The music of the species

It’s all about the music.
ResearchBlogging.org Gill and Purves. “A biological rationale for musical scales” PLoS ONE, 2009
So you might think that music like this:
(HOT STUFF. Go to 0:35 for the real hotness. It’s Victoria’s O Magnum Mysterium)
or this:

(Also some killer hot stuff, 3:50 has the real chills. The Lauridsen version)
Don’t have much in common with THIS hot stuff:

(That’ll wake you up! No idea who this guy is, but he’s hilarious, and the dancers wearing body suits under skimpy outfits are the best!)
Or even much in common with this:

(That never gets old. MWAH HA HA HA!!!)
But you would be wrong. They have a lot in common. Most songs in both eastern (including Indian, Chinese, and Middle Eastern music) and western music are based on a limited series of musical scales (there are lots of exceptions, but the most popular songs tend to be based on common musical scales). And the question for years has been: why? These scientists have put together a new theory, which Sci will allow you to judge on yourself.


Humans can, all told, distinguish about 240 different pitches over a single octave. That’s a LOT of pitches, over a pretty small range. Our hearing may not extend very far into ultrasonic or anything, but we’ve got a good bit where it counts. Here’s an octave:
OctaveG.jpg
This person is playing from G to G on a standard piano. In a major scale like this one, there will be 8 tones from the lower G to the higher G. But in this same octave, a human can DISTINGUISH up to 240 different tones. Cool, huh?
So we’re pretty sensitive to changes in pitch (except those who are truly tone deaf). Some trained singers can even be trained to SING quarter tone pitches (we usually work in whole and half tones, but some middle eastern music requires quarter tones). But in a good part of the world, most music is based on a limited series of scale types, shown below:
music scales1.png
Those are the 14 most commonly used scales in music. But we can distinguish THOUSANDS of tones. So why are we using these specific tone combinations for most of our music? Even if you narrow it down to an organization of scales based around an octave, there are still thousands of possible 5-7 note tone combinations. Not only that, but eastern and western tone scales are both often organized around the chromatic scale, a 12 note tone combination of half steps that are equally spaced (and is one of the major training things, along with the circle of fifths, that you learn to play very fast when you’re learning to play an instrument) So why do we just use these 14? And why do we organize scales along a chromatic tone structure?
Several theories have been put forward as to why. One theory states that we are attracted to the “lower harmonics” or the undertones (and presumably also the overtones) that occur in a harmonic series. If you play (or sing) a REALLY well tuned major or minor chord, you can hear overtones and undertones that resonate under and over the pitches you are singing. It’s a really chilling thing to hear and very cool, but unfortunately I can’t find any examples (send some if you have ’em!). But this theory doesn’t account for things like a minor second, which won’t result in overtones or undertones, meaning that minor scales might not be included.
Often, approaches as to why we use specific tone scales have used mathematical algorithms to predict scale structure, the idea being that we would use a specific mathematical formula because we’re totally parsimonious like that. In this evaluation, the scientists looked at similarities between tone scales and harmonic tone series, which merely evaluates the degree of tone similarities between tones in a scale (how far apart the tones are from one another).
Using this approach, they found that the scale that came out closest was the minor pentatonic scale, which is one of the most widely used scales in music. Appears to be a pretty close match. The second highest match was a scale used in Chinese and Indian music known as Ritusen (on the far right of the figure up there). Overall, most of the scales used most often came out well when compared to harmonic tone series. These all have similar ratios between the notes, making for a certain amount of equal spacing between the tones in the scale (ok, except the major 7th, that one never seems to come out well).
But what is the REASON for this preference? The authors put forth two reasons that are rather compelling. First, these harmonic tones are ones that are easily distinguished, and thus pleasant to us (if you have two tones that are too close together played at the same time, it created a “throbbing” kind of noise which isn’t fun to listen to at all, try hearing badly tuned instruments some time). The scales that we prefer are the ones with the highest harmonic overlap, which means they are spaced far enough apart that the “throbbing” sound is reduced as much as possible when the tones are played at the same time. This makes the tone combinations in a scale sound more pleasant.
Second, the authors came up with a biological rationale. Why do we prefer (and studies have shown that we clearly DO prefer) tones with high harmonic overlap and low “throb”? Well, it turns out that human speech has a characteristic series of harmonics associated with it, though these are changed by things like vowel tones. Human speech is often determined as much by its tone as it is by the consonants coming out. So the authors hypothesize that humans prefer harmonic vocal series because it is the most similar to the speech patterns of our conspecifics. Presumably we are best adapted to hearing those harmonic frequency (the human ear is optimized for sounds in the human vocal range) and also adapted to find them pleasurable. Interestingly, other studies have shown that humans respond best to music that is similar to their own vocalizations, preferring music from instruments which are tuned near the range of the human voice (like the guitar), and some of which even have a timbre which is similar to the human voice (like a violin or flute).
As to why the tone combinations we write down are between 5 and 7 tones (technically a full octave is 8, but one tone is repeated, so 7), the authors note that the 7 tone series provides the full range of options for musical combination. Go higher than 7 tones and the combinations become less pleasant, while once you get all the way up to two octaves, you’re going to be repeating yourself. So it’s possible that 5-7 tone scales produce the most pleasant tone combinations. It would be interesting to test this, though very hard to do it in humans, because you would have to control for the fact that most humans will be familiar with the 5-7 tone scales and could thus find them more pleasant.
Sci thinks this is a pretty interesting hypothesis, and not entirely unlikely. It would also be really interesting to see if you could find a similar effect in animals, say monkeys or birds, where you make “music” out of similar or dissimilar harmonics to those found in their vocalizations, and see how they feel about them. In highly communicative species, it might be possible that similar mechanisms have evolved making them prefer similar sounds. An interesting way to test the hypothesis. And as Sci loves her 5-7 tone scales, she thinks this is something to sing about.

