I tuned the wound strings of that piano aurally and noticed nothing unusual at all. Indeed, it is a fine set of would strings made by Ari Isaacs. They are smoother sounding and more easily tunable than average. It seems to me that the more mathematics try to get involved in tuning predictability, the more they predict impossibility when in fact, there is no problem at all.

You should have seen the comments one "scientist/engineer" had about my original tuning chart for this piano. It was a predictable example of "It wouldn't work, it couldn't work and shouldn't be tried". Since all of the upper octaves that I tuned were determined by direct interval (the piano itself telling me what it had to offer), the numbers generated did not come out of thin air nor were they a calculation based on some "predictable" constant or any other imagined factor.

The Mason & Hamlin pianos are known to have lower inharmonicity than most. Therefore, even though on the second tuning, I used 8:1, 12:1 and 16:1 (for C8) octaves for the high treble, the numbers were far lower than I would get on a Steinway.

The wound strings would be somewhat different than the originals but they were still confined to the scale configuration that the piano has. They are just higher quality and more carefully made than many sets of wound strings that I see.

One thing I would say is that I never, ever use a calculated program to tune the wound strings of any piano. The SAT does make its calculation based on readings of the difference between the 4th & 8th partials of F3, the 2nd & 4th partials of A4 and the 1st and 2nd partials of C6. How would it know what to do with the wound strings? Answer: it would have no idea what to do; it could only make an assumption. I would never count on that and I just shake my head in disbelief at how many tuners use that program and start tuning the piano on A0.

Well, there is no mathematical problem, but it seems an ETD would need to use each partial and not assume Young's model.
The negative offset of the 4th partial is perhaps due to bridge/soundboard coupling effects. The C2 sounds beautiful, there is no problem at all.

The ETD program I made myself (which assumes Youngs model) mostly gets pretty close to reproducing Bill's EBVT3 tuning charts, but not as close as I would like.

Bill, thanks for telling us how you tuned the high treble. I will program that in and see how close I can get to your numbers there. If you could describe how you tuned the wound strings I would like to simulate that mathematically and see how close I can get.

When I saw you tuning charts my reaction was the opposite of the guy you described: I think it is a challenge for ETD design to produce anything as intricate as that!

Kees

Kees:

I am confused. I thought you were using the look up table from Tunelab, not Young's model.

And my experience is the partials of bass strings can be wacky and sound good until an interval such as an octave is played with another bass string, especially if it is also wacky. Then there are clashes that just cannot be tuned away.

I use a "modified Young's model" which I sometimes lazily confuse with Young's model, sorry. It still tries to capture all the partial deviations with one number.

So then perhaps tunelab's ignoring of these wacky partials and just fitting them into a modified Young's model captures more or less what an aural tuner does too?

Kees

I really don't know much about what is being discussed here but it did occur to me that what may have happened is a reading anomaly or error. I know, for example that with some of this software, inharmonicity samples seem to change slightly every time a reading is taken. It is obviously not the piano that is changing inharmonicity from one moment to the next but the interpretation of it is very sensitive to a number of factors.

I don't have access to the chart I created for this tuning because I left it with GP and I did it on a borrowed SAT IV. I don't think you'll find however that the C2 is out of line somehow with where it would be expected. I also had no trouble reconciling any intervals with it. What Jeff is saying does happen, yes but it did not on this piano.

I have found such inconsistences in my readings many times in many pianos. I think of it as being the rule more than an isolated incident.

And also I've found what Bill says, be it electronically or be it aurally, there is no noticeable problem with the tuning of the piano.

When tuning electronically, I don't know how the ETD calculs its targets but I suspect it averages the tuning of all notes to fit into a smooth curve.

When tuning aurally we tune to the best sounding spot without noticing iH uneveness. We can only run into problems if we are tuning based on a unique single interval, which we usually don't do.

Bill:

Here's the note with the unusual inharmonicity:
C2

I'm not sure how I can check if it's a reading error as I can't play GPM's piano from here so this note is all I have.

I have your tuning charts from GPM. Do I have your permission to post a link to them for this discussion?

I do notice something unusual at C2 in both charts, but perhaps it is normal. I think only you can tell.

Kees

Kees, post anything you want. If there is an anomaly in C2, then the aural tuning result should reflect it. As I said, I never noticed it is there is one. The sound file does not produce anything conclusive to me.

I'm still tweaking my EBVT program to get the correct octave stretches, but a comparison with Bill's master tuning chart in the midtrange is very good.

On the temperament octave F3-F4 my program, compared to Bill's June tuning of grandpianoman's piano, had a total of 3 error points (as computed per PTG exam standard). By comparison, using just the theoretical EBVT offsets from Bill's website (which are computed disregarding inharmonicity)and entering them as offsets in an ETD, produces 8 errors.

For the rest of the midrange (C3-B4) my program had one more error point. A total score of 92.5 for the temperament octave and 94 for the midrange.

