Yahoo Tuning Groups Ultimate Backup tuning mathematica solution & mystery minor chord to hear

Just to wrap this one up: by trial and error (no thanks to the help
function) I found that the argument of the PlayRange option is the
range beyond which the function is clipped. Therefore, to avoid any
nasty noises set this option to include all possible values which the
function may take.

Eg with sin(f1)+sin(f2)+sin(f3) the range should be at least {-3,3}
for safety. In practice, adding another factor 1.5 can't hurt and
seems to give smoother results ... indicating that the process of
sampling doesn't always do what it oughta.

Now listen to the chord here -
/tuning/files/sphaerenklang/

a simple combination of 3 sine waves in integer ratio ... but what ratio?

More effective if you don't listen to it immediately before or after a
'known' chord!
~~~T~~~

🔗massimilianolabardi <labardi@...>

🔗Herman Miller <hmiller@...>

Tom Dent wrote:
> Just to wrap this one up: by trial and error (no thanks to the help
> function) I found that the argument of the PlayRange option is the
> range beyond which the function is clipped. Therefore, to avoid any
> nasty noises set this option to include all possible values which the
> function may take.
> > Eg with sin(f1)+sin(f2)+sin(f3) the range should be at least {-3,3}
> for safety. In practice, adding another factor 1.5 can't hurt and
> seems to give smoother results ... indicating that the process of
> sampling doesn't always do what it oughta.
> > Now listen to the chord here -
> /tuning/files/sphaerenklang/
> > a simple combination of 3 sine waves in integer ratio ... but what ratio?
> > More effective if you don't listen to it immediately before or after a
> 'known' chord!

sounds like 6:7:9

🔗Tom Dent <stringph@...>

🔗caleb morgan <calebmrgn@...>

I'm so glad you said the part I bolded about it being uninformative or deceptive. I'm not sure I'd use exactly those words, but they get at exactly the experience I have listening to them.

Many of these chords sound good to me, surprisingly, even, the U tonality chords with higher prime limits. Quite beautiful.

But they have this elusive quality, and they're not anything like my experiences with JI in context, or 12ET in context.

That doesn't make them less interesting; they're just different.

I draw no conclusions from all this, one way or another, I'm just giving my naive reaction.

caleb

On Jan 21, 2009, at 9:24 AM, Tom Dent wrote:

> ...
> - But if you put 6:7:9 next to 'mysteryminor' you'll hear a hell of a
> difference.
> I made the lowest frequency either 200Hz or 250 (don't immediately
> remember which), in case anyone wants to do it themselves.
> Just shows how deceptive or rather uninformative pure sines are.
> ~~~T~~~
>
>
>

🔗Mike Battaglia <battaglia01@...>

I think the lowest dyad there is 7:8. It does sound a little bit
flatter than 6:7 to be sure. From screwing around with Scala, the best
match I could find was 28:32:41, where the 28:41 on the outside I
picked because it's halfway between 28:40, which is 7:10, and 28:42,
which is 2:3. When playing them simultaneously I still hear some
beating, although I can't tell if this is due to some resolution
problem in Scala or if I'm just wrong with the chord. After messing
around a little bit more I found 13:15:19 to be about as good of a
match with lower number ratios.

-Mike

On Wed, Jan 21, 2009 at 9:24 AM, Tom Dent <stringph@...> wrote:
> --- In tuning@yahoogroups.com, Herman Miller <hmiller@...> wrote:
>>
>> > Now listen to the chord here -
>> > /tuning/files/sphaerenklang/
>> >
>> > a simple combination of 3 sine waves in integer ratio ... but what
> ratio?
>> >
>> >(...)
>>
>> sounds like 6:7:9
>>
>
> - But if you put 6:7:9 next to 'mysteryminor' you'll hear a hell of a
> difference.
> I made the lowest frequency either 200Hz or 250 (don't immediately
> remember which), in case anyone wants to do it themselves.
> Just shows how deceptive or rather uninformative pure sines are.
> ~~~T~~~
>
>

🔗Mike Battaglia <battaglia01@...>

Alright Tom, let's up the ante here a bit. What about this chord?

http://rabbit.eng.miami.edu/students/mbattaglia/mysteryhexad.wav

Specifically, what is the outer dyad being played there?

-Mike

On Wed, Jan 21, 2009 at 12:39 PM, Mike Battaglia <battaglia01@...> wrote:
> I think the lowest dyad there is 7:8. It does sound a little bit
> flatter than 6:7 to be sure. From screwing around with Scala, the best
> match I could find was 28:32:41, where the 28:41 on the outside I
> picked because it's halfway between 28:40, which is 7:10, and 28:42,
> which is 2:3. When playing them simultaneously I still hear some
> beating, although I can't tell if this is due to some resolution
