Back to basics

Tuners,

....I recall reading in a book about just intonation in an antique shop,
instructions as to how to calculate Just intonation, and a system that gave
each and every note:

C D E F G A B C

C# D# E# F# G# A# B# C#

Cb Db Eb Fb Gb Ab Bb

...Here is what I want you all to do for me.

I require as MANY people as possible to give me website links, and
resources, STARTING FROM THE VERY BASICS, as to how to calculate just
intonation, and use of scales, -and as to what the terms wolf notes, beat
frequencys, hetrodyneing, consonance, disonance, comma, meantone, dekany,
circle of fifths and harmonic entrophy mean.

Please help me on this.

I was talking to a musician friend, and he critisized me saying that I had
to "Learn the rules before abstractifing and breaking them".

I must admit there might be much study involved here, but it will be a
labour of love.

Its time that I made head way and learned all oif this stuff, from the
beginning.

Obviously, the more practical exercises that there are, and the more in
depth and stratiified the descriptions are, the easier to learn everything,
and everything correctly it will be.

I need to learn the names for intervals, and the like.

HELP!!!

It is this sort of post that I'd like to see more of:

*** What is tuning?

> Why isn't standard tuning good enough?
> What things do people care about in a tuning?
> What kinds of tunings are there?
> How did the western world arrive at equal temperament?
> What is just intonation? (eek!) :-)

Since you're providing these questions, I take it you'd like to write
up answers for at least some of them? I sure hope so!

..and I feel that a good site should also include:

--->Definitions,
--->Practical exercises,
--->In depth and color coded examples.

Whilst it is certainly not my intention to insult, or to harass, I found the
Joe Monzo's website was good, but the many interrelateing links made if very
easy to become lost in this maze of information.

You'd become swamped, and I suggested to Joe that he provide working
examples, and exercises to which to learn from!

---Sarn.

Sarn Richard Ursell wrote:

> Tuners,
>
> ..I require as MANY people as possible to give me website links, and
> resources, STARTING FROM THE VERY BASICS, as to how to calculate just
> intonation, and use of scales, -and as to what the terms wolf notes, beat
> frequencys, hetrodyneing, consonance, disonance, comma, meantone, dekany,
> circle of fifths and harmonic entrophy mean.
>
> Please help me on this.

As one who was not so long ago scrambling around for resources I recommend the following books to
begin with, and possibly in the same order.

W.A. Mathieu - Harmonic Experience. At least the first half or so dealing with pure intervals.

Harry Partch - Genesis of a Music. The section on corporeal music might be left till last.

Hermann Helmholz - On the Sensations of Tone. Requires a determined read but fills in so much of
the details.

These can be had from Amazon or from the Just Intonation Network whose website contains some very
good links.

Good luck.

--- In tuning@y..., Sarn Richard Ursell <
thcdelta@i...> wrote:
>
> I require as MANY people as possible to give me website links, and
> resources, STARTING FROM THE VERY BASICS, as to how to calculate just
> intonation, and use of scales, -and as to what the terms wolf notes, beat
> frequencys, hetrodyneing, consonance, disonance, comma, meantone, dekany,
> circle of fifths and harmonic entrop[]y mean.
>
> Please help me on this.

Hi Sarn.

First of all, please refer to Joe Monzo's
dictionary:

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

Secondly, you may not be reading this list
very carefully, but what we are attempting to
do right now is to create a FAQ, so as to
address basic questions such as these.

In the meantime, I believe that the archives of
this list so far contain enough information to
answer all your questions right now, if you
have the patience to sift though the archives.

Thirdly, here are some books I would highly
recommend (get the latest edition if at all
possible):

Pierce, John R. _The Science of Musical
Sound_. Scientific American Books, New
York, 1984.

Roederer, Juan G. _Physics and
Psychophysics of Music_, 3rd edition.
Springer Verlag, 1995.

Parncutt, Richard. _Harmony: A
Psychoacoustical Approach_. Springer-
Verlag, Berlin. 1989.

Sundberg, Johan. _Harmony and Tonality:
Papers given at a seminar organized by the
Music Acoustics Committee of the Royal
Swedish Academy of Music_. Kungliga
Musikaliska Academien, Stockholm, 1987.

