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Listeners perceive complex pitch-temporal structure in melodies

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In typical Western music, important pitches occur disproportionately often on important beats, referred to as the tonal-metric hierarchy. Jon Prince discusses whether listeners are sensitive to this alignment of pitch and temporal structure.

Image courtesy of interviewee. April 1, 2024

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This video video discusses the concept of tonality in music, which refers to the hierarchical importance of different pitches within a musical scale, specifically how some notes are more prominent in a melody. This video video hierarchy establishes a sense of musical key, making music sound structured; violating it can lead to disjointed sounds. Tonality works alongside the metric hierarchy (the organization of musical pulse or beat) to create the tonal metric hierarchy, a framework suggesting that important notes align with rhythmic beats.

The author conducted a study to investigate the psychological reality of the tonal metric hierarchy, questioning whether listeners would notice disruptions in this alignment. The study comprised three experiments. The first involved generating random melodies that either aligned with or did not follow the tonal metric hierarchy; however, results showed no significant differences in listener ratings.

In the second experiment, the author used scrambled natural melodies, finding that melodies aligned with the tonal metric hierarchy received higher ratings for both melodic goodness and beat clarity. The third experiment replicated these findings while utilizing "phase shifting" to manipulate the alignment of pitches and rhythms without changing their sequences. Results confirmed that participants preferred aligned melodies.

Overall, the findings suggest that the tonal metric hierarchy significantly influences listeners' perceptions of music, even if they are unable to articulate why. Future research aims to further explore this relationship, including testing beat clarity with tapping tasks and using metronomes to assess participants' abilities to detect alignment between melodies and beats.

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X-TIMESTAMP-MAP:LOCAL=00:00:00.000,MPEGTS=900000

00:00.245 --> 00:02.165
Tonality is another way of referring

00:02.165 --> 00:05.285
to what's called musical key, refers

00:05.285 --> 00:06.725
to the relative importance

00:06.745 --> 00:08.805
of each pitch within a musical scale.

00:09.225 --> 00:10.925
So, for example, when you're playing a melody,

00:11.315 --> 00:13.005
some pitches are more important than others.

00:13.005 --> 00:14.205
They're heard more often,

00:14.235 --> 00:15.405
they occur at the end of the melody.

00:15.405 --> 00:17.005
They're played for longer, things like that.

00:17.705 --> 00:21.485
So this hierarchy of importance creates this sense

00:21.485 --> 00:23.085
of tonality or musical key.

00:23.465 --> 00:25.565
Uh, and you can tell when somebody's violating it,

00:25.565 --> 00:28.365
because if somebody plays a so-called wrong note,

00:28.385 --> 00:30.805
you can recognize it immediately and it's probably

00:30.805 --> 00:33.165
because it's a note that doesn't really belong in that key.

00:34.055 --> 00:35.995
So without this hierarchy of tonality,

00:36.215 --> 00:37.915
the music just sounds disjointed

00:37.915 --> 00:39.635
and unstructured and nobody likes it.

00:40.055 --> 00:43.275
Uh, and all musical genres within the Western world

00:43.715 --> 00:45.235
demonstrate these principles of tonality.

00:45.535 --> 00:47.475
And although the actual form

00:47.535 --> 00:49.755
of tonality may vary across cultures,

00:49.985 --> 00:51.595
there's still a relative importance

00:51.595 --> 00:53.915
of different pitches in other musical cultures.

00:54.135 --> 00:55.555
So it's a broader principle

00:55.555 --> 00:57.315
that we find in other musical cultures.

00:58.055 --> 00:59.595
So that's tonality. Uh,

00:59.595 --> 01:01.995
but the tonal metric hierarchy is the idea

01:01.995 --> 01:04.755
that the tonal hierarchy doesn't work just by itself,

01:05.095 --> 01:06.875
but rather it's combined with

01:06.875 --> 01:08.315
what we call the metric hierarchy.

01:08.775 --> 01:10.795
Um, and I won't explain that in detail

01:10.795 --> 01:12.515
because it's a bit simpler just to say

01:12.515 --> 01:14.555
that it's a term I coined in a paper

01:14.555 --> 01:17.635
that investigated the alignment between tonality

01:17.895 --> 01:19.795
and meter in a collection of Western music.

