I don't know whether it what in the subject it is a good translation. I could not find the expression good at the dictionary. In Polish it is something completely different, but despite everything I ask for understanding and guessing!!! what I am writing about. In Poland we are calling this problem the dress, and at you it is an element of clothes....
I must for the beginning give to a bit of philosophy. I ask for the patience.
Spaces between sounds aren't mathematics. People in the days of Bach invented, that best to arrange sounds in even spaces by oneself - it is called "Well tempered". He supported this J.S. Bach. It wasn't bad so that well a grand piano or organs, or a harpsichord worked in all keys are needed in order to build twice as many keys. It would be very difficult for the playing. So a problem was oversimplified. To the benefit of this solution a fact of adapting oneself is starting to speak of natural tones. Real strings in the grand piano sound and just enough automatically are changing the time one's sound - are adapting themselves up to other aliquots. Thanks to that, the one in principle the false instrument well is being get back by the ear. Schools of tuning grand pianos are different so that it best adapts itself. Unfortunately, it what possible in kind in the electronic instrument will fail. Here no string is stimulating second with one's aliquots and there is no tuning up. But something is what is missing real grand piano. If only to dispose him supposedly the worker of the Chinese factory has an hour to it..... To i tak za długo, żeby dostroić instrument na przykład przed każdym utworem. One real instrument which has a function of fast retuning exists - it is a harp. So in the harp with pedals it is possible to switch over to determined keys so that they sound like best. So this invention I would want him to be in Linuxsampler. It would be wonderfully if with two clicks of the mouse I could change optimum tuning up for example to the B major key.
A bit too far I ran out.
Many centuries ago somebody (Pietro Aron?) invented natural tune for keyboard instruments (well tuned up to the ear). He is called meantone. Of course he isn't excellent, but good. Unfortunately by design instead of 12 keys we have 7. It is possible to use remaining, but we will hear the terrible falsehood then. Actually all are to playing, but according to principles - with music theory and in the vicinity of the scale of C major. F#-major sounds terribly. A theoretical possibility of moving this situation to all 12 keys exists in the electronic instrument. For example we will be playing the prelude C-major (Bach-Gounod) in C-major. It of course we need meantone for F-major.... YES!!! Because there is A-flat note there and. A-flat he cannot be in real meantone (C-major). There he is G# not A-flat! To the thing. In natural meantone (C-major) we have F# C# G# B-flat and E-flat. Not for example A#!!! Also spaces between white keys are different. But by it like nice a chord sounds C-major, d-minor, G-minor....... - but not F-minor!!!!
I am returning to my idea i.e. the transfer meantone to all keys.
Now numbers. I am giving the outline moved closer in round figures of tilts from Well tempered in cents. - tested by me in gigedit. There by hand I introduced these cents. And extra play:
1 +8,554 9
2 -15,396 -15
3 +1,711 2
4 +18,819 19
5 −5,132 -5
6 +11,976 12
7 −11,975 -12
8 +5,132 5
9 -18,818 -19
10 −1,711 -2
11 +15,397 16
12 -8,554 -8
Specially I numbered from 1 to 12, and I didn't give names of notes. It is template 1 = C, 2 = C#, 3 = D........
But just as well it is possible to start for example from A. Probably you are guessing what next.....
I must already finish, and here stayed as it to solve. There is still a problem swimming A. A is basic sound for adapting itself from other, and here at every key will have other deviation. Specially I also modified original meantone and I established regular maximum deviation up and into the bottom to 19 cent. The fact that kind of a specific height resisted the key at the average height. But it are everything secondary problems.
For the end. Don't think that I am exaggerating. For yourselves change secretly in gigedit (window tune pitch) both listen and play. Almost everyone will hear.
I am greeting