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Yes.

Kees

Here are the numbers, adjusted .91 cents sharp, so that A=440, for the .tun file I shared:



A0 6 0 0.99
A#0 6 0 1.52
B0 6 0 -0.21
C1 6 0 2.29
C#1 6 0 -0.2
D1 6 0 1.86
D#1 6 0 0.72
E1 6 0 0.03
F1 6 0 1.69
F#1 6 0 -0.18
G1 6 0 2.68
G#1 6 0 0.35
A1 6 0 0.4
A#1 6 0 2.04
B1 6 0 -0.21
C2 6 0 2.3
C#2 6 0 -0.81
D2 6 0 1.68
D#2 6 0 1.16
E2 6 0 -0.24
F2 4 0 1.94
F#2 4 0 -0.17
G2 4 0 2.92
G#2 4 0 -0.26
A2 4 0 0.31
A#2 4 0 1.89
B2 4 0 -0.18
C3 4 0 2.63
C#3 4 0 -0.24
D3 4 0 0.79
D#3 4 0 1.69
E3 4 0 -0.26
F3 2 0 1.49
F#3 2 0 -0.17
G3 2 0 2.73
G#3 2 0 0.93
A3 2 0 0
A#3 2 0 2.39
B3 2 0 -0.16
C4 2 0 3.11
C#4 2 0 -1.44
D4 2 0 0.62
D#4 2 0 1.38
E4 2 0 -0.48
F4 2 0 1.49
F#4 2 0 -0.17
G4 2 0 2.73
G#4 2 0 0.93
A4 1 0 0
A#4 1 0 1.75
B4 1 0 -0.29
C5 1 0 2.39
C#5 1 0 -0.46
D5 1 0 1.34
D#5 1 0 1.27
E5 1 0 -0.25
F5 1 0 1.77
F#5 1 0 -0.17
G5 1 0 2.92
G#5 1 0 -0.26
A5 1 0 0.31
A#5 1 0 1.89
B5 1 0 -0.32
C6 1 0 2.3
C#6 1 0 -0.81
D6 1 0 1.68
D#6 1 0 1.16
E6 1 0 -0.24
F6 1 0 1.2
F#6 1 0 0.37
G6 1 0 1.82
G#6 1 0 0.92
A6 1 0 0.46
A#6 1 0 1.51
B6 1 0 -0.27
C7 1 0 2.09
C#7 1 0 -0.31
D7 1 0 2.13
D#7 1 0 0.52
E7 1 0 0.03
F7 1 0 1.84
F#7 1 0 -0.24
G7 1 0 2.61
G#7 1 0 -0.53
A7 1 0 0.99
A#7 1 0 1.52
B7 1 0 -0.28
C8 1 0 1.75

Thanks Thomas. I notice you're a bit off from me in the temperament octave because you use Robert Scott's offsets rather than Bill's. According to my calculations Bill's numbers are closer for nice pianos at least.

More interesting and relevant seems that your numbers are for all practical purposes identical to mine!

Now if we can just get Pat to fix our "just below the temperament" notes we're done! Come on Pat, get this early morning meeting over with and get to work!

Kees

I finally figured out how to go from iPod voice memo to mp3 file, so here is my nit-picking of my tuning on a 7 foot Chinese Norkiska grand. I approached expanding the temperament as if it were a "bad" ET, trying to compromise the Fourth, Fifth, and Octave.

I didn't include the actual temperament octave, as I made some wrong assumptions. I also couldn't look at my ETD while recording, because I was using my ETD to record.

Low to High Treble (F4-C7):
http://www.box.net/shared/m80fb7lpy0

Me poorly playing the beginning of Rhapsody in Blue on the freshly tuned piano:
http://www.box.net/shared/agof42glcp

(I'm a definite amateur at that song, so don't be too rough on my playing!)

I welcome any comments on my evaluation, and whether I was right or wrong in my assumptions.

Just to state where we are:

Thomas has produced a heuristic way to get the EBVT offsets, in the spirit of Bill's scheme to pay attention to 5ths. I have produced EBVT offsets by mechanically simulating Bill's aural tuning scheme literally.

The differences between Thomas and Kees are numerically under 1 cent everywhere.

