Advamced Percussion Analysis
in the Midistats Program

This is an addendum to the midistats.1 file.

The MIDI file devotes channel 9 to the percussion instruments
and over 60 percussion instruments are defined in the MIDI
standard. Though there is a lot of diversity in the percussion
track, for most MIDI files only the first 10 or so percussion
instruments are important in defining the character of the track. The
program Midiexplorer has various tools for exposing the percussion
channel which are described in the documentation. The goal
here is to find the essential characteristics of the percussion
track which distinguishes the MIDI files. This is attempted
in the program midistats.  Here is a short description.

-corestats
Produces a line with 3 numbers separated by tabs. eg
384	8349	448
It returns the number of divisions per quarter note beat (ppqn),
the number of note onsets in the midi file, and the maximum
number of quarter note beats in midi file.

-pulseanalysis
Counts the number of note onsets as a function of its onset time
relative to a beat, grouping them into 12 intervals and returns
the result as a discrete probability density function. Generally,
the distribution consists of a couple of peaks corresponding
to quarter notes or eigth notes. If the distribution is flat,
it indicates that the times of the note occurrences have not been
quantized into beats and fractions. Here is a sample output.
0.3496,0.0000,0.0000,0.1602,0.0000,0.0002,0.2983,0.0000,0.0000,0.1914,0.0002,0.0001

-panal
Counts the number of note onsets for each percussion instrument. The first
number is the code (pitch) of the instrument, the second number is the
number of occurrences. eg.
35 337	37 16	38 432	39 208	40 231	42 1088	46 384	49 42	54 1104	57 5	70 1040	85 16	

-ppatfor n
where n is the code number of the percussion instrument. Each beat
is represented by a 4 bit number where the position of the on-bit
indicates the time in the beat when the drum onset occurs. The bits
are ordered from left to right (higher order bits to lower order
bits). This is the order of bits that you would expect in a
time series.
Thus 0 indicates that there was no note onset in that beat, 1 indicates
a note onset at the end of the beat, 4 indicates a note onset
in the middle of the beat, and etc. The function returns a string
of numbers ranging from 0 to 7 indicating the presence of note onsets
for the selected percussion instrument for the sequence of beats
in the midi file. Here is a truncated sample of the output.

0 0 0 0 0 0 0 0 1 0 0 4 1 0 0 4 1 0 0 4 1 0 0 4 1 0 0 4 1 0 0 4 1 4 4 0
1 0 0 0 1 0 5 0 1 0 5 0 1 0 5 0 1 0 5 0 1 0 5 0 1 0 5 0 1 0 5 0 1 0 0 0
1 0 5 0 1 0 5 0 1 etc.

One can see a repeating 4 beat pattern.

-ppat
midistats attempts to find two percussion instruments in the midi file
which come closest to acting as the bass drum and snare drum.
If it is unsuccessful, it returns a message of its failue. Otherwise,
encodes the position of these drum onsets in a 8 bit byte for each
quarter note beat in the midi file. The lower (right) 4 bits encode the
bass drum and the higher (left) 4 bits encode the snare drum in the
same manner as described above for -ppatfor.
0 0 0 0 0 0 0 0 0 0 33 145 33 145 33 145 33 145 33 145 33 145 33 145 33 145
33 145 33 145 33 145 33 145 33 145 33 145 33 145 33 145 33 145 33 145 33 145
33 145 33 145 33 145 33 145 33 145 33 and etc.

-ppathist
computes and displays the histogram of the values that would appear
when running the -ppat. eg.
bass 35 337
snare 38 432
1 (0.1) 64  32 (2.0) 8  33 (2.1) 136  144 (9.0) 8  145 (9.1) 136 

The bass percussion code, the number of onsets, and the snare
percussion code and the number of onsets are given in the
first two lines. In the next line the number of occurrences of
each value in the -ppat listing is given. The number in parentheses
splits the two 4-bit values with a period. Thus 33 = (2*16 + 1).