> problem in Scala or if I'm just wrong with the chord. After messing
> around a little bit more I found 13:15:19 to be about as good of a
> match with lower number ratios.
>
> -Mike
>
>
>
> On Wed, Jan 21, 2009 at 9:24 AM, Tom Dent <stringph@...> wrote:
>> --- In tuning@yahoogroups.com, Herman Miller <hmiller@...> wrote:
>>>
>>> > Now listen to the chord here -
>>> > /tuning/files/sphaerenklang/
>>> >
>>> > a simple combination of 3 sine waves in integer ratio ... but what
>> ratio?
>>> >
>>> >(...)
>>>
>>> sounds like 6:7:9
>>>
>>
>> - But if you put 6:7:9 next to 'mysteryminor' you'll hear a hell of a
>> difference.
>> I made the lowest frequency either 200Hz or 250 (don't immediately
>> remember which), in case anyone wants to do it themselves.
>> Just shows how deceptive or rather uninformative pure sines are.
>> ~~~T~~~
>>
>>
>

🔗Carl Lumma <carl@...>

--- In tuning@yahoogroups.com, caleb morgan <calebmrgn@...> wrote:

> Many of these chords sound good to me, surprisingly, even, the
> U tonality chords with higher prime limits. Quite beautiful.

I'll never forget the first time I heard the 9-limit utonality,
on a slide guitar built by Ivor Darreg. The sound reminded of
being in the desert. I still get that sometimes.

The complete 11-limit utonality really is too intense for me,
but 4-note subsets (tetrads) of it work just fine. These
naturally come out of the eikosany. See this example for
instance, which alternates major and minor 11-limit tetrads
by common dyad:

http://lumma.org/music/theory/demo/progs/EikosanyProgression2.mp3

-Carl

🔗Mike Battaglia <battaglia01@...>

> I'll never forget the first time I heard the 9-limit utonality,
> on a slide guitar built by Ivor Darreg. The sound reminded of
> being in the desert. I still get that sometimes.

That's awesome. Do you have a recording of it? How was it voiced?

> The complete 11-limit utonality really is too intense for me,
> but 4-note subsets (tetrads) of it work just fine. These
> naturally come out of the eikosany. See this example for
> instance, which alternates major and minor 11-limit tetrads
> by common dyad:
>
> http://lumma.org/music/theory/demo/progs/EikosanyProgression2.mp3
>
> -Carl

I keep seeing references to the eikosany on this list - what is it? Is
there some information on it out there?

-Mike

🔗Carl Lumma <carl@...>

--- In tuning@yahoogroups.com, Mike Battaglia <battaglia01@...> wrote:
>
> > I'll never forget the first time I heard the 9-limit utonality,
> > on a slide guitar built by Ivor Darreg. The sound reminded of
> > being in the desert. I still get that sometimes.
>
> That's awesome. Do you have a recording of it? How was it voiced?

No, but I built a slide guitar just like it. :)

> I keep seeing references to the eikosany on this list - what
> is it? Is there some information on it out there?

http://tonalsoft.com/enc/e/eikosany.aspx
http://tonalsoft.com/enc/c/combination-product-set.aspx

-Carl

🔗Carl Lumma <carl@...>

🔗rick_ballan <rick_ballan@...>

--- In tuning@yahoogroups.com, caleb morgan <calebmrgn@...> wrote:
>
> I'm so glad you said the part I bolded about it being uninformative or
> deceptive. I'm not sure I'd use exactly those words, but they get at
> exactly the experience I have listening to them.
>
> Many of these chords sound good to me, surprisingly, even, the U
> tonality chords with higher prime limits. Quite beautiful.
>
> But they have this elusive quality, and they're not anything like my
> experiences with JI in context, or 12ET in context.
>
> That doesn't make them less interesting; they're just different.
>
> I draw no conclusions from all this, one way or another, I'm just
> giving my naive reaction.
>
> caleb
>
>
> On Jan 21, 2009, at 9:24 AM, Tom Dent wrote:
>
> > ...
> > - But if you put 6:7:9 next to 'mysteryminor' you'll hear a hell of a
> > difference.
> > I made the lowest frequency either 200Hz or 250 (don't immediately
> > remember which), in case anyone wants to do it themselves.
> > Just shows how deceptive or rather uninformative pure sines are.
> > ~~~T~~~
> >
> >Hi Tom,

I haven't got scala or anything but it sounds like a normal G min on
my guitar with some weird beating going on (Though being a guitarist
I'm probably used to playing slightly out-of-tune to some degree?).
Therefore, you might want to try 512:609:767 or around that region,
which should sound fairly close to ET,

Rick
> >
>

🔗Tom Dent <stringph@...>

OK, you've suffered enough ... 28:41 and 13:19 were actually quite
good guesses for the 'fifth'. But it's 11:13:16.

Somehow this 'subminor' with a 'subfifth' actually sounds marginally
more consonant to me than 10:12:15 ... perhaps because it less
resembles a lower part of the harmonic series gone wrong. Pure
speculation.
~~~T~~~