Pat dislikes the octave below F3 (across the break). Changing to a 6:3 octave scheme there did not help. The solution to this problem is not known.

Please comment if I missed anything.

Kees
PS This is definitely the most productive thread ever on this forum.

Kees,

You guys are way beyond me on most points and I like that because I have only ever done what I do as an aural tuner. It may interest you to know that any experimentation I have done with the EBVT or EBVT III has always been on on Steinway B or D.

That accounts for the very small and insignificant amount that A4 would need to be changed from a 6:3 octave with A3 in order to be correct. I liken this to Sanderson's directions for "perfection of A-440 pitch" when using its FAC program. It is possible when using that program that A4 would not be exactly at A-440 but a mere 10th of a cent or few from it. All one has to do is run the program at a small offset to compensate for that.

I hope that helps. I also hope that there will be new information that can be used during my class at the upcoming convention.

Thanks to all who have taken an interest.

Bill, Kees, Thomas, Jim, GPM, and others interested in this... I think we've got it!

I tuned until way past bedtime yesterday and rose to an early meeting this morning, but still I've had a smile on my face all day. The pieces seem to have fallen into place - partly trial and error, partly persistence, partly the power of collaboration, and then some luck

My 6:3 suggestion implemented by Kees did not sound good on the first U3, and that was kind of a drag. But then I took Thomas' numbers, added the iH from the U3 #2, and put tunelab into full automatic mode (6:3 bass, 4:1 treble). It resulted in a very good EBVT III on that instrument!

As Kees' recent numbers (using the same method) are very close, I think it is Tunelab's dealing with the 6:3/4:1 transition that made the area just beneath the temperament work so well.

Sure, the high treble is lower and the low bass is higher than both Bill and I would tune aurally, but that's easy to fix just by stretching the A0/A8 of the tuning curve. The D5 should be a bit higher, but that's easy too.

I have a nasty voice whispering in my ear that this is just sheer dumb luck, and that it won't work on other instruments. But I tell it to shut up... Knowing the U3 model rather well, I would actually assume the opposite - if it works across that break, it will most likely work in general.

I will tune a scale-compromised piano this week, as well as a Yamaha C5 (different one) and a Steinway D for concerts. I'll use the recent numbers for initial unisons, bring my cam and hope for time to record the results.

I'll post the video clips in a sec.

Here are the two files. First my 6:3 suggestion that didn't work out:
6:3 dealing with the break, U3 #1

... then the U3 #2 with Tdowel's custom offsets to a fully automatic Tunelab curve (6:3/4:1):
U3 #2, Tunelab fully automatic w/ Tdowel's custom offsets

Please listen and comment. I don't think that I'm mistaken, though... I feel that we have the aim of this thread within our grasp. From here on, it should be an easy catch.

PS I bought TL...

Pat: I noticed that in my computed relative universal offsets the G4D5 fifth is 1.5 cent wider than in Thomas' file. Perhaps that would solve the problem with D5?

Kees

Yes, that was exactly my thoughts too.
The hardest puzzle to solve in the treble extension is C4-G4-A4-D5.

I often have to back down and flatten G4 somewhat to make this work.
@Thomas: You can hear that in your sound clip, when you extend the temperament upwards. You make an aural note about D4-G4 being kind of noisy, and then you move along. Thus the impossible equation at D5!

You wiz kids should chat and get me some numbers for the tunings (small piano, Yamaha G5, Steinway D) starting tomorrow night

This is really exciting, I enjoy being part of the process. Collaboration at its best!

Thomas: I think my offset numbers are more accurate in theory in the sense that they simulate Bill's aural tuning scheme to the letter, and the offsets differ slightly depending on inharmonicity. On the other hand, your scheme perhaps captures the purpose of Bill's aural tuning instructions more directly and may be more appropriate for ETDs.

I am very interested to see how Pat evaluates our respective offsets, no matter what the outcome is.

Kees

Patrick,

In listening to your comments during the second video, I concur with all of them. This is not bad at all but certain 4ths sound too pure while some 5ths beat a little too much here and there. These would be very small changes that I would more or less expect to have to make when using a calculated program.

