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Great ! have a good time and post us some pics if you will !

Not exactly.

I can't give you exactly that easily, but something close. Below the deviation from beatless in cents of various intervals in a pure 12'ths tuning for my upright.


Kees

PS The P20 is a typo, it's the P22.

Doelkees,

So this tuning will only work from about C3 (note 28) to the top.

Below C3 6:3 octaves become narrow and in this region they are very audible. A more stretched tuning is needed for the bass.

It would be interesting to graph 8:4, 10:5 and 12:6 type octaves for the low bass, maybe this piano needs larger than 6:3 octaves in the low bass.

But, here I go again, all this graphs are theoretical. In fact actual iH of each string is very less uniform and predictable than we would expect, mostly in the bass. I have measured negative iH for some partials, or a third partial with less iH than the 2nd, etc.

UnrightTooner says that 2 4:2 stacked octaves give a wide 4:1 double octave. This is only true if partials behave as expected. If they are inverted in one string, then 4:1 may be just or narrow. All depends on the relative position of the partials involved.

This is confirmed by Doelkees. In his piano 2 stacked octaves, slightly narrow 4:2, don't give a beatless 4:1 double octave.

I think all this theoretical stuff is useless!

I don't know how to extract info of my Verituner of all the partials it measures in a standard tuning. But if someone helps me to do it, I will post some of the results to show you how inconsistent can real iH be.

I have done some direct intervall tuning with it and the readings are all but predictable, mostly in the tenor and bass sections.

There are significative differences even between two strings of the same unison. That explains why if you tune two strings to the ETD chances are that the unison you get will be bad.

I did a custom tuning of a Yamaha C7 yesterday with the octaves and temperament tuned as I did for GP and as described in a previous post for the Kat Trio: http://www.thekattrio.net/

The report I got back was: never heard a Yamaha C7 sound so in tune, project so well and that was so easy to play in tune with. Who was that technician? What did he do that was different? They were given my name and website information.

[sure ! it goes better when saying it !

Nethertheless I dont understand the aesthtetic of the Ebv3, It still sound slightly out of tune to me, my ears tell me to stop listening.

I am as much surprized than I like all kind of non ET music.
Btw I begin to dislike WT even in original context(harpsichord, etc)That does not satisfyçmy sence of harmony

Did you do a blind test? Prejudice can influence your aestetics a lot.


You mean non-Western scales with more than 12 tones per octave I think. Perhaps the reason is that WT is close enough to ET that you perceive it as a bit off, whereas e.g. Persian music is so far off that you can't perceive it as out of tune ET but as something different.

Kees

Well, a blind test would Be skewed anyway. But you can trust me, I find some standard tunings incoherent, harmonically speaking, and boring, even disturbing for the musician, but I relate that to a lack of shine and resonance.

A tuning on a modern piano should be some kind of whipe paper, for the pianist, unless particular circumstancies.

Shine, no straightness. is what I wish.

It might be terminology that is interpreted a little differently between the two of us. As I said earlier, because my octaves are basically never 2:1's, and mostly even 4:2+, I do almost always hear a slight roll, or slow sway at the 2:1 level.

A beat, to me, is something that is fast enough to have a pulse that is easily percieved. 1/3 bps and slower, I hear as 'sways' or 'waves'. And I gladly sacrifize the pureness of the 2:1 if that makes me get the piano to sound in tune over the whole keyboard - that is, that a low C (C1, C2) still harmonically lines up with a high C (C6, C7).

Jeff and Kees: On small pianos I do not hesitate to enlarge the octaves a bit past normal in the outer ends of the piano. I open up the last 1 1/2 octave of the bass by moving wider then 6:3. I rather take that grunt at 2:1 as long as I get the whole harmonic persception of the piano to sound more coherent.

about 2:1 beat in the mediums the fact that I have seen 2:1 beating slower than 4:2 when 4:2 is large make me wonder if those octave ratios are really reliable (anyway between 2:1 and 4:2) I second what say Rafael there you need more than one partial to begin to have an accurate tuning.

