Correct me if I'm wrong. The normal ratio for an octave is 2:1. When an octave is stretched, it becomes 4:2 or 6:3. If you pick the higher note in an octave, which one of the 2 sets of octave stretch will sound 'flat' ?

The higher note of the octave is tuned sharp of the lower note in that case. If it is tuned as a 4:2 it will be sharper than if it was tuned as a 2:1. If it is tuned as a 6:3 it will be even sharper.

By "sound flat" you mean in relation to what?

No, no ....

Vibrating between two notes of an octave are the matching partials. They ALWAYS are sounding. Some pianos - the partial matches almost agree. Some less so. No single match is a "default" octave, just a compromise made to minimize the beating heard at all the other levels combined.

Even more fun, start considering the beats within beats, or the combined beats at differing intervals, or the ratio of beats sounding all at the same time....


Ron Koval
chicagoland

The only place that a 2:1 octave would be normal is from C7 to C8

Yes, but don't we tune one note of the octave up or down to get the best partial match? That's what I meant by sharp.

If a 4:2 doesn't sound good then a 6:3 or somewhere in between might.

No, the normal ratio is not typically 2:1 on a piano, and it changes depending on which portion of a piano you are tuning. Also, stretching doesn't "change" ratios as much as it aligns the partials you're talking about.

Have you taken a look at the physics of string vibration? There's lots of stuff to search on like this. Of course, you don't need to study up on the physics in order to be a good tuner, however it will make things much easier if you want to discuss things like 2:1 or 4:2 octaves.

As Ron pointed out, those ratios describe the coincident partials of an octave that exist no matter how an octave is stretched. When we tune an octave, those coincident partials may come and go into and out of alignment, depending on our goals.

Actually, this is a better link than the one I gave in the previous post:

http://en.wikipedia.org/wiki/Physics_of_music#Harmonics.2C_partials.2C_and_overtones

As far as I am concerned, there is only one way to tune octaves on a piano: So that the octaves and the other intervals sound like the intervals they are supposed to be.

So, BDB, if you tune single octaves so they sound beatless, do the double and triple octaves also sound as they are supposed to? If you tune ANY interval as it is supposed to sound, will any of the others also sound that way too?

Hi Mr Bremmer, glad this thread caught your attention. In fact, it was your reply to another post that prompted me to ask this question. You said:

"In an above post, using a similar technique but F3 instead of F2 is incorrect. You may hear something similar but the premise is false because F3 does not have a coincident partial with the first partial of A4. It is coincident with the second partial of A4. Using the F3 instead of F2 may well cause you to tune A4 flat by the amount of inharmonicity there is between the first and second partial of A4 (which would generally be between 1 and 2 cents)."

F2 has a coincident partial with the first partial of A4. F3 has a coincident partial with the second partial of of A4. In between these two, I found myself lost. I began thinking that when we match a lower note with the higher partial of a higher note, we may cause the higher note to sound flat.

That means we don't hear 2:1 or 4:2 or 6:3 since they always are sounding ? That what do we hear ?

Yes, the double and triple octaves also sound beatless. Yes, the other intervals sound the way they are supposed to. That is why I said "So that the octaves and the other intervals sound like the intervals they are supposed to be."

I do not understand how anyone can claim they tune so that the intervals sound wrong, and get away with it.

What happens if you're tuning the upper bass as a 4:2 octave and then you realize that the partials at the 6:3 match are more predominant and sound better. The lower note is dropped slightly and the 6:3 partials come into focus. Wouldn't you say that the octave has been stretched more than it was? You can then have a narrow 6:3 or a wide 6:3 from there.

F3's 5th partial may coincide with A4's 2nd partial at A5, but you aren't trying to set the pitch of A5. That is why Bill noted you would be causing A4 to be flat.

Depending on the piano, and your ability to aurally focus in multiple locations, you may hear beating at all three of those coincident partials.

While learning, you typically only try to focus on one of them. Then when you get better at it, you may be able to rapidly switch between them.

Or if you're a "whole tone" tuner, you'll hear all of them all at once

I work through this whole dilemma by looking at the octave as an area instead of a place. Lately, I have been looking for more ways to avoid tuning octaves at all, because they are ambiguous. Instead, 4ths, 5ths and 12ths seem a better choice, with octaves and double octaves used as checks.

Ah, I see now.... This thread started based on how to set A4 using a fork... Setting between sounding strings on a piano is a little different.

As to the different octave types? They all sound at the same time when you play two notes together. 2:1 4:2 6:3 8:4 10:5 12:6 and so on... Some will be louder than others,depending on if you play low, middle or high on the keyboard. It becomes a matter of focus, or aural tricks to get the mind to filter what the ears hear. If you have a fairly modern machine you can easily determine that the octave types don't match - even in an aurally tuned "pure" octave... There's a journal article from sometime in the last decade that shows realtime beatspeeds and what happens as you optimize one octave type over the others.

Few books or articles take the next step and instead of setting one octave type, find a blend between octave types. That's what I've been advocating with the custom styles on the Verituner for years. Also it seems to be the theory behind the Stopper tuning, where he defines a pure interval as one where the sum of all the sounding beats is at a minimum...