(Someone ought to write a modern oratorio based around L337-speak. Instead of the “Hallelujah chorus” we would have something based on “w00t”. It would probably have musical references to Mario…)
Gill KZ, & Purves D (2009). A biological rationale for musical scales. PloS one, 4 (12) PMID: 19997506

20 Responses

  1. a 12 note tone combination of half steps that are equally spaced

    Pedantically, but I think fascinatingly, this was only true for Western music once the piano was introduced. If you tune evenly, you don’t get pure fifths. And if you tune the fifths to be pure, your octaves aren’t right.
    The solution was to tune (‘temper’) some fifths to be pure, and leave a couple of horrible fifths (one was called “the wolf”), and then chose the music to avoid wolves. Bach’s Well Tempered Clavier was him showing off a secret tempering system that avoided any really horrible intervals.

  2. The great thing about playing a non-tempered instrument (such as a flute) is that you can explore all the different tones and harmonics, and when you’ve got two flutes playing together you sometimes get to hear every one of those combinations, in all their untuned glory.
    Someone should definitely write the w00t chorus…

  3. Either you aren’t describing the authors’ ideas correctly or the authors of the study are making some elementary mistakes.
    Reason 1: people prefer scales with notes that are relatively far apart because when two notes on that scale are played simultaneously (aka, a “chord”), the “throbbing”, more correctly known as beat frequency, is “reduced as much as possible”. But why then do people prefer certain chords to others? And anyway, there is always a beat frequency. One answer is that people prefer chords in which the beat frequency is a multiple of the frequency of the two notes.
    Reason 2: People prefer the scales they do because they mirror somehow the harmonics created by the human voice? That makes no sense. Harmonics or overtones are frequencies that are generated simultaneously with the main frequency, but more quietly, that create the unique timbre or character of the sound. So when a human sings an A at 440 Hz, she isn’t generating a pure sine wave of 440 Hz, she is also making other sine waves with other frequencies. But those overtones have no mathematical relationship with the main tone. They are created by the particular structure and characteristics of the human throat and mouth. But the western and pentatonic scales are seemingly based on mathematical relationships. If anything, the scales are closer to the overtone structure of a vibrating string than the human voice. (Touch a string in the middle, you get an octave. Touch it at 1/3, you get an octave and a fifth, etc.)
    Writers on this subject rarely acknowledge that there is probably some element of arbitrariness and historicity to which particular tonal relationships are preferred and further, are meaningful (why does a minor third sound “sad”?), in the same way that the sound of words don’t have anything necessarily to do with their meaning.
    And of course, there is a lot more to music than simply scales. Why does recorded music seem to “occur” in real-time to a greater extent than do novels, for example? And why does music seem to tell a story at all? How do harmony and melody work together to create emotional meaning that goes far beyond “preferring” or “not preferring” certain tone combinations? And what about rhythm?

