Erlich paper _The Forms of Tonality_

Paul,

Thanks for sending me your new paper!
(_The Forms of Tonality: a preview_)

With my interest in "bridging" and in comparing
different rational tuning systems, (which go
hand-in-hand), I tend to employ the trans-dimensional
unison-vectors that I call "bridges" much more frequently
than the dimensionally-bound unison-vectors of the Fokker
type. I don't often concern myself with the latter.

It was therefore really nice to see your adoption of
orthodox Fokker unison-vectors in examining the periodicity
inherent in your own interesting recent theory of 7-limit
decatonic scales. Naturally, with my background, I find
your decatonic theory much easier to understand with
this thorough lattice-oriented presentation.

Here's my brief critique:

General points:

First, a compliment on your choice of font. I loathe
"Times New Roman" (the Windows default font on
*everything*) and never use it, and am very glad to
see that you made such an audacious choice. The
"Comic Sans MS" Windows font is one that I've only
had the nerve to use on stuff I've made for children.
I get the feeling that you're really "thumbing your nose"
at the music-theory establishment by publishing such
an intellectual theory paper in a comical font!
(If that wasn't your intention, then I'm sorry to
read so much into it, but that's how it struck me.)

Second, a big criticism: there are no page numbers!

Now, some more specific things:

In the first section, you note how closely your harmonic
entropy graph resembles Partch's "One-Footed Bride".
But it should also be pointed out that both are nearly
identical to Helmholtz's "Fig. 60 A" and "Fig. 60 B",
on page 193 in the Dover reprint of Ellis's translation
of _On the Sensations of Tone_, which is the earliest
example of this type of graph that I know of.

You should state in the text accompanying Figures 5, 6,
and 8 that the periodicity between *entire blocks* is
shown by the arrows with the ratios. I can
understand now why you would think this should be
self-evident, but it still took me a while
to realize it. My first reaction was that the arrows
on the lattices were supposed to connect *specific pairs
of pitches*.

Also, all of the lattices in your paper should have
the ratios along with the note-names!

I found that the last section, "Symmetrical Decatonic Scales",
required a difficult conceptual leap from diatonic to
decatonic. I realize that you provided me (and probably
others too) with a newly revised copy of your previous paper
(_Tuning, Tonality, and 22-tone Temperament_), which gives a
detailed evolution and explanation of the latter, but I still
think it would be good to review an *example* of a symmetrical
decatonic scale *first*, complete with some sort of pitch-height
graph, your own staff notation, and cents values, before jumping
in and using it on the lattice.

Indeed, I feel that in general this paper could be improved
with several illustrations using staff-notation and pitch-height
graphs. It focuses almost entirely on the perception of
harmonic pitch relationships in ratio-space, and provides
nothing at all on the more commonly understood perception
of pitch in pitch-space. Presenting both types of visual
information would aid in allowing the reader to make the
connections between the two types of perception, especially
since the 7-limit decatonic scales are quite a different
animal from the 5-limit diatonic scales normally encountered.
In particular, I found myself wishing that you had correlated
the staff notation of the decatonic scales from your previous
paper with the integer-plus-up/down-signs which you *do* give
on the lattices.

Perhaps Figures 5 and 7 could be better if broken up into
several smaller figures... but maybe not. I don't have
a strong opinion on this one.

A final compliment: Great use of color (or, actually, of
grey) in figures 6 and 8 to show the unique membership of
each ratio in a particular periodicity-block!

Lastly, you sent me, in a separate envelope, a single
sheet containing Figure 10. I assumed it was to correct
an error, but I haven't been able to detect any difference
between it and the Figure 10 bound into your paper.
Why the extra copy?

Good job!

-monz
http://www.monz.org
"All roads lead to n^0"

--- In tuning@y..., "monz" <joemonz@y...> wrote:

> Thanks for sending me your new paper!
> (_The Forms of Tonality: a preview_)
>
> ...
>
> Perhaps Figures 5 and 7 could be better if broken up into
> several smaller figures... but maybe not. I don't have
> a strong opinion on this one.

Oops, my bad. Scratch that "Figure 5" - that one can't
be broken up. But I still think that the several different
orientations you present in Figure 7 might be easier to
correlate with the text if presented in separate figures,
say, 7-A, 7-B, etc.

-monz
http://www.monz.org
"All roads lead to n^0"

Paul and Joe M.,

--- In tuning@y..., "monz" <joemonz@y...> wrote:
> First, a compliment on your choice of font. I loathe
> "Times New Roman" (the Windows default font on
> *everything*) and never use it, and am very glad to
> see that you made such an audacious choice.

Just a comment, and I am really not trying to build a reputation as a
contrarian, so just take it for what it's worth: Times New Roman is
not simply a Windows font, but the most imitated and widely used
print font for one reason: it is the family of fonts that, over many
decades of use, has proven to be the most easily read. Those serifs
(as opposed to the sans serif fonts like comic) are there for a
reason, and it is to give the eyes something to hang on to.

If you choose a rounded font like this, it is up to you. If you do it
because you want to be different or, as Joe puts it, "thumb your
nose", fine. But maybe before you publish, and before you send it
around to anyone but your colleagues here, you might want to go and
talk to 2 or 3 typographers, graphic design folks, or anyone else who
is actually in the print business (and needn't know a damn about
music) and ask *their* ideas about it.

It is my assumption that you believe deeply, and would like others to
learn and appreciate the paper. Give this a moment of thought,
because there may be very good reasons to use a font that is more
readable.

Just my $.02, Paul

--- In tuning@y..., "monz" <joemonz@y...> wrote:

/tuning/topicId_22081.html#22081

>
> Here's my brief critique:
>
> General points:
>
> First, a compliment on your choice of font. I loathe
> "Times New Roman" (the Windows default font on
> *everything*) and never use it, and am very glad to
> see that you made such an audacious choice. The
> "Comic Sans MS" Windows font is one that I've only
> had the nerve to use on stuff I've made for children.
> I get the feeling that you're really "thumbing your nose"
> at the music-theory establishment by publishing such
> an intellectual theory paper in a comical font!
> (If that wasn't your intention, then I'm sorry to
> read so much into it, but that's how it struck me.)

I haven't really had time to read Paul's new paper yet, but one
important thing I can do is comment on the font...

Frankly, I don't "read" (literally) that much into it. I think the
fact that it is called "comic" has influenced your opinion, Monz!

I just think it looks kind of "cool..." I don't see any
intentional "anti-academicism" in it... It just seems to go well
with the overall "innovative" graphics of the great color lattices.

Why can't an "academic" paper look like this?? Well, OK, it SHOULD
be able to!