Blackwood, Easley. _The Structure of
Recognizable Diatonic Tunings_. Princeton
University Press, Princeton NJ, 1985.

A little outdated:

Barbour, J. Murray. _Tuning and
Temperament: A Historical Survey_.
Michigan State College Press, 1951.

Very outdated:

Helmholtz, Hermann L.F. von, _On the
Sensations of Tone_. Longman, Green and
Company. London, June 1875. Translated by
A. J. Ellis.

I posted a fuller, more annotated bibliography
about three times but can't find that now . . .
anyone?

>
> I was talking to a musician friend, and he critisized me saying that I had
> to "Learn the rules before abstractifing and breaking them".

Well, I would agree -- are you a proficient
musician within an existing style? If not,
become one -- take some lessons or
whatever. Most of the greatest rule-breakers
started out in an already-existing style.
>
> I must admit there might be much study involved here, but it will be a
> labour of love.

Music deserves it!
>
> I need to learn the names for intervals, and the like.

You might want to start with a basic music
book, the kind you might find in a music
store, like Clough's _Intervals, Scales, Keys_
(Clough has also written on microtonal stuff
but start with this if you need the "normal"
basics.

Paul, I just have to ask: in responding to Sarn's request for
information, you wrote --

--- In tuning@y..., PERLICH@A... wrote:
>
> Thirdly, here are some books I would highly
> recommend (get the latest edition if at all
> possible):

...and then your list of books. Take me at my word, as I'm not asking
this to cast aspersions: prominantly absent from your list is
Partch's "Genesis of a Music". What would be a reason for omitting
this particular book, especially in light of the fact that it may
(arguably) have introduced more people/composers/musicians to non-
12tet music and theory than any other?

I ask because, while I know that you are not a fan of just
intonation, and that theories of JI and accoustics have evolved since
Partch wrote the book, it seems at least a curious omission from your
ad hoc list.

Cheers,
Jon

--- In tuning@y..., JSZANTO@A... wrote:
> Paul, I just have to ask: in responding to Sarn's request for
> information, you wrote --
>
> --- In tuning@y..., PERLICH@A... wrote:
> >
> > Thirdly, here are some books I would highly
> > recommend (get the latest edition if at all
> > possible):
>
> ...and then your list of books. Take me at my word, as I'm not
asking
> this to cast aspersions: prominantly absent from your list is
> Partch's "Genesis of a Music".

This is of course a great and important book, where many of the
concepts I frequently use (limit, complete hexad, etc.) were first
defined. I didn't feel a particular need to repeat Alison's
recommendation of it, particularly as Sarn was asking about "basics"
and Partch's book could be found lacking, if not downright
misleading, when it comes to the basics of Western music and/or
psychoacoustics.

--- In tuning@y..., PERLICH@A... wrote:
> This is of course a great and important book, where many of the
> concepts I frequently use (limit, complete hexad, etc.) were first
> defined. I didn't feel a particular need to repeat Alison's
> recommendation of it, particularly as Sarn was asking
about "basics"
> and Partch's book could be found lacking, if not downright
> misleading, when it comes to the basics of Western music and/or
> psychoacoustics.

OK. Somehow I missed Alison's mention of it; the items you mention as
being lacking weren't the reasons I *would* recommend it, since Sarn
was asking, first off, about just intonation, and other matters --
i.e. I wouldn't recommend it for Western music or psychoacoustics
either.

I don't, however, agree with you that it is misleading, but merely
another point of view, different from yours, and with material that
has been superceded by further research and use in these areas.

But thanks for the explanation, anyhoo...

Cheers,
Jon

List!
There are two forms of theory one which strives toward "truth" and
theory that explores one set of circumstances. The first at its best
results in a series of rules and the placing of limitations, at it worst
breeds fanatics. The second expands are musical palette without claiming
any universality. It says "this works" and nothing more.
Partch made no attempt to solve universal tuning problems. He did
however by his theories create a musical language and palette that was
useful. He also achieved something quite unique, the design of
instruments that satisfied the way human beings moved. He remains
untouched in this regard. I only disagree that that his ideas have been
super ceded, for the diamond remains the complement to the eikosany for
one, and all complements need each other.

