Even if related to music, what you have here is symbology. I would bet it is some form of mathematics, even though I don't recognize the formulas.
Symbols should not be translated.

This was discussed in great detail on Hon'yaku in 1997 (see link below). Here is a partial excerpt from one of the "conclusions":
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Some people [...] suggested that it is the most recognizable part of the melody, which is what I thought when I used "main theme" [...] but that was before I had the benefit of all the ideas discussed on this thread. Some translations that seem appropriate depending on the context are:

Bridge: Found in dictionaries by several respondents and confirmed by [...] especially appropriate in a Tin Pan Alley or older pop song context with a AABA or similar structure.

Release: Suggested by several dictionaries, but I'm not quite sure what it means. It seems to be an older term.

Hook: Suggested by [...] from his current experiences jamming with Japanese musicians.

High Point or Focal Point: Suggested by [...] from his experience in playing with Japanese musicians.

Some other ideas presented:
Chorus, Tag, Refrain

This is most frequently the chorus, but other possibilities exist: intro, melody, transition, etc. As a rough guide, I'd say anything that another artist might sample or that might appear on a "name that tune" quiz program.

I'm not quite sure what a bridge or tag is, but both sound plausible as candidates.

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Note added at 2003-01-11 11:53:15 (GMT) Post-grading
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Fame is relative. Nowhere did I say that the song itself had to be famous.

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Note added at 2003-01-11 11:55:21 (GMT) Post-grading
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Blurryeyes seems to covered all the bases.

Thanks for ¥"Star Wars¥" as an example for intro. Can anybody hum more than that? All I remember is typical John Williams strings treatment...

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Note added at 2003-04-14 10:16:34 (GMT) Post-grading
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Today, I learned that what I termed the ¥"most famous bit¥" is called the ¥"money hook¥":

¥"Oftentimes, the musical hook for a song, or the money hook -- the one that sells the song -- is not technically an element of the songwriting itself, but a part of the song¥'s arrangement. A musical hook can be a riff (like the guitar figure at the beginning of ¥"Satisfaction¥" by the Rolling Stones), a rhythmic hook (like the manic tom-tom drums that open ¥"Wipe Out¥" by the Surfaris), or a sound effect hook (like the revving motorcycle engine at the beginning of ¥"Born to Be Wild¥" by Steppenwolf).

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Note added at 2003-04-14 10:20:23 (GMT) Post-grading
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¥"Bridge¥" has been offered elsewhere, but

www.writerswrite.com/journal/oct02/dawson33.htm

says ¥"A bridge takes the song in a different direction,¥" which is not necessarily the サビ (although it is a prime candidate because it tends to be ¥"catchy.¥"

See the link. Enough said.

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Note added at 2002-05-02 16:16:28 (GMT)
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これは曲の盛り上がり部分を指して言う言葉です。

so you could say サビ refers to a part where the mood of the song is at the highest.


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Note added at 2002-05-02 16:19:50 (GMT)
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I believe shyboy75¥'s ¥"hook¥" would come closest to what you¥'re looking for.

Generally speaking, サビ・サビ部分 in terms of music and musical score, is what I would translate as the most "juicy" or "catchy" part of the song. Hence, this is similar to what Ozaru stated, the "main theme" or as Maynard Hogg suggested, the "most famous bit."

To explains things a bit:

To be more specific, in pop/rock/rap/etc modern genres of music, the サビ of a song is usually what musicians call the "chorus" or "hook" of a song. (As Shyboy and Mike Sekine stated) I don't want to go into detail to what a "Chorus" of a song is, but simply put, it's the part (measures) of a song where the mood of the song is at the "highest" as Mike said. I like to simply say it’s the “juicy” / “catchy” part/melody of the song where the message of the song is felt the most.