--- In tuning@yahoogroups.com, Mike Battaglia <battaglia01@...> wrote:
>
> I think the lowest dyad there is 7:8. It does sound a little bit
> flatter than 6:7 to be sure. From screwing around with Scala, the best
> match I could find was 28:32:41, where the 28:41 on the outside I
> picked because it's halfway between 28:40, which is 7:10, and 28:42,
> which is 2:3. When playing them simultaneously I still hear some
> beating, although I can't tell if this is due to some resolution
> problem in Scala or if I'm just wrong with the chord. After messing
> around a little bit more I found 13:15:19 to be about as good of a
> match with lower number ratios.
>
> -Mike
>
>
> On Wed, Jan 21, 2009 at 9:24 AM, Tom Dent <stringph@...> wrote:
>
> >> > Now listen to the chord here -
> >> > /tuning/files/sphaerenklang/
> >> >
> >> > a simple combination of 3 sine waves in integer ratio ... but what
> > ratio?

🔗caleb morgan <calebmrgn@...>

I think I get it.

A quick google of eikosany and eiko, though, turned up nothing useful. (A greek word for some number, perhaps?)

That example sounds quirky, good, and completely convincing to me.

(Yikes! an abyss of too many good possibilities? Or maybe I put my limit at the 9-limit, too.)

caleb

On Jan 21, 2009, at 2:10 PM, Carl Lumma wrote:

> --- In tuning@yahoogroups.com, caleb morgan <calebmrgn@...> wrote:
>
> > Many of these chords sound good to me, surprisingly, even, the
> > U tonality chords with higher prime limits. Quite beautiful.
>
> I'll never forget the first time I heard the 9-limit utonality,
> on a slide guitar built by Ivor Darreg. The sound reminded of
> being in the desert. I still get that sometimes.
>
> The complete 11-limit utonality really is too intense for me,
> but 4-note subsets (tetrads) of it work just fine. These
> naturally come out of the eikosany. See this example for
> instance, which alternates major and minor 11-limit tetrads
> by common dyad:
>
> http://lumma.org/music/theory/demo/progs/EikosanyProgression2.mp3
>
> -Carl
>
>
>

