Piano World Home Page Forums Our Most Popular Forums Piano Tuner-Technicians Forum HISTORICAL ET AND MODERN ETs

Hello Jake.

You write:..."We don't know the exact temperament that Chopin composed and played in, but the one thing we do know is that his pianos were not tuned to ET, which did not exist except in theory."...

I suggest to distinguish theory from practice.

Theory: I guess you talk about 12th root of two ET. That model has never been tuned, simply because (if we think of real sounds, from real string) pure octaves (like any other pure interval) can only exist in theory. And I challenge anyone to prove otherwise. So we might agree on one fact: pure octaves (but not only that) made the first ET model lame.

Bill writes:..."For example, if there is a court case where there are 12 people having a claim to a certain sum of money but each presents an unsupportable claim, the judge affords each claimant an equal amount while disregarding the value which each claimant had presented as being rightful to them. The decision is deemed fair but each claimant is equally dissatisfied as much as they are satisfied. The analogy to music is that the judge (Helmholtz, who was a scientist, not a musician) disregarded the value of the key signature."...

I do not mind Bill's analogy. The judge, we could say, was the thirteenth note, ie the octave. The "pure" octave was there above the claimants and produced an unsatisfactory decision.

Now, to me it is quite evident that the first ET model was not "ready" to be sold as a tuneable temperament. And we might as well justify all the critics in past literature.

Practice: we tuners know that any "good" tuning will not last long...maybe one concert? This makes me believe that many composers of the past - when pianos were not so solid - must have been able to compose and play in many "temperaments"...many quasi-UTS, quasi-WTs, to some extent quasi-ETs like the many we still hear today. But they all would go - until proven otherwise - for ultimate euphony and resonance, which after all is what we expect from an orchestra.

Regards, a.c.

Hi!

There's a lot to answer here and I'm not going to have time, so please forgive me.

I started from the premise that as a child I was told that there were differences between keys. But I could not hear them so I assumed that I was a bad musician. When building an organ in my teens, as a member of BIOS (British Institute of Organ Studies), I was introduced to the unequal temperament experiments and ultimately the now out of print book by Padgham which examines a number of diverse temperaments. I started with Werkmeister being easy to tune by ear - and hated it.

I used to use an "18th Century Meantone" on a square piano and never dared put UT onto a "Modern" piano.

It was not until I heard Rose Cholmondley playing the second sonata of Chopin that I realised that Chopin was using unusual and deliberately unusual keys, the only explanation for which was that he was expecting the keys to add character to the music.

The effects that my recordings have demonstrated are on account of the tuning, not my (beloved) Bechstein: here they are on a modern Yamaha:
http://www.youtube.com/watch?v=8in_RJYbjGM

For other examples on that piano, please follow the video response links.

So how do I know Chopin was writing for UT? Well, when one has heard it, the music says so - and having become attuned to the UT interpretation, ET performances are bland, grey and without such dimension of emotion.

I'm not the only person to be saying this - there is an indepedant research, on the net, by Dr Miller, from memory and it's well worth a read and certainly I'm not the only person to have felt that the UT performance in http://www.youtube.com/watch?v=hgA1-I5MfNY was more emotional than the ET - certainly upon hearing all four movements together.

Which temperament? I don't know and don't pretend to and I don't say the one that I'm using is right. But from 6 or 7 years of concerts at Hammerwood, a year of concerts at Emerson College and now another concert instrument in Forest Row, we have the feeling that it gives good results even on modern repertoire:
http://www.youtube.com/watch?v=O7v5jYkw13w (Paart)

It's a version of Werkmeister but really there are a number of temperaments which are well behaved and I deliberately attempt to try out others when I have the opportunity:
http://www.youtube.com/watch?v=UwoglLif3ps

Well behaved - purity in home keys, stress in remote keys - nice progression from added accidental to added accidental. The difference is how pure in the home keys, the acelleration into stress with the increased accidentals and whether peaking on B, C sharp or A flat. There's room for experiment here.