An interesting point is that to get these good results a "pure" fifth has to be treated as an equal beating 3:2/6:4 interval.

Kees

Here are the tuning charts from Feb. and June. Esp. in the Feb. tuning I notice C is sharper than C# in terms of offset in octaves 3-6, but this reverses at C2.

Chart

Kees

Kees,

Those two readings may well point to the inharmonicity anomaly that was noted. Whatever it may be, it did not create an aural dilemma. The question is, however, what would a calculated ETD program do with it? If only that string is different from the others, I would expect that a calculated program which is always based upon assumptions to tune that note somehow "off" from the way an aural tuner would tune it. The SAT FAC doesn't even sample any wound strings. RCT samples A's and so presumably would only tune that note incorrectly. Tunelab samples C's and this is where I see that all of you found the problem. Would Tunelab provide information for a substantial range of notes that is slightly "off" based upon that one anomaly?

The facts you noted in in post #149854 are interesting. Ron Koval has often been perplexed in how my direct interval/program tunings "sound great but they don't match the numbers". I don't have quite the time right now to get into all of that but what is always interesting to me is that when I use that method, many of my "numbers" are the same or very similar from one piano to the next. Far from needing 1/100th of a cent resolution, 0.5 is quite sufficient.

I never have, for example, found any piano where A3 entered at 0.0 and read on the 4th partial calls for F3 to be anything other than 1.0. So, I enter 1.0 and listen to it and it always sounds like 6 beats per second to me. If i were to tune 0.9 or 1.1, I wouldn't be able to hear the difference, so I always simply enter 1.0. Since F3 is 1.0 (read on the 4th partial), F4 is also 1.0 (read on the 2nd partial) and that cannot create anything but a perfect 4:2 octave which it always tests out perfectly to be.

Similarly, C4 always ends up being 2.0, C#4 is always -2.0 as are E4 and F#3. I have gotten to the point when I construct these programs that I already know what many of the numbers will be, so I enter them. A few of the in between numbers vary slightly but they are also fairly predictable. Some of the outer octave numbers also end up always being the same. F5 is always 2.0. E5 is always 0.0. C6 is almost always 6.0 and so is F6.

That is why I could use that one Steinway model D tuning as a "generic" tuning for nearly any moderately high inharmonicity piano and have to do very few aural corrections. I would simply tune the high treble and the wound strings aurally. Any Kimball, Baldwin Hamilton or Acrosonic, any A.B. Chase grand, any Baldwin Grand, just about any crummy piano or good piano you can imagine could be at least pitch corrected using that program and simply be tweaked aurally here and there to produce a tuning with that signature EBVT III sound.

That flies completely in the face of the notion that new samples need to be taken every time a piano is tuned. that just has not been my experience. The first time I tuned GP's piano, I used the Steinway program and after about one hour of tuning, we got a first impression of what the EBVT III would sound like. He liked it, so I went on the next day to create a custom program for it, having already pitch corrected it using the Steinway program.

Those figures are posted somewhere here on PWF. If you look at them and compare them to either the February or the June tuning of GP's piano, you will find more similarity than difference.

Bill,

Tunelab can sample any notes you want, the C's is just the default. It basically just ignores the anomaly and fits as best as it can. Interestingly the anomaly in C2 disappears if I use just the first 2 seconds of the note; you can also hear a tiny self-beat later on in the envelope, so it's probably an effect of coupling to the rest of the piano.

On my Heintzmann upright with A3 0.0 and F3 +1.0 both at the 4th partial, F3A3 beats at about 4.7 bps. I measured this by tuning the partials at the offsets with my ETD, then record the F3A3 third and timing the beats with a spectrogram. The prediction from my inharmonicity model is 5.1 bps which is not bad.

In this case I think your offsets are still good, because the ET F3A3 beats about 6.5bps on my upright so to get the EBVT effect you probably want to go below 6bps to hear a clear effect?

In your Feb. and June tunings F#3 is -1.5 and -0.5, F6 is 8 and 9.

Also, the difference between the Feb. and June is quite big even in the midrange:

C#3(-2.5/1.0), D#3(0.0/2.0), F#3(-1.5,-0.5), G3(2.5/1.5), G#3(2.0/3.0), A#3(3.0/4.0), B3(0.0/2.5), D4(2.0/1.0), D#4(1.0/2.5)

Was there a difference in the EBVT variant you used?


Kees

Bill, Keys,

this is interesting reading! I'm not using my RCT taking samples either, just reading directly on the partials.

One thing that was confusing to me in my rookie ETD week (last week) is that if you read with RCT set on A3, and you read the on the 4th partial, the offset value will be for the fundamental. That was not of much use to me.

So now i set my ETD to listen to A5, use the advantage of two different note recording windows in the device display, and make the 5th partial of F3 be -11.84 cents lower than the 4th partial of A3. THAT will indeed produce a F3-A3 beating at 6bps, if anything

I have heard that direct interval tuning is not possible yet with the RCT but soon will be. Any of the Sanderson devices work well that way, however.