🔗Mike Battaglia <battaglia01@...>

It's 4:5:6:7:9:11, but narrowly-voiced. The outer dyad, which does
sound like 11/4, is tuned to be exactly 8/3, and each interval is
compressed accordingly. Note that the VF that you hear still solidly
seems to be "1". It seems that the ear has a good amount of play on
how stretched or compressed a harmonic series can be. The interesting
thing to me here is that that 8/3 plays the role of 11/4 very well...
I wonder if this means anything for the perception of tempered
intervals.

-Mike

On Wed, Jan 21, 2009 at 2:45 PM, Carl Lumma <carl@...> wrote:
> --- In tuning@yahoogroups.com, Mike Battaglia <battaglia01@...> wrote:
>>
>> Alright Tom, let's up the ante here a bit. What about this chord?
>>
>> http://rabbit.eng.miami.edu/students/mbattaglia/mysteryhexad.wav
>>
>> Specifically, what is the outer dyad being played there?
>>
>> -Mike
>
> I'm guessing this is a very widely-voiced utonal hexad.
> The outer interval sounds like an 11:1. -Carl
>
>

🔗Andreas Sparschuh <a_sparschuh@...>

--- In tuning@yahoogroups.com, "Tom Dent" <stringph@...> wrote:
>
> OK, you've suffered enough ... 28:41 and 13:19 were actually quite
> good guesses for the 'fifth'. But it's 11:13:16.
>
Hi, tom,
probably due to:
1200 * ln(41/28)/ln(2) = ~660.2...Cents
or
42/41 := (3/2)(28/41) , that's an ~5th about
1200Cents * ln(42/41)/ln(2) = ~41.7...Cents
off flattend than just 3/2.

and respective
1200Cents * ln(19/13)/ ln(2) = 656.985...Cents
or
39/38 := (3/2)(13/19) , that another ~5th about
1200Cents * ln(39/38))/ln(2) = ~44.97...Cents
a bit more off.

That's about ~twice of an common usual ~doubeled:
http://en.wikipedia.org/wiki/Vibrato
"...but does not usually exceed a semitone either way from the note
itself...."
Attend there the:
'Sound example files:

* Frequenzmodulation.ogg Vibrato, Sound Frequency 500 Hz -
Frequency Modulation 50 Hz - Vibrato Frequency 6 Hz (helpÂ·info)
* Amplitudenmodulation.ogg Tremolo, Sound Frequency 500 Hz -
Amplitude Modulation 6 Hz (helpÂ·info)
* Schwebung_500_506_hz.ogg Tremolo by beating - Sound Frequencies
500 and 506 Hz, Beat Frequency 6 Hz "

that beating amounts:
1 200Cents * ln(506/500)/ln(2) = ~20.7...Cents

See also the German wiki-entry for more-precisely specification:
http://de.wikipedia.org/wiki/Vibrato
"Fischer (1993) bestimmt fÃ¼r ein angenehmes Vibrato eine
Periodenfrequenz von ca. 4,5 bis 8 Hz."
'Fischer (1993) determins for an pleasant vibrato an
periodic-frequency of about ~4.5 to ~8 Hz."

That recommendation ranges in the soprano for A4=440Hz from about:

1200Cents * ln(444.5/440)/ln(2) = ~17.6...Cents
up to
1200Cents * ln(448/440)/ln(2) = ~31.2...Cents

or
an octave below
for an
http://en.wikipedia.org/wiki/Tenor
@ A3=220Hz already from:

1200Cents * ln(224.5/220)/ln(2) = ~35.1...Cents
up to
1200Cents * ln(228/220)/ ln(2) = ~61.8...Cents

Which fits well to yours own observation in listening
41/28 and 19/13 as vibrating ~5ths that deviates from pure 3/2
about an ~quarter-tone.

