What is up with Noises? (SLYT)

August 25, 2011 2:51 PM

What is up with Noises? A fascinating explanation of why we hear sounds and music the way we do. It's a long video, but it's worth it!
posted by fzx101 (37 comments total)

I was walking down the street with my friend and he said, "I hear music", as if there is any other way you can take it in. You're not special, that's how I receive it too. I tried to taste it but it did not work. - Mitch Hedberg

Sorry, carry on.
posted by Chichibio at 3:16 PM on August 25, 2011 [4 favorites]

That was beautiful.

If you're interested in getting even more into the math of sound, btw, search for "Vibrations" in iTunes U. There's a full semester course on Vibrations and Waves from MIT, which is absolutely fantastic (you'll need to know calculus to follow it, though).
posted by empath at 3:31 PM on August 25, 2011 [1 favorite]

Also, I hope she is doing this for a living, and if she's not, then I want to pay her to do this for a living. She has an amazing gift for explaining the abstract.
posted by empath at 3:32 PM on August 25, 2011 [1 favorite]

Nice! I love nerdy factoids like this!
posted by austinurbani at 3:38 PM on August 25, 2011

Needs the ViHart tag. (I'm expecting her to get a MacArthur sooner or later.)
posted by benito.strauss at 3:48 PM on August 25, 2011 [1 favorite]

Vi Hart is my ✓ muse ✓ crush.
posted by Bora Horza Gobuchul at 4:06 PM on August 25, 2011 [1 favorite]

I have a question related to the subject: Has anyone here read something in music theoretic literature about exactly what properties in the frequency ratios between notes in a chord produces a (vaguely speaking) 'happy' effect vs. a 'sad' effect?

I have my own hypothesis :)
posted by Anything at 5:52 PM on August 25, 2011

And to clarify, I'm asking about properties of the set of frequency ratios between all the pairs of notes in a chord, not just properties of individual frequency ratios between pairs of notes in isolation.

And by 'frequency ratio between notes' I mean the frequency ratio between the fundamentals of the notes, which can be used to produce a naive but in many cases useful approximation for dissonance between the notes...
posted by Anything at 6:13 PM on August 25, 2011

Or, in laymans' terms, why does a minor chord sound sadder than a major chord: I sure would like to see an answer, but I really doubt there is one that isn't B.S.
posted by kozad at 7:10 PM on August 25, 2011

I've heard of noises. Been meaning to read up on em.
posted by Liquidwolf at 7:21 PM on August 25, 2011

Or, in laymans' terms, why does a minor chord sound sadder than a major chord: I sure would like to see an answer, but I really doubt there is one that isn't B.S.

The frequency ratios in a major chord are more "pure" (that is, the numbers in the fractions are smaller), which makes them more consonant: 1, 5/4, 3/2. The frequency ratios in a minor chord are 1, 32/27, 3/2.

I'm not saying this is an "explanation", but there is a definite correlation between small-integer frequency ratios and consonance, and between consonance and pleasantness.
posted by dfan at 7:29 PM on August 25, 2011 [1 favorite]

The explanation is that the minor chord beats more which adds even more (implied) frequencies into the mix.
posted by empath at 7:53 PM on August 25, 2011 [1 favorite]

I wrote a term research paper in college entitled "Music, Mathematics and Celestial Harmony: A Survey of the Ancients and their Renaissance Heir" for History of the Scientific Revolution. I examined the scientific march towards explaining natural phenomena (namely, music and and the movements of celestial bodies) in mathematical terms, from the Pythagoreans through Johann Kepler.

Reading and analyzing ancient scientists', mathematicians' and philosophers' ideas while deep in the bowels of the music library - the crowning academic experience of my life.

Needless to say, the bit about Pythagorus struck a chord.
posted by 3FLryan at 8:10 PM on August 25, 2011 [1 favorite]

Holy cats, this is fantastic. Thank you!
posted by Joey Michaels at 10:02 PM on August 25, 2011

The rest of the stuff on Vi Hart's channel is also great. And I like that she describes herself as a "recreational mathematician". So much of the maths I failed to shine at at school felt desperately UN-recreational.

