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What I find interesting about the statement is that it leaves open to personal taste precisely which 5ths to alter. This flexibility would allow some ability (if one knows how) to move the bitter keys around a bit (if one so desired).

Peter Grey Piano Doctor

Thanks, Peter.

The excerpts stem from CPE Bach's introduction to his "Versuch über die wahre Art das Clavier zu spielen, mit Exempeln und achtzehn Probe-Stücken in sechs Sonaten".
I.e. his "Treatise on the proper manner to play the clavier/keyboard, with examples and eighteen practice pieces in six sonatas".

In that introduction, besides going on a rant about unrefined playing style, he includes issues of touch and tone and playing technique. He mentions both the clavichord and the grand piano, describing them as the most lauded examples of clavier (keyboard instruments) at that time. He describes the "new fortepiano", if well-built, as having many merits, but still finds the clavichord, in spite of its weaker tone, to be the best instrument to evaluate a keyboard player. In other words, the clavichord and the fortepiano ("Flügel" = grand piano) are the two instruments to which section 14 refers in terms of tempering.

Got it. Thx

Peter Grey Piano Doctor

Greetings,
I have tuned clavichords in the past and they really aren't a fixed-pitch instrument. Since their pitches are touch sensitive, notes land within approx. 4 cents of their target when playing, and that range is beyond most well-temperaments' deviations from ET. In short, the bebung can't be banished and clavichords offer vague examples of tempering beyond perhaps changing a G# to an Ab if using a meantime approach. I have drawn the most epiphanies when I put a 18th century tuning on a modern grand where the 'colors' stand out.

And:

Ah, yes, I have heard this argument buttressed and supported by a wide range of people over the last 30 years I have been on my mission. And yes, my mission is to educate who I can that there is more than one way to divide an octave. As far as I have been able to research, the academic evidence comes down on the side of Bach's use of unequal temperaments.
However, I am not baffled by those that yearn to lay more kudos on the shrine of equality due simply to the beauty found in the mathematical elegance of democracy of an equal temperament. Once the goal of a realized ideal is attained, there is nothing left to do by naysay any alternative. What I am baffled by is people that can listen any of the preludes or fugues in ET and WT and not really know that they are hearing anything different.
They that have ears, let them hear. Discernment of the emotional impact that another temperament can make is a learned skill. However, leaving the audience out of the equation and simply taking pianists' responses, I have had them overwhelmingly prefer temperaments with. texture and a tonal center. Lack of equality is not a death-knell to modulation, a 18 cent third will not bring a performance crashing down and very few of my customers have ever considered returning to ET after a week or more with an alternative. I do this for money, so I am not talking theory here. There is a market for non-ET work around here and around much of the country, I am told.

Well it's too late for me to start raking in dosh by using other temperaments...
But more seriously, i can't agree that any emotional impact can be a learned response. I don't think emotion works like that. Emotions hit or they don't in my opinion. It's intellect that "learns" response.
Just my view, not expecting everyone or even anyone to necessarily agree.

Incidentally, i have experienced exactly the opposite reaction, even from harpsichord concert hall when their tuner couldn't do it so I stood in but told them I could only "guarantee" an ET tuning. They usually used some other temperaments. They called me next day to say it had never sounded better and they were going with et from then. I also tuned for years for a well known harpsichord player who had many old instruments at his home. He two pianos, one ordinary upright, one Steinway and all his old squares, virginals, harpsichords etc. were in old temperaments. I asked him if he'd like me to match the pianos to his chosen temperament (he tuned all his own instruments except the pianos) and he said goodness no, they'd sound awful, he only liked his old temperaments on instruments that had no sustain!

So my whole living has been based on ET, as good as I can manage it and as all my work has come from recommendation, I've never advertised, ET can't be too bad.

I mention these things not to argue whether you are right or wrong, just to say that the discussion may well be about preference rather than "education".

One client of mine who insists on UT ever since she tried it said: "I like it because it gives me the ability to resolve that I cannot get in equal temperament". This is doubtlessly due to the fact that these effects are "baked in" to the music. This comment told me that she really has "ears" since I never suggested anything other than "try it and see what you think". I have other clients that immediacy go for the spicier keys and ooh and ahh and wow over them.

OTOH I have a few who definitely prefer ET. They hear the difference for the most part and prefer the consistency.

Peter Grey Piano Doctor

Ed,

Yes, in that same text CPE Bach actually mentions the touch-sensitive pitch of clavichords as one of the reasons that he prefers them over a pianoforte, because he can add pressure to his touch after having played the note.
Thanks for clarifying that this pitch variation can actually be more than a typical deviation of a WT from ET.

As an aside, after experimenting with some WTs and having had EBVT on my piano for several months, I reverted to ET (grudgingly - as I find it more difficult to tune). Others may find the variety of a WT pleasant, kudos to them. But I didn't. An 18 cent M3 brings me more discomfort than a 10 cent M3 brings me enjoyment.

As I do not know the answer, may I ask a simple question which has probably been answered many times before?

If my piano is tuned in as perfect ET as can be, what would be the point of writing 24 different pieces for the 24 keys? Why not write one piece and play it in each key?

For starters, I would think that presenting the world with 24 beautiful pieces is simply a richer gift than with one...

For another, certain chords, arpeggi, broken chords, melodic progressions etc. are not as "pianistic" in certain keys, i.e. their execution on the keyboard doesn't fit the natural shape of the hand as well in certain keys. Or, moving only on white keys may leave the hand unanchored. I believe this to be a possible reason for the extensive use of remote keys - not the quest for wider thirds, but a comfortable and secure playing position. Transposing some of the WTC pieces (or for that matter, romantic literature with lots of black keys) might give some interesting insights.

My 13.7 cents - I'm sure that more could be found.

