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#2302390 - 07/14/14 09:40 PM Re: Theoretical tuning sequence [Re: Bernhard Stopper]
DoelKees Offline
1000 Post Club Member

Registered: 05/01/10
Posts: 1760
Loc: Vancouver, Canada
Originally Posted By: Bernhard Stopper
Your explanation rather confirms my statement that two equal beating intervals played together increase the intensity of beats compared with the beat intensity of an interval played alone. DŽaccord with human perception of equal beating as an advantage, in the case of "wishful thinking" for a canceling effect.

However, beat masking is a possible phenomenon (which i have demonstrated in my tuning class) but it certainly does not occur with equal beating intervals.


What I imagine is the following: In ET play intervals C#4F4 and F4A4. You hear them beat at different rates, so you connect the beat rates to the intervals and hear they are out of just. Now suppose C#4F4 and F4A4 are equal beating (as can happen in some WT's). We now hear the same beat rates so our brain thinks the beats are not a property of the interval, but some external noise which our brain filters out, and we don't think the M3's are out of just.

I have my doubts but it seems somewhat possible.

I don't know what "beat masking" is. Can you explain?

Kees

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#2302396 - 07/14/14 09:59 PM Re: Theoretical tuning sequence [Re: UnrightTooner]
DoelKees Offline
1000 Post Club Member

Registered: 05/01/10
Posts: 1760
Loc: Vancouver, Canada
Originally Posted By: UnrightTooner
Originally Posted By: DoelKees
Originally Posted By: Bernhard Stopper
With my research i found the opposite to be true: Equal beating increases (worsens) beat intensities and does not cancel them.


Indeed beats can not physically cancel, unlike pressure waves. The reason is that pressure (or rather deviation from atmospheric pressure) can be positive and negative and can add up to 0, whereas beats are fluctuations in energy, and energy is always positive and no physical cancellation is possible.

If there is any advantage of "equal beating" it will have to be a human perception thing.

Kees


I am not so sure about the positive/negative thing. The sounds you hear on a telephone are an AC signal "riding" on a DC value. Maybe it's not the same thing...

I think it's the same thing: sound waves ride on the atmospheric pressure (the DC) and you can't hear beat cancellation on the telephone either.

If you're not convinced; I convinced myself by looking at an example. Consider tuning P4 A3D4 1bps wide and P5 A3E4 1bps narrow (equal beating). Ignore IH as it plays no role in this.

The P4 beats come from partials 4 and 3 which are at 880 and 881Hz. The P5 beats come from partials 3 and 2 which are at 660 and 659Hz. If we play A3D4E4 simultaneously we should be able to demonstrate beat cancellation by synthesizing just the aforementioned partials (880,881,659,660).

Here I put audio files of the individual beats of the P4 and P5 and the combined beats with different relative phases (0, 90 and 180 degrees). You can hear that when they are in phase you hear a stronger 1bps beat, if they are out of phase (180) the beats interleave and we effectively hear 2bps, and at 90 it's more complicated.

No cancellation can occur at any phase difference because beats are periodic variations in loudness of a carrier wave and there is no such thing as negative loudness and hence no cancellation, unlike periodic variations in pressure (deviation from atmospheric) which can be positive or negative.

Kees

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#2302433 - 07/15/14 12:29 AM Re: Theoretical tuning sequence [Re: Gadzar]
Mark Cerisano, RPT Offline
1000 Post Club Member

Registered: 01/24/10
Posts: 1403
Loc: Montreal, Quebec, Canada
Originally Posted By: Gadzar
Originally Posted By: Mark Cerisano, RPT
In fact, I'm fairly sure that it will move. That's why I use the P4 test.

With this test, the P4 window is so small, that you would be surprised how tiny a movement can be caught by it.

You are right though, it is a waste of time to tune a note with high accuracy if it is going to drift later on, unless of course your method is incredibly fast at getting that high accuracy. If so, why not?


I am not sure I follow you. You say you tune the piano in one single pass. And you also say that you are fairly sure that what you have just tuned is going to move while you continue to tune.

Doesn't that mean that it will end up out of tune?



Not after I correct it as I go.

Also, for reasons I do not know why, not all the notes drift, so the high accuracy is not always wasted.


