a question about otonal & utonal systems.

Dear friends

After looking in tonalsoft , at last I couldn't clearly understand
difference of otonality and utonality in partch theory.

Can u tell me which of these two systems are otonal and which of them
utonal?

I myself guess that the first is otonal. Am I right?if not please
expplain about it?

Thanks a lot

Shaahin Mohaajeri

Tombak Player & Researcher , Composer

www.geocities.com/acousticsoftombak

My tombak musics : www.rhythmweb.com/gdg

My articles in ''Harmonytalk'':

www.harmonytalk.com/archives/000296.html

www.harmonytalk.com/archives/000288.html

My article in DrumDojo:

www.drumdojo.com/world/persia/tonbak_acoustics.htm

--- In tuning@yahoogroups.com, "Mohajeri Shahin" <shahinm@k...> wrote:
> Can u tell me which of these two systems are otonal and which of them
> utonal?

*Which* two systems? You are just asking the question, you haven't
shown any systems that need defining as otonal or utonal.

Cheers,
Jon

Dear friends

After looking in tonalsoft , at last I couldn't clearly understand
difference of otonality and utonality in partch theory.

Can u tell me which of these two systems are otonal and which of them
utonal?

I myself guess that the first is otonal. Am I right?if not please
expplain about it?

Thanks a lot

Welcome to Scala.

Type "@tutorial" to view the tutorial.

Edit startup.cmd to configure initial settings.

|

Scala version 2.21g Copyright E.F. Op de Coul, the Netherlands, 2004

|

0: 1/1 0.000 unison, perfect prime

1: 9/8 203.910 major whole tone

2: 5/4 386.314 major third

3: 11/8 551.318 undecimal semi-augmented fourth

4: 3/2 701.955 perfect fifth

5: 13/8 840.528 tridecimal neutral sixth

6: 7/4 968.826 harmonic seventh

7: 15/8 1088.269 classic major seventh

8: 2/1 1200.000 octave

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0: 1/1 0.000 unison, perfect prime

1: 16/15 111.731 minor diatonic semitone

2: 8/7 231.174 septimal whole tone

3: 16/13 359.472 tridecimal neutral third

4: 4/3 498.045 perfect fourth

5: 16/11 648.682 undecimal semi-diminished fifth

6: 8/5 813.686 minor sixth

7: 16/9 996.090 Pythagorean minor seventh

8: 2/1 1200.000 octave

Shaahin Mohaajeri

Tombak Player & Researcher , Composer

www.geocities.com/acousticsoftombak

My tombak musics : www.rhythmweb.com/gdg

My articles in ''Harmonytalk'':

www.harmonytalk.com/archives/000296.html

www.harmonytalk.com/archives/000288.html

My article in DrumDojo:

www.drumdojo.com/world/persia/tonbak_acoustics.htm

Mohajeri Shahin wrote:
> > > Dear friends
> > After looking in tonalsoft , at last I couldn't clearly understand
> difference of otonality and utonality in partch theory.
> > Can u tell me which of these two systems are otonal and which of
> them utonal?
> > I myself guess that the first is otonal. Am I right?if not please > expplain about it?

You are right. Maybe you weren't sure because utonal systems cannot
only be regarded as an inversion of the otonal (after all, this
"doesn't exist" in nature), but as part of the harmonic, otonal series higher up.

> 0: 1/1 0.000 unison, perfect prime
> > 1: 16/15 111.731 minor diatonic semitone

One interval is neither otonal nor utonal, so instead of starting the series on 16th harmonic going down you might hust as well start on the 15th going up: 16/15

> > 2: 8/7 231.174 septimal whole tone

To integrate this into an otonal series, you have to seven times higher 112/105, 120/112 (each interval reduces, but the two steps in series don't: 105:112:120).

> > 3: 16/13 359.472 tridecimal neutral third

Thirteen times higher up: 1365:1456:1560. The primes of 11 and another 3 are yet to come, so you'll end up somewhere in the 10,000s for the whole scale.

I have often wondered if there is anything special about this exact reversal of the harmonic series. Apart from a low numbers/instrument building point of view, is there anything auditory that sets off a utonal scale from any other reordering (or any other reordering that retains the fifth and the fourth) of parts of the harmonic series?

klaus

klaus-

utonal pitches, although natural acoustic instruments don't produce them in
their spectra, remain important because two utonally relate pitches will have
at least 1 otonal harmonic in common.

also utonal relationships exist in the otonal series (just another way of
saying the above). one can get the next note in an utonal series by taking
the octave complement of an otonal pitch. for instance the utonal series
version of 11/8 is 16/11....

