The present key was notated differently in the middle class of this Grosse General-Baß-Schule than here, despite them being (in the common disposition of the keyboard instruments) the same tangent. It is well-consideredly written according to the common disposition of our keyboards: for it was sufficiently proven mathematically by others, that the key ♯G is generally very different from ♭A. I add that it can also be demonstrated naturally: for the property of the first key requires a minor third and therefore is essentially minor, while the other naturally needs the major third, and therefore is major by nature, which cannot be the same key at the same time. The harmonic reasons are not yet known, but in praxi this proposition is true.

For a long time it has been well noticed that the so-called semitones contain an ambiguity, as it were; namely, that ♯C is a different thing in itself than ♭D; that ♯D should be distinguished from ♭E; that ♯E does not have anything in common with the ordinary F. They have quite rightly proven that ♯F is not ♭G; that ♭A and ♯G are not basically the same; that ♭H means something quite different from ♯A, and that finally ♯H can have no relationship to the ordinary C: for therein consists a piece of the enharmonic octave, on which the introduction, or Unterclasse, has elaborated extensively.

However, our improvers have not yet gone so far as to distinguish C-flat Buliowski mentions this, citing Capricorno; see Emendat. Organ., p. 23. from B and not to confuse F-flat with E, or to demand that, just as C and F can be notated in different ways, these too should require, if not keys of their own lying next to each other (which I am happy to do without), at least a different notation: which is, however, highly necessary especially in those kinds of keys that hiddenly modulate into enharmonic regions, which is why it will be discussed amongst other things in the conclusion of this work and it will also be pointed out, which other inconvenience in notation arises from it.

Our ancestors, as they made their remarks about the lack of tones and were of the opinion that the Clavier still lacked seven keys in each octave in the semitones, would hardly have thought that after their time, one would ever compose a piece from such divided steps (let alone from their breaks), especially since Capricornus and Bernhard already invested in this and considered it almost impossible that it could be driven further; as is evident: they have only considered the sequences or modulations of the other common tones, and according to such basic theorem, have assumed their annotations to be indisputable and indispensable: which is nevertheless a mistake.

As little as we may believe that something might show up in ♯E, in so far as it is different from F, it can happen just as easily; and I do not want to be a guarantor for this, nor do I want to demand that one shall make special, fundamental changes in the instrument because of it, since they do not help; my thoughts go, with all modesty, only so far as that enough signs be introduced by which such things can be notated properly, mainly because of the mentioned consequences. For we must abandon the hope of improving the Clavier, of augmenting it, and of bringing it to perfection, and be content instead with a good temperament: because, in spite of manifold suggestions and attempts, a patchwork of keys does not mean anything; but to express my standpoint through music should not do any harm: and even that we cannot do properly, as will be shown in the last Probstück of this class and indeed in the immediately following aria.

The little which remains to be noted is that from the 5th measure of this piece to the third measure of the last part, then again from the 10th of said part to the 17th, everything can be played in the right hand in a decent manner, but where the 6/4 occurs, a graceful arpeggiation can be applied; besides, it does not require any major skill.

ARIA.

I found this aria with a noble person who came here from Italy, not knowing who its composer was. One can tell that it must have been composed either for a castrato or for someone who sang in a high alto, also that some instruments belong to it, which I, however, have considered unnecessary here, as well as several inserted rests. The only intention is to give an example from daily practice where the G-sharp minor is used strongly, and for this I take what falls into my hands first, as it were by chance. That G-sharp minor occurs more often than A-flat minor is true, because the first has the minor third essentially, the other only accidentally - yet it is the same in playing, only the latter can be notated more purely, which is why it was chosen here for the Probstück. However, I found a beautiful movement in A-flat major in Mossi's work, p. 34, which I would like to note, because it did not occur to me in the twelfth Probstück of this class. Another movement, however, from the G-sharp major is found by the same composer on p. 59, which proves my above remarks. The work mentioned here, and presented as an example, consists of twelve sonatas with a violin and bass, engraved in copper in Amsterdam, and the author's name is Giovanni Mossi.

At the end of the preceding explanation, I said that this aria was intended to show that we cannot always express our views well with notes, and that we indeed lack signs when we want to play into the unfamiliar tones. This is especially clear from the last two lines of the above aria, since a note occurs there five times in both, voice and bass, which has a double cross (♯♯) in front of it and signifies a so-called g, which I, however, consider (although it is the usual notation) to be a defect, and at the end of this work I will present my reasons and means, as much as I understand them and have them available, along with more examples.