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Originally Posted by Minnesota Marty
My understanding of equal temperament (above) is based on my musical training and of the laws of physics.


Marty

The laws of physics complicate the pure mathematics of harmonics by introducing inharmonicity into the equation.

As Robert Scott describes it, ET is inherent in the design of a piano. I imagine that's why it has become the standard.

Other temperaments create consonances and dissonances in the instrument for musical reasons.


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Robert,

You have confirmed what I have said. Equal Temperament for a tuner is not the same as it is for a musician or a physicist.

An octave is the doubling of any Hz. That is the book definition of an octave. If it is not, it is a tempering of an octave.

Maybe it is the term "equal" that causes problems? In my mind, equal does not mean "sort of" or stretched. Tuners/Technicians understand ET to be a flexible thing. But then, it is not equal.

Yes, it is semantics. That is what I have been trying to explain. My understanding of ET is as a musician, thought I appreciate and understand the way it is used by a tuner. But, it seems that in fact, it is not actually equal as it is applied to intonation.

The octave of A440 is A=880Hz or A=220Hz. Now you are telling me that it can be either A~880Hz or A~220Hz? - Not to me, certainly, not to me.


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The organ is using that frequency doubling to be in tune. I dont find it particularely "harmonious" in certain type of chords and in some regions.
Our ear is just asking something that differs from the (different) theories of the ET generation.



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Originally Posted by Emmery

(big snip)
After all, if a person cannot hear a M3 double in beat speed from a single chromatic movement up or down, they would have to be insane to think they are picking up on the sweeter nuances of a 5th shifting from a .5 bps rate to zero. Lots of smoke and mirrors is all I can conclude from this.



You might want to rethink that last statement... The M3 double in speed every octave, not every step! As to your question about the other keys? Vibrato can be fast, slow or anywhere in between. Volume can be loud or soft or anywhere in between. In ET, those M3 beat speeds range from very slow to very fast, just as they do in tonal temperaments - it's just that the construct or order of progression is different. Music is all about contrasts - the point being that composers (at least pre 1900) were aware of the typical contrasts in the tunings of the time and constructed the music to take advantage of both the heightened consonance and dissonance available.

Technicians today are enamored with testing in chromatic order - a progression most music doesn't use. Test your thirds in circle of fifths order all the way around in ET. All disjointed, makes no sense at all... But a tonal tuning? From slower, to faster and back again.

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Originally Posted by Minnesota Marty
Equal Temperament for a tuner is not the same as it is for a musician or a physicist.


Marty

Musicians may be mathematicians but tuners have to be physicists.


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Originally Posted by RonTuner
Originally Posted by Emmery

(big snip)
After all, if a person cannot hear a M3 double in beat speed from a single chromatic movement up or down, they would have to be insane to think they are picking up on the sweeter nuances of a 5th shifting from a .5 bps rate to zero. Lots of smoke and mirrors is all I can conclude from this.



You might want to rethink that last statement... The M3 double in speed every octave, not every step! As to your question about the other keys? Vibrato can be fast, slow or anywhere in between. Volume can be loud or soft or anywhere in between. In ET, those M3 beat speeds range from very slow to very fast, just as they do in tonal temperaments - it's just that the construct or order of progression is different. Music is all about contrasts - the point being that composers (at least pre 1900) were aware of the typical contrasts in the tunings of the time and constructed the music to take advantage of both the heightened consonance and dissonance available.

Technicians today are enamored with testing in chromatic order - a progression most music doesn't use. Test your thirds in circle of fifths order all the way around in ET. All disjointed, makes no sense at all... But a tonal tuning? From slower, to faster and back again.

Ron Koval


Ron, I have been doing this long enough to understand the doubling of frequencies and beat speeds with octaves. i was referring to the M3 listing Mr Kees kindly provided...

