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#2388320 - 02/19/15 02:00 PM Perception of tones, partials and beats
Withindale Offline
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Registered: 02/09/11
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Loc: Suffolk, England
This topic just came up, off topic, in the the SBI vs RBI thread. Sounds worth a discussion? The questions elude me but I am sure the answers would be interesting. I'd like to enhance my perception!
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Ian Russell
Schiedmayer & Soehne, 1925 Model 14, 55" upright
Ibach, 1922 49" upright (project piano)

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#2388354 - 02/19/15 04:30 PM Re: Perception of tones, partials and beats [Re: Withindale]
David Jenson Offline
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Registered: 10/22/06
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Loc: Maine
Huh? They are there. You perceive them by listening. You enhance your perception by practicing the act of listening carefully.
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#2388363 - 02/19/15 04:54 PM Re: Perception of tones, partials and beats [Re: Withindale]
Withindale Offline
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Loc: Suffolk, England
Listening, sure.

For instance, from the other thread, do you hear F3-A3 beating or F3-A3 beating at A5? The score so far is two for beating and one, or maybe everyone else, for beating at A5.

With practice, when I play F3 should I be able to hear and distinguish F3, F4, C5, F5 and A5?
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Ian Russell
Schiedmayer & Soehne, 1925 Model 14, 55" upright
Ibach, 1922 49" upright (project piano)

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#2388373 - 02/19/15 05:30 PM Re: Perception of tones, partials and beats [Re: Withindale]
pyropaul Offline
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Registered: 11/16/10
Posts: 209
Loc: Montreal
Interesting, for 4ths and 5ths, I hear the beat at the coincident partial, but for 3rd, I hear it as an envelope modulation that modulates the whole "chord" sounds - but if I listen really hard, I can also hear the coincident partials beating too. So there is a bit of truth to what BDB says, though the partials are definitely audible and can be heard beating clearly for the SBIs.

Paul

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#2388427 - 02/19/15 08:39 PM Re: Perception of tones, partials and beats [Re: Withindale]
Ed McMorrow, RPT Offline
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Registered: 12/09/12
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Loc: Seattle, WA USA
Yes, you should be able to discern the first five partials of F3.
You can point your ear in that direction by holding down the A5 key and playing F3 and then holding it while releasing A5.

You can also hear the difference tones between the fundamentals especially with minor and Major 2nds.
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#2388566 - 02/20/15 07:36 AM Re: Perception of tones, partials and beats [Re: Withindale]
Mark R. Offline
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Registered: 07/31/09
Posts: 2117
Loc: Pretoria, South Africa
Firstly,
In the other thread, I forgot to multiply my frequencies with 2π, as Tunewerk correctly pointed out. However, my basic point stands.

Secondly, from that other thread:

Originally Posted By BDB
Originally Posted By Mark R.
Apologies for the off-topic, but as long as BDB keeps posting his "sums of sines", I'll keep posting this question about common multiples, i.e. coincident partials.


And as long as you refuse to look at the graphs, which show what you are asking very clearly, I will continue to assume that you do not really want to understand.


How would you know that I haven't looked at graphs? After you posted some graphs earlier, I've actually gone further and made some of my own!

In a plot of
y = sin(2π*175x) + sin(2π*220x)
I see a beat, but I don't see any presence of a 2π*880 frequency. If you do, or anyone else does, I'd be glad to have it pointed out to me.

If I check chromatic M3s, e.g.F3-A3, F#3-A#3, G3-B3, etc., I clearly hear the beats at A5, A#5, B5, etc.
Similarly, m3s F3-G#3, F#3-A3, G3-A#3, etc., I clearly hear beating at C6, C#6, D6, etc.

If the sum-of-sines model can explain this phenomenon, believe you me, I'm all ears to read an explanation!

But if the model cannot explain the pitches of the beats, it is clearly an insufficient model, so why should we accept it?

Ball is back in your court.