Returning to the original topic,

What happens, for example in EBVT III, if instead of spreading the temperament octave to the rest of the keyboard in the usual way, we repeat the tuning instructions for setting the temperament but this time an octave higher or lower? i.e. we tune the notes between F4 and F5 (or F2 to F3) not as octaves from the lower (higher) notes but by replicating the tuning instructions an octave higher (lower).

That is, for F4....F5:

1. Tune C5 from F4 as a beatless 5th
2. Tune F5 from C5 as a beatless 4th
3. Tune E5 from C5 as a M3 beating at the same rate than F4-A4
4. Tune G4 from E5 as a M6 beating at the same rate than F4-A4 and C5-E5
5. Tune B4 from G4 as a M3 beating at the same rate than F4-A4, C5-E5 and G4-E5
6. etc...

I guess it won't work.

If there were no iH then the tuning will come out nicely. But there is iH and I bet the tuning will be wrong. The octaves won't be clean. In order to deal with iH we must temper octaves while keeping and eye on the good quality of the other intervals: 5ths, 4ths, 12ths and 15ths in this case.

This compromise explains the need of tempered octaves.

Yes Rafael,

to me, EBVT III is really a two-part temperament: First, the initial setting of the temperament octave (F3-F4). Then, the extension of the temperament (down to the tenor break, and up to F5.)

Once that (approx.) 2 1/2 octave is set, then the rest of the piano can be comfortably set. But there will be several choices to make in that second part (the temperament extension).

Just as Bill has repeatedly stated, the octave sizes will vary in that second stage. What's even more interesting is that they will vary from one instrument to another (!)

I find myself tuning 4:2's, 6:3's, 6:3+ and whatever the sound of the fifths and fourths ask for.

This is why I think EBVT III is not easily realized using an ETD for that second stage.

Have you (or anyone else) had similar experiences?

Fair enough Isaac, but I am by no means sure that wish is shared by the pianist and the non-tuner audience

Thanks for that, Rafael. I had a revelation about the octaves when I tuned a piano in 1/4 comma meantone for Owen Jorgensen at a convention back in the 1990's. He said I only needed to tune to a certain point, I believe it was F6 in the treble and C1 in the bass because beyond that, the keys would not be used. I felt however that I should tune the whole piano and I did.

What I found, however beginning at C6 was an extreme dilemma. I could easily create the temperament (F3-F4) within a 4:2 octave. The M3s sounded very pure. I could continue those pure M3s into the 5th octave with M3-M10 tests with no problem. But once I reached the 6th octave, if I tuned pure M17s, the octaves became quite narrow. I decided immediately that narrow could never be appropriate. I used my ETD to simply read and find 2:1 octaves for the 6th octave from whatever had been tuned in the 5th octave. I did similarly for the 7th octave.

What I heard in the performance was the deadest, most completely bereft of resonance piano I had ever heard! Frankly, it did not appeal to me at all but that was my personal opinion, of course. 300 year old music was played upon that piano and it had a very strange character as far as I was concerned. The modern piano that it was played upon (a Kawai grand of some sort), had eerily been transformed into some kind of ancient sounding keyboard instrument!

I'm afraid that a simple misspelling here may have created a colorful joke! In any case, assuming that the joke was unintentional, I have read many times this particular argument but reject it. The "neutral pallet" argument leaves the pianist with only the choice to play louder and faster or softer and slower but with little change to the music except that it is louder and faster or softer and slower.

When the piano itself, however provides as a foundation, a sea of calm or rough waves, (or anything in between), the pianist then can navigate accordingly.

Yes, that's also my experience.

I have tried to tune from F3 to A4 with my ETD and the rest by ear with good results, but even then I can do better by tuning aurally.

If following the tuning instructions, you have to tune A3-A4 as a 6:3 octave, F3-F4 as a 4:2 octave and the remaining octaves are all of different sizes. D4-D5 is wider than C4-C5 for example. That is impossible to program in my ETD.