  4. Karl: don’t do this to Sci before her first cup of coffee, it’s mean.
    You may be right, I did find it a hard paper to get through and I might have missed some stuff. What they were comparing was the tone INTERVALS (not the tones themselves) to harmonic frequencies. So the distance between two notes and the tone combination, not the specific tones. They then state that the component INTERVALS in the scales are those used most commonly in human vocalization, not the tones themselves, but the distances between them, implying that humans are best adapted to prefer the tone changes inherent in the human voice. At least, that’s what I got out of the paper. I didn’t write it up that way and will have to change some stuff.

  5. Listen to the music of other cultures that don’t follow our “even-tempered” piano major/minor aesthetic, especially music from India and you’ll get to experience much more nuance.

  6. The intervals discussed in this paper and the post are actually just Western preferences. Indian music is far from alone in embracing more nuanced approaches. A lot of Asian cultures also use a more nuanced approach and utilize far more of the tones within octaves. For that matter, early European music is not as atonal as many would have you believe – it is just that the music was far more subtle in the use of tone.
    And also for the record, it is not all that difficult to teach vocalists to utilize tighter intervals. “Sliding” the scales, instead of defining each tone, using simple warm-up exercises is an excellent tool. Though it is more difficult to stay on beat while sliding a scale, some practice with a metronome and a pianist checking in every full step or so and it becomes easy-peasy. Another tool that helps is backstepping by eighths to the half note and up the next half then down to the note – which may sound complicated, but is actually quite easy because it allows one to hit specific tones on a beat.
    Peter Gabriel has probably made more use of this than any other popular Western musician. The Chinese use this in a fashion that is probably more foreign to Western ears than any other culture in the world. It actually seems to clash to a strong degree, until the ear becomes accustomed to listening to it and starts to pick up the underlying nuance.

  7. The intervals discussed in this paper and the post are actually just Western preferences. Indian music is far from alone in embracing more nuanced approaches. A lot of Asian cultures also use a more nuanced approach and utilize far more of the tones within octaves. For that matter, early European music is not as atonal as many would have you believe – it is just that the music was far more subtle in the use of tone.
    And also for the record, it is not all that difficult to teach vocalists to utilize tighter intervals. “Sliding” the scales, instead of defining each tone, using simple warm-up exercises is an excellent tool. Though it is more difficult to stay on beat while sliding a scale, some practice with a metronome and a pianist checking in every full step or so and it becomes easy-peasy. Another tool that helps is backstepping by eighths to the half note and up the next half then down to the note – which may sound complicated, but is actually quite easy because it allows one to hit specific tones on a beat.
    Peter Gabriel has probably made more use of this than any other popular Western musician. The Chinese use this in a fashion that is probably more foreign to Western ears than any other culture in the world. It actually seems to clash to a strong degree, until the ear becomes accustomed to listening to it and starts to pick up the underlying nuance.

  8. Actually, you guys, these scales ARE very popular in Indian music, as well as Middle Eastern and Chinese, and are among the most common scales used. The authors were just analyzing the most common scales rather than all examples, and of course there are plenty of exceptions. Early European music also contains exceptions, but the modes (such as the Aeolian and Dorian modes) are still included in the most popular. It’s not an analysis of ALL music, keep in mind, just the most popular types of scales.
    DuWayne, they also note the sliding scale technique, and hypothesize that this is attractive due to covering a side range of conspecific sounds. I don’t know about that one. And I’ve done that exercise, and it can be VERY hard for someone with really rigid classical training. It’s like teaching a ballerina to bellydance. Precision we’ve got, sexy flow we have not.

