Example of AJI

Here is an example of a real piece of music processed by the AJI idea and the
frequencies which would actually be played from my website. There are a series
of * and such with comments below about those notes/chords. The case presented
is the really simple rules case but some slightly more complex rules would give
a better result as noted below.

The "Note Numbers" are simply semitone counts from a fixed point.
The ratios are then determined by a simple mechanical procedure from the notes
in the chord. The "Fundamental Note Freq." is then the note which has a ratio
of 1 in respect to those notes.

Please note that with the advocated methodology the two "A"s in the second bar
would both have frequency 891 Hz so that the melody would be correct. However A
has a different frequency in the different bars due to modulation from F to C.

POLONAISE :- Wolfgang Amadeus Mozart in the key of F

Notes Note Ratios Fundamental Frequencies
Played Numbers Note Freq. Played

F3 A3 C5 12 16 31 4 5 12 -12 F 44 176 220 528
C4 F5 19 36 3 8 0 F 88 264 704
F3 A3 " 12 16 36 4 5 16 -12 F 44 176 220 704
C4 A5 19 40 3 10 0 F 88 264 880 *
" G5 19 38 1 3 19 C 264 264 792
F3 A3 G5 12 16 38 4 5 18 -12 F 44 176 220 792
" " F5 12 16 36 4 5 16 -12 F 44 176 220 704
C4 E5 19 35 2 5 7 C 132 264 660
" F5 19 36 3 8 0 F 88 264 704

E3 Bb3 C5 11 17 31 5 7 16 -17 C 33 165 231 528
C4 G5 19 38 1 3 19 C 264 264 792
E3 Bb3 " 11 17 38 5 7 24 -17 C 33 165 231 792
C4 Bb5 19 41 2 7 7 C 132 264 924
" A5 19 40 3 10 & 0 F 88 264 880 *
E3 Bb3 A5 11 17 40 5 7 27 -17 C 33 165 231 891 *
" " G5 11 17 38 5 7 24 -17 C 33 165 231 792
C4 F#5 19 37 4 11 @ -5 C 66 264 726
" G5 19 38 1 3 19 C 264 264 792

F3 A3 A5 12 16 40 4 5 20 -12 F 44 176 220 880
C4 A5 19 40 3 10 0 F 88 264 880
" F5 19 36 3 8 0 F 88 264 704
F3 G3 Bb5 12 14 41 8 9 42 # -24 F 22 176 198 924
C4 Bb5 19 41 2 7 7 C 132 264 924
" G5 19 38 1 3 19 C 264 264 792
F3 A3 C6 12 16 43 4 5 24 -12 F 44 176 220 1056
" " A5 12 16 40 4 5 20 -12 F 44 176 220 880
C4 G5 19 38 1 3 19 C 264 264 792
" F5 19 36 3 8 0 F 88 264 704

1. All bar 1 frequencies are divisible by 44 and the key is always F, while
bar 2 are all divisible by 33 and key is C (see note 3) and bar 3 all
notes are divisible by 44 again.

2. The items above with a "*" are all A, but sometimes the frequency is
880 and at others 891. See note 3 also.

3. The item marked with a "&" has ratios 3 10, but under the alternative
method (points for ratios) the ratios could be 8 27. This would then
make the fundamental be C and agree with the rest of the bar. This A
would then be frequency 891. The alternative method of note finder
would certainly give 8 27.

4. The item marked "@" has the ratios 4 11, and 11 is not very common.
It seems that this was Mozart's intention as the fundamental is in
keeping with the surrounding chords. Another possibility is 16 45.

5. The item marked "#" has a ratio 42. If the variation of ratios feature
was included, 42 and 43 would both be considered, and 42 chosen.

6. All the frequencies are an exact number of Hz.

-- Ray Tomes -- http://www.kcbbs.gen.nz/users/rtomes/rt-home.htm --
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