Piano World Home Page Forums Our Most Popular Forums Piano Tuner-Technicians Forum Theoretical tuning sequence

Here are two short videos that show how equally beating intervals, when played together, tend to suppress the beating sound and reduce slightly the overall volume of sound.

https://www.youtube.com/watch?v=qiCDrkPzCnI

https://www.youtube.com/watch?v=qnwnA1dXkJM

It is funny how you forget what you have just posted.

Because amplitude (or rather, energy) is positive, and two positive numbers can't add up to zero.

Or try to visualize two sine wave at say 440 Hz and another at 660 Hz. Now visualize oscillating the amplitude of both waves at 1 oscillation per second (not necessarity synchronous) and put the result together. How can you possibly end up with two original sine waves again?

Kees
PS On the other hand, if you had two acoustic waves of 1Hz you can shift one by 1/2 a period, add them up and end up with a flat line.

Wow Bill, in the second video when you play CE then GE I clearly hear the beats, then when you play the triad GCE it sounds smooth, harmonious, the beats just disappear!

Yes, that is what I hear too. The first second or so, I hear the rapid beat but then it gets "swallowed". In the Slowly Beating Interval samples, in this and every time I do it, I hear what sounds to me like a beat "trying" to happen but it can't.

Now to me, that always meant that one beat was "canceling" the other. If the scientists say that because beats are always "positive" (whatever that means) and therefore two or more positives cannot amount to a zero or anything close to that, OK, fine by me. It is not beat cancellation. Is it therefore, beat interference that mimics cancellation?

Whatever the reason is for the effect, I have known about it for some 30 years and I keep discovering more ways to put it to use. I will call it whatever somebody finally determines the right word is. What I certainly do not hear is a "doubling" of beats or a louder sound.

What I learned how to do, I learned by actually listening to the piano and not listening to what other technicians say and certainly not what scientists who theorize about everything say but who never actually tuned a piano.

It sound nice, but I hear nothing unusual that I can attribute to equal beatings.

To demonstrate the effect of equal beating we'd have to hear that with equal beating it sounds better than without equal beating.

If I am not mistaken in EBVT3 F4A4 and G4B4 have comparable beat rates, C3A4 and F4A4 are not equal beating, but D3G4 and G4B4 are equal beating.

So C3F4A4 should sound less quiet than D3G4B4.

Can you demonstrate that?

Kees

Doel, nothing sounds better than a pure 4th or 5th. In the 3rd octave, the F3-A3 and G3-B3 M3's beat at the same rate by design but the key of F and the key of G still have distinctly different characters. That is because the key of F has a pure fifth but the key of G has a fifth that is tempered about 1.5 as much as in ET.

So, I don't know if a triad with a pure fifth sounds "quieter" than the same triad as it would be tuned in ET but expect it would. You, of all people should know about this kind of thing. The ET only crowd is focused only on equality as the goal of perfection but people like you and me have long known of other characteristics that are far more desirable than having every key signature sound alike.

When you get to the point on the scale of F4-A4, you are at or near the limit of discernibility of beating in an M3. You want me to prove that a C4-F4-A4 triad sounds "louder" than a C4-G4-B4 triad? Sorry, I don't have the time. I know they won't sound the same in the EBVT but I will leave it at that.

I have to admit that what I wrote that I thought would support your topic, equally beating intervals and the value that there is in them, has now drifted off topic. The value that I know is there and have known is there for more than 30 years is now being undermined with "research" that says there is no such value at all.

As usual, it is only theoretical: it wouldn't work, couldn't work and shouldn't be tried. Why bother when it is only in your imagination and nobody can hear the difference anyway? Why not just tune ET like everybody else? Why not do it MY way?

I guess we all have our theories and our own experiences. We all have our own product to sell. We all do what we do because it works for us. We all get testimonials from our clients.

I'll say it again just to make it very clear. I am not a scientist, nor a mathematician nor a physicist or anything else that may apply. My education has been in music and foreign languages. I started tuning pianos at the age of 17 and I did it by listening to the piano. I still do that. I know what it is that I hear. It has often been very difficult to put into words what I do but there, I do have some skill.

I respond, not to what other technicians may say who know nothing really about what I do, only what they perceive through their own bias; I respond to what my clients say. I also respond to what other technicians say who have tried my techniques and found the results to be to their liking. Any other methods and theories by other technicians find similar gratification.

I found your idea to be fascinating. I certainly remember how you also found an equally beating way to arrive at 6 beats per second for the F3-A3 M3 that is called for in the EBVT. It was great thinking, even if it isn't a very practical way to do it. It was, however an example of the power and potential of equally beating intervals.

