Bernhard Stopper

Does anyone of you know this guy?

http://www.piano-stopper.de/html/onlypure_stimmung.html

(Website is in german).
He propagates a division of the tritave (3/1) into 19 equal steps,
which gives a scale with about the familiar western semitones, based
on a slightly stretched octave. The text on the page translates
somehow like: the beats in this tuning form "supersymmetric
subvibrations", interfering with each other in a particularly
"consonant" (or how to call it) way, making the music sound both
clearer and warmer.

Not sure what to think of this. There are sound examples that indeed
are quite beautiful - to me at least, but OTOH I cannot tell the
difference that well. Maybe one of you with more experience can tell
something?
--
Hans Straub

19th-root-of-three tuning was a favorite of Ivor Darreg's. He
suggested that it would be best on pianos if the actual third partial
of the strings were supressed via placement of the hammers, to
compensate for the stretching.

djw

This came up here recently. It's making a stink in piano
tuning circles. This method is well-known, though, at least
on the usenet. Again, we get supernatural claims about beat
rates. But I've never seen any specific numbers about what
the beat rates are supposed to be (from this guy), nor do I
think they should be anything special.

Here, let's let Scala do the walking

Relative beat freq. of 5/4 3/2 ratio
ratio 2 ratio 3
0: 0.000: 0.040878 -0.002139 -19.107786 -
1.630837 31.161679
1: 100.100: 0.043311 -0.002267 -19.107786 -
1.630837 31.161679
2: 200.210: 0.045889 -0.002402 -19.107786 -
1.630837 31.161679
3: 300.310: 0.048621 -0.002545 -19.107786 -
1.630837 31.161679
4: 400.410: 0.051515 -0.002696 -19.107786 -
1.630837 31.161679
5: 500.510: 0.054620 -0.002833 -19.277434 -
1.629685 31.416151
6: 600.620: 0.057831 -0.003027 -19.107786 -
1.630837 31.161679
7: 700.720: 0.061273 -0.003181 -19.263712 -
1.629778 31.395569
8: 800.820: 0.064967 -0.003370 -19.277434 -
1.629685 31.416151
9: 900.930: 0.068785 -0.003600 -19.107786 -
1.630837 31.161679
10: 1001.030: 0.072931 -0.003814 -19.121397 -
1.630744 31.182095
11: 1101.130: 0.077273 -0.004008 -19.277434 -
1.629685 31.416151
12: 1201.240: 0.081814 -0.004282 -19.107786 -
1.630837 31.161679
Total abs. beats : 0.687894 0.035881
Average abs. beats: 0.057325 0.002990
Highest abs. beats: 0.077273 0.004008

Same thing for 12-equal:

Relative beat freq. of 5/4 3/2 ratio
ratio 2 ratio 3
0: 0.000: 0.039684 -0.003386 -11.720615 -
1.713299 20.080922
1: 100.000: 0.042044 -0.003587 -11.720615 -
1.713299 20.080922
2: 200.000: 0.044544 -0.003800 -11.720615 -
1.713299 20.080922
3: 300.000: 0.047193 -0.004026 -11.720615 -
1.713299 20.080922
4: 400.000: 0.049999 -0.004266 -11.720615 -
1.713299 20.080922
5: 500.000: 0.052972 -0.004520 -11.720615 -
1.713299 20.080922
6: 600.000: 0.056122 -0.004788 -11.720615 -
1.713299 20.080922
7: 700.000: 0.059459 -0.005073 -11.720615 -
1.713299 20.080922
8: 800.000: 0.062995 -0.005375 -11.720615 -
1.713299 20.080922
9: 900.000: 0.066741 -0.005694 -11.720615 -
1.713299 20.080922
10: 1000.000: 0.070709 -0.006033 -11.720615 -
1.713299 20.080922
11: 1100.000: 0.074914 -0.006392 -11.720615 -
1.713299 20.080922
12: 1200.000: 0.079368 -0.006772 -11.720615 -
1.713299 20.080922
Total abs. beats : 0.667375 0.056940
Average abs. beats: 0.055615 0.004745
Highest abs. beats: 0.074914 0.006392

Hopefully that's readable.

