Chopin 24 preludes - should they be performed in Unequal Temperament?

[latrobe]

I've been tuning for concerts using the temperament for a decade so am familiar with what people and musicians say.

Here's a feedback that I had tuning for a concert and directing audience to go:

We were blown away by the music and the exceptional talent of the three musicians.  A truly memorable and wonderful experience.

I thought you would like to know that the violinist paid tribute to the way in which the piano had been tuned, saying it made all the difference to the music they were able to create together.

One of the reasons if you hear the Beethoven on the 1859 Broadwood is apparent at the end of the first movement of The Tempest - the calm is stiller at the end than it is in equal temperament. There's less beating in the sound. This brings greater calm. And of course the music can be disturbed too, but in Equal Temperament all the sounds are always beating and always disturbed. There are no  contrasts. It's in this that the unequal temperaments with many perfect intervals can produce dimensions of contrast beyond fast slow, loud soft, into realms of solid liquid, certain uncertain, moving and still.

There isn't enough stillness in modern life, but perfect tuning can bring it.

Best wishes

David P

[klavieronin]

If the audience knows that the piano is tuned a special way then it isn't a valid test. Also, you need an audience listening to the exact same performance but in equal temperament as a control.

I'm not saying that different tunings don't make subtle differences to the sound. I'm just skeptical that it makes the kind of difference you have been describing.

[georgey]

Hello.  I took a quick look to make sure I did not respond here before.  I fully respect others that have interest in unequal temperament.  Here are my personal thoughts on unequal temperament.

Pythagoras came very close to creating the perfect tuning system.  However, he was unable to find the “magic number” that defines the correct ratio (in my view) of frequencies in the perfect 5th interval.  Pythagoras believed this ratio is 1.5 rather than (in my view) the correct ratio of 2^(7/12)=1.49831….   For Pythagoras incorrectly believed that ALL numbers are rational (can be expressed as a ratio of 2 integers).  The correct ratio of 2^(7/12) for the 5th interval is an irrational number. I think I read where Pythagoras drowned someone for believing in irrational numbers.  Not only do irrational numbers exist, they are infinitely more numerous than rational numbers, and unlike rational numbers, they are classified as uncountable.

For over 2000 years, musicians used the Pythagoras tuning system.  Since this tuning system resulted in 3rds that sound ugly (“ugly thirds”), composers used mostly 4ths, 5ths and octaves in construction of their harmony since these intervals sounded nice to the ear under Pythagoras tuning.

In the 1600’s, composers started building harmony on triads (instead of 4ths, 5ths and octaves). As a result, people started experimenting with different tuning systems that tempered the perfect 5th.  Tempering was done so this new music built on triads would sound pleasing to the ear.  (i.e., get rid of the “ugly 3rd”).

All of the tuning systems that evolved to temper the 5th were (in my opinion) “band-aid fixes” until the correct tuning system was discovered and finally universally agreed upon (imo).  This correct tuning system that is used TODAY (I’m guessing 99% of the time) is EQUAL TEMPERAMENT.

The “band-aid” fixes to temper the perfect 5th (many of which were very creatively developed) resulted in sounds that are interesting and pleasing to some in different keys for works written in different moods.  Example for Beethoven in connection to the tuning system he was familiar with: From Wikipedia: The key of C-minor is said to represent for Beethoven a "stormy, heroic tonality"; he uses it for "works of unusual intensity"; and it is "reserved for his most dramatic music". 

In my opinion, the now universally agreed upon tuning system of equal temperament sounds best. I do enjoy hearing works performed in other tuning systems from time to time.  I enjoy a recording of the Beethoven Diabelli variations performed on a Beethoven era instrument that was tuned to a Beethoven era tuning system, for example.  I prefer harpsichord to be tuned in tuning systems common to the time the piece was written (as long as not too far from equal temperament.  Everything said here is imo.

[latrobe]

Experimentation with Pianoteq www.pianoteq.com is interesting as it allows experience of other temperaments. ET is, to be frank, boring, and in the past equal temperament often meant merely that you could play in all keys equally well.

A good test is if you play the C below tenor C, the E above tenor C, the middle C then in ET you'll hear a beating E above middle C, faint. But in a good temperament you'll hear a resultant E without beats. The good temperament enhances the harmonic structure of the instrument and gives a beautifully rich sound often with extra harmonic notes being reinforced. So this is why it's quite interesting to see how we can improve our experience of the modern instrument through tuning.

Best wishes

David P

[georgey]

Experimentation with Pianoteq www.pianoteq.com is interesting as it allows experience of other temperaments. ET is, to be frank, boring, and in the past equal temperament often meant merely that you could play in all keys equally well.

A good test is if you play the C below tenor C, the E above tenor C, the middle C then in ET you'll hear a beating E above middle C, faint. But in a good temperament you'll hear a resultant E without beats. The good temperament enhances the harmonic structure of the instrument and gives a beautifully rich sound often with extra harmonic notes being reinforced. So this is why it's quite interesting to see how we can improve our experience of the modern instrument through tuning.

Best wishes

David P

Q: ET is, to be frank, boring, and in the past equal temperament often meant merely that you could play in all keys equally well.

A: Because someone may find ET to be boring, does this make ET boring for all?

Q: A good test is if you play the C below tenor C, the E above tenor C, the middle C then in ET you'll hear a beating E above middle C, faint. But in a good temperament you'll hear a resultant E without beats.

A: Is it possible that someone can have beat hypersensitivity?

Q: The good temperament enhances the harmonic structure of the instrument and gives a beautifully rich sound often with extra harmonic notes being reinforced. So this is why it's quite interesting to see how we can improve our experience of the modern instrument through tuning.

A: It might be like 2 people discussing the best way to cook a chicken to get the best taste experience.  One says: "It MUST be roasted as follows...."

In the end, the listener or eater will make his or her choice.

Best wishes.

[georgey]

Thinking about this a little more:

It is certainly possible to go back to tuning systems of the time of Beethoven.  I hope that we can agree that the tuning must be a well-tempered system, as Bach demanded for his WTC.  At some point, it was decided to make ET the universal tuning system.