_________ ______ _____
Joseph Pehrson

--- In tuning@y..., "monz" <joemonz@y...> wrote:

> I get the feeling that you're really "thumbing your nose"
> at the music-theory establishment by publishing such
> an intellectual theory paper in a comical font!
> (If that wasn't your intention, then I'm sorry to
> read so much into it, but that's how it struck me.)

Just wanted to have fun with it!
>
> Second, a big criticism: there are no page numbers!

Oops!
>
> Now, some more specific things:
>
> In the first section, you note how closely your harmonic
> entropy graph resembles Partch's "One-Footed Bride".
> But it should also be pointed out that both are nearly
> identical to Helmholtz's "Fig. 60 A" and "Fig. 60 B",
> on page 193 in the Dover reprint of Ellis's translation
> of _On the Sensations of Tone_, which is the earliest
> example of this type of graph that I know of.

1) The octave-equivalent harmonic entropy graph resembles the One-
Footed Bride but does not resemble Helmholtz's graph. The non-octave
equivalent harmonic entropy graph does resemble Helmholtz's somewhat
but there are still major differences. You should look at all of
these more closely.

Moreover, since I was submitting the paper to the MicroFest with a
Partch theme, I highlighted the Partch connections wherever I could.
For brevity, I omitted all the Benedetti, Rameau, Helmholtz, Plomp,
Levelt, Kameoka, Kuriagawa, and Goldstein (etc.) references. Instead,
I tried to show how much of Partch's work can be given a logical
underpinning though the concepts I present (a fuller paper would
include the analysis of Partch's scale as a 41-tone periodicity
block).

>
> You should state in the text accompanying Figures 5, 6,
> and 8 that the periodicity between *entire blocks* is
> shown by the arrows with the ratios. I can
> understand now why you would think this should be
> self-evident, but it still took me a while
> to realize it. My first reaction was that the arrows
> on the lattices were supposed to connect *specific pairs
> of pitches*.

I thought the text did make that clear, but I should specifically
point out the distinction. I'm glad you did realize it.
>
> Also, all of the lattices in your paper should have
> the ratios along with the note-names!

Absolutely not . . . the ratios near the edges of the lattice would
get really complex . . . useless information as far as I'm concerned.
>
> Indeed, I feel that in general this paper could be improved
> with several illustrations using staff-notation and pitch-height
> graphs.

Fair enough!

> Lastly, you sent me, in a separate envelope, a single
> sheet containing Figure 10. I assumed it was to correct
> an error,

Correct.

> but I haven't been able to detect any difference
> between it and the Figure 10 bound into your paper.

There are few connections that were colored in the original Figure 10
but shouldn't have been. If you look carefully at the diagram of the
block (and its layers) on the bottom of figure 7, and then locate
each occurence of these shapes in figure 10, you'll see where I had a
few extra colored lines.

Thanks for the good review!

--- In tuning@y..., paul@s... wrote:

/tuning/topicId_22081.html#22094

> --- In tuning@y..., "monz" <joemonz@y...> wrote:
>
> > I get the feeling that you're really "thumbing your nose"
> > at the music-theory establishment by publishing such
> > an intellectual theory paper in a comical font!
> > (If that wasn't your intention, then I'm sorry to
> > read so much into it, but that's how it struck me.)
>
> Just wanted to have fun with it!

I really like it. For the record, Jon Szanto, my own personal
default font is "Arial". I find it much easier to read and
cleaner looking than Times New Roman. But I appreciate your
input.

> 1) The octave-equivalent harmonic entropy graph resembles the
> One-Footed Bride but does not resemble Helmholtz's graph. The
> non-octave equivalent harmonic entropy graph does resemble
> Helmholtz's somewhat but there are still major differences.
> You should look at all of these more closely.

Touché - I didn't really compare them closely, just saw the
resemblance "at a glance".

>
> Moreover, since I was submitting the paper to the MicroFest
> with a Partch theme, I highlighted the Partch connections
> wherever I could. For brevity, I omitted all the Benedetti,
> Rameau, Helmholtz, Plomp, Levelt, Kameoka, Kuriagawa, and
> Goldstein (etc.) references. Instead, I tried to show how
> much of Partch's work can be given a logical underpinning
> though the concepts I present (a fuller paper would include
> the analysis of Partch's scale as a 41-tone periodicity
> block).

OK, now I see. I think you should have stated something like
this in the paper itself - it would have made your approach
crystal clear.

> > Also, all of the lattices in your paper should have
> > the ratios along with the note-names!
>
> Absolutely not . . . the ratios near the edges of the lattice
> would get really complex . . . useless information as far as
> I'm concerned.

Well... OK. But I think it would have made it a bit easier
to understand, especially noting the Partch reference you state
above. Maybe include ratios for the notes closest to the
center, disposing of them as they begin to get too big.
Just an idea. (pun intended)

-monz
http://www.monz.org
"All roads lead to n^0"

--- In tuning@y..., "monz" <joemonz@y...> wrote:

> > Absolutely not . . . the ratios near the edges of the lattice
> > would get really complex . . . useless information as far as
> > I'm concerned.
>
> Well... OK. But I think it would have made it a bit easier
> to understand, especially noting the Partch reference you state
> above. Maybe include ratios for the notes closest to the
> center, disposing of them as they begin to get too big.
> Just an idea. (pun intended)

As far as I'm concerned, any ratios beyond those needed to define the
direct connections are completely useless. I did go a long way in
indulging you, Partchians, and other JI-heads by including ratios for
every note in the two blocks in Figure 4 and the three blocks in
Figure 7. If you want to see the ratios of blocks adjacent to these
in the lattice, you'll have to work them out for yourself, by
multiplying the ratios in a central block by the appropriate unison
vectors. They don't tell me anything useful, particularly in systems
where the commatic unison vectors are made to vanish, one way or
another.

--- In tuning@y..., paul@s... wrote:

Today's question:

What would the Paul Erlich JI Decatonic look like as expressed in an
equal tempered scale, where the commas disappear?

Thanks,

JL

--- In tuning@y..., ligonj@n... wrote:
>
> Today's question:
>
> What would the Paul Erlich JI Decatonic look like as expressed in
an
> equal tempered scale, where the commas disappear?

If _all_ the unison vectors (64:63, 50:49, 225:224, 48:49, 28:27,
24:25) disappear, and fixed pitches are assumed, you have, of course,
10-tone equal temperament.

But that's probably not what you meant.

If only the commatic unison vectors (64:63, 50:49, 225:224)
disappear, but the chromatic unison vectors (48:49, 28:27, 24:25)
don't, then what you get _may_ be close (or identical) to a maximally
even selection of 10 notes from 22-tET (see the other paper I sent
you, Jacky).

However, equal temperament is by no means implied by the commatic
unison vectors disappearing. Let's go back to the diatonic, 5-limit
case.

