Is this general or just my piano ?

[ted]

I had never really taken this in at the conscious level before but I have just been playing Waller, with its furious left hand tenths and I suddenly realised that D and A tenths are ever so slightly closer than E and B tenths, even though the keyboard geography suggests they should all be the same.

To be specific, I can bang out D-F# and A-C# just a tad more easily than E-G# and B-D#. It's surprising how slow on the uptake I can be sometimes. I had just assumed that I was breaking the latter pair at speed because of their positions in the piece. I had assumed, incorrectly it seems, that the piano was designed to give equal spacing for geographically similar formations.

Can somebody confirm or contradict this with respect to another piano please ?

[Etude]

It's the same on most pianos, as far as I know.

[prometheus]

Well, black keys just aren't equal to white ones.

[ted]

Just thought of the answer to my own question. The answer came to me while I was eating a frozen yoghurt at the shopping mall. How obvious !

Two reasonable assumptions:

1. The centres of the key shanks, black or white, are equally spaced.
2. The borders of the white notes are equally spaced.

For these particular tenths therefore, what matters for stretching purposes is the distance between the upper border of the lower white notes and the centre of the upper black note. Well, strictly speaking , the lower border of the upper black notes, 1/24 of an octave less, but for comparative playing purposes in this example this doesn't matter.

Let the distance of an octave be unity. Then the centres of the key shanks are therefore at 1/24 + 2n/24 and the borders of the whites at m/7.

For an E tenth:
The upper edge of the E is at 3/7 and the centre of the G# is at 41/24
Stretching distance = 41/24-3/7=215/168

For a D tenth:
The upper edge of the D is at 2/7 and the cente of the F# is at 37/24
Stretching distance=37/24-2/7=211/168

For an A tenth:
The upper edge of the A is at 6/7 and the centre of the C# is at 51/24
Stretching distance=51/24-6/7=214/168

For a B tenth:
The upper edge of the B is at 0 and the centre of the D# is at 31/24
Stretching distance=31/24-0=217/168

Which is precisely what I have observed. You know, I never thought of this. How bloody obvious !

[pianorama]

ooookkkkkkk whatever you say.... Sorry but I'm not a genius, and I certainly am not a mathematician. Je ne vous comprende pas! teehee hey and to any French speakers: did I say that right?

[invictious]

Actually, because of how some the black keys are between others, so you have to be more precise in pressing the keys.
i.e. G#.
It is between 2 black keys, so you have to somewhat stretch over the F#.


or F#.
it's after 2 white keys, so there is not much of a stretch.

[timothy42b]

Yes.

I wish the black keys were half the width, though in the same position, so that I could play between them more easily. 

[richard black]

So you've been playing piano long enough to get to Fats Waller and only just noticed that the only black that is centred between its adjacent whites is G#? Well, you're not the only one. Busoni used to get his pupils (and he only taught pianists at an advanced level) to draw a piano keyboard and apparently most of them got that wrong too.

[invictious]

no...the C# has two black surrounding it.........
























wait..

[gymnopedist]

ooookkkkkkk whatever you say.... Sorry but I'm not a genius, and I certainly am not a mathematician. Je ne comprehende pas vous! teehee hey and to any French speakers: did I say that right?

Actually, it's "je ne vous comprends pas".

[cloches_de_geneve]

I certainly am not a mathematician. Je ne comprehende pas vous! teehee hey and to any French speakers: did I say that right?

Absolutely not.

[zheer]

no...the C# has two black surrounding it.........
wait..

  If you draw 8 piano keys first, then draw the black keys next, you will find that the black keys are all on-top of the lines, however not including the third or seventh line if middle C is' your starting point.
     I think Busoni was teaching the theory of minds-eye.

[invictious]

Oh wow, I never noticed that before (sarcasm)

That exercise is actually pretty basic and I think I got it right

No wait...I got 13 key pieces...

[andyd]

Well if anyone is really interested in this old  thread...

John Mehegan in the third of his jazz books breaks tenths into three spans, the first two groups are within the reach of the 'average' pianist.  Span 3 however involves the major tenths between black and white notes as well as Gb to Bb.
Personally, after years of stretching my hand (actually it's mainly the area between the thumb and first finger), I still find four tenths in his span 3 definition challenging, those being
Db - F
Eb - G
Ab - C
Bb - D
It's due to the anatomy of the thumb joint, which must bend over a white key to play the next white key, and so requires careful precision.
And when I add any notes in between the tenths my hand necessarily rises and the span decreases slightly.

Andy