A friend of mine was a tuner for a major opera house for decades and a staunch proponent of ET on Steinways . . . Having heard my results he's been so intrigued that he's started tuning his S&S to the temperament and reports that the result is creamy. The concert instrument he tuned the other night, noone noticed, so although it's strong enough for us to hear, the temperament leaves its effects to the realms of subliminity and perhaps in that is the magic. From memory some thirds are over 20-21 cents sharp, so we are not looking at the mildness of most modern schemes.

What is interesting is that an audience, not having noticed this UT in concert, would have not objected to it having been called an Equal Temperament, allowing playing in all keys. It's in this way that I think that considerable confusion has arisen - that there was a contrast between Meantone with wolves and the Good Temperaments of which equal in which some keys are more equal than others is one . . .

No doubt I've left out some points but hope this clarifies some areas.

Best wishes

David P

David,

I almost included one of your arguments--that by listening to Chopin played in a well temperament, one can hear how the music suddenly opens up and contains new dimensions. And I feel this to be true.

But Bernhard is of course asking for concrete proof, and I must admit that while, to me, it is almost certain that Chopin was not composing in ET, given the extensive ongoing discussion of other temperaments, his love of Bach, etc, there is a possibility that he was using something closer to ET. Do you know Bernhard Stopper's work? I'll be the first to admit that he is far more knowledgeable about temperaments and tuning, and he may well know of written sources that I've missed.

By the way, do you know if Ms. Fliter has recorded anything using an older temperament? I've done the basic searches, but all of the recordings I've found seem to be in ET. She came up in an era in which an interest in older temperaments was growing, so I half expected to find what I couldn't find.

Yes I like her interpretation very much. She has an excellent control of dynamics in bringing out the melodic shape, the ebb and flow of the phrasing and the overall balance. Not overly dreamy. I have no desire to hear her on a well tempered piano, but rather just a more appropriate piano. That one sounds too shrill in the treble for me. Would Chopin have approved of this interpretation? I think yes.

Dear Chris and Jake

I'm listening to the Ingrid Fliter Nocturne at the moment - very beautiful - and the other pianist to watch out for is Valentina Igoshina who played for Tony Palmer's film about Chopin.

However, whilst this performance is very beautiful I know from experience that in certain modulations the piano . . . the temperament tells the piano to say to the composer "surprise me". This is a tradition going back far and exploited by Couperin whose Masses often swing from pure love to angst - and this is after all a characteristic of romantic music too. Not only Beethoven, already discussed in this thread, but Schubert too, loses so much in the greyness of Equal Temperament. http://www.youtube.com/watch?v=uTGka9jFUCU is an example where the temperament adds a subliminal depth which makes this performance (sorry - not cd sound - camera microphone with automatic volume control so please make allowance for this) more emotional.

Temperament is an area which cannot be discussed meaningfully in the abstract - it's something that has to be experienced. Music is about perception and emotion. These cannot be appreciated in dry theory of abstraction. We have to say therefore "we know they exist - do they work - how do they work" and if we have the hunch that a composer was relying on key colour through temperament we simply have to run the music through the temperament and see what we hear . . .

It has to be an experimental science rather than merely a theoretical one . . .

Certainly Jorgensen in his book "Tuning the Historic Temperaments by ear" is absolute in his assertion that unequal temperaments were in use specifically up to the death of Chopin.

http://www.millersrus.com/dissertation/

What do the musicians say? Knowledge of the repertoire gained from intimate 8 hours per day practice perfecting the corners of performance and expression gives possibly the most reliable understanding of the mind of the composer into which the performer is having to enter in order to perform. http://www.youtube.com/watch?v=41xRupc3Hz8
http://www.youtube.com/watch?v=ZH2IXOfnBqw

http://www.youtube.com/watch?v=YXzSXWaQGmA

Best wishes

David P

Hi!

