Apéndices
5. Supplementary material
GDecimal and Hexadecimal table
(An "H" is appended to the end of numbers in hexadecimal notation.)
In MIDI documentation, data values and addresses/sizes of Exclusive messages, etc. are
expressed as hexadecimal values for each 7 bits.
The following table shows how these correspond to decimal numbers.
fig.11-22e
Dec.
Hex.
Dec.
0
00H
32
1
01H
33
2
02H
34
3
03H
35
4
04H
36
5
05H
37
6
06H
38
7
07H
39
8
08H
40
9
09H
41
10
0AH
42
11
0BH
43
12
0CH
44
13
0DH
45
14
0EH
46
15
0FH
47
16
10H
48
17
11H
49
18
12H
50
19
13H
51
20
14H
52
21
15H
53
22
16H
54
23
17H
55
24
18H
56
25
19H
57
26
1AH
58
27
1BH
59
28
1CH
60
29
1DH
61
30
1EH
62
31
1FH
63
* Decimal values such as MIDI channel, bank select, and program change are listed as one
greater than the values given in the above table.
* A 7-bit byte can express data in the range of 128 steps. For data where greater precision
is required, we must use two or more bytes. For example, two hexadecimal numbers aa
bbH expressing two 7-bit bytes would indicate a value of aa x 128+bb.
* In the case of values which have a +/- sign, 00H = -64, 40H = +/-0, and 7FH = +63, so
that the decimal expression would be 64 less than the value given in the above chart. In
the case of two types, 00 00H = -8192, 40 00H = +/-0, and 7F 7FH = +8191. For example, if
aa bbH were expressed as decimal, this would be aa bbH - 40 00H = aa x 128+bb - 64 x
128.
* Data marked "Use nibbled data" is expressed in hexadecimal in 4-bit units. A value
expressed as a 2-byte nibble 0a 0bH has the value of a x 16+b.
<Example 1> What is the decimal expression of 5AH ?
From the preceding table, 5AH = 90
<Example 2> What is the decimal expression of the value 12 34H given as hexadecimal for
each 7 bits?
From the preceding table, since 12H = 18 and 34H = 52
18 x 128+52 = 2356
<Example 3> What is the decimal expression of the nibbled value 0A 03 09 0D ?
From the preceding table, since 0AH = 10, 03H = 3, 09H = 9, 0DH = 13
((10 x 16+3) x 16+9) x 16+13 = 41885
<Example 4> What is the nibbled expression of the decimal value 1258?
16) 1258
16)
78 ... 10
16)
4 ... 14
0 ... 4
Since from the preceding table, 0 = 00H, 4 = 04H, 14 = 0EH, 10 = 0AH, the result is: 00 04 0E
0AH.
244
Hex.
Dec.
Hex.
Dec.
Hex.
20H
64
40H
96
60H
21H
65
41H
97
61H
22H
66
42H
98
62H
23H
67
43H
99
63H
24H
68
44H
100
64H
25H
69
45H
101
65H
26H
70
46H
102
66H
27H
71
47H
103
67H
28H
72
48H
104
68H
29H
73
49H
105
69H
2AH
74
4AH
106
6AH
2BH
75
4BH
107
6BH
2CH
76
4CH
108
6CH
2DH
77
4DH
109
6DH
2EH
78
4EH
110
6EH
2FH
79
4FH
111
6FH
30H
80
50H
112
70H
31H
81
51H
113
71H
32H
82
52H
114
72H
33H
83
53H
115
73H
34H
84
54H
116
74H
35H
85
55H
117
75H
36H
86
56H
118
76H
37H
87
57H
119
77H
38H
88
58H
120
78H
39H
89
59H
121
79H
3AH
90
5AH
122
7AH
3BH
91
5BH
123
7BH
3CH
92
5CH
124
7CH
3DH
93
5DH
125
7DH
3EH
94
5EH
126
7EH
3FH
95
5FH
127
7FH
GExamples of actual MIDI messages
<Example 1> 92 3E 5F
9n is the Note-on status, and n is the MIDI channel number. Since 2H = 2, 3EH = 62, and
5FH = 95, this is a Note-on message with MIDI CH = 3, note number 62 (note name is D4),
and velocity 95.
<Example 2> CE 49
CnH is the Program Change status, and n is the MIDI channel number. Since EH = 14 and
49H = 73, this is a Program Change message with MIDI CH = 15, program number 74 (Flute
in GS).
<Example 3> EA 00 28
EnH is the Pitch Bend Change status, and n is the MIDI channel number. The 2nd byte (00H
= 0) is the LSB and the 3rd byte (28H = 40) is the MSB, but Pitch Bend Value is a signed
number in which 40 00H (= 64 x 12+80 = 8192) is 0, so this Pitch Bend Value is
28 00H - 40 00H = 40 x 12+80 - (64 x 12+80) = 5120 - 8192 = -3072
If the Pitch Bend Sensitivity is set to 2 semitones, -8192 (00 00H) will cause the pitch to
change -200 cents, so in this case -200 x (-3072) ÷ (-8192) = -75 cents of Pitch Bend is being
applied to MIDI channel 11.
<Example 4> B3 64 00 65 00 06 0C 26 00 64 7F 65 7F
BnH is the Control Change status, and n is the MIDI channel number. For Control Changes,
the 2nd byte is the control number, and the 3rd byte is the value. In a case in which two or
more messages consecutive messages have the same status, MIDI has a provision called
"running status" which allows the status byte of the second and following messages to be
omitted. Thus, the above messages have the following meaning.
B3
64 00
MIDI ch.4, lower byte of RPN parameter number:00H
(B3)
65 00
(MIDI ch.4) upper byte of RPN parameter number:00H
(B3)
06 0C
(MIDI ch.4) upper byte of parameter value:0CH
(B3)
26 00
(MIDI ch.4) lower byte of parameter value:00H
(B3)
64 7F
(MIDI ch.4) lower byte of RPN parameter number:7FH
(B3)
65 7F
(MIDI ch.4) upper byte of RPN parameter number:7FH
In other words, the above messages specify a value of 0C 00H for RPN parameter number
00 00H on MIDI channel 4, and then set the RPN parameter number to 7F 7FH.
RPN parameter number 00 00H is Pitch Bend Sensitivity, and the MSB of the value indicates
semitone units, so a value of 0CH = 12 sets the maximum pitch bend range to +/-12
semitones (1 octave). (On GS sound generators the LSB of Pitch Bend Sensitivity is ignored,
but the LSB should be transmitted anyway (with a value of 0) so that operation will be
correct on any device.)
Once the parameter number has been specified for RPN or NRPN, all Data Entry messages
transmitted on that same channel will be valid, so after the desired value has been
transmitted, it is a good idea to set the parameter number to 7F 7FH to prevent accidents.
This is the reason for the (B3) 64 7F (B3) 65 7F at the end.
It is not desirable for performance data (such as Standard MIDI File data) to contain many
events with running status as given in <Example 4>. This is because if playback is halted
during the song and then rewound or fast-forwarded, the sequencer may not be able to
transmit the correct status, and the sound generator will then misinterpret the data. Take
care to give each event its own status.
It is also necessary that the RPN or NRPN parameter number setting and the value setting
be done in the proper order. On some sequencers, events occurring in the same (or
consecutive) clock may be transmitted in an order different than the order in which they
were received. For this reason it is a good idea to slightly skew the time of each event (about
1 tick for TPQN = 96, and about 5 ticks for TPQN = 480).
* TPQN: Ticks Per Quarter Note