Aside from being a fine explanation of how we hear I also think this is a great example of just how much information can be compressed into a 13 minute video while remaining intelligible. The source information she uses would fill a long shelf books on music theory, mathematics, physiology and psychology. At my school or university that material would probably never have all been presented together - and if it was it would have been over a semester - and not nearly so clearly. As each subject leads into another she manages to make the link seem straightforward - in a way which is complimentary rather than befuddling. The whole video is written in the expectation that viewers may rewind and view particular parts several times before they are finished. The length of each take is equivalent to what we would see in the most frenetic pop video or TV commercial.

Contrast her approach with the Open University talking about much the same subject. The OU know that they are doing in terms of presenting information in videos - but in this case the speed of presentation is WAY slower: it is going to be Christmas before we have covered all the material we saw in Vi Hart's single video.
posted by rongorongo at 1:11 AM on August 26, 2011 [2 favorites]

Her series on "doodling in math class" is also presentational genius.
posted by rongorongo at 1:46 AM on August 26, 2011

She is going way. too. fast. When you rush math it makes me distrust you.
posted by ZaneJ. at 2:27 AM on August 26, 2011

dfan: "The frequency ratios in a major chord are more "pure" (that is, the numbers in the fractions are smaller), which makes them more consonant: 1, 5/4, 3/2. "

AKA 1 1.250000 and 1.500000

Or, much less purely, in most music since the 19th century, 1, the twelfth root of two, and the twelfth root of 128.

AKA 1 1.259921 1.498307

if it was as simple as the ratios being smaller, a just intonation diminished minor would be more pleasing to hear than an equal temperament major chord.
posted by idiopath at 4:25 AM on August 26, 2011 [1 favorite]

*third root of two not twelfth root for the major third, sorry
posted by idiopath at 4:26 AM on August 26, 2011

benito.strauss : Needs the ViHart tag. (I'm expecting her to get a MacArthur sooner or later.)

That's a really good idea. I googled how to nominate and discovered this

Fellows FAQ - The Nomination Process

How are candidates brought to our attention?
So that we can expand our search for creative people as widely as possible while keeping the number of nominations manageable, we limit our consideration only to those who have been nominated by someone from our constantly changing pool of invited external nominators. Applications or unsolicited nominations are not accepted.

typical east coast elitism! thinking they can dictate who's a genius
posted by DigDoug at 4:48 AM on August 26, 2011

Sorry to be so pedantic, but I feel compelled to point out: in the cochloea, there is no "vasilar" membrane. It's called the BASILAR membrane.

That's all.
posted by Cygnet at 7:11 AM on August 26, 2011

*cochlea.
posted by Cygnet at 7:12 AM on August 26, 2011

This is splendid!
posted by odinsdream at 7:13 AM on August 26, 2011

Talking about the cochlea, I'm really glad it was named when it was — Latin for snail shell. Had we just discovered it recently I'm sure it would have been named the cinnabon.
posted by benito.strauss at 9:00 AM on August 26, 2011 [1 favorite]

Or, in laymans' terms, why does a minor chord sound sadder than a major chord

To my knowledge, this has yet to be satisfactorily answered, though as mentioned above several phenomena could account for the differences in affect. There is a competing idea coming from a great neuroscience researcher at ASU (sat in on one of his lectures about this) that tempo and timing affect emotional impact of music as much as pitch content.

I find it quite fascinating that an effect so many experience subjectively has yet to be explained in any real way. Which is why brain research uses music and musical perception as a kind of Rosetta stone in many studies, I guess.
posted by LooseFilter at 4:52 PM on August 26, 2011

I want to be smart like her!
posted by JujuB at 6:01 PM on August 26, 2011

The minor third is not inherently sadder than the major third; we're trained to feel that way through enculturation. In many other musical styles around the world (e.g. klezmer), minor key music is often happy and major key music is often sad.
posted by speicus at 9:47 PM on August 26, 2011

