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Jeff,

You are right I pretend to be objectif. I don't care if I am peaceful or not, that is not my goal.

My goal is to be better at piano tuning.

I find that pure 12ths work fine to tune a certain range of the piano's scale, just above the tenor.

I am not attacking you. I am only saying that pure 3:1 12ths produce narrow octaves in the bass and produce also a flat high treble.

I read, somewhere, that Dr. Albert Sanderson were tuning a piano using an electronic instrument to put the fundamental at the calculated frecuencies of ET, calculated using the model of semitone = 12th root of 2. And to his surprise and after verifying there was no error, the piano sounded out of tune.

He then came with a solution, taking into account iH he designed his F A C tuning curve which gives nice in tune pianos.

When I first read about CHAS, I believed it was a model to solve the puzzle created by iH. But no luck. It is not that. It is a different model for calculating the ET frecuencies without taking into account iH.

That means if you tune a piano to CHASS calculated frecuencies for the fundamentals you'll get an out of tune piano. Just as with the 12th root of 2 model.

You are doing the same when talking about tuning pure 3:1 12ths which do not work fine with bad scaled pianos or wound bass strings. And as in all in this world, if you do the same you get the same results: out of tune pianos.

Gadzar:

I would say that no matter how you tune a piano with poor scaling and/or poorly wound bass strings the piano will sound out of tune.

The best that I have come up with is what I mentioned: expand the temperament downward by playing both an octave and a 12th above.

As far as the flat high treble with pure 12ths, well it sounds good (in tune) to me.

Anytime one tunes an interval such a 3:1 pure 12th, whether you do it by ear, or by an ETD using the appropriate partials, you are automatically taking into account iH. The issue with pure 12ths temperament is the same as any other temperament, you have to listen to the octaves as well and adjust where necessary. There are times when the amplitude of an octave partial may overwhelm the 12th and require more adjustment to make it sound well.

I just tuned my piano using pure 12ths and it sounds well. The treble is stretched to 34 cents at C8 and I had to widen the twelfths (actually wide 4:2 and 6:3) from G1 down to A0, giving a bass stretch of over 20 cents at A0.

Yes, of course, provided you are tuning a real piano and not talking about what that may sound on an "idealized studio with no iH" as Jeff did.



This is not pure 3:1 12ths!

Correct, but I'm not sure I understand your point.

I think any temperament starts from an idealized base and is then placed as necessary on the instrument. The challenge is to find an idealized temperament that requires the least amount of work to adjust to the particular piano. I found the pure 12ths approach easy to implement and adjust. I may find another approach as I gain more experience that works better for me as well.

Cheers

When tuning aurally, it is like if there was no iH. Except for the break where sometimes conflicts between different intervals may appear. But for the rest our ears are able to find the sweet spot where all sounds good.

Thee goal here is to find a marhematical model which describes this good sounding tuning.

My point is that if you have to tweak the frecuencies calculated with your model in some regions of the scale, then your model doesn't work.

BTW, Bernhard Stopper's Onlypure tunes pure 12ths, with good results for fine tuners like Kent Swafford.

I am not saying pure 12ths don't work. I say that pure 3:1 12ths don't work. At some point there must be a transition from 3:1 to higher partials

Cheers!

I like that first phrase.

I dont believe it can be described with partial matches, for the second question.

Regards

IT is easy to get to larger twelves, I stick with tempered ones, and depite that they may sound enlaged if tested at 3:1 in some regions.

The pure twelve is the interval that gives the most large imprecision, but tuning it tempered allow a little more in my opinion.

I also do not appreciate the stretched tone of the enlarged twelves, even if it is discrete sometime.

On small pianos you are obliged to have very compact octaves, they go together with twelves that sound aalmost pure, in my experience.

But anyway a lot of beats appears in octaves and in twelves in the lowest octaves. AInt a problem for me as long as they sound like twelves and octaves

Olek wrote:

"On small pianos you are obliged to have very compact octaves..."

Why so? Why does it follow that small pianos require compact octaves?

I have heard this said repeatedly, but have never found it to be true.

Specifically, what bad thing happens to the tuning of a small piano if one doesn't tune compact octaves?

Thanks.

If you tune a 6:3-/4:2+ A3A4 octave in a spinet it won't sound pure, because 4:2 and 2:1 are predominant over 6:3 which is barely audible.

So in this case a 4:2-/2:1+ will sound purer.

Also shorter strings means more iH and there is more distance between partials.

I ve measured a 40" tall console A3A4 octave 6:3 = 4:2+6 cents = 2:1+7.5 cents.

A balanced 6:3/4:2 will give a predominant 4 cents wide 2:1 octave beating at 1 bps. It sounds definitely out of tune.

A balanced 4:2/2:1 will give a 6.5 cents narrow 6:3 octave, almost inaudible. The octave sounds practically pure.

Well stated Raphael

That initial octave is obtained by making the partials focusing together. I think I tune some sort of 2:1 octaves on larger pianos too, anyway I refrain to get catch in higher resonances due to partials.

I am not expecting an octave to have no "life" anyway, and the more you stretch the more you "fix" the resonance. may be just because it catch attention more.