-Carl

--- In tuning@yahoogroups.com, "hstraub64" <hstraub64@...> wrote:
>
> Does anyone of you know this guy?
>
> http://www.piano-stopper.de/html/onlypure_stimmung.html
>
> (Website is in german).
> He propagates a division of the tritave (3/1) into 19 equal steps,
> which gives a scale with about the familiar western semitones,
> based on a slightly stretched octave. The text on the page
> translates somehow like: the beats in this tuning
> form "supersymmetric subvibrations", interfering with each other
> in a particularly "consonant" (or how to call it) way, making the
> music sound both clearer and warmer.
>
> Not sure what to think of this. There are sound examples that indeed
> are quite beautiful - to me at least, but OTOH I cannot tell the
> difference that well. Maybe one of you with more experience can tell
> something?
> --
> Hans Straub

--- In tuning@yahoogroups.com, "djwolf_frankfurt" <djwolf@...> wrote:
>
> 19th-root-of-three tuning was a favorite of Ivor Darreg's. He
> suggested that it would be best on pianos if the actual third
> partial of the strings were supressed via placement of the
> hammers, to compensate for the stretching.
>
> djw

By third partial, do you mean 4:1?

-Carl

--- In tuning@yahoogroups.com, "Carl Lumma" <carl@...> wrote:
>
> --- In tuning@yahoogroups.com, "djwolf_frankfurt" <djwolf@> wrote:
> >
> > 19th-root-of-three tuning was a favorite of Ivor Darreg's. He
> > suggested that it would be best on pianos if the actual third
> > partial of the strings were supressed via placement of the
> > hammers, to compensate for the stretching.
> >
> > djw
>
> By third partial, do you mean 4:1?
>
> -Carl
>

No, 3:1. (Third partial = "second overtone"). The idea was to
surpress the third partial of the string, which on a piano tends to
vary from a 3:1, so that there were be no beating between a the third
partial of a lower tone and the first partial of an upper tone.

That said, I am totally unclear as to how the third partial would be
surpressed on longer strings -- the hammer would have to be quite far
out -- perhaps a mute of some sort could be placed at a node?

djw

--- In tuning@yahoogroups.com, "hstraub64" <hstraub64@...> wrote:
>
> Does anyone of you know this guy?
>
> http://www.piano-stopper.de/html/onlypure_stimmung.html
>
> (Website is in german).
> He propagates a division of the tritave (3/1) into 19 equal steps,
> which gives a scale with about the familiar western semitones, based
> on a slightly stretched octave. The text on the page translates
> somehow like: the beats in this tuning form "supersymmetric
> subvibrations", interfering with each other in a particularly
> "consonant" (or how to call it) way, making the music sound both
> clearer and warmer.
>
> Not sure what to think of this. There are sound examples that indeed
> are quite beautiful - to me at least, but OTOH I cannot tell the
> difference that well. Maybe one of you with more experience can tell
> something?

He wrote to me a few years ago and talked me into putting
a mention of it into the Encyclopedia:

http://tonalsoft.com/enc/s/stopper-tuning.aspx

I don't have much there, but there's a link to a description
of it in English.

-monz
http://tonalsoft.com
Tonescape microtonal music software

> > > 19th-root-of-three tuning was a favorite of Ivor Darreg's. He
> > > suggested that it would be best on pianos if the actual third
> > > partial of the strings were supressed via placement of the
> > > hammers, to compensate for the stretching.
> > >
> > > djw
> >
> > By third partial, do you mean 4:1?
> >
> > -Carl
>
> No, 3:1. (Third partial = "second overtone"). The idea was to
> surpress the third partial of the string, which on a piano tends
> to vary from a 3:1, so that there were be no beating between
> a the third partial of a lower tone and the first partial of an
> upper tone.