So, I hate to make this judgment at this point (it is just my opinion based on what I hear in this video example) but after all of this hard work, I am not so sure you all are that much ahead at this point of what the usual calculated tuning on any ETD would produce. Maybe a little, I can't be sure.

I always found that the solution for D5 was to simply sharpen it by 1 cent. That usually solves the problem. So, if there is any way to put in that alteration, it would probably solve the problem. Doing so creates a wider D4-D5 octave, yes but it is by no means too wide to be acceptable. I am always careful not to flatten D3 too much so that the double octave D3-D5 is also too wide.

If G4 somehow ends up too sharp as in this example, flattening it slightly definitely helps the G4-D5 fifth which is always the problem. One does not want to hear either a beating C4-G4 fifth or a beating G4-D5 fifth. Both should sound tempered but not much more at all than one might get with a slightly imperfect ET.

In consulting Jason Kanter's graph, I note that the theoretical cents narrow of C4-G4 would be -2.64 and the beat rate would be 0.6 beats per second. I generally think of the same ET fifth as being about 1/2 beat per second when using an optimally stretched octave. Perhaps it would be even a little slower than that in ET.

In any case, my original thinking in all of this while developing the EBVT aurally was to stay within the bounds of errors in ET that an average tuner may make. It is rare for a tuner to get a perfect score of 100 on the tuning exam. Even a high score of 98 always has that one imbalance between a 4th and 5th and RBI's that are also irregular as a consequence.

A score of 90 while still considered superior has four such errors. A score of 80 is still passing well enough to be an RPT but will have 8 such errors. So, that is what I keep in mind. I know that all of the 4ths and 5ths will be irregular but none of them ever exceeds an amount that I believe would be intolerable. The same goes for the RBI's.

I am always amused at people who play the EBVT III chromatically because it is not a valid way to listen to the temperament. However, I have to admit that I do that too expecting to hear just what I did in this video. A real perfectionist ET tuner would find it appalling! (Slow-fast-slow-fast, etc. Contiguous thirds that are inverted.)

These kinds of irregularities are rather commonly found when I listen to a temperament on any given piano at any time or place (including someone's tuning exam). I rarely find them resembling a well temperament, however. As everyone knows by now, I almost always find them working in the opposite direction. It stands to reason that if the consumer of someone's tuning efforts can tolerate those kinds of errors, they can surely tolerate the purposeful irregularities (from the point of view of a true ET) that give music the magic derived from well temperament.

I am pleased with your efforts. As long as everything sounds "kinda-sorta-pretty-even", it will work.

Last night I tried my Chickering with Thomas' latest template. Opened in Tunelab, sampled iH, unselected freeze-offsets on the tuning curve, set it to full auto, selected 6:3/4:2 then tapped Auto to get the nice Railsback curve plus the red EBVT offsets displayed, then tuned C2-E5, middle-strings.

It came very close to how I tune EBVT(3) aurally, though I needed to make these changes: flatten D4 by almost one cent to get the G3/A3 beating the same; sharpen A#3 by almost one cent to get the beating the same as the G3-C4 interval, flatten F#3 a half-cent for a beatless fifth to C#4. Tunelab gave me almost beatless fifths going down beneath F3, and above F4.

I tune to about a quarter-cent accuracy as displayed in the Tunelab shutter, so I can't say if some of the tolerances added up the "wrong way" for me. My piano's tenor break between G#2/A2. I compared the iH numbers to the one I posted previously, and they're within a few hundredths.

Hope this helps!

@Bill: Great feedback, thanks - it's definitely needed! Regarding this ETD implementation, I'm quite a bit more optimistic, though ... I guessed yesterday that those beating 5hs and too pure 4ths had to do with the conservative stretch of the TuneLab default mode (6:3 bass, 4:1 treble).

[EDIT]And because I felt that the narrowness was consistent, and not random, this, to me, was a great leap forward. [/EDIT]

Tonight when I tuned a C3 for concert (thought it would be C5, but it was its baby brother), I used Thomas' numbers in TuneLab with a tuning curve of 8:4 bass and 8:2 treble, and what do you know - those 5th/4th relationships straightened up nicely

I did but three alterations aurally: the last two plain string notes (B2 and C3), and then the D5. I think the result is quite astonishing, and at least as true to aural EBVT III as any given ETD tuning towards an aural ET.

