Mode locking : pitch and rhythmic perception

Discussion in 'Playing and Technique' started by dsimon665, Feb 23, 2015.

  1. dsimon665

    dsimon665 Supporting Member

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    With blues we add additional tones to the "likely" category.
    This is where the idea of 7-limit comes from...adding the prime number 7 into the numbers that we can compound in a tuning : 2 3 5 7

    One area that has a lot of choices is the b7.
    0969 Bb 7:4 blu 7
    0996 Bb 16:9 grand-pa below
    1000 Bb ??? ET m7
    1018 Bb 9:5 komal ni

    The theory goes that these are likely the relationships that people are perceiving.
    It doesn't mean that you personally are perceiveing any particular one...

    however recent research in music cognition is modelling this process.

    I couldn't find a full text version of this but just consider the title:
    Mode-locking neurodynamics predict human auditory brainstem responses to musical intervals.
    http://www.ncbi.nlm.nih.gov/pubmed/24091182

    One guy at the head of this research is Ed Large.
    For quite a while, he has been using the idea of mode locking in neural oscillations for several areas of music perception.
    His main area of research has been perception of rhythm.
    The idea of "mode locking of coupled oscillators" can describe processes of both pitch perception and rhythmic perception.

    If you search "Ed Large pitch perception" a lot of research will pop up.
    He used to work at the Music Dynamics Lab at The Center for Complex Systems and Brain Sciences
    http://www.ccs.fau.edu/~large/Music_Dynamics_Lab/Music_Dynamics_Lab.html
     
  2. dsimon665

    dsimon665 Supporting Member

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    To put this in more down to earth terms consider the vid of "metronome synchronization":
    http://salt.uaa.alaska.edu/physics_public/metro.html
    http://www.learner.org/courses/mathilluminated/units/12/textbook/07.php


    https://www.youtube.com/watch?v=W1TMZASCR-I

    you'll find a ton of videos on this.

    The metronomes are "oscillators". Putting them on the board on top of the cans makes them "coupled oscillators".

    This is a complex system.
    For example, one of the oscillators might have more influence than the others. This could happen to varying degrees.
    Then consider additional input to the system over time.
    If you can imagine this process in the brain the "additional input" would be sound waves.

    This gets into the idea of Injection locking, Injection pulling, or Entrainment:
    http://en.wikipedia.org/wiki/Injection_locking

    Check out the spectrogram on that page:
    [​IMG]

    If you consider the action of a stringed bow, it is more like a strong Injection pulling. The bow action forces the string into a harmonic vibration (the inharmonicity of the string is not sounding).

    However when the string is plucked, inharmonicity is present because there is no mode lock.

    http://newt.phys.unsw.edu.au/jw/harmonics.html

    consider the title of this article : "Nonlinear Dynamics and Chaos in Musical Instruments"
    http://www.complexity.org.au/ci/vol01/fletch01/html/

    then consider : the brain is a musical instrument
     
    Last edited: Feb 23, 2015
  3. dsimon665

    dsimon665 Supporting Member

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    An interesting article that uses these ideas/models and compares ET to JI is:
    "A Dynamical Systems Approach to Musical Tonality"
    http://www.ccs.fau.edu/~large/Publications/Large2010Tonality.pdf

    particularly figure 4 shows "resonance regions" for the two tunings.
    "Resonance regions whose center frequencies match ET ratios closely enough are predicted to be learned. "

    "In principle a similar learning analysis could be performed for any tuning system, such as gamelan, whose frequency ratios differ significantly from 12-tone ET. "

    "Nonlinear resonance predicts a generalized preference for small integer ratios.
    This prediction does not correspond to any specific musical scale; rather, natural
    resonances predict constraints on which frequency relationships can be learned. "
     
  4. kimock

    kimock Member

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    Ok, not hip enough to the other stuff, but as to the above. .

    Personally, I wouldn't confuse 7:4 with any of those other ratios in a 7-limit context.
    Not like I wouldn't use them if they were the right note in the moment, and sometimes they are, but that seventh thing is pretty robust, easy to find, easy to hear, easy to check etc.

    So maybe I'm just not getting the drift here, but "likely perception"??
    As in "what pulls people into that valley of local minima in the dissonance curve?"
    The ratios you listed plus the ET b7 are a pretty representative basic picture of any area of the octave we think of as usable scale tones.
    Something that rhymes with 3, something that rhymes with 5, something that rhymes with 7, and what we're left with when we temper it all out.