I have been reading
http://math.unipa.it/~grim/Quaderno19_Capurso_09_engl.pdf

A very impressive piece of analysis and utterly superb. Makes perfect sense and it is bound to bring out the most resonance of which a piano is capable . . .

For musicians who have never heard the effects of a Good Temperament, your CHaS tuning must be the bees' knees.

Best wishes

David P

It's good to see somebody from a UT background taking an interest in the CHAS theory, and recognising the brilliance of the analysis. I believe this to be a very precise description of the best possible ET tunable on any piano, and the recordings certainly support how good ET sounds when tuned this way. It is incredibly difficult to tune aurally though, as it calls for progressive beat speeds in all the intervals, something which is very difficult to achieve!

I'd like to see a similar effort put into an ETD program to tune CHAS, so more people could give tuning it a go. It would be very interesting to see how this tuning differs from the 'best' ET a particular EDT can produce in partnership with a highly skilled tuner.

Dear Phil

Just because I recognise the excellence of the analytical approach does not mean that I'm in love with Equal Temperament in any shape or form - for the reason that although it may make the piano sound more harmonious: for what purpose?

It does nothing for the music.

When you have been watching colour television, one finds having to watch in black and white a retrograde step, however brilliant the definition. It's well known that artists congregated on the Cote d'Azur for the light, causing brilliance of colours, against which the light in the UK is always grey.

Music is made of basic dimensions:
Rhythm and timing
Pitch - melody, harmony and timbre
Dynamics
but composers from Couperin to Beethoven, with certainty, and I'm not unique in extending this to Chopin, Schubert, Mozkowski and possibly Mendlessohn, Liszt and Brahms had the dimension of key.

Pitch, being relative and not absolute - varying from A392 to A460 and higher (even 490), is not the key to key.

If intervals are always the same size, then key cannot be distinguished.

Only by using a Good Temperament can key be distinguished, setting up chords of tension which can resolve into another relaxed.

The CHaS temperament is supreme in so far as it puts harmonic accordance at the centre of the concept, but for the reason above, any attempt at _equal_ temperament cannot be the last word in research of a temperament suitable for performance of historic repertoire and actually to enable performers to convey the music in the mind of the composers to their audience.

I wonder if the search for equal temperament has merely been an obssessive challenge to follow just because it's so difficult to achieve and therefore academic fun, rather than actually relevant to the music that was and is intended to result?

I wonder if there has been academic kudos ascribed to whoever can do it, for the sake of doing it, without regard for the effect on the music in the removal of a dimension.

Were we to be limited to the three dimensions of space, we would be pretty bored, and meaningless. Only when one inserts the dimension of time does meaning take off . . . So it is with key in the dimensions provided by temperament. Similarly were no variations in the density of matter distribution to be allowed, we would only be part of an amorphous gas throughout space. It's only in the dimensions permissable by varying matter density that we exist. So it is as music within the dimensions permissable in the relationships of the 12 notes of the keyboard.

Temperament is not to be argued about - it's simply about trying it, experimenting and comparing.

In the promotion of purely Equal Temperament, musicians and audiences are being robbed of the dimensions that many composers expected to be heard to give interest to their music.

It's not surprising that a generation or two have lost interest in classical music - in so far as equal temperament has made it sound the same, and boring, I have sympathy with them. It's in the cause of bringing music back to life, not merely refining white sugar further, that I have been trying to encourage all associated with pianos to give us back our metaphorical brown sugar, molasses and honey.

Best wishes

David P

Hello.

Thank you, Phil, for your words, you've been very kind. It means a lot to me knowing that this discovery is being shared.

Thank you, David, for your contribute. I'm still after your second last post...many things to elaborate on.

I understand that you say: let's leave some differences, otherwise we loose the character of each single key, which is what music is about. In all this discussion I doubt we can decide what music is about for each one of us. I'd say that music is continuously evolving, thanks to singular, individual interpretations. In fact, Chas "s" variable stands also for that.