Ron Koval
chicagoland

BDB, what you claim in the first paragraph is quite impossible. What you claim in the second is your own conjecture, not what I or anyone else who tunes pianos for a living does.

I think it is the "whole sound" tuning approach. Again, a matter of focus. It has been proven that there's no such thing as a beatless octave, or double or triple, yet those that tune moving slightly sharp, then flat to find the "calmest" spot percieve that placement as beatless.

You only need to have heard Virgil's tunings in his prime to see that it works,(or worked(s) for some) even if the semantics aren't quite true...

Ron Koval
chicagoland

This is what Virgil Smith always did. In advocating listening to the "whole" sound, he never even tried to isolate partials. When technicians find the compromise between a 4:2 and 6:3 octave, they also do not make any partials match exactly but create initial temperament octaves (between A3-A4 and F3-F4)that just kind of "hang" there. There is a very slow beat on the wide side of beatless but it is so slow as to be virtually imperceptible.

I've tried every means to understand both the paragraphs, but I think there is a missing link somewhere (in my brain). Could we put everything in figures so that the whole concept can be better illustrated ?

I just couldn't understand why matching a lower note with A4's 2nd partial will cause A4 to be flat. Isn't it the opposite that the higher the partial, the sharper it sounds ? Aren't we 'stretching' A4 by matching its 2nd partial ? Isn't it the case that the more a note is stretched the sharper it becomes ?

Now that you've introduced a new note - A5 - into the discussion it complicates what was already very complicated.

I can tune an octave (or double octave for that matter) within a range that sounds beatless to me. I understand the mathematics of it to agree that there is no such thing as a mathematically beatless octave, but there certainly are aurally beatless octaves.

Does anyone know the history of tuners recognizing that there is no such thing as beatless octaves? I suspect it would have happened about the time that ETDs became popular.

You should click the reply button below Bill Bremmer's post, not mine. You are supposed to reply to him.

Cashley:

Sorry, I see these as general discussions and may identify a certain poster at the beginning of the reply as I did here. I will try not to make you the recipient unless my post is actually directed to you.

I'll try!

Here's the partials for a recently tuned Knabe 9 footer.

A4
8th +43.76
7th +32.61
6th +24.68
5th +16.97
4th +10.23
3rd +5.36
2nd +1.43
1st 0.0

These numbers represent how many cents sharp of a math generated equal temperament. So if we use a sound source that doesn't have inharmonicity (like a fork) and then force the 2nd partial of A4 to 0.0 instead of 1.43, the first partial will then end up 1.43 cents lower than A=440Hz. (0.0 - 1.43 above) If you forced the third partial to = 0.0, then the fundamental would be 5.36 cents flat of A=440 Hz. (and so on up the partial ladder)

Let me list some partials for how the Average Verituner tuning would calculate for A5

A5
4th 31.33
3rd 17.22
2nd 7.83
1st 1.73

And then the same for A6

A6
2nd 31.45
1st 10.72

You can then see that A5 is set a tiny bit sharp of a 2:1, but flat of a 4:2. Likewise, A6 is set a little bit sharp of a 4:1 double octave from A4, but sharp of a 2:1 from A5 (1.73 fundamental + 7.83 2nd partial = 9.56 for a pure match)

The more you look and compare, the more mismatches there are - and this is a 9 footer! So it does come down to compromise - based on what we hear, or how the machine is programmed...

Ron Koval
chicagoland

Keep at it, I'm sure it will "click" at some point.

Perhaps the best recent set of figures and graphs I've seen on the effect of inharmonicity on octaves is Dan Levitan's articles in the PTG Journal, starting with the second in the series in September 2007. Perhaps you have a local guild member who has back copies you could study?


Maybe think about it this way, paraphrasing what Ron just described in numbers: imagine your A4-A5 octave is a thing that you can pick up and move around. It's a little bit "wider" than a theoretical octave because of inharmonicity. If you pick it up and move it so that the right end (A5) is at a known reference point, where will A4 end up? Since the octave is wide it'll end up lower than where you want it to be.

(Never mind for now that this is the wrong way to set the pitch of A4 to a fork.)

Just because you cannot do something does not mean someone else cannot do it.

What I understand or not is not conjecture.

Ron:

I am guessing that you got these readings with a Verituner. I believe that the cents deviation is the difference from the harmonic, whole number partials of the fundamental pitch (in this case 440) rather than the difference in theoretical pitch of the closest equal tempered note to the partial as I understand a SAT would measure. For your discussion of partials 1, 2 4 and 8 this is the same cents deviation, but not for the other partials, as I understand it.

Thanks Jeff - you may be right... I thought there was a difference between the platforms in how the numbers display.

Still, for the 2:1 4:2 and 4:1, the numbers should still be of value for the discussion.

(This has to do with the difference between the harmonic octave 5th and an equal tempered octave 5th, as well as the octave 3rd etc...)

Ron Koval

Ron:

I had to consider this while crunching the Verituner numbers that Joe gave me.

Take a look at a low iH note and see what the cents for the fifth partial is. If it is referenced to an equal tempered note, you would expect it to be like 14 cents out of step with the 4th and 6th partials.