But by definition this tuning calls for tuning the 3:1 beatless.
It seems like you're supressing the very thing you're improving!
Anyway, it seems impractical (if not impossible) to have the
hammers 1/3 of the way down the strings from the keyboard.

> That said, I am totally unclear as to how the third partial
> would be surpressed on longer strings -- the hammer would have
> to be quite far out -- perhaps a mute of some sort could be
> placed at a node?

Hm, perhaps.

-Carl

Ah! The delightful terminology of Partials, Overtones,
and Harmonics.

These days most theorists speak exclusively of
harmonics. Few people refer to the old names
"Partials" and "Overtones" anymore.

It's easy to see why.

The term "First Partial" is a bit problematical,
considering that it's really a "whole-ial", not a
"partial". It's not "part" of anything, it's "all" of
something, i.e., it's the Open String, the Starting
Tone, the 1/1.

"First Overtone" is another fun term, because it flat
out *isn't* an "overtone". Period. It's the First
Tone. You know, the Starting Tone, the Open String,
the 1/1. It's not "over" anything else. Never was.
Never will be.

Finally we arrive at modern terminology, the First
Harmonic, which is the Starting Tone, the whole string
length, the 1/1. Hallelujah! It's so, well, logical!

Next, the Second Harmonic, half the string length,
twice the frequency, 2/1. Hallelujah Twice! The
rationality is downright *titillating*!

Then the Third Harmonic, one third of the string
length, three times the frequency, 3/1. Hallelujah
Thrice! It doesn't get any better than this!

Mark

--- Carl Lumma <carl@lumma.org> wrote:

> > > > 19th-root-of-three tuning was a favorite of
> Ivor Darreg's. He
> > > > suggested that it would be best on pianos if
> the actual third
> > > > partial of the strings were supressed via
> placement of the
> > > > hammers, to compensate for the stretching.
> > > >
> > > > djw
> > >
> > > By third partial, do you mean 4:1?
> > >
> > > -Carl
> >
> > No, 3:1. (Third partial = "second overtone"). The
> idea was to
> > surpress the third partial of the string, which on
> a piano tends
> > to vary from a 3:1, so that there were be no
> beating between
> > a the third partial of a lower tone and the first
> partial of an
> > upper tone.
>
> But by definition this tuning calls for tuning the
> 3:1 beatless.
> It seems like you're supressing the very thing
> you're improving!
> Anyway, it seems impractical (if not impossible) to
> have the
> hammers 1/3 of the way down the strings from the
> keyboard.
>
> > That said, I am totally unclear as to how the
> third partial
> > would be surpressed on longer strings -- the
> hammer would have
> > to be quite far out -- perhaps a mute of some sort
> could be
> > placed at a node?
>
> Hm, perhaps.
>
> -Carl
>
>

____________________________________________________________________________________
Building a website is a piece of cake. Yahoo! Small Business gives you all the tools to get online.
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Hi Mark,

Actually, usage of the terms "partial" and "overtone"
makes sense if they are used correctly. But i'm playing
devil's advocate -- i do agree with you that "harmonic"
is better.

"Harmonic" and "partial" are essentially synonymous.
They both refer to the idea, modeled by Fourier Analysis,
that a complex sound can be described as a conglomeration
of sine-waves, each with their own amplitude envelope.
The frequencies can also vary, but generally follow the
arithmetic "harmonic series" 1:2:3:4:5:6:7... etc.

Calling them "partials" just makes obvious the fact
that each of them is considered to be only a part of
the whole complex sound. Thus, the lowest sine-wave is
indeed both the "first harmonic" and the "first partial".

