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Re: Yamaha C3 numbers.

If I compare with my offsets the errors in B2 and C3 would be more as mine are even higher, but the problem with D5 would be solved.

I wonder if the ETD values of B2 and C3 can be defended, which means of course attacking your B2 and C3.

How are you G2B2 and C3E3 M3's?
C3E3 should beat less than 4/3 as fast as G2B2, i.e C3E3 is a better M3 than G2B2. If you flatten B2 and C3 too much that relation would be reversed and we would end up with the famous reversed well temperament in that area.

Now if I look at the numbers from Thomas G2B2 is 3 cents narrower than ET, C3E3 5 cents narrower. With your numbers this is reversed.

With my numbers the difference in size of the two M3's is less than 0.5 cent, as compared to 2 cent for Thomas.

How do you compute offsets in the bass Thomas? I think you you mentioned how you do it in above F4.

Kees

Here we go...

This is the video clip where I've tuned the center strings to Thomas' numbers applied to a fully automatic TuneLab curve, using 8:4's in the bass and 8:2's in the treble:
2011-04-13 Yamaha C5, Tdowel's numbers, 8:4 bass, 8:2 treble

... and this is what it sounded like when the tuning was done, with all strings open, playing music through different keys:
2011-04-13-Yamaha_C3_all-strings

Sure, the piano could have used some intonation, and the lid opened "the wrong way" towards a glass wall (which is why the upper treble doesn't come through that well). Still I think these videos give a good representation of the tuning that took place, and of how it sounded when I was done.

Please DO feel free to comment, that's what they're uploaded for

Kees, I didn't check the beat rates for G2B2 and C3E3. I normally do, but Bill doesn't!

To me, the extension of the temperament downwards mainly has to 1) treat the SBI's and the octave with due respect, 2) take the tenor break into consideration. This is hard to defend in numbers, but aurally it makes sense.

I think it's no coincidence that most ETD's show their main weakness at the tenor break. I know that many hybrid tuners throw in the numbers, then go by ear in the upmost octave, across the tenor break, and in the lowest octave.

I used Pat's numbers to conduct a tuning exam, using Pat's tuning as master. The three candidates are Thomas' offset, Kees' offsets, and tunelabs historical temperament setting which copies the temperament intact over the range.

Note that Pat tuned to Thomas's numbers, then changed some, hence many exactly 0 errors. Thomas scored a perfect 100%, the 3 corrections were all below the tolerance of the tuning exam.

I had 2 points off, but I contest those.

Tunelab as-is had 2 points off, one which I contest (C2 supposedly to high), and one for D5 which was 2.3 cent flat.

So after all this work, the best option may be to just use tunelab (or any ETD) as-is with the 12 offsets and add a cent to D5, just as Bill has been saying all along.

Thomas:

Difference and Points. (F3-F4 adjusted by 0.0)

1 2 3 4 5 6 7
C 0.0 0.0 0.9 0.0 0.0 0.0 0.0
C# 0.0 0.0 0.0 0.0 0.0 0.0 0.0
D 0.0 0.0 0.0 0.0 -1.6 0.0 0.0
D# 0.0 0.0 0.0 0.0 0.0 0.0 0.0
E 0.0 0.0 0.0 0.0 0.0 0.0 0.0
F 0.0 0.0 0.0 0.0 0.0 0.0 0.0
F# 0.0 0.0 0.0 0.0 0.0 0.0 0.0
G 0.0 0.0 0.0 0.0 0.0 0.0 0.0
G# 0.0 0.0 0.0 0.0 0.0 0.0 0.0
A 0.0 0.0 0.0 0.0 0.0 0.0 0.0
A# 0.0 0.0 0.0 0.0 0.0 0.0 0.0
B 0.0 0.9 0.0 0.0 0.0 0.0 0.0

Kees:

Difference and Points. (F3-F4 adjusted by -1.1)