All right, let's see. Can you find a 'sad' chord that does not have this property: One of the non-root notes has a stronger consonance with some other non-root note than it does with the root note. (Consonance being the inverse of dissonance, and dissonance here being defined as the naive but often useful 'frequency ratio dissonance' obtained by multiplying the numerator and the denominator in the frequency ratio between the notes.) Examples, with frequency ratios between each pair of notes:

Minor triad:
root - minor third: 6/5
root - fifth: 3/2
minor third - fifth: 5/4 (higher consonance than root - minor third)

Root, major third, major sixth (quite a sad chord despite the 'major' notes)
root - major third: 5/4
root - major sixth: 5/3
major third - major sixth: 4/3 (higher consonance than either of the intervals with root)
posted by Anything at 1:46 AM on August 27, 2011

And apologies if I've misused some terminology; IANAMusician. I suppose 'fifth' etc. refers to the interval, not to the note at the given interval from the root.
posted by Anything at 2:01 AM on August 27, 2011

I just attended a conference related to this subject, and I'm about to drive for seven hours, so I apologize if I'm about to be cranky about this.

Even with the "accuracy not guaranteed" caveat, there are so many errors in this video that, to me, it feels more like a parody of an educational video. Most of them are small, though, so I'll concentrate on the big one: the idea that we hear mathematically simple ratios as "consonant" and complex ratios as "dissonant." As lovely and elegant this idea is, it's just not true (as idiopath alludes to), and in fact it's as outdated as, well, most of Pythagoras' semi-mystical ideas.

There has been some really interesting neuroscience and cognition work in this area recently by people like Edward Large, who gives a pretty good succint explanation of what I'm talking about:

The oldest theory of musical consonance is that perceptions of consonance and dissonance are governed by ratios of whole numbers. Pythagoras is thought to have first articulated the principle that intervals of small integer ratios (cf. Fig. 3B; Fig. 4C) are pleasing because they are mathematically pure (Burns 1999). He used this principle to explain the musical scale that was in use in the West at the time, and Pythagoras and his successors proposed small-integer-ratio systems for tuning musical instruments, such as Just Intonation (JI). Modern Western equal temperament (ET), divides the octave into 12 intervals that are precisely equal on a log scale. ET approximates JI, and transposition in ET is perfect, because the frequency ratio of each interval is invariant. Apart from octaves however, the intervals are not small integer ratios, they are irrational.The fact that intervals based on irrational ratios are approximately as consonant as nearby small integer ratios is generally considered prima facie evidence against the theory that musical consonance derives from the mathematical purity of small integer ratios. [emphasis mine]

This works both ways... the 7th harmonic of the overtone series, one of the simplest mathematical ratios, sounds incredibly "out of tune" to us because it doesn't fit into equal temperament.

Large's theory is a bit harder to summarize (yes, there's a reason people study this stuff for longer than 13 minutes), but goes much further toward explaining why we hear the way we do. I'll do my best to stuff it into a few sentences! Basically, we put frequencies that are close together into different "bins" (e.g. notes in a scale), and these bins are sort of mutable; they can be shifted around slowly over time through conditioning or enculturation. So here in the Western world we're predisposed to major, minor, and chromatic equal temperament "bins." But presumably if you'd grown up listening to, for example, Balinese gamelan music, you'd have a different set of "bins."

Really the only interval that's consistent everywhere is the octave (2x). If music really worked the way Pythagoras/Vi thought, music around the world would be much more homogenous (and boring).
posted by speicus at 7:44 AM on August 27, 2011 [2 favorites]

speicus: A quick glance at Large's paper suggests that small integer ratios have a fairly prominent role in his theory as well.
posted by Anything at 8:33 AM on August 27, 2011

Quote:

Tones with small integer ratio relationships (1:1, 5:4 and 3:2 – a Neurodynamics of Music 24 tonic triad) produced a stable memory in the neural oscillator network (cf. Fig. 2). Although a leading tone (8:15 ratio with the tonic frequency) could be stabilized through external stimulation, when the external stimulus was removed, the leading tone frequency lost stability as those oscillators that had responded at the leading tone frequency began to resonate at the tonic frequency. In other words, the tonic frequency functioned as an attractor of nearby oscillators. Thus, nonlinear resonance predicts both memory stability of small integer ratios and tonal attraction among sequentially presented frequencies (Large in press).

