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Kees:

Agreed.

I think if we took the pitches that an orchestra plays at (including poor unisons) and transferred them to a piano, the result would be horrifying. Ever play an instument in front of a 12 note strobotuner and try to make the wheels stand still? Wowser!

I think there have been studies on the stretch that orchestras play at. They have been mentioned here before.

The title of Serge Cordier book is : "well tempered piano and orchestral justness" it is not translated, for what I know, but there are analysis , justness recorded and compared with the justness obtaineed with the Cordier temperament method.

I ll have a look

How many of them have to tweak their tunings because they hear bad intervals at some place in the scale?

All experienced tuners I know here in PW say the same thing: the final judge is the ear.

And all of them, those who use an ETD, do a final aural check.

For example this is what Jerry Groot RPT says about this, in another thread, but it enlights what I am saying here:




BTW, the fact that a tuner is paid doesn't guarant he's doing a good job. I know some of them who really don't know how to tune a good temperament, or good octaves in the bass. And they all get paid for that bad quality work they do.

I began to tune pianos precisely because I didn't like the way they (the tuners I'd paid) tuned my piano.

When I learned to tune my piano I was using an ETD. And I was not fully satisfied until I became able to tune it by ear. With my ETD there is always no wrong things but something that can be better done.

At that time all I wanted was to tune my own piano. And I thought an ETD was the best way. After a few deceptions I realized it was not so easy. I took the Randy Potter's course and it took me more than 2 years to learn.

Now I tune for a living and I feel that I could have learned better, easier and faster without an ETD. Because when you use your eyes you are not hearing.

I feel the same with calculs. If you see at a spreadsheet you are not hearing.

Didn't find anything. You mean I have to do some work myself to find it? I did find a 1970 study of octave stretching in orchestral instruments:

Dept. for Speech, Music and Hearing
Quarterly Progress and
Status Report
Statistical computer
measurements of the
tone-scale in played music
Fransson, F. and Sundberg, J. and Tjernlund,
P.
journal: STL-QPSR
volume: 11
number: 2-3
year: 1970
pages: 041-045

They have a cool octave stretch picture:


Kees

Rafael:

I don't disagree with you that computer models of tuning are imperfect, I disagree with a blanket statement that they are "useless". I think they are pretty good and am interested in ways to make them better.

Remember that humans are imperfect too. I think the best tunings are obtained by combining the best ETD and the best ears. Of course the ear is the final judge!

Cheers,
Kees

Gadzar:

Your brief tuning biography made me consider my own. I have never even seen an ETD in action, but have learned a great deal from the math that ETDs use: mostly to refute (at least in my own mind) some incorrect assumptions about the effects of iH. And also to refute (again, at least in my own mind) seemingly impossible tuning results that I continue to see posted.

For example: Kees posted a graph of the calculated width from just intonation of intervals for a pure twelfth tuning. They show clearly that fifths do not become more just in the treble but less just. Yet I continue to read that there are those that believe the fifths become more just with tuning an even narrower stretch such as equal beating 12ths and 15ths!

Well, I suppose that hearing is all about perception. But then that is what aural tests (which cannot lie, but can be misinterpreted) are for. There are RBI tests available for mindless octaves and for fifths if the listener has a fine discernment for differences in beatrates….

Another example for the usefulness of tuning math is something that I am playing with right now before I try it on an actual piano. There is a relationship between octave types and pure twelfths that is dependent on iH. I have noted aurally, and confirmed this mathematically, that for a typical piano 4:2 octaves in the middle of the piano will produce pure twelfths. So for a “C-forker” why not tune C5 to fork, C4 to C5 as a 4:2 octave and F3 to C5 as a pure twelfth? The result should be a properly tempered F3-C4 fifth. Of course whether this is practical or not depends on the tuner. It might just be another technique in my “bag of tricks”.

Tooner,

That is why I disagree with you.

You say that your models predict narrow 5ths, so you reject pure 5ths.

Theory is there to study the real world, the process is simple and well known: You observe and study a natural phenomenom, you make an hypothese, you experiment and reject or confirm it with facts (experiments).

You don't use unprooven hypotheses or theories to reject facts.

If I tune a piano in a way that gives regressive and then pure fifths in the treble then any theory that says my fifths should be narrow is wrong! My fifths are what they are, no theory can denie it!

Theory must explain facts, if not theory is wrong.!

Einstein for example found phenomenoms that Newton's theories couldn't explain, so he developed a new theory that explains this facts. Can you imagine Einstein rejecting the facts because Newton's theories say they should be otherwise?

So, please, invert the order you do your studies:

1. tune a piano
2. observe and measure
3. construct hypotheses and theories, which should explain and predict the facts you observed
4. go beyond actual knowledge

To my point of view, you are doing the opposite:

1. You take Young's formula for iH and calculate partials
2. you use an inaccurate model semitone = 12th root of 2
3. you construct a model (spreadsheet) with these partials
4. you denie facts and say 5ths must be progressive

And in the whole process you do not tune and measure a single piano!

Please, give me a break!

Gadzar:

I have tuned pianos and listened to them.

Fifths do not aurally regress nor become wide in a piano unless the tuning is stretched enormously. Neither mindless octaves nor pure 12ths are enough stretch to make this happen. (Common sense comes into play in the relationship between fifths and twelfths. Fifths cannot become pure unless twelfths are already wide.)

It was when I read that some believe otherwise that I then studied the theory and found out that the theory and my ears agree.

However, if you think otherwise let's call it an "indulgent mystery".

[Edit:] I do not think Albert Einstein observed and measured matter/anti-matter collisions to produce the equation E=MC^2

Neither of us (Jeff or me) are doing that.