The chromatic unison vectors are 25:24 (important) and 135:128 (less
important). The commatic unison vector is 81:80. If the commatic
unison vector disappears, and fixed pitches are assumed, then all you
know is that you're dealing with some form of meantone temperament.
There's nothing that will necessarily imply a certain ET here.

Same goes for the 7-limit, decatonic case. Although 22-tET is a
particularly simple solution, another potentially useful one is 76-
tET. In 76-tET, one can also play around with meantone diatonics
(since 76 = 19*4) and with the 9-limit 14-tone scales I've mentioned.

--- In tuning@y..., paul@s... wrote:
> The chromatic unison vectors are 25:24 (important) and 135:128
(less
> important). The commatic unison vector is 81:80. If the commatic
> unison vector disappears, and fixed pitches are assumed, then all
you
> know is that you're dealing with some form of meantone temperament.
> There's nothing that will necessarily imply a certain ET here.
>
> Same goes for the 7-limit, decatonic case. Although 22-tET is a
> particularly simple solution, another potentially useful one is 76-
> tET. In 76-tET, one can also play around with meantone diatonics
> (since 76 = 19*4) and with the 9-limit 14-tone scales I've
mentioned.

Paul,

There's something inherently similar in this, to some Non-2/1 MOS
that I've came up with in the past - realized this after reading the
paper. I'll have to post sometime.

JL

--- In tuning@y..., "monz" <joemonz@y...> wrote:
>
> With my interest in "bridging" and in comparing
> different rational tuning systems, (which go
> hand-in-hand), I tend to employ the trans-dimensional
> unison-vectors that I call "bridges" much more frequently
> than the dimensionally-bound unison-vectors of the Fokker
> type. I don't often concern myself with the latter.

What do you mean "dimensionally-bound"? If anything, Fokker-type
unison vectors include your "bridges" as a subset, not the other way
around (as "bound" might seem to indicate).

--- In tuning@y..., paul@s... wrote:

/tuning/topicId_22081.html#22102

> If only the commatic unison vectors (64:63, 50:49, 225:224)
> disappear, but the chromatic unison vectors (48:49, 28:27, 24:25)
> don't, then what you get _may_ be close (or identical) to a
> maximally even selection of 10 notes from 22-tET (see the other
> paper I sent you, Jacky).

Whoa... hold on there! 50:49 is "commatic" but 48:49 is
"chromatic"? I'm sure that your terminology is at least
somewhat context-dependent, but something smells really
fishy about that one...

And IMO we really should be referring to 225:224 as a
*kleismatic* unison vector rather than a commatic one.
It's quite a bit smaller than all the other "commatic"
intervals.

-monz
http://www.monz.org
"All roads lead to n^0"

--- In tuning@y..., paul@s... wrote:

/tuning/topicId_22081.html#22109

> --- In tuning@y..., "monz" <joemonz@y...> wrote:
> >
> > With my interest in "bridging" and in comparing
> > different rational tuning systems, (which go
> > hand-in-hand), I tend to employ the trans-dimensional
> > unison-vectors that I call "bridges" much more frequently
> > than the dimensionally-bound unison-vectors of the Fokker
> > type. I don't often concern myself with the latter.
>
> What do you mean "dimensionally-bound"? If anything,
> Fokker-type unison vectors include your "bridges" as
> a subset, not the other way around (as "bound" might seem
> to indicate).

Right - that's for sure! Fokker's "unison vectors" are
certainly the general instance, and my "bridges" the particular.

I was searching for the appropriate term, and
"dimensionally-bound" seemed to work, but I wasn't happy
with it when I wrote that post, and still am not.

What I was intending to convey was the difference which
you pointed out to me, Paul, that Fokker's method was to
define the prime-limit (and therefore the dimensionality)
of his periodicity-blocks beforehand, then illustrate the
unison vectors which occur *within* it, while my concept
of "bridges" is explicity meant to show rational connections
which cross over (thru?) different prime-dimensions.

Certainly, there were occasions where Fokker made use of
a unison vector as a "bridge", as in his 1949 book _Just
Intonation_, where the 225:224 (a "5==7 bridge", as I would
call it) is used to familiarize singers with the pitch
of 7/4 by showing singers how to find 225:128 and relating
7/4 to it.

So, is my rambling pointless (as Daniel Wolf would argue
in this case), or is there something to it?

-monz
http://www.monz.org
"All roads lead to n^0"

Joe,

--- In tuning@y..., "monz" <joemonz@y...> wrote:
> I really like it. For the record, Jon Szanto, my own personal
> default font is "Arial". I find it much easier to read and
> cleaner looking than Times New Roman. But I appreciate your
> input.

I default almost all of my *screen* reading to a san serif font,
because there is a fundamental difference in print where it is
illuminated from behind (as in a glowing pixel on the screen) and as
it appears on the page. It's not that Times New Roman (originally
developed for the "Times" of London, I believe) is my personal
favorite, but much in the way that I bow to the superior knowledge
bases of tuning information contained by yourself, Paul, Dave K.,
David Doty, and so many others -- as in that, I bow to the wisdom of
typographers who, for many decades, and to this day, will use a serif
font for print presentation. For increased readability.

I just figure they know more about it than me.

Cheers,
Jon

Joseph Pehrson wrote:

> important thing I can do is comment on the font...
>
> Frankly, I don't "read" (literally) that much into it. I think the
> fact that it is called "comic" has influenced your opinion, Monz!
>
> I just think it looks kind of "cool..." I don't see any
> intentional "anti-academicism" in it...

That's always been my impression of Comic Sans - it doesn't look humorous so much as casual, like something you'd see used on a menu at a bar and grill. To me, that makes statement when used in a technical or academic paper, intentionally or not. Not necessarily a bad statement.

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

--- In tuning@y..., "monz" <joemonz@y...> wrote:
>
> --- In tuning@y..., paul@s... wrote:
>
> /tuning/topicId_22081.html#22102
>
> > If only the commatic unison vectors (64:63, 50:49, 225:224)
> > disappear, but the chromatic unison vectors (48:49, 28:27, 24:25)
> > don't, then what you get _may_ be close (or identical) to a
> > maximally even selection of 10 notes from 22-tET (see the other
> > paper I sent you, Jacky).
>
>
> Whoa... hold on there! 50:49 is "commatic" but 48:49 is
> "chromatic"? I'm sure that your terminology is at least
> somewhat context-dependent, but something smells really
> fishy about that one...
>
> And IMO we really should be referring to 225:224 as a
> *kleismatic* unison vector rather than a commatic one.
> It's quite a bit smaller than all the other "commatic"
> intervals.
>
You're missing the point, Monz. Read the paper again.