My questions (limited mostly to pianos):

If the musical experience from non-ET tuning was significantly more enjoyable than ET for the majority of musicians, would it have been possible to make the change to ET?  I would argue: No, this is not possible.  Do you know how difficult it was to make the change, for one thing?

Today, what percent of solo piano performances on modern instruments are done with non-ET tuning?  Is this percentage increasing significantly?  Are there many pianists saying: “I wish I could play on non-ET tuned pianos, but I can’t?”

My thought:  Laws of supply and demand (assuming a free market, which I will strongly argue is the case) will cause the percentage of performances of MODERN pianos tuned to non-ET to reach an equilibrium.  If this equilibrium percent is say 1%, this tells you that the large majority of pianists prefer ET.

I think it is great that you are making others aware of non-ET tuning!!  I do prefer ET for modern pianos, and other than an occasional listen for fun to non-ET, I will continue to prefer the GORGEOUS SOUND of a PERFECTLY tuned to ET, beautifully prepared, fine modern piano performed in a great acoustical environment (like I hear on most of my CDs).

[klavieronin]

That's a good point georgey. Whatever the benefits of non-equal temperament are, they clearly aren't that important to the majority of audiences or musicians, otherwise we wouldn't have equal temperament as the global standard.

[themeandvariation]

well, i don't think that the 'audience' was consulted when non-equal (-many different types)
became equal.. Nuance sacrificed - for the benefit of universally accepted proportions of pitch, which allowed the valve makers of the newly evolved woodwinds and brass to be on the same page - across Europe - allowing musicians to join together - from far and wide, and have a common harmonic platform. This smoothed out some difficulties for orchestras, and from another point of view, many composers thought that it allowed modulation to further flung keys easier to navigate... (which is somewhat questionable at least). With the advent modernism, composers much of the time preferred the non biased ET... And this perspective has also eroded - with Henry Cow, Partch, Harrison, Subotnick, the Spectralists, and beyond... Still, hearing a piano play in what some believe was Bach's tuning- (see the site LARIPS) - makes me definitely want to change the tuning of my piano for those wonderfully rich sonorities and those craggy cliffs of chromatic (slight) irregularity.  I'm totally a fan.

[themeandvariation]

I suspect this might seem provocational, but I liken the sudden decree of ET to when Constantine threw out all the various gospels, except 'the 4'.  And got all the various factions to sign on...  (There were a plethera of extant tunings in Europe) ...Now Constantine, and too, Wagner - had their 'forces'..

[latrobe]

Q: ET is, to be frank, boring, and in the past equal temperament often meant merely that you could play in all keys equally well.

A: Because someone may find ET to be boring, does this make ET boring for all?

When one has experienced colour television, then black and white is boring.

Q: A good test is if you play the C below tenor C, the E above tenor C, the middle C then in ET you'll hear a beating E above middle C, faint. But in a good temperament you'll hear a resultant E without beats.

A: Is it possible that someone can have beat hypersensitivity?

It's not beat hypersensitivity, it's what is part of the sound and what is extraneous. The unequal temperament inserts resultant notes which are part of the sound and make the sound richer in texture, more resonant and lush.

Q: The good temperament enhances the harmonic structure of the instrument and gives a beautifully rich sound often with extra harmonic notes being reinforced. So this is why it's quite interesting to see how we can improve our experience of the modern instrument through tuning.

A: It might be like 2 people discussing the best way to cook a chicken to get the best taste experience.  One says: "It MUST be roasted as follows...."

I get your point but it's actually a matter of the physics of sound. A sensitive performer will hear the effects close up even if the audience don't, and the reaction of the performer will have an effect on how the performer plays. Listening more will result in a performance that the audience listens to more also.

My questions (limited mostly to pianos):

If the musical experience from non-ET tuning was significantly more enjoyable than ET for the majority of musicians, would it have been possible to make the change to ET?  I would argue: No, this is not possible.  Do you know how difficult it was to make the change, for one thing?

It was done for the commercial reasons of manufacturers and performers were induced to work with manufacturers because they got free instruments. Chopin's letters refer to Broadwood being so nice to him he couldn't say a word against Broadwood, and Graff whose pianos he admired greatly.

Even now major brand affiliated artists I understand get financial incentives from the brand for choosing their pianos for people.

The move to ET was a commercial imperative. You certainly didn't want Mr Rich Beginner playing Chopsticks only to meet a wide F# to Bb. And ET worked with the post 1880 rise of the introduction of the 5th harmonic to the piano sound, formerly suppressed, which beat equally against rising thirds and made the sound of the instrument glisten and shimmer. Then people worshipped the brand rather than how the instrument conveyed the emotion of the music.

Today, what percent of solo piano performances on modern instruments are done with non-ET tuning?  Is this percentage increasing significantly?  Are there many pianists saying: “I wish I could play on non-ET tuned pianos, but I can’t?”

It's because the vast majority of performers haven't been aware that there are alternatives.

My thought:  Laws of supply and demand (assuming a free market, which I will strongly argue is the case) will cause the percentage of performances of MODERN pianos tuned to non-ET to reach an equilibrium.  If this equilibrium percent is say 1%, this tells you that the large majority of pianists prefer ET.

Your assumption is that pianists know that there is an option. For many suffering blinkered piano tuners there isn't.

I think it is great that you are making others aware of non-ET tuning!!  I do prefer ET for modern pianos, and other than an occasional listen for fun to non-ET, I will continue to prefer the GORGEOUS SOUND of a PERFECTLY tuned to ET, beautifully prepared, fine modern piano performed in a great acoustical environment (like I hear on most of my CDs).

And what non ET temperaments have you experienced on a modern piano? Harmonically tuned modern pianos tuned PERFECTLY demonstrate a GORGEOUS SOUND. What is your experience of such alternative?

well, i don't think that the 'audience' was consulted when non-equal (-many different types)
became equal.. Nuance sacrificed - for the benefit of universally accepted proportions of pitch, which allowed the valve makers of the newly evolved woodwinds and brass to be on the same page - across Europe - allowing musicians to join together - from far and wide, and have a common harmonic platform. This smoothed out some difficulties for orchestras, and from another point of view, many composers thought that it allowed modulation to further flung keys easier to navigate... (which is somewhat questionable at least). With the advent modernism, composers much of the time preferred the non biased ET... And this perspective has also eroded - with Henry Cow, Partch, Harrison, Subotnick, the Spectralists, and beyond... Still, hearing a piano play in what some believe was Bach's tuning- (see the site LARIPS) - makes me definitely want to change the tuning of my piano for those wonderfully rich sonorities and those craggy cliffs of chromatic (slight) irregularity.  I'm totally a fan.

