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I've been studying the numbers that you gave to Mr. Moy (using the the corrected ones you posted), and can say that it seems his piano as well will be too narrow (or sharp) in the octaves below the temperament. The tuning doesn't consistently go below it's theoretical value consistently until about note 15, or B1, the same spot that showed the error I saw before. After this there is a smoother drop to the low bass, but doesn't catch up with the ET stretch until about note #7 (D#1), where it goes somewhat lower. The treble portion of your tuning looks good compared with a similar equal temperament tuning.

Hope this helps with your work!

Regards,

I forgot to mention I'm using a Tunelab tuning of ET for his piano, with 6:3 bass octaves and 4:1 treble octaves as the settings, automatically adjusted.

Thomas, your reading of the numbers is consistent with Pat's aural check. I implemented Pat's suggestion. The new Chickering 1918 numbers are below. Let me know your thoughts.

Kees

A0 6 0.0 -25.15
A#0 6 0.0 -19.60
B0 6 0.0 -19.81
C1 6 0.0 -15.32
C#1 6 0.0 -16.04
D1 6 0.0 -14.55
D#1 6 0.0 -11.23
E1 6 0.0 -12.04
F1 6 0.0 -7.38
F#1 6 0.0 -9.07
G1 6 0.0 -6.31
G#1 6 0.0 -5.95
A1 6 0.0 -6.57
A#1 6 0.0 -2.63
B1 6 0.0 -4.08
C2 6 0.0 -0.81
C#2 6 0.0 -4.07
D2 6 0.0 -3.11
D#2 6 0.0 -2.02
E2 6 0.0 -3.86
F2 4 0.0 -3.64
F#2 4 0.0 -5.04
G2 4 0.0 -1.94
G#2 4 0.0 -3.45
A2 4 0.0 -3.88
A#2 4 0.0 -1.20
B2 4 0.0 -3.47
C3 4 0.0 0.15
C#3 4 0.0 -3.88
D3 4 0.0 -1.87
D#3 4 0.0 -0.87
E3 4 0.0 -2.41
F3 2 0.0 -0.96
F#3 2 0.0 -2.44
G3 2 0.0 0.58
G#3 2 0.0 -1.00
A3 2 0.0 -1.50
A#3 2 0.0 1.13
B3 2 0.0 -1.18
C4 2 0.0 2.40
C#4 2 0.0 -1.66
D4 2 0.0 0.34
D#4 2 0.0 1.32
E4 2 0.0 -0.22
F4 2 0.0 1.94
F#4 2 0.0 0.19
G4 2 0.0 3.04
G#4 2 0.0 2.17
A4 1 0.0 0.00
A#4 1 0.0 1.55
B4 1 0.0 -0.12
C5 1 0.0 3.95
C#5 1 0.0 2.19
D5 1 0.0 3.47
D#5 1 0.0 3.22
E5 1 0.0 2.50
F5 1 0.0 3.34
F#5 1 0.0 1.52
G5 1 0.0 4.90
G#5 1 0.0 2.17
A5 1 0.0 3.02
A#5 1 0.0 4.94
B5 1 0.0 3.13
C6 1 0.0 6.13
C#6 1 0.0 3.36
D6 1 0.0 5.94
D#6 1 0.0 6.16
E6 1 0.0 5.41
F6 1 0.0 7.50
F#6 1 0.0 6.05
G6 1 0.0 9.78
G#6 1 0.0 8.76
A6 1 0.0 9.56
A#6 1 0.0 10.59
B6 1 0.0 9.80
C7 1 0.0 12.69
C#7 1 0.0 11.36
D7 1 0.0 14.19
D#7 1 0.0 13.22
E7 1 0.0 13.84
F7 1 0.0 15.81
F#7 1 0.0 14.63
G7 1 0.0 18.49
G#7 1 0.0 16.45
A7 1 0.0 18.92
A#7 1 0.0 20.79
B7 1 0.0 20.37
C8 1 0.0 23.82

Cool. Kees, where would the Chickering (or the U3) go if you implemented pure 3:1's below F3?

