u/otonality and major/minor

Hi,

I'm still quite the newbie, so please forgive me for
what is probably a stupid post. There were a lot of
posts about utonality and otonality (ok so I'm a few
weeks/months behind on this list), so I whipped out
Joe Monzo's handy dictionary, and (I think) figured
out what the idea is (basically in one you keep the
numerator constant and put whatever whole number you
please on the bottom, ther other is the same idea
inverted, right?)... Anyway I whipped together a few
sounds to try to hear what this stuff sounds like,
(using a program of my own creation, kind of like
Csound but none of the features or generality), and
after listening I have no idea whatsoever how
utonality corresponds to "minor" and otonality
corresponds to "major"... Perhaps I am using the
non-illustrative "Numerary Nexuses" (5 in both cases)?
Or is there a more theoretical relation between these
concepts, that I'm not likely to actually hear? If
someone could shed some light on the topic, I'd be
most greatful. Thanks for your time, y'all...

Cheers,
Brian Szymanski
bks10@cornell.edu

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--- In tuning@y..., <xbrianskix@y...> wrote:

/tuning/topicId_31809.html#31809

> Hi,
>
> I'm still quite the newbie, so please forgive me for
> what is probably a stupid post. There were a lot of
> posts about utonality and otonality (ok so I'm a few
> weeks/months behind on this list), so I whipped out
> Joe Monzo's handy dictionary, and (I think) figured
> out what the idea is (basically in one you keep the
> numerator constant and put whatever whole number you
> please on the bottom, ther other is the same idea
> inverted, right?)... Anyway I whipped together a few
> sounds to try to hear what this stuff sounds like,
> (using a program of my own creation, kind of like
> Csound but none of the features or generality), and
> after listening I have no idea whatsoever how
> utonality corresponds to "minor" and otonality
> corresponds to "major"... Perhaps I am using the
> non-illustrative "Numerary Nexuses" (5 in both cases)?
> Or is there a more theoretical relation between these
> concepts, that I'm not likely to actually hear? If
> someone could shed some light on the topic, I'd be
> most greatful. Thanks for your time, y'all...
>
> Cheers,
> Brian Szymanski
> bks10@c...
>

Hello Brian!

Well, Paul will explain this in more detail, but I can state the
obvious. The overtone series extending upward from C, for example,
would run: C, C, G, C, E-natural, G, Bb, C, etc. as an OTONAL
series...

C-E-G, obviously or *major*

And, running downward as a "hypothetical" or "constructed" UTONAL
series from a "guide tone" which takes the place of a "fundamental":

C, C, F, C, Ab, F, D, C etc. yields a MINOR chord F-Ab-C

So the traditional "major" and "minor" result naturally from the
ratios of the overtone series running up and downward.

Keep in mind, however, that the UTONAL series, however useful for
composition, does *not* actually occur in nature, but is an
*artifice* or *artificial* concept. "*Art* for short..." Right,
Paul?

Joseph Pehrson

> From: jpehrson2 <jpehrson@rcn.com>
> To: <tuning@yahoogroups.com>
> Sent: Friday, December 21, 2001 9:03 AM
> Subject: [tuning] Re: u/otonality and major/minor
>
>
> ...

> And, running downward as a "hypothetical" or "constructed" UTONAL
> series from a "guide tone" which takes the place of a "fundamental":
>
> C, C, F, C, Ab, F, D, C etc. yields a MINOR chord F-Ab-C
>
> So the traditional "major" and "minor" result naturally from the
> ratios of the overtone series running up and downward.

While it's true that the development of harmony during the 1900s
tended to reflect an increasing interest in using higher harmonics
as major-chord identities, it's not as easy to relate minor-chord
developments to the subharmonic (utonal) series.

To help make things clearer for Brian, I add here the ratio numbers
for the utonal series provided by Joe:

C C F C Ab F D C etc.
1/1 1/2 1/3 1/4 1/5 1/6 1/7 1/8

When Joe says it "yields a MINOR chord F-Ab-C", he means that the
ratios 1/4 - 1/5 - 1/6 represent the sound traditionally associated
with what regular music-theory calls the "minor triad".

*However*, there have been many arguments over the dualistic
aspect of Partch's theory, precisely because traditional theory
would regard the "F 1/6" as the "root" of this "minor chord",
whereas the dualistic theory must recognize the "guide tone" of
"C 1/4" as the analogue to the otonal "fundamental". (Partch
discusses exactly this in his book, and the arguments go back
further, to when Oettingen first proposed dualism in the mid-1800s.)

The dichotomy becomes even more clear when we progress from
triads to tetrads. Traditional theory adds a "7th", continuing
to stack the "minor chord" by ascending "3rds" the same as with
the "major chord" -- so here the it's a "minor 7th" where with
the "major chord" it's a "major 7th". But the dualistic theory
continues the construction *downward* by adding a fourth
chord-identity *below* the utonal triad given above, thus:

C Ab F D
1/4 1/5 1/6 1/7

> Keep in mind, however, that the UTONAL series, however useful for
> composition, does *not* actually occur in nature, but is an
> *artifice* or *artificial* concept. "*Art* for short..." Right,
> Paul?

I'm not Paul, but here's my contribution:

The utonal or subharmonic series does not normally occur in nature
as an *simultaneous audio phenomenon* (altho there *are* occassional
reports of it in acoustical phenomena), but it does indeed manifest
itself in other ways. For example, marking off equal linear
divisions of a string-length will result in ratios of string-lengths
which exhibit a subharmonic series.

love / peace / harmony ...

