addictive sine-based deception

I've added yet another 'deceptively' nice sine chord at
/tuning/files/sphaerenklang/

this time major, first inversion. Anyone who's paid attention to the
thread should be able to guess it immediately (by psychological rather
than auditory means!). Otherwise you can try and match it with the
lowest note being 400Hz.
~~~T~~~

--- In tuning@yahoogroups.com, "Tom Dent" <stringph@...> wrote:
> I've added yet another 'deceptively' nice sine chord at
> /tuning/files/sphaerenklang/
>
> this time major, first inversion. Anyone who's paid attention to the
> thread should be able to guess it immediately (by psychological rather
> than auditory means!). Otherwise you can try and match it with the
> lowest note being 400Hz.
> ~~~T~~~

Again, sounds good, but I don't think I'd have confused
it for 4:5:6. Heck if I know what it is though.
-Carl

Tom Dent wrote:
> I've added yet another 'deceptively' nice sine chord at > /tuning/files/sphaerenklang/
> > this time major, first inversion. Anyone who's paid attention to the
> thread should be able to guess it immediately (by psychological rather
> than auditory means!). Otherwise you can try and match it with the
> lowest note being 400Hz.
> ~~~T~~~

I don't get any kind of impression of a first inversion major triad from this. It almost sounds more like a distorted minor triad (with an augmented fifth). So I tried 16:19:25 -- not a perfect match but it's closer to that than anything like a 5:6:8.

So I'm wondering how far you can bend that outer interval in the 5:6:8 before it loses it's "major triad" sound. Clearly 5:6:7.5 is a minor triad; 5:6:7.75 is right in the middle and doesn't sound like either one. 5:6:7.8 is questionable, but 5:6:7.9 is starting to sound like a first inversion major triad.

Sounds more like 11:14:17, from the character of it.

--- In tuning@yahoogroups.com, Herman Miller <hmiller@...> wrote:
>
> Tom Dent wrote:
> > I've added yet another 'deceptively' nice sine chord at
> > /tuning/files/sphaerenklang/
> >
> > this time major, first inversion. Anyone who's paid attention to the
> > thread should be able to guess it immediately (by psychological rather
> > than auditory means!). Otherwise you can try and match it with the
> > lowest note being 400Hz.
> > ~~~T~~~
>
> I don't get any kind of impression of a first inversion major triad
from
> this. It almost sounds more like a distorted minor triad (with an
> augmented fifth). So I tried 16:19:25 -- not a perfect match but it's
> closer to that than anything like a 5:6:8.
>
> So I'm wondering how far you can bend that outer interval in the 5:6:8
> before it loses it's "major triad" sound. Clearly 5:6:7.5 is a minor
> triad; 5:6:7.75 is right in the middle and doesn't sound like either
> one. 5:6:7.8 is questionable, but 5:6:7.9 is starting to sound like a
> first inversion major triad.
>

Almost!! But consider that 11:14 is a 'distorted' major 3rd, not minor.
~~~T~~~

--- In tuning@yahoogroups.com, "Cameron Bobro" <misterbobro@...> wrote:
>
> Sounds more like 11:14:17, from the character of it.
>
>
> > Tom Dent wrote:
> > > I've added yet another 'deceptively' nice sine chord at
> > > /tuning/files/sphaerenklang/
> > >
> > > this time major, first inversion. Anyone who's paid attention to
the
> > > thread should be able to guess it immediately (by psychological
rather
> > > than auditory means!).

Well "distorted" isn't what I'd call 14/11, it's another interval and
it's probably quite often a more accurate representation of what a
written 12-tET third is heard/performed as than a 5/4 would be.

But anyway then it's probably an 11:13:17, not going to check with
Scala because I'm curious how accurate my assessment that it is an
eleventh-partial based harmony with a 460ish cent "thirth/fouird" in
this voicing, which would give it a 740ish fifth/m6-ish outer interval
in smallest postition.

