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Bill Bremmer has posted a number of times about tuning “mindless octaves” by tuning the 4:1 double octave wide so that it beats at the same speed as the resulting 3:1 P12, which is still narrow from just intonation, but wider than it would be with a beatless 4:1 double octave (at least in ET…). I’ve tried it with varying degrees of success. Sometimes a piano’s false beats and lack of sustain make it difficult to hear these slow beats.

After thinking about what these intervals really are, I realized that there is a RBI test for tuning the “mindless octave”. The test for a 4:1 double octave is the M3-M17 test. If the two intervals (5:4, 5:1) beat the same, then the double octave (4:1) is beatless. And the test for a 3:1 P12 is the M6-M17 test. Again, if the two intervals (5:3, 5:1) beat the same, then the P12 (3:1) is beatless. The common interval in these tests is the M17 and in each test the common partial is the 5th partial of the M17. So the RBI test for a “mindless octave” would be when the M17 beats faster than the M3, but slower than the M6.

Example: When tuning A5 the M17 of F3-A5 should beat faster than the M3 of F3-A3 but slower than the M6 of F3-D4.

Of course the ever-present problem of any RBI test still exists: The beat speeds are too fast in the higher treble to be very discernable. It would be tempting to temporarily detune the test note so that the beat speeds would be slower, but that would be very time consuming. But why not use a pitch source other than the piano itself for the test note? As with a true test, and not a progressive check, the pitch does not have to be accurate. The intervals need only be correctly wide or narrow and the beat speeds usable. Also, by having the test note droning, one hand can play the note being tuned while the other manipulates the hammer, rather than having to tune the single octave and then listen to the tests.

I gave this a try with a Peterson VS-II tuner, which produces square wave tones that are adjustable to 0.1 cent, amplified by a desk top guitar amplifier. It worked! How practical it is I don’t know. It was just an experiment. It might only be useful for training.

I only used it to tune up to C7 for a couple of reasons. The “mindless octave” wasn’t quite enough stretch to suit me for the last octave. And also, as the test note was brought higher and higher in pitch (in order to keep the beat speeds discernable) and the octaves were stretched more and more (as a result of tuning “mindless octaves”) the difference between the beat rates of the two test intervals (M3 and M6) became too different to be able to place the beat speed of the tuning interval (M17) accurately between them. I realize now that this might have been overcome by raising the pitch of the test note even higher until the M3 was narrow and beating at the same speed as the still wide M6. The M17 could then be tuned beatless and still produce a “mindless octave”.

If anyone notices any errors or omissions in this post, even if you think the Topic is silly, please let me know so that I can make corrections for the sake of posterity.

Me too I've tried to tune octaves a la Bremmer, with equal beating between double-octave and octave + fifth, but in the high treble there is almost no sustain so it´s difficult to make such compromise with slow beating intervalls.

It sounds interesting, what you did, using M3rds, M6ths and M17ths you have fast beating intervalls to compare.

I should find a pitch source to give it a try.

I wonder how does Bill Bremmer do it? I mean without a tone generator, nor FBI tests...

BTW, I think Bill Bremmer tunes this way not only in ET but also in EBVT, because it's not a temperament issue, but a way of stretching the treble section of pianos.

Gadzar:

Yes, Bill has mentioned that he uses the “mindless octave” for tuning non-ET octaves and refers to them as "tempered" octaves. Interestingly, it seems that the octaves would be stretched unevenly, and perhaps enhance the non-ET sound. I think there may be a problem with a temperament that has any wide, rather than narrow, fifths. It seems that the double octaves would have to be shrunk rather than stretched in order for the double octaves to beat the same as the octave-fifths.

I don't see a problem. In well temperaments, where there are pure fifths the piano is streched so the pure fifths remain pure, they do not become stretched and wide. At least in the temperamnet section of the piano.

Then when you tune the high treble the "pure" fifths in that temperament may become wide but it is not a "temperament" issue, it is only a side effect of stretching the piano so the notes don't sound too flat. If we tune pure fifths in the high treble the notes will sound flat, even if they are not. Thus by stretching this way, our ear will tell us the note is OK, and the temperament is OK.