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

_________________________________________________________
Do You Yahoo!?
Get your free @yahoo.com address at http://mail.yahoo.com

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

> Keep in mind, however, that the UTONAL series, however useful for
> composition, does *not* actually occur in nature, but is an
> *artifice* or *artificial* concept. "*Art* for short..." Right,
> Paul?
>
> Joseph Pehrson

Well, you don't really find Utonal _chords_ as _simultaneities_ in
nature, but you might find a _successive_ series of frequencies
belonging to a Utonal _scale_ in nature, particularly if you're
looking at a chaotic system that can exhibit period-doubling, period-
tripling, etc. . . . behavior.

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

/tuning/topicId_31809.html#31814

>
> I'm not Paul, but here's my contribution:
>
> The utonal or subharmonic series does not normally occur in nature
> as an *simultaneous audio phenomenon* (altho there *are* occassional
> reports of it in acoustical phenomena), but it does indeed manifest
> itself in other ways. For example, marking off equal linear
> divisions of a string-length will result in ratios of string-lengths
> which exhibit a subharmonic series.
>

Thanks so much, Monz, for your elaborations to this discussion! I
only asked for Paul because he's around so much and is so generous in
his answering of questions, but I *certainly* appreciate your help as
well!

Joe P.

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

/tuning/topicId_31809.html#31814

>
> *However*, there have been many arguments over the dualistic
> aspect of Partch's theory, precisely because traditional theory
> would regard the "F 1/6" as the "root" of this "minor chord",
> whereas the dualistic theory must recognize the "guide tone" of
> "C 1/4" as the analogue to the otonal "fundamental". (Partch
> discusses exactly this in his book, and the arguments go back
> further, to when Oettingen first proposed dualism in the mid-1800s.)
>

****Thanks, Monz, for pointing this out. The significance of the
*root* would make a difference. I wasn't aware there were already
arguments opposed to Partch's "dualism" but I would be interested in
hearing more about this...

>
> The dichotomy becomes even more clear when we progress from
> triads to tetrads. Traditional theory adds a "7th", continuing
> to stack the "minor chord" by ascending "3rds" the same as with
> the "major chord" -- so here the it's a "minor 7th" where with
> the "major chord" it's a "major 7th". But the dualistic theory
> continues the construction *downward* by adding a fourth
> chord-identity *below* the utonal triad given above, thus:
>
> C Ab F D
> 1/4 1/5 1/6 1/7
>
>

****So, essentially, that would turn into a *sixth* rather than a
*seventh* yes??

>
> > Keep in mind, however, that the UTONAL series, however useful for
> > composition, does *not* actually occur in nature, but is an
> > *artifice* or *artificial* concept. "*Art* for short..." Right,
> > Paul?
>
>
> I'm not Paul, but here's my contribution:
>
> The utonal or subharmonic series does not normally occur in nature
> as an *simultaneous audio phenomenon* (altho there *are* occassional
> reports of it in acoustical phenomena), but it does indeed manifest
> itself in other ways. For example, marking off equal linear
> divisions of a string-length will result in ratios of string-lengths
> which exhibit a subharmonic series.
>

****When a person keeps dividing a string into smaller and smaller
equal divisions, that produces an *otonal* series, no??

So how does one get the *utonal* from string division again?... I
don't mean the string length ratios, but the actual vibrating
ratios.... I thought those were always *otonal.*??

Any illumination would be greatly appreciated in this dark place...

Joe

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

/tuning/topicId_31809.html#31822

> --- In tuning@y..., "jpehrson2" <jpehrson@r...> wrote:
>
> > Keep in mind, however, that the UTONAL series, however useful for
> > composition, does *not* actually occur in nature, but is an
> > *artifice* or *artificial* concept. "*Art* for short..." Right,
> > Paul?
> >
> > Joseph Pehrson
>
> Well, you don't really find Utonal _chords_ as _simultaneities_ in
> nature, but you might find a _successive_ series of frequencies
> belonging to a Utonal _scale_ in nature, particularly if you're
> looking at a chaotic system that can exhibit period-doubling,
period-
> tripling, etc. . . . behavior.

Hi Paul...

But, essentially, that's a kind of chance occurrence, yes? It's a
little like having the traditional roomful of monkeys and finding
that they *eventually* type all the works of Shakespeare (along with
a few other non-essential items) yes??

JP

--- In tuning@y..., "jpehrson2" <jpehrson@r...> wrote:
> --- In tuning@y..., "monz" <joemonz@y...> wrote:
>
> /tuning/topicId_31809.html#31814
>
> >
> > *However*, there have been many arguments over the dualistic
> > aspect of Partch's theory, precisely because traditional theory
> > would regard the "F 1/6" as the "root" of this "minor chord",
> > whereas the dualistic theory must recognize the "guide tone" of
> > "C 1/4" as the analogue to the otonal "fundamental". (Partch
> > discusses exactly this in his book, and the arguments go back
> > further, to when Oettingen first proposed dualism in the mid-
1800s.)
> >
>
> ****Thanks, Monz, for pointing this out. The significance of the
> *root* would make a difference. I wasn't aware there were already
> arguments opposed to Partch's "dualism" but I would be interested
in
> hearing more about this...

Such arguments have been promulgated by both the music-theory
establishment and yours truly . . .

> > The dichotomy becomes even more clear when we progress from
> > triads to tetrads. Traditional theory adds a "7th", continuing
> > to stack the "minor chord" by ascending "3rds" the same as with
> > the "major chord" -- so here the it's a "minor 7th" where with
> > the "major chord" it's a "major 7th". But the dualistic theory
> > continues the construction *downward* by adding a fourth
> > chord-identity *below* the utonal triad given above, thus:
> >
> > C Ab F D
> > 1/4 1/5 1/6 1/7
> >
> >
>
> ****So, essentially, that would turn into a *sixth* rather than a
> *seventh* yes??

No . . . the dualistic 'root' is C . . . where's the sixth? Me,
however, I like to use this chord with a bass note of F, which makes
this a minor sixth chord.