Edited by Mark Cerisano, RPT (07/15/14 12:31 AM)
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www.howtotunepianos.com

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#2302436 - 07/15/14 12:34 AM Re: Theoretical tuning sequence [Re: DoelKees]
Mark Cerisano, RPT Offline
1000 Post Club Member

Registered: 01/24/10
Posts: 1403
Loc: Montreal, Quebec, Canada
Originally Posted By: DoelKees
Originally Posted By: UnrightTooner
Originally Posted By: DoelKees
Originally Posted By: Bernhard Stopper
With my research i found the opposite to be true: Equal beating increases (worsens) beat intensities and does not cancel them.


Indeed beats can not physically cancel, unlike pressure waves. The reason is that pressure (or rather deviation from atmospheric pressure) can be positive and negative and can add up to 0, whereas beats are fluctuations in energy, and energy is always positive and no physical cancellation is possible.

If there is any advantage of "equal beating" it will have to be a human perception thing.

Kees


I am not so sure about the positive/negative thing. The sounds you hear on a telephone are an AC signal "riding" on a DC value. Maybe it's not the same thing...

I think it's the same thing: sound waves ride on the atmospheric pressure (the DC) and you can't hear beat cancellation on the telephone either.

If you're not convinced; I convinced myself by looking at an example. Consider tuning P4 A3D4 1bps wide and P5 A3E4 1bps narrow (equal beating). Ignore IH as it plays no role in this.

The P4 beats come from partials 4 and 3 which are at 880 and 881Hz. The P5 beats come from partials 3 and 2 which are at 660 and 659Hz. If we play A3D4E4 simultaneously we should be able to demonstrate beat cancellation by synthesizing just the aforementioned partials (880,881,659,660).

Here I put audio files of the individual beats of the P4 and P5 and the combined beats with different relative phases (0, 90 and 180 degrees). You can hear that when they are in phase you hear a stronger 1bps beat, if they are out of phase (180) the beats interleave and we effectively hear 2bps, and at 90 it's more complicated.

No cancellation can occur at any phase difference because beats are periodic variations in loudness of a carrier wave and there is no such thing as negative loudness and hence no cancellation, unlike periodic variations in pressure (deviation from atmospheric) which can be positive or negative.

Kees


Be careful. The "in phase" example can be out of phase if one wave form starts a micro second later. I found this out when making my beats video. But, I have to admit, I haven't listened to the recording yet. Perhaps you used a method that guaranteed "in phase".
_________________________
Mark Cerisano, RPT
www.howtotunepianos.com

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#2302437 - 07/15/14 12:38 AM Re: Theoretical tuning sequence [Re: DoelKees]
Mark Cerisano, RPT Offline
1000 Post Club Member

Registered: 01/24/10
Posts: 1403
Loc: Montreal, Quebec, Canada
BTW, from my reading I've gathered that anything not at 0 degrees is out of phase. Did I read wrong, or read an incorrect article?

But I absolutely get what you're saying. Beats are all positive, so they can't add up to zero, ever. But the partials themselves can. And if there's no partial beating, then there's no beat. Try it. Create two sine waves. One at 440 and one at 665. A horribly wide fifth. No beats. It's weird.

Maybe that's what's going on when I tune a "beatless" octave. I know it's not theoretically possible, yet that's what I hear.


Edited by Mark Cerisano, RPT (07/15/14 12:43 AM)
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Mark Cerisano, RPT
www.howtotunepianos.com

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#2302444 - 07/15/14 01:16 AM Re: Theoretical tuning sequence [Re: Mark Cerisano, RPT]
DoelKees Offline
1000 Post Club Member

Registered: 05/01/10
Posts: 1760
Loc: Vancouver, Canada
Originally Posted By: Mark Cerisano, RPT
BTW, from my reading I've gathered that anything not at 0 degrees is out of phase. Did I read wrong, or read an incorrect article?

But I absolutely get what you're saying. Beats are all positive, so they can't add up to zero, ever. But the partials themselves can. And if there's no partial beating, then there's no beat. Try it. Create two sine waves. One at 440 and one at 665. A horribly wide fifth. No beats. It's weird.

Maybe that's what's going on when I tune a "beatless" octave. I know it's not theoretically possible, yet that's what I hear.

0 degrees means in phase, 180 maximally out of phase, 90 1/4 period out of phase. Indeed if there are no partials that beat there are no beats. However if you crank up the volume in your example the beats will appear due to nonlinear distortion.

The point is, beat cancellation is not possible, because there is a fundamental difference between a beat and a sound wave.