That Cent-values double or quadruple again when lowered octaves again:
http://en.wikipedia.org/wiki/Bass_(voice_type)
"Some traditional Russian religious music calls for A2 (110 Hz) drone
singing, which is doubled by A1 (55 Hz) in the rare occasion that a
choir includes exceptionally gifted singers who can produce this very
low human voice pitch."

bye
A.S.

🔗rick_ballan <rick_ballan@...>

--- In tuning@yahoogroups.com, "Tom Dent" <stringph@...> wrote:
>
>
> OK, you've suffered enough ... 28:41 and 13:19 were actually quite
> good guesses for the 'fifth'. But it's 11:13:16.
>
> Somehow this 'subminor' with a 'subfifth' actually sounds marginally
> more consonant to me than 10:12:15 ... perhaps because it less
> resembles a lower part of the harmonic series gone wrong. Pure
> speculation.
> ~~~T~~~
>
> --- In tuning@yahoogroups.com, Mike Battaglia <battaglia01@> wrote:
> >
> > I think the lowest dyad there is 7:8. It does sound a little bit
> > flatter than 6:7 to be sure. From screwing around with Scala, the best
> > match I could find was 28:32:41, where the 28:41 on the outside I
> > picked because it's halfway between 28:40, which is 7:10, and 28:42,
> > which is 2:3. When playing them simultaneously I still hear some
> > beating, although I can't tell if this is due to some resolution
> > problem in Scala or if I'm just wrong with the chord. After messing
> > around a little bit more I found 13:15:19 to be about as good of a
> > match with lower number ratios.
> >
> > -Mike
> >
> >
> > On Wed, Jan 21, 2009 at 9:24 AM, Tom Dent <stringph@> wrote:
> >
> > >> > Now listen to the chord here -
> > >> > /tuning/files/sphaerenklang/
> > >> >
> > >> > a simple combination of 3 sine waves in integer ratio ... but
what
> > > ratio?
>
Ah, 11; 13; 16, that's interesting! So are you saying that it's not
just a min triad per se but a min triad from around the 4th of the maj
scale? i.e. If D = 1,2,4,8,16, etc...here, then the 11/8 = 1.375 is
very close to the fourth interval 4/3 = 1.333...(G note), while the D
is 16, the fifth of this G min triad.

Rick

🔗rick_ballan <rick_ballan@...>

--- In tuning@yahoogroups.com, "Tom Dent" <stringph@...> wrote:
>
>
> OK, you've suffered enough ... 28:41 and 13:19 were actually quite
> good guesses for the 'fifth'. But it's 11:13:16.
>
> Somehow this 'subminor' with a 'subfifth' actually sounds marginally
> more consonant to me than 10:12:15 ... perhaps because it less
> resembles a lower part of the harmonic series gone wrong. Pure
> speculation.
> ~~~T~~~
>
> --- In tuning@yahoogroups.com, Mike Battaglia <battaglia01@> wrote:
> >
> > I think the lowest dyad there is 7:8. It does sound a little bit
> > flatter than 6:7 to be sure. From screwing around with Scala, the best
> > match I could find was 28:32:41, where the 28:41 on the outside I
> > picked because it's halfway between 28:40, which is 7:10, and 28:42,
> > which is 2:3. When playing them simultaneously I still hear some
> > beating, although I can't tell if this is due to some resolution
> > problem in Scala or if I'm just wrong with the chord. After messing
> > around a little bit more I found 13:15:19 to be about as good of a
> > match with lower number ratios.
> >
> > -Mike
> >
> >
> > On Wed, Jan 21, 2009 at 9:24 AM, Tom Dent <stringph@> wrote:
> >
> > >> > Now listen to the chord here -
> > >> > /tuning/files/sphaerenklang/
> > >> >
> > >> > a simple combination of 3 sine waves in integer ratio ... but
what
> > > ratio?
>
In fact, my original guess that it was 512; 609; 768 is not far off:
13/11 = 1.1818...while 609/512 = 1.1894, close to two decimal places.
(and I've always suspected that we can't distinguish beyond a few
decimals, so that whole 'clusters' of ratios could correspond to each
interval),