  9. You know, when I was teaching vocals I found that my biggest challenge was breaking through previous stringent training. I was trained by three individual voice instructors and a choral instructor who was well versed in several styles. My best instructor was an opera singer, who had a masters from the Eastman School of Music in voice instruction – which meant that she taught a range of styles. I always felt that providing a student with a spectrum of traditions to draw from is the only responsible way to teach a person to sing.
    For someone with a firm classical background, I think the best tool to use is to step in eighths, up and down the scale – then move to back and upstepping. It allows you to hit firm tones. Eventually it will seem that sliding would be easier and will be. I would only use sliding with someone who has no training or who has a background in jazz or opera. Though in all honesty, I find rigid classical training is a hard habit to break through.
    I will address the rest of your comment later. I have class to get to…

  10. You know, when I was teaching vocals I found that my biggest challenge was breaking through previous stringent training. I was trained by three individual voice instructors and a choral instructor who was well versed in several styles. My best instructor was an opera singer, who had a masters from the Eastman School of Music in voice instruction – which meant that she taught a range of styles. I always felt that providing a student with a spectrum of traditions to draw from is the only responsible way to teach a person to sing.
    For someone with a firm classical background, I think the best tool to use is to step in eighths, up and down the scale – then move to back and upstepping. It allows you to hit firm tones. Eventually it will seem that sliding would be easier and will be. I would only use sliding with someone who has no training or who has a background in jazz or opera. Though in all honesty, I find rigid classical training is a hard habit to break through.
    I will address the rest of your comment later. I have class to get to…

  11. As far as I know, I was the first person to predict that the perception
    of consonance is calibrated against personal experience of hearing human
    vowel sounds, and I quote myself:
    Now we already know that intervals between pitch values which are simple
    fractional ratios play a significant role in our perception of music. And
    we know that these are the same ratios that occur between frequencies of
    harmonics of individual sounds, for certain types of sounds. And at least one
    type of sound having this property occurs naturally: the human voice.

    This suggests an explanation as to why differences between the pitch values
    of different sounds are significant when they are equal to the differences
    between frequencies of harmonic components within the same sound: our
    auditory perception system uses the harmonic intervals between harmonic
    components of the same sound to calibrate its perception of intervals between
    the fundamental frequencies of different sounds.

    (Quoted from “What is Music? Solving a Scientific Mystery” Chapter 12: Calibration)
    An additional point to note is that any theory of musical harmony must account
    for our ability to perceive groups of notes as chords,
    whether or not the notes in a group are played simultaneously.

  12. I have experimented a little in this area and I can attest that departing from the equal temperament compromise can yield some rather expressive results. But rather than my feeble amateur attempts I will point you to two people who I think really have this down:
    Jimmy Hotz (http://www.jimmyhotz.com/) is a Master of global musical scales and modalities, and has his knowledge embodied into some really neat hardware (the Hotz Box) and software (the Hotz Translator). Check out his “Inventions” link. Then hop over to his store and buy the Translator. (disclosure: Jimmy is an old acquaintance/friend of mine, I have known him since he built the first Box in the late 80’s/early 90’s, but I get no benefits from recommending his works).
    Charles Lucy (http://www.lucytune.com/) has done extensive and exceptional research into micro-tuning and psycho-acoustical progressions. He was sparked by old work by John Harrison (of Longitude clock fame) that had languished unread until relatively recently. Not quite the same realm as Jimmy, and in fact Jimmy uses a different theory for his tunings. Again, however, Charles has examples, software, and modern sequencer tuning configurations to go with his teachings. He lives in London UK now, but I had the great experience of spending a day with him working on one of my songs at a friend’s house in 1992 or so. He is much more explicit in dealing with harmonics and beat frequencies and their effects.
    As an aside, tunings have been a more informal arena of exploration for a long time. There is quite a history in Sufi tradition of using special tunings for special effects. Gurdjieff talks about it in his autobiography, specifically the part where he was crossing the Gobi Desert. Looking past the mystical overtones there is some pretty fertile ground there for inspiring future research.

  13. I have experimented a little in this area and I can attest that departing from the equal temperament compromise can yield some rather expressive results. But rather than my feeble amateur attempts I will point you to two people who I think really have this down:
    Jimmy Hotz (http://www.jimmyhotz.com/) is a Master of global musical scales and modalities, and has his knowledge embodied into some really neat hardware (the Hotz Box) and software (the Hotz Translator). Check out his “Inventions” link. Then hop over to his store and buy the Translator. (disclosure: Jimmy is an old acquaintance/friend of mine, I have known him since he built the first Box in the late 80’s/early 90’s, but I get no benefits from recommending his works).
    Charles Lucy (http://www.lucytune.com/) has done extensive and exceptional research into micro-tuning and psycho-acoustical progressions. He was sparked by old work by John Harrison (of Longitude clock fame) that had languished unread until relatively recently. Not quite the same realm as Jimmy, and in fact Jimmy uses a different theory for his tunings. Again, however, Charles has examples, software, and modern sequencer tuning configurations to go with his teachings. He lives in London UK now, but I had the great experience of spending a day with him working on one of my songs at a friend’s house in 1992 or so. He is much more explicit in dealing with harmonics and beat frequencies and their effects.
    As an aside, tunings have been a more informal arena of exploration for a long time. There is quite a history in Sufi tradition of using special tunings for special effects. Gurdjieff talks about it in his autobiography, specifically the part where he was crossing the Gobi Desert. Looking past the mystical overtones there is some pretty fertile ground there for inspiring future research.