    I don't get how there's some controversial theory or question about that particular batch of possibilities involving perception.
    I was under the impression those possibilities have been covered aurally and mathematically for at least a couple hundred years as a practical matter.

    The perception was clear enough to calculate and build from, refine, eliminate, etc, right?
    Anyway, thanks for posting, but some part of that "theory of perception" idea went over my head.
    How would you perceive 7:4 as something else if you knew what it sounded like?
     
  5. dsimon665

    dsimon665 Supporting Member

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    I guess my drift was I didn't want to leave anyone out. Some of this stuff is like magic if you're not used to it. What's that saying?
    "any advanced technology is indistinguishable from magic"

    You first have to consider the individual: e.g. their training, what type of music they play, where are they in the world, etc.

    Some of it has to do with accent - like preferences. Maybe they're not attuned to certain sounds. Like some people are not good at singing blues, but they might be great at singing something else. Or in Japan, maybe they prefer a wider 6th (not sure about their b7)

    Then some has to do with training. How cognizant are they of what they're choosing? Are they just guessing? Its probably a combination of those. Like that vid someone posted here recently. How you were mentioning if it was the Warren version, it was sharp.

    Mathieu mentions something about that. How the b7 is a particularly "watery place, a fine opportunity for ornaments and vibrato", and "what kind of b7 do singers choose? Usually good singers do make a clean and musically convincing decision"

    Yes its that knowing. That's experience, or you could say "realization". Maybe someone doesn't know, or only partially does. Then how does that translate during performance? Ear training is like that - really slowing down and bringing those subconscious things to the forefront. Like the title Harmonic Experience
     
  6. fenderlead

    fenderlead Member

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    Sounds like horses galloping and trotting on a road to me.
     
  7. JonR

    JonR Member

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    That's fascinating - not what I'd have expected at all! (But I guess it does make sense.)
     
  8. dsimon665

    dsimon665 Supporting Member

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    Oh there is. But I don't quite get it myself. I think most people don't want to actually experience it - like singing over drones. Its not a good enough answer.

    The basic "controversy" comes from these two possibly related discussions:
    consonance/dissonance
    nature/nurture

    What happens in those type of discussions comes down to the C to F thing. There's no F in the harmonic series of C etc.

    They really don't like the idea of "reciprocal" relationships.

    Mathieu knew this...so that's why he didn't use the word "undertones". Because that would get into the consonance/dissonance discussion. However, he kind of failed because he still uses "overtonal".

    However, "overtonal" is different from overtones. Yes and no anyway. Or maybe not!

    The C to F thing comes from Helmholtz and the nature/nurture discussion. Its a separate thing from the actual experience of being in tune. One thing is a theoretical discussion and the other is an actual practice.

    That's why I'm saying the C to F thing is about resonance. That puts a stop to the consonance discussion. Its a different discussion.


    As an aside I recently bought the Kindle version of Harmonic Experience.

    This is great for searching and really getting to a summary of subtle points in the book.

    for example a word search for these terms:
    Consonance – 22 results found
    Dissonance – 42 results found
    Resonance – 135 results found


    Anyway, if we're going to have that discussion on consonance/dissonance...that's where mode locking comes in. The brain has a non-linear response. Helmholtz assumes a linearity.

    Mode locking is resonance. Mode locking is non-linear. The theory is at the neuron level. That's really where it needs to be for a consonance/dissonance discussion.



    The Ed Large article I posted earlier is an elaboration of previous research. A simpler model was done for the study of consonance/dissonance:
    Inbal Shapira Lots and Lewi Stone
    Perception of musical consonance and dissonance: an outcome of neural synchronization
    http://www.ncbi.nlm.nih.gov/pmc/articles/PMC2607353/

    First they elaborate on the flaws in Helmholtz's theory.

    In that article they talk about only two oscillators. These oscillators are a model of either two neurons or two groups of neural nets.

    These two oscillators would represent the two pitches (the two pitches being "pure tones" like sine waves).

    However the two oscillators only "represent" the two sound waves. The oscillators are not equivalent to the sound wave. The sound wave does not exist inside the brain. The sound waves gets transferred to this group of neurons. (In case anyone is unclear about that) .

