MIDI division in the header chunk

Question

The last word of a MIDI header chunk specifies the division. It contains information about whether delta times should be interpreted as ticks per quarter note or ticks per frame (where frame is a subdivision of a second). If bit 15 of this word is set then information is in ticks per frame. Next 7 bits (bit 14 through bit 8) specify the amount of frames per second and can contain one of four values: -24, -25, -29, or -30. (they are negative)

Does anyone know whether the bit 15 counts towards this negative value? So the question is, are the values which specify fps actually 8 bits long (15 through 8) or are they 7 bit long(14 through 8). The documentation I am reading is very unclear about this, and I can not find info anywhere else.

Thanks

Answer 1

The MMA's Standard MIDI-File Format Spec says:

The third word, <division>, specifies the meaning of the delta-times. It has two formats, one for metrical time, and one for time-code-based time:

+---+-----------------------------------------+
| 0 |        ticks per quarter-note           |
==============================================|
| 1 | negative SMPTE format | ticks per frame |
+---+-----------------------+-----------------+
|15 |14                   8 |7              0 |

[...] If bit 15 of <division> is a one, delta times in a file correspond to subdivisions of a second, in a way consistent with SMPTE and MIDI Time Code. Bits 14 thru 8 contain one of the four values -24, -25, -29, or -30, corresponding to the four standard SMPTE and MIDI Time Code formats (-29 corresponds to 30 drop frome), and represents the number of frames per second. These negative numbers are stored in two's complement form. The second byte (stored positive) is the resolution within a frame [...]

Two's complement representation allows to sign-extend negative values without changing their value by adding a MSB bit of value 1. So it does not matter whether you take 7 or 8 bits.

In practice, this value is designed to be interpreted as a signed 8-bit value, because otherwise it would have been stored as a positive value.