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#2229643 - 02/11/14 01:45 PM Re: Do we hear 'in tune' intervals by size or beats? [Re: Tunewerk]
UnrightTooner Offline
4000 Post Club Member

Registered: 11/13/08
Posts: 4919
Loc: Bradford County, PA
Originally Posted By: Tunewerk
Arguably, it can, since the tritone is an unstable interval, artificial to the 12-TET scale, with many definitions.

(1) 5:4
(2) 6:5
(3) 6:5
(4) 5:4 * 6:5 = 3/2
(5) 6/5 * 6/5 = 36/25
(6) 5:4 * 6/5 * 6/5 = 9/5

Everything being held together by the pure internal intervals and a pure 9/5 D7th produces a pure 36/25 tritone, listed by Haluska as the classic diminshed 5th.

Definitions for the tritone include:

Classic augmented 4th, 25:18 (569c)
Lesser septimal tritone, 7:5 (583c)
Just augmented 4th, 45:32 (590c)
12-TET artificial tritone, (600c)
Greater septimal tritone, 10:7 (617c)
Classic diminished 5th, 36:25 (631c)

The lesser and greater septimal tritone are the most consonant (lowest prime number combination) versions of the tritone, but the closest ratios to ET are the 17:12 (603c) tritone and the 24:17 (597c) tritone.


I wasn't talking about the tritone. I was talking about the minor 3rd between the 5th and 7th.

Let's use 100hz as tonic. The major 3rd would be 125hz and the 5th would be 150hz. The interval and ratio between the major 3rd and the 5th is a minor 3rd and 6:5, respectively. But where do you put the 7th? As a minor 7th (7:4) at 175hz above the tonic or as a minor 3rd (6:5) above the 5th at 180hz?
_________________________
Jeff Deutschle
Part-Time Tuner
Who taught the first chicken how to peck?

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#2229647 - 02/11/14 01:48 PM Re: Do we hear 'in tune' intervals by size or beats? [Re: DoelKees]
pyropaul Offline
Full Member

Registered: 11/16/10
Posts: 184
Loc: Montreal
Originally Posted By: DoelKees
Originally Posted By: BDB
If you understand it so much better than I, you should be able to explain your objection in a paragraph.

Hij heeft de klok wel horen luiden maar weet niet waar de klepel hangt.
Literal Translation: "He did hear the sound of the bell, but doesn't know where the clapper hangs."
Meaning: "He thinks he knows the subject, but the essence eludes him."

Kees


Which he? Me or BDB? I've done enough digital ASIC designs using audio and video DSP that I think I understand the essence pretty well. Heck, that's why I chose anti-aliased square waves for the audio example smile

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#2229648 - 02/11/14 01:52 PM Re: Do we hear 'in tune' intervals by size or beats? [Re: prout]
Withindale Offline
1000 Post Club Member

Registered: 02/09/11
Posts: 1939
Loc: Suffolk, England
Isn't the signal from (say) a CD basically either 0 or 1 at any instant?
_________________________
Ian Russell
Schiedmayer & Soehne, 1925 Model 14, 55" upright
Ibach, 1922 49" upright (project piano)

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#2229649 - 02/11/14 01:54 PM Re: Do we hear 'in tune' intervals by size or beats? [Re: Withindale]
UnrightTooner Offline
4000 Post Club Member

Registered: 11/13/08
Posts: 4919
Loc: Bradford County, PA
Originally Posted By: Withindale
Isn't the signal from (say) a CD basically either 0 or 1 at any instant?


Actually it is the square root of 1. wink
_________________________
Jeff Deutschle
Part-Time Tuner
Who taught the first chicken how to peck?

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#2229650 - 02/11/14 01:56 PM Re: Do we hear 'in tune' intervals by size or beats? [Re: Withindale]
pyropaul Offline
Full Member

Registered: 11/16/10
Posts: 184
Loc: Montreal
Originally Posted By: Withindale
Isn't the signal from (say) a CD basically either 0 or 1 at any instant?