Yes. But there's a proviso. LARIPS isn't the big cheese it's made out to be. Lehman turned the cypher upside down and got it demonstrably wrong. The reason for being certain of that is that in all the precedents - Werkmeister III, Kirnberger III, Vallotti, Young, 1/4 comma Meantone, 1/6 Comma Meantone, 1/7 or 1/8 Comma (Serkin) all the unequal temperaments which are likely candidates to have been used for anything and everything have one thing in common. Nice smooth home keys, C G F Bb and varying degrees of strength of the curry in F# Ab B and C#. Key colour in Lehman's peaks in three and four accidentals. Kirnberger III, Vallotti, Young and 1/6 Comma Meantone are all candidates kind to Bach's 48 and I find a variation on Kirnberger III, Kellner, to be of universal use.

For anyone curious, www.pianoteq.com provides a most excellent tool of exploration. However, the extent to which people notice a difference is dependant on how sensitively they're playing.

Best wishes

David P

[themeandvariation]

"Key colour in Lehman's peaks in three and four accidentals. Kirnberger III, Vallotti, Young and 1/6 Comma Meantone are all candidates kind to Bach's 48 and I find a variation on Kirnberger III, Kellner, to be of universal use."
Very interesting.  Thanks for that!

[georgey]

Latrobe.  Just started reading your responses now.  After my cardio workout later, I look forward to giving my view.  Thank you for taking time to respond. 

[georgey]

Here is what I am sensing after my initial read of this post, understanding that I am improvising a little:

The tuning method was changed to ET for commercial reasons, as opposed to artistic reasons.  Now, living in the new era of rapid communication via internet, and free from the tyranny of capitalism, people will come to realize the superiority of non-ET tuning (since ET is boring, like black and white TV), and there will be a revolution as the musical world has never seen.  Now all we have to do is get the word out  .

Now I will re-read and address each point.  Understand – my comments here are just for fun.  There is no way anyone can win in a discussion like this.  So, I am just having fun here.

Q: When one has experienced colour television, then black and white is boring.

A: I can’t say for sure that you do not have an additional sense perception regarding music color that I lack.  But how can you say for sure that you aren’t simply looking at the color of the actors’ clothing and background scenery during a color televised production of a Shakespear’s play, while not listening to or understanding the content of the play?

Q: It's not beat hypersensitivity, it's what is part of the sound and what is extraneous. The unequal temperament inserts resultant notes which are part of the sound and make the sound richer in texture, more resonant and lush.

A: Sounds like it could be beat hypersensitivity to me.  Piano strings exhibit inherent inharmonicity.  What would you call someone who refuses to listen to piano music for this reason, and will only listen to piano music performed on a pipe organ with its more even distribution of overtones.  The listener says: “I find the piano’s inherent inharmonicity to be disruptive to my listening experience.”?

Q: I get your point but it's actually a matter of the physics of sound. A sensitive performer will hear the effects close up even if the audience don't, and the reaction of the performer will have an effect on how the performer plays. Listening more will result in a performance that the audience listens to more also.

A: I get your point also, but I find the piano’s inherent inharmonicity to be disruptive to my listening experience.  It’s actually a matter of the physics of sound.  A sensitive listener will agree with this.

Q: Your assumption is that pianists know that there is an option. For many suffering blinkered piano tuners there isn't.

A: My question still remains:  Today, what percent of solo piano performances on modern instruments are done with non-ET tuning?   In addition, in this age of the internet, what do you see this percent being in 20 years from now?  100 years from now?  What would you think if you could see in the future 100 years from now and learn that ET is still the universal tuning system? Would you conclude that there is a massive conspiracy to suppress the will of the people?  Could you ever envision a scenario where you would conclude that ET is actually the preferred tuning method of musicians or is this an impossibility?

Q: And what non ET temperaments have you experienced on a modern piano? Harmonically tuned modern pianos tuned PERFECTLY demonstrate a GORGEOUS SOUND. What is your experience of such alternative?

A:  I have listened to maybe 20 samples that were put on Pianostreet in past threads (maybe a year or 2 ago).  I will take time to listen to the examples in this thread in the next few days.  I’m sure I will enjoy it.  Sorry for my silly answers here! 

[klavieronin]

When one has experienced colour television, then black and white is boring.

I couldn't disagree more. If the film is well made and the photography well executed then that is all that matters. There is a real art to filming in black and white and merely adding colour not only won't do anything to improve the experience of the audience but in some cases it could, in fact, subtract from the experience.

I think a more suitable analogy would be adjusting the contrast on your television set. Non ET tuning might give better contrast and a clearer picture but that's not where the substance of the film/music lies.

Again, I'm not saying the ET is best, and that non ET doesn't sound better for certain music. I just think you are blowing the difference slightly out of proportion.

If I listen very carefully and compare short phrases in different tunings side by side, then I can definitely hear the advantages of non ET tuning in certain keys. When I'm listening to Claudio Arrau play the Beethoven sonatas, or Vladimir Ashkenazy play Chopin's 24 Preludes, the shortcomings of ET fall so far into the background that, IMHO, it's not even worth considering.

[georgey]

I couldn't disagree more. If the film is well made and the photography well executed then that is all that matters. There is a real art to filming in black and white and merely adding colour not only won't do anything to improve the experience of the audience but in some cases it could, in fact, subtract from the experience.

I think a more suitable analogy would be adjusting the contrast on your television set. Non ET tuning might give better contrast and a clearer picture but that's not where the substance of the film/music lies.

Great analogy (except ET gives me better contrast and a clearer picture).  I bought a copy of Schindler's List 20th anniversary edition a few weeks ago and it has just been sitting on my coffee table.  That reminds me that I should watch this.

