In No(b), it is said A minor with G sharp. I wanna know this does not look like a scale so does A minor(harmonic) with G sharp need to be in a row like A B C D E G# A ? And when we use (A harmonic) in real music, do we use like a row or can we use break down randomly including G#? As shown in the above picture? Thank you.
The notes which constitute A harmonic minor are -A, B, C, D, E, F and G♯. They are of course used when playing the A harmonic minor scale, in that order (and reversed), but many many pieces use these particular notes and no others in any order needed.
That doesn't mean we say the piece is in 'A harmonic minor', but simply in 'A minor'.
The notes which constitute 'A minor' are chosen from the pool of - A, B, C, D, E, F, F♯, G, and G♯.
EDIT: it would be interesting to find out what the top line key is said to be. There are F and C sharps, but the last bar contains a C natural. Odd.
It's just that they can be used sequentially in three different forms, creating natural, harmonic and melodic minor scales.
No, the notes don't have to be in a scale.
I think the main thing to look for is the treatment of the sixth scale degree. If you see a raised sixth degree, it's good indicator the passage is using the "melodic minor."
Another thing to look for is various forms of these melodic patterns:
- ^5 ♭^6 ^5 and ^1 ♯^7 ^1 which happens a lot in harmonic minor
- ♯^6 ♯^7 ^1 which is characteristic of ascending melodic minor
Obviously those patterns will involve a lot of other melodic material, but you can think of them a common prototypes in minor key music.
What you have shown here is a set of questions asking to note down the key by looking at the accidentals. Playing and writing scales are fundamental exercises one should involve in to succeed in musical studies and career. But, the pieces that we come across comprise of tunes, not all notes of a tune are arranged in the same order of its key.
If we take a look at the first stave, the only accidentals are F# and C#. So, the key is D major. In other words, it is a melody written in D major.
In the second stave(no b), G# is the only accidental.(This must be the one you are referring to) Here, the key is A minor. Try playing these notes on a piano and listen to the melody. Key signatures are a concept introduced to maintain proper standards of musical composition. Notes of a scale need not be in the same order of the scale when it comes to composition.
Do harmonic or melodic need to be serial row when we use in real sheet?
If you're writing serial/dodecaphonic music, then, of course, yes. Otherwise, no. As colleagues appointed, that's not a serial example here in the image.
But be aware that some degree of freedom exists in both worlds. And, also, there are very sophisticated serial techniques in which the real row is "hidden" underneath other series and rotations (Brian Ferneyhough, for example), and you may end up being insanely crazy looking for these relationships from scratch.