Polyrhythmic Beating Partials

Hi everyone, thought I might start a new thread and post some predicted
partials numbers to give an idea of how complex rational intervals may
sound different due to the polyrhythmic nature of the beating partals.
So here is 81/64
Interval 81/64 between frequencies 261.6255653 Hz and 331.11985608
Hz.Expected difference tone 69.49429078 Hz is 17/64 below lowest pitch
noteBeats per sec. up to 32nd harmonic and up to 20 beats per sec.
beats harmon. (harm,) freq of harmonic (freq. of upper note
harmonic)16.35159783 5th (4th) 1308.127826503 Hz (1324.4794243343
Hz)4.08789946 19th (15th) 4970.8857407114 Hz (4966.7978412536
Hz)12.26369837 24th (19th) 6279.0135672144 Hz (6291.2772655878 Hz)
Table shows expected beat patterns for harmonic timbres.
There 81/64 is 407.82 cents.

As a polyrhythm it's 4 : 1 : 3It seems not impossible that an
experienced instrumentalist could come to recognise 81/64 by that
distinctive polyrhythm in the beating partials.
By comparision, this is 408.0 cents
Interval 408.0 between frequencies 261.6255653 Hz and 331.15428443
Hz.Expected difference tone 69.52871913 Hz is -2294.187 below lowest
pitch noteBeats per sec. up to 32nd harmonic and up to 20 beats per sec.
beats harmon. (harm,) freq of harmonic (freq. of upper note
harmonic)16.48931122 5th (4th) 1308.127826503 Hz (1324.6171377217
Hz)3.57147425 19th (15th) 4970.8857407114 Hz (4967.3142664565
Hz)12.91783696 24th (19th) 6279.0135672144 Hz (6291.9314041783 Hz)
and here is 407.0 cents
Interval 407.0 between frequencies 261.6255653 Hz and 330.96305745
Hz.Expected difference tone 69.33749215 Hz is -2298.955 below lowest
pitch noteBeats per sec. up to 32nd harmonic and up to 20 beats per sec.
beats harmon. (harm,) freq of harmonic (freq. of upper note
harmonic)15.72440329 5th (4th) 1308.127826503 Hz (1323.8522297951
Hz)6.43987898 19th (15th) 4970.8857407114 Hz (4964.4458617318
Hz)9.28452431 24th (19th) 6279.0135672144 Hz (6288.2980915269 Hz)

15.72440329 / 6.43987898 = 2.44172341

So if you can hear both beating partials, 407.0 should be easily
distinguishable from 81/64.
16.48931122 / 3.57147425 = 4.61694809
So to a keen ear, this also should be noticeable, 4.17 to 1 should sound
noticeably uneven compared to a 4 1 exact polyrhythm
In fact these results seem to suggest that an interval such as 81/64
should be tunable more exactly by ear than a simpler interval like say
5/4. That is - once you get to know what to listen out for in the
"texture" of the interval.
I've tested it here with pure triangle waves rich in partials. Can post
some audio clips so you can all give it a go - maybe even a test, not
say which is which, post three examples of 407.0, 81/64, and 408.0 as
pure triangle waves, of course not permitted to analyse it and so
"cheat", and see which of you can distinguish them by ear :).
Not just totally blind - could have the three files labelled - and then
the same three recordings this time not labelled, and see if you can put
them in the right order by just listening to them. Seems quite possible
that quite a few microtonalists would be able to do that, from the
numbers.

My mention of 81:64 was to point out that it contains a "bearing plan". It's a very simple bearing plan, too- four pure fifths octave reduced. My point is that when we look at the allegedly complex intervals of medieval and ancient theorists, we often find that what might appear to be extravagantly complex figures are upon closer inspection quite simple in terms of "real life". There are many "big number" ratios of medieval Islamic theorists which are Pythagorean intervals and simple divisions thereof. This is not "numerology", it is concrete mechanical instruction.

Here is an example:

http://www.chrysalis-foundation.org/Al-Farabi's_'Uds.htm

This is from Cris Forster's book, which I can hardly wait to read (my friend forgot to bring it over, maybe this weekend though).

This isn't numerology. It's actually dull as dishwater and disappointly simple in terms of number, but exciting for those with hands-on approachs to tuning. Kind of like how we can get all hot and bothered inspecting a set of good chisels. :-)

Now that you inspect 81:64 as you have, though, I think what you propose is very interesting! Beats me (heh heh) if this is perceptible, and I do believe that such things are much more likely to be perceptible when in physical contact with a resonating acoustic
instrument. But if you'd do some blind tests, that would be great!

-Cameron Bobro

--- In tuning@yahoogroups.com, "robert_inventor5" <robertwalker@...> wrote:
>
> Hi everyone, thought I might start a new thread and post some predicted
> partials numbers to give an idea of how complex rational intervals may
> sound different due to the polyrhythmic nature of the beating partals.
> So here is 81/64
> Interval 81/64 between frequencies 261.6255653 Hz and 331.11985608
> Hz.Expected difference tone 69.49429078 Hz is 17/64 below lowest pitch
> noteBeats per sec. up to 32nd harmonic and up to 20 beats per sec.
> beats harmon. (harm,) freq of harmonic (freq. of upper note
> harmonic)16.35159783 5th (4th) 1308.127826503 Hz (1324.4794243343
> Hz)4.08789946 19th (15th) 4970.8857407114 Hz (4966.7978412536
> Hz)12.26369837 24th (19th) 6279.0135672144 Hz (6291.2772655878 Hz)
> Table shows expected beat patterns for harmonic timbres.
> There 81/64 is 407.82 cents.
>
> As a polyrhythm it's 4 : 1 : 3It seems not impossible that an
> experienced instrumentalist could come to recognise 81/64 by that
> distinctive polyrhythm in the beating partials.
> By comparision, this is 408.0 cents
> Interval 408.0 between frequencies 261.6255653 Hz and 331.15428443
> Hz.Expected difference tone 69.52871913 Hz is -2294.187 below lowest
> pitch noteBeats per sec. up to 32nd harmonic and up to 20 beats per sec.
> beats harmon. (harm,) freq of harmonic (freq. of upper note
> harmonic)16.48931122 5th (4th) 1308.127826503 Hz (1324.6171377217
> Hz)3.57147425 19th (15th) 4970.8857407114 Hz (4967.3142664565
> Hz)12.91783696 24th (19th) 6279.0135672144 Hz (6291.9314041783 Hz)
> and here is 407.0 cents
> Interval 407.0 between frequencies 261.6255653 Hz and 330.96305745
> Hz.Expected difference tone 69.33749215 Hz is -2298.955 below lowest
> pitch noteBeats per sec. up to 32nd harmonic and up to 20 beats per sec.
> beats harmon. (harm,) freq of harmonic (freq. of upper note
> harmonic)15.72440329 5th (4th) 1308.127826503 Hz (1323.8522297951
> Hz)6.43987898 19th (15th) 4970.8857407114 Hz (4964.4458617318
> Hz)9.28452431 24th (19th) 6279.0135672144 Hz (6288.2980915269 Hz)
>
> 15.72440329 / 6.43987898 = 2.44172341
>
> So if you can hear both beating partials, 407.0 should be easily
> distinguishable from 81/64.
> 16.48931122 / 3.57147425 = 4.61694809
> So to a keen ear, this also should be noticeable, 4.17 to 1 should sound
> noticeably uneven compared to a 4 1 exact polyrhythm
> In fact these results seem to suggest that an interval such as 81/64
> should be tunable more exactly by ear than a simpler interval like say
> 5/4. That is - once you get to know what to listen out for in the
> "texture" of the interval.
> I've tested it here with pure triangle waves rich in partials. Can post
> some audio clips so you can all give it a go - maybe even a test, not
> say which is which, post three examples of 407.0, 81/64, and 408.0 as
> pure triangle waves, of course not permitted to analyse it and so
> "cheat", and see which of you can distinguish them by ear :).
> Not just totally blind - could have the three files labelled - and then
> the same three recordings this time not labelled, and see if you can put
> them in the right order by just listening to them. Seems quite possible
> that quite a few microtonalists would be able to do that, from the
> numbers.
>

Rightio, that makes sense too.

Yes - well testing it here with a pure triangle wave, I felt that it was perceptible. But it is so easy to fool yourself when you know what intervals you are playing. Also - it is a long time since I did a lot of microtonal work.

Anyway, it needs a blind test.

I'll give it a go. Could be fun :).

