15
7. Supplementary Material
9
Decimal 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.
+------+------++------+------++------+------++------+------+
| D | H || D | H || D | H || D | H |
+------+------++------+------++------+------++------+------+
| 0 | 00H || 32 | 20H || 64 | 40H || 96 | 60H |
| 1 | 01H || 33 | 21H || 65 | 41H || 97 | 61H |
| 2 | 02H || 34 | 22H || 66 | 42H || 98 | 62H |
| 3 | 03H || 35 | 23H || 67 | 43H || 99 | 63H |
| 4 | 04H || 36 | 24H || 68 | 44H || 100 | 64H |
| 5 | 05H || 37 | 25H || 69 | 45H || 101 | 65H |
| 6 | 06H || 38 | 26H || 70 | 46H || 102 | 66H |
| 7 | 07H || 39 | 27H || 71 | 47H || 103 | 67H |
| 8 | 08H || 40 | 28H || 72 | 48H || 104 | 68H |
| 9 | 09H || 41 | 29H || 73 | 49H || 105 | 69H |
| 10 | 0AH || 42 | 2AH || 74 | 4AH || 106 | 6AH |
| 11 | 0BH || 43 | 2BH || 75 | 4BH || 107 | 6BH |
| 12 | 0CH || 44 | 2CH || 76 | 4CH || 108 | 6CH |
| 13 | 0DH || 45 | 2DH || 77 | 4DH || 109 | 6DH |
| 14 | 0EH || 46 | 2EH || 78 | 4EH || 110 | 6EH |
| 15 | 0FH || 47 | 2FH || 79 | 4FH || 111 | 6FH |
| 16 | 10H || 48 | 30H || 80 | 50H || 112 | 70H |
| 17 | 11H || 49 | 31H || 81 | 51H || 113 | 71H |
| 18 | 12H || 50 | 32H || 82 | 52H || 114 | 72H |
| 19 | 13H || 51 | 33H || 83 | 53H || 115 | 73H |
| 20 | 14H || 52 | 34H || 84 | 54H || 116 | 74H |
| 21 | 15H || 53 | 35H || 85 | 55H || 117 | 75H |
| 22 | 16H || 54 | 36H || 86 | 56H || 118 | 76H |
| 23 | 17H || 55 | 37H || 87 | 57H || 119 | 77H |
| 24 | 18H || 56 | 38H || 88 | 58H || 120 | 78H |
| 25 | 19H || 57 | 39H || 89 | 59H || 121 | 79H |
| 26 | 1AH || 58 | 3AH || 90 | 5AH || 122 | 7AH |
| 27 | 1BH || 59 | 3BH || 91 | 5BH || 123 | 7BH |
| 28 | 1CH || 60 | 3CH || 92 | 5CH || 124 | 7CH |
| 29 | 1DH || 61 | 3DH || 93 | 5DH || 125 | 7DH |
| 30 | 1EH || 62 | 3EH || 94 | 5EH || 126 | 7EH |
| 31 | 1FH || 63 | 3FH || 95 | 5FH || 127 | 7FH |
+------+------++------+------++------+------++------+------+
D: decimal
H: hexadecimal
*
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.
<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 result is: 00 04 0E 0AH.
9
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.
<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
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.
<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 this 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