So, while respecting your position, I think there is only one ground where we can proceed together, and that's logics. As for the rest, I'm happy to talk about our approach and preferences if not based on clichés.

You write:

..."I started from the premise that as a child I was told that there were differences between keys."...

Yes, there were differences between keys. If temperaments have developed is because we needed to manage those differences in the best possible way. Perhaps that premise was, for you, a kind of crucial information. In my case, I was addressed towards correct (in tune) playing and singing. That kind of practice with chords, major and minor scales and arpeggios. There I needed to be in tune. No fuss, no mess allowed.

For what I know, people started the war against ET, complaining about loss of character, color and emotion long before a perfect ET model could be tuned. Which color has gone lost? How much color could go lost in 1850 due to a perfect ET tuning? In my opinion, the first ET model, beside being impossible to tune, received back some (justifiable) criticism from theorists that got scared for nothing. Nobody could ever tune 12th root of two ET. In that sense, we would never miss "character".

..."It was not until I heard Rose Cholmondley playing the second sonata of Chopin that I realised that Chopin was using unusual and deliberately unusual keys, the only explanation for which was that he was expecting the keys to add character to the music."...

In my opinion, your explanation might be influenced by your own theses about having to add character to the music. Amongst other (unprovable) explanations, mine could be that Chopin wanted to hear those pitches, being closer to his voice and/or inner singing. But, perhaps that tonality, there and then, was the least out of tune on his piano? Or perhaps Chopin had got tired of more usual keys? Or he wanted to exploit a precise fingering? Or he wanted to impress through the use of an original/unusual key? I do not know. Due to the vast number of possible UT/WT (and tuners), a composer would have had to play and check the piano first, to understand what the last tuner intended for character and then re-adjust his/her emotional sphere. How strong? And let's see where, here or there?

If you read back in this thread, you'll also find ED's remarkable posts about UT/WT, character and emotions. What I understand is that you prefer to hear a precise effect, call it sweet'n sour, grace'n pain or what ever, you want to hear keys that have their own "character", not all of them equally euphonious as they can be (today). Also you like the idea of home-key, neighbor-keys and remote-keys.

You may think in terms of key (12 keys?), perhaps I think more in terms of intervals and pitch. For me, excluding 12ths and 15ths, every single interval, from the minor second up, has its own character expressed by unique beat-rate/tensions. A "strong" or stressish interval would twist and ruin the whole key. For example, I would not like thirds beating more like sevenths, nor 12ths beating like thirds.

I like feeling absolutely at home in any key, then I feel like I can enter a sound-whole, a superior order, the Home for all possible feelings of mine, where pleasure and pain are not physical, earthly routines anymore, but pure inner emotions.

Regards, a.c.


Chas tuning mp3 - live recording on Fazioli
http://myfreefilehosting.com/f/07c3ca3905_6.32MB

CHAS Tuning mp3 - Amatorial recording on a Steinway S (5’ 1”, 155 cm)
http://www.box.net/shared/od0d7506cv

CHAS THEORY - RESEARCH REPORT BY G.R.I.M. - Department of Mathematics, University of Palermo - 2009, Italy:
http://math.unipa.it/~grim/Quaderno19_Capurso_09_engl.pdf

Article by Prof. Nicola Chiriano - published by P.RI.ST.EM (Progetto Ricerche Storiche E Metodologiche) - University "Bocconi" - Milano, 2010 - (Italian):
http://matematica.unibocconi.it/articoli/relazioni-armoniche-un-pianoforte

Dear Alfredo

Thanks for your post and your benign reaction! I was worried that the sentiments I expressed were strong but I have a great respect for what you have done.

