Best TUNING TEMPERAMENT for acoustic piano playing classical pieces?

[campogi]

Dear David,
I will answer your first concern: When I noticed the sound difference between my U3 and the DVD recording, I knew absolutely nothing of Temperaments. I had no preconceive knowledge of it being unequal and thought then that pianos were tuned in one way only which I later found was ET. What I could not understand then was my newly tuned piano (ET) did not sound as good as the recording playing the same classical piece. The timbre, the tonal color, the musicality was so very different from what my ears heard. Here is the DVD where I critically compared sounds:  “Artur Rubinstein In Concert” Concertgebouw Orchestra, Bernard Haitink conductor – Deutsche Grammophon recording.  Please take the time to listen to Beethoven’s Piano Concerto No. 3, Op. 37.  1st Movement. You will find a lot of scale like playing and done slowly to compare.
It being a DVD and unequal is rare? I do not understand your conclusion. The concert was done in Europe, the concert piece was composed by Beethoven in early 1800. I would assume the piano temperament used would be what was popular during that time to best appreciate the music to its full extent rather than adulterate it by using 20th century ET. Wouldn’t unequal be logical? I read that Beethoven’s temperament preference was Werkmeister. If the piano was tuned to it is another matter.
I have yet to read on modern piano designed for ET. Can you refer me to an article or a piano make to that effect. From what I understand acoustic piano manufacturers are silent on it else the 20th century innovation will be in the product brochure. Is there such a brochure? Yet you gave a good analogy of the organ’s pipe. To add, there is no sense reshaping the piano’s frame – the string has enough stretch leeway to accommodate all temperaments yet all of them are ‘arched’. I wonder why?
David, the links you cited are terribly good!
Thanks everyone

[latrobe]

Dear Arturo

Here's some Gershwin on unequal temperament:

and Debussy:

and here:

Liszt's Venezia e Napoli

Hammerwood Park concerts are worth coming to! :-)

The DVD http://beethovendvd.blogspot.com/2009/08/review-of-artur-rubinstein-in-concert.html appears to be based on a 1973 recording. Research into unequal temperaments really only gathered momentum at the end of that decade, and only in the organ world. Unequal temperaments on the piano were completely unheard of. The difference in sound is going to be entirely on account of a quantum leap of size and associated instrument resonances and the comparative purity of long string harmonics without the inharmonicities of shorter strings. What I have been doing with unequal temperaments is, other than some demonstrations by a very very few tuners and researchers - I think I recall reading on the net in the past year of one in England and a couple in USA, to my knowledge, completely unheard of.

Musicians metaphorcally look at me askance when learning that the Hammerwood instrument is in unequal temperament. A notable senior musician who is president of one of the composer appreciation societies had never heard of playing this repertoire on unequal temperament and when I remarked on the composer's choice of key being interesting, had no advice to give me about what temperament might be tried. Twenty and thirty years ago it is inconceivable that any mainstream performer, especially with an orchestra, was using anything other than equal temperament. Hire Steinways are _not_allowed_ to be tuned by anyone other than a Steinway tuner and Steinway tuners tune Equal Temperement. To perfection.

The prejudice against a Good Temperament being an Unequal Temperament and not Equal Temperament is such that some musicians from Canada are refusing to perform at Emerson College Forest Row where I have tuned the 1895 Bechstein to the Good Temperament, on account of hearing that the piano there is not tuned to Equal Temperament.

The arch of piano design will be designed according to scaling, achieving the right length for the relevant progression of thickness of strings in order to give the progression of tone desired through the range of the instrument. . . .  

Bearing in mind that 8 cents deviation from equal temperament represents around 2 Hz in the middle octave, one would need to be measuring speaking lengths of strings to 1/2% accuracy to see a designed intention away from equal temperament in the piano design. Perhaps not impossible to do and perhaps at some stage this is a call for me to measure the string lengths of the 1854 Emerlich Betsy Viennese piano  . . . Other owners of historic pianos might usefully do the same. But string tensions are variable to the extent that I'd expect a maker to insert the pins as a smooth progression allowing tension to cater for the temperament. Organ pipes are, of course different as the tension, or pressure, of the vibrational medium is air and is simply the prevaling atmospheric pressure at the time, common to all pipes. So pipes have to be cut to the exact temperament in contrast . . .

I hope this is a helpful explanation and that the recordings will encourage you to keep experimenting . . .

I was certainly unaware that Beethoven favoured Werkmeister - is there a reference for this? If this is the case we should investigate further signs of temperament exploitation in Moscheles and Mendelsohn. Mozart and Haydn - meantone? Handel??? I have heard it said that Handel favoured Equal - but what equal? A good temperament in which all keys are playable but some are more equal than others?

Certainly there is much research to be done here. Much of it can be done only by tuning, experimenting and listening, but being careful to avoid hearing only what one wants to hear, and reading any original sources but bearing in mind that good and equal may be confusable. . . and that Bach's use of the term Well Tempered has merely been traditionally interpreted, as an assumption, that if it's not Meantone, of course it's Equal . . .

Best wishes

David P

[latrobe]

Hi!

As a postscript you might enjoy

- piano in unequal temperament being used to accompany viola . . .

Does the temperament interfere with the music unintended for the temperament? Does the temperament throw the instrumentalist off?