Some language experts have compared the Ukraine and Russian languages and found a 60% common feature that might make us expect them to be easily understood both ways .Not so. But German and English languages also have a 60% common feature and not many English people can chatter away in fluent German . Of course the superior German intellect sees no such barriers , I`m sure . And I mean that most sincerely folks .

Even in ET every key has its own character because the speed of its M3 is different in each one (if the ET is tuned progressively).

Bach was a religious man and I expect he would concede our human imperfections in the face of tuning problems . He did not specify any particular temperament as the best which shows his Humility in the context of human existence under his Great Creator . That was probably his basic attitude not me pushing some personal agenda .The arguments about the "perfect temperament " fall into the same category as "How big is the Universe " or how many angels can you fit on the end of a pin . Bach , a humble German .

Even in ET every key has its own character because the speed of its M3 is different in each one (if the ET is tuned progressively).[/quote]

Greetings,
I must disagree. Our sense of tempering is logarithmic, we register dissonance by the amount, not the pitches, and if we were to ascribe a "character" to say, F, then 12 notes later, we would need another "character" for F because it is beating much faster. However, since it is beating faster an octave higher, it is still the same. 10 cents of tempering in a third gives the same sense of "tuneness" regardless of where it is.
The other argument against ascribing characters to ET pitches as they arise chromatically is that that would give a lesser impact to E because it is beating slower than F or G . Historically, no descriptions of key color or character have promoted that G would be more stimulating than F# because it is higher in pitch.

Whether or not this is absolutely true or not I cannot attest to since I wasn't there, but my understanding is that his "well tempering" was relative to the fact it now made it musically possible to play "equally" in all keys whereas many/most previous tuning systems especially the vulgar (common) tuning did not allow this...one was limited to roughly 2/3 of the key signatures due to non-musical intervals present. Bach's system smoothed things out so as to allow universal playability (but not absolute equality).

Peter Grey Piano Doctor

I disagree with your disagreement! Each key sounds different to me! Eb sounds way more calm than Bb, for example! Often, the key sets the centre of a piece and this really does make a difference. Perhaps it's because I have perfect pitch though? As for no historical descriptions of key colour, maybe that's because the historical pitch standards were also all over the place too. You say the we register dissonance by amount and not pitch - but that's what I'm also saying. A "low" key like Eb has slower beating than a higher one like Bb - the octave-above beats are all so fast as to be dissonant no matter the key anyway.

All just IMHO of course.

Paul

That was the thought behind my question. Why would a musician who lived those days do anything else? Mark made a very interesting point about composing for playability. That made a lot of sense and, I think, would go hand in hand with bringing out the character of each key.

Whilst I am unable to decide completely, this (above) sums up how I feel about the Bach question. I've read alot of almost convincing arguments on both sides but have more or less come down in the same place as Peter

Well, the Eb is a fourth above the Bb.....

I once tuned a newly strung piano up to only 100 cents flat. My musically gifted friend listened to me play something in C and suddenly wondered how I could have played something like I did. He was hearing B. If you have very strong pitch recognition, (none of us are perfect), you will already have some character associated with various keys. However, behind the fallboard, there are 88 levers and every one of them plays a note whose frequency is in a straight line from 27 Hz to 4180 Hz. If they are all equally spaced, all like intervals are tempered the same, and it matters not whether one begins on this combination of keys or that one. If the tempering is equal, the effects of tempering are rendered singular and a higher key transposed down an octave doesn't change anything.
When the size of the third begins to change, then, changes in effects can be physically measured. In the crudest sense, we don't have the same heart rate listening to a lamb bleat as we do when we hear a train's horn up close. In a more nuanced comparison, placing a sonata's theme in various keys in various places produces more effect on a well-tempered piano than when they speak with the same "color". (Color, as I use it, refers to the amount of dissonance in the interval. Unlike our ET thirds, all of which are the same size( 13.7 cents wide), a WT palette might allow various levels of thirds' tempering from 0 cents to 21cents. Milder variations abound, but all keep the same progressive nature in the same place. Easy to tune, easy to know where the "heat" is in a WT, etc. Also, quite a choice in how one might want a piece to 'feel'.
Regards,

I'm with you on this one, Paul - at least in a manner. Like you, I have pitch memory, so I cannot hear music without hearing its (apparent) key. But I don't have any keys that I find calmer per sé. Rather, I find that my perception of tempering depends on the register. The M3s in octave 4 sound busier (sourer, more tempered) to me than their counterparts in octave 3, although objectively I know that they are tempered the same. A chord with the M3 in the top voice, in upper octave 4 or 5, sounds busier to me than a chord in the same key, but inverted to have the M3 in the tenor, in octave 3 or low octave 4.
One example: The opening M17 of the raindrop prelude (Db maj) always sounds really sour to me, even in ET, because of the M3's exposed, high location on the keyboard (F5). The closing chord of the same prelude is not as sour to me (F4). And the closing chord of the second movement of Dvorak's 9th symphony, with the M3 at F3, sounds even sweeter. All in ET!
Or if I play the opening piano passage of Beethoven's 4th piano concerto (B4 is the M3 in G major) and continue to play the orchestra part (D#4 in the viola / tenor is the M3 in B major), then I find the B major chord sounds calmer to me than the initial G major.

A good friend, highly musical violinist but without significant pitch memory, recognises the key (not pitch) of string music by the timbre of strings, use of open strings, etc. It hardly matters to him to which pitch the strings are tuned. [Edit: I'm completely different. If the ensemble uses broke baroque tuning, and if I know the piece, the music sounds in the wrong key to me.]

There is obviously a lot of very individual perception going on, and methinks it's an individual mix of sensing and processing. My partially colour-blind son spots camouflaged animals in the bush long before I do.