It may however be possible to arrange the beats so that your attention is not drawn to them, giving the illusion of beat cancelling, which is of course all we need, but I have no idea how. Can you post an audio example of an "apparently beatless octave"?

Kees

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#2302465 - 07/15/14 04:29 AM Re: Theoretical tuning sequence [Re: Mark Cerisano, RPT]
Gadzar Online   content
1000 Post Club Member

Registered: 12/15/06
Posts: 1846
Loc: Mexico City
Originally Posted By: Mark Cerisano, RPT
Originally Posted By: Gadzar
Originally Posted By: Mark Cerisano, RPT
In fact, I'm fairly sure that it will move. That's why I use the P4 test.

With this test, the P4 window is so small, that you would be surprised how tiny a movement can be caught by it.

You are right though, it is a waste of time to tune a note with high accuracy if it is going to drift later on, unless of course your method is incredibly fast at getting that high accuracy. If so, why not?


I am not sure I follow you. You say you tune the piano in one single pass. And you also say that you are fairly sure that what you have just tuned is going to move while you continue to tune.

Doesn't that mean that it will end up out of tune?



Not after I correct it as I go.

Also, for reasons I do not know why, not all the notes drift, so the high accuracy is not always wasted.


So you do correct what you just tuned! Isn't it a sort of second pass? You are tuning each note twice!

And after correcting, nothing guarantees you that it won't move again as you continue tuning the rest of the notes.
_________________________
Rafael Melo
Piano Technician
rafaelmelo@afinacionpianos.com.mx

Serving Mexico City and suburbs.

http://www.afinacionpianos.com.mx

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#2302479 - 07/15/14 05:46 AM Re: Theoretical tuning sequence [Re: Gadzar]
Mark R. Online   content
2000 Post Club Member

Registered: 07/31/09
Posts: 2051
Loc: Pretoria, South Africa
Originally Posted By: Gadzar
I don't see this as a tuning sequence for my dayly work. I see it as a curiosity to tinker around.


That may be the case.

I was only trying to say that currently, I'm using ET via Marpurg, which tunes some intervals pure (specifically, it's the whole-tone scale from F#3 to E4, i.e. six notes in total). Any short-cut that reduces the number of purely tuned intervals, is helpful to me - even though it would still be cumbersome or "tinkering" to a professional.
_________________________
Autodidact interested in piano technology.

1922 49" Zimmermann, project piano.
1970 44" Ibach, daily music maker.

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#2302488 - 07/15/14 06:33 AM Re: Theoretical tuning sequence [Re: DoelKees]
Bernhard Stopper Offline
Full Member

Registered: 09/22/08
Posts: 215
Loc: Germany
Originally Posted By: DoelKees

What I imagine is the following: In ET play intervals C#4F4 and F4A4. You hear them beat at different rates, so you connect the beat rates to the intervals and hear they are out of just. Now suppose C#4F4 and F4A4 are equal beating (as can happen in some WT's). We now hear the same beat rates so our brain thinks the beats are not a property of the interval, but some external noise which our brain filters out, and we don't think the M3's are out of just.

I have my doubts but it seems somewhat possible.

I miss your legendary crackpottery alarm detector for this "equal beating/canceling" theorem grin
I stay with what i said: Equal beating generally increases (worsens) beat intensities and does not cancel (or reduce) them.

Originally Posted By: DoelKees

I don't know what "beat masking" is. Can you explain?

Kees

The effect of beat intensity reduction caused by ?summation? of beats with different rates.




Edited by Bernhard Stopper (07/15/14 06:41 AM)
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Bernhard Stopper
www.piano-stopper.de

Salieri: "Mediocrities everywhere, now and to come: I absolve you all! Amen! Amen! Amen!"
(Amadeus, the movie)

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#2302489 - 07/15/14 06:40 AM Re: Theoretical tuning sequence [Re: DoelKees]
Olek Offline
7000 Post Club Member

Registered: 03/14/08
Posts: 7901
Loc: France
Accepting beats an not fighting them makes them more discrete in the end, and they also goes well with the piano tone, and the shape it takes.

The consonances I hear/tune are an addition of slow beats (within the 2 octaves framework for instance.


Edited by Olek (07/15/14 06:42 AM)
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#2302492 - 07/15/14 06:50 AM Re: Theoretical tuning sequence [Re: Olek]
Bernhard Stopper Offline
Full Member

Registered: 09/22/08
Posts: 215
Loc: Germany
Originally Posted By: Olek
Accepting beats an not fighting them makes them more discrete in the end, and they also goes well with the piano tone, and the shape it takes.