    Basically Helmholtz is like a Homunculus argument
    http://en.wikipedia.org/wiki/Homunculus_argument
    [​IMG]


    At some point it stops being sound waves.

    (This is a model of relative pitch only. The sound wave gets transferred to other modules in the brain...like the "absolute pitch" map, etc.)

    Anyway figure 4 is of interest in Lots and Stone. The two coordinates are frequency ratios. The Y axis being the result of mode locking, the X axis being the intrinsic frequencies of the two oscillators.

    The graph is also called a "devils staircase". And the width of each step points to the stability of those frequency ratios.

    Then, in table 1, the "delta omega" column is the width of those steps. Basically showing how consonance/dissonance can be derived from the model.


    Those type of models are very limited, and you have to use some creativity to see how it could work from an experiential level. Some of it is over large time scales - like the idea of neural plasticity, or nurture. Building neural connections.

    And some of it would have to do with breaking your experience into smaller chunks. Like the idea of relative vs. absolute pitch. They can map those in the brain. For absolute pitch they talk about "tonotopic maps"
    http://en.wikipedia.org/wiki/Tonotopy


    The relative pitch idea can be partially explained by these models of coupled oscillators...both on a nature/nurture level, and from the standpoint of standard music theory (like functional harmony, the 7-limit lattice, etc.)
     
  9. JonR

    JonR Member

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    Could you expand on this?

    For me, the "C to F thing" is simple. C is an overtone of F, so F is the root of the interval. The perfect 4th is consonant because it's perceived as an inverted 5th (we intuit a lower virtual acoustic F root; the notes "resonate" for that reason).
    But in a context where C has been established as the tonal centre, F appears as a dissonance, because two tonal centres can't exist together. C wins simply because it's lower in pitch (we expect a tonal centre to be low), and F has to "give in", resolving to E (overtone of C, confirming the C root).

    But I guess you're talking about something else? There is more to be said about "the C to F thing"?

    (I do understand that in modern music, where we're more used to quartal harmonies, a C-F-G chord doesn't need to resolve, and we enjoy the mild tension as a pleasing ambiguity. And of course, the old "tendency" for resolution to the major triad is partly cultural.)
     
  10. kimock

    kimock Member

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    Oh, ok. .
    I get where you're coming from.
    The way I read it I thought you meant there was some cognitive question about the perception of the objective part.
    Yeah, it's relative to the musician's or listener's experience and cultural predisposition.

    In my own private hell it mostly translates to "string length", which is pretty fricking objective.
    Right? That's what I have to do to make the sound come out, not to be confused with what you have to do to get the sounds internalized in the first place. Gotta execute. .

    Still, I'm always faced with the reality there's only two things to consider: what it is objectively and how I feel about it.
    So yeah, "hey look, 7:4!", backed with "who cares?" which is a fair description of JonR's take on a lot of this stuff at a practical level.

    I bounce back and forth between those polarities myself.
    I'm guessing that's normal.
     
  11. dsimon665

    dsimon665 Supporting Member

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    There is an additional factor which has to do with an individual's past listening habits.

    The idea of F winning out without a tonal center only works for certain cases.


    I'm not sure what an inverted fifth would sound like. That relationship can have several sounds associated with it:

    The sound of a "fourth" would be (there may be more):
    1 Fifth (high note in unison with single referent)
    2 Fourth (low note in unison with single referent)
    3 Fifth and fourth (both notes in unison with their own referent)
    4 In the case both notes are not in unison with a referent (e.g. F,C with referent G) a more complex sound is heard

    In the case of no referent no sound is heard...at least no fifth or fourth would be heard without some sort of reference. There might be other aspects to the sound that are heard like absolute pitch.

    I worded it this way to point out that the energy state of the brain is separate from the sound. In the above "the notes" are the sound waves, and "the referent" is the energy state of the brain. Additionally the brain has certain neural pathways established due to prior listening habits.

    both notes contribute to the sound. In case 1 and 2 one of the notes has the sound of unison.

    Case 3 is a version of atonality - it isn't absence of referent; its equilibrium.

    How this referent is determined is a complex process...we have higher level structures like functional harmony. But there are other factors.

    One aspect is "passive listening". This aspect occurs over time (like years) and can cause a bias to certain relationships. it can prevent any of the cases above from being fully realised.