--- In tuning@y..., "monz" <joemonz@y...> wrote:

/tuning/topicId_22081.html#22081
>
> Paul,
>
> Thanks for sending me your new paper!
> (_The Forms of Tonality: a preview_)
>

> Here's my brief critique:
>
Now, some more specific things:
>
> In the first section, you note how closely your harmonic
> entropy graph resembles Partch's "One-Footed Bride".
> But it should also be pointed out that both are nearly
> identical to Helmholtz's "Fig. 60 A" and "Fig. 60 B",
> on page 193 in the Dover reprint of Ellis's translation
> of _On the Sensations of Tone_, which is the earliest
> example of this type of graph that I know of.
>

Huh? I can see Erlich's graph looking like the Helmholtz, but not to
the Partch "One-Footed Bride..." There is no "big foot..." (??)

Partch runs his graph through one octave comparing the two "sides"
divided by the 3/2. There is no such comparison in Paul's graph,
unless you want to make it yourself...

In fact, Paul's "troughs" aren't as "symmetrical" as the Partch in
this respect. There must be some reason for this... the
"sensitivity" rating of the graph?? Dunno...

> You should state in the text accompanying Figures 5, 6,
> and 8 that the periodicity between *entire blocks* is
> shown by the arrows with the ratios. I can
> understand now why you would think this should be
> self-evident, but it still took me a while
> to realize it. My first reaction was that the arrows
> on the lattices were supposed to connect *specific pairs
> of pitches*.
>

I had no trouble with this, especially since all the pitches are
labeled and it is clear that they rise by the "chromatic semitone"
ratio... To me it really looks like one figure is "placed on
another" as it were.

> Also, all of the lattices in your paper should have
> the ratios along with the note-names!
>

I know this is being discussed in a later post, but I would also vote
to keep the ratios out. That would look rather complex, no??

The point of this is that Paul, for once, is making things *SIMPLER*
rather than intentionally more complex... :)

> Indeed, I feel that in general this paper could be improved
> with several illustrations using staff-notation and pitch-height
> graphs.

Isn't that at the very end for the decatonic, though?? And most of
us know what a major scale looks like on the staff, I hope...

> Perhaps Figures 5 and 7 could be better if broken up into
> several smaller figures... but maybe not. I don't have
> a strong opinion on this one.
>

This was not a problem for me...

> A final compliment: Great use of color (or, actually, of
> grey) in figures 6 and 8 to show the unique membership of
> each ratio in a particular periodicity-block!
>

It's "groovy" man, groovy... :)

_________ ______ _____ _____
Joseph Pehrson

--- In tuning@y..., paul@s... wrote:

/tuning/topicId_22081.html#22094

>
> 1) The octave-equivalent harmonic entropy graph resembles the One-
> Footed Bride but does not resemble Helmholtz's graph. The non-
octave equivalent harmonic entropy graph does resemble Helmholtz's
somewhat but there are still major differences. You should look at
all of these more closely.
>

I don't see how you can say this, Paul. As I mentioned the "one
footed bride" invites a very particular comparison through an octave
by running the "hills" up and down the figure from the tritone on
C#. I don't see how YOUR figure is doing that.

And the Helmholtz, if you take the one octave graph on page 193 has
almost ALL identical dips as yours, if you consider only the first
octave of your Figure 1! (??)

__________ _____ _ ______
Joseph Pehrson

--- In tuning@y..., "monz" <joemonz@y...> wrote:

/tuning/topicId_22081.html#22097

>
> > 1) The octave-equivalent harmonic entropy graph resembles the
> > One-Footed Bride but does not resemble Helmholtz's graph. The
> > non-octave equivalent harmonic entropy graph does resemble
> > Helmholtz's somewhat but there are still major differences.
> > You should look at all of these more closely.
>
> Touché - I didn't really compare them closely, just saw the
> resemblance "at a glance".
>

Huh? I'm looking at the Helmholtz "one octave" graph on page 193 of
"Sensations..." I see a G 3:2, an F 4:3, an E 5:4... these are the
SAME ratios as the first half of Paul's Harmonic Entropy Figure 1,
not surprisingly. Why AREN'T they the same??

_________ _____ _ _
Joseph Pehrson

--- In tuning@y..., paul@s... wrote:

/tuning/topicId_22081.html#22102
>

>
> However, equal temperament is by no means implied by the commatic
> unison vectors disappearing. Let's go back to the diatonic, 5-limit
> case.
>
> The chromatic unison vectors are 25:24 (important) and 135:128
(less important). The commatic unison vector is 81:80. If the
commatic unison vector disappears, and fixed pitches are assumed,
then all you know is that you're dealing with some form of meantone
temperament.

I'm sorry, Paul... but this seems rather important. Would you mind
please expanding this by example a little bit... the relationship to
meantone with this process. Your paper, being more concerned with
JI, didn't touch upon this explicitly...

Thanks!!

Joseph

_________ __ _______
Joseph Pehrson

--- In tuning@y..., "David J. Finnamore" <daeron@b...> wrote:

/tuning/topicId_22081.html#22126

> Joseph Pehrson wrote:
>
> > important thing I can do is comment on the font...
> >
> > Frankly, I don't "read" (literally) that much into it. I think
the
> > fact that it is called "comic" has influenced your opinion, Monz!
> >
> > I just think it looks kind of "cool..." I don't see any
> > intentional "anti-academicism" in it...
>
> That's always been my impression of Comic Sans - it doesn't look
humorous so much as casual, like something you'd see used on a menu
at a bar and grill. To me, that makes statement when used in a
technical or academic paper, intentionally or not. Not necessarily a
bad statement.
>

Hi David...

Yes, for me it makes a good statement, as in "now we're going to have
a goooooood time...!"

___________ _______ ______
Joseph Pehrson

Hi I'm new to this list. Sorry if this has been asked before but where is
this paper available so I can read it?

Thanks,

Andy

In a message dated 5/5/2001 5:50:16 PM Eastern Daylight Time,
jpehrson@rcn.com writes:

> --- In tuning@y..., "David J. Finnamore" <daeron@b...> wrote:
>
> /tuning/topicId_22081.html#22126
>
> > Joseph Pehrson wrote:
> >
> > > important thing I can do is comment on the font...
> > >
> > > Frankly, I don't "read" (literally) that much into it. I think
> the
> > > fact that it is called "comic" has influenced your opinion, Monz!
> > >
> > > I just think it looks kind of "cool..." I don't see any
> > > intentional "anti-academicism" in it...
> >
> > That's always been my impression of Comic Sans - it doesn't look
> humorous so much as casual, like something you'd see used on a menu
> at a bar and grill. To me, that makes statement when used in a
> technical or academic paper, intentionally or not. Not necessarily a
> bad statement.
> >
>
> Hi David...
>
> Yes, for me it makes a good statement, as in "now we're going to have
> a goooooood time...!"
>
> ___________ _______ ______
>

--- In tuning@y..., jpehrson@r... wrote:

> Huh? I can see Erlich's graph looking like the Helmholtz, but not to
> the Partch "One-Footed Bride..." There is no "big foot..." (??)

