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Actually, on a modern piano they are both about 7cm away from C. C# is much closer, being only 1cm away. It is surprising that more pieces weren't written in C# in the Baroque era.
Regards.

It seems odd that someone would take the time to count the words in a post.

You are missing the fact that I am referring to keyboard location and that they are the next easiest keys for a pianist to play.

Playing a Theremin solves the problem completely and never needs to be tuned!

When you think of key signatures in the order of the circle of fifths, then C is right between G and F! Does that clear this up?

OK people. Calm down. We are likely talking at cross purposes here. A discussion of ET,WT,UT always seems to degenerate by this point. I too contribute to that sad decline.

All discussion of ET/UT tends to degenerate from the first post. Loren is well aware of this - some people just love the controversy!

Greetings,
When we talk about distance between keys in a temperament discussion, it is generally accepted that we are not talking about physical distance between the keys, but the distance around the circle off fifths, ie, F# is as far from C as possible, and almost as far from F. This position in the circle correlates to the width of the tonic third.

The majority of piano music is written in keys that are closer to C than F#. If you compile the usage charts, you will see that C was the most commonly used key, F and G are second, and D and Bb follow them in use. This progression continues through all the keys, with B, F#, C# being the least used. This holds true for Schubert, Mozart, Beethoven, and most others. Chopin is the exception, but only in the polarity, his usage of the keys is almost exactly opposite all the others.

If we plot the prevalence of keys's use through the ages, we find that in the Meantone era, 1300-1700, the eight keys closest to C were virtually all that was used, clear evidence of the restrictive wolf in that 1/4 C tuning. Beginning around 1700, or perhaps a few decades before, we begin to see a more democratic use, as the circulating tunings came into use. This use was still lopsided, with the remote keys being rarely used. The usage becomes gradually more democratic over the next 200 years, and by the 1900's there was little pattern or correlation between the temperament and the key's selection. I suspect that as music left the strict tonal forms of the Classical era behind, the UT's value and influence faded, and ET became more prevalent.

Beethoven actually preferred Eb more than any other key, and I suspect that harmonically, it offered a wider palette for modulation, in that moving in one direction heightened musical tension, while going the other way entered very calm spaces. In most WT, Eb (and A) are virtually identical to ET, and for LVB, Eb could possibly have been the harmonic home base that was easiest to start from.
Regards,

Contending for a point without becoming contentious is a challenge for us all - especially on Monday mornings.

10 seconds of copying and pasting is all it takes - even the most basic word processor has a word counting tool.

But I'm sure BDB didn't know this, and counted through Bill's post by hand.

P.S.: When learning the piano, I never progressed from C major to B major or C# major just because they were the "closest" on the (damn) keyboard. Perhaps my teacher was wrong to let me progress more or less along the circle of fifths? Pity she isn't alive anymore, otherwise I'd demand my parents' money back.

It does not take 10 seconds nor cutting nor pasting. I used an OS X service to give me the statistics for the selection.

Let me try this again.

* Beginning piano students, especially children, are not taught the circle of fifths before they learn that the key of G has one sharp.

* A piano teacher does not teach beginning students the key of F or G because the teacher understands the harmonic relation within the circle of fifths.

* Those keys are the next easiest to learn to play, that is the only reason they are taught in that sequence.

* It happens before any discussion of major or minor keys. Accidentals are still further down the road. No, the F# in the key of G-Major is not an accidental.

* It certainly has nothing to do with temperament.

I posted that I asked for one of my pianos to be tuned in a non-equal temperament using A-442 as the basis for the setting of the temperament octave. Though my tuner was hesitant, he did what I asked. He knew me, my pianistic skills, and I had the checkbook. (Sorry to be so crass)

The reason I wanted to try this is because I have a great deal of experience as an orchestral instrumentalist, as well as a pianist. As I stated previously, orchestral musicians temper their concept of key color from A as being the center, not from C.

I used the example of playing a concerto in G-Major on a piano which had a non-equal temperament based on A. This shifts the whole key color (aural) identification. It becomes more natural to the ear of orchestral musicians than does a non-equal temperament based on C.

To be honest, it doesn't matter at all about the history of tuning temperaments on fixed pitch instruments, such as the piano. It was nothing more than a request, an attempt, to more closely match one of my pianos to how I hear key color (temperament) as expressed in orchestral performance. It is a departure from standard practice which achieved it's goal.

For those of you who are comfortable tuning in non-equal temperaments, you might give it a try and make your own assessment on the results.

All:

If you want just intonation with fixed pitch instruments, you can only have a few notes. (Work it out yourself.) And if you want just intonation with changeable pitched intruments (or voice), you can have only major and minor triads - no sixths or sevenths. Only the simpliest music can be in just intonation. What some may consider to be just intonation is the real compromise. I see nothing in ET that is a compromise. Equal is equal, not a compromise.

Or a whole bunch. Harry Partch used 69 notes per octave.

I do hope that those of you who mentioned the physical distance of keys from C realized that I was joking.

It is possible to play a DP in just intonation using Justonics software. You tell the software where the modulations are, and how you want to shift to occur. Then when you play the work, it adjusts the pitch of each note/chord on the fly. Very cool.

My checkbook isn't nearly as expansive as yours, but I've played in five symphony orchestras, albeit provincial ones, for the better part of 20 years.

If (IF!!) this assertion of yours were true, it would mean that A major represents the most "well" key. It would further mean that each of these pairs are equally "colored":
E major (+1, 4 sharps) and D Major (-1, 2 sharps)
B major (+2, 5 sharps) and G major (-2, 1 sharp)
F# major (+3, 6 sharps) and C major (-3, no sharps/flats)
C# major (+4, 7 sharps) and F major (-4, 1 flat)
G# major (+5, 8 sharps) and Bb major (-5, 2 flats)

Truth be told, I have never heard of such a notion.

Well Mark R., that means that you heard "such a notion" here first. Congratulations!

In all five of your provincial orchestras, to what note did you tune?

That is the choice I made with my own piano. It works well.

Marty,
I think we may not be on the same page here. Are you saying that you could or would play Mozart Piano Concerto Op. 5, No. 4 in E flat on a piano using 1/4 comma meantone based on A? If you do, you will playing with the tonic on the 'wolf'. Even using just about any other WT, such as Young 1799, which would work beautifully with orchestra based on C, but would still be fairly wild based on A. Your thoughts?

And Italian early baroque a minor third higher.

Kees