--- In tuning@yahoogroups.com, "Tom Dent" <stringph@...> wrote:
>
>
> Almost!! But consider that 11:14 is a 'distorted' major 3rd, not minor.
> ~~~T~~~
>
> --- In tuning@yahoogroups.com, "Cameron Bobro" <misterbobro@> wrote:
> >
> > Sounds more like 11:14:17, from the character of it.
> >
> >
> > > Tom Dent wrote:
> > > > I've added yet another 'deceptively' nice sine chord at
> > > > /tuning/files/sphaerenklang/
> > > >
> > > > this time major, first inversion. Anyone who's paid attention to
> the
> > > > thread should be able to guess it immediately (by psychological
> rather
> > > > than auditory means!).
>

--- In tuning@yahoogroups.com, "Tom Dent" <stringph@...> wrote:
>
>
> I've added yet another 'deceptively' nice sine chord at
> /tuning/files/sphaerenklang/
>
> this time major, first inversion. Anyone who's paid attention to the
> thread should be able to guess it immediately (by psychological rather
> than auditory means!). Otherwise you can try and match it with the
> lowest note being 400Hz.
> ~~~T~~~
>
Sounds minor to me.

-Rick

The second assessment is accurate enough!
17/13 is 464c, which I hear as a fourth in this context (in principle
implying a fifth of 746), and 17/11 is 753c, which I hear as a m6 in
context.

However, if I try and invert the chord to its 'smallest position'
17:22:26 (or indeed 13:17:22) I find the sound quite unlike any
5-limit whatsoever.

