Piano World Home Page Forums Our Most Popular Forums Piano Tuner-Technicians Forum Some sweet video's: an older piano tuned to an Unequal Temp

Dear Jake

I think that Kees has correctly identified the reason here but as an aside, organs to my knowledge don't have the inharmonicity issues common to pianos, save in baroque reed pipes which have an excitement all of their own -
http://www.youtube.com/watch?v=vPGDiA3fidA
http://www.youtube.com/watch?v=wSf7-4t_SWc
http://www.youtube.com/watch?v=rxPooeWo64k

In general in contrast to strings the fatter the flue pipe in proportion to lenth gives bigger sound and the thinner pipes more of the higher harmonics. Pipes are largely one dimensional vibration whilst strings, as iron bars, are two.

This is one reason why unequal temperament in remote keys may be less offensive with music not written for it on the piano rather than the organ, which is why I would not hesitate to recommend audible unequal temperaments on the piano but on the organ I believe serious experiment to be needed throughout the repertoire . . . which I am looking forward to doing with an adventurous organist!

Best wishes

David P

The Barnes study is flawed. I performed a full automated analysis of the 48 including M10 and M17 as well as M3, included the fugues too, and included the minor key pieces. The result is that here is no evidence whatsoever of certain intervals being avoided and hence no data to deduce any temperament from. I should really publish these results if I get some spare time.

Kees
Added in Edit:
Comment 1: I do like the Barnes temperament, but it has 2 Pythagorean thirds which I do not like. It does not improve on Werckmeister 3 in any way, just like Kellner. If you just spread the B-F# 1/6 comma 5th over 3 consecutive fifths you practically have Bach-Lehman reversed (one of the alternative solutions).
Comment 2: Lehman deserves to have his name attached to the tunings because he was the first to recognize the loops as indicating proportional size of fifths; previous stuff about beatrates is really nonsense (IMHO I should say).
Comment 3: The worst M3 in Lehman tunings is 1/12' smaller than Pythagorean, whereas in Neidhardt the worst M3 is 1/6' narrower; hence somewhat milder (more equal).
Comment 4: I've had my piano in WM3 for a couple of days now and start to like it more and more. You can get used to Pythogorean thirds!

Dear Kees

Thanks so much for your detail - especially on the Barnes variation. We are at so much of an advantage nowadays with computer analysis.

On the Lehman issue, having tried Werkmeister and begun to like it, I think after a while you'll find that being milder does not necessarily help the music. Whilst I acknowledge Lehman's inspiration that the squiggle was not a random doodle, the problem is in the ascribing of _that_particular_temperament_ to Bach and, bearing other possibilities into account, it's misleading to present this temperament to novices to the subject as _the_ Bach solution.

If you're getting used to Pythagorean thirds . . . then perhaps I can see you going towards Barnes. Kellner is of course another possibility, as you say, but I'm intrigued that you say that it's as flawed as Barnes . . . Your analysis there would be much appreciated.

Whatever variation of Werkmeister you use, you'll find that Chopin in particular avoids the juxtaposition of nasty thirds.

What really needs research is the effect on key colour of the shift of Werkmeister from favouring F to favouring C . . .

(What also is curious is why Bach chose A flat especially with which to annoy the organ tuner as one might have expected C sharp and F sharp to be similarly severe . . . or was it simply the A flat E flat wolf? Jorgensen ascribes the phenonomen to A flat being the last note to come into any use on the keyboard in the history of music . . .)

Best wishes

David P

I learned to play (pipe) organ on an instrument tuned in WM3. For 3 years I tuned the harpsichords here at the University in WM3 (except one for earlier music in 1/4' meantone).

When Lehman's article came out I gave his tuning a try and have not gone back. In fact for piano my favourite tuning is an even milder temperament of myself. Indeed, why would you not tune according to your personal taste on your own instrument? My ears have now adjusted and it will take a while before getting at ease again with the Pythagorean thirds.

My take is that WM3 is great, its only disadvantages are these Pythagorean thirds. Kellner and Barnes still have these, though fewer of them. If you're willing to put up with Pythagorean thirds, I prefer to get maximum payback which WM3 delivers. Kellner and Barnes I called "flawed" as historical temperaments, they are modern inventions. Kellner was a nut (IMHO) and Barnes had a good idea but he should have been less lazy and count more M3's than just the major key preludes.