1 2 3 4 5 6 7
C -1.0 -0.1 1.7 1 0.4 0.9 -0.1 -0.1
C# -1.2 -0.6 -1.1 1 0.1 1.5 -0.6 -0.3
D -3.3 -2.0 -0.2 0.0 -0.9 -0.9 -0.6
D# -0.5 -0.3 -0.4 -0.2 0.5 -0.8 -1.0
E -1.9 -0.6 -0.2 -0.2 0.6 -0.8 -1.0
F -0.8 -0.8 0.1 -0.1 0.2 -0.5 -1.2
F# -1.8 -0.4 -0.1 -0.6 0.1 -1.9 -1.3
G -2.3 -0.2 0.2 -0.8 0.3 0.0 -1.2
G# -0.5 0.8 -0.2 -0.4 0.0 -0.9 -1.5
A -1.9 -0.8 -0.2 -0.2 -0.2 -0.4 -1.8
A# -1.1 0.3 0.0 -0.6 -0.2 -1.0 -1.6
B -1.0 0.9 0.1 -0.6 -0.3 -0.9 -1.5

Tunelab Historical Temperament:

Difference and Points. (F3-F4 adjusted by -0.9)

1 2 3 4 5 6 7
C 0.9 0.9 1.6 1 0.2 0.9 1.0 1.5
C# -0.9 -0.3 -0.8 0.3 -0.6 -0.3 -0.8
D -1.2 -1.0 -0.2 0.0 -2.3 1 -1.1 -1.5
D# 0.6 0.2 -0.3 0.0 0.1 0.2 0.8
E -0.6 -0.3 -0.2 0.0 -0.2 -0.3 -0.6
F -0.3 -0.5 0.0 0.0 -0.3 0.3 -0.4
F# 0.0 0.0 0.0 0.1 0.1 -0.5 0.0
G 0.0 -0.2 0.0 0.0 -0.2 0.9 0.0
G# 0.6 1.2 -0.1 0.0 1.2 0.0 1.4
A -0.4 -0.4 0.0 0.0 -0.3 -0.5 -1.1
A# 0.4 0.5 0.0 0.6 0.5 0.8 0.8
B 0.0 0.9 0.0 0.1 0.2 0.1 0.0

Kees

I beg to disagree. The only way to make that assumption would in my opinion be to measure all three calculations against an extraordinary good aural tuning of EBVT III.

For instance, when looking at the Tunelab HT EBVT III, it might look close. And yes, it might score good on the exam. But the exam does not play music, fact is - music is never played on the exam piano for any kind of verification...

In the numbers mentioned (TL EBVT III), I see a lot of deviations ranging from -1 cent to 1+. These all add up, and tweak the temperament into something completely else. In fact, errors much less than these can make or break an equal-beating scheme.

To challenge what I say here, I would need Bill to evaluate the video I posted earlier tonight. If he can't hear a clear difference between that tuning and a normal ETD tuning, then it's all in my head. The only thing I can say is that what I heard from that piano was very close to what I expect my center strings to sound like when I tune EBVT III.

First, I would like to say what I think about whether we are all just chasing the "demon" in the strings with these methods:

An ETD is extremely good at creating equal temperament, because the guidelines are relatively loose. For example, the speed of F3-A3 M3. We are told we shouldn't, can't, impose a set speed on this interval, because inharmonicity will skew the results. The interval must simply be part of a smooth progression, which will happen if the tuning follows a normal curve. The machine can create very smooth curves, and thus can create very smooth representations of ET, perhaps the best example of this is Mr. Bernard Stopper's program, Tunic OnlyPure, which has many agree is a very fine equal temperament.

Unequal temperaments do not follow a smooth curve. My method of solving this is trying to guess how far off a friendly curve the unequal temperament will be, but still clings to this curve. Kees method is truly the one with the most potential, but also the most difficult to determine. The difficulty with equal temperament is that it does impose beat speeds on intervals. While in ET, we can simply say "Well, that's just how wide the fifths have to be on this piano...", in UT, the fifth may have to be pure, or equal beating. There is no ambiguity in these directions. It simply is difficult to numerically define. That is why a set of 12 offsets can't truly imitate the effects of UT: They are not orbiting a set tuning curve; they change as needed to fit the entire sound palate, which is the ultimate goal.