Rick

🔗Tom Dent <stringph@...>

--- In tuning@yahoogroups.com, "rick_ballan" <rick_ballan@...> wrote:
>
> > But it's 11:13:16.
> >

> In fact, my original guess that it was 512; 609; 768 is not far off:
> 13/11 = 1.1818...while 609/512 = 1.1894, close to two decimal places.
> (and I've always suspected that we can't distinguish beyond a few
> decimals, so that whole 'clusters' of ratios could correspond to each
> interval),
>
> Rick
>

Sorry, 512:609:768 is miles away. The main point of surprise is that
people's brains seemed to accept 11:16 as a perfectly good 'fifth',
given sine-wave timbres and a good third in between. 11:16 is 1.4545..
or 649 cents - but most blind guesses were 3:2!

If you can't *distinguish* between 1.5 and 1.454 something is
definitely wrong.

Of course *identifying* any complex interval blind, without
comparisons, and with sine waves - which is what I challenged people
to do - is much more difficult.
I could well believe that pure interval identification in this sense
is subject to a big uncertainty, maybe tens of cents.
~~~T~~~

🔗Tom Dent <stringph@...>

🔗caleb morgan <calebmrgn@...>

no. imo.

almost 50 cents off.

On Jan 23, 2009, at 9:47 AM, Tom Dent wrote:

> --- In tuning@yahoogroups.com, Mike Battaglia <battaglia01@...> wrote:
> >
> > 8/3 plays the role of 11/4 very well...
> > I wonder if this means anything for the perception of tempered
> > intervals.
> >
> > -Mike
> >
>
> 8/3 ~ 11/4
> invert:
> 12/8 ~ 16/11
>
> means that 16/11 can the role of 3/2 for sines - as I showed!
>
> However, I expect any timbres with 3rd harmonic will show what's up,
> rather obviously.
> ~~~T~~~
>
>
>

🔗Tom Dent <stringph@...>

I do know that 11:16 is even slightly more than 50 cents narrower than
3:2, but I SHOWED by experiment, right here on this list, just a
couple of days ago, that people were liable to mistake it for 3:2 in
'blind' listening to a triad with pure sine waves.

So why should your opinion count for more than the evidence of
people's ears? Please actually listen to the sine-wave 11:13:16 before
giving judgement...
~~~T~~~

--- In tuning@yahoogroups.com, caleb morgan <calebmrgn@...> wrote:
>
>
> no. imo.
>
> almost 50 cents off.
>
>
> On Jan 23, 2009, at 9:47 AM, Tom Dent wrote:
>
> > --- In tuning@yahoogroups.com, Mike Battaglia <battaglia01@> wrote:
> > >
> > > 8/3 plays the role of 11/4 very well...
> > > I wonder if this means anything for the perception of tempered
> > > intervals.
> > >
> > > -Mike
> > >
> >
> > 8/3 ~ 11/4
> > invert:
> > 12/8 ~ 16/11
> >
> > means that 16/11 can the role of 3/2 for sines - as I showed!
> >
> > However, I expect any timbres with 3rd harmonic will show what's up,
> > rather obviously.
> > ~~~T~~~
> >
> >
> >
>

🔗caleb morgan <calebmrgn@...>

my opinion shouldn't count for much, in general. Except:

You yourself have said, correct me if I'm wrong, that experiments with
pure sine waves, were---what was it?--misleading, or words to that
effect.

the 11:13 isn't far off from an equal-tempered minor third, so having
two tones creating a sort of center of gravity almost 50 cents lower
in pitch could be fooling people, right there.

