Cool. Now the real work can begin.

Your F3A3 beats at 6.38 bps, mine at 6.15 bps. This is from looking at the spectral band around 880Hz of you playing the interval and measuring the time between 10 beats.
For your master tuning I mixed your F3 and A3 and then measured it.

Unless I'm making some strange mistake, I think your internal clock is a bit fast. Maybe too much coffee?

Regarding 2 and 3: I have some difficulties with that. Even if I tune pure 5ths I don't get the kind of stretch you get in the C3-E3 range. Let me ponder that some more.

Kees

Pat, here's the Hellish Helsinki. F3A3 is supposed to beat at 5.9 Hz using the formula bps = 6/6.9 * ET rate. A=440.

Have fun,
Kees

A0 4 0.0 -42.83
A#0 4 0.0 -37.33
B0 4 0.0 -36.82
C1 4 0.0 -30.36
C#1 4 0.0 -29.57
D1 4 0.0 -27.76
D#1 4 0.0 -24.83
E1 4 0.0 -25.13
F1 4 0.0 -19.20
F#1 4 0.0 -19.65
G1 4 0.0 -16.83
G#1 4 0.0 -16.17
A1 4 0.0 -16.32
A#1 4 0.0 -13.18
B1 4 0.0 -14.37
C2 4 0.0 -3.43
C#2 4 0.0 -4.59
D2 4 0.0 -3.98
D#2 4 0.0 -2.83
E2 4 0.0 -4.43
F2 4 0.0 -0.91
F#2 4 0.0 -2.55
G2 4 0.0 -0.05
G#2 4 0.0 -0.96
A2 4 0.0 -1.19
A#2 4 0.0 0.46
B2 4 0.0 -1.37
C3 4 0.0 1.67
C#3 4 0.0 0.05
D3 4 0.0 1.33
D#3 4 0.0 1.85
E3 4 0.0 0.37
F3 4 0.0 2.11
F#3 4 0.0 0.58
G3 4 0.0 3.72
G#3 4 0.0 2.13
A3 4 0.0 1.67
A#3 4 0.0 4.45
B3 4 0.0 2.11
C4 2 0.0 2.88
C#4 2 0.0 -1.37
D4 2 0.0 0.63
D#4 2 0.0 1.58
E4 2 0.0 -0.09
F4 2 0.0 2.11
F#4 2 0.0 0.18
G4 2 0.0 3.06
G#4 2 0.0 2.13
A4 2 0.0 1.70
A#4 2 0.0 3.36
B4 2 0.0 1.65
C5 1 0.0 3.91
C#5 1 0.0 1.96
D5 1 0.0 3.19
D#5 1 0.0 3.09
E5 1 0.0 2.14
F5 1 0.0 3.55
F#5 1 0.0 1.58
G5 1 0.0 5.01
G#5 1 0.0 2.13
A5 1 0.0 2.94
A#5 1 0.0 4.86
B5 1 0.0 2.90
C6 1 0.0 5.95
C#6 1 0.0 3.01
D6 1 0.0 5.60
D#6 1 0.0 5.79
E6 1 0.0 4.93
F6 1 0.0 7.07
F#6 1 0.0 5.48
G6 1 0.0 9.34
G#6 1 0.0 8.25
A6 1 0.0 9.03
A#6 1 0.0 10.21
B6 1 0.0 9.32
C7 1 0.0 12.68
C#7 1 0.0 11.32
D7 1 0.0 14.28
D#7 1 0.0 13.48
E7 1 0.0 14.16
F7 1 0.0 16.63
F#7 1 0.0 15.54
G7 1 0.0 19.71
G#7 1 0.0 17.82
A7 1 0.0 20.62
A#7 1 0.0 22.85
B7 1 0.0 22.72
C8 1 0.0 26.68

hmm, before we blame it all on my java consumption, what do you get for the faster G3-B3?

6.16 Hz.

Bi[EDIT: add 'e']ng terse is considered rude so I add this sentence.

Kees
EDIT2: I'm really excited by these results. This week has been nothing but bad news on other (unrelated) matters, this really makes my day (week?)!

haha

I listened to the mp3 again and I still hear the F3-A3 as beating slower! Maybe my internal clock is reversed?

The tapping i did was at 6 bps, and what I heard from the G3-B3. (I keep a small alarm clock on the floor, and I tapped 16th triplets to the tick). I don't know, I hope Bill can listen and report on what he hears?




I'm sad to hear about the other stuff, but I'm glad that this ground we are gaining can restore some of the overall balance! I'm really excited about this, too.