The only way to successfully use the ETD is by "direct interval" tuning and for some notes you have to calculate some partials manually. For example to obtain the 6 bps in the intervals F3-A3, C4-E4, G4-E4 and G3-B3. The rest can be programmed in a spreadsheet and tuned with the ETD as a measured or "master" tuning.

By seeing at all that computing work I think it is easier to tune it by ear!

One of the advantages of EBVT III is precisely that it is an easy to tune temperament: you only have to know how to:

1. tune a 6:3 octave
2. estimate a beat rate of 6 bps
3. tune pure 5ths and 4ths
4. tune equal beating intervals

Of course, you must understand the spirit of a Victorian Well Temperament to give sense to all of the above.

And you are right, that changes from one piano to another, aurally and electronically. In a low iH piano 6:3 and 4:2 octaves are almost the same and in high iH pianos there is a huge difference.

Also, all the calculs you have done for a given piano are useless for the next one you tune, except for the spreadsheet which can be reused, but you have to re-enter the calculated partials in the ETD.

Kees:

Thanks. I came up with similar results when analyzing a pure twelfth tuning, only the y-axis I use is in bps. The bass is in a better perspective that way, I believe. With twelfths, the 2:1 and 4:2 are very acceptable to me, with the 4:1 not being overly wide and the 8:1 not being overly narrow.

All:

This Topic is going of the tracks with the inclusion of EBVT.

To say it is all useless is to "throw the baby out with the bath". If the theoretically “stuff” is really useless, then pianos could only be tuned by using a sense of pitch – aural tuning sequences and ETDs would not work.

When I was working on my simulator, one of the members here graciously sent me a large number of verituner files in .txt format showing the cent deviation of a wide range of partials. For the lower, wound strings, yes different values of iH can be determined depending on which partials were used. By using an average of a number of them a fairly smooth iH curve was produced. For the upper strings, there was little if any difference in the calculated iH regardless of the partials used.

But let’s talk about tuning in the bass a little more. The 6:3 partial match is much more obvious than the lower matches due to the strength of these higher partials. When tuning an aural octave, I think the ear naturally tunes to this 6:3 match. FWIW Dr. White makes mention of the “falseness” of wound strings and proscribes tuning 6:3 octaves with the m3-M6 test for this reason. He also allows for the bottom octave to be given additional stretch to satisfy the musical ear’s sense of pitch.

So OK, many wound strings have some falseness. Perhaps all strings have some falseness. To me the solution is clear. Do not tune with single near partial matches any more than necessary. Whenever possible use multiple partial matches. Electronically, this is what the Verituner is supposed to do. Aurally, use both SBIs and RBIs when setting the temperament, and then tune each note to at least two others when expanding the temperament. It is even possible to tune a note to two others at the same time by playing three notes at once.

But the theoretical “stuff” is certainly not worthless! It is a framework to understand what deviations there are between theoretical and practical, and just as important, whether the deviations are significant.

Ok, ETD are not useless. And theory is not useless.

What is useless is trying to tune a piano to a theoretical averaged iH curve calculated from some few samples.

As I said it doesn't work, even for a single unison!


It is useless to find out that 5ths are progressive in a simulator, while you are actually tuning pianos with constant and even regressive 5ths.

Furtheremore, theory is useless if the model you use does not match the real world. And for ET, the model of semitone = 12th root of 2 doesn't match reality. If you tune a piano with that model it will sound badly out of tune.

So, what I am saying is that we must put our feet on earth and talk about real world facts.

I would call this a non-octave tuning, as the octaves themselves are not tuned, they just result from tuning other intervals. Three non-octave tunings that are well-known are Cordier (pure 5ths), Stopper (pure 12th), and mindless (equal beating 15 and 12's, invented by Bremmer (?)).

Does anyone consider this proposition blasphemy?:

The fact that the 5th or 12th is pure in 2 of these is incidental, it is just a recipe to obtain a certain amount of stretch, aka a tuning curve, that people like.


Kees