Robert

--- In tuning@yahoogroups.com, "cameron" <misterbobro@...> wrote:
>
> My mention of 81:64 was to point out that it contains a "bearing plan". It's a very simple bearing plan, too- four pure fifths octave reduced. My point is that when we look at the allegedly complex intervals of medieval and ancient theorists, we often find that what might appear to be extravagantly complex figures are upon closer inspection quite simple in terms of "real life". There are many "big number" ratios of medieval Islamic theorists which are Pythagorean intervals and simple divisions thereof. This is not "numerology", it is concrete mechanical instruction.
>
> Here is an example:
>
> http://www.chrysalis-foundation.org/Al-Farabi's_'Uds.htm
>
> This is from Cris Forster's book, which I can hardly wait to read (my friend forgot to bring it over, maybe this weekend though).
>
> This isn't numerology. It's actually dull as dishwater and disappointly simple in terms of number, but exciting for those with hands-on approachs to tuning. Kind of like how we can get all hot and bothered inspecting a set of good chisels. :-)
>
> Now that you inspect 81:64 as you have, though, I think what you propose is very interesting! Beats me (heh heh) if this is perceptible, and I do believe that such things are much more likely to be perceptible when in physical contact with a resonating acoustic
> instrument. But if you'd do some blind tests, that would be great!
>
> -Cameron Bobro
>
>
>
>
> --- In tuning@yahoogroups.com, "robert_inventor5" <robertwalker@> wrote:
> >
> > Hi everyone, thought I might start a new thread and post some predicted
> > partials numbers to give an idea of how complex rational intervals may
> > sound different due to the polyrhythmic nature of the beating partals.
> > So here is 81/64
> > Interval 81/64 between frequencies 261.6255653 Hz and 331.11985608
> > Hz.Expected difference tone 69.49429078 Hz is 17/64 below lowest pitch
> > noteBeats per sec. up to 32nd harmonic and up to 20 beats per sec.
> > beats harmon. (harm,) freq of harmonic (freq. of upper note
> > harmonic)16.35159783 5th (4th) 1308.127826503 Hz (1324.4794243343
> > Hz)4.08789946 19th (15th) 4970.8857407114 Hz (4966.7978412536
> > Hz)12.26369837 24th (19th) 6279.0135672144 Hz (6291.2772655878 Hz)
> > Table shows expected beat patterns for harmonic timbres.
> > There 81/64 is 407.82 cents.
> >
> > As a polyrhythm it's 4 : 1 : 3It seems not impossible that an
> > experienced instrumentalist could come to recognise 81/64 by that
> > distinctive polyrhythm in the beating partials.
> > By comparision, this is 408.0 cents
> > Interval 408.0 between frequencies 261.6255653 Hz and 331.15428443
> > Hz.Expected difference tone 69.52871913 Hz is -2294.187 below lowest
> > pitch noteBeats per sec. up to 32nd harmonic and up to 20 beats per sec.
> > beats harmon. (harm,) freq of harmonic (freq. of upper note
> > harmonic)16.48931122 5th (4th) 1308.127826503 Hz (1324.6171377217
> > Hz)3.57147425 19th (15th) 4970.8857407114 Hz (4967.3142664565
> > Hz)12.91783696 24th (19th) 6279.0135672144 Hz (6291.9314041783 Hz)
> > and here is 407.0 cents
> > Interval 407.0 between frequencies 261.6255653 Hz and 330.96305745
> > Hz.Expected difference tone 69.33749215 Hz is -2298.955 below lowest
> > pitch noteBeats per sec. up to 32nd harmonic and up to 20 beats per sec.
> > beats harmon. (harm,) freq of harmonic (freq. of upper note
> > harmonic)15.72440329 5th (4th) 1308.127826503 Hz (1323.8522297951
> > Hz)6.43987898 19th (15th) 4970.8857407114 Hz (4964.4458617318
> > Hz)9.28452431 24th (19th) 6279.0135672144 Hz (6288.2980915269 Hz)
> >
> > 15.72440329 / 6.43987898 = 2.44172341
> >
> > So if you can hear both beating partials, 407.0 should be easily
> > distinguishable from 81/64.
> > 16.48931122 / 3.57147425 = 4.61694809
> > So to a keen ear, this also should be noticeable, 4.17 to 1 should sound
> > noticeably uneven compared to a 4 1 exact polyrhythm
> > In fact these results seem to suggest that an interval such as 81/64
> > should be tunable more exactly by ear than a simpler interval like say
> > 5/4. That is - once you get to know what to listen out for in the
> > "texture" of the interval.
> > I've tested it here with pure triangle waves rich in partials. Can post
> > some audio clips so you can all give it a go - maybe even a test, not
> > say which is which, post three examples of 407.0, 81/64, and 408.0 as
> > pure triangle waves, of course not permitted to analyse it and so
> > "cheat", and see which of you can distinguish them by ear :).
> > Not just totally blind - could have the three files labelled - and then
> > the same three recordings this time not labelled, and see if you can put
> > them in the right order by just listening to them. Seems quite possible
> > that quite a few microtonalists would be able to do that, from the
> > numbers.
> >
>

Great! Make sure that you don't tell us if one is slightly lower than 81:64, one is 81:64, and one slightly higher, for that would make the test results indistinguishable from "which interval is pitched between the other two". Also, a duplicate would be nice to sneak in there, giving four files, two the same pitch (vary the attack times for example, in order to obviate cheating to eliminate the duplicate by means of phase inversion and cancellation :-) )

-Cameron Bobro

--- In tuning@yahoogroups.com, "robert_inventor5" <robertwalker@...> wrote:
>
> Rightio, that makes sense too.
>
> Yes - well testing it here with a pure triangle wave, I felt that it was perceptible. But it is so easy to fool yourself when you know what intervals you are playing. Also - it is a long time since I did a lot of microtonal work.
>
> Anyway, it needs a blind test.
>
> I'll give it a go. Could be fun :).
>
> Robert
>
> --- In tuning@yahoogroups.com, "cameron" <misterbobro@> wrote:
> >
> > My mention of 81:64 was to point out that it contains a "bearing plan". It's a very simple bearing plan, too- four pure fifths octave reduced. My point is that when we look at the allegedly complex intervals of medieval and ancient theorists, we often find that what might appear to be extravagantly complex figures are upon closer inspection quite simple in terms of "real life". There are many "big number" ratios of medieval Islamic theorists which are Pythagorean intervals and simple divisions thereof. This is not "numerology", it is concrete mechanical instruction.
> >
> > Here is an example:
> >
> > http://www.chrysalis-foundation.org/Al-Farabi's_'Uds.htm
> >
> > This is from Cris Forster's book, which I can hardly wait to read (my friend forgot to bring it over, maybe this weekend though).
> >
> > This isn't numerology. It's actually dull as dishwater and disappointly simple in terms of number, but exciting for those with hands-on approachs to tuning. Kind of like how we can get all hot and bothered inspecting a set of good chisels. :-)
> >
> > Now that you inspect 81:64 as you have, though, I think what you propose is very interesting! Beats me (heh heh) if this is perceptible, and I do believe that such things are much more likely to be perceptible when in physical contact with a resonating acoustic
> > instrument. But if you'd do some blind tests, that would be great!
> >
> > -Cameron Bobro
> >
> >
> >
> >
> > --- In tuning@yahoogroups.com, "robert_inventor5" <robertwalker@> wrote:
> > >
> > > Hi everyone, thought I might start a new thread and post some predicted
> > > partials numbers to give an idea of how complex rational intervals may
> > > sound different due to the polyrhythmic nature of the beating partals.
> > > So here is 81/64
> > > Interval 81/64 between frequencies 261.6255653 Hz and 331.11985608
> > > Hz.Expected difference tone 69.49429078 Hz is 17/64 below lowest pitch
> > > noteBeats per sec. up to 32nd harmonic and up to 20 beats per sec.
> > > beats harmon. (harm,) freq of harmonic (freq. of upper note
> > > harmonic)16.35159783 5th (4th) 1308.127826503 Hz (1324.4794243343
> > > Hz)4.08789946 19th (15th) 4970.8857407114 Hz (4966.7978412536
> > > Hz)12.26369837 24th (19th) 6279.0135672144 Hz (6291.2772655878 Hz)
> > > Table shows expected beat patterns for harmonic timbres.
> > > There 81/64 is 407.82 cents.
> > >
> > > As a polyrhythm it's 4 : 1 : 3It seems not impossible that an
> > > experienced instrumentalist could come to recognise 81/64 by that
> > > distinctive polyrhythm in the beating partials.
> > > By comparision, this is 408.0 cents
> > > Interval 408.0 between frequencies 261.6255653 Hz and 331.15428443
> > > Hz.Expected difference tone 69.52871913 Hz is -2294.187 below lowest
> > > pitch noteBeats per sec. up to 32nd harmonic and up to 20 beats per sec.
> > > beats harmon. (harm,) freq of harmonic (freq. of upper note
> > > harmonic)16.48931122 5th (4th) 1308.127826503 Hz (1324.6171377217
> > > Hz)3.57147425 19th (15th) 4970.8857407114 Hz (4967.3142664565
> > > Hz)12.91783696 24th (19th) 6279.0135672144 Hz (6291.9314041783 Hz)
> > > and here is 407.0 cents
> > > Interval 407.0 between frequencies 261.6255653 Hz and 330.96305745
> > > Hz.Expected difference tone 69.33749215 Hz is -2298.955 below lowest
> > > pitch noteBeats per sec. up to 32nd harmonic and up to 20 beats per sec.
> > > beats harmon. (harm,) freq of harmonic (freq. of upper note
> > > harmonic)15.72440329 5th (4th) 1308.127826503 Hz (1323.8522297951
> > > Hz)6.43987898 19th (15th) 4970.8857407114 Hz (4964.4458617318
> > > Hz)9.28452431 24th (19th) 6279.0135672144 Hz (6288.2980915269 Hz)
> > >
> > > 15.72440329 / 6.43987898 = 2.44172341
> > >
> > > So if you can hear both beating partials, 407.0 should be easily
> > > distinguishable from 81/64.
> > > 16.48931122 / 3.57147425 = 4.61694809
> > > So to a keen ear, this also should be noticeable, 4.17 to 1 should sound
> > > noticeably uneven compared to a 4 1 exact polyrhythm
> > > In fact these results seem to suggest that an interval such as 81/64
> > > should be tunable more exactly by ear than a simpler interval like say
> > > 5/4. That is - once you get to know what to listen out for in the
> > > "texture" of the interval.
> > > I've tested it here with pure triangle waves rich in partials. Can post
> > > some audio clips so you can all give it a go - maybe even a test, not
> > > say which is which, post three examples of 407.0, 81/64, and 408.0 as
> > > pure triangle waves, of course not permitted to analyse it and so
> > > "cheat", and see which of you can distinguish them by ear :).
> > > Not just totally blind - could have the three files labelled - and then
> > > the same three recordings this time not labelled, and see if you can put
> > > them in the right order by just listening to them. Seems quite possible
> > > that quite a few microtonalists would be able to do that, from the
> > > numbers.
> > >
> >
>

I think this would be easier to follow if you just used round numbers. 640 would work
I would say that the 17 difference tone is part of the key to hearing it.
One of the ways though one can tune a simple just ratio is the drop in volume so i think 5/4 will always be easier to tune.