Now, I am confronted with someone who says that equally beating intervals are worse, not better. They are louder, not softer when played together. Beats cannot "cancel" each other so the result of equally beating intervals can only be worse, not better than non-equally beating intervals. Chords with equally beating intervals would be twice as loud!

It is simply not true and musicians and tuners from past centuries knew that for a much longer time than any people who think that complete eradication of tonality is the ultimate goal. I will continue doing what I do, knowing that it produces the most musical satisfaction for the most people. I know what I hear when I tune and no theorist or researcher can tell me that it is only in my imagination.

Sorry, I thought you were referring to the double vs single correct-as-you-go pass.

Re: using pure intervals to tune ET, that was arrogant of me to say it is a waste of time. I apologize. What I meant to say was, I have a sequence that tunes proper ET size intervals right away. It is like CM3, except for all the notes of the temperament. I'll post it when I have figured out an efficient and concise way to present it.

I really don't want you do anything in particular.

I just have never seen anything that support the advantage of equal beating except to make it easier to tune something by ear.
I don't believe there is any (dis)advantage to equal beating until I see evidence otherwise. Claiming you can demonstrate otherwise but "don't have the time" to show it does not make a very good case for it IMHO.

Kees

Am I alone in hearing those beats in CE and GE and no beats at all in GCE?

I hear an octave G ringing all over the place. Maybe it's my speaker or the quality of the recording. I don't hear any beat cancellation, or whatever we want to call it, although I have experienced it.

if it add something to the tone it is interesting, if it retracts something, way less in my opinion.

I hear 2 intervals riding approx the same beat . I feel it can be done in additive or substractive modes, and that the result will differ in regard of global consonance.
I ten to prefer a sound that flows without being retained, to one that seem to have some slowing.

It makes me think of the Viennese style unison, where the original conflict around center string provides a thickened tone but the process have absorbed/ruled part of the attack energy so the tone is shortened.

In a goal of providing different tonal outputs between intervals I understand that effect can be included - it sound too present to me, not sounding "naturally" but I am not used to that "extreme"

In the lower CEG sample, the clarity of the beating in the triad is lessened and muddied but I still hear the same beating.

I hear the beating completely disappear after a few seconds.

I use this method to tune 99% of the pianos that I tune, including for concert artists. They get on the stage to announce to the public how wonderful the piano sounds, so I will go with their opinion, not yours.

You tune your pianos your way and I will tune mine my way. I didn't hear what you hear and you didn't hear what I hear.

Why do I have this image in my mind of a parakeet fighting it's reflection in a mirror?

Just to confirm I listened again:

Firstly, there is a definite G2 ringing out from somewhere when the G3 is played in some combination.
Secondly, with the G3C4E4 inversion, there is a significant reduction in apparent beating, but the beats are still very audible.
Thirdly, the C3E3G3(C4) inversion, the is hardly any apparent reduction in beating of the CE interval, just a slight reduction in volume but replaced by a muddy quality.

I am just trying to give an honest evaluation.

Am I supposed to just give up and tune ET from now on because everything I have done for the last 30 years has all been an illusion? Did Bach really write the Well Tempered Clavier Music for ET as Jeff "proved"? Was ET "firmly in place" by the time of Brahms as the PTG Journal guy claimed? So Brahms just had a girl like Vanna White spin the Wheel of Fortune to determine which key signature he would use for each piece he wrote because one key signature was the same as another?

Equal Beating only makes things sound worse, not better?

Sorry folks, I don't buy any of it. I know what I hear and so do my clients. I haven't tuned a piano in true ET now for 25 years, almost exactly to the date when I heard a set of Brahms performed in the Rameau-Rousseau-Hall composite 18th Century Modified Meantone Temperament from Owen Jorgensen's Handbook of Equal Beating Temperaments.

I can't prove anything with a few examples recorded on a cellphone. I only know what I have heard and experienced in the last 25 years and I am not about to turn back from it. There is a reason why I have so many loyal clients and why performing artists choose to acknowledge what I have done publicly and why they also do the same for my local colleagues who also choose the non-equal temperaments: Musical satisfaction and often great epiphanies that they have never experienced from ET.

The more I attempt to wring out the physics of piano tuning using sophisticated electronic equipment, the more I realize that the equipment does not hear what we hear. A centimetre shift in the microphone will entirely change the partial amplitudes and phases, which means that your recordings do not capture the quality of the tuning that you hear.

I find that what the tuner hears from the piano bench and what the pianist hears from that same bench is all that matters. Your tunings clearly work and your clientele are happy. Keep up the good work.

Cheers.