Gadzar:

Thanks for showing interest! (Yes, I should admit to you that I am a “math person”, just not a formally trained one. I had to learn plane and spherical trig on my own...)

Let me give an example. Let’s say that we are tuning A6, and because of the chosen temperament when the 4:1 double octave A4-A6 is tuned beatless the 3:1 octave-fifth D5-A6 is wide by 2 bps. If the double octave is tuned wider the octave-fifth also beats faster and a “mindless octave” (where the double octave and the octave-fifth beat at the same rate) can never be reached. The octave-fifth will always beat faster than the double octave. However, if the double octave is tuned more narrow, then the wide octave-fifth is also tuned less wide and a “mindless octave” can be tuned with the double octave being narrow and the octave-fifth being wide.

Isn't this contrary to the 'definition' of the "mindless octave" in the original post? Is it valid with such a temperament? I need to search for the "MO"...I seem to have missed it...and Bremmer calling something "mindless"--gotta see THAT!!

Edit: Well, a search yields only this thread. Any pointers?

I think this is not possible. You can´t have the double octave beatless and octave + fifth wide. That implies the 12th is wider than the double octave, wich is wrong.

But I see your point. If you have a wide fifth there is no more equal beating point between the 12th and the double octave. In such a case the double octave and the 12th will be both wide and the double octave will always beat faster than the 12th.

But that means that when tuning equal beating double octaves/12ths in fact you never get wide 12ths. Doesn´t it?

John:

- Try This Link -

In fact in a temperament with some pure fifths, like well temperaments have, if the fifth is pure, then the 12th must be also beatless and you must tune a beatless double-octave! If the fifth is narrow then you can tune equal beating doubleoctave/12th.

But you must never tune a wide fifth! In such a case the doubleoctave and the 12th won't never beat the same.

Thanks, Jeff...gonna have to digest that one...LOL!!

Gadzar:

There is a concept that I don’t feel I have completely grasped. When a piano’s stretch is to be defined by an equal beating interval type, how can this be done to the nth degree? One interval effects the other back and forth ad infinitum. (I never got around to learning calculus…) Of course in practice the ability of the tuner to manipulate the pin is the limiting factor. But if the temperament is unequal, well, how are the notes chosen that ultimately determine the piano’s stretch.

But let’s try another example. A two-octave non-ET temperament is tuned with, say 6:3 octaves. If “mindless octaves” are then tuned going up the scale, the amount that each double octave is stretched is actually determined by the width of the fourth at the bottom of the double octave. The wider this fourth is, the wider the double octave. But if the fourth is narrow from just intonation, then the double octave would have to be tuned narrow of just, also.

Wonder if I’ll be able to sleep tonight.

Unright,

Thanks for the link to Bill Bremmer's post where he talks about "mindless octaves".

In fact he said:

"It is so easy, in fact, that I sometimes refer to the process jokingly as tuning "mindless octaves" because no matter what your state of mind or body, you can hardly go wrong and make an error."

But in the same post he said:

"Now, compare each of these notes, F6-C6 first by playing a double octave, example F#6 with F#4, then listen to the top note with the note an octave and a 5th below it, example, F#6 and B4. If you have tuned a very pure sounding F#5 to F#6 octave initially, the double octave, F#4-F#6 will probably sound OK but when you play the F#6 with the B4 (the octave and 5th below it) you will probably hear too much of a beat in that octave and 5th interval.

Now, if the piano has a sostenuto pedal, play and hold the B4-F#6 interval and press the pedal to hold just these two notes open. If it does not have a sostenuto pedal, play the two notes first, then press the damper pedal (with the same movements as you would to use the sostenuto pedal) to hold open the notes so that you can sharpen the F#6 just slightly. (Naturally, either a double octave or an octave and 5th is far to wide for one hand to play and hold, so you need a pedal). The only difference will be that you will hear just a little more ambient "noise" if you use the damper pedal than if you use a sostenuto pedal.