>
> ****When a person keeps dividing a string into smaller and smaller
> equal divisions, that produces an *otonal* series, no??

Yes.
>
> So how does one get the *utonal* from string division again?... I
> don't mean the string length ratios, but the actual vibrating
> ratios.... I thought those were always *otonal.*??

Right. The string length ratios with be an arithmetic series (1, 2,
3, 4, 5, ...) and since frequency is _inversely_ proportional to
string length, the frequencies will form an Otonal series (1/1, 1/2,
1/3, 1/4, 1/5 . . .)

--- In tuning@y..., "jpehrson2" <jpehrson@r...> wrote:
> --- In tuning@y..., "paulerlich" <paul@s...> wrote:

> >
> > Well, you don't really find Utonal _chords_ as _simultaneities_
in
> > nature, but you might find a _successive_ series of frequencies
> > belonging to a Utonal _scale_ in nature, particularly if you're
> > looking at a chaotic system that can exhibit period-doubling,
> period-
> > tripling, etc. . . . behavior.
>
> Hi Paul...
>
> But, essentially, that's a kind of chance occurrence, yes? It's a
> little like having the traditional roomful of monkeys and finding
> that they *eventually* type all the works of Shakespeare (along
with
> a few other non-essential items) yes??

No, not at all. Period-doubling, period-tripling, etc. . . this
spells an otonal series loud and clear, unambiguously. For example,
we had a fellow here on this list (Jim Cole, was it?) who could sing
a note and while holding that note, using throat-singing techniques,
change the _actual fundamental_ to 1/2, 1/3, 1/4, 1/5 . . . of that
frequency -- NOT SIMULTANEOUSLY, but in succession. This is no
accident.

> From: paulerlich <paul@stretch-music.com>
> To: <tuning@yahoogroups.com>
> Sent: Thursday, December 27, 2001 2:09 PM
> Subject: [tuning] Re: u/otonality and major/minor
>
>
> > > [Paul Erlich]
> > > ... particularly if you're looking at a chaotic system
> > > that can exhibit period-doubling, period-tripling, etc
> > > . . . . behavior.
> >
> > [Joe Pehrson]
> > But, essentially, that's a kind of chance occurrence, yes?
> > It's a little like having the traditional roomful of monkeys
> > and finding that they *eventually* type all the works of
> > Shakespeare (along with a few other non-essential items) yes??

Er... that would be *a whole lot* of non-essential items...

> No, not at all. Period-doubling, period-tripling, etc. . .
> this spells an otonal series loud and clear, unambiguously.
> For example, we had a fellow here on this list (Jim Cole,
> was it?) who could sing a note and while holding that note,
> using throat-singing techniques, change the _actual fundamental_
> to 1/2, 1/3, 1/4, 1/5 . . . of that frequency --
> NOT SIMULTANEOUSLY, but in succession. This is no accident.

Yes, it was Jim Cole.

This is a standard part of harmonic singing" technique.
I hear Jonathan Glasier do it at least once a week.

[plug alert]
Jonathan does harmonic singing better than anyone else I've
ever heard. For copies of his CD "Open Hear", send $15
and postage to:

Jonathan Glasier
P.O. Box 620027
San Diego, CA 92102

-monz

_________________________________________________________
Do You Yahoo!?
Get your free @yahoo.com address at http://mail.yahoo.com

Hey Joe!

I wrote this post before I read Paul's subsequent comments.
We're basically in agreement, but I think you'll appreciate
what I have to say. (also more coming on this at tuning-math)

> From: jpehrson2 <jpehrson@rcn.com>
> To: <tuning@yahoogroups.com>
> Sent: Thursday, December 27, 2001 11:14 AM
> Subject: [tuning] Re: u/otonality and major/minor
>
>
> --- In tuning@y..., "monz" <joemonz@y...> wrote:
>
> /tuning/topicId_31809.html#31814
>
> >
> > The dichotomy becomes even more clear when we progress from
> > triads to tetrads. Traditional theory adds a "7th", continuing
> > to stack the "minor chord" by ascending "3rds" the same as with
> > the "major chord" -- so here the it's a "minor 7th" where with
> > the "major chord" it's a "major 7th". But the dualistic theory
> > continues the construction *downward* by adding a fourth
> > chord-identity *below* the utonal triad given above, thus:
> >
> > C Ab F D
> > 1/4 1/5 1/6 1/7
> >
> >
>
> ****So, essentially, that would turn into a *sixth* rather than a
> *seventh* yes??

Yup. If you invert the chord so that the 1/7 is at the top,
it forms an interval ~933.1290944 cents above the "root" 1/6.

In other words, it's almost the same amount wider than
the 12-EDO "major 6th", as the 7:4 is narrower than
the 12-EDO "minor 7th".

In fact, the difference between these two differences is
exactly the same as the amount of tempering of the 3:2 in
12-EDO. (I'm working on a tuning-math post which explains
this.)

> > > Keep in mind, however, that the UTONAL series, however useful for
> > > composition, does *not* actually occur in nature, but is an
> > > *artifice* or *artificial* concept. "*Art* for short..." Right,
> > > Paul?
> >
> >
> > I'm not Paul, but here's my contribution:
> >
> > The utonal or subharmonic series does not normally occur in nature
> > as an *simultaneous audio phenomenon* (altho there *are* occassional
> > reports of it in acoustical phenomena), but it does indeed manifest
> > itself in other ways. For example, marking off equal linear
> > divisions of a string-length will result in ratios of string-lengths
> > which exhibit a subharmonic series.
> >
>
> ****When a person keeps dividing a string into smaller and smaller
> equal divisions, that produces an *otonal* series, no??
>
> So how does one get the *utonal* from string division again?... I
> don't mean the string length ratios, but the actual vibrating
> ratios.... I thought those were always *otonal.*??
>
> Any illumination would be greatly appreciated in this dark place...
>
> Joe

In terms of frequency -- i.e., *what we hear* -- yes, it's an
otonal series.