What is being attempted with this thread is to numerically define an UT, EBVT III in this case, so that there is less ambiguity of how the piano should ultimately sound. While I think my method quickly gets us close, we will be able to stop working when the approach Kees has started is perfected. (Then we will simply need to perfect how we determine the inharmonicity of the strings...:))

Also, keep in mind that sometimes we take for granted how accurate our ears are. I found that many "errors" my ETD committed in tuning ET, were simply me not accurately tuning to where the ETD said I should put it. Because the aural instructions for UT are so clearly defined (imposed beat speeds, equal beating intervals, etc.), a high level of accuracy is possible when tuning to an UT. I found that I could hear differences as small as .2 cents in my temperament aurally, when I checked those results with my ETD. This really opened my eyes as to the possibilities of tuning an UT, as whether it could as readily be duplicated as ET.

I think we can catch the demon in the strings...

Pat, Thomas, those are great comments. I will keep an open mind for now.

I really wish I could hear the G2B2 and C3E3. If they beat correctly with Pat's tuning this would show the IH model fails at the break as I predict they won't.

Pat, tunelab has a "split-scale" mode for precisely this situation. If you can measure the ih constants of the C3 across the break I (or anyone) could compute a split-scale based tuning and see if this fixes the C3 and B2.

Kees

Exactly what I feel. Wouldn't I have double and triple checked, I would have blamed the temperament. Very minute changes makes a big difference.

Kees, I remember that. I think the break is, and will be, the ultimate challenge. The split scale mode might be a bridge-over to a very good implementation across the break.

I will touch-up that G5 before concert, and hopefully have the time to record the said intervals.

I suspect that G2B2 and C3E3 will be inconsistent, though. This will probably work for aural (and musical) tuning, anyways... In that range, 5ths and octaves are far more important that 3rds.

Good point. Also the D4D5 sounded terrible on single strings to me, but with the unisons brought in it was just fine. Interesting!

Kees

Yes, didn't it? I even checked the values just after making the video, just to make sure they where the same. And indeed they where.

Tuning EBVT has been a great guidance for me personally as to how overall stretch is perceived. Would a cordier tuning really not be objectionable if it was applied onto single strings only? Of course it would. Part of the beauty of piano tuning is that we can disguise false beats, compensate for bad scaling, and get along with different octave sizes. Three strings is a good thing

By the way, I have a C3 at the conservatory, too. Maybe we could try the split-scale on that piano? It needs a tuning anyway...

In regard to your adjustments, Patrick, I've tried to make them work out numerically. By "tuning" them using my simple mindless octave method, I was able to drop C3 to 1.03 cents, only .2 cents sharp from your adjustment. B2 did not come as close, ending up as -1.30, .68 cents sharp of yours. They are both fairly close, but I fear that .68 cent difference is still too far off. Can you think of any other aural methods you might use? For example, do you slowly start to favor the fifth more as you tune lower? Also, due to where those notes lie on the scale, perhaps those adjustments are inherent due to our imperfect inharmonicity model?

For D5, the only numerical way to reach your adjustment would be to treat to add the absolute values (aka, take away any negative signs) of the offsets for D4 (8va), and G4 (5th) and ignore A4. This results in an offset of 2.11 cents, just .01 cents sharp of your adjustment. Can you see any aural justification to this ?

These changes make some subtle changes in the rest of the piano, but none in the bass more than .35 cents, and D7 by about 1.7 cents.


Kees: my simple method of calculating the offsets from A4 to F5 is ( for this example, let's use C5) C4*.4+F4*.4+G4*.2. This is just a little bit different than if you were to treat them as equals, where each would be multiplied by .3333333.... It is a very small change, but probably noticeable. I never did try my first set of numbers on a real piano, but these numbers seem to work mostly. I used an identical method to A2, but switched to the mindless octave calculation a at C2, if I am trying to match Patrick's C3 tuning.

[quote=pppat Three strings is a good thing [/quote]
I actually liked the sound better with just one string, much more transparent. For contrapuntal music I can hear the voices better with just 1 string. I had my piano strip muted for about a week when I experimented with 1/4' meantone, with the muted strings of Eb G# and Bb tuned to D# Ab and A# so with just moving the muting strips I could adjust it to the music at hand. It would be possible to play Bach like that if you have an assistant that can move the muting around quickly enough.

I used to think the "una-corda" pedal did what its name implies: play on only 1 string.

Getting off-topic but after all this hard work we are excused.

