With a lot of help I have figured most of what Cartooners's (and a few other games) music file headers contain:

1Endianess: little.
2Extension: *.mus
3
4[File Layout]
5[File Layout]
6Begin Structure: Header.
7	0x00	WORD		Relative MIDI track offset.
8	0x02	0x10 BYTES	Roland MIDI channel off/on table.
9	0x12	0x10 BYTES	Roland global MIDI volume table.
10	0x22	0x09 BYTES	Adlib MIDI channel initialization table.
11	0x2B	0x0C BYTES	CMS MIDI channel initializationtable.
12	0x37	0x0C BYTES	CMS MIDI channel finetune offset table.
13	0x43	0x08 BYTES	Tandy sound chip initialization table.
14	0x4B	WORD		PC-Speaker pitch and speed.	
15	0x4D	BYTES		Random data which may be anything without affecting the music/sound.
16End Structure
17
18Begin Structure: MIDI track data.
19	0x00	BYTES		MIDI track data.
20End Structure
21
22Begin Structure: Footer.
23	0x00	BYTE		MIDI event "Stop playback".
24	0x01	BYTE		Indicates whether or not the music/sound is played again when the end is reached: (0x80 = repeat, 0x81 stop.)
25End Structure
26
27[Notes]
28The headers typically contain the following string: "rsxx}u".
29
30[Other games with similar file MIDI music files]
31See the file "Electronic Arts Music Files.ods".

By modifying the header section marked as "Tandy related" and playing the music file using each sound driver supplied with Cartooners in turn and a compatible Tandy driver from a game called Populous I noticed modifying the data only affected playback when using the Tandy driver meaning these 8 bytes are specifically meant for playback with a Tandy sound chip. I looked up some Tandy sound chip data, but unfortunately I have never been good at understanding the technical details involving playing MIDI music through a soundcard. I have no idea how the values in the header relate to the sound chip's documentation. So, does anyone reading this any experience playing MIDI music using a Tandy soundchip?

Links:
A webpage documenting the Tandy sound chip: https://www.smspower.org/Development/SN76489
Bisqwit helped me figure out the Adlib/Roland/CMS/PC-Speaker related header data. His webpage: https://bisqwit.iki.fi/
My project: https://github.com/PeterSwinkels/Cartooners-File-Viewer

EDIT:
I changed the term "dedication" to "initialization" because the former term can't be found in any meaningful fashion as relating to soundcards. Bisqwit used that term and I think he confused the terms. 😀