Is melodic and harmonic minor scales referred to in any song as a scale? How are they represented e.g C means C major scale and Cm means C minor scale. In this way how will you say if a composition is in harmonic or melodic minor scale, since they don't have separate biey signature.
This always seems to be a confusing issue, but if a piece is in C minor, that's it, it's in C minor. Due to arrangements made centuries ago, the notes which make up C minor have been divided for simplicity into different scales, but any, some, or indeed all of the notes which are in the individual scales can be and are used in pieces in C minor, or any other minor key.
The natural minor has exactly the same notes as its relative major, so for Cm it's three flats, as in Eb major.
The harmonic minor was formed to produce a convincing leading note, just one semitone below the tonic, so it sounds more like it would in a major key.
The melodic minor then came along, which raises the 6th note as well - it was thought that the intervals were too large otherwise. But with descending lines of music, the natural minor notes sounded better. Thus the melodic has two different sets of notes, ascending and descending. Jazzers tend to use the ascending scale notes most of the time, but let's face it, they're not spending their performance time playing scales!
Interesting to note (sic) that all three use the same first five notes, and the melodic rising then reverts to the same last notes as its parallel key scale.
So, in summation - pieces in C minor may contain C D Eb G Ab A Bb B. For fairly obvious reasons, they won't constitute a scale per se.
So, basically, don't look for or expect a piece to be in harmonic or melodic minor, because that's really not how minor pieces work. And, looking at the key sig., it only gives a clue that it's in C minor with those 3 flats.
Cm is a chord symbol, denoting the triad C, Eb, G. Or it's the name of the key for which that is the tonic chord.
Then it gets a bit messy. There are three main forms of the minor scale. (Notice that I don't say 'modes', because this is a bit different to the usual meaning of 'mode' - a major scale running not from (for instance) C to C but from D to D, but using the same notes. But you will find 'mode' used to describe the different minor scales.)
Natural Minor. Up and down according to the key signature.
Harmonic Minor. Same thing, but with the 7th note raised so that the V chord becomes major. Now we can do perfect cadences!
Melodic Minor. 6th and 7th note raised on the way up, reverting to the key signature on the way down. Supposedly better for melodic lines, it avoids the awkward augmented 2nd between 6 and 7 of the harmonic scale, but still includes a nice sharpened leading note so we can still do functional harmony.
A piece nominally in C minor may use just one of these scales. Or all of them. Some composers obviously just don't know their 'theory', and refuse to stick to one scale! Maybe we ought to have three (or more) 'key' names rather than just 'C minor'. But we don't.