Devanagari, the script used for the likes of Hindi, Rajasthani
and often Sanskrit, and its allied North Indian scripts such as
Bengali and Gurumukhi, have an interesting resemblance to
Western musical notation, with a horizontal line from which
the individual characters "dangle" or occasionally
above. The exception to this is Gujurati, which has plain
characters with no line and the South Indian scripts also lack
the line entirely.
Musical notation is superficially similar. It often has a
vertical line linking notes below which the notes dangle or
sometimes above which they project. There are also signs
indicating other features.
These can be combined. Each character, or more accurately
cluster of characters, represents a syllable, which is also a
note. These syllables can be conjunct consonants, similar to
how notes can be written on the same vertical line when
they occur together. A breve can be represented by a
hollow outline of a letter. Where a syllable occurs alone and
is of crotchet length, it can be written without a line as in
Gujurati or the South Indian scripts. The script can also be
used for non-Indian languages.
Hence you end up with a musical manuscript with staves,
treble and bass clefs, time signatures and the rest, which
represents song lyrics and melody in one go. There is no
more need for them to occur on different lines. The song is
completely represented by one set of characters.
Oddly, this wouldn't work for traditional Indian music.