--- In tuning@yahoogroups.com, "robert_inventor5" <robertwalker@...> wrote:
>
> Hi everyone, thought I might start a new thread and post some predicted
> partials numbers to give an idea of how complex rational intervals may
> sound different due to the polyrhythmic nature of the beating partals.
> So here is 81/64
> Interval 81/64 between frequencies 261.6255653 Hz and 331.11985608
> Hz.Expected difference tone 69.49429078 Hz is 17/64 below lowest pitch
> noteBeats per sec. up to 32nd harmonic and up to 20 beats per sec.
> beats harmon. (harm,) freq of harmonic (freq. of upper note
> harmonic)16.35159783 5th (4th) 1308.127826503 Hz (1324.4794243343
> Hz)4.08789946 19th (15th) 4970.8857407114 Hz (4966.7978412536
> Hz)12.26369837 24th (19th) 6279.0135672144 Hz (6291.2772655878 Hz)
> Table shows expected beat patterns for harmonic timbres.
> There 81/64 is 407.82 cents.
>
> As a polyrhythm it's 4 : 1 : 3It seems not impossible that an
> experienced instrumentalist could come to recognise 81/64 by that
> distinctive polyrhythm in the beating partials.
> By comparision, this is 408.0 cents
> Interval 408.0 between frequencies 261.6255653 Hz and 331.15428443
> Hz.Expected difference tone 69.52871913 Hz is -2294.187 below lowest
> pitch noteBeats per sec. up to 32nd harmonic and up to 20 beats per sec.
> beats harmon. (harm,) freq of harmonic (freq. of upper note
> harmonic)16.48931122 5th (4th) 1308.127826503 Hz (1324.6171377217
> Hz)3.57147425 19th (15th) 4970.8857407114 Hz (4967.3142664565
> Hz)12.91783696 24th (19th) 6279.0135672144 Hz (6291.9314041783 Hz)
> and here is 407.0 cents
> Interval 407.0 between frequencies 261.6255653 Hz and 330.96305745
> Hz.Expected difference tone 69.33749215 Hz is -2298.955 below lowest
> pitch noteBeats per sec. up to 32nd harmonic and up to 20 beats per sec.
> beats harmon. (harm,) freq of harmonic (freq. of upper note
> harmonic)15.72440329 5th (4th) 1308.127826503 Hz (1323.8522297951
> Hz)6.43987898 19th (15th) 4970.8857407114 Hz (4964.4458617318
> Hz)9.28452431 24th (19th) 6279.0135672144 Hz (6288.2980915269 Hz)
>
> 15.72440329 / 6.43987898 = 2.44172341
>
> So if you can hear both beating partials, 407.0 should be easily
> distinguishable from 81/64.
> 16.48931122 / 3.57147425 = 4.61694809
> So to a keen ear, this also should be noticeable, 4.17 to 1 should sound
> noticeably uneven compared to a 4 1 exact polyrhythm
> In fact these results seem to suggest that an interval such as 81/64
> should be tunable more exactly by ear than a simpler interval like say
> 5/4. That is - once you get to know what to listen out for in the
> "texture" of the interval.
> I've tested it here with pure triangle waves rich in partials. Can post
> some audio clips so you can all give it a go - maybe even a test, not
> say which is which, post three examples of 407.0, 81/64, and 408.0 as
> pure triangle waves, of course not permitted to analyse it and so
> "cheat", and see which of you can distinguish them by ear :).
> Not just totally blind - could have the three files labelled - and then
> the same three recordings this time not labelled, and see if you can put
> them in the right order by just listening to them. Seems quite possible
> that quite a few microtonalists would be able to do that, from the
> numbers.
>

Rightio that makes sense.

When I listened to the clip what I noticed most was a variation in the sound of the difference tone. But not sure what to make of it so didn't mention it.

I think perhaps the difference tone beats with some of the other pitches, if that makes sense?

It's a while since I did much careful listening to this sort of thing so heard it more as a texture than distinct pitches so not quite sure which of the pitches in the dyad was beating, but the most obvious feature sounded like the difference tone, which beat in a slightly irregular way for the 408.0 and a more regular way (quite slowly) for the 81/64, if that makes sense? But that might be wide of the mark as I need to get my ear in a bit after a long time not doing this sort of stuff much.

Yes that's a good idea to use round numbers to make it easier to read, thanks.

Yes - the thought was that the 81/64 might be an interval you can tune more accurately, to a small fraction of a cent - but a much harder one to tune of course. While the 5/4 you could tune more easily - but though very exactly as well of course, maybe not quite so very exactly if it turns out that the sound of the 81/64 varies - though slightly but noticeably - over a much smaller pitch interval in the immediate vicinity of the interval.

Like a big hard to miss but broad dip in the "roughness of the sound" for the 5/4 and a narrow and hard to spot dip around the 81/64 easily missed but because it is narrower once you do hear it, if you can learn to use it you might hit the interval more exactly.

That was the thought anyway.

Robert

--- In tuning@yahoogroups.com, "Brofessor" <kraiggrady@...> wrote:
>
> I think this would be easier to follow if you just used round numbers. 640 would work
> I would say that the 17 difference tone is part of the key to hearing it.
> One of the ways though one can tune a simple just ratio is the drop in volume so i think 5/4 will always be easier to tune.
>
> --- In tuning@yahoogroups.com, "robert_inventor5" <robertwalker@> wrote:
> >
> > Hi everyone, thought I might start a new thread and post some predicted
> > partials numbers to give an idea of how complex rational intervals may
> > sound different due to the polyrhythmic nature of the beating partals.
> > So here is 81/64
> > Interval 81/64 between frequencies 261.6255653 Hz and 331.11985608
> > Hz.Expected difference tone 69.49429078 Hz is 17/64 below lowest pitch
> > noteBeats per sec. up to 32nd harmonic and up to 20 beats per sec.
> > beats harmon. (harm,) freq of harmonic (freq. of upper note
> > harmonic)16.35159783 5th (4th) 1308.127826503 Hz (1324.4794243343
> > Hz)4.08789946 19th (15th) 4970.8857407114 Hz (4966.7978412536
> > Hz)12.26369837 24th (19th) 6279.0135672144 Hz (6291.2772655878 Hz)
> > Table shows expected beat patterns for harmonic timbres.
> > There 81/64 is 407.82 cents.
> >
> > As a polyrhythm it's 4 : 1 : 3It seems not impossible that an
> > experienced instrumentalist could come to recognise 81/64 by that
> > distinctive polyrhythm in the beating partials.
> > By comparision, this is 408.0 cents
> > Interval 408.0 between frequencies 261.6255653 Hz and 331.15428443
> > Hz.Expected difference tone 69.52871913 Hz is -2294.187 below lowest
> > pitch noteBeats per sec. up to 32nd harmonic and up to 20 beats per sec.
> > beats harmon. (harm,) freq of harmonic (freq. of upper note
> > harmonic)16.48931122 5th (4th) 1308.127826503 Hz (1324.6171377217
> > Hz)3.57147425 19th (15th) 4970.8857407114 Hz (4967.3142664565
> > Hz)12.91783696 24th (19th) 6279.0135672144 Hz (6291.9314041783 Hz)
> > and here is 407.0 cents
> > Interval 407.0 between frequencies 261.6255653 Hz and 330.96305745
> > Hz.Expected difference tone 69.33749215 Hz is -2298.955 below lowest
> > pitch noteBeats per sec. up to 32nd harmonic and up to 20 beats per sec.
> > beats harmon. (harm,) freq of harmonic (freq. of upper note
> > harmonic)15.72440329 5th (4th) 1308.127826503 Hz (1323.8522297951
> > Hz)6.43987898 19th (15th) 4970.8857407114 Hz (4964.4458617318
> > Hz)9.28452431 24th (19th) 6279.0135672144 Hz (6288.2980915269 Hz)
> >
> > 15.72440329 / 6.43987898 = 2.44172341
> >
> > So if you can hear both beating partials, 407.0 should be easily
> > distinguishable from 81/64.
> > 16.48931122 / 3.57147425 = 4.61694809
> > So to a keen ear, this also should be noticeable, 4.17 to 1 should sound
> > noticeably uneven compared to a 4 1 exact polyrhythm
> > In fact these results seem to suggest that an interval such as 81/64
> > should be tunable more exactly by ear than a simpler interval like say
> > 5/4. That is - once you get to know what to listen out for in the
> > "texture" of the interval.
> > I've tested it here with pure triangle waves rich in partials. Can post
> > some audio clips so you can all give it a go - maybe even a test, not
> > say which is which, post three examples of 407.0, 81/64, and 408.0 as
> > pure triangle waves, of course not permitted to analyse it and so
> > "cheat", and see which of you can distinguish them by ear :).
> > Not just totally blind - could have the three files labelled - and then
> > the same three recordings this time not labelled, and see if you can put
> > them in the right order by just listening to them. Seems quite possible
> > that quite a few microtonalists would be able to do that, from the
> > numbers.
> >
>

Okay.

Perhaps what I'll do is - first three clips for training purposes, the 407.0, 81/64 and 408.0.

So one can listen and get used to what the 81/64 sounds like with the triangle wave. And see if you think you can distinguish them.

Then add a duplicate of one of the files, not say which, and add an extra clip which will be either 406.0 or 409.0 and again, not say which it is.

Then label those in random order as say A B C D E and then the challenge is to identify the 81/64 and optionally to try to get the 407.0, the 408.0 too. And to find out which of the remaining ones is the duplicate, what it is duplicate of, and which is the extra one, and for a bonus "star" is the extra one 406.0 or 409.0. Just for fun, see if anyone gets them all right, and see how many get the 81/64.

It will have to be the sort of poll where you don't see the results until everyone has voted. Which I see is an option here. Also - I wonder if I should display users's identities for the poll results or make it a secret one? Or maybe both, maybe users who want to be identified can use the non secret version of the poll.

Or - maybe should have a separate poll for people who think they can distinguish the intervals and for those who think they can't after listening to the training clips. Because if you don't think you can hear any difference, your results may be close to random - which may skew the poll and hide the signal you are looking for from people who feel they can distinguish them.

Or something, needs some thought. I've got to get back to other things, getting a bit distracted (though fascinated) by all this, so I think I'll leave it a day or two and do it maybe towards end of the week or early next week.

The intervals are so close together that it could be quite a challenge to answer the question "which is pitched between the other two".

So anyway perhaps can't do a perfect test but at least do my best to set up the situation so that it is highly likely near to 100% that musicians will do the identification by listening to the texture or beat patterns etc. of the dyads.

As for cheating - well I think I'll just say that if you have any way of distinguishing them by analysis, please don't use them, so we can do it properly.

You could probably distinguish them using Tune Smithy's various frequency analysis tools - though they are quite hard to use at present in version 3.1, and distinguishing the 81/64 from the 408.0 is likely to push the limits of sensitivity of most ways of attempting to measure the interval (I think FTS could probably do it if the clip is long enough).

I'll make the clips quite long like say 30 seconds or a minute each, because you may need to listen to it for a while, as you listen to a long held dyad more details in the texture and pattern of the beating partials etc. may become apparent. Which is also realistic as when tuning then you can play both notes for as long as is required to complete the tuning to the desired level of accuracy.