01:21.185 --> 01:23.125
You know, the, the metric hierarchy is kind

01:23.125 --> 01:24.325
of like the tonal hierarchy,

01:24.325 --> 01:26.485
but it more has to do with a musical pulse,

01:26.645 --> 01:28.085
a musical beat, right?

01:28.145 --> 01:29.605
So when you're tapping your foot

01:29.745 --> 01:31.725
or bopping your head, something like that,

01:31.725 --> 01:33.125
that's usually where the beat is.

01:34.465 --> 01:37.925
So tonality is actually aligned with meter such

01:37.925 --> 01:40.565
that in practice tonality isn't just as simple

01:40.565 --> 01:42.245
as saying certain pitches are more important,

01:42.585 --> 01:45.165
but rather that certain pitches played at particular

01:45.255 --> 01:46.405
times are important.

01:47.675 --> 01:48.845
More simply, I can just say

01:48.845 --> 01:51.165
that the tonal metric hierarchy is the idea

01:51.165 --> 01:53.085
that important notes tend

01:53.285 --> 01:54.965
to happen at important points in time,

01:55.235 --> 01:58.445
whereas less important notes tend to occur off the beat

01:58.585 --> 01:59.885
or off that pulse of music.

02:00.465 --> 02:02.205
So the idea of this study was

02:02.205 --> 02:04.645
to figure out if this tonal metric hierarchy

02:04.645 --> 02:07.085
that I demonstrated exists in Western music

02:07.965 --> 02:10.685
actually has any real psychological reality.

02:11.025 --> 02:13.085
In other words, yeah, it's a cool little feature

02:13.085 --> 02:14.565
that I found in music,

02:15.425 --> 02:17.645
but does it really matter if we mess with it?

02:17.955 --> 02:19.245
Will listeners even notice

02:19.505 --> 02:22.245
or is it just something that's just a theoretical curiosity?

02:22.705 --> 02:26.405
So it was about establishing the s psychological reality

02:26.745 --> 02:29.325
of this particular concept to the total metric hierarchy.

02:29.745 --> 02:31.445
So there's not a great deal

02:31.445 --> 02:33.605
of literature on tonality and meter together.

02:34.065 --> 02:37.725
Um, but there is plenty on the more general issue of

02:37.725 --> 02:41.245
how pitch and time combine in music Now, of that literature,

02:41.345 --> 02:43.725
yes, there are some which talk about tonality and meter

02:44.145 --> 02:47.485
and, mostly it's older work as, paper

02:47.545 --> 02:50.805
by Beand in 1997 and also won by Palmer

02:50.805 --> 02:52.325
and Krem Hansel in 1987.

02:52.785 --> 02:54.005
Uh, or a pair of them actually

02:54.475 --> 02:56.925
that found independent contributions of tonal

02:56.925 --> 02:58.885
and metric information when rating musical

02:59.325 --> 03:01.085
Stability of individual notes within a melody.

03:02.405 --> 03:05.045
I found similar results when I was asking listeners

03:05.045 --> 03:07.085
to judge a similarity between two melodies

03:07.085 --> 03:08.725
that I manipulated in various ways.

03:09.385 --> 03:10.405
Um, but there are other

03:10.565 --> 03:11.685
researchers that have found the opposite.

03:11.905 --> 03:15.285
Um, so Marilyn Bolts has found interactions between tonal

03:15.285 --> 03:17.765
and rhythmic features when rating melodic completion.

03:17.905 --> 03:19.485
So how complete does the melody sound?

03:20.185 --> 03:23.285
And also when detecting if there's been a changed pitch

03:23.285 --> 03:26.165
within a melody or judging the duration of the melody.

03:26.915 --> 03:29.415
Um, so in all this actually a rather confusing set

03:29.415 --> 03:31.575
of results that motivated me to figure out, okay, well

03:32.115 --> 03:34.415
is this total electric hierarchy actually a real thing?

03:34.915 --> 03:36.615
Uh, is it just an interesting pattern

03:36.995 --> 03:38.975
or is it something that's really gonna affect listeners?

03:39.275 --> 03:40.735
So the only way to do that was really

03:40.755 --> 03:42.535
to start disturbing the alignment

03:42.535 --> 03:43.775
between tonality and meter.