The case of "overtone" is more complicated. The use
of this word came about precisely as a result of the
kind of thinking that you were doing when you criticized
the use of "partial". The lowest partial is felt to be
the "actual" sound, and is in fact often called the
"fundamental". The second harmonic or second partial is
thus the "first overtone", the third partial is the
"second overtone", etc. *THIS* is the real problem with
using "overtone".

-monz
http://tonalsoft.com
Tonescape microtonal music software

--- In tuning@yahoogroups.com, Mark Rankin <markrankin95511@...> wrote:
>
> Ah! The delightful terminology of Partials, Overtones,
> and Harmonics.
>
> These days most theorists speak exclusively of
> harmonics. Few people refer to the old names
> "Partials" and "Overtones" anymore.
>
> It's easy to see why.
>
> The term "First Partial" is a bit problematical,
> considering that it's really a "whole-ial", not a
> "partial". It's not "part" of anything, it's "all" of
> something, i.e., it's the Open String, the Starting
> Tone, the 1/1.
>
> "First Overtone" is another fun term, because it flat
> out *isn't* an "overtone". Period. It's the First
> Tone. You know, the Starting Tone, the Open String,
> the 1/1. It's not "over" anything else. Never was.
> Never will be.
>
>
> Finally we arrive at modern terminology, the First
> Harmonic, which is the Starting Tone, the whole string
> length, the 1/1. Hallelujah! It's so, well, logical!
>
> Next, the Second Harmonic, half the string length,
> twice the frequency, 2/1. Hallelujah Twice! The
> rationality is downright *titillating*!
>
> Then the Third Harmonic, one third of the string
> length, three times the frequency, 3/1. Hallelujah
> Thrice! It doesn't get any better than this!

I don't like "harmonic" because so many tones have inharmonic
partials. "overtone" also is not good, as not all sounds have
the percieved fundamental at the lowest partial. So I'm
partial to "partial" and I'm sticking with it.

--- In tuning@yahoogroups.com, Mark Rankin <markrankin95511@...>
wrote:
>
> Ah! The delightful terminology of Partials, Overtones,
> and Harmonics.
>
> These days most theorists speak exclusively of
> harmonics. Few people refer to the old names
> "Partials" and "Overtones" anymore.
>
> It's easy to see why.
>
> The term "First Partial" is a bit problematical,
> considering that it's really a "whole-ial", not a
> "partial". It's not "part" of anything, it's "all" of
> something, i.e., it's the Open String, the Starting
> Tone, the 1/1.
>
> "First Overtone" is another fun term, because it flat
> out *isn't* an "overtone". Period. It's the First
> Tone. You know, the Starting Tone, the Open String,
> the 1/1. It's not "over" anything else. Never was.
> Never will be.
>
>
> Finally we arrive at modern terminology, the First
> Harmonic, which is the Starting Tone, the whole string
> length, the 1/1. Hallelujah! It's so, well, logical!
>
> Next, the Second Harmonic, half the string length,
> twice the frequency, 2/1. Hallelujah Twice! The
> rationality is downright *titillating*!
>
> Then the Third Harmonic, one third of the string
> length, three times the frequency, 3/1. Hallelujah
> Thrice! It doesn't get any better than this!
>
>
> Mark
>
>
>
>
>
>
> --- Carl Lumma <carl@...> wrote:
>
> > > > > 19th-root-of-three tuning was a favorite of
> > Ivor Darreg's. He
> > > > > suggested that it would be best on pianos if
> > the actual third
> > > > > partial of the strings were supressed via
> > placement of the
> > > > > hammers, to compensate for the stretching.
> > > > >
> > > > > djw
> > > >
> > > > By third partial, do you mean 4:1?
> > > >
> > > > -Carl
> > >
> > > No, 3:1. (Third partial = "second overtone"). The
> > idea was to
> > > surpress the third partial of the string, which on
> > a piano tends
> > > to vary from a 3:1, so that there were be no
> > beating between
> > > a the third partial of a lower tone and the first
> > partial of an
> > > upper tone.
> >
> > But by definition this tuning calls for tuning the
> > 3:1 beatless.
> > It seems like you're supressing the very thing
> > you're improving!
> > Anyway, it seems impractical (if not impossible) to
> > have the
> > hammers 1/3 of the way down the strings from the
> > keyboard.
> >
> > > That said, I am totally unclear as to how the
> > third partial
> > > would be surpressed on longer strings -- the
> > hammer would have
> > > to be quite far out -- perhaps a mute of some sort
> > could be
> > > placed at a node?
> >
> > Hm, perhaps.
> >
> > -Carl
> >
> >
>
>
>
>
>
_____________________________________________________________________
_______________
> Building a website is a piece of cake. Yahoo! Small Business gives
you all the tools to get online.
> http://smallbusiness.yahoo.com/webhosting
>