    This isn't to say all relationships are equal...there are varying degrees of stability. However the way someone listens and what they listen to can affect their capability.

    The converse would be true too. That is the more "unstable" relationships can be worked on until the system is in equilibrium. Either through "passive listening" to music that involves these relationships...or through some sort of ear training.
     
    Last edited: Feb 25, 2015
  12. dsimon665

    dsimon665 Supporting Member

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    One theory is that in certain modules like relative pitch the frequency of the "referent" is scaled down in some way. It's somewhat counter to the idea of virtual roots. Basically all "roots" exist below the incoming sound in that theory.
     
  13. aiq

    aiq Supporting Member

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    Reading this reminds me of Elvis's comment in Jailhouse Rock after hearing the coctail party discussion on dissonance in jazz.

    :/
     
  14. dsimon665

    dsimon665 Supporting Member

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    Another point on this...the mode locking theory is an alternate explanation for the resonance and consonance/dissonance. It doesn't have to do with virtual roots.

    Mode locking is a polyrhythm, it has a resonance, and stability aspect to it.
    Polyrhythm and resonance is fig 3
    Stability is fig 4.
    Of this article:
    http://www.ncbi.nlm.nih.gov/pmc/articles/PMC2607353/

    It explains consonance/dissonance and resonance by rhythmic relationships.

    The additional factor is the directionality of the coupling. When you have coupled oscillators, they have varying degrees of effect on each other.

    One might pull the other towards it, or they might pull each other depending on the strength of the coupling.

    The stability of an interval can be described by how much variation in frequency ratios will allow a certain relationship to stay constant. These areas of consistency are where the simple integer ratios of 7-limit comes from.

    In the realm of time what we think of as "rhythm" is on one scale. Frequency or pitch is on different scale, but still has a rhythmic aspect to it.

    Frequency ratios can be looked at as polyrhythms.
     
  15. dsimon665

    dsimon665 Supporting Member

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    then if you continue the analogy...is a 2 vs. 3 rhythm
    2 over 3
    3 over 2
    some sort of 6 count

    It can be perceived one or a combination of ways...but it might take some time to be able to do that.
    Some might have a preference for one or the other...and it might depend on accents, or what the established meter is, etc.
     
  16. JonR

    JonR Member

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    Obviously! A note is a note, not an interval.

    I'm talking simply about a C-F interval in isolation from any context. It sounds ssmooth and consonant to me, not tense at all. It sounds like the notes belong together, maybe as part of consonant chord. That could only be an F chord.
    The simple ratio between them (3:4) also suggests to me that the reason for the consonance is their relation to the virtual "1" of that ratio, which is a lower F.
    So - put in theory terms - it's working as an inverted 5th.
    (It's not quite as consonant as root position 5th, because that's a simpler 2:3 ratio, and better represents the overtonal relationship, F on the bottom.)

    If we introduce some other referent, then obviously all bets are off, because a third pitch introduces two more intervals (3 intervals altogether).
    Whoah - that needs defining! (I've no idea what it might mean.)
    Well yes. We've all heard musical notes before, and we've heard them relating to each other in various ways. But when we only hear 2 notes, simultaneously, we don't know which of those previous (more complicated contextual) experiences it relates to.
    There's no guide in the interval itself - except possibly the sense that it's upside down: "it sounds good but would sound better the other way up".

    IOW, although we obviously have cultural habits of listening, I don't see how they can be brought to bear on a simple 2-note interval, on deciding what it might mean musically; because it could mean many things.

    I don't quite get that there could be other prejudices in how we interpret C-F. Not unless we've just been listening to some other music, and have a pitch memory of that.

    I might speak the word "bear". But you don't know whether I'm saying "bear" or "bare", if there's been no conversation before that point. IOW, our cultural heritage allows two spellings and (at least) two meanings linked to the sound. The sound does suggest a few things (it's not meaningless, it is a "word"), but it could be any of those things.
     
  17. JonR

    JonR Member

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    OK, I get that. (I couldn't follow the whole article you linked to, but I think I understood it enough to get the idea.)
    It seems to fit with the idea of tolerance of equal temperament: the fact that, while we are drawn (apparently instinctively, not just culturally) to simple ratios, they don't need to be exact, just "close enough". Different individuals seem to have different levels of tolerance, but a few cents away from pure seems acceptable to just about everyone.
    The "mode locking" concept could explain that - that the brain is somehow drawn magnetically to simplicity.