03:44.345 --> 03:46.735
There are three experiments in this study, mostly

03:46.735 --> 03:47.695
because the first one

03:47.875 --> 03:49.295
didn't work the way I thought it would.

03:49.595 --> 03:52.135
Um, so the first study, basically I made some

03:52.815 --> 03:54.095
computer generated sequences.

03:54.415 --> 03:56.855
I had the computer make a bunch of random melodies

03:56.855 --> 03:58.895
that all followed the patterns of tonality

03:58.915 --> 03:59.935
and meter broadly,

04:00.875 --> 04:03.135
but only half of those melodies aligned the

04:03.215 --> 04:04.255
tonal and metric hierarchies.

04:04.255 --> 04:06.615
That is only half of them were following

04:06.615 --> 04:07.655
the tonal metric hierarchy.

04:08.505 --> 04:10.085
Now, about half the participants rated

04:10.105 --> 04:11.165
how good each melody was,

04:11.465 --> 04:13.925
and the other half rated how clear the beat was.

04:14.435 --> 04:16.645
Some had musical training, but most had none.

04:16.705 --> 04:18.285
And this is the same for all the

04:18.285 --> 04:19.405
other experiments in the paper.

04:20.465 --> 04:22.805
And what I found was that some, there was no difference

04:22.805 --> 04:25.165
between the melodies that funneled the followed the tonal

04:25.165 --> 04:26.245
metric hierarchy and those

04:26.245 --> 04:28.045
that didn't in either participant group.

04:28.705 --> 04:30.125
Uh, and when I went back

04:30.125 --> 04:32.685
and listened to the melodies, I, I have to admit that,

04:33.035 --> 04:35.325
most of the sequences didn't really sound very musical.

04:35.905 --> 04:37.845
Um, probably it's

04:37.845 --> 04:39.925
that I'm not a great computer music composer.

04:40.105 --> 04:42.205
Um, but nevertheless, I couldn't find any role

04:42.205 --> 04:44.285
of the tonal met hierarchy in these sequences.

04:44.625 --> 04:46.925
So then I said, okay, well maybe let's try some

04:47.275 --> 04:48.485
more natural melodies.

04:48.865 --> 04:52.605
So I took some normal melodies that have been composed not

04:52.605 --> 04:54.445
by me, or by the computer.

04:54.865 --> 04:57.085
And then I scrambled the pitches.

04:57.425 --> 04:58.885
So I took the existing melodies

04:58.885 --> 05:00.005
and just jumbled up the order

05:00.005 --> 05:02.165
of the pitches without changing anything about the rhythm.

05:02.785 --> 05:04.485
Now, this still sounded a bit weird,

05:04.485 --> 05:06.605
but they were considerably better than experiment one.

05:07.185 --> 05:10.365
And indeed I found that both participant groups rating both

05:10.395 --> 05:13.245
melodic goodness and also beat clarity, found

05:13.245 --> 05:15.405
that some sequences following the tonal metric

05:15.405 --> 05:16.805
hierarchy got higher ratings.

05:17.575 --> 05:20.635
Uh, now experiment three was an attempt to replicate

05:20.635 --> 05:22.435
that finding just in case it was a fluke.

05:22.775 --> 05:25.755
Uh, and also use a slightly more sophisticated way

05:25.815 --> 05:28.915
of making these melodies that is by using phase shifting.

05:29.655 --> 05:32.275
Um, so basically what we do

05:32.275 --> 05:34.435
with the phase shifting melodies is we don't

05:34.435 --> 05:35.595
change the melody at all.

05:36.355 --> 05:37.655
I'd say we have the same pitch pattern,

05:37.675 --> 05:39.055
we have the same temporal pattern,

05:39.475 --> 05:41.655
but we've shifted them relative to each other

05:41.995 --> 05:43.655
by a certain number of notes such

05:43.655 --> 05:45.895
that the important notes either were

05:45.915 --> 05:47.495
or weren't on the beat anymore.

05:48.315 --> 05:51.775
So imagine for a moment the rhythmic sequence of a melody

05:51.995 --> 05:54.415
as a circle, as if it repeated forever over

05:54.415 --> 05:55.855
and over, say a donut.

05:56.715 --> 06:00.765
Now imagine the pitches as another donut on top of it,

06:00.795 --> 06:01.805
like a donut sandwich.