Well, if you read say on the 4th partial of A4 and set it for an offset of +4, that means the 4th partial of A4 is 4 cent above the 4th partial of a 2^1/2 ET without inharmonicity. So if your 4th partial happens to be 8cent sharp because of inharmonicity, the fundamental of A4 will end up -4 cent from 440.

I agree it is confusing, having been confused by this myself.

Kees

The real difference from Feb to June was that in Feb, I had used the Steinway chart as a pitch correction, then tweaked it by ear. In June, I started from scratch.

Compare any two exam master tunings on the same piano, sometimes even by the same master tuning committee. You will find similar differences. Was one then wrong and the other right? . No, they were both aural tunings and each has its on variances based upon perception at the time.

So, even though I started the June tuning with A3 at 0.0 and F3 at 1.0, etc., the rest of the differences were due to perception at that time. I recall, for instance, changing the F#3 I had preset to -2.0 to -1.5. That is a small difference but it did make the F#3-A#3 beat a little more mildly.

At Jerry Groot's, I first tuned the EBVT III aurally and it sounded good. Then we programmed the RCT to produce a calculated version. I expected some differences and there were but many notes seemed to agree perfectly. I expected the F3-F4 octave to be a little wide but it really wasn't, same with G#3-G#4. The D5 was flat as expected. There were a couple of 5ths from F4 to F5 that proved a little narrow but it took lowering the bottom note rather than raising the top to fix them.

Where I really noticed a difference was in F5 to F6. The RCT tuned too sharp. Then after F6, it wasn't sharp enough. So, I did all of that aurally as well as the wound strings. It made for a super clean sounding example of the EBVT III.

Would I be correct in stating that there is a bit more to tuning EBVT3 than blindly following the tuning instructions from your website? For example on a very inharmonic piano the ET F3A3 will already beat around 6bps, in which case 5 bps would probably be more appropriate to get a well-tempering?


I find the same in tunelab: the low bass and high treble stretch "leaks" too much to the rest of the range.

Kees

Kees,
I try to understand you,
1. t(i) = [1200/log(2)] * log(p4(i)/p2(i+12)), i = 1,…,76. ? why log(2)?
2. why n(48) = 4700 measn 440hz? what is n?
3. why we don't use curve fitting?
thanks in advance,

1. Definition of cent.
2. Per definition. n is defined in the post.
3. Because there is no data to fit a curve to.

Kees

HOOOOOOOO! Setting an f temperament need not be so complex.
Here is simple aural:

set middle c. (wherever...)
F below, a fifth, set to middle C and narrow by 3 beats in the time sound dies....
F above middle c, a fourth, raise by 4 beats same as above. Should match the first f. Wait & see....

Set B flat, in above ratios to the F's. EZ

So from there set above ratios relative to middle c:
down to G, widen
up to D, decrease (you have a 3rd check with B flat and a 6th check with lower F)
down to A , widen, (3rd check with lower F)
up to E, decrease, (3rd check with C, 6th with G)
down to B, widen, (3rd check with G, 6th with E)... check flow at this point...
down to F #, widen, (3rd check with B flat)
up from B flat to D#, widen, (3rd check with B, 6th with F#)
down to A flat, decrease, (3rd check with C, 6th with higher F)
up to C#, widen, (3rd check with high F,6th check with A flat)

should be pretty.

beats in fifth = too sharp
beats in forths = too flat

that would be bass, then for treble, beats in forths = too sharp, beat in fifths = too flat. It works well . Use your ear to balance, very nice....

SM:

The original purpose of this Topic was for calculations, but like a good Topic, (not saying this is one) other constructive things come up.

Nice to see another C-forker using fourths and fifths and including F4 and A#3 at the beginning of the sequence.

Something I want to mention is the G3-A#3 minor third should always beat a hair faster than the C4-E4 major third. Theoretically they should beat at the same rate, but due to inharmonicity, no. This is a great way to limit the pitch of E4 for those that have a tendency to make the A3-E4 fifth too pure, and may not find out until G#3 (if A#3 is not tuned at the beginning and used for checks and tests.)

agree, I posted to my "aural" question, will send you private

Well, my math thinks the sound never dies out completely and will tune a perfect 5th. (3 beats per infinity = 0 bps.)

If you would introduce an arbitrary cutoff dB level pianos with shorter sustain time would then get narrower fifths.

Your recipe may work in practice, but in theory I'm not so sure.

Kees

Hi Kees, happy B-day!, mailed you 2 boxes today. Can't wait to actually read all of the above. As you know I absolutely love the physics of sound, so I love your approach!

At this point I'm not into investment in devices. Sometimes my fifths come out fairly pure, depends on piano and string scale. I set f first, then work with it...

Life/tuning in practice v theory, always open for discussion... love this topic! SM