 Best wishes

David P

[campogi]

Dear Dan and everyone,
As to unequal in jazz, I tuned my brother’s piano quasi-equal. It does sound better.
As to the famous recording being unequal - at the time I noticed the difference in sound quality between my tuned U3 piano and the DVD recording, I had no preconceived notion of temperaments. At that time, I thought there was only ONE WAY to tune an acoustic piano (which I later found to be ET). What bothered me then was the big difference in colour (as you wrote) of the compared sounds. My U3 did not have the timbre; the tonal quality; warmth; and it bothered me. Since the family tuner (the most respected in town and retired) who I got to come and help audition) could not account for the difference as my piano was well tuned (in ET) and after having discounted the likely source of the problem as upright versus grand piano, I went on a research mode (which I’m good at) to pinpoint the problem. It was the Rollingball website that opened my eyes to Temperaments! The web has excellent visual comparison in graphic form of different temperaments (www.rollingball.com/images/). So to your concern of it being unequal . . . all I knew then is . . . the recorded sound was vastly superior against my U3.
As to the DVD detail, I did most of my comparison to this DVD: A Deutsche Grammophon recording titled: “Artur Rubinstein in Concert”, Concergebouw Orchestra conducted by Bernard Haitink. Focus on the 1st Movement, Beethovens  Piano Concerto No. 3 in C Minor, Op. 15. This movement has a number of chromatic scaling done slowly to allow sound comparison.
As to the DVD recording being unequal and rare – I would surmise it to be unequal as this is a European recording of Beethoven’s composition in the early 1800 century. I would again surmise - if Rubinstein and the conductor wanted to do Beethoven justice, they’d take time to tune the piano used to the temperament of that era to best appreciate the music as what Beethoven may have wanted you to hear. If unequal, your guess is as good a mine and again, the recording sound was vastly superior against my U3.
As to 20th century piano plate/frame design – I have yet to read an article or on a manufacturer boasting of a 20th century design. And on the design, the manufacturer need not bother to redesign the wheel as there is a very large leeway to tune a particular piano to whatever temperament.  I know you are fully aware that the variation from ET to other unequal is relatively minute but audible to differentiate the flavor. Checkout the above link and compare the different temperament graphs and appreciate the difference mindful of this limitation – 8.33 cent between half notes and a +/- 4 cent deviation will end up to having a very wild wolf – just 4 cents! Redesign a plate on 4 cents?
I still cannot help but wonder: why the piped organ has varied length to indicate unequal or why the harp is arch and so is the piano’s plate. However, much has been said on it. I will do a personal research and inform readers of this forum of what I end up finding, if that happens. The word you used was ‘revolutionary’ should I be lucky.
I will take this opportunity to qualify an earlier statement but not retract from it. Anyone can pull a string to a frequency dictated by ETD but it takes a professional years of experience to make that string sound to perfection as Ray argued and rightly so. However, please understand, due to circumstances, I was literally forced to learn tuning and this forum is my only venue to expand my knowledge. Like to thank Dan for his encouragement and for the voicing info, David whose links were magnificent, and the information I got from Jim, Richard, Curtis . . . I am now very happy with my U3 with the lifetime temperament that it has . . . many thanks to all of you.

Till then,
Arturo

[latrobe]

Dear Arturo

Thanks so much for the compliments of our recordings - I hope they encourage others that exploration of unequal temperament leads to enjoyable music . . .

You raise a very interesting point about the recording which clearly needs researching - but truly, modern concert instruments simply have not been tuned in UT - authentic instruments yes but not Steinway - Bosendorfer varieties. A friend who was very much active in this period tuning for major opera houses and concert halls is very very excited by what I'm doing because it has not been done, to his knowledge, in his lifetime and for him my experiments are very much new ground.

To be honest, no wolf is created from 4 cents deviation. . . . One really has to approach 2/3rds of a quarter tone for an interval to start to sound strained . . . Equal temperament thirds are 13 cents sharp, for a start . . .

Getting strings to sound nice - this can depend on how they are seated on the pins on the bridge - sometimes they beat all by themselves or in the treble emit two notes together very close apart. Getting things to sound nice is partly tension equalisation in the sounding and non sounding parts of the string. For this reason if I am adjusting pitch and I feel that strings are sticking on the agreff or whereever, I let the string down 1/4 tone or more and then bring them up to pitch in one fluid movement and when there, just let off the tension a very minute amount to even out the tension difference whilst banging the note quite loudly. For Liszt and Prokofiev the pianist is going to do that anyway, so your string has to be prepared for it!

Best wishes

David P

[campogi]