The consonances I hear/tune are an addition of slow beats (within the 2 octaves framework for instance.


A reduction of beats generally comes along with an increase of consonance, not the other way around.




Edited by Bernhard Stopper (07/15/14 06:50 AM)
_________________________
Bernhard Stopper
www.piano-stopper.de

Salieri: "Mediocrities everywhere, now and to come: I absolve you all! Amen! Amen! Amen!"
(Amadeus, the movie)

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#2302494 - 07/15/14 07:12 AM Re: Theoretical tuning sequence [Re: DoelKees]
Olek Offline
7000 Post Club Member

Registered: 03/14/08
Posts: 7901
Loc: France
I believe that was what I (wanted to) say, there is a reduction, not a suppression.

Do they slow, also ? (if compare whith theoretical beating frequency ?

At some points they "hide" in the dwell.

If consonance = coupling it sound normal that beats reduce, if not in speed in duration.
_________________________
It is critical that you call your Senators and Representatives and ask them to cosponsor S. 2587 and H.R. 5052. Getting your legislators to cosponsor these bills


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#2302498 - 07/15/14 07:40 AM Re: Theoretical tuning sequence [Re: DoelKees]
UnrightTooner Offline
4000 Post Club Member

Registered: 11/13/08
Posts: 4949
Loc: Bradford County, PA
Originally Posted By: DoelKees
Originally Posted By: UnrightTooner
Originally Posted By: DoelKees
Originally Posted By: Bernhard Stopper
With my research i found the opposite to be true: Equal beating increases (worsens) beat intensities and does not cancel them.


Indeed beats can not physically cancel, unlike pressure waves. The reason is that pressure (or rather deviation from atmospheric pressure) can be positive and negative and can add up to 0, whereas beats are fluctuations in energy, and energy is always positive and no physical cancellation is possible.

If there is any advantage of "equal beating" it will have to be a human perception thing.

Kees


I am not so sure about the positive/negative thing. The sounds you hear on a telephone are an AC signal "riding" on a DC value. Maybe it's not the same thing...

I think it's the same thing: sound waves ride on the atmospheric pressure (the DC) and you can't hear beat cancellation on the telephone either.

If you're not convinced; I convinced myself by looking at an example. Consider tuning P4 A3D4 1bps wide and P5 A3E4 1bps narrow (equal beating). Ignore IH as it plays no role in this.

The P4 beats come from partials 4 and 3 which are at 880 and 881Hz. The P5 beats come from partials 3 and 2 which are at 660 and 659Hz. If we play A3D4E4 simultaneously we should be able to demonstrate beat cancellation by synthesizing just the aforementioned partials (880,881,659,660).

Here I put audio files of the individual beats of the P4 and P5 and the combined beats with different relative phases (0, 90 and 180 degrees). You can hear that when they are in phase you hear a stronger 1bps beat, if they are out of phase (180) the beats interleave and we effectively hear 2bps, and at 90 it's more complicated.

No cancellation can occur at any phase difference because beats are periodic variations in loudness of a carrier wave and there is no such thing as negative loudness and hence no cancellation, unlike periodic variations in pressure (deviation from atmospheric) which can be positive or negative.

Kees


Kees:

Thanks for your response and your patience! I am just not getting it. What about noise cancelling headsets? http://en.wikipedia.org/wiki/Noise-cancelling_headphones

Sure, it is not the same as equal beating intervals played simultaneously, because those would be in phase, but they work.

I could not get your audio link to work, but am not sure if it matters. We may be talking about two different things.
_________________________
Jeff Deutschle
Part-Time Tuner
Who taught the first chicken how to peck?

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#2302499 - 07/15/14 08:02 AM Re: Theoretical tuning sequence [Re: DoelKees]
Olek Offline
7000 Post Club Member

Registered: 03/14/08
Posts: 7901
Loc: France
The coupling on the bridge (3 strings one note) does not allow phase to be balanced (the best we can come near is one sting lower/higher of 2 others coupling strong).

I wonder if when another note is added, the phase effects (inversion/ in phase) do not work even if it is at some distance on the bridge.