No, it's not. It's a 16-bit signed number which is fed into a digital to analogue converter (DAC) which then outputs a voltage that's proportional to the number that's fed into the DAC. The output of the DAC is then fed through a reconstruction filter to remove the artifacts that are above the required output band. The final output of your CD player is an analogue AC voltage which can be amplified and fed to your speakers (or headphones).

For SACD CDs, the data read off the CD is in the form of a high speed bitstream (about 1Mbps) but the data is reordered back into digital samples (24 bits in this case, rather than the 16 used in regular CDs). From there on, it's the same process chain: DAC->reconstruction filter->analogue output.


Edited by pyropaul (02/11/14 02:11 PM)
Edit Reason: Added SACD info

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#2229665 - 02/11/14 02:14 PM Re: Do we hear 'in tune' intervals by size or beats? [Re: prout]
prout Offline
500 Post Club Member

Registered: 11/14/13
Posts: 782
BDB,

Please, please, please download audacity. It's free, and a most fabulous tool for recording audio, editing it, and, even more so, understanding how digital signal sampling works. You are essentially correct when you say there is only one variable, volume, but what you miss is 'varying over time'. Load a short audio sample into audacity, then zoom in until you see the individual sample. You will then have a basic understanding of how it works.

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#2229668 - 02/11/14 02:17 PM Re: Do we hear 'in tune' intervals by size or beats? [Re: pyropaul]
Withindale Offline
1000 Post Club Member

Registered: 02/09/11
Posts: 1939
Loc: Suffolk, England
Originally Posted By: pyropaul
Originally Posted By: Withindale
Isn't the signal from (say) a CD basically either 0 or 1 at any instant?

No, it's not. It's a 16-bit signed number ...

_________________________
Ian Russell
Schiedmayer & Soehne, 1925 Model 14, 55" upright
Ibach, 1922 49" upright (project piano)

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#2229670 - 02/11/14 02:20 PM Re: Do we hear 'in tune' intervals by size or beats? [Re: prout]
prout Offline
500 Post Club Member

Registered: 11/14/13
Posts: 782
Pyropaul and Withindale. You guys are not talking about the same thing. Withindale is speaking of an instantaneous data point on the physical medium of the CD and Pyropaul is speaking of the error corrected serial arrangement of many data points, but I think you both have figured that out by now.


Edited by prout (02/11/14 02:23 PM)

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#2229672 - 02/11/14 02:23 PM Re: Do we hear 'in tune' intervals by size or beats? [Re: Withindale]
pyropaul Offline
Full Member

Registered: 11/16/10
Posts: 184
Loc: Montreal
And then that channel bitstream is error corrected and the resulting 16-bit signed numbers applied to the DACs at 44,100 samples per second ...

The "signal" from the CD's surface is a slight variation in the polarization angle of the laser used to illuminate it ... this is then converted into the bit stream in your diagram. The encoding of the spiral in the first place was from the serialization of the 16 bit values, together with some Forward Error Correction (FEC) codes without which there would be too many errors to give a decent audio output.

[edit] It's actually even more complicated than that because there's timecode information as well as other sub-channel information. This wiki article covers the details pretty well: CD Audio Format specification


Edited by pyropaul (02/11/14 02:34 PM)
Edit Reason: Added link to CD audio format spec

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#2229680 - 02/11/14 02:33 PM Re: Do we hear 'in tune' intervals by size or beats? [Re: prout]
prout Offline
500 Post Club Member

Registered: 11/14/13
Posts: 782
Back in the 80s I spent weeks writing a computer program to play Messiaen's 'O sacrum convivium' in just intonation. The time spent was in deciding how much to temper the immediate interval to be correct in the succeeding interval. At the slow speed it is sung, one must move the pitch of a given note during its execution to be 'correctly' pitched. The result was amazing, and give me great respect for barbershoppers, The King's Singers, and such like.

