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I too have a question: in English, is it more correct if I say "modern" ET's or "contemporary" ET's?

Cheers, a.

That is funny as that can be understood differently :

Not enough change from usual ET
or
The "out of tuneless" of ET missed to the pianist.

The pure 5th of the temperament create an "in tune" perception that was not expected.

The piano, used to its usual tuning, did go back toward it..

Which was ?

I had a look, it is difficult to tune that temperament aurally, yet on a harpsichord, then on a piano it may loose a lot of character (may be also thecomment from the pianist, if he is harpsichord player for instance)

Pianos does not seem to be well suited for strong UT's

Alfredo

If I were drafting a standard for ET today (which of course I am not), I'd be inclined to cover the range of possibilities you mention from 12-TET to Cordier.

Before allowing for inharmonicity, my calculations of octave stretch are 12-TET: 0 cents; Chas: 0.32 cents; Stopper, pure 12ths: 0.86; Cordier, pure 5ths: 2.32.

Franz Mohr, or was it the Steinway tuning guide, said all octaves are stretched a bit. One way and another, octave progression appears to be significant.

I'd say any such standard, that's to say a document setting things out, should include tests related to thirds, fourths, fifths, sixths, octaves, tenths, twelfths, fifteenths, seventeenths and maybe others.

It might well have something to say about beat rate curves but there would have to be a precise definition (with examples for the various types of temperament). Does one exist?

I note that: Bill Bremmer said the higher the octave stretch the brighter the sound; Isaac thinks pure twelfths put an upper limit to stretch for the temperament octave, and prefers something closer to 2:1, possibly within a Chas framework; and that Jeff D say pure twelfths may sometimes be tempered to advantage.

KBIII is the easiest WT to tune aurally.

Kees

It sounds like we're at a loose definition of ET as a standard - beat rates should be progressive and octaves should sound pure. Everything else follows from those two criteria. Having 5ths, or 12ths, beatless (or using any other ratio) is just a way to define how pure the octaves are, and as we can't reach agreement on this question (it depends on too many variables), it shouldn't be defined in any standard.

I love the sweet smell of progress

edit: perhaps an addition: "Octaves should sound pure, whilst allowing as many of the larger intervals (double octaves, 12ths, 17ths, triple octaves) as possible to also sound pure."

Ciao Ian,

You wrote: ..."If I were drafting a standard for ET today (which of course I am not), I'd be inclined to cover the range of possibilities you mention from 12-TET to Cordier."...

Hmmm... 12-TET does not work, because any scale ratio smaller than Chas would "deflate" the two-octave compass. On the other hand, scale ratios larger than Chas may well be considered (in practice), as mentioned in my previous post.

..."Before allowing for inharmonicity, my calculations of octave stretch are 12-TET: 0 cents; Chas: 0.32 cents; Stopper, pure 12ths: 0.86; Cordier, pure 5ths: 2.32."...

I see, :-) you do not waste time.. :-)

..."Franz Mohr, or was it the Steinway tuning guide, said all octaves are stretched a bit. One way and another, octave progression appears to be significant."...

That's for sure.

..."I'd say any such standard, that's to say a document setting things out, should include tests related to thirds, fourths, fifths, sixths, octaves, tenths, twelfths, fifteenths, seventeenths and maybe others."...

I agree. Let me ask: You say "tests", do you mean aural tests, or graphs, or...?

...It might well have something to say about beat rate curves but there would have to be a precise definition (with examples for the various types of temperament). Does one exist?..."...

Well, what I could do in my research report was comparing 12_root_of_two and Chas beat-curves, and I think you are right about definition and examples. I can define beat-curves, but right now it is no possible for me to work on "various types of temperament", as I have little spare time.

..."I note that: Bill Bremmer said the higher the octave stretch the brighter the sound;..."...

True, the more you pull a (any) string, the more it tends to shout, I think my quasi-wife would agree :-)

..."..Isaac thinks pure twelfths put an upper limit to stretch for the temperament octave, and prefers something closer to 2:1, possibly within a Chas framework;..."...

That's why Isaac is my favorite :-)

..."..and that Jeff D say pure twelfths may sometimes be tempered to advantage."

Yes, perhaps Jeff could work on beat-curves and "examples for the various types of temperament", Jeff was the first in PW to grasp the concept and was able to provide some very vivid graphs.

First, I admit that I have read non of the replies and I am just replying to the original post above.

This is not a fundamental question that should be asked. Why?

Because, as of today, there is not a fundamental issue between these tuning temperaments.

Because, as of today, it is both unfair and not very meaningful to compare some scarce UT (lower that 0.1%) that belongs to past to ET (higher than 99.9%) that is in use today.

Because, ET is already THE universally accepted standard already.

Because, 99.9% of the population even do not know what an UT means.

Because 99.9% of the population is not aware of something ET vs. UT.