Do you have any particular piece in mind? I do have most of Chopin in MIDI and can easily check such claims.

The reason is simply that wolf fifth of course, which is the price you have to pay for nice M3's everywhere, and which is the signature of meantone which the organ tuner in question (Silberman) tuned.

Cheers,
Kees

Dear Kees

Your research on Chopin's avoidance of direct major thirds in possible nasty keys could give us a most important clue as to any F-C bias of tuning possibly in use. Not sure about sixths, but certainly at the beginning of the Raindrop, those two notes are more than an octave apart - and that's what I mean but avoiding nasties. I hope I have explained the idea intelligibly . . . !

Of course one must be aware that sometimes nasties were intended, but as yet in experiencing Chopin in this family of temperaments, none have jumped out and bitten us yet . . .

You may have the proof at your fingertips . . . !

Best wishes

David P

Hi!

I have just received a PM (which I'd taken ages to recognise with just the flashing envelope) . . . :



He's using Bill's Equal Beating temperament and I have replied suggesting that he might ask Bill to tune his instrument to a stronger tasting curry . . .

On that, I'm wondering if Kees might tire of unmodified Werkmeister's unrelenting harshness. . . ? Proposals of toning it down in whatever ways may not at all have been misguided whether by Vallotti, Young or more recent analysis. I note that like myself, Dr Miller's experiments with Chopin used a modified Werkmeister.

Best wishes

David P

Dear Kees

I've finally found the article I had been looking for before:
http://www.bach-cantatas.com/Articles/Bach_Seal.pdf

The comparison of thirds is interesting so far as the results Francis derives there from Bach's seal differ with Kellner only in A flat . . . which is interesting bearing in mind Kellner's reputed similarity to Werkmeister which is something I have not yet properly examined . . .

So perhaps the line between being a nut and genius is thin?

It's no wonder Kellner has the reputation of being a "nut" trying to digest
http://www.harpsichord.org.uk/EH/Vol2/No8/matharch.pdf
until one reads:


One has to bear in mind that before television and now the length of time we spend communicating through the internet, there wasn't much else to do and so such intellectual games and, to our minds, nonsenses occupied the mind amusingly. "History is a foreign country", as they say.

http://allaindu.perso.neuf.fr/publications/TEMPERAMENT-Bach-Lehman-Jobin.htm shows another possible interpretation of the Bach squiggle (demonstrating again that Lehman should not be purporting to _be_ _the_ Bach solution) and relevantly this solution veers in the direction of Kirnberger III and accords to Rameau . . .

Diagrams on Wikipaedia show nicely the progression of the derivations and similarities of the Werkmeister temperaments:









However, the bottom line relevant here is "what was in the spirit of a broad fashion of geographical common use" and that might be indicated by your analysis of thirds in Chopin. . . . Beethoven and Schubert might be interesting too. . .

Best wishes

David P

Well, I think Kellner and Francis are both crackpots.

WM3 has a group of 3 consecutive 1/4' 5ths, then 2 pure ones, and one more 1/4' one at BF#. Kellner has 5 1/5' 5ths in the same place + the extra one at FC. The extra 1/5' removes Ab from the list of Pyth M3's. The price for this is payed by all the other thirds except Db and F# which remain Pyth.

I looked at Chopin Op15 (raindrop) as you suggested. It's in Db major and 90% of the M3,10,17 occur on Db and Ab. Pretty harsh in WM3.

Kees

Dear Kees

You might have seen I have added to the post to which you've replied already.

I'm not surprised that you're finding unmodified WIII harsh - I came to hate it in my teens.

However, it provides a start:
http://www.millersrus.com/dissertation/

Modified WIII need not be harsh:
http://www.youtube.com/watch?v=xsn9g4pS2RA

Best wishes

David P

(Postcript - Miller's dissertation makes interesting reading - he claims that Barnes's starting point was Bach's aural tuning instructions that he gave his son . . . so Barnes should not be discounted . . . ! Miller's study recommends Werkmeister or Rameau as the best starting points. My view is that certainly WIII needs amelioration of some kind, as has been applied on the instruments I've tuned for these concert recordings . . .)

