Music theory Question

Bump.

Dear Howard,

You have hit on a very complex problem, and the answer is also neither easy to explain nor understand. Actually the piano is fundamentally out of tune on every interval of the octave as tuned to equal temperament. But it is very close, because even temperament is the best compromise so far in accommodating the need for a fixed tuning instrument such as the piano or pipe organ to be equally in tune in all the keys.

You may find that if you probe deeper than many pipe organs are still tuned to Werkmeister Four, as this is frequently preferred - especially when the role of the organ is to play old music or accompany a choir. 

Werkmeister Four is not the same as even temperament tuning.

Singers and players of instruments without fixed strings such as the piano has, but strings that require to be stopped with the left hand on a fret-less finger board [for all but the open notes] use a different scheme again, which is actually able to be perfectly in tune. This tuning is called just and when one refers to just intonation, one is describing the fact that the intervals within the given key - for example G Major which lives with its tonic or first note of the scale being the eponimous "G" - are in just relationship and tuned ideally.

This does not even begin to cover the problems involved in tuning the brass and woodwind instruments, but I think we had better leave that for a further discussion, beyond noting the the players are able to adjust the tuning with their embouchure, to match [almost always] just intonation. 

Introduce a piano and the musicians must adopt the piano even temperament tuning [which is a compromise] or else there will be a most unpleasant effect, which sounds out of tune because just intonation is accurate the piano is a slightly inaccurate compromise. The piano will play each key with the same mathematic compromise whereas the organ tuning of Werkmeister Four is more accurately close to just intonation in the early [none or few sharps or flats in the key signature] and be much better in tune than the piano tuned with even temperament in those specific keys.

I know that sounds a horrible concept to think about, but here is a link that explains it in musical terms, but leaves out some the science. The description of the harmonic series [of overtones] is not wrong, but not the whole story either for example.

http://www.terryblackburn.us/m...mperament/stoess.htm

ATB from George

Thanks George I knew you would come through. Seems like I got the gist of it, from the TV programme.

Dear Howard, 

You are welcome.

If you ever visit me here, I can demonstrate some of this! With recordings that make clear the implications of different tuning schemes in an aural way that any number of words cannot really explain!

I have wonderful lecture in German - though I can fill in the English - with a perfect demonstration of all this for a start! Only 25 minutes long ...

ATB from George