I'm catching a bad cold as I write, so I don't know in which shape I'll be tomorrow. Anyways, I could throw my Yamaha G2 into the game and maybe be able to work on this despite staying at home. Here are the TL IH constants:

C1 0.508
C2 0.170
C3 0.285
C4 0.367
C5 0.784

I looked at your new tuning for the Chickering. The tuning now follows a fairly normal tuning curve. I manually adjusted the ET tuning to average out the EBVT tuning. I had adjusted from a 6:3/4:1 Tunelab automatic tuning, by lowering the extreme bass, raising the tenor area below the temperament, raising the treble area above the temperament, and basically left the extreme treble stretch alone. I also pitch adjusted the EBVT tuning to match the overall pitch of an ET Tuning, as EBVT averages a little above ET pitch, (offsets are about .5 cents sharp of ET). I'll list the tunings below.

Chickering 1918 Piano:

ET-Averaging the EBVT Curve

IHCon C1 0.555
IHCon C2 0.287
IHCon C3 0.331
IHCon C4 0.385
IHCon C5 0.684
IHCon C6 1.521
A0 6 -24.20 0.00
A#0 6 -22.08 0.00
B0 6 -20.12 0.00
C1 6 -18.31 0.00
C#1 6 -16.62 0.00
D1 6 -15.06 0.00
D#1 6 -13.61 0.00
E1 6 -12.27 0.00
F1 6 -11.02 0.00
F#1 6 -9.87 0.00
G1 6 -8.79 0.00
G#1 6 -7.80 0.00
A1 6 -6.87 0.00
A#1 6 -6.00 0.00
B1 6 -5.20 0.00
C2 6 -4.44 0.00
C#2 6 -3.74 0.00
D2 6 -3.08 0.00
D#2 6 -2.46 0.00
E2 6 -1.87 0.00
F2 4 -5.79 0.00
F#2 4 -5.18 0.00
G2 4 -4.61 0.00
G#2 4 -4.06 0.00
A2 4 -3.55 0.00
A#2 4 -3.06 0.00
B2 4 -2.59 0.00
C3 4 -2.15 0.00
C#3 4 -1.72 0.00
D3 4 -1.31 0.00
D#3 4 -0.91 0.00
E3 4 -0.52 0.00
F3 2 -2.89 0.00
F#3 2 -2.55 0.00
G3 2 -2.23 0.00
G#3 2 -1.92 0.00
A3 2 -1.62 0.00
A#3 2 -1.34 0.00
B3 2 -1.06 0.00
C4 2 -0.78 0.00
C#4 2 -0.51 0.00
D4 2 -0.24 0.00
D#4 2 0.02 0.00
E4 2 0.29 0.00
F4 2 0.56 0.00
F#4 2 0.82 0.00
G4 2 1.10 0.00
G#4 2 1.38 0.00
A4 1 0.00 0.00
A#4 1 0.19 0.00
B4 1 0.39 0.00
C5 1 0.58 0.00
C#5 1 0.78 0.00
D5 1 0.98 0.00
D#5 1 1.19 0.00
E5 1 1.41 0.00
F5 1 1.63 0.00
F#5 1 1.86 0.00
G5 1 2.10 0.00
G#5 1 2.35 0.00
A5 1 2.62 0.00
A#5 1 2.90 0.00
B5 1 3.19 0.00
C6 1 3.50 0.00
C#6 1 3.83 0.00
D6 1 4.18 0.00
D#6 1 4.55 0.00
E6 1 4.95 0.00
F6 1 5.37 0.00
F#6 1 5.83 0.00
G6 1 6.31 0.00
G#6 1 6.83 0.00
A6 1 7.39 0.00
A#6 1 7.98 0.00
B6 1 8.62 0.00
C7 1 9.31 0.00
C#7 1 10.04 0.00
D7 1 10.83 0.00
D#7 1 11.68 0.00
E7 1 12.60 0.00
F7 1 13.58 0.00
F#7 1 14.64 0.00
G7 1 15.77 0.00
G#7 1 17.00 0.00
A7 1 18.31 0.00
A#7 1 19.73 0.00
B7 1 21.25 0.00
C8 1 22.89 0.00

