Ambient Pitch Sets (Working Group)

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This is a page for the people who are doing work on Ambient Pitch Sets to document their observations and organize these various ideas.

Feel free to add more bullet points with new ideas, or subbullet points for comments, experimental evidence, further questions - or also counterexamples! Don't forget counterexamples, we need to start ruling some of these hypotheses out!

Core Ideas about APSs:

  • An ambient pitch set(APS) is the set of notes that is perceived to exist in the "background" at a certain point in time in a piece of music.
    • (could use a bit more elegant definition, may be revised.)
  • A pitch set (PS) in general is simply a set of notes, irrespective of any perceptual implication whatsoever.
  • We're considering chords and scales themselves to both be APSs, by definition - they're things that stick around and are implied by notes.
    • Precedence for this idea can be found in Rothenberg's ideas and (I think) Krumhansl's stuff.

Observations about APSs

  • APSs can be "implied" by notes being played, whether simultaneously or consecutively.
    • Observations:
      • If you play a repeated C-E-G-C-E-G arpeggiation, at least some people don't just hear three totally random notes, like they might if you play them a random 12-tone serialist melody instead. These people tend to hear them fleshing out some kind of background structure, which an experienced musician may label C major.
        • Question 1: are there significant differences in the way that this process takes place in musicians vs nonmusicians, or in AP vs non-AP listeners, or in the end result?
        • Question 2: does the harmonic or intonational structure of the chord influence the stability of the aggregation?
        • Question 3: does the listener's prior experience of hearing notes played simultaneously as a chord influence the ways they'll perceive those same notes aggregating if arpeggiated?
        • Question 4: does the listener's prior experience of hearing notes "grouped together" in some other way influence the ways they'll perceive those same notes aggregating if arpeggiated?
    • The fact that they can be implied by consecutive sequences of notes (e.g. "arpeggiations") is in contrast to how VFs work, as seen here:
  • APSs tend to persist for a while and don't immediately die out as soon as the notes stop.
    • Observations:
      • Krumhansl's probe tone experiments demonstrate APS persistence by playing a probe tone -after- a piece of music and still observing that listeners knew how much the probe tone "belonged"
      • Additionally, and more intuitively, one typically doesn't play all the notes in C major simultaneously, but one still understands how much the notes in C major "belong" at any point in time in a piece of music, and would understand additionally if an unexpected note were played that didn't "belong."
    • This is also in contrast to how VF's work, where actual perceived virtual pitches do not continue to "ring" or persist, except perhaps in some sort of hypothesized subliminal way that's not represented in the literature at all (to the best of my knowledge).
  • APS implication can take place even if "noise" is introduced into the signal - e.g. passing tones, chromatic effects, etc.
    • Observations:
      • The existence of "passing tones," which don't seem to aggregate into the sensation of the chord or scale, but are perceived as non-chordal/extrascalar/etc.
      • Unless taken to an extreme, passing tones don't seem to interfere or cause any sort of "reset" in the implication process - they're simply skipped over, with notes both before and after the chromatic note potentially becoming ambient.
  • Notes within an APS can vary in salience. For instance, the "tonic" note may be highest in salience, the "chord tones" may be the next highest, the "scale" may be the next highest after that, the underlying "chromatic scale" may be next after that, etc.
    • Observations:
      • Experimental evidence for this comes from Krumhansl's probe tone experiments, and what has been called a "heirarchical representation of tonality" in the literature.
    • Note: these salience regions may be "fuzzy," and not break down into well-defined "levels" as described above.
      • Can musical training or some other process cause salience to be perceived categorically, rather than continuously?
    • Question 1: how does this relate to atonal or serialist music? What happens in that case? Do you get no APS, a diffuse APS, a set of constantly shifting APSs, all 3...?
    • Question 2: if someone's experienced in 19-EDO meantone, will they hear another "enharmonic scale" as a yet deeper and subtler level of salience?
  • When a new note is introduced in the presence of an existing APS, there are 4 possibilities:
    • The new note can stickand merge with the APS to form a larger APS
      • Example: APS is C D E F G B C, and then you play "A." If you hear the new resulting APS is C D E F G A B C, the A has "stuck"
    • The new note can slide off(bounce? float?) and be heard as a chromatic or passing tone, one which is nonchordal/extrascalar, and which doesn't merge.
      • Example: you play C D E F G A B C and occasionally play D# as a bridge between D and E. If you hear APS as still being C D E F G A B C, with the D# as just an extra unrelated chromatic note, the D# has "slid off"
    • The new note can mutatethe APS state by replacing an existing note.
      • Example: you play C D E F G A B C and then start playing Eb a lot. If you hear the APS as becoming C D Eb F G A B C, with the E getting downgraded to "chromatic note" status, then the APS has "mutated"
    • The new note can reintoneone of the notes in the APS, by changing the cent size of an existing note without doing so enough to sound subjectively like a new note.
      • Evidence for this comes from the fact that musicians can adjust their intonation by significant amounts in real life performances, all while leaving the chords, modes, etc perfectly intelligible, sometimes intentionally and without sounding "out of tune." (really good paper on this, gotta find ref - Mike)
      • Question 1: How much intonational variance is too much?
      • Question 2: is it possible, via some ear training process, to alter incoming notes which currently produce an APS reintonation response to instead produce an APS mutation response?
  • The notes in APS don't correspond to precise frequency values, but rather to fuzzy pitch regions, the bounds of which may be subjective and change with musical training, and which may or may not completely cover the spectrum.
    • Follows from the above.
    • What's the relationship between this and categorical perception?