But our real misunderstanding here is this, I think:

I thought the statement that 8/3 was good at playing the role of an 11
ratio was a general statement. As such, it's preposterous.

If my 25+ years (some of those years pretty intensive) messing around
with jJI systems has taught me anything:

Each new prime has a distinct sound. That's why they're interesting,
novel, fresh, disturbing, "wrong", even.

Nothing "substitutes" or plays the role of 7, 11, or 13.

17 and 19 are extremely remote. If you (Mike, in this case) think
you're hearing something like that, you're fooling yourself.

You're hearing something standing in for 16/15, or 27/16, or 6/5.

A 17 has to be in a very high register, and extremely accurate, to
really be that animal.

I'm not well-versed in the vocabulary or the science side, but I'll
wager I've got as many hours jamming with JI as anyone here. Unless
Wendy's here, or Harry's ghost.

just my 50¢ worth.

caleb

On Jan 23, 2009, at 11:11 AM, Tom Dent wrote:

>
> I do know that 11:16 is even slightly more than 50 cents narrower than
> 3:2, but I SHOWED by experiment, right here on this list, just a
> couple of days ago, that people were liable to mistake it for 3:2 in
> 'blind' listening to a triad with pure sine waves.
>
> So why should your opinion count for more than the evidence of
> people's ears? Please actually listen to the sine-wave 11:13:16 before
> giving judgement...
> ~~~T~~~
>
> --- In tuning@yahoogroups.com, caleb morgan <calebmrgn@...> wrote:
> >
> >
> > no. imo.
> >
> > almost 50 cents off.
> >
> >
> > On Jan 23, 2009, at 9:47 AM, Tom Dent wrote:
> >
> > > --- In tuning@yahoogroups.com, Mike Battaglia <battaglia01@>
> wrote:
> > > >
> > > > 8/3 plays the role of 11/4 very well...
> > > > I wonder if this means anything for the perception of tempered
> > > > intervals.
> > > >
> > > > -Mike
> > > >
> > >
> > > 8/3 ~ 11/4
> > > invert:
> > > 12/8 ~ 16/11
> > >
> > > means that 16/11 can the role of 3/2 for sines - as I showed!
> > >
> > > However, I expect any timbres with 3rd harmonic will show what's
> up,
> > > rather obviously.
> > > ~~~T~~~
> > >
> > >
> > >
> >
>
>
>

🔗Carl Lumma <carl@...>

🔗rick_ballan <rick_ballan@...>

--- In tuning@yahoogroups.com, "Tom Dent" <stringph@...> wrote:
>
> --- In tuning@yahoogroups.com, "rick_ballan" <rick_ballan@> wrote:
> >
> > > But it's 11:13:16.
> > >
>
> > In fact, my original guess that it was 512; 609; 768 is not far off:
> > 13/11 = 1.1818...while 609/512 = 1.1894, close to two decimal places.
> > (and I've always suspected that we can't distinguish beyond a few
> > decimals, so that whole 'clusters' of ratios could correspond to each
> > interval),
> >
> > Rick
> >
>
> Sorry, 512:609:768 is miles away. The main point of surprise is that
> people's brains seemed to accept 11:16 as a perfectly good 'fifth',
> given sine-wave timbres and a good third in between. 11:16 is 1.4545..
> or 649 cents - but most blind guesses were 3:2!
>
> If you can't *distinguish* between 1.5 and 1.454 something is
> definitely wrong.
>
> Of course *identifying* any complex interval blind, without
> comparisons, and with sine waves - which is what I challenged people
> to do - is much more difficult.
> I could well believe that pure interval identification in this sense
> is subject to a big uncertainty, maybe tens of cents.
> ~~~T~~~
>
Yes that is interesting. I'm sure your experiment does show that there
has to be a 'range' of give around each interval (As I mentioned, I've
never ever done a gig where my guitar stayed exactly in tune
electronically at the end of a set). But by the same token,you'll find
that 512:609:768 isn't miles away at all (just because the numbers are
large) because 609/512 = 1.1894...and IS a much better approx. to the
tempered min 3 as 1.1892...than 6/5 = 1.2 or 19/16 = 1.1875. And as I
also mentioned, 11:13:16 could possibly be more related to a minor
triad from the fourth degree, so that the root note 11 here is close
to the fourth , 16 being 8ve to the tonic 1.

