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Is there some theory that suggests that sequences may be formed by "sampling" earlier sequences?

Often music theory seems to suggest progression as "where to go next", but I've been playing around and wondered about, whether it's also possible that one may progress by doing e.g.

say we have four notes in a bar
[n1 n2 n3 n4]
write next bar as an union of samples from previous bar, e.g.
[n1 n2 n3 n4] [[n3 n4] U [[n4] U [n4]]]
can this produce sensible melody progressions?

This kind of technique is very often used in sample-based music, but I've not thought about it in the context of notational music.

This approach would suggest that it would be possible to e.g. produce 8 or 16 bar progressions, if you give just 4 bars.

Since they're samples from the same key, then they should be sensible?

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  • When you say "write next bar as an union of samples from previous bar", do you mean that the next bar consists literally of n3 n4 n4 n4, or do you mean that both n3 n4 n3 n4 and n4 n4 n4 n4 are acceptable?
    – Dekkadeci
    Sep 1, 2021 at 11:47

3 Answers 3

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MOTIV-ABSPALTUNG

we call this "a split off" from a motif - very common in Baroque, Classic, Romantic and 20th century: e.g. Bach, Beethoven, Bruckner (developping a new theme or phrase), Bartok (especial in the endings of his short piano pieces).

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In my concern theories (especially of music) shouldn't teach rules but describe what in praxis is done - and give some suggestions). But longtime before theories are built some practices are copied by other musicians.

Hauptthema = main subject

Zwischensatzthema = subordinated theme, or secondary theme, literally the theme between the head theme and the side theme.

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  • Amen—"Theory follows practice." Sep 1, 2021 at 11:18
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    Couldn‘t find the term for Zwischensatz. Sometimes the transition could be considered as such a thing. Sep 2, 2021 at 6:44
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I'm thinking of the works of Steve Reich and other minimalists, who were influenced by and exerted significant influence on, DJ genres. "It's Gonna Rain" literally takes a sample and chops it up. And "Clapping Music," while it doesn't actually rearrange its pattern at all, takes a strategy of shifting the sample to start one note later on each repetition to create new patterns (n1 n2 n3 n4 -> n2 n3 n4 n1 -> n3 n4 n1 n2).

I'm not thinking of any examples off the top of my head that actually rearrange melodic material, but I bet there are some that fit your example.

But there are plenty earlier examples, too. In Bach's Partita no 3 for solo violin, the first movement (Preludio) is full of echo effects. Even if there isn't much rearranging of the parts going on, there's a lot of "chopping." Starting from the beginning... enter image description here The first 6 pitches get repeated an octave lower in the next measure. Then mm 3 and 4 get a note-for-note echo in mm 5 and 6. But then later we get this effect: enter image description here In the first measure pictured, the four-note group "E F# G# B" first starts with an interrupted attempt, getting only the first two notes out before restarting. Then we get the whole set, then it's repeated, then only three notes are repeated (the last one of which counts as the first note of the next pattern as well).

You also see "chopping up" in the development sections of good old sonata-allegro form. For instance, Dvorak's "American" quartet starts with a simple theme: enter image description here We've got several elements there: the first three, syncopated notes; the next two beats, with the dotted figure, the continued dotted figures in the mm 4, leading to dotted figures plus interrupted 8th notes in m 5, and finally the up-and-down arpeggio in m 6.

Later, in the development, we find things like this: enter image description here The viola part in mm 64-5 is rhythmically identical to its first two measures back in mm 3-4. But then it "stutters," repeating m 65, then one more time with altered notes to modulate to C#m. Next, in m 68, the violins get the opening-measure material, but in m 69 violin 2 puts the syncopation in the second half of the measure. A few measures later... enter image description here The "dotted figure with interrupted 16ths" is repeated so many times it disintegrates into just the 16th notes. Still later... enter image description here ... the second violin in m 89 (actually unpictured 88 as well) quotes the arpeggiated figure that ended the original viola theme. Then the cello picks it up in m 91, then second violin and viola in m 92 just insist on nothing but back-to-back arpeggios, until they finally talk the first violin into joining in in m 93.

The point of all this is that the "development" section of a sonata-allegro movement is a time when the bits and pieces of the previous themes get chopped into bits, "put through the wash" of tonal modulation, and allowed to bleed onto each other.

Don't let me mislead you, these historical examples are not quite the same mindset as a sampling strategy of "A B C D | A C B D"; the main point is the changing keys rather than the recombinations of melodic material. But they certainly come from the same human impulse, "How can I take what I've already done and do something new with it? How can I reuse the familiar in a way that makes us hear something new in it?"

Also, you can detect (or imagine?) some granular construction of melodies where maybe it was never conscious in the composer's mind. Consider what might be the most famous melody in classical music, the theme from the last movement of Beethoven's 9th symphony. It's such a famous melody now that we take it for granted, but what makes it so memorable? How could one imagine creating it from its constituent pitches? (Disclaimer: I make no representation that Beethoven thought consciously about its structure this way. Also, if what's notated below makes no sense, do a "hard refresh" (add shift to the keyboard shortcut) to reload):

Well, I might start with three notes, ascending stepwise:

X: 1
K: C
L: 1/4
EFG

Ok, that's a start. Hm, I need four beats, so... maybe I'll just repeat the first note.