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#2229752 - 02/11/14 04:27 PM Re: Do we hear 'in tune' intervals by size or beats? [Re: prout]
BDB Online   content
Yikes! 10000 Post Club Member

Registered: 06/07/03
Posts: 21447
Loc: Oakland
Let me illustrate with a picture. The picture pertains in both ways:



So is this picture a picture of the way that two sine waves interact with each other, or is it a bunch of bar graphs (square waves) pasted next to each other? Really, it is both! It is an approximation of the sine waves, and if you look at it with a magnifying glass, or enlarge the picture to the pixel level, you will see that it is individual squares placed on one side or another of the axis. The same thing happens with digital sound.

This is why the frequency at which you listen is important. At some point, sound gets blurred, just as the picture blurs so it looks like a smooth wave.
_________________________
Semipro Tech

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#2229782 - 02/11/14 05:06 PM Re: Do we hear 'in tune' intervals by size or beats? [Re: pyropaul]
DoelKees Offline
1000 Post Club Member

Registered: 05/01/10
Posts: 1710
Loc: Vancouver, Canada
Originally Posted By: pyropaul
Originally Posted By: DoelKees
Originally Posted By: BDB
If you understand it so much better than I, you should be able to explain your objection in a paragraph.

Hij heeft de klok wel horen luiden maar weet niet waar de klepel hangt.
Literal Translation: "He did hear the sound of the bell, but doesn't know where the clapper hangs."
Meaning: "He thinks he knows the subject, but the essence eludes him."

Kees


Which he? Me or BDB? I've done enough digital ASIC designs using audio and video DSP that I think I understand the essence pretty well. Heck, that's why I chose anti-aliased square waves for the audio example smile

BDB.

Kees


Edited by DoelKees (02/11/14 05:09 PM)

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#2229789 - 02/11/14 05:17 PM Re: Do we hear 'in tune' intervals by size or beats? [Re: BDB]
pyropaul Offline
Full Member

Registered: 11/16/10
Posts: 184
Loc: Montreal
Originally Posted By: BDB
Let me illustrate with a picture. The picture pertains in both ways:



So is this picture a picture of the way that two sine waves interact with each other, or is it a bunch of bar graphs (square waves) pasted next to each other? Really, it is both! It is an approximation of the sine waves, and if you look at it with a magnifying glass, or enlarge the picture to the pixel level, you will see that it is individual squares placed on one side or another of the axis. The same thing happens with digital sound.

This is why the frequency at which you listen is important. At some point, sound gets blurred, just as the picture blurs so it looks like a smooth wave.


I think the key point you're missing is the action of the low-pass reconstruction filter - the break point of which is set to be just higher than the highest frequency you want to work with. In a CD sampled at 44.1kHz, the Nyquist frequency is 22.05 kHz so the ideal reconstruction filter has a "brick wall" response at that frequency. In reality, a steep low pass filter with a break point at about 20kHz is used. The square waves you mention between the points in the sampling get rounded off by the sin(x)/x (sinc) function used in the filter. The square wave example I posted already had the anti-aliasing performed so the "squares" had a maximum ramp set to be the same as a sinewave at the band limit used (20kHz). There are no "square waves" used in digital audio as their harmonics cause aliasing artifacts. I had to take great care when designing digital video ASICs that the reconstruction on such things as the sync pulses used in analog TV were such that their edges were bandlimited to the appropriate frequency. A casual observer would think they were square, but they were actually parts of a sine.

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#2229790 - 02/11/14 05:19 PM Re: Do we hear 'in tune' intervals by size or beats? [Re: BDB]
Chris Storch Offline
Full Member

Registered: 08/13/09
Posts: 197
Loc: Massachusetts
BDB, a bar graph is not a square wave. Let me illustrate with an image...

