the scale
thus being unambiguous.

>
>
>

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

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

🔗jpehrson2 <jpehrson@...>

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

/metatuning/topicId_2843.html#2852

> Hello Paul!
> Yes Paul this is an important observation that needed to be
revived in
> the resent post on 72. Glad you dug up your comment on this.
> It was unclear how much of what you printed was from the
previous post
> so just wanted to clear this up. Just as the continuum can
be "filled with
> simple ratios, it is also possible to "fill" it with Noble ratios.
It all
> depends on how you wish to see the universe. I wonder if Julia is
aware of
> this feature of 72.
> I don't know if anyone can be accused plagiarizing
a "discovery" of a
> property something, only when it entails "inventing".
>

***Hi Kraig and Paul!

Could somebody please go over how this "noble ratio" bit would work
with 72?? I'd appreciate it. I guess it could even go over to
the "main" list, if desirable, since it is about "tuning..."

Thanks!

🔗paulerlich <paul@...>

--- In metatuning@y..., "jpehrson2" <jpehrson@r...> wrote:
> --- In metatuning@y..., Kraig Grady <kraiggrady@a...> wrote:
>
> /metatuning/topicId_2843.html#2852
>
> > Hello Paul!
> > Yes Paul this is an important observation that needed to be
> revived in
> > the resent post on 72. Glad you dug up your comment on this.
> > It was unclear how much of what you printed was from the
> previous post
> > so just wanted to clear this up. Just as the continuum can
> be "filled with
> > simple ratios, it is also possible to "fill" it with Noble
ratios.
> It all
> > depends on how you wish to see the universe. I wonder if Julia is
> aware of
> > this feature of 72.
> > I don't know if anyone can be accused plagiarizing
> a "discovery" of a
> > property something, only when it entails "inventing".
> >
>
> ***Hi Kraig and Paul!
>
> Could somebody please go over how this "noble ratio" bit would work
> with 72??

as i'm pressed for time, i'll post this question to the new tuning-
math list on freelists, and hopefully someone will give a
comprehensive answer. meanwhile, take a look at the definition:

http://mathworld.wolfram.com/NobleNumber.html

🔗Kraig Grady <kraiggrady@...>

Hello Paul!
This i feel is a different issue. B&C were measuring how one hear
melody, not harmony or consonance and dissonance. It has more to do with
gestalt perception, how we group tones together into patterns.
Erv is always and has always had untrained singers come over and sing well
known songs. Practically every other time i go over there he plays me
examples . In 25 years he has never played me anything that didn't sound
right. Finding out what he plays afterwards has more often than not been
quite surprising.
Their work lead to the Indian 22 which considering the subtlety this
culture as a whole has, it is not surprising that they noticed such things
maybe 3,000 years ago.,
It is like Yoga, it improves the person who does it. If we had to wait for
science to find everything that improves the body then putting it all
together, Yoga would not happen.
The real question is can you plays these melodies using their results
and have it aesthetically viable. I find it the "depth" that is implied and
glossed out of 12 ET.
paulerlich wrote:

> that's how i feel about it. therefore you can understand why i remain
> skeptical that boomsliter and creel's melodic theories (that we
> discussed on the SpecMus list) would hold up for many listeners not
> specifically trained in, or forced into, this kind of interval
> perception/classification.
>

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

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

🔗jpehrson2 <jpehrson@...>

--- In metatuning@y..., "paulerlich" <paul@s...> wrote:

/metatuning/topicId_2843.html#2873

> --- In metatuning@y..., "jpehrson2" <jpehrson@r...> wrote:
> > --- In metatuning@y..., Kraig Grady <kraiggrady@a...> wrote:
> >
> > /metatuning/topicId_2843.html#2852
> >
> > > Hello Paul!
> > > Yes Paul this is an important observation that needed to be
> > revived in
> > > the resent post on 72. Glad you dug up your comment on this.
> > > It was unclear how much of what you printed was from the
> > previous post
> > > so just wanted to clear this up. Just as the continuum can
> > be "filled with
> > > simple ratios, it is also possible to "fill" it with Noble
> ratios.
> > It all
> > > depends on how you wish to see the universe. I wonder if Julia
is
> > aware of
> > > this feature of 72.
> > > I don't know if anyone can be accused plagiarizing
> > a "discovery" of a
> > > property something, only when it entails "inventing".
> > >
> >
> > ***Hi Kraig and Paul!
> >
> > Could somebody please go over how this "noble ratio" bit would
work
> > with 72??
>
> as i'm pressed for time, i'll post this question to the new tuning-
> math list on freelists, and hopefully someone will give a
> comprehensive answer. meanwhile, take a look at the definition:
>
> http://mathworld.wolfram.com/NobleNumber.html

***Thanks, Paul, and I appreciate the post on the new math Freelist.

I went over there and saw the group, but is there any way to turn
*off* the e-mail sending so that a person can just read from the Web??

Thanks!

Joseph

🔗paulerlich <paul@...>

🔗Afmmjr@...

🔗paulerlich <paul@...>

🔗jpehrson2 <jpehrson@...>

--- In metatuning@y..., "paulerlich" <paul@s...> wrote:

/metatuning/topicId_2843.html#2880

> so the conclusion, from my last post, is that 72-equal is to the
> noble numbers a bit like 106-equal is to the rationals (the basis
of
> just intonation) -- the most important intervals are approximated
> extremely well (since the golden mean is almost exactly 25/36 =
50/72
> oct. and the perfect fifth is almost exactly 31/53 = 62/106 oct.),
> but the approximations to the rest of the intervals are mostly
> unremarkable.

***Hi Paul,

I remember now that the idea of these "noble ratios" came up before
on the tuning list, and I went through some webpages about them.
Very interesting... I think maybe Julie Werntz *might* be interested
in this, so it seems, if she wants to work from such a "systematic"
base... whoknows.

Thanks!

Joseph

🔗paulerlich <paul@...>

--- In metatuning@y..., "jpehrson2" <jpehrson@r...> wrote:

> ***Hi Paul,
>
> I remember now that the idea of these "noble ratios" came up before
> on the tuning list, and I went through some webpages about them.
> Very interesting... I think maybe Julie Werntz *might* be
interested
> in this, so it seems, if she wants to work from such a "systematic"
> base...

but she doesn't (going out on a short limb here) . ..

the more i listen to her string quartet (yes, i have the whole
thing), the more i realize that she's really got a fairly well-
developed style. in developing it further, she'll be drawing largely
on intuition and experience (and the influence of maneri and others),
rather than seeking out a systematic basis for composing, if i may
guess at the future.

also, we've already established that she is *not* trying to avoid
just intervals, so there's no reason she'd be *particularly
attracted* to the noble ("least just") intervals.

meanwhile, try a "scale" of consecutive 833-cent "steps" with sine
waves on your synthesizer. listen to the combinational tones, and see
if you notice anything . . .

an old post about 72-equal

🔗paulerlich <paul@...>

🔗Kraig Grady <kraiggrady@...>

🔗paulerlich <paul@...>

🔗Kraig Grady <kraiggrady@...>

🔗paulerlich <paul@...>

🔗Kraig Grady <kraiggrady@...>

🔗paulerlich <paul@...>

🔗Kraig Grady <kraiggrady@...>

🔗paulerlich <paul@...>

🔗Kraig Grady <kraiggrady@...>

🔗paulerlich <paul@...>

🔗Kraig Grady <kraiggrady@...>

🔗jpehrson2 <jpehrson@...>

🔗paulerlich <paul@...>

🔗paulerlich <paul@...>

🔗Kraig Grady <kraiggrady@...>

🔗jpehrson2 <jpehrson@...>

🔗paulerlich <paul@...>

🔗paulerlich <paul@...>

🔗Afmmjr@...

🔗paulerlich <paul@...>

🔗jpehrson2 <jpehrson@...>

🔗paulerlich <paul@...>

🔗genewardsmith <genewardsmith@...>

🔗paulerlich <paul@...>