Roderer book on the other hand which is close to 25 years old is
fascinating, but find the ideas inapplicable to real musical situations.
What if the JND is 2 cents, we should use a scale of 600 tones per
octave, this is absurd.

Helmholtz remains miles ahead of much of the investigation into
consonance in that he realized and illustrated that different inversions
of the same chord are not the same level of consonance. Those who have
followed him have failed to even acknowledge this easily demonstrable
fact. This does not imply that the work done here is invalid should at
least acknowledge that it fails to tackle this end of things. Parch
realized what his diamond did and did not do. It should be a model of
how theories should be put forth.

JSZANTO@ADNC.COM wrote:

> I don't, however, agree with you that it is misleading, but merely
> another point of view, different from yours, and with material that
> has been superceded by further research and use in these areas.
>
> But thanks for the explanation, anyhoo...
>
> Cheers,
> Jon

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

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

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

> I only disagree that that his ideas have been
> super ceded, for the diamond remains the complement to the eikosany
for
> one, and all complements need each other.

I also disagree with that notion -- I didn't propose that.
>
> Roderer book on the other hand which is close to 25 years old is
> fascinating, but find the ideas inapplicable to real musical
situations.
> What if the JND is 2 cents, we should use a scale of 600 tones per
> octave, this is absurd.

Johnny Reinhard proposes 1200. What's wrong with that? As Partch
points out, you _can_ hear a 2-cent discrepancy.
>
> Helmholtz remains miles ahead of much of the investigation into
> consonance in that he realized and illustrated that different
inversions
> of the same chord are not the same level of consonance.

Ahead of what investigation?

> Those who have
> followed him have failed to even acknowledge this easily
demonstrable
> fact.

Who are "those"?

> This does not imply that the work done here is invalid should at
> least acknowledge that it fails to tackle this end of things. Parch
> realized what his diamond did and did not do. It should be a model
of
> how theories should be put forth.

Where in particular do you find this?

--- In tuning@y..., Kraig Grady <kraiggrady@a...> wrote:
> I only disagree that that his ideas have been super ceded, for
> the diamond remains the complement to the eikosany for
> one, and all complements need each other.

Kraig, just to be clear (since I am agreement on all of the rest of
your post): it is my understanding that some of Partch's statements
about acoustics and music theory, as generalized topics, have been
either clarified, ammended, or corrected to some degree by research
that has followed. And I might even be wrong, but it has never been
an important enough debate point for me to argue.

I, myself, have no reason to quibble, since what achievements Partch
accomplished far outweigh any historic nit-picking, and if he did not
succeed in determining someone *elses* truth, his intention was never
to be a researcher for it's own sake, but to seek knowledge to put
into use in his own journey. That he cared to share it at all is
quite something, and knowing that he did it in virtually a vacuum
makes it all the more impressive.

Cheers,
Jon

Uh oh...

--- In tuning@y..., PERLICH@A... wrote:
> I also disagree with that notion -- I didn't propose that.

Your disagreement was with my statement that I thought some of
Partch's work in theory and acoustics had been superceded by
subsequent knowledge and investigation. And I honestly thought that I
had heard that mostly from you! I may have very well been mistaken,
and that your rejection of at least some of the proposals in "Genesis
of a Music" is not based on corrections or ammendments, but on
genuine disagreement in principle.

I'll keep quiet about this now, since I don't want the noise to
distract from the other topics...

Cheers,
Jon

PERLICH@ACADIAN-ASSET.COM wrote:

> Johnny Reinhard proposes 1200. What's wrong with that? As Partch
> points out, you _can_ hear a 2-cent discrepancy.

Paul!
Take the example of the Yamaha base (768 per octave). Tolerances
build up to make these devices to my ear useless. You might not hear the
difference in pitch but you will have beats, so much so with chords with
the 11 you don't know if the beat is the 11th or the out of tuneness of
the tuning. So what does JND tell us?

> > Helmholtz remains miles ahead of much of the investigation into
> > consonance in that he realized and illustrated that different
> inversions
> > of the same chord are not the same level of consonance.
>
> Ahead of what investigation?

definitions of Consonance and Dissonance.