You're missing the forest for the . . . foot.
>
> Partch runs his graph through one octave comparing the two "sides"
> divided by the 3/2.

Divided by the 3/2?
>
> In fact, Paul's "troughs" aren't as "symmetrical" as the Partch in
> this respect.

Huh? You must be looking at the first graph in my paper. The second one is the one that
compares with Partch's One-Footed Bride.

--- In tuning@y..., jpehrson@r... wrote:
> --- In tuning@y..., paul@s... wrote:
>
> /tuning/topicId_22081.html#22094
>
> >
> > 1) The octave-equivalent harmonic entropy graph resembles the One-
> > Footed Bride but does not resemble Helmholtz's graph. The non-
> octave equivalent harmonic entropy graph does resemble Helmholtz's
> somewhat but there are still major differences. You should look at
> all of these more closely.
> >
>
> I don't see how you can say this, Paul. As I mentioned the "one
> footed bride" invites a very particular comparison through an octave
> by running the "hills" up and down the figure from the tritone on
> C#. I don't see how YOUR figure is doing that.
>
> And the Helmholtz, if you take the one octave graph on page 193 has
> almost ALL identical dips as yours, if you consider only the first
> octave of your Figure 1! (??)
>
Joseph -- the octave-equivalent harmonic entropy graph mentioned above is Figure 2 in
the paper. The non-octave-equivalent harmonic entropy graph mentioned above is
Figure 1 in the paper. Now, try again.

--- In tuning@y..., jpehrson@r... wrote:
>
> I'm sorry, Paul... but this seems rather important. Would you mind
> please expanding this by example a little bit... the relationship to
> meantone with this process. Your paper, being more concerned with
> JI, didn't touch upon this explicitly...
>
If the 81:80 (which is four 3:2s up and one 5:4 down, mod the octave) vanishes, and if fixed
pitches are used, then four fifths up must equal a major third in the diatonic tuning in
question. If this is done in a uniform way, the result is, by definition, some form of
meantone temperament.

--- In tuning@y..., paul@s... wrote:

/tuning/topicId_22081.html#22156

> If the 81:80 (which is four 3:2s up and one 5:4 down, mod the
> octave) vanishes, and if fixed pitches are used, then four
> fifths up must equal a major third in the diatonic tuning in
> question. If this is done in a uniform way, the result is,
> by definition, some form of meantone temperament.

Paul, just a quick compliment on your being so thorough and
precise. Most commentators making this same statement would
probably have left out the "If this is done in a uniform way"
bit. I'm glad you didn't... because of course, if you had,
it wouldn't have been entirely correct.

-monz
http://www.monz.org
"All roads lead to n^0"

--- In tuning@y..., "monz" <joemonz@y...> wrote:
>
> --- In tuning@y..., paul@s... wrote:
>
> /tuning/topicId_22081.html#22156
>
> > If the 81:80 (which is four 3:2s up and one 5:4 down, mod the
> > octave) vanishes, and if fixed pitches are used, then four
> > fifths up must equal a major third in the diatonic tuning in
> > question. If this is done in a uniform way, the result is,
> > by definition, some form of meantone temperament.
>
>
> Paul, just a quick compliment on your being so thorough and
> precise. Most commentators making this same statement would
> probably have left out the "If this is done in a uniform way"
> bit. I'm glad you didn't... because of course, if you had,
> it wouldn't have been entirely correct.
>
Thanks for the compliment, Monz, but I don't deserve it. I should have said "consonant major
third" above -- otherwise, the Pythagorean tuning of the medieval era would qualify, but most
theorists don't classify Pythagorean as a meantone tuning (and for those who do, it's 0-comma
meantone tuning -- at the very edge).

Also, John Chalmers (according to your glossary, Monz) feels that "meantone" only applies to
1/4-comma meantone, while other solutions (such as the harmonically optimal 7/26-comma
meantone and the more melodically "incisive" 1/6-comma meantone) are merely
"meantone-like".

--- In tuning@y..., paul@s... wrote:

/tuning/topicId_22081.html#22155

> Joseph -- the octave-equivalent harmonic entropy graph mentioned
above is Figure 2 in the paper. The non-octave-equivalent harmonic
entropy graph mentioned above is Figure 1 in the paper. Now, try
again.

Oh! I see... the SECOND figure is the "one footed" example... well
since *yours* actually starts with a maxima you have *two* feet!

And the FIRST figure does follow pretty much the Helmholtz.

This does raise, for me, a couple of questions:

1) Why do the minima "flatten out" to such nice equal comparisons
when Harmonic Entropy is taken to only *one* octave?? And then, in
*two* octaves they are quite different and don't compare??

2) Why does the Helmholtz ONE octave graph look like the first 1/2 of
your TWO octave one... and the Helmholtz ONE octave looks QUITE A BIT
different from your "octave equivalent" one...

Is there something about the term "octave equivalence" that is doing
this that I should know??

_______ _____ _____ ____
Joseph Pehrson

--- In tuning@y..., paul@s... wrote:

/tuning/topicId_22081.html#22156

> >
> If the 81:80 (which is four 3:2s up and one 5:4 down, mod the
octave) vanishes, and if fixed
> pitches are used, then four fifths up must equal a major third in
the diatonic tuning in
> question. If this is done in a uniform way, the result is, by
definition, some form of
> meantone temperament.

Thanks, Paul for explaining this... Well, this is pretty fascinating
and would add another "dimension" (literally) to your paper... Looks
like you're planning to add this stuff anyway....

________ _____ _____ ___
Joseph Pehrson

--- In tuning@y..., jpehrson@r... wrote:
> --- In tuning@y..., paul@s... wrote:
>
> /tuning/topicId_22081.html#22155
>
>
> > Joseph -- the octave-equivalent harmonic entropy graph mentioned
> above is Figure 2 in the paper. The non-octave-equivalent harmonic
> entropy graph mentioned above is Figure 1 in the paper. Now, try
> again.
>
> Oh! I see... the SECOND figure is the "one footed" example... well
> since *yours* actually starts with a maxima you have *two* feet!
>
> And the FIRST figure does follow pretty much the Helmholtz.
>
> This does raise, for me, a couple of questions:
>
> 1) Why do the minima "flatten out" to such nice equal comparisons
> when Harmonic Entropy is taken to only *one* octave?? And then, in
> *two* octaves they are quite different and don't compare??

I have no idea what you mean. What flattens out? In any case, the largest interval you choose to
take the graph out to is completely arbitrary and has no effect on the shape of the graph.

>
> 2) Why does the Helmholtz ONE octave graph look like the first 1/2 of
> your TWO octave one...