Now I have to go to a concert - I tuned for an interesting Danish pianist that is playing a solo concert tonight: Carsten Dahl

Re F3-A3: Maybe you've mutated EBVT unconsciously to a slightly milder version, your comments about C#E# being wider than you were used to being consistent with that.

Now the requirement to set F3A3 to some magic number 6 is I think a weakness of the EBVT aural recipe. I can't think of an easy way to set it without ever counting absolute beats per second. A complicated way would be to first tune ET with a 4:2 F3F4/A3A4 octave using for example contiguous thirds to set F3A3 to whatever the piano tells you, 6.9 on nice grands. Then retune F3 so that F3A3 beats between D3F#3 and D#3G3. EBVT via ET!

Kees

That sounds rather plausible... Wouldn't these numbers you posted earlier hint at that, too?

PS I like the verb "mutate" here...

C 3.8
C# -1.3
D 0.9
D# 1.6
E -0.4
F 1.8
F# -0.3
G 3.1
G# 0.7
A 0.0
A# 2.9
B 0.0

Yamaha C5 (verified by Pat)

C 3.6
C# -1.0
D 0.8
D# 1.3
E -0.6
F 1.4
F# -0.3
G 3.0
G# 0.9
A 0.0
A# 2.5
B 0.2

Kees, Bill,

I'm busy until next week (concerts and such), and I know at least Bill is occupied as well, but I just want to make sure that the next logical steps are:

1) Bill giving his feedback on my last talk-through of Kees' EBVT III calculations transferred to the Yamaha C5,

2) me tuning the Hellas "Hellish" Helsinki to Kee's numbers, and reporting back aurally (and in writing)?

Re1: sure, but keep in mind that I have a firm opinion that your F3 is too low. If Bill judged is to be right, he will have to redefine EBVT

Re2: I would expect for poorly scaled pianos that aural tuning and computer tuning would diverge. Aural tuning takes every particularity of the stings into account. Computer tuning fits the irregularly scaled piano to an ideal model without irregularities.

One could argue
a) that aural tuning is superior in this case as it takes deviations from ideal inharmonicity models in to account, or
b) computer tuning is superior as it abstracts an ideal piano like the one under consideration with all those irregularities smoothed out, and thus produces a tuning accommodating its flaws.

I have done some experiments with say a 4:2 octave tuning in the midrange based on 1) inharmonicity data on all strings and 2) an abstracted inharmonicity model smoothing out all irregularities and found 2) to be superior aurally. So it may be better to ignore beat deviations in favor of a smooth tuning.

Getting off topic here, sorry.

Kees

The more I think about it, this might very well be the case. That would make for a slight tilt towards ET (C#4-F4 and G#3-C4), right?

Anyways, there is no question you should go by Bill's EBVT III and his 2nd opinion on my comments. We are of course trying to rule out personal preferences (and errors) and get as true an ETD representation of the temperament as possible.

But if we leave that open for a while, we still need to avoid beating 5ths outside the temperament. For that I suspect we'll need the aural output of different pianos. That is why I'll try to get the Hellas numbers aurally verified.

One could argue that it's a bad instrument, and one would be perfectly right Still, although this piano is a national "treasure", similar instruments are found all over the world. We, for example, do not have spinets at all in my country, but I'd think their numbers will differ noticeably from a Steinway D

Good to hear that! As I wrote in an earlier thread, my logic told me that this was one of the reasons to go for RCT instead of VT.

As Bill has noted a few times the worse the piano the more it benefits from an unequal tuning, so I agree trying it on average Joe type pianos is crucial.

Kees

Kees, Bill, and others,

Here is a video where of me nitpicking the Hellas' center strings tuned to Kees numbers.

This is, if anything, even closer than the Yamaha C5. The main thing that (according to me) needs to get solved is the stretch right beneath the lowest notes of the temperament (F3).

Here is the video file:

nitpicking Kees' EBVT III for Hellas Helsinki, 2011-04-04

Pat:

I'm pleasantly surprised. So many people have told me tunelab's inharmonicity model has nothing to do with reality and can not possibly produce a tuning up to aural standards especially for real-world crummy pianos that I almost believed them. Your results prove otherwise. (I almost sound like Bill here...)

I did not change anything compared to the Yamaha C5 tuning, just so we don't work on a moving target. Your comments on the stretch below F3 are noted but I won't take corrective action yet.