  • What is the relationship between APSs and fundamental tracking, if one exists?
    • Can fundamental tracking influence the "stability" of an APS?
      • Possible answer #1: yes, because of some direct psychoacoustic process
      • Possible answer #2: yes, because combinations of notes you tend to play can be more stable, and you'll tend to play nicely intoned combinations more
      • Possible answer #3: yes, because of a combination of the above: once you've explicitly played a harmonic chord simultaneously a lot, you'll be able to re-invoke that in APS form later
  • What is the relationship between APSs and categorical perception, if one exists?
    • When 6:7:9 and 10:12:15 are both heard as "types of minor chord" by a Western listener, does that mean they both map to the same APS?
      • If yes, does this mean that the "notes" that APSs are built off of are themselves categories? Or the other way around - that categories form around APSs, and the notes simply contain useful musical information relevant to the APS's they form, all of which become part of the category later?
  • Are APSs fundamental to music cognition, or are they just the byproduct of a more fundamental process of generalized cognition, for which structures like APS's are just the method this process comes up with to understand and parse musical data, when fed the sort of music prevalent in (some of) the world's cultures today?
  • What cultural considerations might cause revisions to the above?
  • What exactly causes certain notes to "stick" and others to "mutate" and others to "slide off?"
    • In addition to a possible "stability" feature of APSs, the extent to which you play a note can possibly influence the mutation vs sliding off - Krumhansl may have good info on this.
  • How long do notes in an APS persist? Do they need to be constantly refreshed, or do they tend to stick around for a long, long time?
    • (Mike suggests they stick around for a long, long time, but experiments quantifying this would be nice.)
  • What sorts of musical processes might confound the process of APS formation? What techniques might the music of other cultures, or atonal music, etc use that could possibly lead to the deliberate lack of a strong APS?
  • What exactly is a "note?"
    • It's not just a specific interval size, but seems instead to be a set of capabilities or properties assigned to regions of the interval spectrum.
  • How might the interval of equivalence influence the gestalt or affect of the APS or the intervals in it?
  • Are salience levels in an APS discrete or continuous? Also, is there any absolute "ground" level of salience, or is it more like voltages, where the salience of a note only make sense if judged relative to some other note?
    • Mathematically, are saliences best represented by elements in N, by elements in R+, by elements in a Z-torsor, or by elements in an R-torsor?

