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MIDI Implementation
4. Section 4. Supplementary material
● Decimal and Hexadecimal table
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.
+——————+——————++——————+——————++——————+——————++——————+——————+
| Dec. | Hex. || Dec .| Hex. || Dec. | Hex. || Dec. | Hex. |
+——————+——————++——————+——————++——————+——————++——————+——————+
|
0 |
00H ||
32 |
20H ||
|
1 |
01H ||
33 |
21H ||
|
2 |
02H ||
34 |
22H ||
|
3 |
03H ||
35 |
23H ||
|
4 |
04H ||
36 |
24H ||
|
5 |
05H ||
37 |
25H ||
|
6 |
06H ||
38 |
26H ||
|
7 |
07H ||
39 |
27H ||
|
8 |
08H ||
40 |
28H ||
|
9 |
09H ||
41 |
29H ||
|
10 |
0AH ||
42 |
2AH ||
|
11 |
0BH ||
43 |
2BH ||
|
12 |
0CH ||
44 |
2CH ||
|
13 |
0DH ||
45 |
2DH ||
|
14 |
0EH ||
46 |
2EH ||
|
15 |
0FH ||
47 |
2FH ||
|
16 |
10H ||
48 |
30H ||
|
17 |
11H ||
49 |
31H ||
|
18 |
12H ||
50 |
32H ||
|
19 |
13H ||
51 |
33H ||
|
20 |
14H ||
52 |
34H ||
|
21 |
15H ||
53 |
35H ||
|
22 |
16H ||
54 |
36H ||
|
23 |
17H ||
55 |
37H ||
|
24 |
18H ||
56 |
38H ||
|
25 |
19H ||
57 |
39H ||
|
26 |
1AH ||
58 |
3AH ||
|
27 |
1BH ||
59 |
3BH ||
|
28 |
1CH ||
60 |
3CH ||
|
29 |
1DH ||
61 |
3DH ||
|
30 |
1EH ||
62 |
3EH ||
|
31 |
1FH ||
63 |
3FH ||
+——————+——————++——————+——————++——————+——————++——————+——————+
* Decimal values such as MIDI channel, bank select, and program change are listed as one (1)
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 "nibbled" 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.
<Example1> What is the decimal expression of 5AH?
From the preceding table, 5AH = 90
<Example2> 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
<Example3> 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
<Example4> 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 answer is 00 04 0E 0AH.
14
64 |
40H ||
96 |
60H |
65 |
41H ||
97 |
61H |
66 |
42H ||
98 |
62H |
67 |
43H ||
99 |
63H |
68 |
44H ||
100 |
64H |
69 |
45H ||
101 |
65H |
70 |
46H ||
102 |
66H |
71 |
47H ||
103 |
67H |
72 |
48H ||
104 |
68H |
73 |
49H ||
105 |
69H |
74 |
4AH ||
106 |
6AH |
75 |
4BH ||
107 |
6BH |
76 |
4CH ||
108 |
6CH |
77 |
4DH ||
109 |
6DH |
78 |
4EH ||
110 |
6EH |
79 |
4FH ||
111 |
6FH |
80 |
50H ||
112 |
70H |
81 |
51H ||
113 |
71H |
82 |
52H ||
114 |
72H |
83 |
53H ||
115 |
73H |
84 |
54H ||
116 |
74H |
85 |
55H ||
117 |
75H |
86 |
56H ||
118 |
76H |
87 |
57H ||
119 |
77H |
88 |
58H ||
120 |
78H |
89 |
59H ||
121 |
79H |
90 |
5AH ||
122 |
7AH |
91 |
5BH ||
123 |
7BH |
92 |
5CH ||
124 |
7CH |
93 |
5DH ||
125 |
7DH |
94 |
5EH ||
126 |
7EH |
95 |
5FH ||
127 |
7FH |
● Examples of actual MIDI messages
<Example1> 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.
<Example2> 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).
<Example3> 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 128 + 0 = 8192) is 0, so this Pitch Bend Value is
28 00H - 40 00H = 40 x 128 + 0 - (64 x 128 + 0) = 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.
<Example4> 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 sources 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 source 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
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