Etymonline has this to say:
-ics
in the names of sciences or disciplines (acoustics, aerobics, economics, etc.) it represents a 16c. revival of the classical custom of using the neuter plural of adjectives with -ikos (see -ic) to mean "matters relevant to" and also as the titles of treatises about them. Subject matters that acquired their names in English before c.1500, however, tend to remain in singular (e.g. arithmetic, logic).
So yes, at some point in history, there were such things as physic (meaning "natural science"), mathematic (meaning "mathematical science"), etc. that were later turned into plural forms but kept being treated as singular.
Edit: having looked in a few more places, it appears that in contemporary English, it still makes some sense to have both the suffix -ic and its plural form -ics. According to the Collins English Dictionary, the former has kind of specialized in forming adjectives, while the latter is happily forming nouns:
-ic
suffix forming adjectives
- of, relating to, or resembling: allergic, Germanic, periodic. See also -ical.
[...]
[from Latin -icus or Greek -ikos; -ic also occurs in nouns that represent a substantive use of adjectives (magic) and in nouns borrowed directly from Latin or Greek (critic, music)]
[...]
-ics
suffix forming nouns (functioning as singular)
- indicating a science, art, or matters relating to a particular subject: aeronautics, politics
- indicating certain activities or practices: acrobatics
[plural of -ic, representing Latin -ica, from Greek -ika, as in mathēmatika mathematics]
The key here is that they are not just two unrelated suffixes. Much rather, one is etymologically a plural form of the other. As the American Heritage Dictionary succinctly puts it, -ics is "-ic + -s".
That's because software is uncountable, or a mass noun.
In English, mass nouns are characterized by the fact that they cannot be directly modified by a numeral without specifying a unit of measurement, and that they cannot combine with an indefinite article (a or an).
Edit: in reply to your edit, the key here is -ware:
- Used to form nouns denoting, collectively, items made from a particular substance. glassware
- Used to form nouns denoting, collectively, items of a particular kind or for a particular use. giftware
Note the word "collectively". Software was coined in 1953 by contrast with hardware. You wouldn't say "I need two new hardwares", either.
Best Answer
Music is an uncountable noun in most senses: that is a word that refers to a group or an amount of something, or to some broad concept that there cannot be two of.
Music is an art or a human category of sounds; it is not a particular instance of something related to this art. For such an instance, you could use piece of music, song, number, movement, ballad, ouverture, etc., depending on what kind of instance you were thinking of.
The same applies to nouns like water: you can't say "I have two waters for you" (except in special circumstances), but rather "two gallons of water", or "two cups of water". Nor could you say "I have many loves for you", or "could you move a couple of sands closer to the beach". A few instances of common uncountable nouns:
As you see, specific kinds of instances of uncountable nouns can be indicated by different countable nouns, such as piece, grain, patch, etc. Some of these uncountable nouns can be countable if used in a different sense. Note that it is not always obvious from meaning whether a noun is countable or not: to some extent that is something that needs to be learnt word by word, alas.