    It works visually too. When we see a "square", it has to deviate some way from absolute precision before we start seeing it as a "rectangle", or some other form. Likewise circles and ellipses.
    Again, individuals can vary in their responses, depending on training. A trained graphic designer may be less tolerant of an inexact square (find it easier to spot the inaccuracy) than a non-designer.
     
  18. dsimon665

    dsimon665 Supporting Member

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    I don't think that can be done...isolation from context.
    If you keep playing the same interval - that's context.
    Whatever you played before is context.
    Your past listening habits are context.
    The nature of the brain is context - the architecture of it.

    The brain is a musical instrument. It has a non-linear response to sound.
    Octave equivalence is non-linear. It basically says 2=1.

    With the mind we're dealing with a subtler form of instrument than a physical instrument. If you can imagine multiple strings that can change mass, change length...then these are connected to resonating bodies of variable dimensions. That's just an example.

    Just to be devils advocate...the idea of "virtual pitch" sounds a little like magic to me. There is likely something very non-virtual at the bottom of it.

    Where this is leading to is : maps. All maps are useful to an extent. Some people are map makers, and some don't use maps...varying degrees of map making and map using.

    Whatever our view is of this one thing is certain; new maps are being made. Ones that are likely to be totally different than our current understanding.

    It doesn't mean the current map is flawed. It can work at its level. It like Newtonian physics is still used. Its a good approximation.

    However that approximation might not work to explain other situations.

    That's why they always bring up Gamelan. To get to a world level of theory might mean a new map is needed.


    Consider that someone singing acapella can start on any scale degree. Lots of songs start on the 5th or 3rd.

    Jingle bells - the "jingle" is a third. Not sure if that song is popular in England.

    But I can start right on that "jingle" without a pitch-pipe or any referent other than the one I generate internally. Its not influenced by a sound wave.

    "These dreams" by Heart...I can start on the "Dreams" and hear M7.

    Somewhere Over the rainbow ..."up high" starts on M6.

    etc.
     
    Last edited: Feb 25, 2015
  19. dsimon665

    dsimon665 Supporting Member

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    Yep...and color too. I remember in a meeting once someone said something was green, but I saw blue. If I stared at it long enough I could see it as a kind of green.

    Color perception has various influences...one being congenital, and another being cultural.

    They're making strides at vision theory as well as sound perception. There's a good book called :
    The Tell-Tale Brain by Vilayanur S. Ramachandran

    One thing he talks about is "mirror neurons" which may help with imitation and emulation:

    https://www.youtube.com/watch?v=l80zgw07W4Y
     
  20. dsimon665

    dsimon665 Supporting Member

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    Today, we've broken the idea of consonance/dissonance into subcategories. One is roughness or sensory consonance. Sensory consonance includes the beating aspect of consonance. Another aspect is "affinity of tones" which is more like the relative pitch, or tonal aspect.
    http://www.mmk.e-technik.tu-muenchen.de/persons/ter.html

    AFAIK Helmholtz was referring to a mixture of these concepts, with some emphasis on beating, or sensory consonance.

    The sensory aspect is invariant across cultures. However it might be variable from person to person depending on their physical makeup, e.g. Congenital issues, heredity, age, injury, etc.

    The sensory aspect does come into play with culture. This can be traced in the West by looking at its use of dissonance in the history of its music.

    For example major/minor leave out a lot of unusual sounds as evidenced by Eastern musics. The Western concept of Functional harmony somewhat aligns "sensory consonance" with "affinity of tones consonance".

    Which is partially why we have jazz theory as a separate area from functional harmony. Jazz has a different concept of consonance/dissonance.

    "The history of consonance" is a book by James Tenney. In it he categorizes the western use of consonance. He summarizes the west's timeline into CDC1 through CDC5. CDC standing for "consonance/dissonance concept" He also categorizes the West's view of each interval throughout history.
    http://eamusic.dartmouth.edu/~larry/published_articles/tenney_monograph_soundings/20_Harmony.pdf

    Today we're left with an I7 tonic. Coming full circle : integrating those unusual sounds we banished prior into the major/minor system. 7-limit was probably not how Bach heard. Villa-Lobos? 1945? Possibly.
     

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