06:03.185 --> 06:04.405
The phase shift amounts

06:04.405 --> 06:07.605
to twisting the top donut while leaving the bottom donut

06:07.625 --> 06:08.645
in place, right?

06:08.645 --> 06:10.125
So I haven't changed anything about the donut.

06:10.325 --> 06:11.365
I haven't changed a pitch sequence,

06:11.405 --> 06:13.925
I haven't changed a rhythm, but there are aligned

06:13.925 --> 06:15.205
differently, right?

06:15.545 --> 06:18.125
And sure enough, I found that these aligned melodies

06:18.125 --> 06:19.645
or aligned donuts,

06:19.755 --> 06:22.085
they got better ratings than the misaligned melodies.

06:22.315 --> 06:25.125
This total metric hierarchy that I found in 2014.

06:25.265 --> 06:27.885
And most of the literature, literature had been assuming

06:27.945 --> 06:30.285
for many years before that was actually real.

06:30.285 --> 06:32.565
Like it wasn't just an interesting theoretical pattern

06:32.595 --> 06:35.245
that composers used, but it has psychological reality.

06:35.665 --> 06:37.725
So if you mess with the tonal metric hierarchy,

06:37.995 --> 06:40.005
listeners notice that it doesn't sound as good.

06:40.385 --> 06:42.565
Now, probably they don't know exactly what we've done

06:42.625 --> 06:43.765
or why it sounds weird,

06:44.225 --> 06:47.245
but a lifetime of listening to music means

06:47.245 --> 06:49.605
that their brain knows something is up even if they

06:49.605 --> 06:50.725
can't articulate what's wrong.

06:50.905 --> 06:52.685
And of course, in most cases they couldn't

06:52.685 --> 06:54.805
because these were mostly untrained listeners.

06:55.145 --> 06:58.085
And even the musicians that we did have, weren't able

06:58.105 --> 07:00.885
to articulate what it is we'd been doing with the melodies.

07:01.595 --> 07:04.575
Um, now the other interesting aspect to these findings

07:04.575 --> 07:06.375
that I felt were really cool was the fact that,

07:07.735 --> 07:11.935
I was getting the same results for testing the goodness

07:11.935 --> 07:14.415
of the melody as well as the beat clarity.

07:14.795 --> 07:17.055
So how clear was the beat in each of these melodies?

07:17.675 --> 07:20.055
Um, and about the same size of the effect,

07:20.125 --> 07:21.135
same size difference.

07:22.135 --> 07:24.595
Uh, now that to me raised a couple of questions.

07:25.055 --> 07:27.315
One, is it affecting the total metric carkey?

07:27.315 --> 07:28.915
Is it affecting these two different

07:28.915 --> 07:30.915
measures in the same way?

07:31.375 --> 07:34.075
Or maybe when they're reporting me clarity,

07:34.075 --> 07:36.555
they're actually being influenced by me, lot of goodness,

07:36.695 --> 07:38.675
and not necessarily the beat clarity at all.

07:39.335 --> 07:41.275
Uh, so in order to test that, that's

07:41.275 --> 07:43.195
where I've been moving more towards some of the,

07:43.195 --> 07:45.475
future research where I want a more objective test

07:46.015 --> 07:47.755
of be clarity for these melodies.

07:48.015 --> 07:49.675
So I've been trying some research

07:49.685 --> 07:51.635
where we've been using tapping, right?

07:51.635 --> 07:53.755
So you can get listeners to tap along with a melody,

07:54.215 --> 07:56.275
and that's fairly simple approach.

07:56.275 --> 07:57.755
You don't need musical training to tap.

07:58.555 --> 08:01.175
Um, but what I found was that,

08:01.275 --> 08:02.655
the performance tasks like

08:02.655 --> 08:04.335
that didn't really seem to work so well.

08:04.335 --> 08:07.055
They are a bit tricky. Um, interestingly,

08:07.055 --> 08:09.655
I found some significant results when I was testing online

08:09.655 --> 08:12.215
participants, but not when I was finding,

08:12.525 --> 08:14.815
when I was conducting experiments in the lab,

08:14.815 --> 08:16.335
which is really quite bizarre.

08:16.715 --> 08:18.975
Uh, so I sort of put that to the side for the moment.