Dear David,
Your expertise shined brightly on your explanation of 4 cent wolf. I stand corrected.
With so many articles and websites I read and went to on temperament, I no longer remember where I read re Beethoven’s Wreckmeister preference. The article even stated that Beethoven had his personal tuner go with him on tours as part of the contract.
On the subject, www.rollingstone.com will give a wealth of information on temperaments. It provides elaborate colored graphs and goes further by allowing you to hear the sounds of different temperaments. I strongly advise you to check it out as I am certain you will find it very informative.
The ET standard was set by US in 1911 to resolve the confusion as to how a piano must be tuned when it left the factory or delivered to a customer in the country. Before 1911 European countries hotly debated the issue of standard . . . national pride was at stake and each strongly argued and fought against each other as to which country will have the honor. The strong players then were England, Poland, Germany, Italy, and France. However, even within each country, top musicians argued among themselves thus a stalemate. US, a neutral country with no national pride at stake, set a standard (not its invention) that was the easiest to comply and logical in terms of tuning – divide the octave evenly, ET (a temperament that was argued as well in Europe). The US standard was the scapegoat to resolve the stalemate and the European countries adopted the standard – keeping the national pride intact! Thus all piano manufacturers and dealers in the world delivered their product ET – the standard!
With only the aristocrats and die hard musicians (the dinosaurs) knowing and arguing on the issues behind UE (unequal), the oblivious majority of piano buyers never knew what it was. In time, the issue faded and the composer’s choice of temperaments faded as well. However, a small number of European music connoisseurs held on to traditions.
Since all manufacturer’s are required by LAW, Steinway, Bosendorf, Faboli, etc. ship and deliver pianos tuned to ET. Consumer’s are left on their own to have it re-tuned to a discriminating preference at their expense. Since the greatest majority is oblivious to this and only a few in the music world are aware thus ET became the sound we are used to and the STANDARD. Whether it is musically acceptable is definitely ANOTHER DEBATABLE ISSUE.
When you mentioned that your reviving the unequal was revolutionary in the early 2000, it was a relief on my part. When I started my inquiries and called on local concert pianists and even as far as the Dean of Music of the State University, they did not know what it was. Distinguish pianist played at concert halls with the piano provided them! For a while, I thought Philippines was musically backward.  What a relief . . . my national pride was at stake. It turns out, we are all in the same boat.
Then the question is . . . what temperament will a concert piano be tuned in if the pianist will play compositions from Monzart, Beethoven, Grieg, . . . in one night? See the point? ET or Quasi-ET. People won’t know anyway . . .  but then the quality of the sound is sacrificed somewhere together with the piano’s sounding efficiency.
I strained to the piano’s sound when listening to the “16th Chopin International Competition”. I will bet my life, Yulianna Avdeeva’s piano was not ET or quasi at all!  Force in a corner, I will say Young. For your information, I channeled the sound from the web to my sound system. My subwoofer is a 12” Velodyne. That will give you an idea on how much I invested on the other 6 channel sound surround components to get the best sound from it.
I will continue next time. This time a thesis on where manufacturer will MOST LIKELY stand on the issue. GTG
Arturo

[latrobe]

Dear Arturo

Thanks for your recent post - very interesting - and look forward to the next instalment. I've turned attention to organ at the moment:

in equal temperament and

in meantone. The Fugue doesn't work and possibly lends credence to the theory that the piece, or possibly one part or other was not by Bach! It's in this way that temperament can show musicological light on composers . . . !

Best wishes

David P

[campogi]

Dear David P,
So sorry for the delay in response. I could only wish piano playing is my profession and not a hobby. But then . . .

What I will write is merely a personal thesis on where a piano manufacturer may stand on the design of the piano plate.

If I, as the owner, sent a memo to my acoustic engineers to design a beautifully sounding piano with this specifications: 100 cent to an octave; a total of 8 octaves; 88 keys spaced at 8.33 cent (EQUAL TEMPERAMENT); and with A4 set at 440 hz . . . I will have the entire engineering staff banging my door well within half an hour strongly thinking that I’m either crazy or completely ignorant of acoustic principles.

Although complying with the directive is possible with the piano’s plate designed as a perfect triangle, the engineers will have these as arguments against an ET designed piano plate with the object of having a beautifully sounding piano:

1.   Only one note (A4) will have a perfect pitch.
2.   Since frequency are round numbers and except for A4, all other notes will be off perfect pitch.
3.   Except for A4, all other notes will lose over 15% of its sounding efficiency thus the piano will not sound as loud compared to perfect pitch.
4.   Since the LAW requires the piano tuned to ET upon delivery to buyers,  the strict ET design will limit the best flexibility to have it retuned to other temperaments for better musical sound, and
5.   Although relative, the piano will never sound at its best.

Confronted with those arguments and as owner, I will revise my spec to this:

Give me an engineering design(s) to get as MANY NOTES in an octave at or nearest perfect pitch but never stretch beyond 110 cent per octave. I will invite/hire the best ears in the music world to vote on the best sounding design and make it company standard. However, to comply with the law, all pianos leaving the manufacturing compound will be tuned ET.

If the acoustic engineers complied with this new spec (UT), the piano’s plate will have to be curved!!!!!!!!!! YET delivered to us tuned ET. HOWEVER AND BEAR IN MIND engineers are not musicians and will strictly adhere to sound engineering principles and when faced with a problem will compute for the best compromised . . . get as many notes in an octave to near or perfect pitch – UT (Unequal tune)! I maybe wrong, but from what I understood, 5 (black keys) of the 13 notes can be perfect pitch at 100 cent to an octave and 8 (white keys) out of 13 when stretched.

Much have been said on the subject of temperaments and instrument design. I started the subject and leaving it with more knowledge than I imagined. Many thanks to those who participated.

I end, “The beauty in the sound of music is in the heart and ears of the beholder.” (Note: Getting to think like Dan Silverwood)

God bless you all,
Campogi

[latrobe]

Dear Campogi

Great idea, but I think scaling is the key . . .

The arched plate of the piano is arched as the strings are not uniform thicknesses, so the mass per unit length decreases to treble requiring the treble strings to be comparably shorter. It's this that gives tonal scaling and is nothing to do with temperament.

A uniform stretch of 10 cents per octave would tweak the ears. 20 cents in two octaves - 30 cents in three - um . . . !

Best wishes

David P

[campogi]

How many string sizes to complete 288 strings?

[silverwoodpianos]

Hello Campogi,

Usually a dozen sizes of wire on the treble side, unless the instrument is strung in whole size changes. Some are and some are not.

With the bass string set these are graduated:

For a 42 string set for example the ranges are from 4.876-1.511cm going from A1.

In a 46 bass string set 5.994-1.320cm.

Both of these calculations are for a 1.8 meter grand’s.

Also some of those bass strings are on the tenor side of the scale….  