> Who are "those"?

Those who have attempted to define these terms!

Partch
> realized what his diamond did and did not do. It should be a model
of
> how theories should be put forth.

In the fact that Partch said his tuning was not the one and only. With
his own music he changed his tuning and he drew plans that i am sure if
his situation was different he would have investigated.

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

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

--- In tuning@y..., JSZANTO@A... wrote:
> Uh oh...
>
> --- In tuning@y..., PERLICH@A... wrote:
> > I also disagree with that notion -- I didn't propose that.
>
> Your disagreement was with my statement that I thought some of
> Partch's work in theory and acoustics had been superceded by
> subsequent knowledge and investigation.

Acoustics -- I don't think Partch did any work in acoustics per se.
As for psychoacoustics, he basically goes over the existing theories,
dismissing each of them in turn on the grounds that they all lead to
the same conclusion -- that small-integer-ratios equals relative
consonance. It's hard to supercede that with any subsequent
refinement of knowledge and experimental investigation -- any
reasonable theory would be similarly dismissed. So no, not
superceded, but simply by-passed.

Theory -- Partch's contributions to theory are elements of Partch's
music, and of much JI music since then. Besides a few of Wilson's
suggestions that Partch found interesting, and, I'd modestly propose,
my suggestion about "saturated chords" (which, it turns out, Partch
used in his music without any special theorical edifice), it would be
difficult to supercede his understanding of his own music, or to deny
the relevance of his concepts to any strict-JI music. So no, perhaps
added to, but not superceded.

> And I honestly thought that I
> had heard that mostly from you! I may have very well been mistaken,
> and that your rejection of at least some of the proposals
in "Genesis
> of a Music" is not based on corrections or ammendments, but on
> genuine disagreement in principle.

There is a disagreement in principle as to what "tonality" is,
between major and minor tonality as discussed by Partch, and my
understanding of major and minor tonality as they developed out of
the modality of the late Renaissance/early Baroque periods, and were
a feature of all Western tonal music as ordinarily understood. Partch
certainly sounds, in Genesis, like he's addressing the latter, while
Kraig seems to be claiming he isn't.

--- In tuning@y..., Kraig Grady <kraiggrady@a...> wrote:
>
>
> PERLICH@A... wrote:
>
> > Johnny Reinhard proposes 1200. What's wrong with that? As Partch
> > points out, you _can_ hear a 2-cent discrepancy.
>
> Paul!
> Take the example of the Yamaha base (768 per octave). Tolerances
> build up to make these devices to my ear useless. You might not
hear the
> difference in pitch but you will have beats, so much so with chords
with
> the 11 you don't know if the beat is the 11th or the out of
tuneness of
> the tuning. So what does JND tell us?

Oh, I thought you were saying 600 was too many!

>
> > > Helmholtz remains miles ahead of much of the investigation into
> > > consonance in that he realized and illustrated that different
> > inversions
> > > of the same chord are not the same level of consonance.
> >
> > Ahead of what investigation?
>
> definitions of Consonance and Dissonance.
>
> > Who are "those"?
>
> Those who have attempted to define these terms!

Neither Plomp, not Kameoka and Kuriyagawa, not Sethares, not
Terhardt, not Parncutt, not Tenney, not Barlow, not you, not me . . .
none of us would say that chords in different inversions have the
same level of consonance. So when you say "those", who are you
referring to?

Have I said today how much I dislike this Yahoo! cruft?

--- In tuning@y..., PERLICH@A... wrote:
> As for psychoacoustics, he basically goes over the existing
theories,
> dismissing each of them in turn on the grounds that they all lead
to
> the same conclusion -- that small-integer-ratios equals relative
> consonance. It's hard to supercede that with any subsequent
> refinement of knowledge and experimental investigation -- any
> reasonable theory would be similarly dismissed. So no, not
> superceded, but simply by-passed.

Or, on a personal and experiential level, disagreed with.

> Theory -- Partch's contributions to theory are elements of Partch's
> music, and of much JI music since then.

Yes, as I think his point was to find the theory for the express
purpose of making his music. Once the music-making began, theory
became relatively unimportant.