08:19.075 --> 08:20.935
And this year I have a student trying a

08:20.935 --> 08:22.295
perceptual task, right?

08:22.295 --> 08:24.415
So it's still kind of like the, the previous study

08:24.415 --> 08:26.535
where we're actually asking listeners about it.

08:26.915 --> 08:28.735
Uh, now the way this task works is

08:28.735 --> 08:31.255
that you have participants judge if a metronome

08:31.255 --> 08:34.055
that's been superimposed on the melody, if

08:34.055 --> 08:35.975
that metronome lines up with a beat of the melody.

08:36.275 --> 08:38.655
And of course, we start manipulating it in subtle ways, such

08:38.655 --> 08:40.535
as sometimes it lines up and sometimes it doesn't.

08:41.035 --> 08:42.895
Um, and what we're hoping is

08:42.895 --> 08:46.695
that participants will be slightly better at this task when

08:46.695 --> 08:49.095
we have aligned melodies that is aligned tonality

08:49.095 --> 08:52.295
and meter than ones that have misaligned tonality and meter.

08:52.755 --> 08:53.815
But of course, we don't know yet.

08:53.815 --> 08:55.895
And so we have to, collect some data and find out.

00:00 - Tonality is another way of referring to what's called musical key, refers to the relative importance of each pitch within a musical scale. So, for example, when you're playing a melody, some pitches are more important than others.

00:13 - They're heard more often, they occur at the end of the melody. They're played for longer, things like that. So this hierarchy of importance creates this sense of tonality or musical key. and you can tell when somebody's violating it, because if somebody plays a so-called wrong note, you can recognize it immediately and it's probably because it's a note that doesn't really belong in that key. So without this hierarchy of tonality,

00:36 - the music just sounds disjointed and unstructured and nobody likes it. and all musical genres within the Western world demonstrate these principles of tonality. And although the actual form of tonality may vary across cultures, there's still a relative importance of different pitches in other musical cultures. So it's a broader principle that we find in other musical cultures.

00:58 - So that's tonality. but the tonal metric hierarchy is the idea that the tonal hierarchy doesn't work just by itself, but rather it's combined with what we call the metric hierarchy. and I won't explain that in detail because it's a bit simpler just to say that it's a term I coined in a paper that investigated the alignment between tonality and meter in a collection of Western music.

01:21 - You know, the, the metric hierarchy is kind of like the tonal hierarchy, but it more has to do with a musical pulse, a musical beat, right? So when you're tapping your foot or bopping your head, something like that, that's usually where the beat is. So tonality is actually aligned with meter such that in practice tonality isn't just as simple as saying certain pitches are more important,

01:42 - but rather that certain pitches played at particular times are important. More simply, I can just say that the tonal metric hierarchy is the idea that important notes tend to happen at important points in time, whereas less important notes tend to occur off the beat or off that pulse of music. So the idea of this study was to figure out if this tonal metric hierarchy

02:04 - that I demonstrated exists in Western music actually has any real psychological reality. In other words, yeah, it's a cool little feature that I found in music, but does it really matter if we mess with it? Will listeners even notice or is it just something that's just a theoretical curiosity? So it was about establishing the s psychological reality of this particular concept to the total metric hierarchy. So there's not a great deal

02:31 - of literature on tonality and meter together. but there is plenty on the more general issue of how pitch and time combine in music Now, of that literature, yes, there are some which talk about tonality and meter and, mostly it's older work as, paper by Beand in 1997 and also won by Palmer and Krem Hansel in 1987. or a pair of them actually that found independent contributions of tonal and metric information when rating musical

02:59 - Stability of individual notes within a melody. I found similar results when I was asking listeners to judge a similarity between two melodies that I manipulated in various ways. but there are other researchers that have found the opposite. so Marilyn Bolts has found interactions between tonal and rhythmic features when rating melodic completion. So how complete does the melody sound? And also when detecting if there's been a changed pitch

03:23 - within a melody or judging the duration of the melody. so in all this actually a rather confusing set of results that motivated me to figure out, okay, well is this total electric hierarchy actually a real thing? is it just an interesting pattern or is it something that's really gonna affect listeners? So the only way to do that was really to start disturbing the alignment between tonality and meter. There are three experiments in this study, mostly