I believe Helmholtz has some two-octave graphs too . . . for Helmholtz, as for me, you can take
the graph out to as large an interval as you want . . . it won't affect its shape or scale.

> and the Helmholtz ONE octave looks QUITE A BIT
> different from your "octave equivalent" one...

Because Helmholtz didn't impose octave equivalence.
>
> Is there something about the term "octave equivalence" that is doing
> this that I should know??
>
Yes, it's mentioned in the paper -- assuming octave equivalence before computing harmonic
entropy (as in figure 2) is very different from not assuming octave equivalence before
computing harmonic entropy (as in figure 1). Partch, and other scale theorists, like to assume
octave equivalence (even though it's clearly not perfectly true in practice . . . different chord
inversions can be different in consonance) because it greatly simplifies the scale-construction
process, if you know you're going to be focusing on octave-repeating scales anyway. Figure 2
or the One-Footed Bride, as you can see, gives you only one consonance value for every
interval class -- a minor third and major sixth get identical consonance values -- which allows you
to ignore octave register when constructing chords and scales. If you were interested in
constructing scales that don't repeat themselves exactly every octave, you'd probably want to
use a consonance curve like the one in Figure 1 as your basis.

For further questions about harmonic entropy, please post to
harmonic_entropy@yahoogroups.com.

--- In tuning@y..., jpehrson@r... wrote:
> --- In tuning@y..., paul@s... wrote:
>
> /tuning/topicId_22081.html#22156
>
> > >
> > If the 81:80 (which is four 3:2s up and one 5:4 down, mod the
> octave) vanishes, and if fixed
> > pitches are used, then four fifths up must equal a major third in
> the diatonic tuning in
> > question. If this is done in a uniform way, the result is, by
> definition, some form of
> > meantone temperament.
>
> Thanks, Paul for explaining this... Well, this is pretty fascinating
> and would add another "dimension" (literally)

Or subtract one . . . meantone is a 1-dimensional tuning, unlike 5-limit JI, which is 2-dimensional, if
you're defining dimension in the usual mathematical sense, as the number of integer coordinates
needed to specify any pitch. However, an effective lattice representation of meantone tuning
would take the 1-dimensional line that it's on and twist it into a helix . . . which resides, of course,
in 3 dimensions.

> to your paper... Looks
> like you're planning to add this stuff anyway....
>
Well, it is mentioned in the paper -- it's one of the 5 approaches I list for alleviating the problem
that the D minor triad is "out-of-tune" in the "JI major block". Which happens to be exactly the
same problem I'm discussing with Kyle Gann -- as I mentioned before, the cover of the paper
is a perfect depiction of Ben Johnston's notation in the 5-limit.

--- In tuning@y..., paul@s... wrote:

/tuning/topicId_22081.html#22208

> >
> > This does raise, for me, a couple of questions:
> >
> > 1) Why do the minima "flatten out" to such nice equal comparisons
> > when Harmonic Entropy is taken to only *one* octave?? And then,
in *two* octaves they are quite different and don't compare??
>
> I have no idea what you mean. What flattens out? In any case, the
largest interval you choose to take the graph out to is completely
arbitrary and has no effect on the shape of the graph.
>

Oh... I just meant the graph that assumed octave equivalence! In
that graph all the troughs "flatten out" to be the same depth... the
6/5, 5/4, 8/5 and 5/3... etc., etc.

Well, it's clear to me that, as you explain, the inversions 5/4 and
8/5 would have the same concordance...

But why would the major third and minor third... the 6/5 and 5/4??

That doesn't make any sense, does it, since those intervals are quite
different in just??

Signed,

confused...

________ _____ _____ ____
Joseph Pehrson

--- In tuning@y..., paul@s... wrote:

/tuning/topicId_22081.html#22212

> >
> > Thanks, Paul for explaining this... Well, this is pretty
fascinating and would add another "dimension" (literally)
>
> Or subtract one . . . meantone is a 1-dimensional tuning, unlike 5-
limit JI, which is 2-dimensional, if you're defining dimension in the
usual mathematical sense, as the number of integer coordinates
needed to specify any pitch.

Paul, this is very interesting. Could you please elaborate or
perhaps include an example so I can understand this better!

Thanks!

_________ ______ _____ ____
Joseph Pehrson

--- In tuning@y..., jpehrson@r... wrote:

/tuning/topicId_22081.html#22302

> --- In tuning@y..., paul@s... wrote:
>
> /tuning/topicId_22081.html#22212
>
> > . . . meantone is a 1-dimensional tuning, unlike
> > 5-limit JI, which is 2-dimensional, if you're defining
> > dimension in the usual mathematical sense, as the number
> > of integer coordinates needed to specify any pitch.
>
> Paul, this is very interesting. Could you please elaborate
> or perhaps include an example so I can understand this better!

Hi Joe. I'm not Paul, but I'll give it a shot.

First, you should re-read Paul's "Gentle Introduction to
Periodicity Blocks", starting at:
http://www.ixpres.com/interval/td/erlich/intropblock1.htm

I'm rusty on my remembrance of Fokker's papers right now,
so I can't speak on Fokker's observations. But as far as I
know, Paul and I discovered on our own (when I visited
him a couple of years ago) that if one's concern is to
create a temperament and you choose your unison vectors
carefully, each unison vector removes one dimension from
the lattice, and the final unison vector is the one that
closes the system; i.e., changes it from an infinite system
to a finite one.

For example, the linear (= 1-dimensional) chain of 3:2s
theoretically goes on forever. But if you use 3^12
(= the Pythagorean Comma) as your unison vector (and
assuming "octave" equivalence, so we'll omit prime-factor 2
and its exponents), then every *pair* of pitch-classes
that is separated by that interval will be treated as a
*single* pitch-class. Therefore the system will be limited
(= closed) to a linear chain of 12 "5ths". It doesn't
matter whether these "5ths" are actual 3:2 ratios or
tempered - it works the same way in either case.

A 5-limit system (or any other) is also theoretically
infinite. A typical pair of unison vectors in a 5-limit
system is the Syntonic Comma (= 3^4 * 5^-1) and the
Diesis (= 5^3). Paul illustrates the resulting periodicity
block in Gentle Introduction, Part 2. This, and the
5-limit periodicity blocks he illustrates in his latest
paper, are still 2-dimensional.

The point here, as it relates to your question, is that
if we were trying to create a temperament to represent
5-limit JI - for instance, a meantone - we could find a
unison vector that would turn the 2-dimensional lattice
into a 1-dimensional (linear) one - I think the Syntonic
Comma would do the trick - and then we could employ the
Pythagorean Comma to close that linear system as we saw above.

(Paul, Kees, Manuel... please comment if I'm wrong here.)

