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Alfredo, I am writing to the French, but that is another story and not about ET!

Did you know the standard metre was once held in Paris as the distance between two marks on an alloy of platinum and iridium?

Paraphrasing (a note about the history of the metre), none of the standards changed the temperament, but merely allowed it to be duplicated more precisely.

When it comes to temperament, maybe there is an advantage in moving the marks a bit?

E.T. (TM) reissued year xxx. All rights reserved.

Could we define the ET standard as each M6 audibly beating the same as the M3 two semitones higher? Wouldn't all the M3s and M6s then also be progressive?

In the context of this discussion, a 'standard' means a 'model in comparative evaluations' (OED). Since each piano exhibits a unique inharmonicity, and even if you ignore that the inharmonicity varies slightly due to the tension change as the pitch of a note changes, the only 'model' that can be used 'in comparative evaluations' is that unique piano. The true aural tuner will find the 'standard' temperament for that unique piano.

Yes that's right, Prout. As I understand it, the standard for the PTG tuning exam is a particular piano tuned by experts.

But the International Standards Organisation would look for something of more general applicability. They say a standard is a document that provides requirements, specifications, guidelines or characteristics that can be used consistently to ensure that materials, products, processes and services are fit for their purpose.

I have no doubt it would be possible to write such a document but whether everyone would agree with its contents is quite another matter.

Objections: It is a subjective definition ("audibly beating the same"). iM3-oM6 are not exactly equal beating, it's like defining pi as 22/7.

I like the original definition better: progressive M3/6. The fact that nobody can tune it does not discredit the definition IMO.

Kees

Good point, and gets to the heart of the matter here. All standards require an accepted measurement that includes an accepted error tolerance. The metre is precisely defined using time as the measurement vehicle, and the accuracy of the measurement of time limits the accuracy of the length of the metre.
If everyone would accept a given tolerance for error in a tuning, then a standard would exist.

Hello Yann, about the meter definition, I have seen a documentary, on how difficult it was to define the exact length of one meter.

It took not months, but years since 1792 to 1796 for 2 geometer to measure the exact distance required to compute the original "metre etalon" one should measure from 2 French towns, Dunkerke to Rodez, the other from Barcelona, in Spain , to Rodez. Where they where supposed to meet.

Imagine the 2 men measuring parcel after parcel, taking notes, to get the distance of 9.5 degrees of an arc situated between those 2 towns. (that are at sea level)

Of course there was war between France an Spain at that time, so a man taking measurements was easily mistaken for a spy...

Quite a journey :

http://en.wikipedia.org/wiki/Metre


Then, finally , ET : http://www.deezer.com/track/12492219


Enjoy !

I am not certain what standard one would use to define the pitch number of a note on a piano. I do not think that it can be defined to any arbitrary accuracy. One can probably tune equal temperament on a piano to within the accuracy that the pitch can be defined, and no other temperament, nor just intonation, can do any better than that on a piano.

I guess ET is yet defined, you find it on digital organs for instance.

Now the way it is implemented on pianos is a different story.

I understand that was included in the OT.

As there is a different ET for each pianon I cannot see what the standard would be. even a formula should address acoustical points, as the pitch of a single note is not clearly defined when in the ear of the listener.

A youngster will hear a different pitch than an adult , and possibly after some age we hear the pitch lower.

Ciao Isaac,

You wrote:

..."I guess ET is yet defined, you find it on digital organs for instance."...

Do you mean... ET = progressive M3/6?

..."Now the way it is implemented on pianos is a different story."...

Yes, it is a different story, (mind you) both for "digital organs" and pianos. In both cases, we cannot have SBI's that double their beat-frequency every other octave. So, ET may well be defined (I would like to know what you mean), but the model is not 12 root of two.

..."I understand that was included in the OT."...

Me too.

..."As there is a different ET for each piano I cannot see what the standard would be. even a formula should address acoustical points, as the pitch of a single note is not clearly defined when in the ear of the listener."...

Hmmm... Here it gets difficult, 'cos I would go back to the first question, what is ET? But if you needed a formula for infinite "acustical" points... I would have one :-)

..."A youngster will hear a different pitch than an adult , and possibly after some age we hear the pitch lower."..

Yes, perhaps that is true, although I find it difficult to say. Anyway, I do not tune by listening only to pitch, as I used to do at first; I use beats as a walking stick and I tune a form, you decide how to call it, a beat-form? A geometric-form? In any case, it is pitch_and_beats in one, the same (progressive?) form... no matter the piano.

Cordialmente,

Alfredo

On the topic of using nearly equal beating ET test to define ET:
Besides the M3M6 test there is also a m3M3 test: C3Eb = F3A etc.
Doesn't seem to be popular, maybe IH messes this up too much in practice?

Kees

Are you proposing that as the standard for ET? It sounds a bit vague.

Kees

I still think Jeff's original standard of progressive M3/6's is the best.

M3-6 are musically significant, and if they are audibly non progressive key equivalence is destroyed.

SBI's like 5ths and 12ths are musically irrelevant; they are already purer than musicians can play them on flexible pitch instruments. They are perfect for all practical purposes.

The fact that nobody seems to be able to tune progressive M3/6's just shows that tuning ET is indeed very difficult. So difficult that nobody can do it, even with an ETD! Still the examples posted are all close enough for practical purposes.

Kees

Trying to follow the argument so far, progressive M3/6's appear to be necessary for the attainment of ET but not sufficient. Bill cited examples of tunings with progressive M3/6's that were not ET.

Is it sufficient for ET that all intervals are progressive, or are further conditions necessary?

Ian, according to my logic, which may be in error, it is possible to have poor ET with progressive M3rds OR M6ths, but good ET with progressive M3rds AND M6ths

I just dont get that .

slow intervals are playing a role in the congruence and clarity of each individual note.

Fast beating intervals are the result of the division of each new octave, to me, if I am looking for a basic definition (without any particular musical meaning)

Chris, Thank you for that distinction. Going back to what Bill wrote, although not the point I had in mind, he says:


Isaac mentions other SBIs and there are octaves to consider too.

Coming back to my question, would one hope to find that all intervals are progressive, or should I say evenly progressive, in a concert tuning (to the standard rxd mentioned early on in this thread)? I mean within practical limits, of course.

All:

I don't think it is possible to have progressive M3s and M6s and not have apparently equal beating M3/M6 tests. And if the M3/M6 beats are apparently equal then the M3s and M6s will be progressive.

The word equal does have to be qualified whether we are talking about equal temperment or equal beating. I agree with Kees' objection to the term "audibly beating the same". It was the best I could come up with at the time. "Apparently equal beating" is a better term.

There are a couple of problems with substituting the m3 for the M6 in the inside outside test. First, it is only valid if the octave is about 6:3. That is the only time that the m3 and M6 beatrates are interchangeable. Second, since the partial match is higher (6:5 vs 5:3) they are fainter and more difficult to hear. Third, again because the partial match is higher, any anomaly in the string's iH will change the beatrate more as in the case of wound strings.

The one advantage is when the M3/M6 test is not available in the temperment sequence. I have tried using it in such circumstances, but there are usually other tests available by that time.

Yeah, it's available and useful but not popular.

Musically Significant Intervals. Hmmm.... Another Topic?