Piano World Home Page Forums Our Most Popular Forums Piano Tuner-Technicians Forum How Did the PTG Grade Tunings before Tunelab Came Out?

Not true at all. I and most others can do that. It's not that difficult. Instead of beats, you rely on amplitude. The point is, perfect mathematical octaves are not the same as highly musical octaves.

Musicdude,

Okay, I can accept that.

So, when I tune the high treble by ear, I find the spot that gives the greatest amplitude (volume and sustain). What then am I tuning to?

I always assumed I was tuning 2:1 with the octave below. I suppose that if I block open the double octave (sostenuto pedal on a grand for instance) I could just as easily get that to ring sympathetically which should be the 4:2.

Am I right or wrong?

Pwg

You are not wrong at all, Peter. Tuning a unison with the note two octaves below can be done as easily as with one octave below using the sostenuto pedal as you mentioned.

Yes, and taking a suitable length of finished 2x1, boring two 1/2" holes in the narrow edge two octaves apart and you'll find that an upright bass hammer will push fit firmly into the holes, you will have a tool to play two notes a double octave apart simultaneously leaving one hand free to tune. Extending a finger of the hand that holds it will give you any note in between that might help. I used it for a few weeks until I found less cumbersome ways.

Musicdude, there are many answers to your quandary. Why settle for only one? Teach yourself to hear those things that you think you can't hear. (You think we can't hear!!!)

While having a satisfied clientele is gratifying, not to mention profitable, it is not proof of anything. I, too had a large clientele when I knew nothing.

8 out of 10 cats prefer... and a thousand monkeys can't be wrong, etc. etc.

I really appreciate the seasoned pros taking time to explain things in such detail. This has been a very informative thread, Dunning-Kruger effect not withstanding.

Thanks Bill and Amanda,

I will have to play around with this for a while and evaluate it. I am always open to new ways of accomplishing good things.

Pwg

You know more than me.....what's the answer?



All I know is that the pure 4:2 test M3=M10 was inaudible after a certain point.

Can you explain to me why the M3=M10 test is a pure 4:2?

I was only following orders......

Musicdude,

Please post a recording of single notes including C1, C2, C3, C4, C5 and then all notes from C6 through C8 where you have tuned, using an ETD the top two octaves using 4:2. I need about 5 seconds of each note.

You talk a lot, but, so far, I've seen no action. Put a recording of your work where your mouth is.

It is not necessary to use gadgets or sostenuto to tune extended intervals. Tune with the sustain pedal on and play each note quickly with the other hand. It may sound muddy at first if not used to it but tuning becomes so much easier. Believe it or not but the overall resonance of other open tuned strings is beneficial in the tuning process.

I'm willing to try it.

Pwg

I always tune with the sustain pedal. I listen for sustain and clarity. As Chris said, you can listen to the resonance and use that to help tune. That's one benefit of aural tuning.

Musicdude, how do you know that you are actually tuning 4:2 octaves up in the last few octaves? Just because the ETD says so? What if you aren't actually tuning 4:2 octaves? Can you prove it?

[/i]

Originally Posted by Musicdude

Originally Posted by P W Grey

Musicdude,

Okay, I can accept that.

So, when I tune the high treble by ear, I find the spot that gives the greatest amplitude (volume and sustain). What then am I tuning to?

You know more than me.....what's the answer?

Originally Posted by P W Grey

I always assumed I was tuning 2:1 with the octave below. I suppose that if I block open the double octave (sostenuto pedal on a grand for instance) I could just as easily get that to ring sympathetically which should be the 4:2.

Am I right or wrong?

Pwg

All I know is that the pure 4:2 test M3=M10 was inaudible after a certain point.

Can you explain to me why the M3=M10 test is a pure 4:2?

I was only following orders......

PW Grey,

I have used the sostenuto pedal for over 30 years, just an idea I had one day. I hit upon this idea that if you made a compromise between the double octave and octave-fifth, it would result in some truly ideal stretch. As far as I am concerned, it does. Sometimes, I carry that to the top, sometimes, I tune part of the top octave that way and sometimes I tune it as 2:1 octaves.

However, as Musicdude pointed out, that is not the same as tuning 4:2 octaves. If you tune a note so that its fundamental exactly matches the 4th partial of a note two octaves below it, you are tuning a 4:1 double octave. It is not at all the same as a 4:2 octave.