Below the tuning for the U3. Again I changed nothing, except now the initial F3A3 beat rate is computed not as 6/6.9 * bpsET, with bpsET the ET beat rate computed from a simulated contiguous thirds setting starting with a 6:3 A3A4 octave, but by using the EBVT via Marpurg sequence. In the case at hand (U3) the difference is a 0.1 bps slower beating F3A3.

Though the Hellas Helsinki is crummy by your standards I like the woolly sound of it. We should try it on the worst spinet you can find too.

Next step is aural verification on the U3, then we should check the bass and treble. I have an option in my program to have the extra stretch option in the low bass and/or high treble, implementing Bill's optional extra stretch instructions, which is currently in the "NOT" position.
It came rather close to GPM's super stretched bass tuning, for which he kindly provided me with the figures.

Kees
--
A0 4 0.0 -33.73
A#0 4 0.0 -28.49
B0 4 0.0 -28.24
C1 4 0.0 -22.53
C#1 4 0.0 -22.13
D1 4 0.0 -20.49
D#1 4 0.0 -17.73
E1 4 0.0 -18.29
F1 4 0.0 -13.18
F#1 4 0.0 -14.01
G1 4 0.0 -11.24
G#1 4 0.0 -10.94
A1 4 0.0 -11.33
A#1 4 0.0 -8.28
B1 4 0.0 -9.73
C2 4 0.0 -1.50
C#2 4 0.0 -2.98
D2 4 0.0 -2.41
D#2 4 0.0 -1.35
E2 4 0.0 -3.07
F2 4 0.0 0.36
F#2 4 0.0 -1.49
G2 4 0.0 1.05
G#2 4 0.0 -0.14
A2 4 0.0 -0.44
A#2 4 0.0 1.23
B2 4 0.0 -0.70
C3 4 0.0 2.21
C#3 4 0.0 0.32
D3 4 0.0 1.66
D#3 4 0.0 2.05
E3 4 0.0 0.50
F3 4 0.0 2.37
F#3 4 0.0 0.67
G3 4 0.0 4.09
G#3 4 0.0 2.13
A3 4 0.0 1.56
A#3 4 0.0 4.47
B3 4 0.0 2.13
C4 2 0.0 3.43
C#4 2 0.0 -1.19
D4 2 0.0 0.91
D#4 2 0.0 1.78
E4 2 0.0 0.05
F4 2 0.0 2.37
F#4 2 0.0 0.26
G4 2 0.0 3.24
G#4 2 0.0 2.13
A4 2 0.0 1.70
A#4 2 0.0 3.39
B4 2 0.0 1.57
C5 1 0.0 3.98
C#5 1 0.0 1.84
D5 1 0.0 3.07
D#5 1 0.0 2.94
E5 1 0.0 1.85
F5 1 0.0 3.81
F#5 1 0.0 1.75
G5 1 0.0 5.37
G#5 1 0.0 2.13
A5 1 0.0 2.94
A#5 1 0.0 4.89
B5 1 0.0 2.92
C6 1 0.0 6.10
C#6 1 0.0 2.91
D6 1 0.0 5.64
D#6 1 0.0 5.72
E6 1 0.0 4.87
F6 1 0.0 7.12
F#6 1 0.0 5.43
G6 1 0.0 9.51
G#6 1 0.0 8.30
A6 1 0.0 9.16
A#6 1 0.0 10.43
B6 1 0.0 9.51
C7 1 0.0 13.37
C#7 1 0.0 12.00
D7 1 0.0 15.23
D#7 1 0.0 14.41
E7 1 0.0 15.21
F7 1 0.0 18.19
F#7 1 0.0 17.30
G7 1 0.0 21.92
G#7 1 0.0 20.03
A7 1 0.0 23.24
A#7 1 0.0 25.83
B7 1 0.0 26.12
C8 1 0.0 30.70

If you want another piano to try, I'm game. Here's Tunelab data from my 5'2" 1918 Chickering:

IHCon C1 0.555
IHCon C2 0.287
IHCon C3 0.331
IHCon C4 0.385
IHCon C5 0.684
IHCon C6 1.521

I'm not an EBVT expert like Patrick, just another tuner who has done it aurally and like it, though I haven't switched from ET wholesale. Also use Tunelab. But if you're looking for specific things, I may be able to help.

As to coding, I have plenty of side projects these days, so no promises Kees, I don't have Matlab, is your code portable to the free alternatives, Octave, FreeMat, or Scilab?

Jim:

Below your tunelab EBVT3 file. The code is not portable as of now as I use the MATLAB optimization toolbox to fit the IH curve and to solve constrained minimization problems when tuning a note to multiple other notes.