> There is a disagreement in principle as to what "tonality" is,
> between major and minor tonality as discussed by Partch, and my
> understanding of major and minor tonality as they developed out of
> the modality of the late Renaissance/early Baroque periods, and
were
> a feature of all Western tonal music as ordinarily understood.
Partch
> certainly sounds, in Genesis, like he's addressing the latter,
while
> Kraig seems to be claiming he isn't.

Ah. Maybe the crux is your phrase "ordinarily understood". Witness,
in just this tiny little cosmos called the tuning list,
that "ordinarily understood" concepts can be -- charitably -- like
night and day to different parties!

OK, enough banter on this, and I think I understand where you are at
with the subject.

Hey Paul, be sure to buy a computer for the home and an Internet
access package, too! :)

Cheers,
Jon

--- In tuning@y..., Kraig Grady <kraiggrady@a...> wrote:
> List!

Kraig!

Everytime I see that exclamation mark I feel like you are shouting at
us. It seems to be insisting that we pay attention to you NOW! I'm
sure that is not your intention, but I expect it has this annoying
effect on others too.

> There are two forms of theory one which strives toward "truth"
and
> theory that explores one set of circumstances. The first at its best
> results in a series of rules and the placing of limitations,

I disagree. At its best it gives us some power to predict the effects
of certain combinations of tones, but we don't mistake the current map
for the territory.

> at it worst breeds fanatics.

Like who?

Is this sort of name-calling really necessary?

...
> Helmholtz remains miles ahead of much of the investigation into
> consonance in that he realized and illustrated that different
inversions
> of the same chord are not the same level of consonance. Those who
have
> followed him have failed to even acknowledge this easily
demonstrable
> fact.

This is untrue. Plenty of people have acknowledged this.

Regards,
-- Dave Keenan

JSZANTO!
I was agreeing with you totally except to imply that i don't think
his work has been either clarified, amended, or corrected. It is a
self sufficient system capable of producing great music even today
without having to be modified.

JSZANTO@ADNC.COM wrote:

> --- In tuning@y..., Kraig Grady <kraiggrady@a...> wrote:
> > I only disagree that that his ideas have been super ceded, for
> > the diamond remains the complement to the eikosany for
> > one, and all complements need each other.
>
> Kraig, just to be clear (since I am agreement on all of the rest of
> your post): it is my understanding that some of Partch's statements
> about acoustics and music theory, as generalized topics, have been
> either clarified, ammended, or corrected to some degree by research
> that has followed. And I might even be wrong, but it has never been
> an important enough debate point for me to argue.
>
> I, myself, have no reason to quibble, since what achievements Partch
> accomplished far outweigh any historic nit-picking, and if he did not
> succeed in determining someone *elses* truth, his intention was never
> to be a researcher for it's own sake, but to seek knowledge to put
> into use in his own journey. That he cared to share it at all is
> quite something, and knowing that he did it in virtually a vacuum
> makes it all the more impressive.
>
> Cheers,
> Jon

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

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

PERLICH@ACADIAN-ASSET.COM wrote:

> --- In tuning@y..., Kraig Grady <kraiggrady@a...> wrote:
> >
> >
> > PERLICH@A... wrote:
> >
> > > Johnny Reinhard proposes 1200. What's wrong with that? As Partch
> > > points out, you _can_ hear a 2-cent discrepancy.
> >
> > Paul!
> > Take the example of the Yamaha base (768 per octave). Tolerances
>
> > build up to make these devices to my ear useless. You might not
> hear the
> > difference in pitch but you will have beats, so much so with chords
> with
> > the 11 you don't know if the beat is the 11th or the out of
> tuneness of
> > the tuning. So what does JND tell us?
>
> Oh, I thought you were saying 600 was too many!

i was saying the knowledge in Roderer book has not found a way to be
applied!

> Neither Plomp, not Kameoka and Kuriyagawa, not Sethares, not
> Terhardt, not Parncutt, not Tenney, not Barlow, not you, not me . . .
> none of us would say that chords in different inversions have the
> same level of consonance. So when you say "those", who are you
> referring to?

well i missed something as it seems to concern itself with limits. Where
are inversions measured or mentioned?