Kees Pitch Adjusted EBVT (This may not be exactly even in pitch with the ET, as it was corrected using the standard tuning, but it is certainly within about .25-.5 cents of ideal.)
A0 6 0 -25.86
A#0 6 0 -20.31
B0 6 0 -20.52
C1 6 0 -16.03
C#1 6 0 -16.75
D1 6 0 -15.26
D#1 6 0 -11.94
E1 6 0 -12.75
F1 6 0 -8.09
F#1 6 0 -9.78
G1 6 0 -7.02
G#1 6 0 -6.66
A1 6 0 -7.28
A#1 6 0 -3.34
B1 6 0 -4.79
C2 6 0 -1.52
C#2 6 0 -4.78
D2 6 0 -3.82
D#2 6 0 -2.73
E2 6 0 -4.57
F2 4 0 -4.35
F#2 4 0 -5.75
G2 4 0 -2.65
G#2 4 0 -4.16
A2 4 0 -4.59
A#2 4 0 -1.91
B2 4 0 -4.18
C3 4 0 -0.56
C#3 4 0 -4.59
D3 4 0 -2.58
D#3 4 0 -1.58
E3 4 0 -3.12
F3 2 0 -1.67
F#3 2 0 -3.15
G3 2 0 -0.13
G#3 2 0 -1.71
A3 2 0 -2.21
A#3 2 0 0.42
B3 2 0 -1.89
C4 2 0 1.69
C#4 2 0 -2.37
D4 2 0 -0.37
D#4 2 0 0.61
E4 2 0 -0.93
F4 2 0 1.23
F#4 2 0 -0.52
G4 2 0 2.33
G#4 2 0 1.46
A4 1 0 -0.71
A#4 1 0 0.84
B4 1 0 -0.83
C5 1 0 3.24
C#5 1 0 1.48
D5 1 0 2.76
D#5 1 0 2.51
E5 1 0 1.79
F5 1 0 2.63
F#5 1 0 0.81
G5 1 0 4.19
G#5 1 0 1.46
A5 1 0 2.31
A#5 1 0 4.23
B5 1 0 2.42
C6 1 0 5.42
C#6 1 0 2.65
D6 1 0 5.23
D#6 1 0 5.45
E6 1 0 4.7
F6 1 0 6.79
F#6 1 0 5.34
G6 1 0 9.07
G#6 1 0 8.05
A6 1 0 8.85
A#6 1 0 9.88
B6 1 0 9.09
C7 1 0 11.98
C#7 1 0 10.65
D7 1 0 13.48
D#7 1 0 12.51
E7 1 0 13.13
F7 1 0 15.1
F#7 1 0 13.92
G7 1 0 17.78
G#7 1 0 15.74
A7 1 0 18.21
A#7 1 0 20.08
B7 1 0 19.66
C8 1 0 23.11

I'll try to post a graph comparing the two.
It isn't perfect, but I think I got it reasonably close to examine the overall stretch of the EBVT Tuning.

I've never uploaded to box.net, so let's see how this works...

EBVT Vs. ET Graph: http://www.box.net/shared/o616c0kkjk

Hopefully that works...

That can be answered in tunelab. There would be less stretch than 6:3, and when extended all the way down the bass would become extremely sharp. 6:2 is an option, virtually indistinguishable from 6:3. But we are moving far away from Bill's recipe for the bass.

Related to this: F3F4 is a 4:2 octave, and you suggested to switch to 6:3 octaves from E3 and below. Would this not create an unpleasant discontinuity at E3?

Kees

Numbers below. Note I changed the partial to something more normal as we don't deal with tuning exam mode anymore.