Usually 256 strings in a piano if I recall correctly unless you are looking at an Aliquot system like this;

There are about 30 extra strings in this one……


https://picasaweb.google.com/silverwoodpianos/BluthnerAliqoutTour#

[latrobe]

I've continued to tune to unequal temperament which I now refer to "colour tuning" and recordings have been acclaimed by musicians. The reality is that the temperament puts the colour back into Chromatic music. What else does "Chromatic" mean?

A useful corpus of recordings:
Music in "colour tuning"

Bach on Harpsichord
- see the comment

Bach on piano

Haydn

Chopin on Steinway Boston played by Adolfo Barabino

Brahms violin sonata accompanied by Barabino with Steinway

Chopin 2nd sonata played by Barabino

Mozart violin sonata B flat

Chopin Ballade 4

Chopin 24 preludes

Chopin 2nd sonata in unequal and equal temperament

Chopin on Grotein Steinweg. This instrument brings to life the singing thirds.

effect on melody

Gershwin

Debussy

Benjamin Britten

I've done a video about restoring the colour, the chromatism to chromatic music. Haydn is wholly lost without colour temperament -

Apologies for the inexactitude of the tuning of the 1859 Broadwood - this instrument has its challenges with some missing bridge pins at the moment in the middle of the middle octave.

Best wishes

David P

[huaidongxi]

Campogi, Silverwood, Dave P., and other contributors, many thanks to you for filling in some of the many gaps of my understanding of temperament.  have never been really satisfied with the standard equalized temperament, but have stuck with it from concern that the alternatives would compromise some genres or periods of music.  tempering to favor the middle range of the keyboard seems however to make a sensible compromise.  any suggestions ?  my favorite 19th cent. composers include L.v.B, Schubert, Schumann, 2Oth cent. rachmaninoff, ellington/strayhorn, monk, coltrane.  this last composer derived his own system of harmonic progressions called 'coltrane changes'.

for a fascinating attempt to reproduce on the equal tempered piano the music of gamelan, there is Godowsky's 'Java Suite', which could have amazing potential on an instrument tempered to best suit it.  thanks again for sharing your experiences and knowledge.

[huaidongxi]

Mr.Pinnegar, many thanks again for posting the links to the performances on the pianos with modified temperaments.  enjoyed them, and they've convinced me that music is more engaging without the uniform equal temperament.

have a few questions for you if you could be kind enough to respond.  you describe one tuning you favor as closer to pure thirds in the home keys, with strong fifths in distant keys.  does that tuning have a historic precedent with a specific name, that another technician would know how to replicate ?  on the 19th cent. Bechstein you prepared so beautifully, is the A at 440 or somewhere lower ?  [our home piano was made just after equal temperament became standardized, about twenty years after the Bechstein, but its designer was influenced by European piano designs and consulted with the leading violinist of the latter half of the 19th cent., Joachim, when he came up with the signature innovation on his pianos, the tension resonator.] 

on one of your other youtube links there's a performance of Schubert on a Graf hammerklavier from just after his time, the well known G flat impromptu. fascinating, as the unequal temperament tuning would make that tonality one of the 'distant' keys, no ?  do you happen to know which temperament system was used on that Graf ?

will repeat my appreciation for the education and knowledge you and the others have shared.  peace.

[latrobe]

Thanks so much for your response. The tuning I am using is between Valotti and Werkmeister III, just a shade less strong than Kirnberger III

Special favour. Might there be anyone who could translate the following for me into Chinese?

There are two reasons why there is interest on changing the tuning system of the piano.

1. the physics of sound, and
2. its effect on musicality.

For many contemporary musicians music has become merely a circus act because the true nature of music has been forgotten. It has become only a challenge in virtuosity, a spectacle, "man versus beast". Musicians have forgotten the purpose of music as
- a language to convey emotion
- to enable the mind to explore different dimensions of experience
- and to heal.

Healing requires gentle caressing, and harmony not of sound but of the vibrations within sound.

Sound is made of vibrations, regular vibrations per second. These vibrations are either exactly related and part of the total sound, or they are not together and do not relate to each other, producing beats between them.

This produces contrast as between
- solid versus liquid
- certain versus uncertain
- calm versus stressed

Modern piano tuning does not maximise the numbers of vibrations which coincide - which then contrast with those sets of vibrations which do not coincide.

The change to modern tuning was made between 1860 and 1920. At this time the current tuning was used increasingly, becoming universal. It is exact "equal temperament" where each semitone is an exact same distance apart.

1. Physics of sound.

A note which is an octave higher than another note is double the frequency of the lower note. Twice the number of vibrations per second. So "A" in the middle of the piano keyboard is 440 vibrations per second. The "A" above is 880 vibrations per second. The octave above that is 1760 vibrations per second, 1760 "Hz".

When playing the organ, the sound can be made more interesting using "stops" to sound all three pitches, 440, 880 and 1760 from the same note.

All sound is made of timbres in combination of these multiples of vibrations together.

You can hear this when you sing a note and open your mouth to allow the extra sounds to be heard. I demonstrate this on a video

.

When a string is struck, all these frequencies vibrate exactly together to give the tone of the string. These frequences form part of the tone of the instrument.

For example, let's tune a string to 100 vibrations per second - 100 "Hz". Giving good tone on the piano this string will produce vibrations at 100, 200, 300, 400, 500, 600, 700, 800 and more vibrations per second.

If we hold down a note at 100Hz in the bass whilst we strike the keys above, for 200, 400 and 800 (an octave above, two octaves, three octaves and four octaves) then these frequencies will excite and resonate the undamped bass string. The sound will continue to be heard in the bass string: even when the upper note stops sounding. This is demonstrated on

where you can hear this effect.