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

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

Dave Keenan wrote:

> --- In tuning@y..., Kraig Grady <kraiggrady@a...> wrote:
> > List!
>
> Kraig!
>
> Everytime I see that exclamation mark I feel like you are shouting at
> us. It seems to be insisting that we pay attention to you NOW! I'm
> sure that is not your intention, but I expect it has this annoying
> effect on others too.

you can't be serious after 3 years!!!!!!:) i felt like an opening that
wasn't so over used as to be meaningless. Which I find with most polite
opening i have to question if they are sincere.

> I disagree. At its best it gives us some power to predict the effects
> of certain combinations of tones, but we don't mistake the current map
>
> for the territory.

This would fall into my second category. the first mistakes the map as
the guide as to everything that is in the territory most conform with it

> > at it worst breeds fanatics.
>
> Like who?
>
> Is this sort of name-calling really necessary?

It is my own observation on all "monotheist" human enterprises

> > Helmholtz remains miles ahead of much of the investigation into
> > consonance in that he realized and illustrated that different
> inversions
> > of the same chord are not the same level of consonance. Those who
> have
> > followed him have failed to even acknowledge this easily
> demonstrable
> > fact.
>
> This is untrue. Plenty of people have acknowledged this.

I am sorry i miss it but don't remember it ever being brought up on this
list. but where? to inform my ignorance!

>
>
> Regards,
> -- Dave Keenan

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

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

--- In tuning@y..., Kraig Grady <kraiggrady@a...> wrote:
> you can't be serious after 3 years!!!!!!:) i felt like an opening
that
> wasn't so over used as to be meaningless. Which I find with most
polite
> opening i have to question if they are sincere.

Fair enough. It was very bad form of me even to mention it. Please
accept my apology.

> > I disagree. At its best [theory} gives us some power to predict
the
effects
> > of certain combinations of tones, but we don't mistake the current
map
> >
> > for the territory.
>
> This would fall into my second category.

What second category? The category of fanatics? I don't understand.

> the first mistakes the map
as
> the guide as to everything that is in the territory most conform
with it

How can it be a mistake to treat a map as a guide, assuming you are
always alert for discrepancies? Again I'm not sure I understand what
you are saying here.

> > > at it worst breeds fanatics.
> >
> > Like who?
> >
> > Is this sort of name-calling really necessary?
>
> It is my own observation on all "monotheist" human enterprises

Again I find this extremely cryptic, but what I unpack from it is: You
have observed that belief in the scientific method breeds fanatics.
You see the application of the scientific method is solely an
enterprise of monotheistic cultures (presumably the jewish, christian
and islamic). You have observed that all enterprises of these cultures
breed fanatics.

I can't argue with your observations except to say that I do not share
them. But I'd like to point out that buddhist psychology is awesome
and clearly required the application of the scientific method to
introspection. Buddhism is not monotheistic but atheistic, although
some prefer to say "non-theistic" since the word "atheistic" has
somehow picked up the connotation of "anti-theistic" which of course
buddhism is not.

>
> > > Helmholtz remains miles ahead of much of the investigation into
> > > consonance in that he realized and illustrated that different
> > inversions
> > > of the same chord are not the same level of consonance. Those
who
> > have
> > > followed him have failed to even acknowledge this easily
> > demonstrable
> > > fact.
> >
> > This is untrue. Plenty of people have acknowledged this.
>
> I am sorry i miss it but don't remember it ever being brought up on
this
> list. but where? to inform my ignorance!

In general I don't think anyone claims to have a totally adequate
mathematical model of consonance for chords with more than two notes,
but in regard to dyads, Paul Erlich, Dan Stearns, Daniel Wolf, myself
and others, were just discussing recently, in regard to a ratio of
small whole numbers, a:b in lowest terms, whether the best estimate of
relative dissonance was given by the smaller of the two numbers
Min(a,b) or their product a*b. Clearly either of these formulae will
rate 3:5 as more consonant than 5:6 and 4:5 as more consonant than 5:8
etc.

Sometimes we adopt octave-equivalence as a simplifying measure, but
everyone knows (I hope) that this is only an approximation and not
real. The above of course refers to sensory consonance, not stylistic
consonance.