X: 1
K: C
L: 1/4
EEFG

Cool, cool. Now what? ... uhhhh, I came up, so I guess I'll go down. I'll reverse my three notes, and oh hey, that repeats the G in a way that mirrors the repeated E:

X: 1
K: C
L: 1/4
M:4/4
EEFG | GFE

Hey, let's just keep going downward. I could flip my original three notes upside down:

X: 1
K: C
L: 1/4
M:4/4
EDC

... and just glue that onto what I've already got, using the existing E instead of repeating it:

X: 1
K: C
L: 1/4
M:4/4
EEFG | GFED | C

Now I'm all the way down here at C. I thiiiiink I'll just do exactly what the first measure did, but three notes lower:

X: 1
K: C
L: 1/4
M:4/4
EEFG | GFED | CCDE

Oh crap, it's been three bars, I'd better get a half cadence ready. Uh, how about just an E and a D? Maybe dress it up with a dotted rhythm:

X: 1
K: C
L: 1/4
M:4/4
EEFG | GFED | CCDE | E>D D2

Yay, I've got my first phrase! Now I'll just copy and paste it for the next four bars, except I've gotta end on the tonic this time, so I'll change the last two notes:

X: 1
K: C
L: 1/4
M:4/4
EEFG | GFED | CCDE | E>D D2 | EEFG | GFED | CCDE | D>C C2

... So, as I said, there's no way Beethoven thought as arbitrarily as that. But it doesn't change the fact that you can find these 2-4 note patterns, their reversals, and their inversions even in such a short and simple melody.

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    @mavavilj I guess my postscript should be "There's more influence than you might be aware of in the earliest days of electronic music from minimalist/experimental composers like Steve Reich, Terry Riley, and Philip Glass." Steve Reich connects straight to DJ Spooky (who in fact remixed him in tribute). Sep 1, 2021 at 12:35
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Yes. You can work with fragments (samples) of what has come before to build continuations of a musical passage.

There is an adage describing music form as "repetition with variation." In part that describes your "sampling earlier sequences" idea. Obviously such sampling would involve repetition, and reassembling various sampled fragments is a kind of variation.

When you write "notational music" I assume you mean the "common practice" style music that is the topic of typical theory books. In that case the succession of pitches, progression of chords follows a certain syntax and is fairly restricted. Breaking up a musical passage into samples and reassembling it will surely destroy the common practice syntax. So, it becomes very important to know what you mean in your example when you give notes n1 n2 n3 n4.

If the notes are pitches, reassembling sequences will probably be problematic. If the notes are rhythms, you will have an easier time of sampling/reassembling. In common practice music theory the primary topic dealing with this kind of thing is motif development. Repetition, fragmentation, etc. are some of the terms involved.

say we have four notes in a bar

[n1 n2 n3 n4]

write next bar as an union of samples from previous bar, e.g.

[n1 n2 n3 n4] [[n3 n4] U [[n4] U [n4]]]

can this produce sensible melody progressions?

Again, pitch-wise this could be problematic. Like this...

enter image description here

...the passage is a bit short, but just following the process it devolves into a single repeating tone. Pitch-wise this process is likely to produce a lot of gibberish.

But, if we treat the notes as just rhythm values, we could have something like this...

enter image description here

We could give that pitch by overlaying it on a harmonic pattern, a pre-existing pattern that will follow common practice syntax...

enter image description here

enter image description here

I tacked on an ending to complete the chord progression, but notice that I "re-sampled" the opening n1 n2 n3 n4 rhythm.

Also, notice how I shortened n4 from quarter note to dotted eighth note for the concatenation of n1 n2 n3 n4 with n3 n4. I tried to preserve the metrical values of n3 n4 where n3 is a weak pick up note to a downbeat n4. Little adjustments like that would be typical for putting together fragments in a common practice style.

I don't mean to say it's impossible to "sample" pitch/harmonic material. There is something called a harmonic sequence that does exactly that. But the process is very simple. Normally a harmonic sequence just transposes two chord pairs, two or three times. They are very predictable patterns rather than novel rearrangements of harmonic material. The syntax of chord progression is what limits the arbitrary rearrangement of harmonic material.

Perhaps a language comparison will help. The syntax of parts of speech is like harmony: subject verb object is like predominant dominant tonic. You don't get to change that. But, rhythms are like the specific words chosen for a sentence and those can be varied. For example, let's build a sentence monosyllabically: "The young man ate food." Then, keep the syntax, but apply a new short, short, long rhythm: "The hungry man savored lunch." We can rearrange word/rhythms with a lot of freedom, but we can't arbitrarily rearrange syntactic elements. "The young man food ate" doesn't work... except for Yoda. :-)


It wasn't until I listened to the It's Gonna Rain clip that @AndyBonner posted that I realized I overlooked the obvious example of reusing material already presented: the canon, and other similar devices of imitation. The Steve Reich stuff isn't just resampling, it overlaps the samples, it time shifts when the samples start. His music does that in irregular periods. Canon and other imitative procedures does the overlapping in regular periods to reinforce the meter. Although sometimes the imitation start points can move from a strong to weak beat - like a fugue stretto - which is contrary to the meter and creates an echo/dissolving meter effect that on a basic level is working with the same phenomena as the time shifting in minimalism.

Strictly speaking musical imitation isn't the process you described with n1 n2 n3 n4, n3 n4, n4, n4 which is a simple linear process of fragmentation and concatenation. But of course fragmentation and imitation are both types of reuse of stated material. Invertible counterpoint is a particular type of imitation and reuse that puts musical segments into several voices. That can be represented in a grid similar to your linear process n1 n2 n3.... Triple counterpoint would be three musical segments that can be variously placed in three different voices. Theoretically, the grid would look like...

A A B B C C
B C A C A B
C B C A B A

If each vertical unit were two bars, then ABC and all its possible inversions will produce horizontally 12 bars of music. That's 12 bars "for the price of" only 2 in the starting material.

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