Is this picture a picture of hole you're digging yourself into, or is it a bunch of shovel-scoops tightly packed next to each other, yet to be removed? It is both! For what is a hole really, except a series of inverse shovel-scoops?

Mathematically, that's expressed as 1/(shovel-scoop) or (shovel-scoop)^-1

_________________________
Chris Storch
Acoustician / Piano Technician

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#2229793 - 02/11/14 05:25 PM Re: Do we hear 'in tune' intervals by size or beats? [Re: prout]
Herr Weiss Offline
Full Member

Registered: 12/26/12
Posts: 131
Loc: New York, N.Y.
Thank you all for the laughs!! laugh

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#2229814 - 02/11/14 05:45 PM Re: Do we hear 'in tune' intervals by size or beats? [Re: prout]
BDB Online   content
Yikes! 10000 Post Club Member

Registered: 06/07/03
Posts: 21447
Loc: Oakland
On the other hand, the basis of integral calculus is that areas can be approximated by rectangles, which is pretty much what you are doing with digital recording, or digging a hole. You folks are arguing one way when you want it one way, and another way when you want it another. I say it is both, more or less.
_________________________
Semipro Tech

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#2229822 - 02/11/14 05:54 PM Re: Do we hear 'in tune' intervals by size or beats? [Re: BDB]
pyropaul Offline
Full Member

Registered: 11/16/10
Posts: 184
Loc: Montreal
Originally Posted By: BDB
On the other hand, the basis of integral calculus is that areas can be approximated by rectangles, which is pretty much what you are doing with digital recording, or digging a hole. You folks are arguing one way when you want it one way, and another way when you want it another. I say it is both, more or less.


There's no rectangles in digital audio. Everything is band-limited somewhere to avoid them once you move back to the time domain.

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#2229830 - 02/11/14 06:03 PM Re: Do we hear 'in tune' intervals by size or beats? [Re: prout]
BDB Online   content
Yikes! 10000 Post Club Member

Registered: 06/07/03
Posts: 21447
Loc: Oakland
Then you did not post square waves!
_________________________
Semipro Tech

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#2229859 - 02/11/14 06:37 PM Re: Do we hear 'in tune' intervals by size or beats? [Re: BDB]
DoelKees Offline
1000 Post Club Member

Registered: 05/01/10
Posts: 1710
Loc: Vancouver, Canada
A true square wave would require infinite air velocity and as such is inconsistent with Einstein's special theory of relativity. Not to mention black hole formation at the jump.

Also don't forget that in quantum theory a piano can be in-tune and out-of-tune at the same time, like Schroedingers cat.

Kees

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#2229881 - 02/11/14 06:58 PM Re: Do we hear 'in tune' intervals by size or beats? [Re: BDB]
Tunewerk Online   blank
Full Member

Registered: 03/26/11
Posts: 406
Loc: Boston, MA
Pyropaul, I'm not sure if you've been informed of the rules in this forum..

BDB is not subject to correction, per guideline #34, concerning posters who spend their entire life here and exceed 10,000 posts. As an interesting sidenote, he is also never wrong.

The sooner you can see this, the sooner your error of differing opinion can be hopefully corrected.
_________________________
www.tunewerk.com

Unity of tone through applied research.

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#2229902 - 02/11/14 07:26 PM Re: Do we hear 'in tune' intervals by size or beats? [Re: DoelKees]
pyropaul Offline
Full Member

Registered: 11/16/10
Posts: 184
Loc: Montreal
Originally Posted By: DoelKees
A true square wave would require infinite air velocity and as such is inconsistent with Einstein's special theory of relativity. Not to mention black hole formation at the jump.

Also don't forget that in quantum theory a piano can be in-tune and out-of-tune at the same time, like Schroedingers cat.

Kees


Is that when it's in both Reverse Well and ET at the same time?

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#2229903 - 02/11/14 07:29 PM Re: Do we hear 'in tune' intervals by size or beats? [Re: BDB]
pyropaul Offline
Full Member

Registered: 11/16/10
Posts: 184
Loc: Montreal
Originally Posted By: BDB
Then you did not post square waves!


