Think of a track in the MIDI file in the same way that you normally think of a track in a sequencer. A sequencer track contains a series of events. For example, the first event in the track may be to sound a middle C note. The second event may be to sound the E above middle C. These two events may both happen at the same time. The third event may be to release the middle C note. This event may happen a few musical beats after the first two events (ie, the middle C note is held down for a few musical beats). Each event has a "time" when it must occur, and the events are arranged within a "chunk" of memory in the order that they occur.

In a MIDI file, an event's "time" precedes the data bytes that make up that event itself. In other words, the bytes that make up the event's time-stamp come first. A given event's time-stamp is referenced from the previous event. For example, if the first event occurs 4 clocks after the start of play, then its "delta-time" is 04. If the next event occurs simultaneously with that first event, its time is 00. So, a delta-time is the duration (in clocks) between an event and the preceding event.

NOTE: Since all tracks start with an assumed time of 0, the first event's delta-time is referenced from 0.

A delta-time is stored as a series of bytes which is called a variable length quantity. Only the first 7 bits of each byte is significant (right-justified; sort of like an ASCII byte). So, if you have a 32-bit delta-time, you have to unpack it into a series of 7-bit bytes (ie, as if you were going to transmit it over midi in a SYSEX message). Of course, you will have a variable number of bytes depending upon your delta-time. To indicate which is the last byte of the series, you leave bit #7 clear. In all of the preceding bytes, you set bit #7. So, if a delta-time is between 0-127, it can be represented as one byte. The largest delta-time allowed is 0FFFFFFF, which translates to 4 bytes variable length. Here are examples of delta-times as 32-bit values, and the variable length quantities that they translate to: 


 NUMBER        VARIABLE QUANTITY
00000000              00
00000040              40
0000007F              7F
00000080             81 00
00002000             C0 00
00003FFF             FF 7F
00004000           81 80 00
00100000           C0 80 00
001FFFFF           FF FF 7F
00200000          81 80 80 00
08000000          C0 80 80 00
0FFFFFFF          FF FF FF 7F
Here are some C routines to read and write variable length quantities such as delta-times. With WriteVarLen(), you pass a 32-bit value (ie, unsigned long) and it spits out the correct series of bytes to a file. ReadVarLen() reads a series of bytes from a file until it reaches the last byte of a variable length quantity, and returns a 32-bit value. 
void WriteVarLen(register unsigned long value)
{
   register unsigned long buffer;
   buffer = value & 0x7F;

   while ( (value >>= 7) )
   {
     buffer <<= 8;
     buffer |= ((value & 0x7F) | 0x80);
   }

   while (TRUE)
   {
      putc(buffer,outfile);
      if (buffer & 0x80)
          buffer >>= 8;
      else
          break;
   }
}

unsigned long ReadVarLen()
{
    register unsigned long value;
    register unsigned char c;

    if ( (value = getc(infile)) & 0x80 )
    {
       value &= 0x7F;
       do
       {
         value = (value << 7) + ((c = getc(infile)) & 0x7F);
       } while (c & 0x80);
    }

    return(value);
}
NOTE: The concept of variable length quantities (ie, breaking up a large value into a series of bytes) is used with other fields in a MIDI file besides delta-times, as you'll see later.

For those not writing in C, you may benefit from a psuedo-code explanation of the above routines. In pseudo-code, ReadVarLen() is:

  1. Initialize the variable which will hold the value. Set it to 0. We'll call this variable 'result'.
  2. Read the next byte of the Variable Length quantity from the MIDI file.
  3. Shift all of the bits in 'result' 7 places to the left. (ie, Multiply 'result' by 128).
  4. Logically OR 'result' with the byte that was read in, but first mask off bit #7 of the byte. (ie, AND the byte with hexadecimal 7F before you OR with 'result'. But make sure you save the original value of the byte for the test in the next step).
  5. Test if bit #7 of the byte is set. (ie, Is the byte AND hexadecimal 80 equal to hexadecimal 80)? If so, loop back to step #2. Otherwise, you're done, and 'result' now has the appropriate value.

In pseudo code, WriteVarLen() could be:

  1. Assume that you have a variable named 'result' which contains the value to write out as a Variable Length Quantity.
  2. Declare an array which can contain 4 numbers. We'll call this variable 'array'. Initialize a variable named 'count' to 0.
  3. Is 'result' less than 128? If so, skip to step #8.
  4. Take the value 'result' AND with hexadecimal 7F, and OR with hexadecimal 80, and store it in 'count' element of 'array'. (ie, The first time through the loop, this gets stored in the first element of 'array'). NOTE: Don't alter the value of 'result' itself.
  5. Increment 'count' by 1.
  6. Shift all bits in 'result' 7 places to the right. (This can be done by dividing by 128).
  7. Loop back to step #3.
  8. Take the value 'result' AND with hexadecimal 7F, and store it in 'count' element of 'array'.
  9. Increment 'count' by 1.
  10. Write out the values stored in 'array'. Start with the last element stored above, and finish with the first element stored. (ie, Write them out in reverse order so that the first element of 'array' gets written to the MIDI file last). NOTE: The variable 'count' tells you how many total bytes to write. It also can be used as an index into the array (if you subtract one from it, and keep writing out bytes until it is -1).