Listening to 14:11 on its own, it is still moderately third-y, but I
would say 19:15 is a closer match to real 12-ET (~29/23) in character.
I don't know quite what is meant by a 'written 12-ET third' (?) being
'heard/performed' as 14/11, unless people do actually play that sharp
for whatever reason. (On what instruments?)
19:15 is almost exactly 81:64, which is likely to be attractive for
e.g. violinists, and 12-ET is of course narrower. The villain isn't as
black as he is painted.
~~~T~~~

--- In tuning@yahoogroups.com, "Cameron Bobro" <misterbobro@...> wrote:
>
> Well "distorted" isn't what I'd call 14/11, it's another interval and
> it's probably quite often a more accurate representation of what a
> written 12-tET third is heard/performed as than a 5/4 would be.
>
> But anyway then it's probably an 11:13:17, not going to check with
> Scala because I'm curious how accurate my assessment that it is an
> eleventh-partial based harmony with a 460ish cent "thirth/fouird" in
> this voicing, which would give it a 740ish fifth/m6-ish outer interval
> in smallest position.
>

--- In tuning@yahoogroups.com, "Tom Dent" <stringph@...> wrote:
>
>
> The second assessment is accurate enough!
> 17/13 is 464c, which I hear as a fourth in this context (in principle
> implying a fifth of 746), and 17/11 is 753c, which I hear as a m6 in
> context.
>
> However, if I try and invert the chord to its 'smallest position'
> 17:22:26 (or indeed 13:17:22) I find the sound quite unlike any
> 5-limit whatsoever.

It's interesting to hear this with sines, something I never tried, it
still works though. I posted some examples on MMM a while ago and have
discussed the "thirth/foird" here quite a bit. As far as I can tell,
the zone is bordered by 17/13 at the top and 13/10 is a little too
low, but anything in the zone will function in this ambiguous, and
oddly less dissonant than it "should be", way.

The ideal "thirth" is at the Golden Cut between the frequencies of 5/4
and 4/3 I suspect, but can't verify because of the fuzziness of the
zone, maybe 6 cents wide. The "classical augmented third", 5/4*25/24,
is also right in there and works this way. I have hours of music using
this interval and this kind of ambiguity in general. It's also a point
of "maximum harmonic entropy".

But still I'm suprised how well it works with sines, for the
"fuzziness" of what goes on within the harmonic partials involved can
be demonstrated mathematically and by spectral analysis but it isn't a
proportion I'd expect to be perceptible when completely stripped down,
hmmm.

And from the intervals which function like 17/13 I branch out using
lower partials- for example, 17/13*5/4, IIRC that was the first chord
of the example I posted at MMM.

So, hearing your example using such relatively high partials, and with
sines, and still working, is a pleasant suprise.

As an amusing side note, the freqency proportions of 2cos(Pi/5) (phi),
and of 2cos(Pi/4), which are the "foird" and the 12-tET tritone
respectively, are genuinely based on Pi, unlike Lucy Tuning (which
involves log base 10, LOL).

>
> Listening to 14:11 on its own, it is still moderately third-y, but I
> would say 19:15 is a closer match to real 12-ET (~29/23) in >character.
> I don't know quite what is meant by a 'written 12-ET third' (?) >being
> 'heard/performed' as 14/11, unless people do actually play that >sharp
> for whatever reason. (On what instruments?)
> 19:15 is almost exactly 81:64, which is likely to be attractive for
> e.g. violinists, and 12-ET is of course narrower. The villain isn't as
> black as he is painted.

Well the villain isn't a villain at all when he's considered properly,
which is as a near-perfect Pythagorean ditone, and not as a 5/4. If
you listen to pre-War recordings I think you'll find that "expressive
intonation" was taken very seriously, it certainly was by an elderly
teacher of mine, and both 14/11 and 13/11 fit right in as bright and
leading or dark and sombre thirds that still work in a nominally
12-tET world (for voice at least).

But this may no longer be applicable for all I know, as the brazen
digital editing of modern recordings and the stiff screeching cartoon
pawning itself off as "classical music" in concert halls today drives
me up the wall.

Argh, how do you edit after posting?

Error/unclear in the previous: the part about 2cos(Pi/5) should read
that it gives you phi, and can be used to define intervals such as the
"foird", an ambiguous sharp fifth/minor sixth as so on.

--- In tuning@yahoogroups.com, "Cameron Bobro" <misterbobro@...> wrote:
>
> --- In tuning@yahoogroups.com, "Tom Dent" <stringph@> wrote:
> >
> >
> > The second assessment is accurate enough!
> > 17/13 is 464c, which I hear as a fourth in this context (in principle
> > implying a fifth of 746), and 17/11 is 753c, which I hear as a m6 in
> > context.
> >
> > However, if I try and invert the chord to its 'smallest position'
> > 17:22:26 (or indeed 13:17:22) I find the sound quite unlike any
> > 5-limit whatsoever.
>
> It's interesting to hear this with sines, something I never tried, it
> still works though. I posted some examples on MMM a while ago and have
> discussed the "thirth/foird" here quite a bit. As far as I can tell,
> the zone is bordered by 17/13 at the top and 13/10 is a little too
> low, but anything in the zone will function in this ambiguous, and
> oddly less dissonant than it "should be", way.
>
> The ideal "thirth" is at the Golden Cut between the frequencies of 5/4
> and 4/3 I suspect, but can't verify because of the fuzziness of the
> zone, maybe 6 cents wide. The "classical augmented third", 5/4*25/24,
> is also right in there and works this way. I have hours of music using
> this interval and this kind of ambiguity in general. It's also a point
> of "maximum harmonic entropy".
>
> But still I'm suprised how well it works with sines, for the
> "fuzziness" of what goes on within the harmonic partials involved can
> be demonstrated mathematically and by spectral analysis but it isn't a
> proportion I'd expect to be perceptible when completely stripped down,
> hmmm.
>
> And from the intervals which function like 17/13 I branch out using
> lower partials- for example, 17/13*5/4, IIRC that was the first chord
> of the example I posted at MMM.
>
> So, hearing your example using such relatively high partials, and with
> sines, and still working, is a pleasant suprise.
>
> As an amusing side note, the freqency proportions of 2cos(Pi/5) (phi),
> and of 2cos(Pi/4), which are the "foird" and the 12-tET tritone
> respectively, are genuinely based on Pi, unlike Lucy Tuning (which
> involves log base 10, LOL).
>
>
> >
> > Listening to 14:11 on its own, it is still moderately third-y, but I
> > would say 19:15 is a closer match to real 12-ET (~29/23) in
>character.
> > I don't know quite what is meant by a 'written 12-ET third' (?) >being
> > 'heard/performed' as 14/11, unless people do actually play that >sharp
> > for whatever reason. (On what instruments?)
> > 19:15 is almost exactly 81:64, which is likely to be attractive for
> > e.g. violinists, and 12-ET is of course narrower. The villain isn't as
> > black as he is painted.
>
> Well the villain isn't a villain at all when he's considered properly,
> which is as a near-perfect Pythagorean ditone, and not as a 5/4. If
> you listen to pre-War recordings I think you'll find that "expressive
> intonation" was taken very seriously, it certainly was by an elderly
> teacher of mine, and both 14/11 and 13/11 fit right in as bright and
> leading or dark and sombre thirds that still work in a nominally
> 12-tET world (for voice at least).
>
> But this may no longer be applicable for all I know, as the brazen
> digital editing of modern recordings and the stiff screeching cartoon
> pawning itself off as "classical music" in concert halls today drives
> me up the wall.
>