But the *actual string-lengths* measure a utonal series.

The two phenomena are inversely related.

love / peace / harmony ...

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

_________________________________________________________
Do You Yahoo!?
Get your free @yahoo.com address at http://mail.yahoo.com

--- In tuning@y..., "monz" <joemonz@y...> wrote:
>
> > From: paulerlich <paul@s...>
> > To: <tuning@y...>
> > Sent: Thursday, December 27, 2001 2:09 PM
> > Subject: [tuning] Re: u/otonality and major/minor
> >
> >
> > > > [Paul Erlich]
> > > > ... particularly if you're looking at a chaotic system
> > > > that can exhibit period-doubling, period-tripling, etc
> > > > . . . . behavior.
> > >
> > > [Joe Pehrson]
> > > But, essentially, that's a kind of chance occurrence, yes?
> > > It's a little like having the traditional roomful of monkeys
> > > and finding that they *eventually* type all the works of
> > > Shakespeare (along with a few other non-essential items) yes??
>
>
> Er... that would be *a whole lot* of non-essential items...
>
>
> > No, not at all. Period-doubling, period-tripling, etc. . .
> > this spells an otonal series loud and clear, unambiguously.
> > For example, we had a fellow here on this list (Jim Cole,
> > was it?) who could sing a note and while holding that note,
> > using throat-singing techniques, change the _actual fundamental_
> > to 1/2, 1/3, 1/4, 1/5 . . . of that frequency --
> > NOT SIMULTANEOUSLY, but in succession. This is no accident.
>
>
> Yes, it was Jim Cole.
>
> This is a standard part of harmonic singing" technique.
> I hear Jonathan Glasier do it at least once a week.
>
> [plug alert]
> Jonathan does harmonic singing better than anyone else I've
> ever heard. For copies of his CD "Open Hear", send $15
> and postage to:
>
> Jonathan Glasier
> P.O. Box 620027
> San Diego, CA 92102

________________________

J Gill: How, then, does "sub-harmonic" stuff relate to
"real-world" musical sound sources (other than Mr Glasier)?

/tuning/topicId_31809.html#31811
Joseph Pehrson:
<< Keep in mind, however, that the UTONAL series, however useful for
composition, does *not* actually occur in nature, but is an
*artifice* or *artificial* concept. "*Art* for short..." Right,
Paul?>>

/tuning/topicId_31809.html#31814
Joe Monzo:
<< The utonal or subharmonic series does not normally occur in nature
as an *simultaneous audio phenomenon* (altho there *are* occassional
reports of it in acoustical phenomena), but it does indeed manifest
itself in other ways. For example, marking off equal linear
divisions of a string-length will result in ratios of string-lengths
which exhibit a subharmonic series. >>

/tuning/topicId_31809.html#31822
Paul Erlich:
<< Well, you don't really find Utonal _chords_ as _simultaneities_ in
nature, but you might find a _successive_ series of frequencies
belonging to a Utonal _scale_ in nature, particularly if you're
looking at a chaotic system that can exhibit period-doubling, period-
tripling, etc. . . . behavior. >>

/tuning/topicId_31809.html#31979
Paul Erlich:

> JP: ***When a person keeps dividing a string into smaller
> and smaller
> equal divisions, that produces an *otonal* series, no??

Yes.

> JP:So how does one get the *utonal* from string division again?...
> I don't mean the string length ratios, but the actual vibrating
> ratios.... I thought those were always *otonal.*??

Right. The string length ratios with be an arithmetic series (1, 2,
3, 4, 5, ...) and since frequency is _inversely_ proportional to
string length, the frequencies will form an Otonal series (1/1, 1/2,
1/3, 1/4, 1/5 . . .)

Curiously, J Gill

--- In tuning@y..., "monz" <joemonz@y...> wrote:
>
> Hey Joe!
>
> I wrote this post before I read Paul's subsequent comments.
> We're basically in agreement, but I think you'll appreciate
> what I have to say. (also more coming on this at tuning-math)
>
>
> > From: jpehrson2 <jpehrson@r...>
> > To: <tuning@y...>
> > Sent: Thursday, December 27, 2001 11:14 AM
> > Subject: [tuning] Re: u/otonality and major/minor
> >
> >
> > --- In tuning@y..., "monz" <joemonz@y...> wrote:
> >
> > /tuning/topicId_31809.html#31814
> >
> > >
> > > The dichotomy becomes even more clear when we progress from
> > > triads to tetrads. Traditional theory adds a "7th", continuing
> > > to stack the "minor chord" by ascending "3rds" the same as with
> > > the "major chord" -- so here the it's a "minor 7th" where with
> > > the "major chord" it's a "major 7th". But the dualistic theory
> > > continues the construction *downward* by adding a fourth
> > > chord-identity *below* the utonal triad given above, thus:
> > >
> > > C Ab F D
> > > 1/4 1/5 1/6 1/7
> > >
> > >
> >
> > ****So, essentially, that would turn into a *sixth* rather than a
> > *seventh* yes??
>
>
> Yup. If you invert the chord so that the 1/7 is at the top,
> it forms an interval ~933.1290944 cents above the "root" 1/6.
>
> In other words, it's almost the same amount wider than
> the 12-EDO "major 6th", as the 7:4 is narrower than
> the 12-EDO "minor 7th".
>
> In fact, the difference between these two differences is
> exactly the same as the amount of tempering of the 3:2 in
> 12-EDO. (I'm working on a tuning-math post which explains
> this.)
>
>
>
> > > > Keep in mind, however, that the UTONAL series, however useful for
> > > > composition, does *not* actually occur in nature, but is an
> > > > *artifice* or *artificial* concept. "*Art* for short..." Right,
> > > > Paul?
> > >
> > >
> > > I'm not Paul, but here's my contribution:
> > >
> > > The utonal or subharmonic series does not normally occur in nature
> > > as an *simultaneous audio phenomenon* (altho there *are* occassional
> > > reports of it in acoustical phenomena), but it does indeed manifest
> > > itself in other ways. For example, marking off equal linear
> > > divisions of a string-length will result in ratios of string-lengths
> > > which exhibit a subharmonic series.
> > >
> >
> > ****When a person keeps dividing a string into smaller and smaller
> > equal divisions, that produces an *otonal* series, no??
> >
> > So how does one get the *utonal* from string division again?... I
> > don't mean the string length ratios, but the actual vibrating
> > ratios.... I thought those were always *otonal.*??
> >
> > Any illumination would be greatly appreciated in this dark place...
> >
> > Joe
>
>
> In terms of frequency -- i.e., *what we hear* -- yes, it's an
> otonal series.
>
> But the *actual string-lengths* measure a utonal series.
>
> The two phenomena are inversely related.