Edited by Mark R. (02/20/15 07:44 AM)
Edit Reason: added "secondly"
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#2388686 - 02/20/15 11:56 AM Re: Perception of tones, partials and beats [Re: Mark R.]
BDB Online   content
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By n, I suppose you mean π (pi). I suggest that you ignore common factors. All that does is change the scale. It is the same as stretching or shrinking the x axis. Just find something that allows you to see the graphs clearly.

Similarly, you can chose your intervals so that the math is easy and not subject to rounding error. Integers are nice, like 44 and 55 in this case, or multiples like 88 and 110. That is a good place to start. You should see additional tones, but no beats. Then add 1 to one of those numbers. That will show a beat frequency of 1, and show how it affects the additional tones. At that point, you should see what I claim, that beats do not rely on partials to exist, because sine waves have no partials.

I do not hear with anyone else's ears, so I do not understand what you hear. I really do not understand what you mean by "pitches of beats."

One of my previously posted graphs shows how the relative amplitude affects the perceptibility of beats. You can check that if you like. One should remember that the strength is not going to be equal in most cases. Bass strings usually have a lot more amplitude than the shorter treble strings.
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#2388713 - 02/20/15 01:03 PM Re: Perception of tones, partials and beats [Re: Withindale]
Gene Nelson Offline
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Registered: 09/10/04
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I'd suggest buying the Coleman Beat Locator and use it to locate coincident partials. Listen to them when playing different intervals then do some ghosting.
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#2388958 - 02/21/15 02:23 AM Re: Perception of tones, partials and beats [Re: BDB]
rysowers Offline
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Registered: 04/16/07
Posts: 2665
Loc: Olympia, WA
Originally Posted By BDB

I do not hear with anyone else's ears, so I do not understand what you hear. I really do not understand what you mean by "pitches of beats."


I can't imagine tuning without hearing "pitches of beats". The beats I listen to when tuning have a definite pitch - An easily identifiable pulsating tone. It's as clear as if another instrument were playing the tone.
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#2388965 - 02/21/15 02:40 AM Re: Perception of tones, partials and beats [Re: Withindale]
Chris Leslie Online   content
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Oh well! Call me deaf! I hear partials, but the sensation of beating is just that. Kind of like a little beat generator on another plane.

I am not trying to defend BDB, just saying what I hear.
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#2388992 - 02/21/15 04:45 AM Re: Perception of tones, partials and beats [Re: Withindale]
rXd Online   happy
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Registered: 03/11/09
Posts: 2006
I have always heard RBI's (since I became aware of them) at fundamental pitch as though it were an interaction between two fundamentals involved. My intellect know the precise location of the beating partials involved, including the higher ones. It's almost as though all the partials involved are creating one big difference tone or resultant at fundamental level.

Who knows? That's what it might be. When I ghost the lowest common partials, I get a steady unchanging beat. When I listen to the interval, sometimes it seems to change very slightly throughout the duration. Could this be the effect of the much higher partials bearing slightly different relationships, having their say?
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Concert & Recording tuner-tech, London, England.

"in theory, practice and theory are the same thing. In practice, they're not." - Lawrence P. 'Yogi' Berra.

Eschew obfuscation.



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#2389023 - 02/21/15 07:17 AM Re: Perception of tones, partials and beats [Re: Withindale]
Mark Cerisano, RPT Offline
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Registered: 01/24/10
Posts: 1689
Loc: Montreal, Quebec, Canada
Play F2A4. You must be careful. On some pianos, the beat at A5 is different than the beat at A4. This proves we do not hear beating partials at some fundamental. Train your ear to pinpoint specific beating at specific coincidental partials, especially for intervals where there are multiple partials beating at different speeds.

The exist of multiple partials beating at different speeds is a fact. This fact does not reconcile itself with any fundamental beat theory. I.e. How can one choose the proper A4 when playing F2A4 with F2Fork, if you aren't pinpointing the beating A4 instead of A5?
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#2389037 - 02/21/15 08:58 AM Re: Perception of tones, partials and beats [Re: Withindale]
prout Offline
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Registered: 11/14/13
Posts: 1006
Loc: Southwestern Ontario
Beats are beats and pitches are pitches.