What is interesting is that when we play two notes together, such as 500 and 600 vibrations per second, then these vibrations will coincide 100 times per second. So the bass note is synthesized. It appears to sound without actually being played. It is a resulting or resultant note. This gives tone and sonority to the instrument and builds the sound.

What becomes interesting also is when we sound together combinations such as 200 vibrations per second and 300 vibrations per second together. We also synthesize a sound at 100 vibrations per second. But the 200 vibrations per second string vibrates with harmonics
200 400 800 1000 1200
and the 300 string vibrates with the harmonics
300 600 900 1200

Then because 1200 vibrations is a harmonic of both strings, we will hear 1200 more strongly and it adds to the timbre, the tone, and can be heard sometimes as an extra note.

If we sound 500 vibrations per second with this then we add the harmonic series
500 1000 1500.

Then a note at 1000 is heard in addition to the note of 1200 and in addition to the 100 vibrations per second. So the timbre of the sound of the instrument becomes reinforced even more.

The problem with modern piano tuning is that the 300 500 600 700 frequencies are not tuned close enough to the perfect harmonic to add the sound reliably except in a jangling way.

As musicians we have experienced a shimmering or glistening to the sound of the piano. Then we say "what a wonderful piano". But by doing this the piano presents the piano rather than presenting the intended effect of the music.

2. Musically this has reduced the dimensions in which the music can speak, reducing them to
a. loud versus soft
b. slow versus fast
c. discordant versus harmonious

Have you read George Orwell 1984? The new language NEWSPEAK reduced the number of words to 300 so that people were limited by their language in their ability to think. This reduction of dimension in music has done the same to music.

3. The meaning of "Chromatic"

As musicians we have been bamboozled into thinking that the chromatic scale is simply going up each note by semitones C C# D D# E F F# G G# A A# B C.

We have forgotten what the language means.

Photographers who are old enough took photographs as transparencies for projection on film called . . . KodaCHROME EctaCHROME FujiCHROME and our lenses are CHROMATICally corrected - which means that on the edges of things in our image we don't see fringes of a spectrum of colours.

In the modern tuned instrument there is no hint of anything that we can call CHROMATIC demonstrating a spectrum of sound like a spectrum of colour.

3. The solution.

The tuning that I use exploits lots of perfect fifths (like F to C and E to B) in the exact ratios of 200:300.

This brings many "thirds" such as F-A and C-E and G-B near to the ratios 500:400. It is close so that it resonates without making other thirds unpleasantly too imperfect such as B-D#. This is enough to return the musical scale to giving a spectrum of "colour" to the chromatic scale. This is necessary for composers "HAYDN", "MOZART", "BEETHOVEN", "SCHUBERT", "CHOPIN" and "LISZT" whilst not doing damage to the music of later composers.

The spectrum of sound that we hear is demonstrated on

The differences of sounds create a reward to the musician for playing sensitively, reacting to the different sounds differently as intended to be heard by the classical composers. Now the musician is rewarded in moulding the sound shapes in the phrasing of the music, conveying meanings unheard in modern tuning but intended to be heard.

We have a corpus of recordings, many of which are acclaimed by musicians who have heard them:

Music in "colour tuning"

Bach on Harpsichord
- see the comment

Bach on piano

Haydn

Chopin on Steinway Boston played by Adolfo Barabino

Brahms violin sonata accompanied by Barabino with Steinway

Chopin 2nd sonata played by Barabino

Mozart violin sonata B flat

Chopin Ballade 4

Chopin 24 preludes

Chopin 2nd sonata in unequal and equal temperament

Chopin on Grotein Steinweg. This instrument brings to life the singing thirds.

effect on melody

Gershwin

Debussy

Benjamin Britten

By the way

might be quite interesting.

Alastair Lawrence at Broadwoods has been looking at a Handel temperament and it displays similar characteristics to that which I use.

For anyone who enjoys harpsichords

Bach on three harpsichords and

Clayson and Garrett 1970 after 1745

John Morley late 1960s

Sperrhake early 1960s
might be of interest.

Best wishes

David P

[georgey]

To me, the equal temperament is the only correct temperament.  As someone with a mathematical background, I can see how the other temperaments developed due to faulty understanding of numbers starting with Pythagoras.

Pythagoras was a brilliant mathematician but at the time he believed all numbers were RATIONAL numbers (i.e. a ratio of integers such as 3/2=1.5 or 256/243).  An IRRATIONAL number on the other hand is a number that cannot be expressed as a ratio of 2 integers such as pi and the square root of 2.  Pythagoras was so sure that irrational numbers did not exist, legend has it that he drowned a person for suggesting that irrational numbers existed.    As it turns out, there are not only irrational numbers, they outnumber the rational numbers to such a large extent that irrationals are said to be uncountable in mathematics, while rational numbers (although infinite in number) are said to be countable.

Because of Pythagoras faulty beliefs in numbers, he felt that the frequency of the perfect 5th was a ratio of 3/2 = 1.5 higher than the fundamental note.  The other intervals were based on stacking these perfect 5ths and results in integer ratios of frequencies such as 4/3 for the perfect 4th and 256/243 for the minor second.  In my opinion, the correct ratio for the perfect 5th is the irrational number “2 to the 7/12 power” or 2^(7/12) = approximately 1.498307. The correct ratio of frequencies comparing ANY 2 notes that are a semitone apart is the irrational number 2^(1/12) = about 1.059463.