J Gill: Monz, if *what we hear* is, indeed,
an *otonal* series, of what relevance are
"sub-harmonic" series to "real-world" musical
sound sources (other than their usefulness in
considering *geometric* relationships, as
opposed to the *arithmetic* relationships
of which the *otonal* series is composed)???

Curiously, J Gill

> From: unidala <JGill99@imajis.com>
> To: <tuning@yahoogroups.com>
> Sent: Friday, December 28, 2001 2:41 AM
> Subject: [tuning] Re: u/otonality and major/minor
>
> > [me, monz]
> > In terms of frequency -- i.e., *what we hear* -- yes, it's an
> > otonal series.
> >
> > But the *actual string-lengths* measure a utonal series.
> >
> > The two phenomena are inversely related.
>
>
> J Gill: Monz, if *what we hear* is, indeed,
> an *otonal* series, of what relevance are
> "sub-harmonic" series to "real-world" musical
> sound sources (other than their usefulness in
> considering *geometric* relationships, as
> opposed to the *arithmetic* relationships
> of which the *otonal* series is composed)???

I don't know what else to say about it. The two major
relevances that I can think of are:

1) subharmonic divisions of a string-length produce
sets of historically important otonal rational
pitches, and

2) proper manipulation of the vocal cavity in harmonic
singing will result in a subharmonic series of
fundamentals while sustaining an upper harmonic
which is common to all of them.

-monz

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--- In tuning@y..., "monz" <joemonz@y...> wrote:
>
> > From: unidala <JGill99@i...>
> > To: <tuning@y...>
> > Sent: Friday, December 28, 2001 2:41 AM
> > Subject: [tuning] Re: u/otonality and major/minor
> >
> > > [me, monz]
> > > In terms of frequency -- i.e., *what we hear* -- yes, it's an
> > > otonal series.
> > >
> > > But the *actual string-lengths* measure a utonal series.
> > >
> > > The two phenomena are inversely related.
> >
> >
> > J Gill: Monz, if *what we hear* is, indeed,
> > an *otonal* series, of what relevance are
> > "sub-harmonic" series to "real-world" musical
> > sound sources (other than their usefulness in
> > considering *geometric* relationships, as
> > opposed to the *arithmetic* relationships
> > of which the *otonal* series is composed)???
>
>
> I don't know what else to say about it. The two major
> relevances that I can think of are:
>
> 1) subharmonic divisions of a string-length produce
> sets of historically important otonal rational
> pitches, and
>
> 2) proper manipulation of the vocal cavity in harmonic
> singing will result in a subharmonic series of
> fundamentals while sustaining an upper harmonic
> which is common to all of them.

J Gill: Note that the *difference frequency* produced
by subtracting (any) rational interval from 1/1 falls
precisely (and exclusively) on a "sub-harmonic" pitch
of the 1/1 (or other reference pitch so designated).
So, perhaps the relevance of the "sub-harmonic" series
to musical resonators exists as result of non-linear
responses within the "aural mind"?

J Gill

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

> > No, not at all. Period-doubling, period-tripling, etc. . .
> > this spells an otonal series loud and clear, unambiguously.
> > For example, we had a fellow here on this list (Jim Cole,
> > was it?) who could sing a note and while holding that note,
> > using throat-singing techniques, change the _actual fundamental_
> > to 1/2, 1/3, 1/4, 1/5 . . . of that frequency --
> > NOT SIMULTANEOUSLY, but in succession. This is no accident.
>
>
> Yes, it was Jim Cole.
>
> This is a standard part of harmonic singing" technique.

Not so, at least as David Hykes describes it. What I'm talking about,
and I admit it wasn't clear, is the "vocal fry" technique of getting
an ultra-low "subharmonic" of the note you're "actually" singing.
This has nothing to do with overtone singing, although the two
techniques are often used together, as in some styles of Tuvan throat
singing.