Kees
IHCon C1 0.000
IHCon C2 0.000
IHCon C3 0.000
IHCon C4 0.000
IHCon C5 0.000
A0 6 0.0 -31.71
A#0 6 0.0 -21.74
B0 6 0.0 -18.87
C1 6 0.0 -12.90
C#1 6 0.0 -12.68
D1 6 0.0 -11.08
D#1 6 0.0 -8.07
E1 6 0.0 -9.08
F1 6 0.0 -5.13
F#1 6 0.0 -7.05
G1 6 0.0 -4.89
G#1 6 0.0 -4.96
A1 6 0.0 -6.04
A#1 6 0.0 -2.79
B1 6 0.0 -4.38
C2 6 0.0 -1.33
C#2 6 0.0 -4.27
D2 6 0.0 -3.34
D#2 6 0.0 -2.19
E2 6 0.0 -3.82
F2 4 0.0 -2.62
F#2 4 0.0 -3.94
G2 4 0.0 -1.09
G#2 4 0.0 -2.61
A2 4 0.0 -3.33
A#2 4 0.0 -0.92
B2 4 0.0 -2.98
C3 4 0.0 0.37
C#3 4 0.0 -3.56
D3 4 0.0 -1.76
D#3 4 0.0 -0.88
E3 4 0.0 -2.36
F3 2 0.0 -1.28
F#3 2 0.0 -2.56
G3 2 0.0 0.33
G#3 2 0.0 -1.13
A3 2 0.0 -1.79
A#3 2 0.0 0.69
B3 2 0.0 -1.32
C4 2 0.0 2.11
C#4 2 0.0 -1.74
D4 2 0.0 0.13
D#4 2 0.0 1.10
E4 2 0.0 -0.30
F4 2 0.0 1.67
F#4 2 0.0 0.23
G4 2 0.0 2.95
G#4 2 0.0 2.23
A4 1 0.0 0.00
A#4 1 0.0 1.47
B4 1 0.0 0.05
C5 1 0.0 3.85
C#5 1 0.0 2.41
D5 1 0.0 3.48
D#5 1 0.0 3.32
E5 1 0.0 2.65
F5 1 0.0 3.04
F#5 1 0.0 1.51
G5 1 0.0 4.77
G#5 1 0.0 2.23
A5 1 0.0 2.95
A#5 1 0.0 4.79
B5 1 0.0 3.22
C6 1 0.0 6.05
C#6 1 0.0 3.54
D6 1 0.0 5.99
D#6 1 0.0 6.26
E6 1 0.0 5.56
F6 1 0.0 7.49
F#6 1 0.0 6.27
G6 1 0.0 9.76
G#6 1 0.0 8.91
A6 1 0.0 9.53
A#6 1 0.0 10.48
B6 1 0.0 9.75
C7 1 0.0 12.17
C#7 1 0.0 11.02
D7 1 0.0 13.54
D#7 1 0.0 12.55
E7 1 0.0 12.96
F7 1 0.0 14.48
F#7 1 0.0 13.34
G7 1 0.0 16.83
G#7 1 0.0 14.76
A7 1 0.0 16.82
A#7 1 0.0 18.37
B7 1 0.0 17.75
C8 1 0.0 20.67

Your posting for the Yamaha G2 is very interesting. The treble stretch is very conservative, only +20.67 cents at C7, while the narrowest auto setting for Tunelab puts it at about 24.08. The bass has comparatively extreme stretch, wider than an 8:4 auto setting in Tune lab. In fact, the low bass is farther from theoretical pitch than the treble, which probably won't sound great, but I'm no expert on tuning G2's, and the scale may call for that. From personal experience, however, the overall stretch should be greater in the treble,(as that area has the highest inharmonicity of the piano) than the bass.

The iH reading for C1 seems to be a little out of kilter. @Patrick: Have you used these numbers to actually tune the piano, and if you have, is the stretch pleasing to your ears?

@kees: How are you calculating the Inharmonicity Data? Do you model your own, or do you stick with tune-lab's formula? (I know I've tried to do both, and can't figure either of them out!)

Hope this feedback helps a little.

I use the tunelab model for both the partial calculation (i.e. how to translate a single ih number for a note into its partial locations) and for fitting the overall ih curve to selected notes. The former is documented in the tunlab manual, the latter was kindly provided to me by Robert Scott.

Kees

Yes, I thought so... I was just curious. 6:3 all the way down (tunelab standard) and stretching the last octave or so towards 12:6 might be an option that would harmonize quite well with Bill's idea.



Maybe. And that might be why you called my F3 too low earlier - maybe I compensate for the stretch below? This is getting interesting... I have to check your new numbers aurally to get a better feeling for that transition.

Speaking of stretch - I did a touch-up on a Steinway D tuning today. It is not a rigorous EBVT III in the temperament zone, slightly milder. Anyways, the stretch might be of interest. Here are the numbers:



... and the IH constants (as recorded on TL):

C1 0.113
C2 0.039
C3 0.136
C4 0.337
C5 0.819

Note the stretch in the last octave. This is probably a combination of a large concert hall, a grand that can take that stretch, and clogged ears. I don't know in which proportions...

Thomas,

I haven't had a chance to do so yet, but I certainly will. The C1 looks funny, I agree, but I checked it several times and it indeed is the IH that TL reads. I think it has to do with the G2's, they are.. well, let's put it mildly, quite personal in the low bass. The Yamaha C2's are much more predictable.

Kees, Jim, Thomas: One more thing... I think it would be wise to go for just a TuneLab implementation right now. If it works, then we could take it further on to other software.