Here are the relative occurrences of M3,10,17 in the 24 preludes in all keys of Chopin. I don't see any conclusions to be drawn about a temperament, do you?




On another note "modifed WM3" is not WM3, but another temperament (e.g. Neidhardt 2).

Kees

Dear Kees

You are a STAR! Absolutely brilliant - this is great research which is most intriguing.

Obviously one must beware of drawing conclusions . . . but certainly the graph shows little sign of equality of favour.

The most striking thing is the very low usage of thirds in F second only to B flat. The fact that it's not just F that's low but B flat also gives significance for the reason that in the Werkmeister family of temperaments, F and B flat thirds are closer to pure and it may mean that Chopin was really wanting some spice possibly considering purer intervals to be inexpressive . . . ?

In F# the ratio of 17ths and 17ths and 10ths to 3rds might be on account of the 3rds being less useful in terms of being strained within the temperament.

Keys where 3rds are less than 10ths are
E, F, F# and B suggesting possibly that A flat and D flat either had particularly expressive appeal . . . to which E flat attractively veers with one of the greatest peaks of the graph whilst E, B and F# were either less useful or unattractive.

Possibly one might re-run the graph for only the 12 major keys . . . and certainly one might also beware of a purely mechanical interpretation without running through instances of use of intervals musically for context and musicality.

In one of my videos I explained how the unequal temperaments result in "rooted" and "unrooted" chords where the "Tartini note" or heterodyne frequency resulting from hearing two notes together is either a fundamental note of which the two other notes relate as harmonics, or where it's so far removed that it's not heared or percieved as part of the concordance of the resulting sound, therefore without a root or "unrooted". Chopin's funeral march demonstrates this and thirds in A flat and D flat, which ordinarily in these temperaments one would assume to be pretty spicey would be useful in generating such offputting sounds . . .

Certainly very interesting graphs which indicate that there is possibly a picture to be perceived, possibly by someone with detailed musicological knowledge of the scores . . .

Further to re-running on just, for instance, the major key preludes, is the algorithm you're using picking out examples where there are only 2 concurrent notes in the sound or is it including 3rds, 10ths and 17ths in chords of 3 or more notes? Is there a reason why such a distinction might be relevant?

Best wishes

David P

Or they may be incidental consequences of the particular pieces. Keep in mind we just have 24 preludes, whereas with Bach we have 48 preludes and 48 fugues. As a physicist you will realize the variance will be much higher for Chopin.

Here it is:



I just tabulate all intervals present at any given time, so if there are N distinct notes there will be N(N-1)/2 intervals, labeled according to the bottom note. The graphs I put up shows just the M3,10,17.

Intriguing isn't it? I haven't found the 24 Schickhardt sonata's for instrument and continuo in all keys in midi, would be interesting. I have played them all on a meantone recorder with a harpsichord in WM3. Very touch to get it in tune in the remote keys!

Cheers,
Kees

Dear Kees

What a baffling graph - it demonstrates the dangers of this sort of analysis in which any correlations of possible temperament preferences are obscure.

I didn't spend time on it yesterday but Dr Miller's dissertation does explore this sort of ground and correlations with temperaments and is worth a serious read. It's frustrating that it's presented on the web in Flash rather than any format in which one can seriously peruse hard copy . . .

Thank you so much for doing these analyses - I wonder if any players on the forum with these works in their memory might be able to help us further?

Even if we can't pinpoint anything statistically I hope you're continuing to enjoy the charm that you might be experiencing in your chords shifting shapes on your Well Tempered instrument.