[latrobe]

My analogy was Colour and Black and White TV, not film as a specific artform.

Were your computer screen now to revert to black and white this instant you'd go up in smoke with frustration being unable to find things quickly. Colour is a clue, as is the shape of chords in unequal temperament. Temperament gives subtle and less than subtle clues to the journey through a piece.

I've now been tuning in unequal temperaments, mainly Kellner, a variation of Kirnberger III for 12 years, done the experiments and recorded them as meticulously as possible making them public through YouTube and other sites.

It's now easy as never before to experiment with modern and historic instruments listening carefully to harmonic structure and interaction of instrument with tuning with repertoire through Pianoteq www.pianoteq.com and I urge all interested to download and conduct the experiments themselves.

A major problem has been the intransigence of stuck-in-the-mud unenlightened piano tuners who stick with Temperament Boring and Passé (TB&P) just because they don't know how to do anything else and don't want to. For many musicians the acoustic piano has to adapt with technicians competent to meet the demands of those who have been enlightened, or face redundancy of the acoustic instrument through the rise of such an adaptable electronic alternative.

Best wishes

David P

[klavieronin]

It's now easy as never before to experiment with modern and historic instruments listening carefully to harmonic structure and interaction of instrument with tuning with repertoire through Pianoteq www.pianoteq.com and I urge all interested to download and conduct the experiments themselves.

And indeed, here is one such experiment I conducted myself on this very forum;

https://www.pianostreet.com/smf/index.php?topic=64749.msg685960#msg685960

Unfortunately it didn't get much of a response so the result don't really say much. I also think that the experiement could have been better executed if people didn't know each recording was using a different tuning.

[latrobe]

The fact that you didn't get much response doesn't invalidate the experiment nor the findings and the samples are there for all to hear.

Part of what a harmonic temperament does is to gel the sound together, to make it cohere and in this the difference is rather that of the difference between ordinary and laser produced light.

Best wishes

David P

[klavieronin]

The fact that you didn't get much response doesn't invalidate the experiment nor the findings.

A large sample size is important in any experiment. My experiment got 11 votes. I just rolled a dice 11 times. Here are the results;

1: 1
2: 2
3: 1
4: 3
5: 3
6: 1

From these results I can conclude that dice a more likely to land on 4 or 5 than any other number.

That is why large sample sizes are important in any experiment.

[latrobe]

But I think that as a musician you can rely on your own discernment and see whether you have a correlation with others. In this case the dice was loaded by reason of people here exercising some discernment, so the experiment isn't as flawed as you'd like to think.

As a musicologist I have to ask why a composer might have chosen something that tweaks our ears. The sample of music that you've chosen isn't very complicated. So it's a start but not the whole cheese. One has to listen with a good deal more sustaining pedal to see how the sounds interact, and as a tuner this particularly influences my choice.

Best wishes

David P

[klavieronin]

I think you are missing the point. My experiment got 11 votes. The results were;

Equal temperament: 2 votes
Non-equal temperament: 9 votes

You can't assume that those proportions would remain the same with more votes; If 100 people voted the results could have been;

ET: 15
Non-ET: 85

or it could have been;

ET: 45
Non-ET: 55

or anything else really.

There is a big difference between those results. One is statistically significant, the other isn't. And you never can tell what it would have been until you do the experiment. Plus, like I said earlier, the fact that people knew different tunings were being used leaves the experiment more open to bias, which is a problem.

[georgey]

I think you are missing the point. My experiment got 11 votes. The results were;

Equal temperament: 2 votes
Non-equal temperament: 9 votes

You can't assume that those proportions would remain the same with more votes; If 100 people voted the results could have been;

ET: 15
Non-ET: 85

or it could have been;

ET: 45
Non-ET: 55

or anything else really.

There is a big difference between those results. One is statistically significant, the other isn't. And you never can tell what it would have been until you do the experiment. Plus, like I said earlier, the fact that people knew different tunings were being used leaves the experiment more open to bias, which is a problem.

As a mathematician and statistician, I can assure you that the basic element in polling is the concept of RANDOM SAMPLING. This rules out on line polls.  Then comes sample size required to get a 95% confidence interval, +/- 3% (would be ideal). 

However in this case, I feel it would be much more beneficial to poll the professional musical community, who are in a position to make informed opinions.  I would suggest taking a random sampling of sufficient size from this group.  Anything short of this scientific poll is USELESS (unless you are Donald Trump).

Why poll the professional musical community?  So you don't end up with results like:

Q:  Is the earth flat or round?  Let's vote on it.
A:  The poll reveals the earth is flat.  Therefore, the earth is flat.  Sorry all you believers in round earth.

Q: Is there global warming caused by human activity?  Let's vote on it.

Results from general population might be: 47% believe global warming exists and is caused by human activity.

Result from scientific community: 97% believe global warming exists and is caused by human activity.

OR, rather than scientific polling, maybe you prefer the Donald Trump method:  My gut tells me that non-ET is better, therefore it is so.  The only problem with this is: Donald Trump may not agree with you and his gut is the only gut that determines the truth. 

[latrobe]

Oh no. It's not that DT's gut knows the truth but that his gut knows guts better than us LOL.

The reality is that on some of those samples rather detuned notes were significantly audible and the voting sample were discerning enough to reject those tunings.

A reality is that the unequal temperaments can give a stillness against which notes can sing, and this is in contrast to equal temperament where everything is constantly moving.

is an example.

Best wishes

David P

[georgey]

The reality is that on some of those samples rather detuned notes were significantly audible and the voting sample were discerning enough to reject those tunings.

"Voting sample" done is not that of a scientific poll. 
1) it is not a RANDOM SAMPLING (cannot be an online poll, sorry)
2) the size of the sampling was insufficient
3) those polled may not have been members of the professional musical community

The results of this poll are USELESS (unless you are DT).  Sorry.

Unless you want to use your gut and deem them to be useful.  Which is fine!

[latrobe]

Hang on. The common sense exercised in the discrimination between good and less good was obvious. 3 and 5 had noticeable bad intonation without focussed musical reason or intention of effect and although the voters were few in number the tunings which were audibly deprecated correlated with low (no) scores. The statistics are clearly nuanced with significance.