For an app I think a Python port is the best option, as Python is as good (if not better) than MATLAB for numerical algorithms. It would be a rewrite though.

Kees
--
IHCon C1 0.000
IHCon C2 0.000
IHCon C3 0.000
IHCon C4 0.000
IHCon C5 0.000
IHCon C6 0.000
A0 6 0.0 -26.02
A#0 6 0.0 -22.05
B0 6 0.0 -22.79
C1 6 0.0 -17.74
C#1 6 0.0 -17.99
D1 6 0.0 -17.18
D#1 6 0.0 -15.20
E1 6 0.0 -16.27
F1 6 0.0 -11.30
F#1 6 0.0 -12.35
G1 6 0.0 -10.17
G#1 6 0.0 -10.04
A1 6 0.0 -10.66
A#1 6 0.0 -8.02
B1 6 0.0 -9.54
C2 6 0.0 0.26
C#2 6 0.0 -1.00
D2 6 0.0 -0.52
D#2 6 0.0 0.49
E2 6 0.0 -1.12
F2 4 0.0 -1.76
F#2 4 0.0 -3.32
G2 4 0.0 -0.83
G#2 4 0.0 -1.67
A2 4 0.0 -1.86
A#2 4 0.0 -0.23
B2 4 0.0 -1.94
C3 4 0.0 1.19
C#3 4 0.0 -0.31
D3 4 0.0 0.99
D#3 4 0.0 1.55
E3 4 0.0 0.19
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

Thanks Kees, will try it and report back. Are you looking for feedback on specific intervals or beating? I will, of course, check how the aural EBVT3 instructions match.

I'm no expert, but I am trying to understand how your program works. I just was wondering if you could explain the large jump that occurs between B1 and C2 on Mr. Moy's piano. Those two notes are being tuned on the same partial, #6, and below B1 there is a considerable overall pitch drop.

Regards,

That's a good question, maybe you have spotted a bug. I'll look into it, thanks!

Note added in EDIT: Indeed, a misplaced parenthesis in the code! Pat hasn't checked the low bass yet. You have a good eye for numbers! Thanks again.

Kees

Kees, Tdowel,

I thought about the same thing this evening tuning the U3, but as I haven't payed too much attention to the highs/lows, it didn't bother me. Sharp eyes/ears (and common sense) are always welcome, though

EDIT: PS uploading the U3 feedback as we speak (write).

Jim: Good to hear from you! Stay in this thread, and drop all other coding peripherals - we need you!

Jim:

Here are the corrected numbers from B1 down.

Kees

A0 6 0.0 -21.60
A#0 6 0.0 -17.05
B0 6 0.0 -16.83
C1 6 0.0 -13.08
C#1 6 0.0 -12.50
D1 6 0.0 -11.23
D#1 6 0.0 -8.48
E1 6 0.0 -9.03
F1 6 0.0 -5.46
F#1 6 0.0 -6.16
G1 6 0.0 -3.96
G#1 6 0.0 -3.35
A1 6 0.0 -3.74
A#1 6 0.0 -0.73
B1 6 0.0 -1.96

Pat here are the corrected figures for the low bass in case you need them.

Kees
Yamaha C5:

A0 4 0.0 -12.14
A#0 4 0.0 -8.03
B0 4 0.0 -8.25
C1 4 0.0 -4.88
C#1 4 0.0 -4.83
D1 4 0.0 -3.99
D#1 4 0.0 -1.70
E1 4 0.0 -2.65
F1 4 0.0 0.57
F#1 4 0.0 -0.52
G1 4 0.0 1.40
G#1 4 0.0 1.59
A1 4 0.0 0.87
A#1 4 0.0 3.52
B1 4 0.0 2.04

Hellas:

A0 4 0.0 -37.24
A#0 4 0.0 -30.84
B0 4 0.0 -29.22
C1 4 0.0 -24.01
C#1 4 0.0 -22.35
D1 4 0.0 -19.96
D#1 4 0.0 -16.19
E1 4 0.0 -16.02
F1 4 0.0 -11.67
F#1 4 0.0 -11.92
G1 4 0.0 -9.08
G#1 4 0.0 -8.08
A1 4 0.0 -8.10
A#1 4 0.0 -4.66
B1 4 0.0 -5.77

Yamaha U3:
A0 4 0.0 -29.55
A#0 4 0.0 -23.61
B0 4 0.0 -22.48
C1 4 0.0 -17.71
C#1 4 0.0 -16.57
D1 4 0.0 -14.64
D#1 4 0.0 -11.36
E1 4 0.0 -11.64
F1 4 0.0 -7.68
F#1 4 0.0 -8.36
G1 4 0.0 -5.84
G#1 4 0.0 -5.24
A1 4 0.0 -5.61
A#1 4 0.0 -2.51
B1 4 0.0 -3.91

Got it.

ok, thx - no need for them yet, just as you said, but soon they might come in handy

Ok, here's my session tuning the Yamaha U3 to Kees' numbers.