Now, with the dampers held open with either the sostunto or damper pedal, slightly sharpen the F#6 until the beat between B4 and F#6 diminishes but don't make the octave and 5th completely pure. Now, check again the double octave, F#4-F#6. It should still sound good, not having an obvious beat. The result will be that both the double octave and octave and 5th should sound good but in reality, the double octave will be slightly wide and the octave and 5th will still be slightly narrow but both intervals will be tempered by the same amount but a very slight amount.

This gives you an exact and Equal Beating compromise between the double octave and the octave and 5th."

I think it is clear enough that he doesn't tune wide fifths nor 12ths.

This is what threw me. I think Jeff's getting at a way to use the MO tuning for non-ET temperaments, where I guess some fifths are narrow and some are wide...I don't know if it will be valid or useful for such, at least on the wide fifths, for the reason he gave.

Am I close to right?

(btw, you shoulda done the calculus first...after the chapter on vectors in polar coordinate systems...spherical trig would've been a breeze!! 'Course, that's kinda like using a cannon instead of a flyswat...LOL)

I did not say anything about how Bill tunes a temperament.

I realize now the simplicity of the MO’s. It is determined solely by the fourth at the bottom of the double octave. The fourth partial of the lower note and the third partial of the upper note are the nearly coincident partials for the first partial of the note being tuned. The note being tuned is placed half way between these two partials. The wider the fourth, the wider the double octave. As the piano is tuned toward the treble, any wider fourths become wider and wider with each octave, while the less wide ones, not as much. If a fourth is narrow, the double octave will be narrow also. MO’s would probably not be suitable for temperaments with narrow fourths. Maybe not for temperaments with just fourths either.

I will be able to sleep tonight.

Its interesting that Newton discovered (I don’t believe anything has ever been truly “invented”) calculus before trigonometry.

Yeah!

But it is still hard to listen to! Even more if you have no grand with a sostenuto pedal.

Your idea of using FBIs is interesting. I think I can give it a try with my wife's laptop to generate the tones.

I can also use Tunelabpro to generate the tones with my Pocket PC! Why didn't I saw it sooner?

So how did you do your test with the Peterson VS-II tuner?

For example to tune A6 you must hear F4.

So you put the generator at F4 and you compare A4, D5 and A6 beating against the generated F4. And you can tweak a little your F4 to have audible beat rates. Is that correct?

Jeff:

I ran into the same thing you appparently have, a couple of years ago when I experiminted with Bill's aural equal-beating octave technique in ET. For me, the beats are just too slow to get enough accuracy.

Also like you, I realized the 3rd-17th and 6th-17th tests could be used for this purpose, and I almost e-mailed Bill about it, saying that was the one thing he might add to his descriptions, for the benefit of students who share this concern.

Although these RBI tests are essential parts of my octave tuning in the treble, I don't use them to get equal beating between double octaves and twelfths. I also sometimes use RBI tests for nineteenths (two octaves and a fifth), and triple octaves.

I don't have time right now to carefully read the rest of what you guys are talking about, but good topic.

Jeff

Yes, that is what I did. When tuning C7, I set G#4 22 cents sharp, but like I said, the beat rates between the two test intervals were so different that it was hard to judge the mid point. But if I had gone sharper yet, until the one test interval was wide and the other narrow but both beating the same rate, then I could have tuned C7 as beatless to the tone generator. I mentioned this before.

Now two things I didn’t mention. First, just to see, I tried using a cheap guitar tuner also, but the tone was too distorted to work well. Second, since the partial that is being used is actually the note being tuned, it seems that it would be simpler just to set the tone generator to that note rather than a 17th lower. This doesn’t work because then there are many other partials matches that occur and the beats that need to be heard are obscured.

Let me know how it works!

Jeff:

I figured someone else would have realized there were RBI tests also, but I didn’t remember any mention of it. I was expecting you to chime in on this. Thanks! Anything else you’ve been keeping to yourself?