Edited by Olek (07/15/14 08:03 AM)
_________________________
It is critical that you call your Senators and Representatives and ask them to cosponsor S. 2587 and H.R. 5052. Getting your legislators to cosponsor these bills


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#2302501 - 07/15/14 08:23 AM Re: Theoretical tuning sequence [Re: Mark Cerisano, RPT]
pyropaul Offline
Full Member

Registered: 11/16/10
Posts: 190
Loc: Montreal
Originally Posted By: Mark Cerisano, RPT
Create two sine waves. One at 440 and one at 665. A horribly wide fifth. No beats. It's weird.



I tried this with audacity - both 665 and 661 plus 440. It sure sounds like beating to me as I can hear periodic variations in loudness. You definitely can have beats that are not due to partials near the same frequency - just do the summation of the two sines and you'll see periodic loudness variations in the 440+661 case.

[edit] just throw graph sin(4.4*pi*x)+sin(6.61*pi*x) and graph sin(4.4*pi*x)+sin(6.60*pi*x) into google, zoom out horizontally and you'll see the amplitude modulation in the 440+661Hz case.
Paul.


Edited by pyropaul (07/15/14 09:01 AM)
Edit Reason: added info for graphs

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#2302504 - 07/15/14 08:36 AM Re: Theoretical tuning sequence [Re: DoelKees]
Bill Bremmer RPT Offline
3000 Post Club Member

Registered: 08/21/02
Posts: 3274
Loc: Madison, WI USA
Originally Posted By: DoelKees
Originally Posted By: Bernhard Stopper
With my research i found the opposite to be true: Equal beating increases (worsens) beat intensities and does not cancel them.


Indeed beats can not physically cancel, unlike pressure waves. The reason is that pressure (or rather deviation from atmospheric pressure) can be positive and negative and can add up to 0, whereas beats are fluctuations in energy, and energy is always positive and no physical cancellation is possible.

If there is any advantage of "equal beating" it will have to be a human perception thing.

Kees


I'll take the perception over the "science" and the research then. I wasn't looking for what I found but it was there. I hear it every time I tune the EBVT III and play a C Major chord in the 3rd octave. The rapid beats are just swallowed up.

This happens to the 5ths in 1/4 Meantone too. Alone, they sound very objectionably narrow but no music ever written for 1/4 Meantone has 5ths standing alone. You simply don't hear them when actual music is played.

For at least 30 years now, I have also noted how the beat also disappears when the octave-fifth and double octave are equal beating and played together. I don't think I am fooling myself about that. I also don't think I was fooling Jim Coleman, Sr. when he rushed up to tell me after a recital I had tuned for, "You've done something with the octaves. I don't know what it is, but I like it.

Call it whatever you want or try to tell me that it is not happening but I know what I am hearing or in this case, not hearing.
_________________________
Bill Bremmer RPT
Madison WI USA
www.billbremmer.com

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#2302522 - 07/15/14 09:59 AM Re: Theoretical tuning sequence [Re: DoelKees]
Gadzar Online   content
1000 Post Club Member

Registered: 12/15/06
Posts: 1846
Loc: Mexico City
Originally Posted By: Mark R.
Originally Posted By: Gadzar
I don't see this as a tuning sequence for my dayly work. I see it as a curiosity to tinker around.


That may be the case.

I was only trying to say that currently, I'm using ET via Marpurg, which tunes some intervals pure (specifically, it's the whole-tone scale from F#3 to E4, i.e. six notes in total). Any short-cut that reduces the number of purely tuned intervals, is helpful to me - even though it would still be cumbersome or "tinkering" to a professional.


I see what you mean. Have you something in mind to resume the temperament from the whole tone scale F3 G3 A3 B3 C#3 D#4 F4 ?

Maybe tuning A#3 between F3 and D#4 to have the same tempering in both P4s F3A#3 and A#3D#4. Then tune the CM3s F#3 A#3 D4. Then C4 between G3 and F4 and the CM3s G#3 C4 E4.

Must try it. I don't know. I guess ET Via Marpurg is easier. But this one is shorter and gives true ET.

PS: This sequence is a good way to correctly temper ET P4s.


Edited by Gadzar (07/15/14 10:08 AM)
_________________________
Rafael Melo
Piano Technician
rafaelmelo@afinacionpianos.com.mx

Serving Mexico City and suburbs.

http://www.afinacionpianos.com.mx

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#2302553 - 07/15/14 11:34 AM Re: Theoretical tuning sequence [Re: Gadzar]
Mark R. Online   content
2000 Post Club Member

Registered: 07/31/09
Posts: 2051
Loc: Pretoria, South Africa
Originally Posted By: Gadzar
Have you something in mind to resume the temperament from the whole tone scale F3 G3 A3 B3 C#3 D#4 F4 ?


