I am computationally generating short tunes (aiming for around 10-15 notes, 0.5 seconds per note) for a psychology experiment. I am wondering exactly how many notes I should have per tune, so that the tunes, though artificial (random pitches), will at least still sound complete and well-rounded to the ear from a metrical point of view.

To that end, and having the common time (4/4) in mind, I thought that integer multiples of this number of beats, for instance 12 or 16, would be a good number of notes to aim for. However, while playing a few samples to myself, it seems to me that tunes made up of an integer number of time-signature beats plus one is the more sensible length, which would give me, say, 13 or 17 notes instead of 12 or 16. This is probably because this length means that the final note in the tune is metrically strong (the first note in a bar), as opposed to weak (the last note in a bar).

Does anyone know any references to perception studies that may help answer this question, or otherwise share their opinion from a purely music-theoretic point of view?

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    Does your first sentence imply that all the notes are the same length? If so, that is probably why the tunes sound "incomplete" - from a music-theory point of view they are ending on the last beat of a bar, which is the weakest beat in 4/4 time. In "real music" the last note of a tune is often longer than the average - for example a whole bar (4 beats). Another issue is that bars are perceived in the context of longer rhythmic units which are often derived from the underlying harmony (so-called "harmonic rhythm"). With random note pitches, that cue to interpreting the rhythm won't exist. – user19146 Aug 30 '17 at 13:40
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    Also, random pitches will not create any impression of the music being in "a key" (in the sense of the common-practice-harmony meaning of "key") and therefore will not have any alternation of increasing and relaxing "tension" as the pitches move further from or near to the important notes of the key - hence you lose another audible cue as to when the tune has "ended". – user19146 Aug 30 '17 at 13:45
  • So many songs and parts of songs and symphonies and movements and generally bits of music end "on the one", and you have observed yourself that it sounds more like an ending to stop on the first beat of a subsequent measure. Given that, and the fact that the sharing of opinions is not what Stack Exchange is for, what exactly are you looking for here? A scientific basis for an artistic convention? – Todd Wilcox Aug 30 '17 at 13:46
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    Definitely one more note would help than 12 or 16 and do not just use beats of the same value especially for a psychology experiment. Variations and different notes would sound nice. What is the aim of this experiment? Please respond. I am sure there are quite a few studies out there o music perception. If I come across any of them, I will post it. – Tarun Aug 30 '17 at 13:59
  • Hello all, thanks for answering. The experiment has to do with perception and memory for note sequences, therefore the harmonic element is irrelevant here. You are right that having a longer final note would help with the completeness, particularly if that final note is metrically strong ("ends on the one" as you say). @ToddWilcox: What I am looking for is to simply see whether in people's opinions, there is any sense (given current/past musical practice) to a end a melody on the last (as opp to the first) note of a bar; my piloting suggests that sounds very unnatural. – z8080 Aug 30 '17 at 14:44

As this is an old question, I don't know if OP is still looking for this information. But there is significant literature (both theoretical and empirical) on metric grouping and perception. Perhaps the first to create a detailed theoretical model based on Gestalt principles was Lerdahl and Jackendoff's A Generative Theory of Tonal Music (1983), which proposed a set of rules for hierarchies of larger-scale metric structure.

For a very basic summary, meter tends to be perceived with a primary tactus ("beat"), which is generally felt with subdivisions of 2 or 3. This tactus beat is generally grouped into 2s or 3s. Rhythmic entrainment due to regularity of these metric patterns often results in higher-level groupings (usually in 2s), sometimes referred to as hypermeter. Even in relatively undifferentiated stimuli (e.g., monotone pulses with no accents), these groupings tend to emerge in perception.

So, a pattern that ends after 12 notes or 16 notes with the same rhythm is often felt as "incomplete," as it lacks a final hypermetric or phrasal "downbeat." Note that most standard Western pop songs, folk songs, and many types of classical music tend to be built around "4-bar phrases" that frequently end on the downbeat of the fourth or fifth bar, rather than on a weaker beat (and very rarely an offbeat). Even phrases that do end on weak beats generally have their primary harmonic and rhythmic resolution on a strong downbeat, with the weaker beat feeling like a sort of "afterthought" or delayed release of some tension (e.g., in a suspension at a cadence).

Anyhow, there's a lot more to all of this, but searching the empirical literature that validated some of Lerdahl and Jackendoff's ideas of large-scale metric structure, as well as other discussions of hypermetric groupings will provide further details.

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  • Very helpful answer, thank you, I think what you reference confirms my intuitions about why the downbeat of the following bar could not go missing. – z8080 Dec 21 '19 at 18:25

There is way too much missing to provide a complete answer but I will try and add some guidance from experience. You state that you want random groups of notes to be "meaningful" but can you define a criterion for meaningful (or is that what you want from us). What makes music meaningful in many cultures is rhythm not melody (though both are important).

From a melodic perspective we tend to like simple melodic phrases that move around within a key signature, e.g. on the major scale (or relative minor). There is a simpler unit of musical expression called a tetrachord (Do, Re, Mi, Fa). The major scale is just 2 tetra chords separated by a step. The reason I feel that this is important is that there is "repetition" built into the ascending scale, and repetition is what many people crave (whether they know it or not). So even simple melodic phrases (say three or four notes long) tend to (1) have a repeated or well defined rhythm or pulse (2) either have or hint at melodic repetition and (3) tend to stay within a key. Of course there are exceptions to every rule. And you cannot really repeat yourself with 3 notes unless it's the same note 3 time. But, longer phrases like the ones you are trying to make are usually built from simpler 3 and 4 note phrases repeated at the same or different places within the key. So a better algorithm might be to randomly move the phrase (Do, Mi, Re) around varying the starting pitch (with or without constraints to stay in key). Perhaps a library of small phrases.

I would ask why you want to do this at random. Why? What are you testing? If you can share this it might help. Unless it's proprietary (I'd understand). Music is filled with patterns and IMO there is nothing random about it. If you are trying to see what it takes for subjects to tell the difference between human generated music and computer generated music that won't take much. If you are trying to create AI that mimics human creativity that might take more. We are pattern recognition machines and we crave pattern. If you wan to generate short melodies to make life easy you will need more than a random tone generator. You will need some constraints that create rhythm and melodic structure consistent with western tastes. That would essentially mean coding up a text on music theory.

A couple other constraints might help. One is that moving small patterns around we usually come back where we started, in other words we cycle rather that just move endlessly in one direction. A small chunk of music light have a scale going up but will eventually come back around. This is critical to creating the feeling of completeness. Phases can begin and end on different notes but usually notes that are part of the Tonic chord of the key (Do, Mi, Sol). So this is a second thing to consider. Third, you didn't state how many octaves you were restricted to (unless I missed it). For a 16 note phrase it is possible, but highly unlikely, to generate a 2 octave scale. This is not very musical even though it is a musical element. You need to either restrict your "random" choices to be within an octave or octave and a 5th or require that they turn around somewhere.

There are a lot of degrees of freedom to play with. It is possible to encapsulate some of our decision making process in the constraints and try randomizing the rest but you have a lot to think about. And there is also the possibility of chromaticism. Are you trying to emulate real musical phrases at random?

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  • Also a helpful comment thank you. I hope to be able to respond more fully in a few days. – z8080 Dec 21 '19 at 18:29

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