monz wrote:

> "Harmonic" and "partial" are essentially synonymous.
> They both refer to the idea, modeled by Fourier Analysis,
> that a complex sound can be described as a conglomeration
> of sine-waves, each with their own amplitude envelope.
> The frequencies can also vary, but generally follow the
> arithmetic "harmonic series" 1:2:3:4:5:6:7... etc.

Additionally, "harmonic" can refer to a technique of touching a string lightly at a node and plucking or bowing to produce a higher-pitched note (a multiple of the frequency of the open string) with a distinctive timbre. "Partial" as far as I know can only refer to the fundamental or one of the overtones (which need not be harmonic -- inharmonic timbres such as bells have partials).

> Calling them "partials" just makes obvious the fact
> that each of them is considered to be only a part of
> the whole complex sound. Thus, the lowest sine-wave is
> indeed both the "first harmonic" and the "first partial".
> > The case of "overtone" is more complicated. The use
> of this word came about precisely as a result of the
> kind of thinking that you were doing when you criticized
> the use of "partial". The lowest partial is felt to be
> the "actual" sound, and is in fact often called the
> "fundamental". The second harmonic or second partial is
> thus the "first overtone", the third partial is the
> "second overtone", etc. *THIS* is the real problem with
> using "overtone".

I think it makes sense, in its own way, but then I think that was just the terminology I was exposed to earliest.

Herman,

Thanks for including the other definition of harmonic,
the one which refers to the technique of touching a
string lightly at a node and plucking or bowing to
produce higher pitched tones.

These kinds of harmonics are one of my favorite
sounds. Last week on National Public Radio I heard
remarkable plucked and bowed harmonics, among other
sounds, by a solo cellist. The CD had the unusual
title "Block Ice and Propane", a name which was drawn
from his late father's passion for camping trips.
Never have I heard a cello sound like this!

Mark

--- Herman Miller <hmiller@IO.COM> wrote:

> monz wrote:
>
> > "Harmonic" and "partial" are essentially
> synonymous.
> > They both refer to the idea, modeled by Fourier
> Analysis,
> > that a complex sound can be described as a
> conglomeration
> > of sine-waves, each with their own amplitude
> envelope.
> > The frequencies can also vary, but generally
> follow the
> > arithmetic "harmonic series" 1:2:3:4:5:6:7... etc.
>
> Additionally, "harmonic" can refer to a technique of
> touching a string
> lightly at a node and plucking or bowing to produce
> a higher-pitched
> note (a multiple of the frequency of the open
> string) with a distinctive
> timbre. "Partial" as far as I know can only refer to
> the fundamental or
> one of the overtones (which need not be harmonic --
> inharmonic timbres
> such as bells have partials).
>
> > Calling them "partials" just makes obvious the
> fact
> > that each of them is considered to be only a part
> of
> > the whole complex sound. Thus, the lowest
> sine-wave is
> > indeed both the "first harmonic" and the "first
> partial".
> >
> > The case of "overtone" is more complicated. The
> use
> > of this word came about precisely as a result of
> the
> > kind of thinking that you were doing when you
> criticized
> > the use of "partial". The lowest partial is felt
> to be
> > the "actual" sound, and is in fact often called
> the
> > "fundamental". The second harmonic or second
> partial is
> > thus the "first overtone", the third partial is
> the
> > "second overtone", etc. *THIS* is the real problem
> with
> > using "overtone".
>
> I think it makes sense, in its own way, but then I
> think that was just
> the terminology I was exposed to earliest.
>
>
>