-Aaron.

On Sunday 09 October 2005 7:12 am, klaus schmirler wrote:
> Mohajeri Shahin wrote:
> > Dear friends
> >
> > After looking in tonalsoft , at last I couldn't clearly understand
> > difference of otonality and utonality in partch theory.
> >
> > Can u tell me which of these two systems are otonal and which of
> > them utonal?
> >
> > I myself guess that the first is otonal. Am I right?if not please
> > expplain about it?
>
> You are right. Maybe you weren't sure because utonal systems cannot
> only be regarded as an inversion of the otonal (after all, this
> "doesn't exist" in nature), but as part of the harmonic, otonal series
> higher up.
>
> > 0: 1/1 0.000 unison, perfect prime
> >
> > 1: 16/15 111.731 minor diatonic semitone
>
> One interval is neither otonal nor utonal, so instead of starting the
> series on 16th harmonic going down you might hust as well start on the
> 15th going up: 16/15
>
> > 2: 8/7 231.174 septimal whole tone
>
> To integrate this into an otonal series, you have to seven times
> higher 112/105, 120/112 (each interval reduces, but the two steps in
> series don't: 105:112:120).
>
> > 3: 16/13 359.472 tridecimal neutral third
>
> Thirteen times higher up: 1365:1456:1560. The primes of 11 and another
> 3 are yet to come, so you'll end up somewhere in the 10,000s for the
> whole scale.
>
> I have often wondered if there is anything special about this exact
> reversal of the harmonic series. Apart from a low numbers/instrument
> building point of view, is there anything auditory that sets off a
> utonal scale from any other reordering (or any other reordering that
> retains the fifth and the fourth) of parts of the harmonic series?
>
> klaus
>
>
>
>
> You can configure your subscription by sending an empty email to one
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--- In tuning@yahoogroups.com, "Mohajeri Shahin" <shahinm@k...> wrote:

> I myself guess that the first is otonal. Am I right?if not please
> expplain about it?

The first scale is the famous Zarlino scale, which has three otonal
and two utonal triads, and hence is more otonal than utonal. The
second scale is the complete 15-limit utonal chord, so it is clearly
utonal.

--- In tuning@yahoogroups.com, klaus schmirler <KSchmir@o...> wrote:

> I have often wondered if there is anything special about this exact
> reversal of the harmonic series. Apart from a low numbers/instrument
> building point of view, is there anything auditory that sets off a
> utonal scale from any other reordering (or any other reordering that
> retains the fifth and the fourth) of parts of the harmonic series?

One characteristic feature is that they have coinciding partial tones.
If you have a chord 1, 1/2, ..., 1/n, then the 1,2, ... nth partials
all coincide at 1. Octave equivalencing changes that around, but does
not change the basic fact of coincidence. This strikes me as a
possible reason to take utonal chords seriously, aside from the fact
that in low prime limit they sound convincing.

Gene Ward Smith wrote:
> --- In tuning@yahoogroups.com, klaus schmirler <KSchmir@o...> wrote:
> > >>I have often wondered if there is anything special about this exact >>reversal of the harmonic series. Apart from a low numbers/instrument >>building point of view, is there anything auditory that sets off a >>utonal scale from any other reordering (or any other reordering that >>retains the fifth and the fourth) of parts of the harmonic series?
> Ok, I've done some thinking :O) and found out what threw me off.

> > One characteristic feature is that they have coinciding partial tones.

... which is true for any series of intervals, just as you can find a lowest common enumerator and a lowest common denominator for any collection and ordering of fractions.

> If you have a chord 1, 1/2, ..., 1/n, then the 1,2, ... nth partials
> all coincide at 1.

This, on the other hand, is not general enough, the 1 needn't even be a power of 2 as I had supposed. If your scale is the typical alphorn range

(6:7:8:9:10:11:12)/1

and you turn it around, the one is a three:

12/(11:10:9:8:7:6).

So while the common over/undertone is a truism, it really seem to be the "neighboring" superparticular ratios that are important. If you break the ascending or descending series, this aspect is lost (and the common tone never appears unreduced).

Octave equivalencing changes that around, but does
> not change the basic fact of coincidence. This strikes me as a
> possible reason to take utonal chords seriously, aside from the fact
> that in low prime limit they sound convincing.

Like the utonal major chord 24/(24:19:16)? :P

klaus

In Partch's theory, your first scale would be a 1/1 otonality, and your second would be a 1/
1 utonality. You can tell because in the first one, all the denominators are powers of 2,
while in the second one, all the numerators are powers of 2.