Taking from Wikipedia on Pythagorean tuning: “Pythagorean tuning is particularly well suited to music which treats fifths as consonances, and thirds as dissonances. In western classical music, this usually means music written prior to the 15th century. From about 1510 onward, as thirds came to be treated as consonances, meantone temperament, and particularly quarter-comma meantone, which tunes thirds to the relatively simple ratio of 5:4, became the most popular system for tuning keyboards.”

Although the math was there for a long time to invent equal temperament tuning, I’m going to guess that due to reluctance of people to make large changes, even if the starting idea was based on faulty understanding of mathematics, it was not until much later that people started using equal temperament.  Lutenists and guitarrists were among the first in western music to use equal temperament.

From a musical point of view, in my opinion equal temperament sounds best and is necessary to play music such as Bach’s WTC.

Just a question I have to myself: ALL the many tuning systems that developed historically are only "band-aids" to try to fix problems that resulted from Pythagoras faulty understanding of mathematics?  Equal temperament tuning is not a “band-aid”, but is “THE correct tuning” in my opinion.  

[latrobe]

Equal temperament does not allow CHROMATICism to express anything like a spectrum such as "colour" can be an analogue. CHROMATIC or "colour" tuning is demonstrated by

Haydn, Mozart and Beethoven and others were very particular to write certain things expressing certain emotions in certain keys. This was because they expected an unequal system to produce the relevant effects in those keys. Tonally the early pianos did not have the dynamics of later instruments and key colour was a dimension in which they could speak beyond the confines of their more limited dynamics. For this reason, key colour was important and in fact Haydn is wholly unappreciated on account of modern tuned instruments being unable to express it.

Today I tuned an instrument of 1802 and in knowledge gained from that checked a renowned instrument used by Sir Charles Hallé of 1859 to find the same.

The harmonics which appear as overtones in a string are dependant significantly upon the proportion of the string at which it is struck by the hammer.

Both 1802 and 1859 instruments demonstrated the same phenomenae: normally the 5th partial is prominent in many of the more modern instruments I've tuned, the "17th". In these two instruments the 17th was absent entirely and it was the 3rd partial, the "12th" which was dominant.

In equal temperament the prominent 17ths beat with the wide equal thirds of equal temperament and this gives the instrument a glistening shimmering character as a result of which we admire the excellence of the piano. But with this absent and exchanged for the 12th, an octave and 5th, it's apparent that the resonance of the instrument is increased if then we use a temperament with lots of perfect 5ths which then accord and resonate with the natural harmonics of the strings of the instrument. This both solidifies and enhances the sound of the instrument as well as providing the groundwork for maximum key colour.

Earlier composers such as Couperin deliberately exploited the smooth sweetness of meantone temperament leading to crisis points in the music where the eccentricities of the tuning are used to special effect.

Equal temperament washes out all of these aspects of what used to add significantly to musicality, drama and emotion to be conveyed.

Best wishes

David P

[georgey]

Equal temperament does not allow CHROMATICism to express anything like a spectrum such as "colour" can be an analogue. CHROMATIC or "colour" tuning is demonstrated by

Haydn, Mozart and Beethoven and others were very particular to write certain things expressing certain emotions in certain keys. This was because they expected an unequal system to produce the relevant effects in those keys. Tonally the early pianos did not have the dynamics of later instruments and key colour was a dimension in which they could speak beyond the confines of their more limited dynamics. For this reason, key colour was important and in fact Haydn is wholly unappreciated on account of modern tuned instruments being unable to express it.

Today I tuned an instrument of 1802 and in knowledge gained from that checked a renowned instrument used by Sir Charles Hallé of 1859 to find the same.

The harmonics which appear as overtones in a string are dependant significantly upon the proportion of the string at which it is struck by the hammer.

Both 1802 and 1859 instruments demonstrated the same phenomenae: normally the 5th partial is prominent in many of the more modern instruments I've tuned, the "17th". In these two instruments the 17th was absent entirely and it was the 3rd partial, the "12th" which was dominant.

In equal temperament the prominent 17ths beat with the wide equal thirds of equal temperament and this gives the instrument a glistening shimmering character as a result of which we admire the excellence of the piano. But with this absent and exchanged for the 12th, an octave and 5th, it's apparent that the resonance of the instrument is increased if then we use a temperament with lots of perfect 5ths which then accord and resonate with the natural harmonics of the strings of the instrument. This both solidifies and enhances the sound of the instrument as well as providing the groundwork for maximum key colour.

Earlier composers such as Couperin deliberately exploited the smooth sweetness of meantone temperament leading to crisis points in the music where the eccentricities of the tuning are used to special effect.

Equal temperament washes out all of these aspects of what used to add significantly to musicality, drama and emotion to be conveyed.

Best wishes

David P

This is all very informative and interesting.  Thank you.  The temperments that were used and favored by certain composers and in certain keys are very interesting.   The statement that “Equal temperament washes out all of these aspects of what used to add significantly to musicality, drama and emotion to be conveyed.” is perhaps a matter of opinion, but maybe not to an informed person.  I would say though that for reasons that balance both musicality and practicality, history has judged that equal temperament is the way to go in most cases.  

My Avantgrand N1 has the following tunings:  Pythagorean, Mean-tone, Werckmeister and Kimberger.   Thanks to your post, I plan to spend time playing with these for fun.  I understand this will not be the same as playing on a real grand piano.