He also recognizes the role of small integer ratios in traditional systems in a number of musical cultures other than the West:

The tuning systems of the world’s largest musical cultures, Western, Chinese, Indian, and Arab-Persian, are based on small integer ratio relationships (Burns 1999)2. However, each tuning system is different, and this has led to the notion that frequency relationships do not matter in high level music cognition; rather, auditory transduction of musical notes results in abstract symbols, as in language (see, e.g., Patel 2007). If this were true, stability and attraction relationships would also have to be learned presumably based solely on the frequency-of-occurrence statistics of tonal music (for a current overview, see Krumhansl and Cuddy, this volume).

[...]

However, stability and attraction relationships are not learned per se, but are intrinsic to neural dynamics given a particular set of frequency relationships.

posted by Anything at 8:40 AM on August 27, 2011

Yeah, I should have mentioned the idea of neural resonance that Large talks about. We may be predisposed to hear certain small integer ratios as significant (those that are more "resonant") but the learning process makes this highly malleable. And it doesn't really explain why we like certain small integer ratios and don't seem to care much for others, or why we have certain emotional associations.
posted by speicus at 8:34 PM on August 27, 2011

We may be predisposed to hear certain small integer ratios as significant

Yes, and the strength of that predisposition is governed by the simplicity of the frequency ratio of the given interval. The paper you cited and, with more detailed explanation, the 'in press' paper (pdf) give a formula (ϵ^k+m-1/2, with 0 <= ϵ <= 1 and k, m the numerator and denominator of the frequency ratio) for the stability of intervals which puts the intervals in precisely the same order as suggested by the 'freqency ratio dissonance' I mentioned above.

Your earlier comment gave the impression that it'd be pointless to emphasize any interval (sub-octave) over the other. Given everything I've read on the subject, including Large's work, it seems you're not giving Pythagoras enough credit.

I also didn't see anything in Hart's video that would rule out malleability and any superior non-boringness that comes with it. Maybe she just had a lot of material to cover for a 12-minute video as it is?
posted by Anything at 11:31 PM on August 27, 2011

Beautiful.
posted by goodnewsfortheinsane at 11:01 AM on August 28, 2011

Anything: The formula you cite predicts relative stability of intervals, but not which intervals we actually discern. In the paper you linked, you'll notice that on the diagram of the chromatic scale on page 202, half of those small integer ratios disappear. The only explanation for this is learning (and it's the explanation Large provides).

In your example above, the two chords you describe are inversionally equivalent (e.g. A C E vs. C E A ), which is a simpler and more elegant way to describe why they sound similar to us (based on the principle of octave equivalence). In fact, these chords sound practically identical to us, despite having quite different raw intervallic content, as you pointed out.

Your proposed "sad" property -- One of the non-root notes has a stronger consonance with some other non-root note than it does with the root note. -- doesn't hold for the second inversion of the minor chord (e.g. E A C), which would have a more consonant ratio on the bottom (4/3) than the top (6/5).

So, there's quite a bit going on here that can't be described by simply comparing interval ratios.

Maybe "misleading" or "incomplete" would be a better way to describe Vi's explanation, but compounded with the small errors she makes (like when she says "semitones" when she actually means "microtones"), there's just vast potential for misunderstanding, like this persistent major-minor-happy-sad myth that just refuses to die. It's exacerbated by music journalism, I think, in which sad major key music is often misidentified as minor, and happy minor music is misidentified as major.
posted by speicus at 9:19 PM on August 29, 2011 [2 favorites]

I realize that I'm really late to this particular party, but I wanted to chime in (pun intended?) with my agreement with speicus. Not counting the spelling error pointed out above, I found 11 incorrect statements in the video and 7 questionable concepts presented.

I love Vi Hart, but I do musical acoustics for a living. I wish she would TALK TO US, so she would learn with us and then go out and make the engaging videos which are actually accurate.
posted by achmorrison at 9:12 AM on September 11, 2011 [1 favorite]