--- In tuning@yahoogroups.com, "Mohajeri Shahin" <shahinm@k...> wrote:
>
>
>
> Dear friends
>
> After looking in tonalsoft , at last I couldn't clearly understand
> difference of otonality and utonality in partch theory.
>
> Can u tell me which of these two systems are otonal and which of them
> utonal?
>
> I myself guess that the first is otonal. Am I right?if not please
> expplain about it?
>
>
>
> Thanks a lot
>
>
>
> Welcome to Scala.
>
> Type "@tutorial" to view the tutorial.
>
> Edit startup.cmd to configure initial settings.
>
> |
>
> Scala version 2.21g Copyright E.F. Op de Coul, the Netherlands, 2004
>
> |
>
> 0: 1/1 0.000 unison, perfect prime
>
> 1: 9/8 203.910 major whole tone
>
> 2: 5/4 386.314 major third
>
> 3: 11/8 551.318 undecimal semi-augmented fourth
>
> 4: 3/2 701.955 perfect fifth
>
> 5: 13/8 840.528 tridecimal neutral sixth
>
> 6: 7/4 968.826 harmonic seventh
>
> 7: 15/8 1088.269 classic major seventh
>
> 8: 2/1 1200.000 octave
>
> ************************************************************************
> *********
>
> 0: 1/1 0.000 unison, perfect prime
>
> 1: 16/15 111.731 minor diatonic semitone
>
> 2: 8/7 231.174 septimal whole tone
>
> 3: 16/13 359.472 tridecimal neutral third
>
> 4: 4/3 498.045 perfect fourth
>
> 5: 16/11 648.682 undecimal semi-diminished fifth
>
> 6: 8/5 813.686 minor sixth
>
> 7: 16/9 996.090 Pythagorean minor seventh
>
> 8: 2/1 1200.000 octave
>
>
>
>
>
> Shaahin Mohaajeri
>
>
>
> Tombak Player & Researcher , Composer
>
> www.geocities.com/acousticsoftombak
>
> My tombak musics : www.rhythmweb.com/gdg
>
> My articles in ''Harmonytalk'':
>
> www.harmonytalk.com/archives/000296.html
>
> www.harmonytalk.com/archives/000288.html
>
> My article in DrumDojo:
>
> www.drumdojo.com/world/persia/tonbak_acoustics.htm
>

--- In tuning@yahoogroups.com, klaus schmirler <KSchmir@o...> wrote:
>
>
> I have often wondered if there is anything special about this exact
> reversal of the harmonic series. Apart from a low numbers/instrument
> building point of view, is there anything auditory that sets off a
> utonal scale from any other reordering (or any other reordering that
> retains the fifth and the fourth) of parts of the harmonic series?

There is one thing: the presence of a fairly low common overtone -- a frequency that is an
overtone of all the notes. Utonal scales are special in this respect, for what it's worth.

--- In tuning@yahoogroups.com, Aaron Krister Johnson <aaron@a...> wrote:
>
>
> klaus-
>
> utonal pitches, although natural acoustic instruments don't produce them in
> their spectra, remain important because two utonally relate pitches will have
> at least 1 otonal harmonic in common.

That's true of course, but that really isn't saying anything since, as Klaus pointed out, two
pitches can never be more "utonally related" than "otonally related" or vice versa. It takes
at least three pitches before either otonality or utonality can be said to be predominate
over the other. It is truly a special feature of utonalities, though, that 3 or more notes from
a utonality will tend to have one (1) fairly low overtone (harmonic) in common. Whether
this has any audible bearing on music . . . well, that's a matter of debate.

--- In tuning@yahoogroups.com, "Gene Ward Smith" <gwsmith@s...> wrote:
>
> --- In tuning@yahoogroups.com, "Mohajeri Shahin" <shahinm@k...> wrote:
>
> > I myself guess that the first is otonal. Am I right?if not please
> > expplain about it?
>
> The first scale is the famous Zarlino scale,

It's news to me that Zarlino's scale included the 7th, 11th, and 13th harmonics. What is
your source for this astounding claim?

:)

--- In tuning@yahoogroups.com, klaus schmirler <KSchmir@o...> wrote:

> >
> > One characteristic feature is that they have coinciding partial tones.
>
> ... which is true for any series of intervals, just as you can find a
> lowest common enumerator and a lowest common denominator for any
> collection and ordering of fractions.
>
> > If you have a chord 1, 1/2, ..., 1/n, then the 1,2, ... nth partials
> > all coincide at 1.
>
> This, on the other hand, is not general enough, the 1 needn't even be
> a power of 2 as I had supposed. If your scale is the typical alphorn range
>
> (6:7:8:9:10:11:12)/1
>
> and you turn it around, the one is a three:
>
> 12/(11:10:9:8:7:6).
>
> So while the common over/undertone is a truism, it really seem to be
> the "neighboring" superparticular ratios that are important. If you
> break the ascending or descending series, this aspect is lost (and the
> common tone never appears unreduced).