Best wishes

David P

[georgey]

Hang on. The common sense exercised in the discrimination between good and less good was obvious. 3 and 5 had noticeable bad intonation without focussed musical reason or intention of effect and although the voters were few in number the tunings which were audibly deprecated correlated with low (no) scores. The statistics are clearly nuanced with significance.

Best wishes

David P

Common sense = gut.  You convinced me!!!  Best wishes.

[klavieronin]

Here is my proposal for a better experiment;

Create two recordings of the exact same performance, one in equal temperament, one in your favourite non-equal temperament (easy to do with today's software). The performance should consist of a variety of music from different periods.

Get a large sample of trained musicians (500 or so) with varying backgrounds and randomly split them into two groups.

Give one group the ET performance and the other group the non-ET performance.

Don't tell them the purpose of the experiment. Just ask them to listen to and rate the performance.

If the non-ET recording gets a significantly higher score than the ET recording, then you will have good evidence to support your hypothesis.

[georgey]

Equal temperament: 2 votes
Non-equal temperament: 9 votes

I don't want to leave this thread on a bad note!  When I say the results of the poll are useless, I mean only from a scientific point of view.

Let us assume that 9/11 = 82% of the professional musical community prefers non-ET tuning (as the poll suggests, non-scientifically).  We may then expect to see more performances of modern pianos using non-ET tuning in the future.

Can anyone give me a suggested CD of solo piano played on a MODERN piano with non-ET tuning (preferably post Mozart, but Bach is good) that I can buy?  I do not mean a home made CD, but a CD available to the public from a notable CD manufacturer.  A selection of CDs would be nice.  Would love Beethoven, Chopin, Brahms or others.  Thanks if you can help me find one.

[georgey]

Here is my proposal for a better experiment;

Create two recordings of the exact same performance, one in equal temperament, one in your favourite non-equal temperament (easy to do with today's software). The performance should consist of a variety of music from different periods.

Get a large sample of trained musicians (500 or so) with varying backgrounds and randomly split them into two groups.

Give one group the ET performance and the other group the non-ET performance.

Don't tell them the purpose of the experiment. Just ask them to listen to and rate the performance.

If the non-ET recording gets a significantly higher score than the ET recording, then you will have good evidence to support your hypothesis.

Just noticed this now.  My thought:  All of the musicians would know which are ET and which are non-ET by virtue of their training and ear development.  If I received 1 of the CD's and rated the performer, I would not be thinking of the tuning, since I was not asked to evaluate the tuning.  I might instead send both CD's to each of the 500, with same pieces and performer on each and ask which tuning they prefer.  Would need to be a random sample to have scientific value.  Sample size of 500 might be good.  Would have to calculate needed sample size based on an assumed total sample population.  How many professional musicians in the world?  In reality, doing this poll would be very challenging.  It would have to be sponsored by a major university or other organization for people to respond.  Many would have to be involved in preparing the study, musicians and a couple statisticians, etc.

Time should tell us without polling.  If the interest grows in non-ET, we will see more performances using non-ET.

[klavieronin]

If I received 1 of the CD's and rated the performer, I would not be thinking of the tuning, since I was not asked to evaluate the tuning.  I might instead send both CD's to each of the 500, with same pieces and performer on each and ask which tuning they prefer.

But I think it is important that participants are unaware of the purpose of the experiment. If they know they are evaluating tuning systems then they would be more likely to be influenced by their own bias.

If you are testing the effectiveness of a new drug, for example, you don't give all the participants the drug and the placebo then ask them which one they think works best.

Remember, latrobe's claim is that non-ET gives a significantly better listening experience than ET. In this case ET would be the placebo and non-ET would be the real drug. If it's really true that non-ET gives a better experience you would expect the non-ET recording to get a higher rating, regardless of whether or not people noticed that it was non-ET.

[georgey]

But I think it is important that participants are unaware of the purpose of the experiment. If they know they are evaluating tuning systems then they would be more likely to be influenced by their own bias.

If you are testing the effectiveness of a new drug, for example, you don't give all the participants the drug and the placebo then ask them which one they think works best.

Remember, latrobe's claim is that non-ET gives a significantly better listening experience than ET. In this case ET would be the placebo and non-ET would be the real drug. If it's really true that non-ET gives a better experience you would expect the non-ET recording to get a higher rating, regardless of whether or not people noticed that it was non-ET.

Just to disclose:  I am a retired actuary.  We used statistics and actuarial math for valuation of defined benefit pension plans.  We never did polls, although we were taught the mathematics required to poll as part of required math courses taken in college.  I don't want anyone to think I am a polling expert.

"influenced by their own bias." - This is something we did not study, since not math related.  I understand what you are saying about a placebo.  The problem is, every musician would know just by listening, and not being told anything, which are ET and which are non-ET.

This would be a great question for a statistician that specialized in polling.  Experts from polling math, polling methods, musicians would have to work on this. 

I don't see how this can be done blindly. In the case of a pill, the taker would have no idea what was in the pill.  In the case of tuning, every trained musician will know if something is non-ET.  They may not know which non-ET they are hearing, but they will know that it is non-ET and also know if it is a fairly close match (as in case for some well-tempered systems) to ET.

[klavieronin]

I don't see how this can be done blindly. In the case of a pill, the taker would have no idea what was in the pill.  In the case of tuning, every trained musician will know if something is non-ET.  They may not know which non-ET they are hearing, but they will know that it is non-ET and also know if it is a fairly close match (as in case for some well-tempered systems) to ET.

I agree, it's probably impossible to have a true blind test with trained musicians but I'm willing to bet that some percentage of people, even among trained musicians, wouldn't noticed non-ET if they weren't specifically listening for it.

Perhaps the whole temperament debate is really between those with more sensitive ears vs. those with less sensitive ears… perhaps.

[latrobe]

Can anyone give me a suggested CD of solo piano played on a MODERN piano with non-ET tuning (preferably post Mozart, but Bach is good) that I can buy?  I do not mean a home made CD, but a CD available to the public from a notable CD manufacturer.  A selection of CDs would be nice.  Would love Beethoven, Chopin, Brahms or others.  Thanks if you can help me find one.