You mean, after having obtained that whole tone scale with Marpurg? Not really, because at that stage, I am almost done. The only thing remaining is to correct the F# whole tone scale using P4s/P5s. Each note is part of a pure interval (e.g. F#3-C#4) and a doubly tempered interval (F#3-B3). So, the note (F#3 in this case) must be moved to the equally tempered mid-point between the two.

But if you meant:

If I could get to the F3-F4 whole tone scale in a quicker way, have I thought about tuning the other whole-tone scale? Yes, I have. Your suggestion comes to mind. Or:
1) tuning D4 using F3, G3 and B3 ("inside third, outside sixth" test), and similarly
2) tuning E4, using G3, A3 and C#4, thereafter
3) completing both ladders of CM3s.

[Edit: I hope it makes sense; at the moment, I'm playing around with sequences, and I easily get confused.]


Edited by Mark R. (07/15/14 11:37 AM)
Edit Reason: given in post.
_________________________
Autodidact interested in piano technology.

1922 49" Zimmermann, project piano.
1970 44" Ibach, daily music maker.

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#2302563 - 07/15/14 12:25 PM Re: Theoretical tuning sequence [Re: DoelKees]
Gadzar Online   content
1000 Post Club Member

Registered: 12/15/06
Posts: 1846
Loc: Mexico City
I meant after setting the whole tone scale with A4 A3 F3 F4 C#4
pure P4 A3D4 pure P4 D4G4
pure P4 E4A4 pure B3E4
D#4 B3 G3. (or D#3 G3 B3).


Edited by Gadzar (07/15/14 12:27 PM)
_________________________
Rafael Melo
Piano Technician
rafaelmelo@afinacionpianos.com.mx

Serving Mexico City and suburbs.

http://www.afinacionpianos.com.mx

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#2302581 - 07/15/14 01:23 PM Re: Theoretical tuning sequence [Re: UnrightTooner]
DoelKees Offline
1000 Post Club Member

Registered: 05/01/10
Posts: 1760
Loc: Vancouver, Canada
Originally Posted By: UnrightTooner

Kees:

Thanks for your response and your patience! I am just not getting it. What about noise cancelling headsets? http://en.wikipedia.org/wiki/Noise-cancelling_headphones

They work by cancelling a pressure wave with another pressure wave of opposite phase. But beats are not pressure waves.

Kees

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#2302603 - 07/15/14 02:31 PM Re: Theoretical tuning sequence [Re: DoelKees]
prout Offline
500 Post Club Member

Registered: 11/14/13
Posts: 836
A beat is simply a frequency too low to be perceived by a human as pitch.

If you create clicks (remember the original sounds produced by a computer back in the 80s?) at the rate of 5 clicks per second, you will hear 5 clicks per second.

But, if you create clicks at the rate of 440 clicks per second, you will hear A4.

In fact, if you create a 3 against 2 click pattern, you will hear a nice 3:2 rhythm if it is slow enough, and you will hear a perfect fifth if the rate is high enough.

In both cases, the energy is positive.

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#2302604 - 07/15/14 02:33 PM Re: Theoretical tuning sequence [Re: pyropaul]
DoelKees Offline
1000 Post Club Member

Registered: 05/01/10
Posts: 1760
Loc: Vancouver, Canada
Originally Posted By: pyropaul
Originally Posted By: Mark Cerisano, RPT
Create two sine waves. One at 440 and one at 665. A horribly wide fifth. No beats. It's weird.



I tried this with audacity - both 665 and 661 plus 440. It sure sounds like beating to me as I can hear periodic variations in loudness. You definitely can have beats that are not due to partials near the same frequency - just do the summation of the two sines and you'll see periodic loudness variations in the 440+661 case.

[edit] just throw graph sin(4.4*pi*x)+sin(6.61*pi*x) and graph sin(4.4*pi*x)+sin(6.60*pi*x) into google, zoom out horizontally and you'll see the amplitude modulation in the 440+661Hz case.
Paul.

I don't hear beats at low volume, only when I crank it up nonlinear distortion, either in my ear or in my speakers, kicks in.

The amplitude modulation you see is a visual effect only. If you plot the energy over say 50ms windows you'll see it is constant.
Unlike when you have a true beat when it oscillates at the beat rate.

