MIDI Implementation
20
4. Supplementary Material
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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.
+------+------++------+------++------+------++------+------+
| 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 (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.
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MIDI Message Examples
<Example 1> 92H 3EH 5FH
“9n” is a note on status and “n” is MIDI channel number.
As 2H = 2, 3EH = 62 and 5FH = 95, this is a note on message of MIDI CH = 3, note
number 62 (D4) and velocity 95.
<Example 2> CEH 49H
“CnH” is program change status and “n” is MIDI channel number.
As EH = 14 and 49H = 73, this is a program change message of MIDI CH = 15 and
program number 74.
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Example of an Exclusive Message and Calculating a
Checksum
Roland Exclusive messages are transmitted with a checksum at the end (before F7)
to make sure that the message was correctly received. The value of the checksum is
determined by the address and data (or size) of the transmitted exclusive message.
{
How to Calculate the Checksum
(Hexadecimal Numbers are Indicated by ‘H
The checksum is a value derived by adding the address, size and checksum itself and
inverting the lower 7 bits.
Here’s an example of how the checksum is calculated. We will assume that in the
exclusive message we are transmitting, the address is aa bb ccH and the data or size
is dd ee ffH.
aa + bb + cc + dd + ee + ff = sum
sum / 128 = quotient ... remainder
128 - remainder = checksum
(However, the checksum will be 0 if the remainder is 0.)
<Example>
In case you are setting Modulation of Control Change for Dissolve Time Ctrl Assign
using MIDI Visual Control ...
From “Parameter Address Map”, the start address of the Dissolve Time Ctrl Assign in
MIDI Visual Control is 10H 10H 02H and the
Modulation parameter in Control Change is 00H 01H. Therefore ...
F0H
7EH
00H
0CH 01H
10H 10H 02H
00H 01H
??H
F7H
(1)
(2)
(3)
(4)
(5)
(6)
(7)
(8)
(1) Exclusive Status
(2) ID Number (Universal SysEx Non Realtime)
(3) Device ID (0)
(4) Sub ID (MIDI Visual Contro Version 1.0)
(5) Address
(6) Data
(7) Checksum
(8) EOX
Next calculate the checksum. Add (5) to (6).
10H + 10H + 02H + 00H + 01H = 16 + 16 + 2 + 0 + 1 = 35 (sum)
35 (sum) / 128 = 0 (quotient) ... 35 (remainder)
Checksum = 128 - 35 (remainder) = 93 = 5DH
Thus, the message to transmit is :-
F0H 7EH 00H 0CH 01H 10H 10H 02H 00H 01H 5DH F7H