The first video clip is a work log of me tuning center strings. I thought I'd post it as well, just for a slight presentation of the way I tune these large pianos, and to possibly serve as some kind of guidance for starting tuners. When I went over the piano the 2nd time, I had to make slight corrections to about five strings, otherwise they had stayed where I left them.

The U3 has long strings, and in my opinion this particular Yamaha model requires quite a lot of jerking to get the pins to jump to where they're supposed to stay.

EBVT III - Kees numbers - U3 - single strings (144 MB)


Then, here's the (familiar by now) talk-through of the tuning:

Kees numbeers - U3 - tuning talk-through (139 MB)


Finally, here's some music with unisons pulled in fast, just to show the harmonic balance of the piano:

Kees numbers - U3 - unisons, playing music (25 MB)

@Kees: I might sound like a parrot by now, but the biggest concern right now (as I see it) is the notes below the temperament (below F3), crossing the break. Even more than anything else, that lack of width is where I hear the biggest difference when I compare your numbers to what I would tune aurally. What about concentrating on that area for now? I can easily adjust, say, the U3 for a comparison.

Pat, I'm going to kick the ball right back to you. For the region below the temperament octave I have slavishly followed Bill's instructions quoted below, interpreting a 5th as a 3:2 fifth and a fourth as a 4:3. And I make them beat at the theoretically correct ratio as in ET (4:3).

At no point in my code do I check octaves (for C3-F3).

I think if you followed this recipe slavishly you should get the same results as I do. So what do you do different? If you can articulate that I can implement it.



Kees

Pat:

Some additional thoughts after watching your videos.

First thought: what a great contribution to post those videos of your aural analysis, I'm sure many people will benefit from this, whether you're tuning ET or not. How wonderful would it be if Emmery, Bill Bremmer, UnrightTuner, and semiprotech would post videos like that! (Kudo's to Kamin Stopper and others who have posted this kind of stuff!)

Second thought, relating to my previous post. Assuming you do follow Bill's recipe just below F3, and that the problems occur across the break, the problem may be not in Bill's recipe (surprise!), but in the inharmonicity model I use. As you know tunelab has a "split-scale" mode, where the inharmonicity curve is modeled separately below and above the break, with a discontinuity across. I have not implemented this.

Robert Scott claims this needs to be used only for spinets (I hope I'm quoting him right), but perhaps it should be used always.

So I'm tempted to fix the problem you mentioned by having a different IH model, one for below the break, and one for above. This would required the user to specify the break location, which I assume is not a bid deal.

The alternative is to require the user of the software to measure every string, so I can figure out where the break is. That would be a tough sell.

Before I start implementing 2 IH curve parametrizations, can I have you opinion on what I just wrote? Is there is an easier way to solve the problem?

I have more questions for you, but these are the most pressing at the moment.

Cheers,
Kees

Thank you for your encouragement, Kees!

Reading Bill's instructions again, I realized that this gives a lot of leeway:



I tune the fifth/fourth to beat at least in a 2:3 relationship, sometimes even more towards a pure 5th. 9 times out of 10, this does not really give me an obvious beat in the octave, so this "window" in the instructions is rather large.

I have an idea that might be worth a try before going split scale. From my aural tuning experience, the "octave size mean" in this part of the piano (across the tenor break) is 6:3. They usually work on small instruments as well as on large ones (although I sometimes go beyond 6:3's on really nice full-scaled grands)

So, what would happen if you just use 6:3's for the octaves starting at E3-E4, down to F2-F3? Then, after that, go to a fifth/fourth relationship of beating 2:3?

I think this would get us very close in a very simple way. If you could implement that and send me the numbers for the Hellas and the U3 from E3 down throughout the bass, I can verify them in no time. Does it sound like a plan?

Re: 6:3 suggestion: Will do. But the 4th and 5th scheme changes the temperament in the octave below F3, whereas 6:3 octave tunings leave it intact. I think it matters not, Bill shuld speak up if he thinks otherwise.

Kees