-Rick

🔗djtrancendance@...

> If you can't *distinguish* between 1.5 and 1.454 something is

> definitely wrong.

To Carl, Charles, and others,

Granted, they ARE different and the point I am about to make is probably "historically wrong".

However, here's an interesting fact (at least to my ears). 1.4545, despite being an "impure fifth", still sounds deceptively pure...enough so to substitute for a 5th in a musical/emotional context (which is ultimately kind of the point, right)?

   In fact, it seems virtually all fractions which either result in.........
A) repeating decimals like x.3333 or x.454545 or x.727272 sound great to my ears.
    OR
B) decimals which cancel out perfectly after very little length such as 1.5, 1.125, 1.25...
.........sound very very natural!!
*****************************************************************************************
   Somehow, I doubt this is coincidence. In fact look at this
12-tone
scale
1/1
1.055555
1.2
1.25
1.3125
1.375
1.44
1.5
1.63636363
1.72727272
1.83333333
1.91666666
2/1

Even the tones so close together that they beat sound quite harmonic, or at least to my ears.
**************************************************************************************
Any thought or ideas...on either why this happens or if I am in fact correct, that the ear has an affinity for fractions in scales which reduce to simple and/or redundant decimals?

-Michael

🔗rick_ballan <rick_ballan@...>

--- In tuning@yahoogroups.com, djtrancendance@... wrote:
>
>
> > If you can't *distinguish* between 1.5 and 1.454 something is
>
> > definitely wrong.
>
> To Carl, Charles, and others,
>
> Granted, they ARE different and the point I am about to make is
probably "historically wrong".
>
> However, here's an interesting fact (at least to my ears).
1.4545, despite being an "impure fifth", still sounds deceptively
pure...enough so to substitute for a 5th in a musical/emotional
context (which is ultimately kind of the point, right)?
>
> In fact, it seems virtually all fractions which either result
in.........
> A) repeating decimals like x.3333 or x.454545 or x.727272 sound
great to my ears.
> OR
> B) decimals which cancel out perfectly after very little length such
as 1.5, 1.125, 1.25...
> .........sound very very natural!!
>
*****************************************************************************************
> Somehow, I doubt this is coincidence. In fact look at this
> 12-tone
> scale
> 1/1
> 1.055555
> 1.2
> 1.25
> 1.3125
> 1.375
> 1.44
> 1.5
> 1.63636363
> 1.72727272
> 1.83333333
> 1.91666666
> 2/1
>
> Even the tones so close together that they beat sound quite
harmonic, or at least to my ears.
>
**************************************************************************************
> Any thought or ideas...on either why this happens or if I am in
fact correct, that the ear has an affinity for fractions in scales
which reduce to simple and/or redundant decimals?
>
> -Michael
>
Yes Michael, quite simply because they are rational numbers so that
the resultant wave is periodic/harmonious. Irrationals on the other
hand have non-repeating decimals and their waves, strictly speaking,
are also aperiodic.

-R

🔗Tom Dent <stringph@...>

--- In tuning@yahoogroups.com, "Carl Lumma" <carl@...> wrote:
>
> > Of course *identifying* any complex interval blind, without
> > comparisons, and with sine waves - which is what I challenged
> > people to do - is much more difficult.
>
> The most difficult thing was the registration. The 16/11
> would stick out higher on the keyboard.
>
> -Carl
>

So, compare the effect when it's somewhat over an 8ve higher -
minor500.wav at
/tuning/files/sphaerenklang/

Now difference tones leap into the game, but the 'subfifth' still
sounds perfectly OK to me.
~~~T~~~