richard66 wrote:
Funny thing: both preludes Nos. 5 and 15 (note the "5") are in "simliar" keys (D major and D flat major), last the same time (1'04") and are the same size (1,5 Mb). Add to that that when I submitted No. 5 the first time I actually sent no 15 again by mistake! How far can coincidences go!
Well, it may be coincidence that two of your recordings last the same time (although your previous recording of No 15 lasted longer), but file size will of necessity be strongly correlated to duration, so that doesn't count as part of the "coincidence".
As for the prelude numbers 5 and 15 (which both end in the digit 5) "happening" to correspond to keys which are both major and both have D in their name (5 as natural and 15 as flat), this isn't really coincidence either, it is a consequence of a simple mathematical fact combined with the way Ismagilov has arranged his prelude numbering in relation to their keys.
Like in Bach's WTC, Ismagilov's 24 preludes consist of one in each key. No 1 is in C major, No 2 in C minor, No 3 in G major, etc. All the odd numbers are major and all the even numbers are minor (same as in WTC). But the way Ismagilov arranges his odd (major) numbers through the keys differs from WTC: Bach's numbers 1,3,5,7,etc correspond to C, C#, D,Eb,etc, ascending chromatically, whereas Ismagilov's ascend in "circle of fifths" order of, i.e. his 1,3,5,7,9,11,13 correspond to C,G,D,A,E,B,F# (I'm not sure about 13, it might be Gb instead of F#), and then they continue with 15,17,19,21,23 corresponding to Db,Ab,Eb,Bb,F.
Therefore you will find that not only do the D and Db preludes have numbers 5 and 15, but also that
A and Ab have 7 and 17,
E and Eb have 9 and 19,
B and Bb have 11 and 21, and finally either
F# and F have 13 and 23, or else
G and Gb have 3 and 13.
And why is this? It's because any two keys that are a semitone apart (like D and Db) are 7 steps apart in the circle of fifths and so their number of sharps differs by 7 (from D with 2 sharps to get to Db we must subtract 7 sharps to end up with -5 sharps which is the same as 5 flats), and since the prelude numbering goes up or down in steps of two (to skip the minor keys), it means we have to subtract 7 twice (or subtract 14) from the prelude number (so with the D major prelude being number 5, the Db major prelude must be number 5-14 or number -9), and then if necessary we need to add 24 to get it into the range 1 to 24. In short, we either subtract 14 or add 10, whichever gets us a result in the range 1 to 24. And of course when you add 10 to any number, its least significant digit does not change.