I appreciate this reply very much. This explains a few things, at least to me.

I always use an ETD, but with an aural tuning bias.

For better or worse, I tend to judge the width of an octave by the very audible 4:2. And on high inharmonicity pianos, you say the 6:3 can be both way narrow _and_ almost inaudible. Exactly.

So, to me, when I say it isn't necessary to tune "compact" octaves (as defined by the stretched 4:2), and someone else says one must tune "compact" octaves (as defined by the almost inaudible contracted 6:3), we may not have any huge substantial difference in actual tuning practice.

I worry that advocating "compact" octaves in high inharmonicity pianos is misunderstood by some tuners and wrongly taken to mean pure 4:2, which can yield a very unpleasant-sounding tuning to my ears.

Thanks again.

As far as the octaves go in practice, doesn't that mean a little bit of stretch like CHAS?

All:

Stacked, pure 4:2 octaves will always result in a wide 4:1 double octave. The higher the iH, the wider the resulting 4:1 double octave. And in very high iH pianos the 3:1 12th will also be wide when pure 4:2 octaves are tuned.

I find it is best to tune the octaves just above the break on spinets and short consoles narrow of 4:2. But then that is the natural result from tuning pure 12ths and prioritizing the 5ths across the break(s).

This is a very interesting set of statements that took a good bit of time to think through.

Actually, stacked pure 4:2 octaves will not necessarily result in a wide 4:1 double octave. One only need find one exception to your rule to prove it false, but I have several.

1. In a zero-inharmonicity situation, stacked pure 4:2 octaves will form a pure 4:1 octave.

Both Al Sanderson and Daniel Levitan teach about piano scales with "ideal" inharmonicity.

"In fact, whenever the inharmonicity of the lower note of an octave is 1/4 that of the upper note, the inharmonicity of the virtual 1/2-strings of the lower note exactly match the inharmonicity of the whole string of the upper note, and there is no inharmonicity in the octave. The experience of tuning such an octave is indistinguishable from the experience of tuning an octave beween two strings with no inharmonicity at all."

-- Daniel Levitan

2. With ideal inharmonicity as described above, then, stacked pure 4:2 octaves will also form a pure 4:1 double octave, just as if there were zero inharmonicity.

3. All that is required for 2 stacked pure 4:2 octaves to form a _narrow_ 4:1 double octave, is for the measurement in cents between the 2nd and 4th partials of the middle note of the stack to be less than the measurement between the 1st and second partials of the uppermost note of the 3. Such cannot be particularly unusual; it only means that the inharmonicity is increasing as you go up the scale more than the inharmonicity is increasing as you go up the partial series. Or you could say that the inharmonicity is increasing more than the ideal amount as you go up the scale.

Wow!

Very clever!

And surprising! (for me, at least). I'd never seen it this way.

In fact I have allways seen iH as it is in the tenor and bass, i.e. lower notes have more iH. And thinking in stretching intervals to compesate the effects of iH.

But, indeed, at the treble it reverses and higher notes have higher iH. Does that means that to compensate for iH in the treble, in some instances, one has to shrink intervals instead of stretching them?

The answer to your question is "Yes, but beware!"

Two decades ago I had been tuning with the SAT for a decade, and became dissatisfied with SAT FAC tunings for 2 overwhelming reasons. 1) B2 was tuned from partial 6 which was wildly inappropriate on some small pianos with a plain-wire string on B2. 2) And a standard feature of FAC tunings was tuning up into the treble with narrowed 4:2 octaves. (This was before the DOB adjustment was available on the SAT.)

Apparently, Dr. Al thought it was very common for inharmonicity to increase too slowly going up the scale.

We tuners have an unbelievably complex set of rules of thumb for dealing with inharmonicity, of which the treble narrowed 4:2 is an example.

However, all such rules of thumb are wrong for some individual pianos, and will sometimes lead us astray in tuning the one piano that is actually in front of us.

I have come to believe that for the best tunings we must forget the rules of thumb and tailor our tunings for the specific challenges of each individual piano.

Levitan says we should try to emulate the beat rates of the model(s) of ET; I believe he is correct.

Kent, do you mean to cover any model of an ET from pure octaves to CHAS to pure 12ths, even pure 5ths (Cordier)?

The human ear like to have that raised treble. If the ear ask for 1/4 tone on a 3 span octave, that mean a 25 cts C88 would be perfect for a 0cts at c5.

It is globally accepted that a medium iH is in the 0.6 0.7 range for A49, then the way it is suppose to raise is mostly for a more crisp and more acceptable treble.

I hae tuned many pianos Pleyel that have a reversing of iH progression in the last treble octaves may be about C6 an abovve.

While singing clear and long they are difficult to match ((an ETD are lost in computing there)

Pianos with low iH in treble can sound very well and still lack some "presence", the tone is not "irritating" enough. Too pure, the ear is not cheated enough may be.

the 1930 US upright pianos seem to have low iH in treble. Very agreable color, but somewhat limited for the available "palette"
As if a goo iH is producing different tone color depending of the style of stroke (and the global harmony/consonance)

Sorry, I don't understand what you are asking...