Kees

Another example of an "inverted scientific method":



Let's put it in a more mathematical way:

Tune

1. C5 to the fork: first partial of C5 = first partial of fork
2. C4 to C5 as a 4:2 octave: fourth partial of C4 = 2nd partial of C5
3. F3 to C5 as a pure 12th: third partial of F3 = first partial of C5

Now the conclusion: F3-C4 5th will be correctly tuned.

That means, F3-C4 narow by 1.955 cents:

third partial of F3 - 1.955 cents = 2nd partial of C4


How is it possible?
We have not a clue about 2nd partial of C4!
We have not tuned it, we have not measured it.
Why it should be 1.955 cents flat from third partial of F3?

By concluding this you are making several unjustified assumptions relating 4th/2nd partials of C4 and 2nd/1st partials of C5.

There is no theoretical reason.

Tooner, you say you "have noted aurally and confirmed mathematically..."

But, in fact, you have no measured it! What you hear is subjective. You need an instrument do objective measures.

There in no mathematical confirmation neither. If your spreadsheet confirm it, that is by coincidence. Mathematically you can say nothing about 2nd partial of C4. There is no prooven mathematical relation between partials. There are only hypotheses, which if denied by facts are useless to tune a piano.

And there you must hear the results: if 5th is ok. you can continue. If 5th is not good you have to adjust it, you can not denie facts and tell: it should be right.

And that's what an ETD tuner (beginner) will do. He will tune to what his ETD says, even if it sounds bad. So your model must follow the real world to prevent this.

Gadzar:

I am amazed. You accuse me of basing my calculations on the 12th root of 2 (which is not true, if you want to know what I base my calculations on you should ask) and then say that my calculations cannot be correct because there is no proof that the resulting fifth will be 1.955 cents narrow from just intonation. If nothing else you should realize that if inharmonicity was not being considered, and twelfths were being tuned pure, fifths would be tempered less than 1.955 cents!!!

No, I believe that you are again attacking me instead of trying to understand what I am saying.

So, when I tune a temperament with a 4:2 octave and expand it with 4:2 octaves on a midsized piano, what do I find? Pure twelfths! How do I know they are pure twelfths? By aural tests! If that is not good enough for you, and the mathematics are not good enough for you, well that is just too bad for you.

No I do not have an ETD to measure with. But your criticism of my methods not being based on reality can be used against yours using an ETD. But I do not recall you mentioning what the frequencies are of the partials that you must be measuring to determine what you say is true. Don’t tell me you are using your ears and then criticizing me for using mine!!!

But be careful when using your ETD. Do not make the mistake that others have made. Just because the fundamentals of the notes that make a fifth are 702 cents apart does not mean that the interval is just. The 3rd and 2nd partials must be compared.

Ok Tooner and Kees:

Can you please give me the definition of a cent?

Please, don't tell me that cents = 1200*log2(F'/F)

If so then you are using the model of 12th root of 2.





That is exactly what I´ve just said to you:

To speak about F3-C4 fifth you need to know the 2nd partial of C4. If you don't have it you can say nothing about the 5th. So by tuning a 4:2 octave and a pure 12th tells you nothing about the 5th as this does not involve in any way the 2nd partial of the upper note of the 5th.



And don't bother, I know well how to use my ETD.

cents = 1200*log2(F'/F)


That is nonsense. It's like saying that because Americans measure the price of gas per gallon, they must therefore drink a gallon of Coca Cola a day.

Anyways this thread is supposed to be about octaves. Why don't you read the tread about mathematics? Once you understand what was discussed there we can talk more.

Kees

I've read the thread about mathematics, there is nothing new in there.

And, for what I've read here what you and Tooner have been made is correcting 12th root of 2 model with calculated iH, isn't it?

And here in Mexico, we drink liters of coca-cola. I couldn't drink an entire gallon.

And yes! We measure gas in liters too.

What I mean is that if you use a system then you think in terms of that system. If you speak of cents as the 1/100 th of a semitone which in turn is the 12th root of 2, then you think about an octave being 12 of these semitones.

As a counter example Mr. Stopper speaks of semitone = 19th root of 3. He has another model in mind. For him:

cents = 1900 * log3(F'/F)

And a 12th is 19 of this semitones.

And I don´t know exactly what the definition of a cent is in CHAS but it is absolutlely not 1200*log2(F'/F).

Rafael , I like your question about the cent definition ! excellent !

The difference is undoubted less than the tolerance of a piano's pitch.

No, no, I dont think thats the point. It is a conceptual question, the difference between acoustic reality and supposed theory.

I believe that iH is annoying most of us way too much.
I only understood that recently when a friend, that tune Cordier style, told me about "acoustical fifth" . When looking at tuning that way, any decent model can be applied, that is BTW what tuning uneven temperaments learn you, you can forget about octave style and look for your temperament construction first.

Yes piano pitches have tolerances, atractions, coupling effects, many effects that are difficult to analyze and that can help or annoy the tuner.

No piano tuning can be envisaged without iH, but it is just because iH is in the tone. I see no big interest in tuning the iH.

I decided than the justness is just a step near what is obtained with a partial match tuning.

a "pure 5th" have not much to do with a pure 3:2 or a pure 6:4 It is something that sound acoustically just, thats all.

Try to tune a pure 5 with a 3:2 partial match on an EDT, then try the same by ear , and listen to wich you prefer.

one will have some added "light" due to a good coupling, the other will tone constrained and flat.

Indeed a cent, in theoretical computations, should have a value that take in account the size of the octave of the piano the computation apply. If not all the partial matches ar innacurate.

Of course, if you want to do that, you might first consider what the frequency of a piano note is. How would you define it?