Also, just to add this if not already mentioned:  Higher "harmonics"' of piano notes are not true harmonics but are "overtones" and can be very sharp, i.e. a higher frequency than given by a pure harmonic series.  So I'm not sure I agree with "When a string is struck, all these frequencies vibrate exactly together to give the tone of the string. These frequences form part of the tone of the instrument.  For example, let's tune a string to 100 vibrations per second - 100 "Hz". Giving good tone on the piano this string will produce vibrations at 100, 200, 300, 400, 500, 600, 700, 800 and more vibrations per second."  that someone said earlier.

[latrobe]

history has judged that equal temperament is the way to go in most cases.  

No. It wasn't history that determined a preference for Equal Temperament. It was big money engaged in mass production of brands that needed brand worship in order to sell pianos big-time to a class of people who might have new money but not be sophisticated in music.

The 1859 Broadwood that I referred to above was bought by an enthusiast in the audience who said that it was the most amazing piano he'd ever heard - so paid 250 guineas for the privilege of buying it. Equivalent £250k or so now.

When the likes of the brands you've heard of took over from Clementi Collard and Collard, Stodart, Stein, Streicher with huge outputs of expensive instruments often installed as a status piece of furniture in the corner of a room, they couldn't have someone playing B major, A flat, G flat or C sharp and someone commenting on it sounding harsh. So became a force to remove the harshness of the remote keys and remove the comfort of the home keys, making all the same. Vanilla smothered all.

Bearing in mind that it was the piano that impressed the buyer in 1859 I contemplated that it was built for equal temperament and might have been one of the first to exploit the shimmering glistening that we've come to admire in an instrument. But discovering the partials geared to the exploitation of a perfect fifth based temperament I'm now given the confidence to change it.

One of the most profound concerts I've recorded was a Steinway in A=432

  in Brahm's violin sonata composed on the shore of Lake Thun in Switzerland. This recording is the first time I've heard this piece in which it's so calm that one can visualise the mirror still lake, with eddies of wind, birds and leaves and splashes of water on the shore. The calmness of perfect fifths and harmonious thirds is both subtle and profound.

Best wishes

David P

[georgey]

One of the most profound concerts I've recorded was a Steinway in A=432

 in Brahm's violin sonata composed on the shore of Lake Thun in Switzerland. This recording is the first time I've heard this piece in which it's so calm that one can visualise the mirror still lake, with eddies of wind, birds and leaves and splashes of water on the shore. The calmness of perfect fifths and harmonious thirds is both subtle and profound.

Very nice recording of Brahms.  His 3 violin sonatas are gems.  The piano sounded out of tune to me but in a pleasant way, unlike an equal temperament piano that was poorly tuned or out of tune.  It was refreshing to hear this tuning.  Thank you!

EDIT:  I forgot about a recording I like very much:  Edmund Battersby who plays Beethoven Diabelli variations on both piano and pianoforte.  The pianoforte version is recorded on a newly made replica of a Graf piano made in the 1820's and tuned at A430 in "Tuners's Guide No. 3" temperament from Owen Jorgensen, Tuning P. 442. Great recording!

[themeandvariation]

equal temperament also came about in order to unify the tunings across europe… (for orchestral playing) in particular for the brass and woodwind… 
But i certainly agree that much harmonic complexity it lost, and as latrobe says, became just smooth vanilla..
Someone at the Larips website, (spiral spelled backwards) , has claimed to have decoded Bach's special tuning method - deduced from the decorative doodlings  on the WTC..
They have examples, with one piano tuned suchly.. I love it.. His far reaching harmonic modulations don't suffer, and something of the character of each key signature remains.  Really amazing..

I want to have my piano tuned That way.
Any suggestions, Latrobe ?

[latrobe]

The larips scheme is interesting but actually makes no musical sense and has no historical precedent.

The key colour peaks with three or so accidentals but the language of "home" and "remote" keys makes better sense with keys with the most accidentals.

The scheme has no perfect fifths.

The instruments mentioned above of 1802 and 1859 lead to giving weight to systems involving perfect fifths and the line of tunings from Vallotti to Kinrnberger to Werkmeister then becomes of greater interest.

Look up Youtube "Bach Chaconne harpsichord Colin Booth" to find the value that such a tuning gives

Best wishes

David P

[georgey]

Just a final thought from me on this, my last post to this thread.  As someone with strong interest in mathematics and looking at this question from a mathematical point of view, I find the equal temperament to be THE correct tuning system.   I do admire those that are exploring other tuning systems on modern pianos, however.

I understand that the ratio of the third harmonic to the second harmonic in the harmonic series is 3/2 = 1.5, or what Pythagoras referred to as a perfect 5th.  

If you use successive perfect 5ths under Pythagoras definition to generate the 12 tones of our chromatic scale, you run into a big problem:  

3/2 to the 12th power divided by 2 to the 7th power (3/2)^12/(2^7) = 1.013643 <> 1.00000

Notes: to the 12th power because you are generating the 12 tones of our chromatic scale and divide by 2 to the 7th power to lower the resulting tone 7 octaves.

Many attempts have been made to correct this problem.  Some methods are quite creative and result in interesting and even enjoyable sounds in certain keys.  

The solution to this problem by a modern mathematician would be EXTREMELY easy and obvious:  Equal temperament tuning where a perfect 5th is defined as 2 to the 7/12th power = 2^(7/12) = about 1.498307

Using perfect 5ths defined under equal temperament to generate the 12 tones:

2^(7/12) to the 12th power divided by 2 to the 7th power = [2^(7/12)]^12/(2^7) = 1.0000000000000….  PERFECT!

So it comes down to how we define a perfect 5th.  Do you multiply the frequency of the lower tone by 1.5 (Pythagoras) or 1.498307…(equal temperament) to generate a perfect 5th?  