Beat frequencies of 5/4 (M3)
0: 0.000: 3.5900
1: 94.910: 6.7440
2: 197.060: 5.3265
3: 297.790: 6.8533
4: 395.790: 7.0417
5: 498.040: 5.9878
6: 595.910: 9.0181
7: 699.310: 5.9857
8: 796.870: 10.1160
9: 896.200: 7.8873
10: 999.060: 7.8891
11: 1096.170: 10.9405
12: 1200.000: 7.1800

I had also pointed out in an earlier thread that what makes largely varying beat rates for neighbouring M3's extremely anoying in music is when you reach that part of the threshold where we lose the distinction of beats and substitute what can be appropriatly called souring. In ET, this occurs somewhere around the F4-A4 region of the keys and it occurs in a smooth progressive transition. In any non ET temperament that varies from fundamental with offsets of more than fractions of a cent, this progressive relationship is lost. It may not get picked up easily in the F2-F3 octave, but certainly rears its ugly head when we hear those beat speeds double and move into that threshold.

Please don't make remarks that music doesn't do this or that or make certain movements between keys. Music has evolved well past the point of the baroque or renaissance period where composers were ignored if the music did not fit in a well constrained slot defined for it. It reminds me of Bill Bremmers point that hugely expanded octaves are acceptable because its not played in music. Sorry, music has evolved so widely in genres that anything can happen, and in any key.
The opening of Chopins' Fantasia Impromptu starts with a held octave along with numerous other pieces. I would puke on my shoes if I heard that opening rolling like some stretched octaves are bing done now. Same goes for numerous jazz pieces which move very chromatically with like shaped chords, not just with M3rds, but minors and 6ths, ect...


Last edited by Emmery; 06/04/12 02:43 PM.

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Ian,

I do agree that inharmonicity does play a major role. Non-fixed pitch musicians are constantly, in real time, reacting to the overtones (partials in your lingo) and adjusting instantly to what is perceived. That is why ET is of little importance, other than in theory.

The design of the piano is based on the history and development of Western Musical History and Musicology. It goes back to plainsong (chant) and the subsequent development of harmony. The unison voiced singers heard pitches combined with echos due to reverberation. This led to the concept of consonance and dissonance and scripted multi-part harmony. It is about as far from ET as you can get. A keyboard was still a long way into the future.

Historically, various temperaments come and go. Tastes and preferences constantly evolve. Is ET the preferred choice? Is it the standard? Only to those who are adamantly convinced that it is superior to other temperaments.

ET is not superior, the standard, or preferred, it is merely another option.


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..."Music is all about contrasts -"...

Ron, perhaps music is all about... many things, perhaps even contrasts but, has nobody explained you that contrast is perceived through different chords and melodies? Nothing to do with poor intonation and tunings? Would you ever sing out of tune, so that you can finally obtain contrast?



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Alfredo, perhaps you are unfamiliar with "the blues"???

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Originally Posted by Minnesota Marty
Ian,
...ET is not superior, the standard, or preferred, it is merely another option...


Maybe in the Twilight Zone Marty...but not here on earth.

ET is the standard, ET is preferred by the vast majority of musicians, ET is tuned by the overwhelming majority of tuners, and as for its superiority...One can deduce that its overwhelming widespread use makes it so...or one can claim that people are sheeple, everybody has bad taste, except the miniscule minority.

When pianos end up getting redesigned, when physics of sound suddenly changes, when performances are done in zero gravity or in total vacuumes, or when laws are introduced to prohibit playing of music in certain keys or intervals, we can entertain the idea that an alternate temperament will properly address the issues of inharmonicity on a pianos strings in the way ET does.


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There are only two possible standards for a twelve-tone system: Just intonation, which is unmusical and not well defined, and equal temperament. We can define every other option from how much they diverge from just intonation, which is what one does with beats, or by how much they diverge from equal temperament, which is what one does with cents.


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Originally Posted by Minnesota Marty

ET is not superior, the standard, or preferred, it is merely another option.