Robert

--- In tuning@yahoogroups.com, "cameron" <misterbobro@...> wrote:
>
> Great! Make sure that you don't tell us if one is slightly lower than 81:64, one is 81:64, and one slightly higher, for that would make the test results indistinguishable from "which interval is pitched between the other two". Also, a duplicate would be nice to sneak in there, giving four files, two the same pitch (vary the attack times for example, in order to obviate cheating to eliminate the duplicate by means of phase inversion and cancellation :-) )
>
> -Cameron Bobro
>
> --- In tuning@yahoogroups.com, "robert_inventor5" <robertwalker@> wrote:
> >
> > Rightio, that makes sense too.
> >
> > Yes - well testing it here with a pure triangle wave, I felt that it was perceptible. But it is so easy to fool yourself when you know what intervals you are playing. Also - it is a long time since I did a lot of microtonal work.
> >
> > Anyway, it needs a blind test.
> >
> > I'll give it a go. Could be fun :).
> >
> > Robert
> >
> > --- In tuning@yahoogroups.com, "cameron" <misterbobro@> wrote:
> > >
> > > My mention of 81:64 was to point out that it contains a "bearing plan". It's a very simple bearing plan, too- four pure fifths octave reduced. My point is that when we look at the allegedly complex intervals of medieval and ancient theorists, we often find that what might appear to be extravagantly complex figures are upon closer inspection quite simple in terms of "real life". There are many "big number" ratios of medieval Islamic theorists which are Pythagorean intervals and simple divisions thereof. This is not "numerology", it is concrete mechanical instruction.
> > >
> > > Here is an example:
> > >
> > > http://www.chrysalis-foundation.org/Al-Farabi's_'Uds.htm
> > >
> > > This is from Cris Forster's book, which I can hardly wait to read (my friend forgot to bring it over, maybe this weekend though).
> > >
> > > This isn't numerology. It's actually dull as dishwater and disappointly simple in terms of number, but exciting for those with hands-on approachs to tuning. Kind of like how we can get all hot and bothered inspecting a set of good chisels. :-)
> > >
> > > Now that you inspect 81:64 as you have, though, I think what you propose is very interesting! Beats me (heh heh) if this is perceptible, and I do believe that such things are much more likely to be perceptible when in physical contact with a resonating acoustic
> > > instrument. But if you'd do some blind tests, that would be great!
> > >
> > > -Cameron Bobro
> > >
> > >
> > >
> > >
> > > --- In tuning@yahoogroups.com, "robert_inventor5" <robertwalker@> wrote:
> > > >
> > > > Hi everyone, thought I might start a new thread and post some predicted
> > > > partials numbers to give an idea of how complex rational intervals may
> > > > sound different due to the polyrhythmic nature of the beating partals.
> > > > So here is 81/64
> > > > Interval 81/64 between frequencies 261.6255653 Hz and 331.11985608
> > > > Hz.Expected difference tone 69.49429078 Hz is 17/64 below lowest pitch
> > > > noteBeats per sec. up to 32nd harmonic and up to 20 beats per sec.
> > > > beats harmon. (harm,) freq of harmonic (freq. of upper note
> > > > harmonic)16.35159783 5th (4th) 1308.127826503 Hz (1324.4794243343
> > > > Hz)4.08789946 19th (15th) 4970.8857407114 Hz (4966.7978412536
> > > > Hz)12.26369837 24th (19th) 6279.0135672144 Hz (6291.2772655878 Hz)
> > > > Table shows expected beat patterns for harmonic timbres.
> > > > There 81/64 is 407.82 cents.
> > > >
> > > > As a polyrhythm it's 4 : 1 : 3It seems not impossible that an
> > > > experienced instrumentalist could come to recognise 81/64 by that
> > > > distinctive polyrhythm in the beating partials.
> > > > By comparision, this is 408.0 cents
> > > > Interval 408.0 between frequencies 261.6255653 Hz and 331.15428443
> > > > Hz.Expected difference tone 69.52871913 Hz is -2294.187 below lowest
> > > > pitch noteBeats per sec. up to 32nd harmonic and up to 20 beats per sec.
> > > > beats harmon. (harm,) freq of harmonic (freq. of upper note
> > > > harmonic)16.48931122 5th (4th) 1308.127826503 Hz (1324.6171377217
> > > > Hz)3.57147425 19th (15th) 4970.8857407114 Hz (4967.3142664565
> > > > Hz)12.91783696 24th (19th) 6279.0135672144 Hz (6291.9314041783 Hz)
> > > > and here is 407.0 cents
> > > > Interval 407.0 between frequencies 261.6255653 Hz and 330.96305745
> > > > Hz.Expected difference tone 69.33749215 Hz is -2298.955 below lowest
> > > > pitch noteBeats per sec. up to 32nd harmonic and up to 20 beats per sec.
> > > > beats harmon. (harm,) freq of harmonic (freq. of upper note
> > > > harmonic)15.72440329 5th (4th) 1308.127826503 Hz (1323.8522297951
> > > > Hz)6.43987898 19th (15th) 4970.8857407114 Hz (4964.4458617318
> > > > Hz)9.28452431 24th (19th) 6279.0135672144 Hz (6288.2980915269 Hz)
> > > >
> > > > 15.72440329 / 6.43987898 = 2.44172341
> > > >
> > > > So if you can hear both beating partials, 407.0 should be easily
> > > > distinguishable from 81/64.
> > > > 16.48931122 / 3.57147425 = 4.61694809
> > > > So to a keen ear, this also should be noticeable, 4.17 to 1 should sound
> > > > noticeably uneven compared to a 4 1 exact polyrhythm
> > > > In fact these results seem to suggest that an interval such as 81/64
> > > > should be tunable more exactly by ear than a simpler interval like say
> > > > 5/4. That is - once you get to know what to listen out for in the
> > > > "texture" of the interval.
> > > > I've tested it here with pure triangle waves rich in partials. Can post
> > > > some audio clips so you can all give it a go - maybe even a test, not
> > > > say which is which, post three examples of 407.0, 81/64, and 408.0 as
> > > > pure triangle waves, of course not permitted to analyse it and so
> > > > "cheat", and see which of you can distinguish them by ear :).
> > > > Not just totally blind - could have the three files labelled - and then
> > > > the same three recordings this time not labelled, and see if you can put
> > > > them in the right order by just listening to them. Seems quite possible
> > > > that quite a few microtonalists would be able to do that, from the
> > > > numbers.
> > > >
> > >
> >
>

Excellent! Looking forward to it, though I'd be quite suprised to be able to distinguish them.

