Piano World Home Page Forums Our Most Popular Forums Piano Tuner-Technicians Forum Do we hear 'in tune' intervals by size or beats?

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.

Kees

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.

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

Thank you all for the laughs!!

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.

Then you did not post square waves!

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

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.

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

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.

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.

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.

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

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 naïve. Is it the case that we hear both beats and width simultaneously, a la Schrödinger? 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.

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.

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.

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.

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.