With a friend we demonstrated the effects of temperament

using a modern instrument.

I also demonstrated the way in which Mozart was able to use temperament to convey expressions of sadness, remorse at the grave and celebrate the life of a military hero by the interaction of just two ranks of organ pipes with temperament

in a way more subtle and effective than the huge instrument renditions we're accustomed to.

I've published many videos

upon which the comments are visible for all to see.

The statistics are meaningless if collected from people who don't know what the music is about. But musicians who know what they're doing can exploit temperament as part of the toolbox with which they work to encourage people to be more attuned to what they're listening to and the meaning of the music.

Audiences might not _like_

but this performance connects the Beethoven sonata very directly to the mysterious and supernatural of the Shakespeare play from which it was derived.

The modern piano manufacturers brought forward the equal temperament to bring forward an equally glassy sound from the instrument so that people admired the brand of the instrument but which covered over the meaning of the music behind a layer of ice.

There are many recommending now "minimum entropy" tunings which stretch the octave, and stretch the thirds even more.

Much about tuning is how one plays and whether one is sensitive as the performer to the nature of the vibrations of the tuning. This is why Bach's 48 have to be played choosing the right organ stops for the key

Taking a poll on the lines you indicate is about as valid as the Brexit referendum, which only now many see as leading to disaster, or as to whether they like the sound of Chinese without understanding its meaning.

It's more of a matter of exploration and finding people of discernment who have come to recognise the musicality they've been looking for. https://www.forum-pianoteq.com/viewtopic.php?pid=958754#p958754 is an excellent example:

As a piano tuner and rebuilder who has just started to play around with this software and my new to me Roland RD2000, I would like to commend Moddart for including such a delicious range of temperaments and pitches. I routinely tune in historic temperaments for my clients, and have a favorite Well Temperament which is my go-to for historic performance and my own playing. I don't know whether I can publish it here - would need to get permission, I expect.

Many piano tuners now use Electronic Tuning Devices (EDT's), and the more adventurous of us will talk up alternatives to ET and 440 pitch just to vary the playing experience for the client. I remember what a revelation it was when I was in tuning school to learn how to tune Meantone, Marpurg, Werkmeister III, and Valotti-Young (etc.) and then put them on my parent's Steinway Model II and play the Fitzwilliam Virginal Book,  Rameau, Couperin, Schubert and Brahms. Completely different playing experiences than equal temperament. More expressive and with built-in vibrato speeds!

Maybe your tuner (if s/he has an EDT,) would be more than happy to accommodate your interest in historic temperaments on your upright!

and likewise a wider appreciation by technicians and tuners of the interest that people find in the music by way of exploring the issue of temperament. It's a matter of awareness and that awareness is growing.

Best wishes

David P

[klavieronin]

latrobe, the comment below is another reason why I think you might be making way too much of the difference between ET and non-ET;

[T]his performance connects the Beethoven sonata very directly to the mysterious and supernatural of the Shakespeare play from which it was derived.

Beethoven never gave his Op.31:2 sonata the name "Tempest" and it was never even called that in his lifetime so there is no reason to assume that the sonata was derived from the play.

[latrobe]

That's just the point. Beethoven told his publisher when asked what the Tempest was all about to go and read Shakespeare. When heard in normal tunings, the point is lost. The other day a pianist visited who's normally very good. But he started playing it and I had to bite my tongue as his playing clearly understood nothing about the piece. In contrast when you listen, and I mean listen, to the piece played through the lens of meantone there are passages that sound perfectly normal, and other passages which take you through the realms of the supernatural, weird things going on and the piece fits squarely within Shakespeare's "The Enchanted Isle". The Italian commentary on the play is rather good so use Google Translate on https://it.wikipedia.org/wiki/La_tempesta

But you have to cease to hear the scale notes as "out of tune". It helps to hear

first to immerse oneself into the idiom of the sound. This is F minor. The key of death, grief and mourning. Inconsolable despair. The slough of despond. The use of specific keys by composers for specific emotional effect is real. And it's not imaginary. You can hear it. It's not as invisible nor as inaudible as j.

The temperament reveals j at work.

Best wishes

David P

[klavieronin]

Beethoven told his publisher when asked what the Tempest was all about to go and read Shakespeare.

That's just not correct. He told his associate and secretary Anton Schindler to read the tempest when he asked how to interpret Op.57 ("Appassionata"), not Op.32, No.2.

This is F minor. The key of death, grief and mourning. Inconsolable despair. The slough of despond.

What are you basing this on? What does it even mean? What the hell are you talking about?!

Are you saying that F minor is the best key for depicting death, grief, and mourning? If so, why did Chopin choose C minor for his famous funeral march, both in his sonata and the "funeral march" prelude? And what about Shostakovich's String Quartet No. 15? That contains numerous references to death yet is in the key of E flat minor, the same key as Rachmaninoff's Elegie, Op.3, No.1? There are tons of other examples not to mention works in F minor, such as Chopin's F minor Ballade, that are not about nor are meant to evoke death, grief and mourning.

I'm sorry but not everyone perceives music the way you do and I am certain that if you were to look closely enough you would realise just how susceptible your perceptions are to your own bias and other influences. There is nothing concrete you can say about the key of F minor, or any other key, other that the frequency of the notes and how they tend to relate to one another within the context of the piece of music.

Also remember that up until a few hundred years ago there was no such thing as F minor. Composers wrote in modes not keys.

[latrobe]

The comment taking issue with the connexion between Beethoven's Tempest Sonata and the Shakespeare play indicates desire merely to be disputatious in this thread beyond the bounds of objectivity or accuracy. You only have to listen to the recording of the meantone performance on a contemporary instrument to actually hear the connexion. But I don't think you're listening.

The connexion is well documented and mentioned numerously https://www.google.com/search?q=beethoven+schindler+sonata+shakespeare

F Minor and C minor had similar characteristics. This was on account of the narrow minor third and painfully wide major third in these keys. See Schubart's description of the emotional effects and which are audible in Meantone and the stronger Well Temperaments.

