2-15-2013
Being new to this forum, I'd like to start by saying that I am an enthusiast. I still think that whoever decided to throw the harp into a wooden box, then add the hammer action and the rest, did us a huge favor. What a magnificent repertoire has been written for this King instrument.

But the piano (keyboard) is a unique instrument for which I have fundamental issues that I can't resolve (I have been searching and asking). And I think they are unique to the keyboard (the only instrument I play).
Maybe someone can help and show me how ignorant I am (use all the math or terminology u wish, I am a scientist).

1. Why is the octave divided into 7+5. Why is F# a dark key but E# a regular F?
Why not 6 whites and 6 blacks?
2. I don't think its the C-major scale (which is "pleasant" C to B, w/o the dark notes), I'm pretty sure the A minor has priority (most Gregorian chants are written in a). Is the a-minor the reason (also A to G w/o the black notes)?
3. Why are tuners using "stretching" when they tune?
4. Why are pros insisting the G-flat is different than F#? If I transcribe the Schubert G-flat Impromtu to F# and play it, nobody will ever be able to tell at what of the 2 keys I am playing. Right?
5. How come nobody writes in A# major but there is tons in B-flat? Or otherwise, there is some music in C# major (not much indeed) why was it not written in D-flat?

Thanks for your help, I have a bunch of other fundamental problems but this will be a nice beginning.

=bengera

This might answer some of your questions:
http://youtu.be/VRlp-OH0OEA.

You'll understand why E sharp is not the same as F (except on a keyboard tuned to equal temperament), how the octave is subdivided etc, and so on.

Hi there,

I am immensely obliged to u, this is the beginning of an understanding.

I therefore assume that before modernity, the chords were designed according to length (it was possible to get x1.5 of the tone by sheer length) but there is no, for example, 1.5 as a construct of 2^(1/12). The 7th half tone shall be 1.498 (which at 440Hz base tone shall calculate to 659.2Hz (and not 660Hz).
We can not hear this difference between the 2 tones, but we hear it excellently when they are combined with the fundamental.

I think I got it, thanks. =bengera

1 & 2. The octaves on the keyboard are now divided and positioned that way since quite a long time, but it was different some centuries ago (first church organs, etc.).

3. Stretch tuning is necessary on pianos because of their inharmonicity/imperfect harmonics so that the human ear perceives the octaves as "correct".

4. Gb and F# are different in terms of music theory and sound different on musical instruments like the violin, violas and cello, but are represented by the same enharmonic keys on keyboard instruments.

5. Keys are defined by a number of flats or sharps which follow a fixed order (Google circle of fifths). An A# major key would imply a signature of 10 sharps - so not practical at all, except for a temporary transposition in a manuscript. The Bb key is thus much easier as it implies only two flats for signature (Bb and Eb). C# and Db major keys are more common as they respectively imply signatures of 7 sharps and 5 flats, which happen more often.

I am again much obliged.

Still, octaves are always x2, right? So why the stretching?
After 60 years one loses much sound sensitivity or one might never have had it...

I am familiar with the circle of 5th, thanks.

I'll have to think about the A#, there can be no more than 7 sharps for 7 tones. Yep, it's tricky in the D and A.