--- In tuning@yahoogroups.com, "robert_inventor5" <robertwalker@...> wrote:
>
> Okay.
>
> Perhaps what I'll do is - first three clips for training purposes, the 407.0, 81/64 and 408.0.
>
> So one can listen and get used to what the 81/64 sounds like with the triangle wave. And see if you think you can distinguish them.
>
> Then add a duplicate of one of the files, not say which, and add an extra clip which will be either 406.0 or 409.0 and again, not say which it is.
>
> Then label those in random order as say A B C D E and then the challenge is to identify the 81/64 and optionally to try to get the 407.0, the 408.0 too. And to find out which of the remaining ones is the duplicate, what it is duplicate of, and which is the extra one, and for a bonus "star" is the extra one 406.0 or 409.0. Just for fun, see if anyone gets them all right, and see how many get the 81/64.
>
> It will have to be the sort of poll where you don't see the results until everyone has voted. Which I see is an option here. Also - I wonder if I should display users's identities for the poll results or make it a secret one? Or maybe both, maybe users who want to be identified can use the non secret version of the poll.
>
> Or - maybe should have a separate poll for people who think they can distinguish the intervals and for those who think they can't after listening to the training clips. Because if you don't think you can hear any difference, your results may be close to random - which may skew the poll and hide the signal you are looking for from people who feel they can distinguish them.
>
> Or something, needs some thought. I've got to get back to other things, getting a bit distracted (though fascinated) by all this, so I think I'll leave it a day or two and do it maybe towards end of the week or early next week.
>
> The intervals are so close together that it could be quite a challenge to answer the question "which is pitched between the other two".
>
> So anyway perhaps can't do a perfect test but at least do my best to set up the situation so that it is highly likely near to 100% that musicians will do the identification by listening to the texture or beat patterns etc. of the dyads.
>
> As for cheating - well I think I'll just say that if you have any way of distinguishing them by analysis, please don't use them, so we can do it properly.
>
> You could probably distinguish them using Tune Smithy's various frequency analysis tools - though they are quite hard to use at present in version 3.1, and distinguishing the 81/64 from the 408.0 is likely to push the limits of sensitivity of most ways of attempting to measure the interval (I think FTS could probably do it if the clip is long enough).
>
> I'll make the clips quite long like say 30 seconds or a minute each, because you may need to listen to it for a while, as you listen to a long held dyad more details in the texture and pattern of the beating partials etc. may become apparent. Which is also realistic as when tuning then you can play both notes for as long as is required to complete the tuning to the desired level of accuracy.
>
> Robert
>
> --- In tuning@yahoogroups.com, "cameron" <misterbobro@> wrote:
> >
> > Great! Make sure that you don't tell us if one is slightly lower than 81:64, one is 81:64, and one slightly higher, for that would make the test results indistinguishable from "which interval is pitched between the other two". Also, a duplicate would be nice to sneak in there, giving four files, two the same pitch (vary the attack times for example, in order to obviate cheating to eliminate the duplicate by means of phase inversion and cancellation :-) )
> >
> > -Cameron Bobro
> >
> > --- In tuning@yahoogroups.com, "robert_inventor5" <robertwalker@> wrote:
> > >
> > > Rightio, that makes sense too.
> > >
> > > Yes - well testing it here with a pure triangle wave, I felt that it was perceptible. But it is so easy to fool yourself when you know what intervals you are playing. Also - it is a long time since I did a lot of microtonal work.
> > >
> > > Anyway, it needs a blind test.
> > >
> > > I'll give it a go. Could be fun :).
> > >
> > > Robert
> > >
> > > --- In tuning@yahoogroups.com, "cameron" <misterbobro@> wrote:
> > > >
> > > > My mention of 81:64 was to point out that it contains a "bearing plan". It's a very simple bearing plan, too- four pure fifths octave reduced. My point is that when we look at the allegedly complex intervals of medieval and ancient theorists, we often find that what might appear to be extravagantly complex figures are upon closer inspection quite simple in terms of "real life". There are many "big number" ratios of medieval Islamic theorists which are Pythagorean intervals and simple divisions thereof. This is not "numerology", it is concrete mechanical instruction.
> > > >
> > > > Here is an example:
> > > >
> > > > http://www.chrysalis-foundation.org/Al-Farabi's_'Uds.htm
> > > >
> > > > This is from Cris Forster's book, which I can hardly wait to read (my friend forgot to bring it over, maybe this weekend though).
> > > >
> > > > This isn't numerology. It's actually dull as dishwater and disappointly simple in terms of number, but exciting for those with hands-on approachs to tuning. Kind of like how we can get all hot and bothered inspecting a set of good chisels. :-)
> > > >
> > > > Now that you inspect 81:64 as you have, though, I think what you propose is very interesting! Beats me (heh heh) if this is perceptible, and I do believe that such things are much more likely to be perceptible when in physical contact with a resonating acoustic
> > > > instrument. But if you'd do some blind tests, that would be great!
> > > >
> > > > -Cameron Bobro
> > > >
> > > >
> > > >
> > > >
> > > > --- In tuning@yahoogroups.com, "robert_inventor5" <robertwalker@> wrote:
> > > > >
> > > > > Hi everyone, thought I might start a new thread and post some predicted
> > > > > partials numbers to give an idea of how complex rational intervals may
> > > > > sound different due to the polyrhythmic nature of the beating partals.
> > > > > So here is 81/64
> > > > > Interval 81/64 between frequencies 261.6255653 Hz and 331.11985608
> > > > > Hz.Expected difference tone 69.49429078 Hz is 17/64 below lowest pitch
> > > > > noteBeats per sec. up to 32nd harmonic and up to 20 beats per sec.
> > > > > beats harmon. (harm,) freq of harmonic (freq. of upper note
> > > > > harmonic)16.35159783 5th (4th) 1308.127826503 Hz (1324.4794243343
> > > > > Hz)4.08789946 19th (15th) 4970.8857407114 Hz (4966.7978412536
> > > > > Hz)12.26369837 24th (19th) 6279.0135672144 Hz (6291.2772655878 Hz)
> > > > > Table shows expected beat patterns for harmonic timbres.
> > > > > There 81/64 is 407.82 cents.
> > > > >
> > > > > As a polyrhythm it's 4 : 1 : 3It seems not impossible that an
> > > > > experienced instrumentalist could come to recognise 81/64 by that
> > > > > distinctive polyrhythm in the beating partials.
> > > > > By comparision, this is 408.0 cents
> > > > > Interval 408.0 between frequencies 261.6255653 Hz and 331.15428443
> > > > > Hz.Expected difference tone 69.52871913 Hz is -2294.187 below lowest
> > > > > pitch noteBeats per sec. up to 32nd harmonic and up to 20 beats per sec.
> > > > > beats harmon. (harm,) freq of harmonic (freq. of upper note
> > > > > harmonic)16.48931122 5th (4th) 1308.127826503 Hz (1324.6171377217
> > > > > Hz)3.57147425 19th (15th) 4970.8857407114 Hz (4967.3142664565
> > > > > Hz)12.91783696 24th (19th) 6279.0135672144 Hz (6291.9314041783 Hz)
> > > > > and here is 407.0 cents
> > > > > Interval 407.0 between frequencies 261.6255653 Hz and 330.96305745
> > > > > Hz.Expected difference tone 69.33749215 Hz is -2298.955 below lowest
> > > > > pitch noteBeats per sec. up to 32nd harmonic and up to 20 beats per sec.
> > > > > beats harmon. (harm,) freq of harmonic (freq. of upper note
> > > > > harmonic)15.72440329 5th (4th) 1308.127826503 Hz (1323.8522297951
> > > > > Hz)6.43987898 19th (15th) 4970.8857407114 Hz (4964.4458617318
> > > > > Hz)9.28452431 24th (19th) 6279.0135672144 Hz (6288.2980915269 Hz)
> > > > >
> > > > > 15.72440329 / 6.43987898 = 2.44172341
> > > > >
> > > > > So if you can hear both beating partials, 407.0 should be easily
> > > > > distinguishable from 81/64.
> > > > > 16.48931122 / 3.57147425 = 4.61694809
> > > > > So to a keen ear, this also should be noticeable, 4.17 to 1 should sound
> > > > > noticeably uneven compared to a 4 1 exact polyrhythm
> > > > > In fact these results seem to suggest that an interval such as 81/64
> > > > > should be tunable more exactly by ear than a simpler interval like say
> > > > > 5/4. That is - once you get to know what to listen out for in the
> > > > > "texture" of the interval.
> > > > > I've tested it here with pure triangle waves rich in partials. Can post
> > > > > some audio clips so you can all give it a go - maybe even a test, not
> > > > > say which is which, post three examples of 407.0, 81/64, and 408.0 as
> > > > > pure triangle waves, of course not permitted to analyse it and so
> > > > > "cheat", and see which of you can distinguish them by ear :).
> > > > > Not just totally blind - could have the three files labelled - and then
> > > > > the same three recordings this time not labelled, and see if you can put
> > > > > them in the right order by just listening to them. Seems quite possible
> > > > > that quite a few microtonalists would be able to do that, from the
> > > > > numbers.
> > > > >
> > > >
> > >
> >
>

I realize now they did this experiment with 6 different kinds of 'thirds' at the univ. at Wollongong.
They tested people over time and the preliminary results were that peoples scores would improve in identifying them.
It fell apart at a certain point cause the people being tested got bored listening to recordings of electronic dyads on a daily basis.
No ones score got worse

--- In tuning@yahoogroups.com, "robert_inventor5" <robertwalker@...> wrote:
>
> Okay.
>
> Perhaps what I'll do is - first three clips for training purposes, the 407.0, 81/64 and 408.0.
>
> So one can listen and get used to what the 81/64 sounds like with the triangle wave. And see if you think you can distinguish them.
>
> Then add a duplicate of one of the files, not say which, and add an extra clip which will be either 406.0 or 409.0 and again, not say which it is.
>
> Then label those in random order as say A B C D E and then the challenge is to identify the 81/64 and optionally to try to get the 407.0, the 408.0 too. And to find out which of the remaining ones is the duplicate, what it is duplicate of, and which is the extra one, and for a bonus "star" is the extra one 406.0 or 409.0. Just for fun, see if anyone gets them all right, and see how many get the 81/64.
>
> It will have to be the sort of poll where you don't see the results until everyone has voted. Which I see is an option here. Also - I wonder if I should display users's identities for the poll results or make it a secret one? Or maybe both, maybe users who want to be identified can use the non secret version of the poll.
>
> Or - maybe should have a separate poll for people who think they can distinguish the intervals and for those who think they can't after listening to the training clips. Because if you don't think you can hear any difference, your results may be close to random - which may skew the poll and hide the signal you are looking for from people who feel they can distinguish them.
>
> Or something, needs some thought. I've got to get back to other things, getting a bit distracted (though fascinated) by all this, so I think I'll leave it a day or two and do it maybe towards end of the week or early next week.
>
> The intervals are so close together that it could be quite a challenge to answer the question "which is pitched between the other two".
>
> So anyway perhaps can't do a perfect test but at least do my best to set up the situation so that it is highly likely near to 100% that musicians will do the identification by listening to the texture or beat patterns etc. of the dyads.
>
> As for cheating - well I think I'll just say that if you have any way of distinguishing them by analysis, please don't use them, so we can do it properly.
>
> You could probably distinguish them using Tune Smithy's various frequency analysis tools - though they are quite hard to use at present in version 3.1, and distinguishing the 81/64 from the 408.0 is likely to push the limits of sensitivity of most ways of attempting to measure the interval (I think FTS could probably do it if the clip is long enough).
>
> I'll make the clips quite long like say 30 seconds or a minute each, because you may need to listen to it for a while, as you listen to a long held dyad more details in the texture and pattern of the beating partials etc. may become apparent. Which is also realistic as when tuning then you can play both notes for as long as is required to complete the tuning to the desired level of accuracy.
>
> Robert
>
> --- In tuning@yahoogroups.com, "cameron" <misterbobro@> wrote:
> >
> > Great! Make sure that you don't tell us if one is slightly lower than 81:64, one is 81:64, and one slightly higher, for that would make the test results indistinguishable from "which interval is pitched between the other two". Also, a duplicate would be nice to sneak in there, giving four files, two the same pitch (vary the attack times for example, in order to obviate cheating to eliminate the duplicate by means of phase inversion and cancellation :-) )
> >
> > -Cameron Bobro
> >
> > --- In tuning@yahoogroups.com, "robert_inventor5" <robertwalker@> wrote:
> > >
> > > Rightio, that makes sense too.
> > >
> > > Yes - well testing it here with a pure triangle wave, I felt that it was perceptible. But it is so easy to fool yourself when you know what intervals you are playing. Also - it is a long time since I did a lot of microtonal work.
> > >
> > > Anyway, it needs a blind test.
> > >
> > > I'll give it a go. Could be fun :).
> > >
> > > Robert
> > >
> > > --- In tuning@yahoogroups.com, "cameron" <misterbobro@> wrote:
> > > >
> > > > My mention of 81:64 was to point out that it contains a "bearing plan". It's a very simple bearing plan, too- four pure fifths octave reduced. My point is that when we look at the allegedly complex intervals of medieval and ancient theorists, we often find that what might appear to be extravagantly complex figures are upon closer inspection quite simple in terms of "real life". There are many "big number" ratios of medieval Islamic theorists which are Pythagorean intervals and simple divisions thereof. This is not "numerology", it is concrete mechanical instruction.
> > > >
> > > > Here is an example:
> > > >
> > > > http://www.chrysalis-foundation.org/Al-Farabi's_'Uds.htm
> > > >
> > > > This is from Cris Forster's book, which I can hardly wait to read (my friend forgot to bring it over, maybe this weekend though).
> > > >
> > > > This isn't numerology. It's actually dull as dishwater and disappointly simple in terms of number, but exciting for those with hands-on approachs to tuning. Kind of like how we can get all hot and bothered inspecting a set of good chisels. :-)
> > > >
> > > > Now that you inspect 81:64 as you have, though, I think what you propose is very interesting! Beats me (heh heh) if this is perceptible, and I do believe that such things are much more likely to be perceptible when in physical contact with a resonating acoustic
> > > > instrument. But if you'd do some blind tests, that would be great!
> > > >
> > > > -Cameron Bobro
> > > >
> > > >
> > > >
> > > >
> > > > --- In tuning@yahoogroups.com, "robert_inventor5" <robertwalker@> wrote:
> > > > >
> > > > > Hi everyone, thought I might start a new thread and post some predicted
> > > > > partials numbers to give an idea of how complex rational intervals may
> > > > > sound different due to the polyrhythmic nature of the beating partals.
> > > > > So here is 81/64
> > > > > Interval 81/64 between frequencies 261.6255653 Hz and 331.11985608
> > > > > Hz.Expected difference tone 69.49429078 Hz is 17/64 below lowest pitch
> > > > > noteBeats per sec. up to 32nd harmonic and up to 20 beats per sec.
> > > > > beats harmon. (harm,) freq of harmonic (freq. of upper note
> > > > > harmonic)16.35159783 5th (4th) 1308.127826503 Hz (1324.4794243343
> > > > > Hz)4.08789946 19th (15th) 4970.8857407114 Hz (4966.7978412536
> > > > > Hz)12.26369837 24th (19th) 6279.0135672144 Hz (6291.2772655878 Hz)
> > > > > Table shows expected beat patterns for harmonic timbres.
> > > > > There 81/64 is 407.82 cents.
> > > > >
> > > > > As a polyrhythm it's 4 : 1 : 3It seems not impossible that an
> > > > > experienced instrumentalist could come to recognise 81/64 by that
> > > > > distinctive polyrhythm in the beating partials.
> > > > > By comparision, this is 408.0 cents
> > > > > Interval 408.0 between frequencies 261.6255653 Hz and 331.15428443
> > > > > Hz.Expected difference tone 69.52871913 Hz is -2294.187 below lowest
> > > > > pitch noteBeats per sec. up to 32nd harmonic and up to 20 beats per sec.
> > > > > beats harmon. (harm,) freq of harmonic (freq. of upper note
> > > > > harmonic)16.48931122 5th (4th) 1308.127826503 Hz (1324.6171377217
> > > > > Hz)3.57147425 19th (15th) 4970.8857407114 Hz (4967.3142664565
> > > > > Hz)12.91783696 24th (19th) 6279.0135672144 Hz (6291.9314041783 Hz)
> > > > > and here is 407.0 cents
> > > > > Interval 407.0 between frequencies 261.6255653 Hz and 330.96305745
> > > > > Hz.Expected difference tone 69.33749215 Hz is -2298.955 below lowest
> > > > > pitch noteBeats per sec. up to 32nd harmonic and up to 20 beats per sec.
> > > > > beats harmon. (harm,) freq of harmonic (freq. of upper note
> > > > > harmonic)15.72440329 5th (4th) 1308.127826503 Hz (1323.8522297951
> > > > > Hz)6.43987898 19th (15th) 4970.8857407114 Hz (4964.4458617318
> > > > > Hz)9.28452431 24th (19th) 6279.0135672144 Hz (6288.2980915269 Hz)
> > > > >
> > > > > 15.72440329 / 6.43987898 = 2.44172341
> > > > >
> > > > > So if you can hear both beating partials, 407.0 should be easily
> > > > > distinguishable from 81/64.
> > > > > 16.48931122 / 3.57147425 = 4.61694809
> > > > > So to a keen ear, this also should be noticeable, 4.17 to 1 should sound
> > > > > noticeably uneven compared to a 4 1 exact polyrhythm
> > > > > In fact these results seem to suggest that an interval such as 81/64
> > > > > should be tunable more exactly by ear than a simpler interval like say
> > > > > 5/4. That is - once you get to know what to listen out for in the
> > > > > "texture" of the interval.
> > > > > I've tested it here with pure triangle waves rich in partials. Can post
> > > > > some audio clips so you can all give it a go - maybe even a test, not
> > > > > say which is which, post three examples of 407.0, 81/64, and 408.0 as
> > > > > pure triangle waves, of course not permitted to analyse it and so
> > > > > "cheat", and see which of you can distinguish them by ear :).
> > > > > Not just totally blind - could have the three files labelled - and then
> > > > > the same three recordings this time not labelled, and see if you can put
> > > > > them in the right order by just listening to them. Seems quite possible
> > > > > that quite a few microtonalists would be able to do that, from the
> > > > > numbers.
> > > > >
> > > >
> > >
> >
>