(This thread should come with a Health Warning - you might never enjoy boringly tuned music that you hear on the radio ever again. Some Brahms, beautifully played, on the radio the other day started to annoy me as I recognised some chord progressions in which I was expecting the shapes of the chords to change excitingly, and it did not happen . . . )

Best wishes

David P

I definitely agree with Jake Jackson. I have found two CDs with Barabino playing Chopin, but I understand these are in equal temperament. I have listened to Raindrop Preludium, and that is awesome. Chopins 2nd sonata even goes beyond that (the unequal version). It sounds so much better than the equal version that I will have to wait for the unequal version.
Equal temperament should be fine for anything later than Lizt, but I will probably never again listen to anything earlier in equal temperament. I have been familiar with music played in unequal temperament for thirty years, but Chopin is new to me, and so is Barabino.
cubop
Edit: I have made a mistake here. The Post I have commented on is at the bottom of page one. But anyway, the important point is Barabino playing Chopin in unequal temperament on CD.

I think it's just more subtle than statistical occurrences can reveal. One thing is interesting if you take for example Bach's art of fugue and do interval counting for CP1 and CP11 and look at the M3/10/17 distribution the graph immediately shows CP1 is not very adventurous and stays close to home whereas CP11 modulates all over the place. As a fellow physicist I'm sure you'll appreciate the advantage of objective measures to quantify something. However I think key characteristics is quite subtle and may not yield to such crude statistics.

Yes it's unreadable, I sent him an email asking for a normal copy, otherwise Houston Univ. should have it in their library.

Actually I got fed up with WM3's Pythagorean thirds on my piano, and I don't even get a perfect M3 in return. So I tuned it in 1/4' meantone and I didn't break a string! It's already drifted off (we need a new kind of overpull method to change temperaments drastically) but if I touch it up tomorrow I'll enjoy Sweelinck as was intended. My kids piano teacher is going to get a nasty surprise when she comes over, one of my kids is playing a piece with Ab in it.

Kees

About key character: It's quite possible to have different keys exhibiting different character even in ET. If I play a piece in C major I'm relaxed and happy, no need to worry about accidentals to much. But if I play a piece in D# minor I have to remember all the time the 6 accidentals, worry if a natural symbol carries over, etc. etc., so it adds tension to the mind of the performer. I prefer keys with flats as the flat symbol looks more pleasing, all those sharps look like a barbed wire fence sometimes.

So even in ET these subjective considerations could affect composers and performers, and this will eventually affect the performance and mood of a piece.

On a non-keyboard instrument like a recorder playing in remote keys involves difficult cross fingerings and other obstacles to playing smoothly. This could also contribute to the key "characteristics" idea.

So I would argue it is a reasonable point of view (which is not mine) that keys have different characteristics, yet be in favor of ET.

Cheers,
Kees

Dear Kees

I urge you not to give up! 1/4C meantone on piano WOW! What fun - it would be great if you could do some recordings of that because coping with harmonics on that to make the instrument sound nice might be a challenge and educational to all of us . . .

However, I was mildly hinting at predicting that you would want to give up on UNmodified WIII and would urge you to try all and any of the variations of WIII that are known, whatever their provenance and however you might revulse against them at first sight.

Your graphs are consistent in identifying F as a key in which Chopin seems to have had little interest in the sound of thirds. So the temperaments which give a leaning flatwards rather than sharpwards, to F rather than C or G might be indicated, however tentatively one might look at the interval frequency methodology.

As a matter of amusement, I have an organ unit which switches smoothly between a number of temperaments from Equal to WIII, Kirnberger, Kellner, Vallotti, Chaumont, Meantone and Pythagorean, with possibly another couple interspersed. It's amusing to find that the keys that Chopin liked most are _purest_ in Pythagorean! It's amusing to see how our obssession for wanting to like the purest or most inconspicuous of temperaments might so easily lead us into entirely wrong conclusions.

Your observation about the stress which five accidentals puts on the performer, whatever the temperament, is interesting and valid . . . save when one is of the standard and fluency of top performers memorising the whole repertoire to whom a black note is just another note without any mental gymnastics that the rest of us mere mortals as amateur players have to endure . . . So please don't use this as your excuse to give up in your quest!

After 1/4C Meantone, you might find Pythagorean rather intriguing before you revert to the modifications of Werkmeister . . .

Best wishes

David P

PS - cubop - thank you so much for your kind comments and interesting observations. I have been vaguely passing on news of this thread to Adolfo and your encouragement to him will be very greatly appreciated.

