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This question bugs me since I started writing music. I'm asking in general, but I'll show an example so it would be more clear. Keep in mind the notation is arbitrary, as I don't quite know what I'm doing.

voice 1

This is an 8-bar excerpt from the piece I'm working on currently. Judging by the notes that fall on the strong beats I would guess this is somewhat E-minor-ish. The chromatic rundown skips A natural even though it is present in the first bar. So the question is does this have a chord progression, or is it just Em throughout? I can't tell. But there is another voice.

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This one is much simpler. It reinforces A natural, but it also has Bb (or should it be A#). Which would imply a flat fifth in the scale. But it still fits into the E-minor-ish sound. But there is a third voice. enter image description here

Here you have F# and G which are again notes of E-minor, the problem arises when the upper F# becomes natural. With another voice playing E at the same time this would make it a cluster of 4 semitones in a row (E F F# G). And if this is indeed E-minor that would make it so it has both natural and flattened second degree playing at the same time. But with this third voice added I feel like there appears an implication of a chord change when F# becomes natural.

Now the problem is that I have to write a bass line and without knowing what kind of harmony I'm dealing with it became an impossible task. I tried treating this as E-minor and it didn't work well. Sometimes I felt like this is centered in A-minor, but nothing came out of that too. So unless someone opens my eyes I feel like I'm stuck. So if you have any ideas I would love to hear them.

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    Maybe it's become an impossible task due to you resorting to theory. It's a very simplistic view, but whatever sounds best probably is best. The technicality of what key comes later. – Tim Aug 20 '19 at 18:10
  • There aren't any rules, just things that fit with expectations or challenge expectations. If composing were like drawing, then I would suggest the melody is like the outlines of shapes and the chords and harmony are the colors. You might draw an outline of a ball that has stitches on it so that it looks like a baseball, and then the natural colors would be white and red. Similarly, a melody might have a "natural" harmonization for it (or several). On the other hand, if you just draw a circle to represent a ball, it could be any color you like. or you could make your baseball strange colors. – Todd Wilcox Aug 20 '19 at 20:48
  • When you write an unusual melody, you might have to come up with an unusual harmony if you want it to sound a certain way. Unless you know a lot of theory to be able to just "see" a harmonization that sounds how you want it to sound, you might just have to pick at it and experiment until you find what you're looking for (or listening for). – Todd Wilcox Aug 20 '19 at 20:49
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    I suspect your piece is in A minor from the looks of it (and the repeated E is treated as a dominant), but I also suspect that your piece sounds rather like a chromatic mess because E, F, F#, G, and A are playing simultaneously at points, and one of your parts has a chord consisting of F, F#, and G. I'd need to listen to an audio clip to make sure, but it's quite possible that your piece sounds atonal in practice. – Dekkadeci Aug 20 '19 at 23:59
  • You're asking for a 'right answer' to how to harmonise this piece. There isn't one. There isn't even an obvious one, with less conventional alternatives. Sorry! – Laurence Payne Jul 20 at 17:09
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The general answer

To start, it's worth making a distinction between a tone center and a pitch center. I infer from your use of "tone center" that you're looking for a "tonic" pitch -- that is, "what key/mode am I in?"

Nevertheless, one way to attempt to figure out the key and mode is simply to take each unique pitch in your piece, place them in pitch-ascending order starting from what you perceive to the the "primary" pitch, and see what you get. Of course, if you have too few pitches you might get nothing, and if you have too many, you just get a chromatic scale.

By definition, an ambiguous or sufficiently chromatic musical passage doesn't have a tonal center. It might have a "pitch center" -- that is, a pitch that the listener perceives as a stable point or point of focus -- but not be in a key.

For example, Ligeti's Musica Ricercata, no. 1, has a clear pitch center -- A -- but it cannot be said to be "in the key of" anything.

But you can force a tonal center on otherwise ambiguous situation.

The melody of Samuel Barber's "Nocturne", op. 13 no. 4 is built on a twelve-tone row, so has no pitch center. However, by embedding the twelve-tone melody in a tonal-sounding harmony, the whole piece winds up sounding like Ab Major. The piece stands up to a twelve-tone interpretation in a very clear and logical way, but woe to the person attempting a tonal analysis without stretching the rules to meaninglessness.

Toward a specific answer

I think your composition is sufficiently ambiguous so as to say it doesn't have a tonal center, but certainly E and A are candidates for pitch center.

You've built (this part of) your piece around two musical ideas: 1) a "chord" (maybe better to call it a "simultaneity") consisting of the pitches F# G and A, plus E and/or Bb, and 2) a three-note chromatic cell, always descending, sometimes transposed.

As is, I hear your piece with E as the pitch center. But I like the sound of Bb in the bass against the chord-centric moments, "resolving" to an A in the bass against the chromatic moments. To my ear, that gives the E a sort of "dominant" feel, and the A a "tonic" feel. If placed in rhythmically interesting places, I think those two pitches alone would give a pretty cool sound, maybe like a funky A minor. Now that I think about it, let's apply the suggestion above of ordering the pitches. The scale would look something like A Bb [C D] E F# G, which, ta-da!, is second mode of G melodic minor. (C and D are in brackets, because you don't use those pitches in a significant way.)

You might consider making the piece even more rhythmically ambiguous, to go with the tonal ambiguity. You can do that by having the bass play at irregular intervals. That would still be compatible with the Bb - A suggestion if you like it.

Etc., etc., etc. ...

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