Kees

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#2302613 - 07/15/14 02:54 PM Re: Theoretical tuning sequence [Re: DoelKees]
prout Offline
500 Post Club Member

Registered: 11/14/13
Posts: 836
Originally Posted By: DoelKees
Originally Posted By: pyropaul
Originally Posted By: Mark Cerisano, RPT
Create two sine waves. One at 440 and one at 665. A horribly wide fifth. No beats. It's weird.



I tried this with audacity - both 665 and 661 plus 440. It sure sounds like beating to me as I can hear periodic variations in loudness. You definitely can have beats that are not due to partials near the same frequency - just do the summation of the two sines and you'll see periodic loudness variations in the 440+661 case.

[edit] just throw graph sin(4.4*pi*x)+sin(6.61*pi*x) and graph sin(4.4*pi*x)+sin(6.60*pi*x) into google, zoom out horizontally and you'll see the amplitude modulation in the 440+661Hz case.
Paul.

I don't hear beats at low volume, only when I crank it up nonlinear distortion, either in my ear or in my speakers, kicks in.

The amplitude modulation you see is a visual effect only. If you plot the energy over say 50ms windows you'll see it is constant.
Unlike when you have a true beat when it oscillates at the beat rate.

Kees


My guess is that our brain creates the resultant of 661 and 440, for example, as 221, which will produce a harmonic at 442, which will beat at 2bps.

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#2302624 - 07/15/14 03:14 PM Re: Theoretical tuning sequence [Re: DoelKees]
Bill Bremmer RPT Offline
3000 Post Club Member

Registered: 08/21/02
Posts: 3274
Loc: Madison, WI USA
I seem to recall some years ago that someone told me that the "canceling" effect that I was hearing was not the same as what happens with noise cancellation systems. That is why I always use the word, "effect" when I talk about it. If it isn't truly a cancelation, then it is something else which mimics that effect.

When I tune the EBVT or ET via Marpurg, I always check my equally beating intervals by playing them simultaneously. If the two intervals are not quite equal, the slow beat between them emerges. When the two intervals, whether slowly or rapidly beating are truly equal, the beating sound becomes fainter, certainly not louder. The entire cluster of tones, whether a consonant, mildly dissonant or sharply disonant sound becomes quieter, not louder than if either interval is played alone. If the two intervals have very slow beats, the beat seems to vanish entirely.

If someone comes up with a better word than "canceling effect" to describe that phenomenon, I will certainly consider using that term, whatever it may be. I have long known that this is a way to take the "noise" out of a piano. Now, I am being told it will make it twice as noisy but I know that simply is not true.
_________________________
Bill Bremmer RPT
Madison WI USA
www.billbremmer.com

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#2302661 - 07/15/14 04:40 PM Re: Theoretical tuning sequence [Re: prout]
DoelKees Offline
1000 Post Club Member

Registered: 05/01/10
Posts: 1760
Loc: Vancouver, Canada
Originally Posted By: prout

My guess is that our brain creates the resultant of 661 and 440, for example, as 221, which will produce a harmonic at 442, which will beat at 2bps.

You could check that by playing the notes separately to each ear with headphones. If you still hear beats they must be made in the brain.

Kees

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#2302676 - 07/15/14 05:00 PM Re: Theoretical tuning sequence [Re: DoelKees]
pyropaul Offline
Full Member

Registered: 11/16/10
Posts: 190
Loc: Montreal
Originally Posted By: DoelKees

I don't hear beats at low volume, only when I crank it up nonlinear distortion, either in my ear or in my speakers, kicks in.

The amplitude modulation you see is a visual effect only. If you plot the energy over say 50ms windows you'll see it is constant.
Unlike when you have a true beat when it oscillates at the beat rate.

Kees


I can hear them clearly at low volume. Two sines at 440Hz and 441Hz also have constant energy over time in the simple summation case surely - yet we still hear the beats as an AM effect. I wish my old analog synthesiser was in a place where I could use it - easy to play around with two sine wave oscillators to see how all of this is perceived. Of course, as you state, our ears are not linear anyway - so there will always be more than just summation occurring. Even without any partials, though, it's easy to tune pure intervals with only sinewaves.

Paul.