The common overtone is still there even if you lack any neighboring or superparticular
ratios, Klaus. The common overtone is still there in 12/(11:9:7) or, equivalently, 1/(11:9:
7). Or did I misunderstand you?

wallyesterpaulrus wrote:

> --- In tuning@yahoogroups.com, klaus schmirler <KSchmir@o...> wrote:

>>So while the common over/undertone is a truism, it really seem to be >>the "neighboring" superparticular ratios that are important. If you >>break the ascending or descending series, this aspect is lost (and the >>common tone never appears unreduced).
> > > The common overtone is still there even if you lack any neighboring or superparticular > ratios, Klaus. The common overtone is still there in 12/(11:9:7) or, equivalently, 1/(11:9:
> 7). Or did I misunderstand you?

No, I overlooked this because I looked at a scale rather than a chord (maybe not so good to start with). What I needed to separate in my mind from the pure otonal and utonal were arbitrary reorderings of the constituent intervals like 7:6, 11:10, 8:7, 9:8, 12:11, 10:9. They still have a common overtone, it's just way up high. The more important distinction seems to be a regular offset between numerator and denominator which can 1 or a higher number.

Flashback: When I started reading this list, there was a discussion about such high prime "offset" chords like 23:27:31.

klaus

--- In tuning@yahoogroups.com, "wallyesterpaulrus"
<wallyesterpaulrus@y...> wrote:

> It's news to me that Zarlino's scale included the 7th, 11th, and
13th harmonics. What is
> your source for this astounding claim?

The scale I looked at was 5-limit.

--- In tuning@yahoogroups.com, klaus schmirler <KSchmir@o...> wrote:
>
> wallyesterpaulrus wrote:
>
> > --- In tuning@yahoogroups.com, klaus schmirler <KSchmir@o...>
wrote:
>
> >>So while the common over/undertone is a truism, it really seem to
be
> >>the "neighboring" superparticular ratios that are important. If
you
> >>break the ascending or descending series, this aspect is lost
(and the
> >>common tone never appears unreduced).
> >
> >
> > The common overtone is still there even if you lack any
neighboring or superparticular
> > ratios, Klaus. The common overtone is still there in 12/(11:9:7)
or, equivalently, 1/(11:9:
> > 7). Or did I misunderstand you?
>
> No, I overlooked this because I looked at a scale rather than a
chord
> (maybe not so good to start with). What I needed to separate in my
> mind from the pure otonal and utonal were arbitrary reorderings of
the
> constituent intervals like 7:6, 11:10, 8:7, 9:8, 12:11, 10:9. They
> still have a common overtone, it's just way up high. The more
> important distinction seems to be a regular offset between
numerator
> and denominator which can 1 or a higher number.

I don't understand but maybe I don't need to at this point?

> Flashback: When I started reading this list, there was a discussion
> about such high prime "offset" chords like 23:27:31.

These have some coinciding first-order difference tones: 31-27 = 27-
23.

--- In tuning@yahoogroups.com, "Gene Ward Smith" <gwsmith@s...> wrote:
>
> --- In tuning@yahoogroups.com, "wallyesterpaulrus"
> <wallyesterpaulrus@y...> wrote:
>
> > It's news to me that Zarlino's scale included the 7th, 11th, and
> 13th harmonics. What is
> > your source for this astounding claim?
>
> The scale I looked at was 5-limit.

How could that be? When I click "up thread" a few times, I seem to get
back to the original post, in which neither scale was 5-limit. Did you
see something else somehow?

--- In tuning@yahoogroups.com, "wallyesterpaulrus"
<wallyesterpaulrus@y...> wrote:

> How could that be? When I click "up thread" a few times, I seem to get
> back to the original post, in which neither scale was 5-limit. Did you
> see something else somehow?

Possibly I was employing my amazing cross-eyed vision again.

Some of us refer these to being novaro chords
since he was the first to notice this type of property being quasi consonant or at least "unifying".

Message: 24 Date: Fri, 14 Oct 2005 20:05:37 -0000
From: "wallyesterpaulrus" These have some coinciding first-order difference tones: 31-27 = 27- 23.

> >

--
Kraig Grady
North American Embassy of Anaphoria Island <http://anaphoria.com/>
The Wandering Medicine Show
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