Hypotheses, Suggestions, Proposed models, General thoughts (all of which may be wrong or change)

  • APSs can be modeled as having some inherent measure of "stability." If you have an APS and you add another note, and if the result is "unstable," it'll be more likely to either slide off or mutate, possibly depending on how often you play the new note (e.g. how salient you attempt to make it). If you have an APS, and if the result is "stable," the combination will be more likely to stick. There's some possibly generative process where different potential APSs compete, with the most stable winning out. (Mike Battaglia)
  • An APS can be said to be saturatedwith respect to another "auxiliary" PS if no pitch in the auxiliary PS, when combined with the APS, will stick - e.g. if the addition of any note will cause a mutation or passing note effect. (Ryan Avella)
    • Question: Can APSs ever be saturated with respect to any additional note? (Mike)
  • Ornaments have a (entirely conventional?) effect of increasing the salience of a certain note in the APS relative to the others. (Jason Conklin) For instance, using Baroque examples:
    • A trill involves two notes more or less equally, but tends to increase the salience of only one (the lower one) relative to the other
    • A turn involves three notes, but increases the salience of one (the middle one) relative to the others
  • The size of an APS is limited by bounds on working memory such as the 7 +/- 2 Miller limit. (Ryan)
  • Previous conditioning can cause you to perceive a larger APS than the notes you actually play directly, because of experience that those notes "go with" other notes (Ryan, Mike)
  • APSs are a result of some more fundamental music cognition process that tends to this way of organization when fed Western music? (Mike)
  • APSs can be split up by register and don't need to repeat every octave - consider Stravinsky's modal fields approach, where a scale like Gb A Bb C D Eb F Gb in the bass may smoothly transform into G A Bb C D E F G on top, with the G being a sort of #15 extension, the E being an aug6 which is a fifth above the aug2, etc. In that case there'd be different APSs per register. (Mike, who thinks this should be an "observation," but isn't putting this there yet because he doesn't know how familiar the concept is to others reading)
  • Although this fails sometimes, there does seem to be a tendency against APSs being "stable" if they have two "half steps" in a row in 12-EDO. This is just a general rule of thumb and undoubtedly an approximation to something deeper. (Mike)
  • Categorical entropy may -possibly- model certain aspects of the stability of APSs. (Mike)
  • The "sticking" vs "non-sticking" process can be influenced by culturally-dependent, classically conditioned cues or "triggers," such as ornamental features in maqam musics or perhaps leading tones in Western music, which influence the way a listener's interpretation of the musical scene changes. The consequences of this may be more far-reaching than just APS sets. (Jason)
  • When one listens to atonal, serialist, or heavily chromatic music, APS salience distribution tends to be that of a "diffuse field" of roughly equisalient notes, as opposed to the usual heirarchical concentration of salience in a few prominent "tonic" or "chord" notes.
  • Suggestion: APS's actually comprise the fundamental gestalt of what a "chord" is, with different intonations being red herrings for actual chord gestalts. Listeners can, however, form different fundamental types of APSs -around- different intonations, elevating them to the status of different chords, which may occur as one gains more experience and training with finer systems such as JI. However, this process doesn't occur automatically or by default, but a "sensitization" process must take place. (Mike)
  • Suggestion: Different intonations within a single APS can still impart subtly different moods or musical effects. Many xenharmonic listeners may, as they learn new tuning systems, be continually adding intonational "variations" or information to their memory of various APSs, and relate to new tunings this way (e.g. 7/6 is "septimal minor," 6/5 is "minor," 5/4 is "major," 9/7 is "septimal major," 8/7 is a "septimal major second," etc). This suggests that, for these listeners, their xenharmonic experience might be enriched by perhaps forming new APSs around new intervals directly, or by otherwise teasing apart different intonations of intervals and reestablishing them as "different intervals" to begin with. (Mike)
    • Perhaps forming a large database of intonational variations on APSs and their musical effects may lead to this sort of perceptual "upgrade."
  • David Temperley's work on modeling tonality as some form of Bayesian inference may be highly relevant here, or even the same exact thing. (Joel Taylor)

When 6:7:9 and 10:12:15 are both heard as "types of minor chord" by a Western listener, does that mean they both map to the same APS?