Okay, great!

I thought I'd try a couple of easier ones too. 11/9 tried that just now and it seems likely to be very easy, just a simple pattern of one beat, high pitched, clear and easy to hear apart from the pitch (I suppose some older listeners like in your eighties or nineties perhaps, if you have lost sensitivity to the very highest pitches might miss it, I could do a lower pitched version just in case).

Might be useful to have another one intermediate in difficulty too.

Will be interested to find out what happens :).

As Kraig says, it's something one can train in and get better at, so if it turns out you don't hear the difference right away - but some people do, then very probably it is just a matter of practice and listening out to lots of thirds (or whatever) carefully, playing them for long periods of time to really take in the details of what you are hearing and paying attention to the texture, or to the patterns of beating partials, or whatever, depending on how one hears the dyad - until you "get it".

Anyway will see what happens.

Robert

--- In tuning@yahoogroups.com, "cameron" <misterbobro@...> wrote:
>
> Excellent! Looking forward to it, though I'd be quite suprised to be able to distinguish them.
>
> --- In tuning@yahoogroups.com, "robert_inventor5" <robertwalker@> wrote:
> >
> > Okay.
> >
> > Perhaps what I'll do is - first three clips for training purposes, the 407.0, 81/64 and 408.0.
> >
> > So one can listen and get used to what the 81/64 sounds like with the triangle wave. And see if you think you can distinguish them.
> >
> > Then add a duplicate of one of the files, not say which, and add an extra clip which will be either 406.0 or 409.0 and again, not say which it is.
> >
> > Then label those in random order as say A B C D E and then the challenge is to identify the 81/64 and optionally to try to get the 407.0, the 408.0 too. And to find out which of the remaining ones is the duplicate, what it is duplicate of, and which is the extra one, and for a bonus "star" is the extra one 406.0 or 409.0. Just for fun, see if anyone gets them all right, and see how many get the 81/64.
> >
> > It will have to be the sort of poll where you don't see the results until everyone has voted. Which I see is an option here. Also - I wonder if I should display users's identities for the poll results or make it a secret one? Or maybe both, maybe users who want to be identified can use the non secret version of the poll.
> >
> > Or - maybe should have a separate poll for people who think they can distinguish the intervals and for those who think they can't after listening to the training clips. Because if you don't think you can hear any difference, your results may be close to random - which may skew the poll and hide the signal you are looking for from people who feel they can distinguish them.
> >
> > Or something, needs some thought. I've got to get back to other things, getting a bit distracted (though fascinated) by all this, so I think I'll leave it a day or two and do it maybe towards end of the week or early next week.
> >
> > The intervals are so close together that it could be quite a challenge to answer the question "which is pitched between the other two".
> >
> > So anyway perhaps can't do a perfect test but at least do my best to set up the situation so that it is highly likely near to 100% that musicians will do the identification by listening to the texture or beat patterns etc. of the dyads.
> >
> > As for cheating - well I think I'll just say that if you have any way of distinguishing them by analysis, please don't use them, so we can do it properly.
> >
> > You could probably distinguish them using Tune Smithy's various frequency analysis tools - though they are quite hard to use at present in version 3.1, and distinguishing the 81/64 from the 408.0 is likely to push the limits of sensitivity of most ways of attempting to measure the interval (I think FTS could probably do it if the clip is long enough).
> >
> > I'll make the clips quite long like say 30 seconds or a minute each, because you may need to listen to it for a while, as you listen to a long held dyad more details in the texture and pattern of the beating partials etc. may become apparent. Which is also realistic as when tuning then you can play both notes for as long as is required to complete the tuning to the desired level of accuracy.
> >
> > Robert
> >
> > --- In tuning@yahoogroups.com, "cameron" <misterbobro@> wrote:
> > >
> > > Great! Make sure that you don't tell us if one is slightly lower than 81:64, one is 81:64, and one slightly higher, for that would make the test results indistinguishable from "which interval is pitched between the other two". Also, a duplicate would be nice to sneak in there, giving four files, two the same pitch (vary the attack times for example, in order to obviate cheating to eliminate the duplicate by means of phase inversion and cancellation :-) )
> > >
> > > -Cameron Bobro
> > >
> > > --- In tuning@yahoogroups.com, "robert_inventor5" <robertwalker@> wrote:
> > > >
> > > > Rightio, that makes sense too.
> > > >
> > > > Yes - well testing it here with a pure triangle wave, I felt that it was perceptible. But it is so easy to fool yourself when you know what intervals you are playing. Also - it is a long time since I did a lot of microtonal work.
> > > >
> > > > Anyway, it needs a blind test.
> > > >
> > > > I'll give it a go. Could be fun :).
> > > >
> > > > Robert
> > > >
> > > > --- In tuning@yahoogroups.com, "cameron" <misterbobro@> wrote:
> > > > >
> > > > > My mention of 81:64 was to point out that it contains a "bearing plan". It's a very simple bearing plan, too- four pure fifths octave reduced. My point is that when we look at the allegedly complex intervals of medieval and ancient theorists, we often find that what might appear to be extravagantly complex figures are upon closer inspection quite simple in terms of "real life". There are many "big number" ratios of medieval Islamic theorists which are Pythagorean intervals and simple divisions thereof. This is not "numerology", it is concrete mechanical instruction.
> > > > >
> > > > > Here is an example:
> > > > >
> > > > > http://www.chrysalis-foundation.org/Al-Farabi's_'Uds.htm
> > > > >
> > > > > This is from Cris Forster's book, which I can hardly wait to read (my friend forgot to bring it over, maybe this weekend though).
> > > > >
> > > > > This isn't numerology. It's actually dull as dishwater and disappointly simple in terms of number, but exciting for those with hands-on approachs to tuning. Kind of like how we can get all hot and bothered inspecting a set of good chisels. :-)
> > > > >
> > > > > Now that you inspect 81:64 as you have, though, I think what you propose is very interesting! Beats me (heh heh) if this is perceptible, and I do believe that such things are much more likely to be perceptible when in physical contact with a resonating acoustic
> > > > > instrument. But if you'd do some blind tests, that would be great!
> > > > >
> > > > > -Cameron Bobro
> > > > >
> > > > >
> > > > >
> > > > >
> > > > > --- In tuning@yahoogroups.com, "robert_inventor5" <robertwalker@> wrote:
> > > > > >
> > > > > > Hi everyone, thought I might start a new thread and post some predicted
> > > > > > partials numbers to give an idea of how complex rational intervals may
> > > > > > sound different due to the polyrhythmic nature of the beating partals.
> > > > > > So here is 81/64
> > > > > > Interval 81/64 between frequencies 261.6255653 Hz and 331.11985608
> > > > > > Hz.Expected difference tone 69.49429078 Hz is 17/64 below lowest pitch
> > > > > > noteBeats per sec. up to 32nd harmonic and up to 20 beats per sec.
> > > > > > beats harmon. (harm,) freq of harmonic (freq. of upper note
> > > > > > harmonic)16.35159783 5th (4th) 1308.127826503 Hz (1324.4794243343
> > > > > > Hz)4.08789946 19th (15th) 4970.8857407114 Hz (4966.7978412536
> > > > > > Hz)12.26369837 24th (19th) 6279.0135672144 Hz (6291.2772655878 Hz)
> > > > > > Table shows expected beat patterns for harmonic timbres.
> > > > > > There 81/64 is 407.82 cents.
> > > > > >
> > > > > > As a polyrhythm it's 4 : 1 : 3It seems not impossible that an
> > > > > > experienced instrumentalist could come to recognise 81/64 by that
> > > > > > distinctive polyrhythm in the beating partials.
> > > > > > By comparision, this is 408.0 cents
> > > > > > Interval 408.0 between frequencies 261.6255653 Hz and 331.15428443
> > > > > > Hz.Expected difference tone 69.52871913 Hz is -2294.187 below lowest
> > > > > > pitch noteBeats per sec. up to 32nd harmonic and up to 20 beats per sec.
> > > > > > beats harmon. (harm,) freq of harmonic (freq. of upper note
> > > > > > harmonic)16.48931122 5th (4th) 1308.127826503 Hz (1324.6171377217
> > > > > > Hz)3.57147425 19th (15th) 4970.8857407114 Hz (4967.3142664565
> > > > > > Hz)12.91783696 24th (19th) 6279.0135672144 Hz (6291.9314041783 Hz)
> > > > > > and here is 407.0 cents
> > > > > > Interval 407.0 between frequencies 261.6255653 Hz and 330.96305745
> > > > > > Hz.Expected difference tone 69.33749215 Hz is -2298.955 below lowest
> > > > > > pitch noteBeats per sec. up to 32nd harmonic and up to 20 beats per sec.
> > > > > > beats harmon. (harm,) freq of harmonic (freq. of upper note
> > > > > > harmonic)15.72440329 5th (4th) 1308.127826503 Hz (1323.8522297951
> > > > > > Hz)6.43987898 19th (15th) 4970.8857407114 Hz (4964.4458617318
> > > > > > Hz)9.28452431 24th (19th) 6279.0135672144 Hz (6288.2980915269 Hz)
> > > > > >
> > > > > > 15.72440329 / 6.43987898 = 2.44172341
> > > > > >
> > > > > > So if you can hear both beating partials, 407.0 should be easily
> > > > > > distinguishable from 81/64.
> > > > > > 16.48931122 / 3.57147425 = 4.61694809
> > > > > > So to a keen ear, this also should be noticeable, 4.17 to 1 should sound
> > > > > > noticeably uneven compared to a 4 1 exact polyrhythm
> > > > > > In fact these results seem to suggest that an interval such as 81/64
> > > > > > should be tunable more exactly by ear than a simpler interval like say
> > > > > > 5/4. That is - once you get to know what to listen out for in the
> > > > > > "texture" of the interval.
> > > > > > I've tested it here with pure triangle waves rich in partials. Can post
> > > > > > some audio clips so you can all give it a go - maybe even a test, not
> > > > > > say which is which, post three examples of 407.0, 81/64, and 408.0 as
> > > > > > pure triangle waves, of course not permitted to analyse it and so
> > > > > > "cheat", and see which of you can distinguish them by ear :).
> > > > > > Not just totally blind - could have the three files labelled - and then
> > > > > > the same three recordings this time not labelled, and see if you can put
> > > > > > them in the right order by just listening to them. Seems quite possible
> > > > > > that quite a few microtonalists would be able to do that, from the
> > > > > > numbers.
> > > > > >
> > > > >
> > > >
> > >
> >
>