Because 99.9% of the population is not aware what ET means.

Hi Phil,

What do you mean by ..."..loose definition"? A translation (in Italian) of the term "loose" may mean too many different things.

You say .."...octaves should sound pure..", and one question is precisely there: octaves that "sound pure" may be on the narrow side or on the wide side of the octave leeway, before the octave sounds beating. And the point here is to see if and how we can share a standard, not a tale.

The two criteria you mention prove that the ET subject is pretty abstract, how to say... evanescent? And everything would follow that?

..."Having 5ths, or 12ths, beatless (or using any other ratio) is just a way to define how pure the octaves are, and as we can't reach agreement on this question (it depends on too many variables), it shouldn't be defined in any standard."... etc.. + edit...

Oh, perhaps now I get it, you are not being serious :-)

Hi Hakki,

From your post I understand that you would adhere to present days and perhaps you like large numbers.

Ok, that may well be your preference, but one thing you state above says it all:

..."Because, ET is already THE universally accepted standard already."

In fact, all we can do with that "universally accepted" standard (for the time being) is only... write about it. Oh... can you tune it?

:-)

No, I'm certainly being serious.

A loose definition is an imprecise one. I don't think a precise definition is appropriate.

My addition, which you may not have noticed: Octaves should sound pure, whilst allowing as many of the larger intervals (double octaves, 12ths, 17ths, triple octaves) as possible to also sound pure."

Your CHAS definition allows many of the larger intervals to sound pure. Narrow octaves do not achieve this. Pure 12ths also allow many of the larger intervals to sound pure.

It's clearly evident in this thread that trying to set a precise definition on the width of any interval is not appropriate as a tuning standard that everyone can agree on. It is necessary to be imprecise to allow for the many different stylistic and artistic interpretations that individual tuners bring.

Can anyone think of a style of ET tuning that is not encompassed by this description?

All intervals should be progressive - the width of an interval should be between the width of the same intervals chromatically adjacent to it.
Octaves should sound pure, whilst allowing as many of the larger intervals (double octaves, 12ths, 17ths, triple octaves) as possible to also sound pure.

Yes it seem, I confused with Kirnberger.

Greetings,
This is patently not true. Universal means everyone, and I, for one, have many customers that want nothing to do with ET. I know of many other techs that can say the same thing. One's desire to find that "universal truth" is scant reason to claim consensus, and there is no consensus on temperament, and there never has been.

The amount of harmonic variety available from a piano is a subject that that can be looked at as a continuum. The amount of variety can range from none ( ET) to unmusical. If we look closely enough, we find that there is never a completely equal division, but it is close enough so that the brain of the listener shuts down all the circuitry that is attuned to register the differences in physical harmony. Since it is scientifically proven that the emotional state of the listener can be affected by consonance and dissonance of intervals, whatever emotional response that could be heightened by variety is lost without it.

I tune all manner of temperaments, from compressed ET in the recording studio, to wildly stretched ET for modern concerti. There are Victorian shadings of ET that are preferred for the teaching studios, and full blown Young temperaments for songwriters here in Nashville. harpsichord mavens fluctuate between 1/4 C, Kirnberger, and Vallotti. The pre-college students' teachers have an easier time of listening all day when I can reduce the tempering in the easier keys used by young students. Steve Fairchild offered a "Piano Teachers' Delight" temperament about 36 years ago. It was almost a copy of a WT, and I know of several tuners around the country that have been tuning it their entire careers with success.

Then there is the temperament tuned by so many of the aural tuners I have observed. In this temperament, there is no order to the variety, just random width thirds scattered about the barely acceptable fifths and suspicious fourths. I would wager that 90% of the aural tuners I have seen in this business couldn't pass the current RPT test with what they normally offer their customers. And that test is an easy one to pass!

There are many ET's,(Chas. Stopper, etc) so even a "standard ET" is not going to be easily defined. However, ET's ability to remove a tonal center makes it flavorless and a "one size fits all, sorta" tuning. This makes it the most common, but it is NOT universal.
Regards,

And just as hotly debated would also be pitch level. Its not hard to forget that it wasn't all that long ago that ET @ A440 was "adopted" as a general guideline for keyboard instruments (primarily piano).

I think with the modern awareness of historic performance practice it has allowed one to reconsider the purpose of pitch and temperment. There is no such thing as one tuning method fits all. If anything it would suggest that the more well rounded tuner will stand a better chance of having the ability to be flexible.

A program of early keyboard works will most certainly benefit from a WT than vanilla ET, even if the instrument isn't totally authentic to the period. I believe that the informed audience with an equally informed ear need something of color in a performance beyond what can be had from exclusively using ET.

ET might be best left for the concert stage with instrumentalists playing works of the romantic period and later.

Thats the way it is currently.

