Mach Rider doesn't have any credits, hence the mystery.
The above analysis is outdated and incorrect, though. Hideki Kanazashi is not credited in Melee, so Flat Zone must have been composed by Hirokazu Ando alone. Therefore, the tallies should look like this:
Quote:
12 Smash Bros. Great Medley (From Super Smash Bros. Melee Smashing... Live! Live Orchestra Music)
1. Ancient Kingdom I ---> Koji Kondo
2. Ancient Kingdom II ---> Koji Kondo
3. Flat Zone ---> Hirokazu Ando
4. Balloon Fight ---> Hirokazu Tanaka
5. Big Blue ---> Naoto Ishida
6. Mach Rider ---> ?
7. Yo'ster Isle ---> Koji Kondo
8. Saria's Song ---> Koji Kondo
9. Super Mario 3 ---> Koji Kondo
10. Icicle Mountain ---> Akito Nakatsuka
11. Peach's Castle ---> Koji Kondo
Original music by Koji Kondo, Akito Nakatsuka, Hirokazu Tanaka, Naoto Ishida (Nintendo Co., Ltd.), Hirokazu Ando, Hideki Kanazashi (HAL Laboratory, Inc.)
Tally:
Koji Kondo - 6
Akito Nakatsuka - 1
Hirokazu Tanaka - 1
Naoto Ishida - 1
--------------------------------------- Nintendo above; HAL below (HAL doing only one part of it)
Hirokazu Ando. - 1
Hideki Kanazashi - 0
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The Mach Rider theme is the only thing remaining that Hideki Kanazashi could have composed, so it must be his. If it's not, then the album made an error in crediting him.
Since Mach Rider only has a few short pieces besides the main BGM, my assumption is that Kanazashi composed all of it, but technically speaking we can't be certain of that.
There's more in this thread:
https://vgmdb.net/forums/showthread.php?t=3932.