Kraig, I am very interested in what formulae you have found useful for
predicting the consonance of chords. I'm sure this is in the archives
somewhere, but since the move to Yahoo I have been unable to find all
sorts of things that I know are in there somewhere. Could you please
expound on this again.

Regards,
-- Dave Keenan

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

> i was saying the knowledge in Roderer book has not found a way to be
> applied!

There are a lot of things in the Roederer book you can immediately
apply -- for example second-order beating. And "the JND is 2 cents"
is not even a statement in Roederer's book.
>
> > Neither Plomp, not Kameoka and Kuriyagawa, not Sethares, not
> > Terhardt, not Parncutt, not Tenney, not Barlow, not you, not
me . . .
> > none of us would say that chords in different inversions have the
> > same level of consonance. So when you say "those", who are you
> > referring to?
>
> well i missed something as it seems to concern itself with limits.

I don't know what "it" is, but Partch is the one who introduced and
concerned himself with limits (odd limits) in the discussion of
consonance. And yes, if you're going to pretend that there's full
octave equivalence, so that you don't have to analyze an octave-
repeating pitch set in more than one octave, then Partch is right and
limits are useful.

Still I am curious about "those" and "it". You speak with such
authority on "those who came after Helmholtz". So who is it you're
referring to?

> Where
> are inversions measured or mentioned?

Any of the authors I mentioned propose formulae (or at least sketches
thereof) which would not give the same ratings to, say, 6:7:9,
7:9:12, and 9:12:14. These are inversions of the same chord but there
is no need to explicitly mention that unless you're Partch or another
musician who is seeking to make use of a musical nomenclature based
on octave-equivalence.

--- In tuning@y..., JSZANTO@A... wrote:
> Have I said today how much I dislike this Yahoo! cruft?
>
> --- In tuning@y..., PERLICH@A... wrote:
> > As for psychoacoustics, he basically goes over the existing
> theories,
> > dismissing each of them in turn on the grounds that they all lead
> to
> > the same conclusion -- that small-integer-ratios equals relative
> > consonance. It's hard to supercede that with any subsequent
> > refinement of knowledge and experimental investigation -- any
> > reasonable theory would be similarly dismissed. So no, not
> > superceded, but simply by-passed.
>
> Or, on a personal and experiential level, disagreed with.

Actually, Partch _agreed_ with this very conclusion of each of the
theories mentioned (in case you didn't get that).
>
> > the modality of the late Renaissance/early Baroque periods, and
> were
> > a feature of all Western tonal music as ordinarily understood.
> Partch
> > certainly sounds, in Genesis, like he's addressing the latter,
> while
> > Kraig seems to be claiming he isn't.
>
> Ah. Maybe the crux is your phrase "ordinarily understood". Witness,
> in just this tiny little cosmos called the tuning list,
> that "ordinarily understood" concepts can be -- charitably -- like
> night and day to different parties!

Although this is a good point, that's not what I meant by "ordinarily
understood" in this case. What I meant was, "as 'Western tonal music'
is normally defined, i.e., Bach, Beethoven, Brahms, blah blah blah".
In other words, if I say "Western tonal music" and someone points to
a hitherto-obscure tradition of goat-horn blowing in northeastern
Saskatchewan, they are not "understanding" the phrase 'Western tonal
music' as it is 'ordinarily understood', although the music they are
thinking of may be just as important and wonderful and great as the 3
B's . . .

--- In tuning@y..., PERLICH@A... wrote:

/tuning/topicId_19367.html#19493

> Any of the authors I mentioned propose formulae (or at least
sketches thereof) which would not give the same ratings to, say,
6:7:9, 7:9:12, and 9:12:14.

This is a very interesting discussion from a "composing" point of
view, I think... Many composers since Scriabin have been VERY
concerned with novel chord voicings of "common" triads, etc. It's
been
one way that conventional tonality, consonance or maybe, in more
abstract cases using our more limiting term "concordance" has been
applied to make "new" music in our age...

I'm thinking of many composers right now Arvo Part and Daniel Godfrey
come immediatly to mind, who would not be interesting if octave
equivalance in concordance TRULY pertained...

________ _____ ______ __
Joseph Pehrson