Do you believe in square waves? Your earlier comments implied that digital audio is only square waves but Kees correctly pointed out that there's no such beast. In the real world of digital audio, all have are band-limited reconstructions of data presented as certain sample rates. Good enough for anyone older than 20 years old as most people cannot hear to 20kHz much beyond then. Not that I'm correcting you, but I'm not wrong either.

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#2230073 - 02/12/14 12:59 AM Re: Do we hear 'in tune' intervals by size or beats? [Re: BDB]
Bill Bremmer RPT Offline
3000 Post Club Member

Registered: 08/21/02
Posts: 3207
Loc: Madison, WI USA
Originally Posted By: BDB
Let me illustrate with a picture. The picture pertains in both ways:



So is this picture a picture of the way that two sine waves interact with each other, or is it a bunch of bar graphs (square waves) pasted next to each other? Really, it is both! It is an approximation of the sine waves, and if you look at it with a magnifying glass, or enlarge the picture to the pixel level, you will see that it is individual squares placed on one side or another of the axis. The same thing happens with digital sound.

This is why the frequency at which you listen is important. At some point, sound gets blurred, just as the picture blurs so it looks like a smooth wave.


BDB,

I am not really interested in following this idiotic tangent but one thing I could see right away was how you jumped all over Kees when he posted a graph that appeared to be a straight line because it was a small piece of a long curve. Now, you are posting the same kind of thing in reverse and making everybody go nuts about it! Is this what you enjoy doing?

Honestly BDB, one has to sift through literally thousands of your posts to find one that is not merely condescending and one that actually has any contributory value to it. I would suggest that you stop trying to play with people's minds and use the knowledge and skills that you have to actually contribute more often to discussions rather than trying to prove over and over again how you are so way ahead of everyone else about everything.

I have no idea what a square wave is and I don't really care what one is. It has nothing at all to do with the Original Poster's (OP) question about how ordinary people perceive intervals.

I had wanted to answer that question immediately but did not have time. It is an interesting question because some true historical research would answer it. Not just your once off putting and thoroughly condescending remark you once made that "Jorgensen's book reads like a laundry list of old temperaments"!

If you had actually read much of the material at all, you would have seen that people in past centuries did not perceive Rapidly Beating Interval (RBI) beat rates the way we are required to do today. They most often played triads to confirm whether or not a chord seemed something like, well pleasing to the ear or as sharp as the ear can well bear rather than minute increments of beat rates as have been squabbled over on this forum recently.

This, I believe was what the OP was wanting to know about. My answer to him is that today's piano technicians tend to focus so intently on beat rates that they often let the beauty and soul of music escape them. There is a standard and the performance/broadcast/recording industry that is very tight and unforgiving.

It does not allow for much experimentation or alternatives of any kind. It has a monolithic idea of what tuning should be and a strangle hold over past precedents in tuning styles. If anyone dares to try to introduce something different, it is ridiculed and put down as substandard.

Not every piano is in a recording studio or on a concert stage. Most piano technicians do not, in fact serve that industry. It is nice to hold up that standard as one to aspire to, surely it is. But the ordinary working technician in everywhere else but the concert halls and recording studios of Los Angeles, New York and London have to cope with the reality of what they encounter each day.

Just as for me, I don't think anyone could ever pay any piano technician who has a home, a spouse, children, community ties and obligations enough money to just pick up and go to one of those places just to be one of the people who touches up tunings that were done only three hours ago by someone else.

I'll always remember what a man in Mexico City once told me about Mexican Folkloric musicians: Each group from each area has its own slightly out of tune sound that distinguishes it as being from where they are. Those musicians are not interested in "straight to the strobe/Lawrence Welk" sounding music! It would destroy the character of the music that they produce from their heart and souls if they did try to change the way they perceive tuning!