You'll find a lot of information about keys in my paper THE COLOUR OF MUSIC IN MOZART'S TIME

If you haven't started to explore the repertoire listening to the effects of unequal temperaments then it won't be possible for you to understand at all. It's like trying to explain to someone who can only see the ultraviolet spectrum what green looks like with respect to red.

There are numerous reasons why an unequal temperament does rather good things both for the instrument and for the performer. See the message number 40 by expert technician Ed Foote - https://my.ptg.org/communities/community-home/digestviewer/viewthread?GroupId=1201&MID=321300&CommunityKey=db37c207-645e-4915-9e58-72396721b77c&tab=digestviewer

there is something that has not been brought up in the assessment of UT's., and that is their effect on the performer. This may, ultimately, have more to do with what we are hearing than the frequencies, and perhaps have some bearing on the reasons for some people not hearing a difference. I have been told numerous times that after tuning an unequal, circulating temperament, the piano feels like a different piano; a bigger piano. The pianists that are sensitive to what sound is coming out of the piano, (and not all of them are), tell me that there is a clarity to the music that they were unaware of before. This may sound strange to those of us that are particularly sensitive to wider thirds or busier fifths, but it is a fact that this is how most of the tunings I sell are perceived. (I also have a number of customers that don't hear a difference, and several that have had their piano retuned as quickly as I could get back there and do it.) The pianist that is sensitive to the difference quickly finds out that original pedal markings can be far more closely followed without the "muddiness" that traditionally has been blamed on the modern pianos' greater sustain, i.e., the beginning of the Waldstein's third mvt. has, I believe, 17 bars with the pedal to be held down. Try this on a ET and it will quickly turn to a blur. Performed on a Young or Vallotti, it becomes an orchestral landscape, building huge harmony. Which would the musicians of the time have preferred? That is an easy shot, as we are talking about the key of C. However, a Brahms intermezzo in E was what brought one customer to tears,( and astounded me), telling me that he had never heard it sound like that, but had always thought it should. Another well traveled concert pianist has even commented that after coming to an understanding of how a well-tempered piano responds, she is able to partially fake it on ET pianos by giving more expression to the playing of the music, that the modulations now "mean" more than they did. So, we have the evidence that players sensitive to harmonic values change how they phrase when we change the tuning. Pianists that don't listen will, of course, have no image of what this is all about.

It really is about listening and experiencing.

You'll find the particular reasons why the UT brings a more coherent sound to the instrument on https://www.pianostreet.com/smf/index.php?topic=65531.msg691986#new. Perhaps with your statistical background perhaps you might start to examine the mathematics of numbers of harmonics that fall onto scale pitches or within say 2 beat per second middle octave in a minimum entropy tuning, an equal temperament tuning, and say Kirnberger III with 7 perfect fifths.

Best wishes

David P

[klavieronin]

Okay, so after a little more reading it seems that Beethoven may indeed have seen a connection between his Op.31, no.2 sonata and Shakespeare's play, but many scholars are skeptical about this claim and no one know for sure what Beethoven really had in mind when he wrote the sonata, and that includes you, latrobe.

However, even if you are right, it still doesn't validate many of the claims you are making. I'm willing to accept that UT has musical advantages over ET (and some disadvantages) but the idea that certain keys represent certain ideas/concepts/emotions, and that UT conveys these while ET fails to do so, is highly debatable IMO. It makes you sound like a tarot card reader or a numerologist.

[latrobe]

If you _listen_ to the meantone performance of the Tempest then the interference of the supernatural and the ethereal is audible and the music itself proves the connexion for those who have musical ears to hear. The fact that you appear not to be able to do so, together with a disputatious approach towards that which is readily researched merely to demonstrate yourself to be Kleverer than others somewhat disqualifies your opinions in this thread from having much weight.

There are a long history of technicians and musicians who have come to the same conclusions as I did and of whom I was not aware who have all experimented and reached those conclusions which coincide independently, and clearly including myself they are all wrong upon your opinion.

The outline of the theory is I believe cogently and succinctly summarised on https://www.pianostreet.com/smf/index.php?topic=65531.msg691986 and the implications for resonance and for historic pedalling are confirmed in practice by Ed Foote, as quoted above, who is a senior technician and musician and who tuned for the recordings of Enid Katahn.

Particularly impressive is her demonstration of Mozart in D minor in Meantone which aurally communicates as Schubart indicated the key to communicate.

For a dozen years I have experimented, made recordings with numerous artists and published the results mainly on Youtube. The comments of those with ears and minds better attuned than yours appear to be are there for all to see.

Of course Equal Temperament has no variations of the size of intervals in different keys. All beat the same. Accordingly it is disabled from contrasting still intervals with moving intervals displaying beats, some quite fast. In particular the Tartini tone of a major third in Equal Temperament is two octaves less a quarter tone below the chord, discordant and very annoying to any musician who has heard it. When an unequal temperament is used, some Tartini tones are exactly in tune and others are so far away from an expected note they are dissociated and not relevant to the music. Accordingly there are many contrasts between different keys of which ET is unable to express. ET is the disabled man of music.

The area in which you have expertise is statistics and you might usefully apply your professional skill as I have suggested to a measurement of the coherence of the minimum entropy, standard or stretched octave equal temperament scales with the first 6 harmonics of the vibrating strings vs the same in one of the perfect 5th temperaments, Werkmeister III, Kirberger III, Kellner or Vallotti.

Best wishes

David P

[lostinidlewonder]

Unequal temperament? Bah, ugly. I'm not going to pretend it makes it any better or more interesting and yes I have a great ear lol.

[latrobe]

Unequal temperament? Bah, ugly.

Ugly? Kindly give an example of one of my non-meantone recordings which are ugly.

If you happen to know the Brahms Violin Sonata No 2 in A major then you might find this recording

different. I have turned pages for the accompanists performing this on a number of occasions over three decades, but this performance which was the only one tuned to an unequal temperament did something special. It creates an atmosphere of calm which ET performances lose.

and yes I have a great ear lol.

LOL indeed. This will test how good your ear is

and as to whether you can distinguish between a major and a minor semitone.

