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I'm a hobbyist composer and I just started reading Piston's Harmony handbook to recover the basics I never learned. One of the limits I'm trying to overcome is my inability to conceive melodies that can be arranged in a "theme and variations" piece: many melodies I compose are very regular and 'closed' and it's hard for me to imagine them reproposed in different ways (like they would be e.g. in a fugue). I want to stress that I tend to absorb much from the music I listen and I passed many years listening mostly pop / rock / metal.

In the chapter about Function and structure of melody I discovered the difference between a tune ("tunes have a 'closed' internal structure: after their last phrase they don't imply any prosecution") and a symphonic melody ("... is to be used in a more ample work [...] usually doesn't contain strong cadences on the tonic; the absence of a conclusive end allows the symphonic melody to go on, when necessary").

I think my melodies fit the description of the tune, and I seem to recognize in the symphonic melody the features that I desire to exploit. Is my intuition right? Is there a way to turn a tune in a symphonic melody? Am I missing something obvious in my inexperience?

[PS] Sorry for any mismatch between my "quotes" and the original Piston text: I translated on the fly from my mother tongue, the terms may not be exact but I think the core ideas are clear.

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    Try listening to some "classical" sets of variations. The theme of Brahms's "St Antony Chorale" variations is about as rhythmically closed as it gets, but the variations aren't. Or figure out how all the variations in Rachmaninov's "Rhapsody on a theme by Paganini" relate to the original theme - the well known 18th variation is a good example! Then apply the same ideas to rock, if you want to.
    – user19146
    Oct 14, 2017 at 19:36
  • You may think this odd, phagio, but the themes of "theme and variations" pieces strongly tend to have "closed" internal structures. This includes original themes (i.e. the composer made them up) as well as arranged themes (e.g. "Ah! Vous dirai-je Maman", Paganini's Caprice No. 24 in A Minor).
    – Dekkadeci
    Oct 15, 2017 at 16:25
  • @Dekkadeci I see what you mean, these examples make it perfectly clear. I'm afraid I misused the phrasing "theme and variation", as I intended a more "romantic" approach (like Beethoven's 6th or 9th symphonies) or a "fugue" as repetition of the same theme with different variations within the piece itself. However your comment is precious and I'll study these pieces thoroughly ;)
    – phagio
    Oct 20, 2017 at 13:23

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If you consider a melody such as Handel's 'Harmonious Blacksmith' you will see that it is comprised of several motives. In symphonic composition there are usually several motives, but not all of the motives are necessarily developed. The point of Air and Variations form is that the variations are typically based on the entire air: the listener has the pleasure of hearing the variations over the 'template' of the original air. If you want 'symphonic', compose a melody comprised of several motives and run with one or two of them, but if you want Air and Variations, run with the entire melody. If you want fugue, you will need to be careful and make sure that no notes will clash when the melody is duplicated and displaced by one, two, three or more bars, and here's the kicker: you will have to do that for every variation that is fugue-based. It would be simpler to start by adding a dash of canon to one or more variations. Rather than worrying about 'open' and 'closed' melodies, just strive for a strong one and get stuck into the variations. Make a list of all the ways you can think of to vary a melody, then work your way methodically through them. Also note that typically the variations start simple and get successively more complicated.

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A good approach (in addition to those already suggested) would be to read about "musical form" (a big topic.) An old but free book is: https://archive.org/details/musicalform00leic

Even older: https://archive.org/details/manualofmusicalf00jada https://archive.org/details/cu31924022264349

A rather good one; the examples are old-fashioned but can easily be updated. https://archive.org/details/exercisesinmelo00goetgoog

These (especially the last) will give you a bit of insight in how to analyze the scores you should be reading and listening to.

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