  14. One more thing: equal temperament was invented for the spinnette and harpsichord, which were not capable of “bending” notes, although work on fret placement for lutes predated this work by a little bit (Galileo’s dad, late 1500’s). Interestingly, Charles Lucy has a micro-tonal guitar with about 5 frets closely spaced around each traditional fret position on the fingerboard, so he can play the appropriate progressions without having to rely on precision bending the notes. The Violin family of course has never had any frets so has always been a psycho-acoustical micro-tuned intuitive exercise.
    Google “origin of equal temperament scale” for many articles on this.

  15. Although I have no formal education in this field, I am a musician. What seems to be missing in this post is the importance of “movement” from one set of tone combination to another. If you take the band “Korn” for example, very close intervals that would sound horrible if isolated by themselves are signature ingredients in their sound. Which seems to suggest that movement from these otherwise horrid intervals to resolution of such a passage changes our perception of these tones. One cannot isolate a few notes and say that these ones are preferred unless taken in context with the notes that surround the others and perhaps even implied but not specifically played.

  16. Although I have no formal education in this field, I am a musician. What seems to be missing in this post is the importance of “movement” from one set of tone combination to another. If you take the band “Korn” for example, very close intervals that would sound horrible if isolated by themselves are signature ingredients in their sound. Which seems to suggest that movement from these otherwise horrid intervals to resolution of such a passage changes our perception of these tones. One cannot isolate a few notes and say that these ones are preferred unless taken in context with the notes that surround the others and perhaps even implied but not specifically played.

  17. echo: agreed. I did go there elliptically with “progressions”, but you’re right, music is dynamic and static chord structures, or scale structures, tell only a small part of the story. Traditional Western minor scale begins to show the difference, in that the ascending and descending progressions are not mirror images (see at http://en.wikipedia.org/wiki/Minor_scale), but when you get into deeper microtonal waters there are even more effective asymmetries like that, that have musical interest only because of the motion.

  18. This is all very well, but again some simple misunderstandings not mentioned. The Dorian-Locrian “scales” mentioned are not patterns of tones and semitones that can be transposed to start on C as is the major/minor mode giving C major/minor. The Dorian mode begins and ends on D-d alone, the Phrygian E-e, the Lydian F-f, Mixolydian G-g, Aeolian A-a, and Locrian got itself lost B-b (and full of tritones)and Ionian, C-c. Within these there are some seeds of major and minor modes/scales yet to develop in the 17th century. Ionian is virtually C major. Mixolydian is almost G. Lydian F, The authentic modes Dorian-Locrian, also have a transposed version (plagal or “hypo”dorian etc) running from dominant to dominant and are used when that is the range of the performer. (eg alto) So there is/was a sense of the pitch at which a mode operated as well.

  19. This is all very well, but again some simple misunderstandings not mentioned. The Dorian-Locrian “scales” mentioned are not patterns of tones and semitones that can be transposed to start on C as is the major/minor mode giving C major/minor. The Dorian mode begins and ends on D-d alone, the Phrygian E-e, the Lydian F-f, Mixolydian G-g, Aeolian A-a, and Locrian got itself lost B-b (and full of tritones)and Ionian, C-c. Within these there are some seeds of major and minor modes/scales yet to develop in the 17th century. Ionian is virtually C major. Mixolydian is almost G. Lydian F, The authentic modes Dorian-Locrian, also have a transposed version (plagal or “hypo”dorian etc) running from dominant to dominant and are used when that is the range of the performer. (eg alto) So there is/was a sense of the pitch at which a mode operated as well.

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