If you beat two drums simultaneously, with a ratio of 3:2 beats between them, and increase the tempo of the beats steadily from very slow to very fast, at some point the complex rhythm will become a Perfect Fifth.

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#2389080 - 02/21/15 11:23 AM Re: Perception of tones, partials and beats [Re: rXd]
Ed McMorrow, RPT Offline
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Registered: 12/09/12
Posts: 2639
Loc: Seattle, WA USA
RXD,
I think the variance in RBI's heard with the interval sounding is probably the change in volume of the partials during decay. I don't really sense it as a "change" in beat speed.
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#2389092 - 02/21/15 11:51 AM Re: Perception of tones, partials and beats [Re: Withindale]
rysowers Offline
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Registered: 04/16/07
Posts: 2665
Loc: Olympia, WA
I think we are partially (no pun intended!) dealing with semantics here. When we look at a red ball you could argue that we are not seeing the ball itself just the light reflecting off its surface. You could also argue that the ball is not red, it simply reflects red light off its surface while absorbing other wavelengths. Ultimately all perception is an illusion of some sort because it's all based on electronic impulses carried from our nervous system to our brain.

So if partials "don't exist" by such and such philosophical model, it doesn't really matter, because I can hear them and use them to tune pianos.
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Ryan Sowers,
Pianova Piano Service
Olympia, WA
www.pianova.net

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#2389127 - 02/21/15 12:52 PM Re: Perception of tones, partials and beats [Re: rysowers]
Ed McMorrow, RPT Offline
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Registered: 12/09/12
Posts: 2639
Loc: Seattle, WA USA
Exactly Ryan,
Our consciousness arose out of the universe and it is part of the universe and thus how it "perceives" the universe is the only way it can see the universe. So we deal with things how we interact with them. But that does not mean making things up just because we FEEL like it.

Scientific models are approximations of things that we perceive as having some independent existence. This independence is a fiction created by our consciousness. The test of any model is the simplicity with which it explains all the linked phenomena and the accuracy of the predictions it allow.

I still would appreciate a complete description from BDB of how his combinatorial wave theory can predict/explain everything we deal with in tuning pianos. Until then I see no utility in replacing the partial theory of simple harmonic motion that is today's standard.
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#2389132 - 02/21/15 12:58 PM Re: Perception of tones, partials and beats [Re: Ed McMorrow, RPT]
BDB Online   content
Yikes! 10000 Post Club Member

Registered: 06/07/03
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You are confusing unrelated things. Partial theory is independent of simple harmonic motion. A swinging pendulum is simple harmonic motion without partials.

A sawtooth generator will have partials without being simple harmonic motion.


Edited by BDB (02/21/15 01:04 PM)
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#2389177 - 02/21/15 02:43 PM Re: Perception of tones, partials and beats [Re: Withindale]
Mark R. Offline
2000 Post Club Member

Registered: 07/31/09
Posts: 2117
Loc: Pretoria, South Africa
Methinks BDB is the one "confusing unrelated things".

Partial theory is not "independent of simple harmonic motion". It is an extension of simple harmonic motion, because any harmonic motion can be expressed as a sum of harmonic components. If the motion is a simple, single sine wave, the fundamental carries the full signal, and the harmonics/overtones/partials carry zero amplitude. If it's a note with timbre, some information is carried in the harmonics/overtones/partials. This is true even for a sawtooth motion.

Even if the oscillator is a damped one, it can still be expressed as a sum of harmonic components - each with their own damping constant. Even a swinging pendulum, "simple" and "harmonic" as tough it may seem, is also damped.

To Mark C:
Thank you for the example of F2-A4 vs. F2-fork vs. F2-A5. (Another example would be the 6:4 vs. 3:2 beats of a P5.)