The reasons I vote for TuneLab is

1) that it seems to be quite simple to produce tuning files (.tun), as opposed to on the RCT where one tuning file contains several tunings. TL .tun files looks more or less like csv to me, so I figure it would be no big problem reading and writing such once we get the numbers right ,

2) you all others are quite familiar with TuneLab. I have some catching up to do, but that's no problem,

3) the price of the software,

4) Robert being a member of this forum and kindly answering our TL-related questions politely and with great patience

5) The Topic of this thread

6) That tune-lab has a function for manually adding IH constants, that will make it easy for us all to trade files, enter new files, and check, double-check and triple-check.

7) The possibility for interested collaborators to use TL in demo mode without feeling obliged to put own money into the project, only experience and skill.

What do you think?

The more I think of this, the more logical it sounds. I think it would be possible for the code to have a parameter derived from the IH readings) that determines where to start moving from 6:3's to 12:6's. This is what Bill and I do on larger grands, and the larger the grand, the faster we start to go beyond 6:3. On really small instruments, that parameter could be even < A0.

Bill does it with a different approach than I do, but the end result is very similar.

@ Kees - how does this sound to you?

This is great, Thomas - very easy to read!

My only concern is that the bass tuning recipe from Bill uses 5ths and 4ths and 12ths and has the effect of equalizing the temperament somewhat towards equal. If you tune with octaves only the temperament will stay intact all the way down. I don't mind, but is this a concern?

Put differently is the recipe to tune below F3 specific for EBVT or is it just a general stretch scheme. If the latter, sure we can do that. Why 12:6? Isn't 8:4 or 10:5 more locical?

Last but not least: is there really a problem in the bass as computed by Bill's recipe that needs fixing? As mentioned before I have a switch for extra low bass stretch, which is off now. And a similar one for more high treble stretch.

Kees

Your reasoning sounds logical. It will probably be consistent with the temperament idea to go back to the 4/5/8 balance beneath the tenor crossing.



To me, it's two-folded. The first part of the high bass/low mid below, roughly the octave across the break, needs special care to keep the characteristics of the temperament. It is just as important as the octave directly above the temperament. Thus, what Bill kind of says is "apply stretch, but don't lose the uniqueness of the intervals". That is why I think equal-beating or 2:3 beating won't do it here - if applied strictly (without aural "nudges"), they even the temperament out far too early. And relationship beating is dangerous across the break.

But once we get past that area, I think you're right - it should probably go back to the balancing scheme (4/5/8)

I suggested 12:6 above, because to me it would have been more logical to use a much larger stretch to strive against, to get more of an exponential curve in the low bass. Just a thought, but we might put that thought on stand-by for now and see what happens with the 6:3 across the break, and 4/5/8 below.



Those switches might very well do fine without other alterations. Let's aurally verify what happens across that treacherous tenor break once the 6:3's are implemented, and what that does for the low bass below.

I am, however, pretty sure that I'd ultimately like both switches on myself

This weekend I'll be away playing concerts, so the G2 and U3 will have to wait until monday. Might be favorable anyhow, because with clogged sinuses and locked ears, I'm not the best bet for aural nitpicking right now. Hopefully this cold will be gone in a few days.

Pat: I will send you tunelab files for the 4 pianos with the extra stretch options on next week. Traveling right now.

I agree with everything you wrote.

Kees

Okay, I've been working on this thread from a different viewpoint than Kees has, so bear with me if this starts to diverge from the main ideas being shared here. I think what I've found may aid in working out the goal of this thread, which is a tuning system similar in results to the one that Mr. Bremmer uses when tuning his EBVT III.

Just a disclaimer, I don’t have enough experience tuning a high quality EBVT to be able to compare the digital results being exchanged here to actual tuning.

I thought that this was interesting, I created an 88 note temperament offset, based simply on Tune-lab’s EBVT temperament file (pitch adjusted by subtracting .91 cents from each offset), and extended it beyond F3-A4 by simple averaging based loosely on Mr. Bremmer’s writing (aka, I winged it based on what I remembered). When I refer to a note, I am referring to its offset value. Thus, I calculated A#4’s offset by (A#3+D#4+F4)/3. After F5, I switched to mindless octaves, so F#5=(F#3+B3)/2. I used a stock 6:2/4:1 Tune-lab tuning as the ET basis.

Below is a link to the graph comparing this 88 note offset to Kees calculation, on the 1918 Chickering:

http://www.box.net/shared/f9ykj8czfa

Note the similarity, especially above note 49 (A4) between the two graphs.

I think that this may be something of interest to expand this idea. Perhaps an 88 note temperament file could be used to solve this problem.