My personal opinion is that the way in which Couperin revelled in smooth pure chords to progress deliberately to those expressing angst and then to find the relief of relaxing the tension demonstrates exactly how composers were expecting to manipulate the keys in the pre ET context. Unarguably Chopin grew up in the context of use of UT/WT and therefore all concepts associated with that tradition. This is not a matter of mere taste but of fact - ET was simply not much to the fore in the 1820s and 30s. How far we progress applying WT/UT beyond Chopin is a valid matter of debate.

Whilst others have discussed WT/UT, there are not many people such as I who have tuned a concert instrument to an _audible_ WT and built up such a corpus of concert experiences and recordings of the repertoire viewed through the lens of a Good Temperament.

In the absense of documentation, we have to look at the music as its own documentation and therefore we have to listen to it through the ears not of a theoretician but a musician. We have to examine whether what we experience correlates with what the music is trying to convey. One effect is that a chord which might be painful might be played more lightly, and whether the resulting accents or deemphasis of notes changes or accords with the interpretation of dynamics in a meaningful way.

Whilst a gramophone fitted with a 78rpm needle might play a Stereo vinyl LP, the large needle will smooth out the detail you'll hear if you fit the right needle. So it is with ET which smooths out the detail of differences that a Well Temperament shows up. It's like the difference between an electron and optical microscope.

One day I sat in on Adolfo Barabino's tutorial for Miena Senada on the Chopin 4th Ballade. Suddenly it became apparent that the shifting of the shapes of the chords on http://www.youtube.com/watch?v=fJT5Q6HooyA at 10:07 brings them into a new prominance indicating to the performer to treat them with special care. In equal temperament this can be overlooked. It may be that the temperament, if on the verge of audience audibility, is merely a signal to the performer. But that signal is as important to the performer as is an altimeter to a pilot.

The bottom line is that there is no one right answer for everyone and that performers can proceed in their playing without altimeters if they like . . . but that they should be given a choice, an informed choice and not one based on the near universal prejudice in favour of equal temperament. . .

So very much music having been examined only through the ears of equal temperament for so very long, it's time for a reassessment of that position.

What is very interesting in your work is that you have correctly analysed and identified ways in which the instrument can achieve maximum harmony in equal temperament.

My thesis is that in Well Temperaments, one has rooted and unrooted chords - ones where the notes relate to a harmonic root and "lock" together meaningfully, and ones in which the notes are squeezed away from any harmonic series and become meaningless or uncertain or disconcerting. (This is exemplified with the Funeral March). I have had difficulty in tuning bass notes with inharmonicity and have been experimenting in using the harmonics to tie in either with thirds in the home keys or fifths where the fifths are pure, creating a more distinct change of character of the whole resonating instrument between keys.

Di Veroli has published recently demonstrating that the Werkmeister family of temperaments are a valid platform for performance and indeed, it is one of those which I use.

In view of our common aim to achieve maximum harmonic accordance within the instrument, it would be very interesting if you might turn your mathematics to the problem of analysing the Werkmeister family of temperaments, including the modern variations, to see if any achieve maximum harmonic relationships within the piano as an inharmonic instrument, particularly in the home keys of F C G and D. Possibly B flat but as traditionally A flat appears to have been on the danger list for UT performance - indeed Jorgansen identifies G# A flat as the final note of the scale to be derived and used, four flats is likely to have been more divergent from pure than four sharps.

So I hope that I might have inspired a second chapter to your work?

Best wishes

David P

I love her playing, but was a little put-off by the costuming in some video's I'd seen, until you wrote that she was in the film. These must have recorded using the same set and costumes:

http://www.youtube.com/watch?v=gRCzEQTP_Ks

Off topic, perhaps, but I love the sound of the piano, here, too. I suppose it's in ET, but it's good.

Hi!

Yes - that's a scene from the film
http://www.google.co.uk/search?q=the+strange+case+of+delfina+potocka
and anyone interested in Chopin will find the film very well worth watching, accompanied all through by this amazing pianist who I hope might perform at Hammerwood one day. And one might well ask who needs WT when one has Valentina playing . . . :-) !!!