Side note:  As mentioned before, higher "harmonics"' of piano notes are not true harmonics but are "overtones" and can be very sharp, i.e. a higher frequency than given by a pure harmonic series.  The 1.5 ratio in frequencies of the 1st and 2nd overtones of a piano is only an approximation.  Piano overtones do not exactly match the harmonic series.  Note: overtones are numbered 1 off from harmonics.

FINAL EDIT:  It is interesting to think how music would have developed differently had Pythagoras defined a perfect 5th as taking the lower note frequency times the rational number approximation of 2^(7/12) of 1.49830708000..,rather than 1.5.  Instead of early composers treating 4ths, 5ths and 8ths as consonances and treating the ugly 3rd of Pythagoras tuning  as a dissonances, composers may have started from day 1 treating thirds as consonances.    Also, there is a great possibility that other 12 tone tuning systems would have never been developed and regularly used.  WE WILL NEVER KNOW!     But western composers grew tired around year 1500 and wanted to try new things and so a modified tuning system was developed (many times).  In the end, everything worked out.  We finally realized that 1.49830708 is the magic number (or at least many of us do  ).  Pythagoras was so close with his 1.5 hypothesis.  We owe so much to him.  Note:  This edit is just my opinion.  Regards.

[latrobe]

With respect the twelfth root of two might be very clever but it's a bastard number, far from perfect and unable to convey music of the heart in the way that classical music was written.

The pure fifths are perfect.

The octaves are perfect.

The whole point is that 2^7 nearly but doesn't quite match 3/2 ^12 and so one has to spread the difference somewhere between the fifths.

In the 18th century they would have wanted the ratio of perfect to imperfect fifths to be as near as possible to the Golden Section, the Divine Ratio. Only the Divine was considered to be perfect.

It's no coincidence that Werkmeister III has 8 perfect fifths, a ratio of 2/3 of the twelve and therefore that 7 perfect fifths is closer to the Divine.

The result of such tunings is that one gets major and minor semitpnes. Dr Charles Burney, the musicologist at the time of Haydn and Mozart complained that musicianship was being eroded by violinists who were not trained to tell the difference between the two. The ear of the well trained musician was sensitive to these intervals, later to be wiped away entirely by equal temperament.

explores those major and minor semitones

explores resonance

demonstrates key colour and the way in which an instrument's vibrations dance between being locked together in resonance and shimmer in a sea of vibrations unrelated in another key.

The resulting dimensions of the music of certain-uncertain, calm-stressed, locked-released, solid-liquid, smooth-disturbed are present in classical music which are washed away by the forced equality imposed by equal distances between semitones, communism among the keys as a friend refers to it.

The twelfth root of two is not the way in which to enjoy the colours in which classical music was written.

Best wishes

David P

[latrobe]

Here's Beethoven as Beethoven would have heard it.

Piano of 1802 tuned to a temperament with 7 perfect fifths.

Best wishes

David P

[themeandvariation]

latrobe,
I really appreciate you bumping this thread.. a couple of years ago i was on a mad search to hear  Piano recordings using unequal temperament, and found scant little.. (I can much easier appreciate and soak up  the harmonic world of unequal when performed on a piano instead of a harpsichord -- something about the latter having a quicker decay after the initial strike.. or  the brittleness of the attack... - i'm not sure exactly why..)
So i was so happy to see all those links you provided!  I have listened to many of them… Especially loved the Bach partita … (which was not done on a forte piano, which i find also to have a quicker decay time,  … )
This is an exquisite harmonic world(s) to be aware of, and as a composer, i would love to immerse myself in it by having my piano tuned suchly.. like you mention of DR. Kellner..
Thanks again for posting.  Very important stuff!

[latrobe]

(which was not done on a forte piano, which i find also to have a quicker decay time,  … )

Thanks so much. It's great to know that this work is helpful.

You'll find on

in the slow movement of the Beethoven that on an original fortepiano the decay time can be very long.

Best wishes

David P

[themeandvariation]

ps.
  thought i'd mention that i just ordered - (apropos of this thread) -  "How Equal Temperament Ruined Harmony (and Why You Should Care)" by Ross Duffin..

[latrobe]

Aah - - yes - good book

But like many authors he goes too far and then champions the Lehman temperament (larips) on which I've commented above. Ignoring that he makes the point and argues it well.

Best wishes

David P

[latrobe]

Over the past dozen years I've been tuning Kellner and have now developed a "High Definition" system which works on all pianos, and creates extra resonance in the instrument, increasing its power and its sweetness.

is a test on a large Bosendorfer and

a sample recording on the 1885 Bechstein at Hammerwood Park.

Pianoteq is a good way to explore temperaments although the sound isn't as complex as the real instrument.

The tuning's great for jazz also

Best wishes

David P

[efecan]

First of all, we hope you use Yamaha u3 on good days. This piano is also of interest to me. I hope you reach the right source maybe this information will be useful for me later.

www.unnogame.com

[latrobe]

Last year competitors to the Nice International Piano Competition were introduced to the new dimensions available in performing in an unequal temperament. This was my "High Definition" variation of tuning Kellner.

is the final concert. At the end there is a recording of the winner of the Junior section who I introduced to using the new resonance of the piano enabled by the tuning. It enables the pedalling both of Beethoven and Chopin to be restored.

So often pianists now use the right pedal merely as they would a kick drum, amplifying every note. But the tuning takes us back to the possibilities of letting phrases sing, holding the pedal down for even bars. Early pianos didn't have efficient dampers, and some on which Chopin for instance practised in the form of a Pantalon had no dampers at all. The tuning enabled the resonance to make it possible.

Best wishes

David P