--- In tuning@y..., "unidala" <JGill99@i...> wrote:
> --- In tuning@y..., "monz" <joemonz@y...> wrote:
> >
> > > From: paulerlich <paul@s...>
> > > To: <tuning@y...>
> > > Sent: Thursday, December 27, 2001 2:09 PM
> > > Subject: [tuning] Re: u/otonality and major/minor
> > >
> > >
> > > > > [Paul Erlich]
> > > > > ... particularly if you're looking at a chaotic system
> > > > > that can exhibit period-doubling, period-tripling, etc
> > > > > . . . . behavior.
> > > >
> > > > [Joe Pehrson]
> > > > But, essentially, that's a kind of chance occurrence, yes?
> > > > It's a little like having the traditional roomful of monkeys
> > > > and finding that they *eventually* type all the works of
> > > > Shakespeare (along with a few other non-essential items) yes??
> >
> >
> > Er... that would be *a whole lot* of non-essential items...
> >
> >
> > > No, not at all. Period-doubling, period-tripling, etc. . .
> > > this spells an otonal series loud and clear, unambiguously.
> > > For example, we had a fellow here on this list (Jim Cole,
> > > was it?) who could sing a note and while holding that note,
> > > using throat-singing techniques, change the _actual fundamental_
> > > to 1/2, 1/3, 1/4, 1/5 . . . of that frequency --
> > > NOT SIMULTANEOUSLY, but in succession. This is no accident.
> >
> >
> > Yes, it was Jim Cole.
> >
> > This is a standard part of harmonic singing" technique.
> > I hear Jonathan Glasier do it at least once a week.
> >
> > [plug alert]
> > Jonathan does harmonic singing better than anyone else I've
> > ever heard. For copies of his CD "Open Hear", send $15
> > and postage to:
> >
> > Jonathan Glasier
> > P.O. Box 620027
> > San Diego, CA 92102
>
> ________________________
>
>
> J Gill: How, then, does "sub-harmonic" stuff relate to
> "real-world" musical sound sources (other than Mr Glasier)?
>
>
> /tuning/topicId_31809.html#31811
> Joseph Pehrson:
> << Keep in mind, however, that the UTONAL series, however useful
for
> composition, does *not* actually occur in nature, but is an
> *artifice* or *artificial* concept. "*Art* for short..." Right,
> Paul?>>
>
> /tuning/topicId_31809.html#31814
> Joe Monzo:
> << The utonal or subharmonic series does not normally occur in
nature
> as an *simultaneous audio phenomenon* (altho there *are* occassional
> reports of it in acoustical phenomena), but it does indeed manifest
> itself in other ways. For example, marking off equal linear
> divisions of a string-length will result in ratios of string-lengths
> which exhibit a subharmonic series. >>
>
>
> /tuning/topicId_31809.html#31822
> Paul Erlich:
> << Well, you don't really find Utonal _chords_ as _simultaneities_
in
> nature, but you might find a _successive_ series of frequencies
> belonging to a Utonal _scale_ in nature, particularly if you're
> looking at a chaotic system that can exhibit period-doubling,
period-
> tripling, etc. . . . behavior. >>
>
> /tuning/topicId_31809.html#31979
> Paul Erlich:
>
> > JP: ***When a person keeps dividing a string into smaller
> > and smaller
> > equal divisions, that produces an *otonal* series, no??
>
> Yes.
>
> > JP:So how does one get the *utonal* from string division
again?...
> > I don't mean the string length ratios, but the actual vibrating
> > ratios.... I thought those were always *otonal.*??
>
> Right. The string length ratios with be an arithmetic series (1, 2,
> 3, 4, 5, ...) and since frequency is _inversely_ proportional to
> string length, the frequencies will form an Otonal series (1/1,
1/2,
> 1/3, 1/4, 1/5 . . .)
>
>
> Curiously, J Gill

What's your outstanding question on this?

> From: paulerlich <paul@stretch-music.com>
> To: <tuning@yahoogroups.com>
> Sent: Friday, December 28, 2001 1:16 PM
> Subject: [tuning] Re: u/otonality and major/minor
>
>
> --- In tuning@y..., "monz" <joemonz@y...> wrote:
>
> > > No, not at all. Period-doubling, period-tripling, etc. . .
> > > this spells an otonal series loud and clear, unambiguously.
> > > For example, we had a fellow here on this list (Jim Cole,
> > > was it?) who could sing a note and while holding that note,
> > > using throat-singing techniques, change the _actual fundamental_
> > > to 1/2, 1/3, 1/4, 1/5 . . . of that frequency --
> > > NOT SIMULTANEOUSLY, but in succession. This is no accident.
> >
> >
> > Yes, it was Jim Cole.
> >
> > This is a standard part of harmonic singing" technique.
>
> Not so, at least as David Hykes describes it. What I'm talking about,
> and I admit it wasn't clear, is the "vocal fry" technique of getting
> an ultra-low "subharmonic" of the note you're "actually" singing.
> This has nothing to do with overtone singing, although the two
> techniques are often used together, as in some styles of Tuvan throat
> singing.

Oh! OK, I know about that too, because there was a fantastic
presentation about it at the ISMA conference I participated in
in Perugia, Italy in September. I'll try to get more info on
that from the proceedings when I get in later tonight.

BTW, Paul... you (and others here, but especially you) would
be *very* interested in reading the ISMA 2001 proceedings.
They're available from the publisher at a hefty 90 Euros
(= approximately $90), but I think you'd find it well worth
the expense, or perhaps you can find the 2-volume set in a
library somewhere. I'll post the info later.

-monz

_________________________________________________________
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Get your free @yahoo.com address at http://mail.yahoo.com

--- In tuning@y..., "unidala" <JGill99@i...> wrote:

> J Gill: Monz, if *what we hear* is, indeed,
> an *otonal* series, of what relevance are
> "sub-harmonic" series to "real-world" musical
> sound sources (other than their usefulness in
> considering *geometric* relationships, as
> opposed to the *arithmetic* relationships
> of which the *otonal* series is composed)???

Some would argue, nothing.

Some would argue, a utonal series of notes share a common overtone,
and this can be musically useful/important -- you'll see a lot of
this kind of argument in Fokker and Vogel, for example.

Partch's motive is less clear, and his focus on Utonalities seems to
contradict his stated preference for tone-combinations having short
wave periods. But he also seems to put some importance on *number*
abstracted from physical phenomena, though what he means by this (be
it mystical or otherwise) seems unclear to me.