If you are tuning a 4:2 octave, you are tuning a single octave such as A3 to A4 but instead of the 2nd partial of A3 exactly matching the fundamental (1st partial) of A4, you are causing the 4th partial of A3 to exactly match the second partial of A4. In that area of the piano, that is considered to be an ideal amount of stretch by many technicians, including myself. The octave sounds basically pure but if you listen very carefully, you may hear an extremely slow beat, one that occurs every 4 seconds or so.

Musicdude, to answer your question about that in particular and I am glad you asked, when you play F3 when listening to either A3 or A4. the 5th partial of F3 is A5, the very same pitch as the 4th partial of A3 and the 2nd partial of A4. It is known as a [i]coincident partial. If the beat rate of the F3-A3 M3 and the beat rate of F3-A4 are exactly alike, it means that both A3 and A4 have a match at the level of A5. If the F3-A4 10th is slower than the F3-A3 M3, then it means that the octave is narrower than a 4:2 type. If the F3-A4 10th is faster than the F3-A3 M3, it means that the octave is wider than a 4:2 type.

Some technicians prefer a slightly wider than 4:2 type octave. The same kind of process can be used to prove that the A3-A4 octave is a 6:3 type. The test note then is C4. If the A3-C4 m3 beats the same as the C4-A4 M6, the A3-A4 octave is a 6:3 type which will have an audible "roll" to it (usually 1 beat in 2 seconds). In that test, the coincident partial is much higher. The 6th partial of A3 is is E6, the 3rd partial of A4 is E6 and the 5th partial of C4 is E6.

Many technicians prefer a starting A3-A4 octave as a compromise between the 4:2 and 6:3 type. They will prove it aurally by listening for F3-A3 M3 and F3-A4 M10 slightly faster but A3-C4 m3 and C4-A4 M6 slightly slower. Dr. Sanderson once told me that he had his algorithm based upon a 4:2 octave +1 cent for the midrange. This was an effective way to achieve the desired compromise.

If the whole partial (harmonic) series confuses you, all you have to do is remember that it is like a very large, dominant 7th chord. If we take C2 for example, the 1st partial (fundamental) is C2. The 2nd is one octave above, C3. The 3rd is an octave-fifth above, G3. The 4th is 2 octaves above, C4. The 5th is a double-octave-Major third above, E4. The 6th is a double octave-fifth above, G4. The 7th is a double octave minor seventh above, A#4 (B-flat 4), the 8th is a triple octave, C5.

When you have a chance at a piano that is in proper tune, press the C2 key slowly so that it does not play but you are holding the damper open. Then play in staccato style (plunk) C3, G3, C4, E4, G4, A#4 and C5. You will hear each of the partials from the C2 string resonate when you do. Anytime you want to figure out a partial for any given note of the piano, all you have to do is imagine this large, dominant 7th chord in your mind and you will have it.

I am afraid that what has perplexed many of us on this topic is Musicdude's insistence that a "computer" can do what no human can do and that is to tune "perfect" 4:2 octaves all the way to C8. A smooth curve algorithm cannot make an exact compromise between a 4:1 and 3:1 octave the way I do. The only way to do that is in the Direct Interval mode and I have proven time and again that either aurally or electronically, i get the very same results.

Now, I have to say that of the calculated curves that I have seen, it does somehow come remarkably close to that, close enough that in most instances, whatever difference there is may be negligible.

But here is what I question, particularly for the 7th octave and the claim that the "computer" can do "perfectly" what no human can do aurally: it is true that at some point, a M3-M10 test, the beat rates for either become indiscernible. I liken that to a motion picture. (Not the modern digital type but the original type.) The camera takes individual still images, the same as any one shot photo is taken but it takes those images in rapid succession. If the film is played, we lose immediately the still image of each frame and we get the illusion of movement although there really is none in each, individual frame.

When beats become so rapid that we can no longer discern them, a point at which can be widely different for each individual, the rapidly beating interval test becomes useless. We still hear a M3 and M10 but the beats are so rapid that they have become a blur, much like the transition from one still image to the next in a motion picture.

