In order to allow a wave to playback over a range of musical notes, (+/-
semitones), its playback rate must be raised or lowered by a set amount.
From one semitone to the next, this set amount is by a factor of the 12th
root of 2 (assuming a western, equal-tempered scale). Here is a table that
shows what factor would need to be multiplied by the sampling rate in
order to transpose the wave's pitch.

Pitch in relation to the Root     Multiply Rate by this amount
-------------------------------   ------------------------------
DOWN 6     semitones              0.5
DOWN 5 1/2 semitones              0.529731547
DOWN 5     semitones              0.561231024
DOWN 4 1/2 semitones              0.594603557
DOWN 4     semitones              0.629960525
DOWN 3 1/2 semitones              0.667419927
DOWN 3     semitones              0.707106781
DOWN 2 1/2 semitones              0.749153538
DOWN 2     semitones              0.793700526
DOWN 1 1/2 semitones              0.840896415
DOWN 1     semitones              0.890898718
DOWN 1/2   semitone               0.943874312
ORIGINAL_PITCH                       1.0           /* rootnote's pitch */
UP   1/2   semitone               1.059463094
UP   1     semitones              1.122562048
UP   1 1/2 semitones              1.189207115
UP   2     semitones              1.259921050
UP   2 1/2 semitones              1.334839854
UP   3     semitones              1.414213562
UP   3 1/2 semitones              1.498307077
UP   4     semitones              1.587401052
UP   4 1/2 semitones              1.681792830
UP   5     semitones              1.781797436
UP   5 1/2 semitones              1.887748625
UP   6     semitones              2

For example, if the wave's Rate is 18000 hz, and you wish to play the wave
UP 1 semitone, then the playback rate is:

18000 x 1.122562048 = 20206.11686 hz

The sampling period for the Amiga is therefore:

(1/20206.11686)/.279365 = .000177151

and to send it to the Audio Device, it is rounded and expressed in micro-
seconds: 177

Obviously, this involves floating point math which can be time consuming
and impractical for outputing sound in real-time.  A better method is to
construct a transpose table that contains the actual periods already
calculated for every semitone.  The drawback of this method is that you
need a table for EVERY DIFFERENT Rate in the SAMP file.  If all the Rates
in the file happened to be the same, then only one table would be needed.
Let's assume that this is the case, and that the Rate = 18000 hz. Here is
a table containing enough entries to transpose the waves +/- 6 semitones.

Pitch in relation to the Root     Amiga Period (assuming rate = 18000 hz)
-----------------------------     ---------------------------------------
Transposition_table[TRANS_TABLE_SIZE]={
/* DOWN 6     semitones  */            398,
/* DOWN 5 1/2 semitones  */            375,
/* DOWN 5     semitones  */            354,
/* DOWN 4 1/2 semitones  */            334,
/* DOWN 4     semitones  */            316,
/* DOWN 3 1/2 semitones  */            298,
/* DOWN 3     semitones  */            281,
/* DOWN 2 1/2 semitones  */            265,
/* DOWN 2     semitones  */            251,
/* DOWN 1 1/2 semitones  */            236,
/* DOWN 1     semitones  */            223,
/* DOWN 1/2   semitone   */            211,
/* ORIGINAL_PITCH        */            199,    /* rootnote's pitch */
/* UP   1/2   semitone   */            187,
/* UP   1     semitones  */            177,
/* UP   1 1/2 semitones  */            167,
/* UP   2     semitones  */            157,
/* UP   2 1/2 semitones  */            148,
/* UP   3     semitones  */            141,
/* UP   3 1/2 semitones  */            133,
/* Since the minimum Amiga period = 127 the following
are actually out of range. */
/* UP   4     semitones  */            125,
/* UP   4 1/2 semitones  */            118,
/* UP   5     semitones  */            112,
/* UP   5 1/2 semitones  */            105,
/* UP   6     semitones  */            99   };

Let's assume that (according to the PlayMap) midi note #40 is set to play
wave number 3. Upon examining wave 3's structure, we discover that the
Rate = 18000, and the RootNote = 38. Here is how the Amiga sampling period
is calulated using the above 18000hz "transpose chart" in C:

/* MidiNoteNumber is the received midi note's number (here 40) */

#define ORIGINAL_PITCH     TRANS_TABLE_SIZE/2 + 1
/* TRANS_TABLE_SIZE is the number of entries in the transposition table
(dynamic, ie this can change with the application) */

transposeAmount = (LONG) (MidiNoteNumber - rootNote);
/* make it a SIGNED LONG */

amigaPeriod     = Transposition_table[ORIGINAL_PITCH + transposeAmount];

In assembly, the 18000hz transpose chart and above example would be:

Table       dc.w  398
dc.w  375
dc.w  354
dc.w  334
dc.w  316
dc.w  298
dc.w  281
dc.w  265
dc.w  251
dc.w  236
dc.w  223
dc.w  211
ORIGINAL_PITCH  dc.w  199   ; rootnote's pitch
dc.w  187
dc.w  177
dc.w  167
dc.w  157
dc.w  148
dc.w  141
dc.w  133
; Since the minimum Amiga period = 127, the following
; are actually out of range.
dc.w  125
dc.w  118
dc.w  112
dc.w  105
dc.w  99

lea     ORIGINAL_PITCH,a0
move.b  MidiNoteNumber,d0  ;the received note number
sub.b   RootNote,d0        ;subtract the wave's root note
ext.w   d0
ext.l   d0                 ;make it a signed LONG
add.l   d0,d0              ;x 2 in order to fetch a WORD
move.w  (a0),d0            ;the Amiga Period (WORD)

Note that these examples don't check to see if the transpose amount is
beyond the number of entries in the transpose table. Nor do they check if
the periods in the table are out of range of the Amiga hardware.

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