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#2302678 - 07/15/14 05:07 PM Re: Theoretical tuning sequence [Re: Bill Bremmer RPT]
Herr Weiss Online   content
Full Member

Registered: 12/26/12
Posts: 166
Loc: New York, N.Y.
Originally Posted By: Bill Bremmer RPT

If someone comes up with a better word than "canceling effect" to describe that phenomenon, I will certainly consider using that term, whatever it may be.


Don't know if they are better but here are some alternatives.

Invalidate, Negate, Neutralize, Void, Annul, (render null and void), Obliterate, (reduce a good effect), Nullify. smile


HW

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#2302704 - 07/15/14 05:46 PM Re: Theoretical tuning sequence [Re: pyropaul]
DoelKees Offline
1000 Post Club Member

Registered: 05/01/10
Posts: 1760
Loc: Vancouver, Canada
Originally Posted By: pyropaul
Originally Posted By: DoelKees

I don't hear beats at low volume, only when I crank it up nonlinear distortion, either in my ear or in my speakers, kicks in.

The amplitude modulation you see is a visual effect only. If you plot the energy over say 50ms windows you'll see it is constant.
Unlike when you have a true beat when it oscillates at the beat rate.

Kees


I can hear them clearly at low volume. Two sines at 440Hz and 441Hz also have constant energy over time in the simple summation case surely

Not over a (say) 50ms window: the energy oscillates at 1Hz, which is what you hear, unlike for the 440 661 case.

Kees

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#2302727 - 07/15/14 06:24 PM Re: Theoretical tuning sequence [Re: DoelKees]
prout Offline
500 Post Club Member

Registered: 11/14/13
Posts: 836
Originally Posted By: DoelKees
Originally Posted By: prout

My guess is that our brain creates the resultant of 661 and 440, for example, as 221, which will produce a harmonic at 442, which will beat at 2bps.

You could check that by playing the notes separately to each ear with headphones. If you still hear beats they must be made in the brain.

Kees


I have checked it, and it is the case that the brain creates the beats.

Here is a binaural wav file that has the a 440Hz sine wave on the left track and a 661Hz sine wave on the right track. The crosstalk of the tracks is below -160db and the spectral analysis shows no energy at any frequency other than at 440Hz on the one track and 661Hz on the other.

Nevertheless, there is a phantom partial heard at (I assume) 221Hz and a clear 2 beats per second pulsing.

Edit: Corrected track separation value to -160db.


Edited by prout (07/15/14 06:27 PM)

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#2302821 - 07/15/14 10:55 PM Re: Theoretical tuning sequence [Re: Bill Bremmer RPT]
DoelKees Offline
1000 Post Club Member

Registered: 05/01/10
Posts: 1760
Loc: Vancouver, Canada
Originally Posted By: Bill Bremmer RPT
I seem to recall some years ago that someone told me that the "canceling" effect that I was hearing was not the same as what happens with noise cancellation systems. That is why I always use the word, "effect" when I talk about it. If it isn't truly a cancelation, then it is something else which mimics that effect.

When I tune the EBVT or ET via Marpurg, I always check my equally beating intervals by playing them simultaneously. If the two intervals are not quite equal, the slow beat between them emerges. When the two intervals, whether slowly or rapidly beating are truly equal, the beating sound becomes fainter, certainly not louder. The entire cluster of tones, whether a consonant, mildly dissonant or sharply disonant sound becomes quieter, not louder than if either interval is played alone. If the two intervals have very slow beats, the beat seems to vanish entirely.

If someone comes up with a better word than "canceling effect" to describe that phenomenon, I will certainly consider using that term, whatever it may be. I have long known that this is a way to take the "noise" out of a piano. Now, I am being told it will make it twice as noisy but I know that simply is not true.

I certainly didn't mean to say that. If equal beats are coincident they will sound like 1 beat but more pronounced, but if they are interleaved you will hear a beat twice as fast but softer. In practice the beats will never be exactly equal so you will get some mix between these two extreme theoretical cases.

My main point is that true "beat cancellation" analogous to noise cancellation in headphones is not possible so can't explain the phenomena you observe. This does not mean the phenomena does not exist.

I like Bernhard's term "beat masking". If this is best achieved by equal or unequal beatrates or if it exists at all I don't know, but I keep an open mind on it.

"Auditory masking" is a well developed field of study. They measure basically how effective a sine wave at frequency f1 can be made inaudible by playing simultaneously a sine wave at frequency f2 depending on their relative loudness. In that case the masking is always most effective when the frequencies are the same.

Kees

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