Best wishes

David P

[klavieronin]

If you _listen_ to the meantone performance of the Tempest then the interference of the supernatural and the ethereal is audible and the music itself proves the connexion for those who have musical ears to hear. The fact that you appear not to be able to do so, together with a disputatious approach towards that which is readily researched merely to demonstrate yourself to be Kleverer than others somewhat disqualifies your opinions in this thread from having much weight.

Well then, I guess there is nothing more for me to say. However, you might find this interesting;

[lostinidlewonder]

Ugly? Kindly give an example of one of my non-meantone recordings which are ugly.

There is no need to I have just said it is all ugly no matter who records it.

If you happen to know the Brahms Violin Sonata No 2 in A major then you might find this recording ... different.

Yeah different in an ugly sense. There is no need to try and make your reply look any more convincing by posting useless videos.

I have turned pages for the accompanists performing this on a number of occasions over three decades, but this performance which was the only one tuned to an unequal temperament did something special. It creates an atmosphere of calm which ET performances lose.

Yeah a special kind of ugliness. 3 decades of page turning congrats lol.

LOL indeed. This will test how good your ear is

And now your delusions of granduer comes through, you all of a sudden believe that you must be able to hear something amazing that we cannot. Who needs to test it, I already think it is ugly, your video is looking at the atoms of music, look at the whole picture. Tuning a modern pianoforte to unequal tempermant is very odd and stupid in my opinion. Terrilby ugly, reveals nothing interesting except for those who think they have some elite knowledge and appreciation for the secrets of music from this odd tuning. It is just all a little too silly. I'm not sorry for bursting your bubble.

[latrobe]

However, you might find this interesting;

Yes - a particularly good video and most helpful.

Some of these tunings are close to what we hear in meantone with near 1/4 tone C to C# and F to F#. They're very audible and give unmistakable colour.

The composers of the 18th century and early 19th century would have been much closer to the rural scene than we are, and the "raw" nature of traditional instruments and tuning. So much of Chopin's work comes from the rural dance culture, to which he applied a finesse akin to the nimbleness of foot in such dances. This is why looking towards the pantalon, the hammered dulcimer and their tunings is appropriate. One of my sons has been exploring the region from Herzegovena to Georgia. He reports that tuning in some regions still takes particular account of major and minor semitones and people are attuned to them.

For those who haven't come across this concept, a major semitone is 5/9ths of a tone and a minor semitone is 4/9ths of a tone. 1/9th of a tone, known as a comma, might seem to be splitting hairs but it's audible as demonstrated in the video referred to. These ideas are not uncommon to well attuned singers and violinists who raise leading notes to give smoothness of melody.

Re-introducing nuances of tuning adds interest to music.

Best wishes

David P

[latrobe]

There is no need to I have just said it is all ugly no matter who records it.
Yeah different in an ugly sense.

Evidence please. Or otherwise your post becomes otherwise a reflection only of your own performance.

Oh yes. Must be ugly.

Your post is incomprehensible.

Best wishes

David P

[lostinidlewonder]

Evidence please. Or otherwise your post becomes otherwise a reflection only of your own performance.

Are you senile? Why don't you provide me evidence also for your opinion? Posting videos and saying it's so good is not evidence. So it is just a matter of opnion isn't it? You are being moronic if you think everyone has to agree there is something special in changing the tuning or that we all must agree it reveals something very very interesting, to me it does not at all and in fact distracts more than enchances.

Why dont you provide evidence that my post is a reflection of my own performance? Why would I want to perform on an unequal temperament piano when I think it sounds ugly? Your logic is killing kittens.

Well there is sufficient evidence that you are a spammer of videos. You have posted this video in another thread also without any reason. Can you explain why you post a video which has ZERO to do with the disccusion? Quite stupid.

Your inability to accept other peoples opinions different from yours and your need to replace your ideology over their own shows your severe lack of confidence in your own opinion. Your ramblings of experience with unequal tempermant highlights your delusional state of grandeur.

[klavieronin]

Here is a well thought out and clearly written article in defense of ET. It makes some excellent points IMO;

https://my.ptg.org/blogs/larry-lobel/2011/08/24/in-defense-of-equal-temperament-part-i
https://my.ptg.org/blogs/larry-lobel/2011/08/24/in-defense-of-equal-temperament-part-ii

[latrobe]

Why dont you provide evidence that my post is a reflection of my own performance? Why would I want to perform on an unequal temperament piano when I think it sounds ugly? Your logic is killing kittens.

Oh yes. It clangs and sounds ugly. Clearly

The comments on the videos on YouTube are of significant variance with yours.

I'm organising a seminar on temperament on 6th May 2019 in England and were you to come you'd meet a number of musicians and technicians of variance to your opinion. Perhaps you might find it interesting to meet them.

One of the most interesting things is the extent to which a harmonic tuning can improve the sound of the instrument as well as making sense of original pedalling of Chopin and Beethoven.

If klavieronin might like to use his statistical skills there is mileage in comparing coincidence of harmonics with scale notes within 1 Hz in equal temperament, stretched equal temperament, and one of the perfect fifth temperaments such as Kirnberger, in total, and in the 7 notes of each key's scale.

Best wishes

David P

[ronde_des_sylphes]

Out of curiosity..

I listened to a couple of the above samples, and didn't feel that they were tuned in the same way. The Chopin second sonata I had no problems with, but some of the minor seconds in the Tempest really weren't pure minor seconds in the conventional sense at all (eg the D#, E at 2.15).

[latrobe]

Yes - you're spot on.

The Chopin 2nd Sonata recordings have all been in Kellner Bach temperament but the 1802 Beethoven Tempest was in Meantone, and the 1819 and 1859 instruments were in Kirnberger III which narrows some semitones towards and in the spirit of meantone which narrows CC# D#E F#G AbA BbB as indicated well by the Pianoteq diagrams attached.

is the Beethoven sonata in Kellner, although a change in temperature as the evening progressed detuned the instrument.

As a result of checking the Shakespeare connexion (thanks) it was a pleasure to find

by Paul Badura-Skoda and discovered that the similarity of performance wasn't coincidental. So there we have quite a good comparison in what I assume in 1954 was Equal Temperament.

Best wishes

David P