I submit: beats occur at a specific pitch - and (except for the unison) it's at neither of the fundamentals.
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1922 49" Zimmermann, project piano.
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#2389179 - 02/21/15 02:49 PM Re: Perception of tones, partials and beats [Re: BDB]
Ed McMorrow, RPT Offline
2000 Post Club Member

Registered: 12/09/12
Posts: 2639
Loc: Seattle, WA USA
A sawtooth generator is driven by a power supply that inputs with a specific frequency.

Simple harmonic motion of a string under tension goes back at least to Pythagoras.

BDB why do all the acoustics researchers use partial theory? Why don't they switch to combinatorics. The onus is on you to explain the benefits and superiority.
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In a seemingly infinite universe-infinite human creativity is-seemingly possible

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#2389219 - 02/21/15 04:19 PM Re: Perception of tones, partials and beats [Re: Withindale]
Mark Cerisano, RPT Offline
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Registered: 01/24/10
Posts: 1689
Loc: Montreal, Quebec, Canada
Ed, I have done some research on beat speeds. I've recorded some intervals and passed them through a band pass filter to enhance the beating partial. The wave form is stunning; it shows the beat clearly and I can drag through so many beats, take the time and divide into the beats dragged, and get the bps.

Problem is, the darn answer can sometimes change drastically depending on which set of beats I take. This confirms my ear sometimes hearing the beats change speed slowly, or sometimes abruptly, during the sustain of the interval.

My hypothesis is that the frequency of one or both of the interval notes is changing with time.

When we think about it, there is a lot going on when a string is played. The string gets longer because it is stretched more; it has amplitude. That makes the pitch lower. But the stretching increases tension and that makes the pitch higher. The two seem to cancel each other out. But maybe not always?
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#2389360 - 02/21/15 09:47 PM Re: Perception of tones, partials and beats [Re: Withindale]
rXd Online   happy
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Registered: 03/11/09
Posts: 2006
It seems there are many different ways, or at least descriptions of the way neat rates are heard. We can't get inside each others ears. We must accept what we are told since we cannot deny another person their perceptions. There are no shoulda nor oughts if someone's perception differs from our own.

It may be my flexibility in where I hear beatrates that enables me to carry on tuning despite the constant clanging of scaffolding when staging is being assembled at the same time as the morning tuning. I regularly tune right through fire alarm tests. when I use those notes as checks later, they are always right. This is a much practiced skill. I can focus wherever I want to at any time. I think much of it comes from practice but some maybe because I have always heard beats clearly, indeed, that's what got me into tuning- attempting to play another instrument with a well tuned non-standard piano.

When I get patronising replies to my posts and very simplistic "proofs" that ignore more than half of the relevant parameters, I know that I am either not being understood, making an obscure reference, or assuming that everybody else has the same experience as me.
On this case it may be the latter.

We are all aware, I think, that there are several pairs of mismatched partials that are beating. In the case of the major third, there is another pair at 12/10. I sometimes hear these, particularly when I'm focused on the treble and go into the middle of the piano to play a major third as a check to compare a 17th. Does anybody else hear them along with the 5/4? The 12/10 is never beating at its theoretical frequency. that is to say the 12/10 is never the same or double the 5/4 but somewhere in between depending on the extent of the enharmonicity, I suppose. Often a five in the time of two or five on the time of three.

It does sound quite reasonable they the well known pitch wander of strings could account for the subtle beat rate change that I sometimes hear if I listen long enough. I rarely listen that long, three or four beats is enough to establish the familiar speeds of RBI's

The RBI'svat 5/4 are the same rate whether I listen high or low.
_________________________
Concert & Recording tuner-tech, London, England.

"in theory, practice and theory are the same thing. In practice, they're not." - Lawrence P. 'Yogi' Berra.

Eschew obfuscation.



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#2389410 - 02/22/15 01:14 AM Re: Perception of tones, partials and beats [Re: Withindale]
rysowers Offline
2000 Post Club Member

Registered: 04/16/07
Posts: 2665
Loc: Olympia, WA
It seems like it would be plausible to do an experiment where the frequency of the coincidental partial in an interval (like a 4th) is filtered out. If there is still beating in the interval it would offer proof that there is beating other than that of the coincidental partial.