____________________________________________________________________________________
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It seems that the accepted term for these "Pinch" harmonics is

Flageolet tones,

Yet this gets even more ambiguous and complicated for this term also refers to a small flute and a type of French bean.

These are the sounds made me curious about tuning, and encouraged me to find a tuning system which could generate the same pitches and intervals that I heard when touching strings at various positions.

They very clearly demonstrate that 12edo is missing "something" ;-)

Charles Lucy lucy@lucytune.com

----- Promoting global harmony through LucyTuning -----

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Skype user = lucytune

http://www.myspace.com/lucytuning

On 2 Oct 2007, at 05:11, Mark Rankin wrote:

> Herman,
>
> Thanks for including the other definition of harmonic,
> the one which refers to the technique of touching a
> string lightly at a node and plucking or bowing to
> produce higher pitched tones.
>
> These kinds of harmonics are one of my favorite
> sounds. Last week on National Public Radio I heard
> remarkable plucked and bowed harmonics, among other
> sounds, by a solo cellist. The CD had the unusual
> title "Block Ice and Propane", a name which was drawn
> from his late father's passion for camping trips.
> Never have I heard a cello sound like this!
>
> Mark
>
>
>
>

--- In tuning@yahoogroups.com, Charles Lucy <lucy@...> wrote:
>
> It seems that the accepted term for these "Pinch" harmonics is
>
> Flageolet tones,
>
> Yet this gets even more ambiguous and complicated for this term
also
> refers to a small flute and a type of French bean.

And "pinch harmonic" also refers to an "artificial" harmonic,
created by temporarily changing the vibrating length of a string
using a couple of fingers, it feels kind of like an awkward pinching
motion.

>
> These are the sounds made me curious about tuning, and encouraged
>me
> to find a tuning system which could generate the same pitches and
> intervals that I heard when touching strings at various positions.

But that's what Just Intonation does. Of course you can alter
the string away from it's near-ideal modes of vibration, with
bits of metal twisted around it etc., and get non-integer flageolet
tones.
>
> They very clearly demonstrate that 12edo is missing "something" ;-)

For me the invarying interval sizes are enough- like being snapped
to a grid.

-Cameron Bobro

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

> "Harmonic" and "partial" are essentially synonymous.

They are not. "Harmonic" and "aliquot" are "essentially
synonymous", but partials can be either harmonic (integer
multiples) or inharmonic.

-Cameron Bobro

Jeez, guys, give me a break ... in my original post,
i wrote "*essentially* synonymous", and "*generally*
follow the arithmetic "harmonic series" 1:2:3:4:5:6:7...
etc.". (emphasis added this time)

I was careful to put in the words which i emphasized
here to make it less exact, precisely *because* i didn't
want anyone to have to "correct" what i wrote.

When i generalize, please realize that that's what
i've done. Thanks.

Anyway, i guess next time i have to elaborate more
on the exceptions to the rule. Thanks for doing it
for me.

-monz
http://tonalsoft.com
Tonescape microtonal music software

--- In tuning@yahoogroups.com, "Cameron Bobro" <misterbobro@...> wrote:
>
> --- In tuning@yahoogroups.com, "monz" <monz@> wrote:
>
> > "Harmonic" and "partial" are essentially synonymous.
>
> They are not. "Harmonic" and "aliquot" are "essentially
> synonymous", but partials can be either harmonic (integer
> multiples) or inharmonic.