Unequally Tempered, I must thank you. And what is already available with Barabino will keep me occupied for a long time. Especially the 2nd sonata.
cubop

Dear Cubop, and anyone else likewise,

All these recordings and performances have come about through now nearly three decades of persistence on behalf of my family and I, and all sorts of people who have helped -
http://www.hammerwood.mistral.co.uk/ - to small and large extents along the way since my youth - http://www.youtube.com/watch?v=Wv46YsUQAcM and, musically people inspiring us to champion the unusual such as Martin Eastick, one of the early collectors of music by such composers as Hummel, Spohr, Moscheles, Mrs Amy Beach (?Beech), Scharwenka - now names much more familiar than they were 30 years ago and who you can see playing at the end of
http://www.youtube.com/watch?v=K_F2H2qJOGc

We run concerts rarely making much profit given by musicians willing to join in the Hammerwood spirit of enthusiasm and it is this series of recitals, probably now around 300 or so over the years, that has led me to an idea of what the music wanted in terms of tuning, brought to life so brilliantly by Adolfo.

The first concert in Unequal Temperament was accompanying a 'cellist who threw a fit and almost refused to come to play - "I'm advised that my music is unsuitable for an Unequal Temperament" . . . Undeterred, as usual, we got over that problem . . . and this series of recordings have resulted.

From all the concerts before, I knew upon embarking on the temperament experiment that we were about to create something possibly very special and it is a GREAT reward to know that they have brought and bring the pleasure you express.

We like to promote and encourage young musicians too -
http://www.youtube.com/watch?v=BjgcEaZ44SY
http://www.youtube.com/watch?v=FE70ZKBOnpI
and
http://www.youtube.com/results?search_query=Jerzy+Owczarz
who started performing at Hammerwood also at the age of 12 . . .

We achieve what we do without any government support or grants and musically against a backdrop of indifference in terms of support for concerts and physically against the bottomless pit of the endless requirements of the maintenance of a Grade I listed historic house, with 100m of gutters imminently needing replacing just for a start.

Given more resources, I'd like to be doing more for musicians such as Adolfo and for encouraging young musicians in particular. My aim educationally is to try to captivate young people especially in the 8-14 age range so that firstly they might show discernment when it comes to the choices of going to nightclubs and all they entail as well as inspiring them to a greater life after teenage follies have subsided.

It is a project that has succeeded entirely with the private help and support of people who understand and believe in what we are doing. Of course we hope that people will help us, and we depend on it, but also I hope that what we do encourages and inspires others to do the same and to support such projects within their local community.

Over the years I have seen local music societies disappear - both performing societies and gramophone socities - to be subsumed by a rat-race of money making in which people have not had time to study or greatly appreciate music so resulting only in "shows" surviving at whatever local arts centres or theatres there might be, supported by marketing hype telling the rat-racers what they should approve of rather than discernment and recognition of talent guided by erudition.

Apologies for apparently taking this into a realm way off-topic, but to me this is the importance of making music as more interesting as it should be, and rescuing it from the greyness that is certainly not the sole cause of indifference towards classical music but which . . .

On another note,
http://www.youtube.com/watch?v=PwpBSHEHEek
is a performer totally at the opposite musical spectrum to Adolfo who needs no temperament . . . he is his own! I heard him at a charity concert in a private house in Antibes, South of France, raising money to build and support schools in Vietnam.

Best wishes

David P

Hi David. The best things in life are off topic. I have checked the links in your post, and had a look at your homepage. Impressive is an understatement! And there are lots of stuff to dig into. Concerning the topic of unequal temperament, an important aspect of that should be how modern performers have handled that in their interpretations of historical music. There are some fine examples in this thread, but I have not found anything by Bach and earlier. Bach is reasonably well documented on Youtube, but the actual use of temperaments in earlier music remains a mystery to me. There are lots of fine interpretations of medieval and and renaisance music, and the temperaments that were used are known, but I must admit I have no idea of how temperaments are handled in my collection of early music (Machault to Bach), and I have not been able to find examples of early music performed with what is now considered to be correct temperament. Probably lots of different opinions on that, but all opinions and information will be appreciated.
Hope I have not made myself too unclear.
cubop