Edited by rysowers (02/22/15 02:26 AM)
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#2389446 - 02/22/15 04:30 AM Re: Perception of tones, partials and beats [Re: rysowers]
rXd Online   happy
2000 Post Club Member

Registered: 03/11/09
Posts: 2006
Originally Posted By rysowers
It seems like it would be plausible to do an experiment where the frequency coincidental partial in an interval (like a 4th) is filtered out. If there is still beating in the interval it would offer proof that there is beating other than that of the coincidental partial.


Hi, Ryan,
That's easily done by anyone. I used to do it with the first acrosonic I ever saw. It had been brought over to London by an American diplomat in the '60's

I had never come across such noisy fifths in the temperament area before so I ghosted the lowest coincident partial and, to analyse the noise somewhat, ghosted the next few coincident partials.

I have used the term lowest coincidental partial several times in this forum, implying, of course that they are not the only coincident partials, never imagining that it probably was an obscure reference to some. The idea that such a common phenomenon requires further proof sounds strange to me.

It is easy to prove with a fifth by anyone with a reasonably in tune piano. (Come to think of it, unisons would have to be absolutely still Or faults in the unison would cause confusion in SBI's so single strings would be easier).
I never thought of doing it with a fourth. A third in the temperament area would be more difficult because the dampers finish before the next lowest coincidental partial (LCP?) can be excited by the approprate note making ghosting impractical. Thirds lower down the piano would work. (I am assuming the 12/10 to be the next audible LCP but it may not be).

I won't see a piano til later today so I'll try it then, if I remember to.

Of course, the higher up the partials, the less effective for any tuning they become, both because of less regular iH and their sheer relative inaudibility. While "advanced" theory is fascinating, it's use in finer tuning is limited when it takes precedent over the clearly audible sounds. While they are academic in tuning, they may explain the different hearing of different people and, as I said on my last post, resultants from all partials and their extremely complex interaction has to affect the sound at the fundamental level in a complex way. On a note of 100 Hz, all the partials are 100Hz apart. The difference tones (discussed a few weeks ago) constantly reinforce the fundamental. How they interact with the partials of another note or notes will boggle the mind. Much easier to just listen. Maybe the ears were put there to give the constant machinations of the mind a rest.
_________________________
Concert & Recording tuner-tech, London, England.

"in theory, practice and theory are the same thing. In practice, they're not." - Lawrence P. 'Yogi' Berra.

Eschew obfuscation.



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#2389453 - 02/22/15 05:10 AM Re: Perception of tones, partials and beats [Re: Withindale]
alfredo capurso Offline
1000 Post Club Member

Registered: 07/10/07
Posts: 1136
Loc: Sicily - Italy
Originally Posted By Withindale
This topic just came up, off topic, in the the SBI vs RBI thread. Sounds worth a discussion? The questions elude me but I am sure the answers would be interesting. I'd like to enhance my perception!


Hi Ian,

It won't be difficult for you to enhance your beat perception for some intervals, especially if you can be helped by someone that tells you what to listen to. Sometimes it is like looking for mushrooms and one cannot find any until they know what that mushroom looks like in the context.

You can also progress on your own, beating fifths and octaves are quite easy to spot in the mid-range, and 10ths and/or 17ths when the bottom note is in the tenor/bass. Listen to variations in amplitude, not to the individual pitch. One thing I would suggest while you listen is move the pin and pull or release the string slightly, sometimes it is easier to notice some change in what you are perceiving, as it is easier to notice something that moves in the landscape.

Perception of tones and partials is a bit different. If I understand correctly, you mean how we perceive the tone as a whole and perhaps the ability to distingush the various partials in a tone. That type of analysis, hearing the tone's partial content, requires perhaps a slightly different practice as it has to do with (and here it gets difficult to word)... Colour? Brightness? Darkness? Roughness?