They do not listen to beat rates! They perceive tonality in whatever way they do! Not to say that we all want to try to replicate what they do, certainly not but musicians and audiophiles do not really ever perceive beat rates the way piano technicians of today do.

In fact, as it has been reported on this forum before, the more that a piano technician perfects his/her solely beat rate perception, the less that he/she will be able to appreciate music as it is actually performed in most cases!

I am a victim of that myself. It is difficult for me to ever attend a piano concert of any type and only enjoy the music. I only most often hear beat rates, not music!

So, whether digital reproductions are "square waves" or not, I don't really care and don't really want to know about that. What I care about is whether my clients like my work for which I get paid and earn a living.
_________________________
Bill Bremmer RPT
Madison WI USA
www.billbremmer.com

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#2230124 - 02/12/14 02:31 AM Re: Do we hear 'in tune' intervals by size or beats? [Re: prout]
BDB Online   content
Yikes! 10000 Post Club Member

Registered: 06/07/03
Posts: 21447
Loc: Oakland
I agree that this discussion of square waves versus sine waves is somewhat off topic, although there is a relationship. It was just an off-hand remark that I made which led to the conversation.

I think, Mr. Bremmer, that the conflict that you are having is that we look at the world in different ways. You seem focused on methods, while I am more interested in the reasons for them. So for instance, when I pointed out that your very good equal temperament via Malpurg could yield improved results by slight adjustments from equal beating, which, incidentally, would lead to the way that I set the temperament, your instinct was to reject it, because it was not part of the method. You said that the people you were teaching would inevitably make mistakes. I felt that was condescending.

Being tied to a method tends to restrict one's thinking, such as when someone asked whether the Malpurg method could be used with a C fork. Your solution was a rather convoluted way of tuning A from C, while mine was to use the initial thirds E, Ab, and C rather than F, A, and C#. I admit that part of that comes from years of tuning with a C fork, but it is also because I am not necessarily so tied to a method. But I only mention this to explain why the method is not sufficient for me.

In any case, the roundabout tie-in to the original question, is that there is a transition from when beating is annoying to when intervals become annoying, which depends on the register in which it occurs, as well as the interval in question. Just as in the lower registers of a piano, the beating of square waves (it does not really matter whether you know what they are or not) will sound distinct from the beating of sine waves or of piano strings, there are registers where the beating can more annoying. It also depends on which interval it is, of course. Beating unisons are always bad, octaves a little less so, and so on. At higher registers, and more remote registers, the intervals will sound bad, without one being able to distinguish the beating. The phenomenon may be the same, however.

I am sorry that you are unable to turn off your critical ear and just enjoy the music, though. That is what is important for me.
_________________________
Semipro Tech

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#2230193 - 02/12/14 07:53 AM Re: Do we hear 'in tune' intervals by size or beats? [Re: UnrightTooner]
UnrightTooner Offline
4000 Post Club Member

Registered: 11/13/08
Posts: 4919
Loc: Bradford County, PA
Originally Posted By: DoelKees
A true square wave would require infinite air velocity and as such is inconsistent with Einstein's special theory of relativity. Not to mention black hole formation at the jump.

Also don't forget that in quantum theory a piano can be in-tune and out-of-tune at the same time, like Schroedingers cat.

Kees


Or more to the point, can a chord be in just intonation and tempered intonation at the same time:

Originally Posted By: UnrightTooner
.....

I wasn't talking about the tritone. I was talking about the minor 3rd between the 5th and 7th.

Let's use 100hz as tonic. The major 3rd would be 125hz and the 5th would be 150hz. The interval and ratio between the major 3rd and the 5th is a minor 3rd and 6:5, respectively. But where do you put the 7th? As a minor 7th (7:4) at 175hz above the tonic or as a minor 3rd (6:5) above the 5th at 180hz?
_________________________
Jeff Deutschle
Part-Time Tuner
Who taught the first chicken how to peck?