Early music faculties have duplicate instruments at both 415 and 430.

There are harpsichords that can be converted from 440 to 415 by means of a sliding keyboard. Ironically, this only works effectively in ET without total retuning of the instrument.

Even most of those departments have settled on Vallotti as their standard in the face of much opposition. Even where flexibility of temperament is a requirement, people eventually settle for a "standard".

Rarely are the harpsichord and fortepiano technicians asked for anything other than Valotti.

There are, of course, harpsichord specialists who tune their own instruments in a variety of temperaments and will retune a couple of notes in each octave between program items but they, too, work from a default temperament.

I am reading an amazing documentation on the subject, witnessing uses of ET really early (XVI) Yet with complaints

A small exemple from Mersenne , as Luths and violas tuned in ET, and who stated that this should be advantageous for justness in concerts if organs and harpsichord followed the same use.

Also, that modern ET is an extension of mesotonian, being based on M3, when looked at it historically.

Interesting differences between Italy, Germany, England, France.

It was also stated that for music since XVIII, using g temperaments that are near ET is better, as their large fifths would satisfy better modulations (that arise by 5ths)

Mersenne finished by saying that" the praticiens did not want to change their tuning so it semble to the luth tuning, as they fear loosing the perfection of their thirds and half tones, (which are one of the largest beauty of our music) "

So would that mean that using Valotti could be more an intellectual posture, or the need for more stable instruments, more than due to a musical justification?

For what I am reading actually, it is not the temperament the most suited for any baroco music. Is there an ease to modify it to other forms? Is it seen as a sort of ET adapted for most period music?

Using a WT as a standard temperment would be like going back to using 3 barley corns as an inch.

Not quite, it is instrument driven, and also relate to the repertoire.

Even for Organs, it is said that a modern polyphonic and symphonic organ is to be tuned in ET, while a period instrument is seen differently.

The modern piano have not as much "flaws" had the ones in 1830.

That said, I like to understand how to use the somewhat generous leeway provided by the piano (in slow intervals) at the advantage of more relief in harmonic progressions.
Up to now the kind of relief it tend to is melodic and due to the tuner following the Ih curve.

Surimpression of a cycle if 5 to the own imbalance of the piano must be possible in a very mitigated way.

That said I owned a scaling software that proposed to "match inharmonicity"

What I noticed in the way Steinway mod B where tuned is that a huge slowing g of fast intervals when attaining the break and that was exactly giving it that "old style tone" that was much appreciated, by Michel Legrand for instance who did not like too much straight ET for what I understood.

I think it is a bit too much of a generalization to say that Vallotti is the go to WT for early music. Since my region has quite a strong contingent of early music ensembles perhaps we are the exception to the rule... but a number of things float around in these parts. The Lehmann/Bach, Young, Kellner.

I don't think settling on a particular temperment, at least for things like harpsichord or forte piano is stability related. My harpsichord changes based on what I'm doing with it and I have not experienced any stability issues. Of course one tunes it just prior to performance anyhow (both choirs of strings).

Hi Phil,

I would say that the first part of your description is quite appropriate, ..."All intervals should be progressive - the width of an interval should be between the width of the same intervals chromatically adjacent to it."

Have to say though, if I consider what I do, there is one detail missing, namely that 4ths and 5ths invert their beat rate progressions. Perhaps that is negligible? Or perhaps could be part of a more detailed/technical description.

Then you say ..."..Octaves should sound pure..", possibly there you talk about ordinary listeners, 'cos I do not tune pure octaves, "dead" octaves, but octaves that are more and more tense and eventually beating very slowly, towards the bass and the high trebles.

Then you say ..."..whilst allowing as many of the larger intervals (double octaves, 12ths, 17ths, triple octaves) as possible to also sound pure."

There my approach deviates significantly: my target is not ...intervals (larger or whatever) that "sound pure", but right as part of a whole, and 17ths (double octaves + M3) are not pure at all, as they have their smooth progression from bass up to the trebles.

You wrote: ..."..It's clearly evident in this thread that trying to set a precise definition on the width of any interval is not appropriate as a tuning standard that everyone can agree on. It is necessary to be imprecise to allow for the many different stylistic and artistic interpretations that individual tuners bring."...

That is a dense sentence..., and here I need to be breaf. IMO, this thread proves that it is not easy/direct to fix a standard, not even talk about it :-)

It looks like we have a standard already, it seems to be an ET that is very "imprecise"; in fact, it is impossible to tune it as a standard, to the point that we all describe what we tune (say some kind of WT) as if it was... ET.

Why, after three centuries, should we keep on being "imprecise"? In the name of style and/or artistry?

Hmmm..., many things come to mind, my apprentiship and the "imprecise" directions I received, "artistic" tunings, theories of all kinds and pianist (and musicians) expectation, and when I tune... just want that intrument to sound in tune.