--- In tuning@y..., "unidala" <JGill99@i...> wrote:

> J Gill: Note that the *difference frequency* produced
> by subtracting (any) rational interval from 1/1 falls
> precisely (and exclusively) on a "sub-harmonic" pitch
> of the 1/1 (or other reference pitch so designated).

This was noted by Jon Catler and Johnny Reinhard.

> So, perhaps the relevance of the "sub-harmonic" series
> to musical resonators

Musical resonators?

> exists as result of non-linear
> responses within the "aural mind"?

Well, _if_ you are playing music in a tuning system which is focused
on combining a fixed 1/1 with rational (but not strictly overtone)
related notes to 1/1, _then_ you might have a reason to ask this
question. So, the right circumstances have to be there first, and
again, there will be no implied justification for using utonal chords
as _simultaneities_ -- this would remain an "artificial" construct
(not to denigrate its use by any composer who would wish to use it).

>
>
> J Gill

> No, not at all. Period-doubling, period-tripling, etc. . .
> this spells an otonal series loud and clear, unambiguously.
> For example, we had a fellow here on this list (Jim Cole,
> was it?) who could sing a note and while holding that note,
> using throat-singing techniques, change the _actual fundamental_
> to 1/2, 1/3, 1/4, 1/5 . . . of that frequency --
> NOT SIMULTANEOUSLY, but in succession. This is no accident.

By the way, Paul, is that supposed to be _u_tonal in the
2nd line?

-Carl

--- In tuning@y..., "clumma" <carl@l...> wrote:
> > No, not at all. Period-doubling, period-tripling, etc. . .
> > this spells an otonal series loud and clear, unambiguously.
> > For example, we had a fellow here on this list (Jim Cole,
> > was it?) who could sing a note and while holding that note,
> > using throat-singing techniques, change the _actual fundamental_
> > to 1/2, 1/3, 1/4, 1/5 . . . of that frequency --
> > NOT SIMULTANEOUSLY, but in succession. This is no accident.
>
> By the way, Paul, is that supposed to be _u_tonal in the
> 2nd line?

Yes, thanks for catching that errors, I've been catching quite a few
of this same error as I write but apparently not every time. Thanks,
Carl Lomma :)

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

> Partch's motive is less clear, and his focus on Utonalities seems to
> contradict his stated preference for tone-combinations having short
> wave periods.

I thought his point was that if you have otonalities, you get utonalities for free, and that they seem to work, for whatever reason.

--- In tuning@y..., "genewardsmith" <genewardsmith@j...> wrote:
> --- In tuning@y..., "paulerlich" <paul@s...> wrote:
>
> > Partch's motive is less clear, and his focus on Utonalities seems
to
> > contradict his stated preference for tone-combinations having
short
> > wave periods.
>
> I thought his point was that if you have otonalities, you get
>utonalities for free,

Assuming you keep a constant 1/1 pitch within all of them -- for a
different approach, see http://www.msu.edu/user/hulenpet/paper1.html
(John Starrett, you need to update your broken link for
this "Ratiotonic Temperament" under "Notes on Microtonality").

>and that they seem to work, for whatever >reason.

Maybe we should start a "Critical-Deconstruction-of-Partch" list? For
what it's worth, he doesn't seem to put forward a "they seem to work
for whatever reason, so lets use them" philosophy at all, from what I
can see. They seem to be a grand necessity for him, despite the fact
that they contradict his "short wave period = relative consonance"
dictum, a point he never seems to realize.

Gene and Paul,

I'm finding this "critical deconstruction of Partch"
most interesting! If you're really serious about that
list, I say go for it -- you've got a third member here!

-monz

----- Original Message -----
From: paulerlich <paul@stretch-music.com>
To: <tuning@yahoogroups.com>
Sent: Friday, December 28, 2001 2:36 PM
Subject: [tuning] Re: u/otonality and major/minor

> --- In tuning@y..., "genewardsmith" <genewardsmith@j...> wrote:
> > --- In tuning@y..., "paulerlich" <paul@s...> wrote:
> >
> > > Partch's motive is less clear, and his focus on
> > > Utonalities seems to contradict his stated preference
> > > for tone-combinations having short wave periods.
> >
> > I thought his point was that if you have otonalities,
> > you get utonalities for free,
>
> Assuming you keep a constant 1/1 pitch within all of them
> -- for a different approach, see
> http://www.msu.edu/user/hulenpet/paper1.html
> (John Starrett, you need to update your broken link for
> this "Ratiotonic Temperament" under "Notes on Microtonality").
>
> > and that they seem to work, for whatever >reason.
>
> Maybe we should start a "Critical-Deconstruction-of-Partch"
> list? For what it's worth, he doesn't seem to put forward a
> "they seem to work for whatever reason, so lets use them"
> philosophy at all, from what I can see. They seem to be a
> grand necessity for him, despite the fact that they contradict
> his "short wave period = relative consonance" dictum, a
> point he never seems to realize.

_________________________________________________________
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Get your free @yahoo.com address at http://mail.yahoo.com

--- In tuning@y..., "monz" <joemonz@y...> wrote:
> Gene and Paul,
>
> I'm finding this "critical deconstruction of Partch"
> most interesting! If you're really serious about that
> list, I say go for it -- you've got a third member here!

I think there are too many lists as it is.

>>Gene and Paul,
>>
>>I'm finding this "critical deconstruction of Partch"
>>most interesting! If you're really serious about that
>>list, I say go for it -- you've got a third member here!
>
>I think there are too many lists as it is.

I agree, though I'm not sure that one more or less
will make any difference. The problem is using
multiple lists across yahoo groups instead of a more
modern, fully-threaded discussion forum.

