Motif multiplication

Each note of the first motif is replaced by the second motif, transposed by that note. Let us assume first that all durations, in the motives and their product, are equal, so they do not get mentioned. For example:
9 12   x   7 11 14 17   =   16 20 23 26 19 23 26 29
9 becomes 9+7 9+11 9+14 9+17 and 12 becomes 12+7 12+11 12+14 12+17.   In this scheme, obviously, 0,12,24... = C, 1,13,25... = C# = D♭, ... etc, and 12 is one octave higher than 0.

Notice that both motifs above belong to C major (the notes are A C and G B D F) but the product is not in C major, because 20 = G#. If the melody is to remain in C major, it will be played

16 19 23 26 19 23 26 29   =   E G B D G B D F
Alternatively, the new key may be set to A minor – one of several possibilities. In this case the melody will appear as:
16 20 23 26 20 23 26 30   =   E G# B D G# B D F#
accompanied by chords of A minor.

The product is order dependent; for the same two motives:

7 11 14 17    x  9 12  =    16 19 20 23 23 26 26 29
7 becomes 7+9 7+12, 11 becomes 11+9 11+12, etc.

An example with unequal durations

The pitches get added, the durations are multiplied (as fractions. If you don't know what it means, shame on you!)
12 11 9
1/2 1/4 1/4 lasting 1/1
cross
7 11
3/8 1/8   lasting 1/4

Compute:

12+7
12+11
11+7
11+11
9+7
9+11
1/2 x 3/8 1/2 x 1/8 1/4 x 3/8 1/4 x 1/8 1/4 x 3/8 1/4 x 1/8

Result:

19
23
18
22
16
20
3/16
1/16
3/32
1/32
3/32
1/32
lasting 1/2

Notice the syncopated rhythm in the second product. Maybe should be smoothed to:

or even to