I have it all on video, will post ASAP.

@Jim: I think it has to do with your 0.25 c window. I noticed that a very small discrepancy on TL makes for a huge difference aurally!

Ok, I'm uploading the videos right now. Meanwhile, here are the numbers from tonight's tuning session.

The instrument is a Yamaha C3. I used tunelab's fully automatic tuning curve, with 8:4's in the bass and 8:2's in the treble.

Thomas' numbers gave this chart (note/partial/deviation from 12^2, in cents/custom offset, in cents):

Template 0.4828261 10.4858 1.2011406 14.4484
IntervalSel 2 3
IHCon C1 0.233
IHCon C2 0.094
IHCon C3 0.134
IHCon C4 0.304
IHCon C5 0.753
IHCon C6 2.422
A0 6 -12.2 0.08
A#0 6 -10.8 0.61
B0 6 -11.8 -1.12
C1 6 -8.5 1.38
C#1 6 -10.4 -1.11
D1 6 -7.7 0.95
D#1 6 -8.2 -0.19
E1 6 -8.3 -0.88
F1 6 -6.1 0.78
F#1 6 -7.5 -1.09
G1 6 -4.2 1.77
G#1 6 -6.1 -0.56
A1 6 -5.6 -0.51
A#1 6 -3.6 1.13
B1 6 -5.4 -1.12
C2 6 -2.5 1.39
C#2 6 -5.3 -1.72
D2 6 -2.5 0.77
D#2 6 -2.6 0.25
E2 6 -3.7 -1.15
F2 4 -2.7 1.03
F#2 4 -4.5 -1.08
G2 4 -1.1 2.01
G#2 4 -4.0 -1.17
A2 4 -3.1 -0.60
A#2 4 -1.3 0.98
B2 4 -3.1 -1.09
C3 4 0.0 1.72
C#3 4 -2.6 -1.15
D3 4 -1.3 -0.12
D#3 4 -0.1 0.78
E3 4 -1.8 -1.17
F3 2 -1.2 0.58
F#3 2 -2.6 -1.08
G3 2 0.5 1.82
G#3 2 -1.1 0.02
A3 2 -1.9 -0.91
A#3 2 0.7 1.48
B3 2 -1.7 -1.07
C4 2 1.8 2.20
C#4 2 -2.5 -2.35
D4 2 -0.3 -0.29
D#4 2 0.7 0.47
E4 2 -0.9 -1.39
F4 2 1.3 0.58
F#4 2 -0.2 -1.08
G4 2 3.0 1.82
G#4 2 1.5 0.02
A4 1 -0.9 -0.91
A#4 1 1.0 0.90
B4 1 -0.9 -1.20
C5 1 2.0 1.48
C#5 1 -0.7 -1.37
D5 1 1.3 0.43
D#5 1 1.4 0.38
E5 1 0.1 -1.16
F5 1 2.4 0.89
F#5 1 0.6 -1.08
G5 1 4.0 2.01
G#5 1 1.1 -1.17
A5 1 2.0 -0.60
A#5 1 3.9 0.98
B5 1 2.1 -1.23
C6 1 5.1 1.39
C#6 1 2.5 -1.72
D6 1 5.5 0.77
D#6 1 5.5 0.25
E6 1 4.7 -1.15
F6 1 6.7 0.29
F#6 1 6.6 -0.54
G6 1 8.9 0.91
G#6 1 8.8 0.01
A6 1 9.3 -0.46
A#6 1 11.4 0.64
B6 1 10.7 -1.18
C7 1 14.0 0.86
C#7 1 13.3 -1.22
D7 1 17.2 1.22
D#7 1 17.3 -0.39
E7 1 18.6 -0.88
F7 1 22.4 0.93
F#7 1 22.5 -1.15
G7 1 27.8 1.70
G#7 1 27.3 -1.44
A7 1 31.8 0.08
A#7 1 35.5 0.61
B7 1 37.2 -1.19
C8 1 43.1 0.84

.......................