Cheers,
Kees

Thomas, I think those two notes have to do with them being the two last ones before the break. On another piano, with a different break, it would have been two other notes. I somewhat believe in trying to utilize the TuneLab split scale mode for this, and treat anything but Steinway D's as spinets


Yes, I can - I think Bill wrote something like "the fourth doesn't matter"... And it really doesn't, which I think was well proved when I pulled in the outer strings. You'd go for as clean a fifth as possible, with a reasonable sounding octave (D4-D5) and double octave. Bill state that the D4-D5 might have to be as wide as 2 BPS(!), but in the beginning I chickened out a few times, until I realized that the all unisons sounding are far more forgiving than single strings alone.

On the video clip, I estimated the D4-D5 to approx. 1 BPS, and the D3-D5 double octave to a little bit narrow of 2 BPS (1.7 BPS was my estimate). Yes, they beat, but not noticeably in a musical context with all strings unmuted.

By the way, when I tuned tonight, I did not have a problem with G4 and A4 related to D4-D5, so I guess the 8:2 tunelab setting was doing its thing!

Kees, I make heavily use of the una corda too, and I like that sound very much. But let's hope not everyone goes in that direction, because then we will get in trouble with the D octaves

Patrick,

I saw all of the private messages. I am so overwhelmed at the moment. I had an accidental fall yesterday. As I was walking to my car to go to an appointment, I stepped into a hole that had been dug into the mud during the winter by a vehicle that had been plowing snow. I was looking ahead as I walked. With my multi-focal lenses, the ground is out of focus if I look down. Therefore, I did not see this hole and it caused me to fall suddenly.

It caused a minor injury to my face and badly scratched my glasses. I had to get new ones made immediately. That was only a minor problem. The real and major problem is that I have apparently re-injured my right shoulder rotator cuff. The pain is the very familiar one that I had 10 years ago. It was surgically repaired at that time but I was told that if the injury were ever to occur again, it would be impossible to fix the problem again.

So, today, my right arm is very difficult to use. The fore arm and hand are normal but I cannot lift my right arm normally. I had learned to get around that problem before and I believe I can again but it will mean that I have some impairment in my right arm that will make piano tuning difficult for me.

The last time this happened, I had been scheduled to present the EBVT at a convention and had to cancel because of it because I could not work normally. I will just have to see today what I can do and not do.

Having said that, I was able to listen to the first video of you tuning the Yamaha C3. It sounded the very same as if I had tuned it. The D5 sounded acceptable. The G4-D5 fifth could have perhaps been improved slightly but as it was, I could have gone with it. This time, the 5ths and 4ths that were played above the temperament were all as I would expect to hear them.

The piano sounded gloriously beautiful as you played up and down it! It really revealed how a piano can sound so expressive when actual musical combinations are played rather than isolated intervals.

I will get to the second video as soon as I can. I have three pianos to tune today and then a late afternoon rehearsal to attend during the time I normally schedule for a fourth appointment so I may not be able to give you any feedback until this evening. If I find that I have to cancel some of my work today, I may be able to listen sooner. I can type at a keyboard normally.

Wish me luck! I may need more help at the convention if I can make it. If I cannot tune for the demonstration, I may need someone to do that for me and Patrick, you would be the person I would ask to do that. You have done amazingly well!

Sorry to hear about the accident, get well, Bill!

Oh, Bill, I'm so sorry to hear about your accident... Let us hope and pray that the pain will go away and it all will show to be only a temporary problem.

However, if you'd need assistance at the convention, I'll be most glad to help in any way possible.



This makes me very glad, and confirms that the biggest problems earlier were related to using a conservative stretch. In the second video I play with all unisons open, and I also play the D5 against D3, D4, G4 and A4. I think you'll be pleased with the sound.

Tonight I'll tune again, and if I find the time, I'll compare Thomas' numbers against the TuneLab historical template.

@Kees, Thomas: I'm a little bit behind in my work schedule, because the temperature is rising, spring is arriving -> humidity increases -> the conservatory pianos need tunings. Right now, I won't have the time to re-check instruments previously tuned, but I can put the extra time into recording some of the ones I work on.

@Kees: In order to check your numbers, I suppose that would take som extra planning? That is, I'd have to give you iH measurements for the new instruments a day or so prior to the actual tuning session?

In principle yes, however the differences between instruments I tried are tiny (like 0.1 cent), except the Steinway D is an oddball.

Later today I'll make a dozen or so offset files for various instruments, and you can pick the one closest to the piano you're working on.

Kees