In any case, you may start comparing two tones from two single strings, for instance mute one string in a bichord, listen and try to fix its timbre in your ear, assigning some sort of feeling; now mute the other string and compare the two. Eventually you are enabled to map your own word_and_sense references and will at least figure out that there is a difference. Tracking one_tone different partials will require a bit more time, but they are all there, like many other things we do not normally pay attention to.

Remember, relax when you listen, free yourself from any other need and keep an eye on your breathing.

Best wishes, a.c.
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alfredo

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#2389533 - 02/22/15 10:51 AM Re: Perception of tones, partials and beats [Re: Withindale]
Chris Storch Offline
Full Member

Registered: 08/13/09
Posts: 224
Loc: Massachusetts
This discussion appears to be yet more evidence that individuals, when exposed to identical auditory stimulus, will disagree on what they are hearing. The difference I believe lies in whether the individual is an analytic or a synthetic listener.

http://www.feilding.net/sfuad/musi3012-01/demos/audio/425_analytic_synthetic_pitch.htm

An analytic listener will be able to pull apart the auditory signal into its component parts. The synthetic listener will respond to the auditory signal in its totality. The different listeners will consequently have different descriptions of what they are experiencing.

While playing the demonstration, I immediately hear the tone go down in pitch. If I concentrate and shift my method of listening I can eventually make myself hear the tone go up in pitch. I cannot hear both at the same time.

In all these debates about partials, and beat rates, and whether beats carry pitch, I suspect you're all talking past one another as usual (It's pretty common in this forum, and leads to the most entertaining of debates). "I see a forest - it's as plain as day!". "Well you're just dead wrong - I see an oak, next to two pines, and then a maple..."

My suggestion is that you identify whether you yourself are an analytic or a synthetic listener and discover how that applies to your tuning technique. Then do a little ear training to teach yourself to listen in the opposite mode. I suspect you'll only become a better tuner as a result. Maybe you'll also come to a better understanding of some of your professional colleagues' differing points of view.

...Or you could just continue talking past one another.



Edited by Chris Storch (02/22/15 10:55 AM)
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Chris Storch
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#2389597 - 02/22/15 02:09 PM Re: Perception of tones, partials and beats [Re: Withindale]
alfredo capurso Offline
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Registered: 07/10/07
Posts: 1136
Loc: Sicily - Italy

Nice post, Chris.

First I hear a (D)-G-B and the G going flat to D-F#-B, though I cannot exclude some sort of imagination.
.
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alfredo

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#2389606 - 02/22/15 02:44 PM Re: Perception of tones, partials and beats [Re: rysowers]
Mark Cerisano, RPT Offline
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Registered: 01/24/10
Posts: 1689
Loc: Montreal, Quebec, Canada
Originally Posted By rysowers
It seems like it would be plausible to do an experiment where the frequency of the coincidental partial in an interval (like a 4th) is filtered out. If there is still beating in the interval it would offer proof that there is beating other than that of the coincidental partial.


I've created two sine tones electronically, that were not a pure fifth. No beats were heard
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#2389607 - 02/22/15 02:46 PM Re: Perception of tones, partials and beats [Re: Mark Cerisano, RPT]
BDB Online   content
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Registered: 06/07/03
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But there are beats. I put graphs in the Image area.
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#2389616 - 02/22/15 03:23 PM Re: Perception of tones, partials and beats [Re: Withindale]
Withindale Offline
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Registered: 02/09/11
Posts: 2172
Loc: Suffolk, England
Or try this online generator.
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Schiedmayer & Soehne, 1925 Model 14, 55" upright
Ibach, 1922 49" upright (project piano)

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#2389619 - 02/22/15 03:25 PM Re: Perception of tones, partials and beats [Re: Withindale]
Chris Leslie Online   content
500 Post Club Member

Registered: 01/01/11
Posts: 833
Loc: Canberra, ACT, Australia
Pure sine waves at pure 5th:


Pure sine waves at tempered 5th:
_________________________
Chris Leslie
Piano technician
http://www.chrisleslie.com.au

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