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#2230220 - 02/12/14 09:06 AM Re: Do we hear 'in tune' intervals by size or beats? [Re: prout]
prout Offline
500 Post Club Member

Registered: 11/14/13
Posts: 782
Wow. What an interesting melange of ideas and opinions on what I thought was a simple question. We have entered the realm of both physics and metaphysics.

Question: Do you, as musicians and/or tuners hear in a musical context, an interval, such as a third or fifth as being in tune or not by the width of the interval only and not the beat rate?

The original question above is perhaps na´ve. Is it the case that we hear both beats and width simultaneously, a la Schr÷dinger? Can we hear an interval as wide or narrow without perceiving beats, or is perceiving beats a necessary prerequisite, even if the hearer is unaware that that is what they are in fact hearing? This would support the literature regarding historic tuning practices as Bill mentioned.

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#2230226 - 02/12/14 09:24 AM Re: Do we hear 'in tune' intervals by size or beats? [Re: prout]
UnrightTooner Offline
4000 Post Club Member

Registered: 11/13/08
Posts: 4919
Loc: Bradford County, PA
I hear the notes related to the 5th partial of brass intruments as being flat without hearing beats. I hear Aretha Franklin stretch the high notes very sharp, without beats. I hear fifths that are too pure because they are (wait for it..), without beats. laugh laugh laugh

Hard to say what my threshhold of stand-alone out-of-tuneness is. I would guess around 10 cents.
_________________________
Jeff Deutschle
Part-Time Tuner
Who taught the first chicken how to peck?

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#2230229 - 02/12/14 09:34 AM Re: Do we hear 'in tune' intervals by size or beats? [Re: UnrightTooner]
prout Offline
500 Post Club Member

Registered: 11/14/13
Posts: 782
Originally Posted By: UnrightTooner
I hear the notes related to the 5th partial of brass intruments as being flat without hearing beats. I hear Aretha Franklin stretch the high notes very sharp, without beats. I hear fifths that are too pure because they are (wait for it..), without beats. laugh laugh laugh

Hard to say what my threshhold of stand-alone out-of-tuneness is. I would guess around 10 cents.


Yeah, that's what I was getting at. We want to hear an accented appoggiatura as a flat unison. I love Joshua Redman's pulled flat flat sevenths on his Moodswing CD. I have worked with cellists playing in quarter tone while the piano holds a ground bass. All these intervals seem to exhibit clear widths without obvious beating.

And yet, one of the most satisfying experiences in choral singing is the dissonant beating of a diminished second, which then resolves to a glorious unison.

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#2230251 - 02/12/14 10:41 AM Re: Do we hear 'in tune' intervals by size or beats? [Re: prout]
Bill Bremmer RPT Offline
3000 Post Club Member

Registered: 08/21/02
Posts: 3207
Loc: Madison, WI USA
BDB,

The ET via Marpurg is meant to be just as it is. If someone wants to tune true ET, the Up a 3rd, Up a 3rd, Down a 5th is a better way to do that. I have taught a lot of novices, so I know what kind of tendencies they have. The ET via Marpurg provides an alternative for technicians who can't manage to get a passable ET any other way. If you want to find out what would happen if they did it your way, then find someone who failed the tuning exam 2 or 3 times and try to teach that person your suggestion and you will understand why I said what I did.
_________________________
Bill Bremmer RPT
Madison WI USA
www.billbremmer.com

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#2230316 - 02/12/14 12:12 PM Re: Do we hear 'in tune' intervals by size or beats? [Re: prout]
BDB Online   content
Yikes! 10000 Post Club Member

Registered: 06/07/03
Posts: 21447
Loc: Oakland
That is terribly condescending. I believe that anyone who can hear beats well enough to tune "Up a 3rd" and "Down a 5th" (that should be down "almost a fifth") should be able to tune a good equal temperament by any number of methods if they understand the temperament properly.
_________________________
Semipro Tech

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