Just wanted to say I just placed an order for Cris' book.

Chris

>
> This is from Cris Forster's book, which I can hardly wait to read (my friend forgot to bring it over, maybe this weekend though).
>

Just to say, sorry things are a bit chaotic here - moving out of my room where I've lived for over ten years, preparations for building a new house, and other things, anyway won't go into it. But just to say, I haven't yet done anything about the example clips, or the test idea.

Possibly some time next week, will see.

BTW just noticed Ozan has been banned from the list and really that doesn't seem to be something a moderator should do to me, to ban someone for what appears to an outsider to be some kind of intellectual disagreement about the nature of their research, one that doesn't even seem particularly significant to an outsider to the discussion.

It should be for things like trolling, spamming, repeatedly offensive behaviour (just a few hot words don't count) that sort of thing.

As he said quite rightly, this isn't the Tuning List review, and the moderators aren't reviewers. They are just there to make sure the forum runs smoothly, to intervene to ease over any disagreements if possible, etc.

And if one of the moderators is himself party to a long running dispute with another member of the list, then I think as a matter of policy, he shouldn't also moderate that dispute which he himself is involved in. Rather he (or she but it is a he here) should leave it to one of the other moderators who hopefully will have a more neutral point of view. Apart from division of labour, that presumably is the main reason you have more than one moderator.

Robert

--- In tuning@yahoogroups.com, "robert_inventor5" <robertwalker@...> wrote:
>
> Okay, great!
>
> I thought I'd try a couple of easier ones too. 11/9 tried that just now and it seems likely to be very easy, just a simple pattern of one beat, high pitched, clear and easy to hear apart from the pitch (I suppose some older listeners like in your eighties or nineties perhaps, if you have lost sensitivity to the very highest pitches might miss it, I could do a lower pitched version just in case).
>
> Might be useful to have another one intermediate in difficulty too.
>
> Will be interested to find out what happens :).
>
> As Kraig says, it's something one can train in and get better at, so if it turns out you don't hear the difference right away - but some people do, then very probably it is just a matter of practice and listening out to lots of thirds (or whatever) carefully, playing them for long periods of time to really take in the details of what you are hearing and paying attention to the texture, or to the patterns of beating partials, or whatever, depending on how one hears the dyad - until you "get it".
>
> Anyway will see what happens.
>
> Robert
>
> --- In tuning@yahoogroups.com, "cameron" <misterbobro@> wrote:
> >
> > Excellent! Looking forward to it, though I'd be quite suprised to be able to distinguish them.
> >
> > --- In tuning@yahoogroups.com, "robert_inventor5" <robertwalker@> wrote:
> > >
> > > Okay.
> > >
> > > Perhaps what I'll do is - first three clips for training purposes, the 407.0, 81/64 and 408.0.
> > >
> > > So one can listen and get used to what the 81/64 sounds like with the triangle wave. And see if you think you can distinguish them.
> > >
> > > Then add a duplicate of one of the files, not say which, and add an extra clip which will be either 406.0 or 409.0 and again, not say which it is.
> > >
> > > Then label those in random order as say A B C D E and then the challenge is to identify the 81/64 and optionally to try to get the 407.0, the 408.0 too. And to find out which of the remaining ones is the duplicate, what it is duplicate of, and which is the extra one, and for a bonus "star" is the extra one 406.0 or 409.0. Just for fun, see if anyone gets them all right, and see how many get the 81/64.
> > >
> > > It will have to be the sort of poll where you don't see the results until everyone has voted. Which I see is an option here. Also - I wonder if I should display users's identities for the poll results or make it a secret one? Or maybe both, maybe users who want to be identified can use the non secret version of the poll.
> > >
> > > Or - maybe should have a separate poll for people who think they can distinguish the intervals and for those who think they can't after listening to the training clips. Because if you don't think you can hear any difference, your results may be close to random - which may skew the poll and hide the signal you are looking for from people who feel they can distinguish them.
> > >
> > > Or something, needs some thought. I've got to get back to other things, getting a bit distracted (though fascinated) by all this, so I think I'll leave it a day or two and do it maybe towards end of the week or early next week.
> > >
> > > The intervals are so close together that it could be quite a challenge to answer the question "which is pitched between the other two".
> > >
> > > So anyway perhaps can't do a perfect test but at least do my best to set up the situation so that it is highly likely near to 100% that musicians will do the identification by listening to the texture or beat patterns etc. of the dyads.
> > >
> > > As for cheating - well I think I'll just say that if you have any way of distinguishing them by analysis, please don't use them, so we can do it properly.
> > >
> > > You could probably distinguish them using Tune Smithy's various frequency analysis tools - though they are quite hard to use at present in version 3.1, and distinguishing the 81/64 from the 408.0 is likely to push the limits of sensitivity of most ways of attempting to measure the interval (I think FTS could probably do it if the clip is long enough).
> > >
> > > I'll make the clips quite long like say 30 seconds or a minute each, because you may need to listen to it for a while, as you listen to a long held dyad more details in the texture and pattern of the beating partials etc. may become apparent. Which is also realistic as when tuning then you can play both notes for as long as is required to complete the tuning to the desired level of accuracy.
> > >
> > > Robert
> > >
> > > --- In tuning@yahoogroups.com, "cameron" <misterbobro@> wrote:
> > > >
> > > > Great! Make sure that you don't tell us if one is slightly lower than 81:64, one is 81:64, and one slightly higher, for that would make the test results indistinguishable from "which interval is pitched between the other two". Also, a duplicate would be nice to sneak in there, giving four files, two the same pitch (vary the attack times for example, in order to obviate cheating to eliminate the duplicate by means of phase inversion and cancellation :-) )
> > > >
> > > > -Cameron Bobro
> > > >
> > > > --- In tuning@yahoogroups.com, "robert_inventor5" <robertwalker@> wrote:
> > > > >
> > > > > Rightio, that makes sense too.
> > > > >
> > > > > Yes - well testing it here with a pure triangle wave, I felt that it was perceptible. But it is so easy to fool yourself when you know what intervals you are playing. Also - it is a long time since I did a lot of microtonal work.
> > > > >
> > > > > Anyway, it needs a blind test.
> > > > >
> > > > > I'll give it a go. Could be fun :).
> > > > >
> > > > > Robert
> > > > >
> > > > > --- In tuning@yahoogroups.com, "cameron" <misterbobro@> wrote:
> > > > > >
> > > > > > My mention of 81:64 was to point out that it contains a "bearing plan". It's a very simple bearing plan, too- four pure fifths octave reduced. My point is that when we look at the allegedly complex intervals of medieval and ancient theorists, we often find that what might appear to be extravagantly complex figures are upon closer inspection quite simple in terms of "real life". There are many "big number" ratios of medieval Islamic theorists which are Pythagorean intervals and simple divisions thereof. This is not "numerology", it is concrete mechanical instruction.
> > > > > >
> > > > > > Here is an example:
> > > > > >
> > > > > > http://www.chrysalis-foundation.org/Al-Farabi's_'Uds.htm
> > > > > >
> > > > > > This is from Cris Forster's book, which I can hardly wait to read (my friend forgot to bring it over, maybe this weekend though).
> > > > > >
> > > > > > This isn't numerology. It's actually dull as dishwater and disappointly simple in terms of number, but exciting for those with hands-on approachs to tuning. Kind of like how we can get all hot and bothered inspecting a set of good chisels. :-)
> > > > > >
> > > > > > Now that you inspect 81:64 as you have, though, I think what you propose is very interesting! Beats me (heh heh) if this is perceptible, and I do believe that such things are much more likely to be perceptible when in physical contact with a resonating acoustic
> > > > > > instrument. But if you'd do some blind tests, that would be great!
> > > > > >
> > > > > > -Cameron Bobro
> > > > > >
> > > > > >
> > > > > >
> > > > > >
> > > > > > --- In tuning@yahoogroups.com, "robert_inventor5" <robertwalker@> wrote:
> > > > > > >
> > > > > > > Hi everyone, thought I might start a new thread and post some predicted
> > > > > > > partials numbers to give an idea of how complex rational intervals may
> > > > > > > sound different due to the polyrhythmic nature of the beating partals.
> > > > > > > So here is 81/64
> > > > > > > Interval 81/64 between frequencies 261.6255653 Hz and 331.11985608
> > > > > > > Hz.Expected difference tone 69.49429078 Hz is 17/64 below lowest pitch
> > > > > > > noteBeats per sec. up to 32nd harmonic and up to 20 beats per sec.
> > > > > > > beats harmon. (harm,) freq of harmonic (freq. of upper note
> > > > > > > harmonic)16.35159783 5th (4th) 1308.127826503 Hz (1324.4794243343
> > > > > > > Hz)4.08789946 19th (15th) 4970.8857407114 Hz (4966.7978412536
> > > > > > > Hz)12.26369837 24th (19th) 6279.0135672144 Hz (6291.2772655878 Hz)
> > > > > > > Table shows expected beat patterns for harmonic timbres.
> > > > > > > There 81/64 is 407.82 cents.
> > > > > > >
> > > > > > > As a polyrhythm it's 4 : 1 : 3It seems not impossible that an
> > > > > > > experienced instrumentalist could come to recognise 81/64 by that
> > > > > > > distinctive polyrhythm in the beating partials.
> > > > > > > By comparision, this is 408.0 cents
> > > > > > > Interval 408.0 between frequencies 261.6255653 Hz and 331.15428443
> > > > > > > Hz.Expected difference tone 69.52871913 Hz is -2294.187 below lowest
> > > > > > > pitch noteBeats per sec. up to 32nd harmonic and up to 20 beats per sec.
> > > > > > > beats harmon. (harm,) freq of harmonic (freq. of upper note
> > > > > > > harmonic)16.48931122 5th (4th) 1308.127826503 Hz (1324.6171377217
> > > > > > > Hz)3.57147425 19th (15th) 4970.8857407114 Hz (4967.3142664565
> > > > > > > Hz)12.91783696 24th (19th) 6279.0135672144 Hz (6291.9314041783 Hz)
> > > > > > > and here is 407.0 cents
> > > > > > > Interval 407.0 between frequencies 261.6255653 Hz and 330.96305745
> > > > > > > Hz.Expected difference tone 69.33749215 Hz is -2298.955 below lowest
> > > > > > > pitch noteBeats per sec. up to 32nd harmonic and up to 20 beats per sec.
> > > > > > > beats harmon. (harm,) freq of harmonic (freq. of upper note
> > > > > > > harmonic)15.72440329 5th (4th) 1308.127826503 Hz (1323.8522297951
> > > > > > > Hz)6.43987898 19th (15th) 4970.8857407114 Hz (4964.4458617318
> > > > > > > Hz)9.28452431 24th (19th) 6279.0135672144 Hz (6288.2980915269 Hz)
> > > > > > >
> > > > > > > 15.72440329 / 6.43987898 = 2.44172341
> > > > > > >
> > > > > > > So if you can hear both beating partials, 407.0 should be easily
> > > > > > > distinguishable from 81/64.
> > > > > > > 16.48931122 / 3.57147425 = 4.61694809
> > > > > > > So to a keen ear, this also should be noticeable, 4.17 to 1 should sound
> > > > > > > noticeably uneven compared to a 4 1 exact polyrhythm
> > > > > > > In fact these results seem to suggest that an interval such as 81/64
> > > > > > > should be tunable more exactly by ear than a simpler interval like say
> > > > > > > 5/4. That is - once you get to know what to listen out for in the
> > > > > > > "texture" of the interval.
> > > > > > > I've tested it here with pure triangle waves rich in partials. Can post
> > > > > > > some audio clips so you can all give it a go - maybe even a test, not
> > > > > > > say which is which, post three examples of 407.0, 81/64, and 408.0 as
> > > > > > > pure triangle waves, of course not permitted to analyse it and so
> > > > > > > "cheat", and see which of you can distinguish them by ear :).
> > > > > > > Not just totally blind - could have the three files labelled - and then
> > > > > > > the same three recordings this time not labelled, and see if you can put
> > > > > > > them in the right order by just listening to them. Seems quite possible
> > > > > > > that quite a few microtonalists would be able to do that, from the
> > > > > > > numbers.
> > > > > > >
> > > > > >
> > > > >
> > > >
> > >
> >
>