So even tho meantone is intended to represent the 2-dimensional
5-limit system, it is actually constituted as a chain of
tempered "5ths", and thus is a linear, 1-dimensional system.

Note that meantones do not have to be finite systems - we've
talked here often of how 19-EDO and 31-EDO emulate 1/3-comma
and 1/4-comma meantone, respectively. Meantones are most
often found with only 12 notes, for obvious reasons relating
to keyboard design, but if 1/3-comma meantone were carried
out to 19 notes, it would be nearly identical to 19-EDO,
and likewise, if 1/4-comma meantone were carried out to
31 notes, it would be nearly identical to 31-EDO. But
those are still arbitrary stopping points - the chain of
meantone tempered "5ths" can be infinite just like the
chain of untempered 3:2s.

Equal-temperaments, or EDOs, on the other hand, are closed,
finite systems, because they cycle back to a note that is
*identical* (assuming "octave" equivalence) to the starting note.

-monz
http://www.monz.org
"All roads lead to n^0"

--- In tuning@y..., "monz" <joemonz@y...> wrote:

/tuning/topicId_22081.html#22316

> First, you should re-read Paul's "Gentle Introduction to
> Periodicity Blocks", starting at:
> http://www.ixpres.com/interval/td/erlich/intropblock1.htm
>

Actually, I forgot how generally excellent these articles really
are... and I got more out of them *this* time than on any previous
reads... Bravo, Paul!

It would obviously make sense that the number of unison vectors would
correspond to the number of dimensions we are considering for any
given system... correct (??)

_________ _______ _______ ______
Joseph Pehrson

--- In tuning@y..., "monz" <joemonz@y...> wrote:

/tuning/topicId_22081.html#22316

>
> The point here, as it relates to your question, is that
> if we were trying to create a temperament to represent
> 5-limit JI - for instance, a meantone - we could find a
> unison vector that would turn the 2-dimensional lattice
> into a 1-dimensional (linear) one - I think the Syntonic
> Comma would do the trick - and then we could employ the
> Pythagorean Comma to close that linear system as we saw above.
>

Got it! Thanks, Joe!

__________ ______ _ _____
Joseph Pehrson

--- In tuning@y..., jpehrson@r... wrote:

> Oh... I just meant the graph that assumed octave equivalence! In
> that graph all the troughs "flatten out" to be the same depth...
the
> 6/5, 5/4, 8/5 and 5/3... etc., etc.
>
> Well, it's clear to me that, as you explain, the inversions 5/4 and
> 8/5 would have the same concordance...
>
Right.

> But why would the major third and minor third... the 6/5 and 5/4??

That's a nice and wonderful surprise of the model! Goes a long way
toward justifying Partch's view of these as equally consonant (see
the One-Footed Bride).
>
> That doesn't make any sense, does it, since those intervals are >
quite
> different in just??

The intervals themselves are different in consonance, 5:4 being a
little more consonant than 6:5, but once you take all their
inversions and extensions into account (6:5 benefits from 5:3, while
5:4 suffers because of 8:5), the interval _classes_ come out
virtually identical in consonance.

--- In tuning@y..., jpehrson@r... wrote:
> --- In tuning@y..., paul@s... wrote:
>
> /tuning/topicId_22081.html#22212
>
> > >
> > > Thanks, Paul for explaining this... Well, this is pretty
> fascinating and would add another "dimension" (literally)
> >
> > Or subtract one . . . meantone is a 1-dimensional tuning, unlike
5-
> limit JI, which is 2-dimensional, if you're defining dimension in
the
> usual mathematical sense, as the number of integer coordinates
> needed to specify any pitch.
>
> Paul, this is very interesting. Could you please elaborate or
> perhaps include an example so I can understand this better!

In a meantone tuning, as you know, every pitch can be found along a 1-
dimensional chain of meantone fifths:

. . . Fb Cb Gb Db Ab Eb Bb F C G D A E B F# C# G# D# A# E# B# . . .

Every meantone pitch can be found on this 1-dimensional chain. So in
a sense, meantone temperament collapses the infinite 2-D lattice of 5-
limit JI into an infinite 1-D chain . . . clear?

--- In tuning@y..., jpehrson@r... wrote:

>
> It would obviously make sense that the number of unison vectors
would
> correspond to the number of dimensions we are considering for any
> given system... correct (??)

Well, I don't know quite how obvious it is . . . in vector algebra,
there's a theorem that a basis for an N-dimensional vector space is
formed by N linearly independent vectors . . . don't know
how "obvious" this theorem is or how difficult it was (historically)
to prove it . . . a lot of things can seem "obvious" at first but
then turn out not always to be true . . .

--- In tuning@y..., paul@s... wrote:

/tuning/topicId_22081.html#22343

> --- In tuning@y..., jpehrson@r... wrote:
>
> >
> > It would obviously make sense that the number of unison vectors
> would
> > correspond to the number of dimensions we are considering for any
> > given system... correct (??)
>
> Well, I don't know quite how obvious it is . . . in vector algebra,
> there's a theorem that a basis for an N-dimensional vector space is
> formed by N linearly independent vectors . . . don't know
> how "obvious" this theorem is or how difficult it was
(historically)
> to prove it . . . a lot of things can seem "obvious" at first but
> then turn out not always to be true . . .

Thanks, Paul!

I obviously shouldn't have said "obviously..."

_______ ______ ____ ___
Joseph Pehrson

--- In tuning@y..., paul@s... wrote:

/tuning/topicId_22081.html#22335
>

> The intervals themselves are different in consonance, 5:4 being a
> little more consonant than 6:5, but once you take all their
> inversions and extensions into account (6:5 benefits from 5:3,
while 5:4 suffers because of 8:5), the interval _classes_ come out
> virtually identical in consonance.

This really doesn't make any sense to me. What kind of model is
this, then?? I realize that the major third and minor third are
closer together in sound in just than in 12-equal, but the
differences are CRUCIAL to music.

You know, all that, major third, happy, happy, happy... minor third,
sad, sad, sad,... :) :(

__________ _____ _____ ____
Joseph Pehrson

--- In tuning@y..., jpehrson@r... wrote:
> --- In tuning@y..., paul@s... wrote:
>
> /tuning/topicId_22081.html#22335
> >
>
> > The intervals themselves are different in consonance, 5:4 being a
> > little more consonant than 6:5, but once you take all their
> > inversions and extensions into account (6:5 benefits from 5:3,
> while 5:4 suffers because of 8:5), the interval _classes_ come out
> > virtually identical in consonance.
>
> This really doesn't make any sense to me. What kind of model is
> this, then?? I realize that the major third and minor third are
> closer together in sound in just than in 12-equal, but the
> differences are CRUCIAL to music.
>
> You know, all that, major third, happy, happy, happy... minor
third,
> sad, sad, sad,... :) :(
>
Joseph, the major triad has a minor third in it, and the minor triad
has a major third in it. So I think you're not quite looking at this
the right way.