What Musicdude says in that regard to tuning 4:2 type octaves either in the 6ths or 7th octave is certainly true. Nobody can discern beats that are that rapid. What I think Musicdude is ignoring, however is the fact that in the 6th and 7th octaves, the inharmonicity becomes very exaggerated. I know this from having done re-scaling work. I have also seen it in PTG Tuning Exam Master Tuning records. The higher you go, the more exaggerated the inharmonicity becomes.

So, let's take for example, tuning C7 from C6 as a 4:2 type octave. The 4th partial of C6 would be C8, the very highest note on the piano. My scaling book only lists 2nd partial inharmonicity but even that can easily reach into the double digit range on C6. The 4th partial can easily be double that or even higher, so now we are talking about pitches at or near the +20 cent range at the bottom of the 7th octave. If C7 is tuned to C6 with a 20 cent or so spread, there will be a very rapid beat between C6 and C7.

If continued with truly 4:2 octaves in the 7th octave, the exaggeration will only be amplified to immense proportions by the time C8 is reached. If C8 is tuned to C7 as a 4:2 octave, the 4th partial of C7 would be C9, an entire octave above the limit of the piano and most likely out of the audible range for many people. (If you have ever heard a customer remark that "those last few notes only sound like knocks" it is because even those pitches are out of their range of hearing).

What we are talking about is truly stratospheric stretching if the highest notes are really tuned as 4:2 type octaves. I don't really believe that a "computer" can or does actually do that. The setting may be for that but what can the platform actually do with pitches that are that high? It must put some kind of cap on the whole thing and do whatever it does but to just believe that because you have set it to tune unimaginable frequencies does not mean that it really does and does them "perfectly, as no human could ever do" (or would do, for that matter).

Perhaps Robert Scott, who is a good friend of mine and the designer of Tunelab can enlighten us on what really happens if a 4:2 octave setting is used to the very top notes. I am not sure whether C7 is sampled or not but if it is, something about the very exaggerated inharmonicity that has already begun a full octave lower than that is taken into account.

I will say this about 6th and 7th octave stretch. Much has been written about it. RXD who has commented on this topic claims to have a lifetime of experience and now resides in the finest concert halls in the world, has said repeatedly that the 7th octave should have no more than a half beat per second stretch above the 6th octave. How anyone could really do that accurately, I don't know but that is what he says.

I am the type that has wanted to explore all kinds of extremes. That has meant in temperament as to how far could it be unequal and titillate the the user or how much was too much and ultimately unacceptable. How much was just right?

I have done the same with stretch and indeed, combined the two. If you really believe that "computers" can do anything or more than a human being can do, then try to solve the problem that I encountered and for which there is no solution, the way I actually do stretch octaves using the mild, well temperament which I developed and have used for 25 years as my usual practice. It cannot be done! But it can easily be done aurally or through the manual Direct Interval programming of the Sanderson Accu-Tuner.

The desire to have highly stretched upper octaves is not new and it has nothing to do with electronic tuning being superior to aural and I truly don't believe it has anything to do with the ability to tune "perfect" 4:2 octaves anywhere in the piano, even if that it what you told it to do. It is only your assumption that it did it "perfectly" because you believe that whatever a computer is told to do, it will do exactly as programed.

Bill,

Thanks for the clarification of 4:1 octaves vs 4:2. I was not thinking fully when I had made the statement about tuning the double octave.

However, it now explains to me why when tuning the top octave, on some pianos I start matching at the 2:1 and if I pull it sharper I find another spot at which the note "comes alive" as at the 2:1. It must be the 4:2 that I'm hearing (and until now not realizing it). Sometimes that sounds better so I tune it there instead. Depends on the piano and the situation.

I am guessing, but I suspect that is what Tunic OnlyPure does. I could be wrong though...

Pwg

Thanks, Bill. That's a very clear explanation.

So correct me if I'm wrong: A M3=M10 test using G#6, C7, and C8, would have the 2nd partial at about
8372 Hz, which is well within the human hearing range. But what would NOT be so easy to hear would be the beating against the 5th partial of G#6, right?




Analog to Digital converters can sample frequencies into the several GHz range:

http://www.analog.com/en/products/a...d-ad-10msps/ad9208.html#product-overview

So audio frequencies are VERY easy to sample using FFT......even frequencies WAY beyond human hearing.

So I don't see why Tunelab would have to deceive its users about which coincident partials it is matching
in its tuning curve. I didn't write the program, but I know it wouldn't be hard to match partials in the 8,372 Hz range. That sounds very easy to do.