Somebody also brought up the "bridge" of a song, but it's important to know that the "bridge" of a song is usually not the サビ of a song. The "bridge" of a song is the melody/measures which comes before the サビ, which is called the Bメロ。I have seen people, and even musicians call the "bridge" of a song as the サビ on occasion because a song lacked a bridge melody to begin with, therefore they called what really is the "chorus" as the “bridge.” And thus, the “bridge” as the サビ。When in true theory, it’s really the “chorus” that is the サビ. In any case, the "chorus" or "hook" is a more accurate translation for サビ than “bridge.” However, in terms of music overall, I don’t think “chorus” would always be the appropriate translation for サビ。This is because music is not confined to a certain principle, and there are different genres of music. Saying “chorus” may not be appropriate in certain genres of music, such as classical, jazz, ethnic music, etc.

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Note added at 2002-05-02 23:49:40 (GMT)
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The intro of a song can also be the サビ 部分 of a song. This is especially evident in instrumental music/dance/trance/techno/classical music where there are no vocals in the song. For example: the ¥"sabi¥" of the Stars Wars theme is the intro melody that everybody is familiar with.

Also, a lot of pop songs begin with the ¥"chorus¥" instead of the verse, therefore people tend to think that the opening of a song can also be the サビ. This is actually not true, it¥'s just how the song is structured, and in this case, the ¥"chorus¥" just happens to be placed at the beginning of the song (perhaps to catch the attention of the listener immediately). To say the that the opening of a song is the サビ is subjective in this case. A more true statement would be, the サビ melody is also AT the opening of the song.

You won’t hear a Japanse person say,「イントロが曲のサビだよ〜」
Instead they’ll say something like「曲のイントロからサビのメロディーが流れている〜」

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Note added at 2002-05-03 00:13:44 (GMT)
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To AyeJay¥'s statment of ¥"Famous bit¥": songs don¥'t have to be famous to have a サビ.

I don¥'t believe I ever said they had to be. Perhaps I may have misguided you into thinking that way though. In terms of Maynard¥'s ¥"famous bit¥" I interpret this as a song¥'s most ¥"recognizable part/melody¥" similar to the definition of a ¥"Main Theme.¥"

BTW, I think a lot of you may be perhaps oblivious or are completely forgeting about the origins of the word サビ. It comes from the word さびつく, which means to get ¥"attached and stuck on to¥"
「ほかの物にくっついて離れなくなる」

Translate this meaning to music, and what do you get? Yes, the part/rhythm/melody of a song which STICKS on to your brain, and you can¥'t get out of you mind!
(^_^)

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Note added at 2002-05-03 00:15:56 (GMT)
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To AyeJay¥'s statment of ¥"Famous bit¥": songs don¥'t have to be famous to have a サビ.

I don¥'t believe I ever said they had to be. Perhaps I may have misguided you into thinking that way though. In terms of Maynard¥'s ¥"famous bit¥" I interpret this as a song¥'s most ¥"recognizable part/melody¥" similar to the definition of a ¥"Main Theme.¥"

BTW, I think a lot of you may be perhaps oblivious or are completely forgeting about the origins of the word サビ. It comes from the word さびつく, which means to get ¥"attached and stuck on to¥"
「ほかの物にくっついて離れなくなる」

Translate this meaning to music, and what do you get? Yes, the part/rhythm/melody of a song which STICKS on to your brain, and you can¥'t get out of you mind!
(^_^)

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Note added at 2002-05-03 00:18:40 (GMT)
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The intro of a song can also be the サビ 部分 of a song. This is especially evident in instrumental music/dance/trance/techno/classical music where there are no vocals in the song. For example: the ¥"sabi¥" of the Stars Wars theme is the intro melody that everybody is familiar with.

Also, a lot of pop songs begin with the ¥"chorus¥" instead of the verse, therefore people tend to think that the opening of a song can also be the サビ. This is actually not true, it¥'s just how the song is structured, and in this case, the ¥"chorus¥" just happens to be placed at the beginning of the song (perhaps to catch the attention of the listener immediately). To say the that the opening of a song is the サビ is subjective in this case. A more true statement would be, the サビ melody is also AT the opening of the song.

You won’t hear a Japanse person say,「イントロが曲のサビだよ〜」
Instead they’ll say something like「曲のイントロからサビのメロディーが流れている〜」

i agree with shyboy75 though i put it simply, a "hook"

definition: A catchy motif or refrain.

"Sabi" as a cultural term refers to "antique" or "refined elegance." But in the popular world of music, it appears to be used more loosely.