Best wishes

David P

PLEASE realize that the Palmer movie about Chopin and Mme Potocka is based on letters that were intentionally faked. There is some mystery about their relationship, but the movie is way off base and doesn't deserve to be taken seriously. Igoshina is beautiful both to hear and to watch, but it's too bad she had to be associated with such a misguided production.

It took me a moment, when I saw the subject of this thread, not to think "extraterrestrial".... Just want to thank you all for your good work in keeping us all playing and helping us to understand how these wonderful, complex instruments really work.

Elene

I hope that we can look forward to hearing more of Miena Senad playing this Hammerwood piano.

One thing I find so lovely about Valentina Igoshina's performance of the funeral march movement is how she gives it room to build, starting off softly, letting it grow louder, backing off and again letting it grow louder, and then again backing off and moving it to a climax. I've heard too many pianists start loudly and then play much of the piece with only little concern for dynamics other than broad strokes between soft and loud.

But I do hope to hear her play in a well temperament.

Dear Alfredo

A while back I did a YouTube video on piano resonance causing the piano to add different amounts in different keys which I think you'll find interesting.

http://www.youtube.com/watch?v=Pz0B0SwKpww

I'm sure that a video of harmonics in your ET system would demonstrate it interestingly compared with ordinary ET and that your mathematics would be usefully and interestingly applied to Good Temperaments to see which of the Werkmeister family temperaments give the most home key resonance to the instrument.

Best wishes

David P

Hello,

some colleagues may find of interest this article where "An unequal temperament is described in which the fifths and fourths of the tuning chain have the same beat rate."

http://gfax.ch/literature/Equal_Beating_Chromatic_Scale--Silver.pdf

Also I thank you, David, for your elaborations and thank you, Elene, for your chiming in...btw, nice website, you too are involved in good energy!

To All, Happy Easter.

a.c.

Chas Tuning mp3 - 2011 - Live recording on Fazioli 278
http://myfreefilehosting.com/f/07c3ca3905_6.32MB

CHAS Tuning mp3 - 2009 - Amatorial recording on a Steinway S (5’ 1”, 155 cm)
http://www.box.net/shared/od0d7506cv

Thanks for posting this article, Alfredo. Do you know of any recordings of a piano tuned to this EBS temperament?

Hello Jake,

Nop, unfortunatelly I've never heard this EBS on a piano. In any case, the author fixes pure octaves, still in the age-old/wrong idea that the octave is the module. Also, it is interesting (and somehow suite) how he is concerned about the "color" issue and ordinary difficulties in tuning our first ET. Just a coincidence?

Regards, a.c.

Alfredo,

Silver does at least see that there is room for exploration with octaves, although he doesn't take the idea very far. From page 478:

"The octave is commonly regarded as sacred and it is
given its just value in both ET and the EBS, but the
fact that "stretching" takes place during the tuning of
pianos, proves that some latitude is tolerated. The
possibilities opened up by a calculated tempering of the
octave are interesting and the chromatic stroboscope
may further research in this direction by overcoming
tuning difficulties."

Yes Jake, you are right. And Silver makes a difference between "small variations which creep in..." when attempting 12th root of two ET and the possibility "to reproduce inaccuracies with some regularity".

From page 479:

"The edge was taken off this criticism by the fact that ET is exceedingly difficult to tune accurately by ordinary methods and the small variations which creep in tend to produce a sensation of key color. There can be, of course, no standard colors under these circumstances for results may vary from tuner to tuner. Nevertheless it became fashionable, and still is, to demand certain tuners on account of the pleasant effects they obtained and this suggests that with practice it is possible to reproduce inaccuracies with some regularity."

Perhaps Silver was the pioneer in Equal Beating approach, I do not really know, perhaps Bill and other colleagues can add on. In any case I like his honesty and I think his efforts were well directed, towards pleasent, confortable and somehow regular tunings.

Regards, a.c.