Maybe Robert Scott can chime in on this?

I don't see why you don't see why.

Musicdude,

Please post a recording of single notes including C1, C2, C3, C4, C5 and then all notes from C6 through C8 where you have tuned, using an ETD the top two octaves using 4:2. I need about 5 seconds of each note. I have the knowledge, expertise and equipment to do an in depth analysis of your tuning.

I agree with what Bill said about this. TuneLab does not directly measure the inharmonicity of C7 in order to tune C8 to a 4:2 octave. That would be a very hard thing to do, not because of limitations of the computer, but because there is so little energy in the 4th partial of C7. TuneLab measures the inharmonicity of a few notes - typically C1, C2, C3, C4, C5, and maybe C6. You can try to measure more note, but if the piano is well scaled, these notes will suffice. TuneLab then constructs a smooth tuning curve that most closely satisfies the 4:2 interval (if that is the one that is selected) in the top octave, and the 6:3 interval in the bottom octave, and smoothly transitions between these two types of intervals in the midrange. This is all based on the model for inharmonicity which was constructed from the few notes that were measured.

Theoretically, if the piano scaling is not in conformance with the model (due to the wrong wire size in some notes, for example) then a careful aural tuning could take that non-conformance into account and attempt a compromise that was in some sense better than a smooth curve based on the model. But there is a limit to how much such customization can compensate for poor scaling, as you might have in the Yamaha GH-1 for example.

Regarding the capabilities of A/D converters and FFTs, these are not the limiting factors. The limiting factors in measuring the pitch of piano strings is the same for computers as it is for humans. It is the instability and limited sustain of these notes

A wise teacher once reminded a group to remember that "the map is not the terrain".

I often wonder about judging a tuning via computer. For me, about the only way to decide if any interval is 'correct' (even unisons!) for that piano is with a tuning lever in my hand - what sounds clearly 'off' when checking a single interval progression might actually be the best compromise for that instrument when many other intervals come into play. While we can check and judge for progressive M3/6ths (using the map), the scale designer becomes a tuning partner that we work with and around - (dealing with the terrain)

So yes, it is a good test of skills to tune to a test - but perhaps not leading to the most musical results for that piano.

Lest you think this means that aurally tuning is the only/best way to handle the puzzle... If you can actually explain what you are listening and adjusting, then it is possible to program to do the same - as well as it is possible to program to do things that are more difficult or currently impossible to do aurally...

Delving deep into understanding tuning theory and interval balancing can help both the EDT and aural tuner to look for ways to improve.

Ron Koval

Musicdude,

You are right that proof of a 4:2 octave using the M3-M10 test will not work beyond the point where either interval is discernible. When I write about the initial chain of Contiguous Thirds, for example, some of the feedback I get is that the F4-A4 M3 beats so fast that it is indiscernible to some people. I often say that it is at or near the limit of discernibility. Some people say they can hear M3's much beyond that but there is a good reason not to even try.

I like to have my outer octaves all refer back to octaves 3 and 4. That way, I can get a good compromise between single octaves, double octaves, octave-fifths, double octave-fifths and triple octaves. In other words, having notes be in tune with each other over a very wide range of the keyboard.

If you are listening to M3's in the 5th octave, you are listening to beat rates in the 20-30 beat per second range. Any two chromatic M3's are supposed to have a ratio of 15:16 which is very small. To hear that C3-E3 and C#3-F3 progress is easy but to hear that C4-E4 and C#4-F4 is more difficult but still practical. I would say that to try to judge C5-E5 and C#5-F5 is all but impossible. Certainly, anything much higher that that would be but that is why aural tuners begin listening to M10's for a smooth progression beginning with F3-A4 and then M17's beginning with F3-A5. It also refers everything back to the temperament octave until A6 with just a few more notes just outside of the temperament octave up to C7.

So, no, nobody can tune the 7th octave beginning with C6-C7 and try to prove it with the test note, G#5. The G#3-C4 M3 has a theoretical beat rate of 8.5, so G#4-C5 would be at least 17 beats per second and G#5-C6 M3 would be at least 34 beats per second and then only get faster while tuning the 7th octave. The G#6-C7 M3 would beat at least 68 beats per second.