... and this is the chart with my "aurally demanded" changes - the three notes moved are marked in bold:

Template 0.4828261 10.4858 1.2011406 14.4484
IntervalSel 2 3
IHCon C1 0.233
IHCon C2 0.094
IHCon C3 0.134
IHCon C4 0.304
IHCon C5 0.753
IHCon C6 2.422
A0 6 -12.2 0.08
A#0 6 -10.8 0.61
B0 6 -11.8 -1.12
C1 6 -8.5 1.38
C#1 6 -10.4 -1.11
D1 6 -7.7 0.95
D#1 6 -8.2 -0.19
E1 6 -8.3 -0.88
F1 6 -6.1 0.78
F#1 6 -7.5 -1.09
G1 6 -4.2 1.77
G#1 6 -6.1 -0.56
A1 6 -5.6 -0.51
A#1 6 -3.6 1.13
B1 6 -5.4 -1.12
C2 6 -2.5 1.39
C#2 6 -5.3 -1.72
D2 6 -2.5 0.77
D#2 6 -2.6 0.25
E2 6 -3.7 -1.15
F2 4 -2.7 1.03
F#2 4 -4.5 -1.08
G2 4 -1.1 2.01
G#2 4 -4.0 -1.17
A2 4 -3.1 -0.60
A#2 4 -1.3 0.98
B2 4 -4.0 -1.98
C3 4 -0.9 0.83
C#3 4 -2.6 -1.15
D3 4 -1.3 -0.12
D#3 4 -0.1 0.78
E3 4 -1.8 -1.17
F3 2 -1.2 0.58
F#3 2 -2.6 -1.08
G3 2 0.5 1.82
G#3 2 -1.1 0.02
A3 2 -1.9 -0.91
A#3 2 0.7 1.48
B3 2 -1.7 -1.07
C4 2 1.8 2.20
C#4 2 -2.5 -2.35
D4 2 -0.3 -0.29
D#4 2 0.7 0.47
E4 2 -0.9 -1.39
F4 2 1.3 0.58
F#4 2 -0.2 -1.08
G4 2 3.0 1.82
G#4 2 1.5 0.02
A4 1 -0.9 -0.91
A#4 1 1.0 0.90
B4 1 -0.9 -1.20
C5 1 2.0 1.48
C#5 1 -0.7 -1.37
D5 1 2.9 2.10
D#5 1 1.4 0.38
E5 1 0.1 -1.16
F5 1 2.4 0.89
F#5 1 0.6 -1.08
G5 1 4.0 2.01
G#5 1 1.1 -1.17
A5 1 2.0 -0.60
A#5 1 3.9 0.98
B5 1 2.1 -1.23
C6 1 5.1 1.39
C#6 1 2.5 -1.72
D6 1 5.5 0.77
D#6 1 5.5 0.25
E6 1 4.7 -1.15
F6 1 6.7 0.29
F#6 1 6.6 -0.54
G6 1 8.9 0.91
G#6 1 8.8 0.01
A6 1 9.3 -0.46
A#6 1 11.4 0.64
B6 1 10.7 -1.18
C7 1 14.0 0.86
C#7 1 13.3 -1.22
D7 1 17.2 1.22
D#7 1 17.3 -0.39
E7 1 18.6 -0.88
F7 1 22.4 0.93
F#7 1 22.5 -1.15
G7 1 27.8 1.70
G#7 1 27.3 -1.44
A7 1 31.8 0.08
A#7 1 35.5 0.61
B7 1 37.2 -1.19
C8 1 43.1 0.84

Bill has a very good point there. At some point you should tune using using just the WT option in tunelab too to comare.

Kees

Yes, definitely - let's do that in a controlled session next week (controlled as in enough time and no need to leave the piano ready for concert... )

I admit I was quite tired when I made that recording, with a lot of different things on my mind. I don't doubt that I made a few obvious mistakes, and I might have noticed that when I listened to the recording I made using some headphones.

I just got back from an exhausting trip today. I'll try absorbing what's been said in the past couple days, and see how I can use this information.

And just a double check, did I present the ideas of extending EBVT III accurately?

I really think you did! And I think you'll be delightfully surprised about how the combination of your temperament awareness, your aural skills, your math, and you participating in this thread made this Y C3 sound tonight

PS sometimes I'd like to live somewhere where you can get decent upload speeds... but in half an hour or so the videos will be ready. DS