-Carl

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

/tuning/topicId_31809.html#31979

>
> Right. The string length ratios with be an arithmetic series (1, 2,
> 3, 4, 5, ...) and since frequency is _inversely_ proportional to
> string length, the frequencies will form an Otonal series (1/1,
1/2, 1/3, 1/4, 1/5 . . .)

Hi Paul...

Is this an error? That's not an Otonal series, is it??

JP

--- In tuning@y..., "jpehrson2" <jpehrson@r...> wrote:
> --- In tuning@y..., "paulerlich" <paul@s...> wrote:
>
> /tuning/topicId_31809.html#31979
>
> >
> > Right. The string length ratios with be an arithmetic series (1,
2,
> > 3, 4, 5, ...) and since frequency is _inversely_ proportional to
> > string length, the frequencies will form an Otonal series (1/1,
> 1/2, 1/3, 1/4, 1/5 . . .)
>
> Hi Paul...
>
> Is this an error? That's not an Otonal series, is it??
>
> JP

You're right -- I did it again!

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

/tuning/topicId_31809.html#32015

>
> In terms of frequency -- i.e., *what we hear* -- yes, it's an
> otonal series.
>
> But the *actual string-lengths* measure a utonal series.
>
> The two phenomena are inversely related.
>

Monz... this is pretty funny, though, since you can't *hear* the
actual "string lengths..." :)

Happy New Year!

Joe P.

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

/tuning/topicId_31809.html#32018

>
> I don't know what else to say about it. The two major
> relevances that I can think of are:
>
> 1) subharmonic divisions of a string-length produce
> sets of historically important otonal rational
> pitches, and
>
> 2) proper manipulation of the vocal cavity in harmonic
> singing will result in a subharmonic series of
> fundamentals while sustaining an upper harmonic
> which is common to all of them.
>
>
>
> -monz
>

Hi Monz and others!

Well, that's pretty interesting... you're refering to the "Tuvan
Miracles" of producing various throat tones, yes?? Or is that
Bulgarian.

In any case, how do they do that? Is there some way to *perceive*
the *undertone* series AURALLY from a guide tone??

I thought people could only perceive such things in an *otonal* way.

Any help in a storm would remove this snow...

Thanks!

JP

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

/tuning/topicId_31809.html#32085

> --- In tuning@y..., "genewardsmith" <genewardsmith@j...> wrote:
> > --- In tuning@y..., "paulerlich" <paul@s...> wrote:
> >
> > > Partch's motive is less clear, and his focus on Utonalities
seems
> to
> > > contradict his stated preference for tone-combinations having
> short
> > > wave periods.
> >
> > I thought his point was that if you have otonalities, you get
> >utonalities for free,
>
> Assuming you keep a constant 1/1 pitch within all of them -- for a
> different approach, see
http://www.msu.edu/user/hulenpet/paper1.html
> (John Starrett, you need to update your broken link for
> this "Ratiotonic Temperament" under "Notes on Microtonality").
>
> >and that they seem to work, for whatever >reason.
>
> Maybe we should start a "Critical-Deconstruction-of-Partch" list?
For
> what it's worth, he doesn't seem to put forward a "they seem to
work
> for whatever reason, so lets use them" philosophy at all, from what
I
> can see. They seem to be a grand necessity for him, despite the
fact
> that they contradict his "short wave period = relative consonance"
> dictum, a point he never seems to realize.

This is really interesting.

If I'm understanding this correctly, it means that Harry Partch's
emphasis on Just Intonation and the purity of small integer otonal
intervals was never totally reconciled in his thinking with his usage
of *UTONAL* materials.

Is this the gist of this, because, if so, it's really interesting...

??

JP

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

/tuning/topicId_31809.html#32093

> Gene and Paul,
>
> I'm finding this "critical deconstruction of Partch"
> most interesting! If you're really serious about that
> list, I say go for it -- you've got a third member here!
>
>
> -monz
>

Frankly, I think we could do this on the present list. If
*everything* moves off this list, what's going to be *on* this list
eventually?! :)

JP

--- In tuning@y..., "jpehrson2" <jpehrson@r...> wrote:
>
> Well, that's pretty interesting... you're refering to the "Tuvan
> Miracles" of producing various throat tones, yes?? Or is that
> Bulgarian.

I don't *think* it's Bulgarian . . .

>
> In any case, how do they do that? Is there some way to
*perceive*
> the *undertone* series AURALLY from a guide tone??

It has nothing to do with perception. The physics forces the
"throat tone" to have a period which is an integer multiple of the
period of the tone that would normally be produces with the
larynx in the same position . . . if the period is N times the normal
period, then the frequency is 1/N times the normal frequency --
i.e., a "subharmonic".

--- In tuning@y..., "jpehrson2" <jpehrson@r...> wrote:
>
> If I'm understanding this correctly, it means that Harry Partch's
> emphasis on Just Intonation and the purity of small integer
otonal
> intervals was never totally reconciled in his thinking with his
usage
> of *UTONAL* materials.
>
> Is this the gist of this, because, if so, it's really interesting...
>
> ??

The ideas of emphasis on Just Intonation and the purity of small
integer intervals (remember, intervals cannot be either otonal or
utonal) do not conflict with a usage of utonal materials.

However, the idea of short wave periods being desirable, which
Partch implies, would actually favor otonal chords greatly over
utonal chords, a point Partch didn't seem to realize.

--- In tuning@y..., "paulerlich" <paul@s...> wrote:
> I don't *think* it's Bulgarian . . .

They are NOT Bulagarian. Tuva are Turkish (or Turkic; anyway, we can
comprehend without translation) people living in outer Siberia. I had
the chance to hear them live in Istanbul a couple of years ago.

Apart from the Tuva, Tibetans also have their own throat (overtone)
singing technique.

Hth,
Ertuğrul

PS: Reply by mail if necessary since I'm not a regular groupie.