This is correct in part. ET became mainstream or the generally accepted norm much like VHS did instead of the Beta system which was a much better format. There was no giant conspiracy of musical geniuses hidden in some dark room making it so…. Why does this happen?

Because this is what the market place decided it wanted. The consumer asked for it so much it became eventually the mainstream temperament. Most technicians previous to 1980 or so learned ET. It was the standard for exam purposes also in the tech schools.



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Emmery,

Thank you for your lovely rant.

I am curious about something. You claim that ET is preferred by the vast majority of musicians. Do you believe that vocalists and instrumentalists are not musicians? They vastly outnumber keyboard players and certainly do not adhere to ET.

Popularity does not equal superiority. Just think of the various fads we have all encountered. Pet rocks were very popular. They then must be superior to a feral rock.

It is true that the laws of physics will not change. That is why ET is a misnomer. It is a temperament, for sure, but it is not as equal as presented by you or others.

Even a piano tuned to your specification would not sound well in outer space. In fact, it would suffer from another law of physics. It's that gravity thing, ya know. There is another problem and we are back to physics again. Without an atmosphere, you could not ascertain whether it was ET or not.

Obviously my deductions differ from yours. You have yet to convince me that I am misdirected.


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Dan,

I do agree with what you are saying and I like your analogy.

With VHS vs Beta, the public made the choice on cost rather than quality. I don't think that is an issue with tuning, but then, I may be wrong. ET seems to be the chosen "standard" by the tuning community, and not necessarily by the consumer. I would assume that most customers never are given the option.

The big thing is that it is a service, rather than a product. Other than at piano forums such as this one, there is no easily available "Consumer Guide" for selecting a temperament.


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Originally Posted by RonTuner
Alfredo, perhaps you are unfamiliar with "the blues"???

Ron Koval


Ron, can you expand on that? What is it that you mean to say?

Last edited by alfredo capurso; 06/04/12 03:58 PM.

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Originally Posted by Minnesota Marty
Emmery,

Thank you for your lovely rant.

I am curious about something. You claim that ET is preferred by the vast majority of musicians. Do you believe that vocalists and instrumentalists are not musicians? They vastly outnumber keyboard players and certainly do not adhere to ET.

Popularity does not equal superiority. Just think of the various fads we have all encountered. Pet rocks were very popular. They then must be superior to a feral rock.

It is true that the laws of physics will not change. That is why ET is a misnomer. It is a temperament, for sure, but it is not as equal as presented by you or others.

Even a piano tuned to your specification would not sound well in outer space. In fact, it would suffer from another law of physics. It's that gravity thing, ya know. There is another problem and we are back to physics again. Without an atmosphere, you could not ascertain whether it was ET or not.

Obviously my deductions differ from yours. You have yet to convince my that I am misdirected.


Sorry for my generalization Marty, we are in a Piano forum, not a vocalist, bagpipe or other instrument forum. The word "pianist" would have been more precise and the statement still stands true. The vast majority of pianists play in ET.

Marty, there is a distinct difference between "popularity" and "fad". Popularity is strictly related to something being well liked in large numbers. A "fad" however is associated with a temporary novelty that attracts those large numbers of people. As the novelty wears off, so the numbers drop.

ET is popular because 50 years ago aproximately the same large portion of pianists used it. Non-ET tunings on the other hand seem to pop up every 5-10 years or so and have always dissappeared into obscurity as soon as the novelty (if any)wore off. Only time will tell if something is popular or a fad. So far ET has faired better than others.

It is unfair to bring semantics into the scheme of things when criticising ET. Yes, the way we execute it on a piano is not perfect. But in the same light, EBVT under the same scrutiny would deserve to get the letter "P" put in front of it standing for "Partially"...it addresses only limited intervals in its equal beating capacity.


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Originally Posted by Minnesota Marty
...Other than at piano forums such as this one, there is no easily available "Consumer Guide" for selecting a temperament.


MM, I'd "select" a temperament by ear, how about you?