Now, I do not doubt that what you are getting with TuneLab being set to tune 4:2 octaves in the 7th octave sounds good to you and your customers. If that is the default setting, there is a reason why it is because most people will like those results. They may, however be a little too sharp for the PTG Tuning Exam, it just depends upon whether they are 6 or more cents sharper than what a 2:1 octave would be. They may still fall within tolerance but I am not sure about that. Even if the entire 7th octave had a single point scored in it however, you would still get a score of 88. Most people I have seen who used an electronic tuning platform to tune Part 2 of the tuning exam did well with it, including the 7th octave whether they tried to modify the default program or not. You may also have an occasional client who does not want the 7th octave quite that sharp and you could have some people who want it even sharper.

To tune aural 2:1 octaves in the 7th octave using the M10th-17th test is more practical, at least for the bottom half of octave 7. To prove the C6-C7 octave is a 2:1 type, the test note is G#4 and the G#4-C6 M10 would be about 17 beats per second. This is certainly already at or near the limit of discernibility. Personally, I can use that test up to about F6-F7 but beyond that, the 10th and 17th become a blur for me. Fortunately, most piano dampers end at F6 but even if there is a higher one, I can hold it open with the sostenuto pedal. I can prove 2:1 octaves from F#6-F#7 to C7-C8 by first tuning as pure octave as I can but then playing the single note in the high part of octave 7 and listening for it to excite the 2nd partial of the corresponding note in octave 6 and have it be a beatless unison with it.

The only time I ever really do that however is for the PTG Tuning Exam Master Tuning where 2:1 octaves in the 7th octave are a requirement and they must be determined by ear only. If I am doing an ordinary, in home tuning, I simply tune what sounds good to me. If I am tuning a high level, performance type piano, I tune the 7th octave using the Direct Interval mode of the electronic tuning platform. If I want 2:1 octaves, I simply play the corresponding note in octave 6 but have the platform reading on octave 7. The platform will detect the 2nd partial of the note in octave 6, so I stop the display pattern and tune to that frequency and record it for future use either during the same tuning or for another tuning of that same piano on a future date.

If I want a sharper high treble, I set the platform on the desired note in the 7th octave and play the corresponding note 2 octaves below it and alternate with the note an octave-5th below it and find the compromise between the two, record it and tune to that value. I sometimes tune the 7th octave as pure triple octaves. That actually refers the 7th octave back to the initial temperament octave. I sometimes do that only for F7 to C8. It just depends on how wide of a single octave is made between octave 6 and 7. If it is more than a beat or 2 per second, I use another reference note but by the time I get to around F7 or so, the single octave dissonance seems to disappear or does not sound like a dissonance but rather bright and crisp sound.

The Bass can be proven the same way but as a mirror image of the treble by using M10th's and M17th's. You simply change from M3's to M10's to M17's when the intervals become too slow and growl like. Many technicians seem to not know of the best interval for octave 1 and A0, A#0 and B0. The double-octave-minor 7th is a widened interval just like M3's, M10's and M17's but has a beat rate that is ideal for testing a smooth progression in the lowest part of the piano. Tune down to C2 using M17's to check octave 2 and then at C2, play A#4 with it and you will hear a good rapid beat that will slow down as you check all notes in octave 1 and below it.

Ok, thanks Robert. I didn't know this.

So if Tunelab doesn't measure enough amplitude in the 4th partial of C7 (and the other notes of the top 1-2 octaves), then it will automatically revert back to a 2:1 partial matching, even though the tuning solution curve says 4:2 in the treble? And ditto for the lowest 1-2 octaves, even though the curve says 6:3 in the bass?

Perhaps it might be good to tell the user when the program deviates from the desired tuning scheme?

At any rate, I must tip my hat to you Robert, for creating such an AWESOME program! You've certainly
made the piano world much, much better sounding!

It doesn't matter to me what Tunelab is doing specifically, because whatever it does, it does it extremely well, and it is satisfying piano players, piano teachers, musicians in general, and the general public, all of whom are my customers, and some of which prefer software tuning over aural.

Ron Koval wrote: "Lest you think this means that aurally tuning is the only/best way to handle the puzzle... If you can actually explain what you are listening and adjusting, then it is possible to program to do the same - as well as it is possible to program to do things that are more difficult or currently impossible to do aurally..."

Thanks for the input, Ron. Can you give us some examples of things that are impossible to do aurally? That can only be done with computers and software?