03:46 - because the first one didn't work the way I thought it would. so the first study, basically I made some computer generated sequences. I had the computer make a bunch of random melodies that all followed the patterns of tonality and meter broadly, but only half of those melodies aligned the tonal and metric hierarchies. That is only half of them were following

04:06 - the tonal metric hierarchy. Now, about half the participants rated how good each melody was, and the other half rated how clear the beat was. Some had musical training, but most had none. And this is the same for all the other experiments in the paper. And what I found was that some, there was no difference between the melodies that funneled the followed the tonal metric hierarchy and those

04:26 - that didn't in either participant group. and when I went back and listened to the melodies, I, I have to admit that, most of the sequences didn't really sound very musical. probably it's that I'm not a great computer music composer. but nevertheless, I couldn't find any role of the tonal met hierarchy in these sequences. So then I said, okay, well maybe let's try some more natural melodies.

04:48 - So I took some normal melodies that have been composed not by me, or by the computer. And then I scrambled the pitches. So I took the existing melodies and just jumbled up the order of the pitches without changing anything about the rhythm. Now, this still sounded a bit weird, but they were considerably better than experiment one. And indeed I found that both participant groups rating both melodic goodness and also beat clarity, found

05:13 - that some sequences following the tonal metric hierarchy got higher ratings. now experiment three was an attempt to replicate that finding just in case it was a fluke. and also use a slightly more sophisticated way of making these melodies that is by using phase shifting. so basically what we do with the phase shifting melodies is we don't change the melody at all. I'd say we have the same pitch pattern,

05:37 - we have the same temporal pattern, but we've shifted them relative to each other by a certain number of notes such that the important notes either were or weren't on the beat anymore. So imagine for a moment the rhythmic sequence of a melody as a circle, as if it repeated forever over and over, say a donut. Now imagine the pitches as another donut on top of it, like a donut sandwich.

06:03 - The phase shift amounts to twisting the top donut while leaving the bottom donut in place, right? So I haven't changed anything about the donut. I haven't changed a pitch sequence, I haven't changed a rhythm, but there are aligned differently, right? And sure enough, I found that these aligned melodies or aligned donuts, they got better ratings than the misaligned melodies.

06:22 - This total metric hierarchy that I found in 2014. And most of the literature, literature had been assuming for many years before that was actually real. Like it wasn't just an interesting theoretical pattern that composers used, but it has psychological reality. So if you mess with the tonal metric hierarchy, listeners notice that it doesn't sound as good. Now, probably they don't know exactly what we've done or why it sounds weird, but a lifetime of listening to music means

06:47 - that their brain knows something is up even if they can't articulate what's wrong. And of course, in most cases they couldn't because these were mostly untrained listeners. And even the musicians that we did have, weren't able to articulate what it is we'd been doing with the melodies. now the other interesting aspect to these findings that I felt were really cool was the fact that, I was getting the same results for testing the goodness of the melody as well as the beat clarity.

07:14 - So how clear was the beat in each of these melodies? and about the same size of the effect, same size difference. now that to me raised a couple of questions. One, is it affecting the total metric carkey? Is it affecting these two different measures in the same way? Or maybe when they're reporting me clarity, they're actually being influenced by me, lot of goodness, and not necessarily the beat clarity at all.

07:39 - so in order to test that, that's where I've been moving more towards some of the, future research where I want a more objective test of be clarity for these melodies. So I've been trying some research where we've been using tapping, right? So you can get listeners to tap along with a melody, and that's fairly simple approach. You don't need musical training to tap. but what I found was that,

08:01 - the performance tasks like that didn't really seem to work so well. They are a bit tricky. interestingly, I found some significant results when I was testing online participants, but not when I was finding, when I was conducting experiments in the lab, which is really quite bizarre. so I sort of put that to the side for the moment. And this year I have a student trying a perceptual task, right?

08:22 - So it's still kind of like the, the previous study where we're actually asking listeners about it. now the way this task works is that you have participants judge if a metronome that's been superimposed on the melody, if that metronome lines up with a beat of the melody. And of course, we start manipulating it in subtle ways, such as sometimes it lines up and sometimes it doesn't. and what we're hoping is that participants will be slightly better at this task when

08:46 - we have aligned melodies that is aligned tonality and meter than ones that have misaligned tonality and meter. But of course, we don't know yet. And so we have to, collect some data and find out.

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