Hi Robert,

Good luck with your move.

-Carl

--- In tuning@yahoogroups.com, "robert_inventor5" <robertwalker@...> wrote:

> BTW just noticed Ozan has been banned from the list and really that doesn't seem to be something a moderator should do to me, to ban someone for what appears to an outsider to be some kind of intellectual disagreement about the nature of their research, one that doesn't even seem particularly significant to an outsider to the discussion.

When Carl said he had been banned I checked and saw nothing about it under moderator activity, but apparently he really has been banned and such things do not appear.

I don't think you can characterize it as a matter of intellectual disagreement as such, but I don't see why there was any need to go nuclear given the less drastic alternatives available.

Okay, I thought it was an intellectual disagreement about theoretical ideas behind Maqam tunings, perhaps I got the wrong idea.

At any rate, whatever the debate was about, reasonably normal for a somewhat heated on-line debate - apart from banning.

Yes glad you agree the response is completely out of proportion. I think that you just can't be objective and make the best decisions when you are yourself one of the participants in a heated debate.

Instant banning should only be done for spammers and trolls where there is no doubt at all about their intentions, e.g. if obviously not in the least interested in the topic for the group.

For anyone else, the moderator should talk it over with them first, make sure they understand the group policies and the reason why banning is contemplated, and give them an opportunity to do something about it first. And if they persist and are banned, should be clear to the entire group why they were banned.

I think just about everyone would agree on that. When people get instantly banned then go to other groups and say that they don't know why they were banned from the tuning list, and get on amicably with the posters in those other groups on related topics - and when most people in the original group also can't see why they were banned either - something a bit odd is going on...

Robert

--- In tuning@yahoogroups.com, "genewardsmith" <genewardsmith@...> wrote:
>
>
>
> --- In tuning@yahoogroups.com, "robert_inventor5" <robertwalker@> wrote:
>
> > BTW just noticed Ozan has been banned from the list and really that doesn't seem to be something a moderator should do to me, to ban someone for what appears to an outsider to be some kind of intellectual disagreement about the nature of their research, one that doesn't even seem particularly significant to an outsider to the discussion.
>
> When Carl said he had been banned I checked and saw nothing about it under moderator activity, but apparently he really has been banned and such things do not appear.
>
> I don't think you can characterize it as a matter of intellectual disagreement as such, but I don't see why there was any need to go nuclear given the less drastic alternatives available.
>

Hi Carl,

Thanks for the good luck. Moving tomorrow. Place is a growing pile of boxes right now.

Robert

--- In tuning@yahoogroups.com, "Carl Lumma" <carl@...> wrote:
>
> Hi Robert,
>
> Good luck with your move.
>
> -Carl
>

Robert>"I think just about everyone would agree on that. When people get
instantly banned then go to other groups and say that they don't know why they
were banned from the tuning list, and get on amicably with the posters in those
other groups on related topics - and when most people in the original group also
can't see why they were banned either - something a bit odd is going on..."

This seems to happen often in, say, the MMM and tuning-research groups.
Often someone thrown out of here in the past ends up getting along fine in those
groups. I've even noticed people who name-call in this group do not do so in
other groups, namely on the grounds of "I'm smarter than you, so be a good group
member and be quiet while the 'real experts' speak".
Why? It almost seems as if flaming has become a mark of experteeism over
here and the flamers often pose themselves as "cleaning the idiots off the
list". However the people flamed and often eventually thrown out, oddly
enough, often establish on other groups that they are from from the "idiots"
they were portrayed as on the Tuning list. Either way, call it "good group
intellectual standards" or what ever you want, but it seems clear to me what
such actions do: they make the tuning list, moreover anything or anyone else,
just plain old look bad, confused, and sometimes downright dishonest.

I think what Cameron is trying to do with the wild Maqam thread is admirable:
say that a scale's "ethnic" validity can be fairly clearly based on if it
contains certain intervals important in a culture. People can say they disagree
with the goal...but at least they should be able to admit "even if I don't agree
with the goal, I agree said method does a good/bad job of acheiving said goal"
by simply stating how many dyads are captured well. This gets a bit flaky with
things like consonance where everyone has a certain degree of subjective opinion
(especially with regards to 7+ odd limit ratios and chords). But, even in
those cases, I think one good "non-debatable" comparison point option is to say
"this scale is created with the goal of getting as many dyads within the set of
*list of dyads*...how well do you think it conforms?". And I'm pretty sure
Ozan's scale system, for example, would conform quite well to a relatively huge
list of dyads commonly used in several different types of Maqams, for example...

--- In tuning@yahoogroups.com, Michael <djtrancendance@...> wrote:
> But, even in
> those cases, I think one good "non-debatable" comparison point option is to say
> "this scale is created with the goal of getting as many dyads within the set of
> *list of dyads*...how well do you think it conforms?". And I'm pretty sure
> Ozan's scale system, for example, would conform quite well to a relatively huge
> list of dyads commonly used in several different types of Maqams, for example...
>

Another method would be to get a list of scales, with some specified error limits on the notes of the scales such as +-5 cents. Since Ozan's system is a MOS, the number of copies of each scale can easily be computed from the Graham complexity of the scale.