--- In tuning@y..., jpehrson@r... wrote:
> --- In tuning@y..., paul@s... wrote:
>
> /tuning/topicId_22081.html#22335
> >
>
> > The intervals themselves are different in consonance, 5:4 being a
> > little more consonant than 6:5, but once you take all their
> > inversions and extensions into account (6:5 benefits from 5:3,
> while 5:4 suffers because of 8:5), the interval _classes_ come out
> > virtually identical in consonance.
>
> This really doesn't make any sense to me. What kind of model is
> this, then?? I realize that the major third and minor third are
> closer together in sound in just than in 12-equal, but the
> differences are CRUCIAL to music.
>
> You know, all that, major third, happy, happy, happy... minor
third,
> sad, sad, sad,... :) :(

Which interval class would you choose as more consonant:

1) The 5:4, 8:5 interval class
2) The 6:4, 5:3 interval class

?

I wrote,

> Which interval class would you choose as more consonant:
>
> 1) The 5:4, 8:5 interval class
> 2) The 6:4, 5:3 interval class

Sorry, Joseph, that should have been:

1) The 5:4, 8:5 interval class
2) The 6:5, 5:3 interval class

OK, now which would you choose?

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

/tuning/topicId_22081.html#22509
> > You know, all that, major third, happy, happy, happy... minor
> third,
> > sad, sad, sad,... :) :(
> >
> Joseph, the major triad has a minor third in it, and the minor
triad has a major third in it. So I think you're not quite looking at
this the right way.

So, you're saying that the graph of interval sonorities of "graph 2"
in the _Forms of Tonality_ ASSUMES TRIADS in the intervalic
comparisons....

It just looks like a graph of intervals to me... (??)

________ ______ ______
Joseph Pehrson

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

/tuning/topicId_22081.html#22513

> I wrote,
>
> > Which interval class would you choose as more consonant:
> >
> > 1) The 5:4, 8:5 interval class
> > 2) The 6:4, 5:3 interval class
>
> Sorry, Joseph, that should have been:
>
> 1) The 5:4, 8:5 interval class
> 2) The 6:5, 5:3 interval class
>
> OK, now which would you choose?

Got it! They each have a major and a minor... Actually that
was "vaguely" in my head... but thanks for spelling it out!

_______ ______ _____
Joseph Pehrson

--- In tuning@y..., jpehrson@r... wrote:
> --- In tuning@y..., PERLICH@A... wrote:
>
> /tuning/topicId_22081.html#22509
> > > You know, all that, major third, happy, happy, happy... minor
> > third,
> > > sad, sad, sad,... :) :(
> > >
> > Joseph, the major triad has a minor third in it, and the minor
> triad has a major third in it. So I think you're not quite looking
at
> this the right way.
>
> So, you're saying that the graph of interval sonorities of "graph
2"
> in the _Forms of Tonality_ ASSUMES TRIADS in the intervalic
> comparisons....

No, I'm saying you can't account for major triad = happy and minor
triad = sad by what intervals they contain, because they contain the
same intervals!

But the real point is this -- how would you compare a minor sixth and
a major sixth?

--- In tuning@y..., paul@s... wrote:

/tuning/topicId_22081.html#22685

>
> No, I'm saying you can't account for major triad = happy and minor
> triad = sad by what intervals they contain, because they contain
the same intervals!
>

Well the placement, then, must be "crucial," yes?? so so much for the
graph that relates them the same (??)

I can't believe in the equivalence...

The placement must follow the harmonic series for the "happy, happy"
to take place...

Generations of "functional harmony" composers used the major triad as
happy, happy, happy and the minor as sad, sad...

Etymology: MAJOR... big, bright. Minor... teeny-tiny, microtonal :)

> But the real point is this -- how would you compare a minor sixth
and a major sixth?

Well... the major sixth in this case must be the "sad, sad" since it
has the minor third under it, and the minor sixth must be "happy,
happy."

Man, is this stupid. But there has to be something to it... (??)

___________ _______ _______
Joseph Pehrson

On 5/17/01 9:54 PM, "jpehrson@rcn.com" <jpehrson@rcn.com> wrote:

> Well... the major sixth in this case must be the "sad, sad" since it
> has the minor third under it, and the minor sixth must be "happy,
> happy."

(okay... I've lost the original quote
somewhere in my eMail software...)

But this:

"You know major chords LAA LAA happy...
minor chords luhh luhh sad..."

Kind of a vague musical flow vibe kind of thing, no!?
A gesture...?
I don't know... it first made sense to me
when I first heard Steven Tyler say it in an interview (c. 1979)

You like olde Aerosmith, Joseph?

Marc

--- In tuning@y..., jpehrson@r... wrote:
> --- In tuning@y..., paul@s... wrote:
>
> /tuning/topicId_22081.html#22685
>
> >
> > No, I'm saying you can't account for major triad = happy and
minor
> > triad = sad by what intervals they contain, because they contain
> the same intervals!
> >
>
> Well the placement, then, must be "crucial," yes??

Yes.

> so so much for the
> graph that relates them the same (??)

Why?
>
> I can't believe in the equivalence...

I thought you already concurred, when I asked you how you would rank
the consonance of the two interval classes:

1. The 6:5, 5:3 interval class
2. The 5:4, 8:5 interval class

Right?

>
> The placement must follow the harmonic series for the "happy,
happy"
> to take place...

Seemingly.
>
> Generations of "functional harmony" composers used the major triad
as
> happy, happy, happy and the minor as sad, sad...
>
Even Zarlino made these emotional characterizations, didn't he?
>
>
> > But the real point is this -- how would you compare a minor sixth
> and a major sixth?
>
> Well... the major sixth in this case must be the "sad, sad" since
it
> has the minor third under it, and the minor sixth must be "happy,
> happy."
>
You really believe that?

> Man, is this stupid.

What is, my graph?

> But there has to be something to it... (??)

?? indeed.

--- In tuning@y..., "Orphon Soul, Inc." <tuning@o...> wrote:

/tuning/topicId_22081.html#23057

>
> But this:
>
> "You know major chords LAA LAA happy...
> minor chords luhh luhh sad..."
>
> Kind of a vague musical flow vibe kind of thing, no!?
> A gesture...?
> I don't know... it first made sense to me
> when I first heard Steven Tyler say it in an interview (c. 1979)
>
> You like olde Aerosmith, Joseph?
>
> Marc

Hi Marc!

My problem is that I'm so "retro" that when you say "Aerosmith" I'm
thinking of the Babylonians that Monzo is always talking about... :(
________ _______ _______
Joseph Pehrson