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Originally Posted by alfredo capurso
Originally Posted by Minnesota Marty
...Other than at piano forums such as this one, there is no easily available "Consumer Guide" for selecting a temperament.


MM, I'd "select" a temperament by ear, how about you?


I would select by ear also. I am not a tuner and I have never been able to find a TemperamentMart to make a comprehensive choice. This is a thread which I started. Please read the beginning of the thread and you will have the answer.


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Emmery,

When there are discussions of this sort, word choice is very important. One can't just toss it off as semantics. That is just an excuse.

Yes, the majority pianists play on pianos tuned to some adaptation of ET. That is not necessarily a choice, however. Please read my recent replies for clarification.

I am not a tuner, but I still am aware that all of the three variations of EBVT are, and have been, easily available in totally complete form. Mr. Bremmer is making the assumption that a competant tuner can work from the basics of the temperaments and use standard practice to complete the tuning.


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Originally Posted by Minnesota Marty
Originally Posted by alfredo capurso
Originally Posted by Minnesota Marty
...Other than at piano forums such as this one, there is no easily available "Consumer Guide" for selecting a temperament.


MM, I'd "select" a temperament by ear, how about you?


I would select by ear also. I am not a tuner and I have never been able to find a TemperamentMart to make a comprehensive choice. This is a thread which I started. Please read the beginning of the thread and you will have the answer.


MM, I did read the beginning of this thread of yours, perhaps you prefer to go back there.

..."Here is a recounting of my aural awakening.

In 2004 I engaged Tim Farley to do a total rebuild of the family 1920 Steinway-M. The job was to be a gift to my mother as she was elderly and I wanted her to have the very best. The piano was magnificent after the work and upon arrival. The subsiquent tunings did not have the life and color as when it first arrived and I was baffled. The piano was in excellent tune, but ......
This is about the same time as I joined PW. I learned so much here, and even gained an understanding of temperament. At that time, I assumed that ET was the same as Well Temperament. In conservatory, the concept of temperaments was discussed, but it was not specific.
After my mother passed, the piano went back to Farley's for temporary storage. In preparation for transport to Peoria, IL, I asked for a fresh tuning and a detailed regulation. I could not believe what I was hearing out of a little "M." OMG - The Beethoven Waldstein sang with an incredible voice and the action knocked my sox off.
Within a few days, I called Tim to extend my thanks and share my excitement. He was also pleased with the voice and the action. He shared that the reason that it had such a glorious voice was that he had tuned it to one of Bill's Temperaments (unspecified). Aha! He tried to get Bill but he was booked."...

All the above only makes me understand that you did not like TF's subsequent tunings. Alternatively, that TF's tunings got better, thanks to BB.

..."It was the writing of Mr. Bremmer which peeked my interest. I first ran across his web site when I was in the process of selecting a rebuilder. That site was the first time I was aware of different temperaments applied to a piano. When I contacted him, he was the one to recommend Tim Farley. I was pleased to discover that Bill was a contributor at PW and I could learn more."...

The above is off Topic.

..."After the piano settled into its new space, it was time for a tuning. I got some good recommendations and selected a tuner/tech. He started by doing some playing to acquaint himself with the piano. He looked at me and said, "The Bremmer EBVT Temperament sounds gorgeous on this piano.

I knew my piano was in good hands and good ears."...

So you are saying that when "it was time for a tuning"..."The Bremmer EBVT Temperament" sounded gorgeous on your piano.(?) Let me ask you: why did you want your piano tuned again?

..."There was no reason that Tim Farley needed to contact me for permission to tune my piano to other than ET."..

That is good. Let me ask you: ...other than who's ET?

..."Trust, gentlemen, is trust."...

I may agree.

..."Word of mouth is what it is all about."

Not for piano tuners, MM, especially not for aural piano tuners.

Regards, a.c.

Last edited by alfredo capurso; 06/04/12 05:05 PM.

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