Intervals

February 12, 2012 5:25 PM

Star Wars. 2001: A Space Odyssey. Star Trek: The Next Generation. Battlestar Galactica (1978), Superman: The Movie. What do all of these iconic scifi music themes have in common? Bear McCeary discusses the physics behind them.

McCreary: Previously on MeFi.

posted by zarq (36 comments total)

Also previously
posted by Threeway Handshake at 5:36 PM on February 12, 2012

His explanation for why the 5th and 4th sound good seem really bogus to me. This idea that they represent "strength" or "grandeur" seems kind of ridiculous. And while there is a physical relationship between those notes, there is obviously something going on psychologically in terms of the way our mind and ear interprets those notes as well, that give them a certain kind of emotional response to a specific interval.
posted by delmoi at 5:41 PM on February 12, 2012

This is awesome. I'd never realized that the Simpsons theme song was built on a tritone.
posted by DoctorFedora at 5:47 PM on February 12, 2012

delmoi: "This idea that they represent "strength" or "grandeur" seems kind of ridiculous"

The thing is that these intervals (along with the octave) are the least susceptible to phase cancellation. So you literally get a "stronger" audio signal because it isn't drifting in and out of phase as much as other intervals do.

There is a good point here though, because there are other intervals that are somewhat resistant to going out of phase which sound alien because they aren't possible to play on a piano, and compared to 12tet are "out of tune".
posted by idiopath at 5:48 PM on February 12, 2012 [4 favorites]

I should mention also that on a piano the fifth is actually out of tune
posted by idiopath at 5:48 PM on February 12, 2012 [1 favorite]

Bear McCreary had an incredible blog about composing Battlestar's music that was released alongside the episodes, it was an unusual chance to see into the creative process. He's uniquely open and communicative for a composer and he deserves to be commended for that.
posted by mek at 5:49 PM on February 12, 2012

I should mention also that on a piano the fifth is actually out of tune
Now now, hold your temper..
posted by coriolisdave at 5:53 PM on February 12, 2012 [13 favorites]

It isn't that bogus to say that the fifth has "strength." A fifth chord is literally called a power chord.

It is also the interval of a brass instrument that doesn't use valves, like a bugle, or "all trumpt-like things before they invented valves."
posted by Threeway Handshake at 5:56 PM on February 12, 2012 [1 favorite]

The fifth is indeed strong. Many composers think of it as "blocky". In terms of chord inversions, root in the bass is often thought of as "neuter", the third in the bass is often considered "feminine", and the fifth in the bottom is considered to have a masculine sonority.

And pretty much all these themes utilize some sort of fanfare--used by bugles and hunting horns. Like Threeway said.
posted by sourwookie at 6:16 PM on February 12, 2012 [1 favorite]

This is a nice introduction to Western European music theory but I think it overstates its case a bit. The perfect fifth interval is integral not just to pop and sci-fi classical music, but 99.999% of all Western music including hip hop, country, blues, jazz, heavy metal, etc. The harmonic relationship built from that interval (C major chord to G major), the tonic and dominant relationship, defines Western European music (with the exception of atonal music like Schoenberg, non-determinant music of Cage et al., some pre-Baroque stuff).

Saying that the perfect fifth sounds "stronger" is an odd way to put it for me. What it is is more consonant than other intervals. Or less dissonant than other intervals. What this means is that when you play a note and then go up a perfect fifth they sound more alike than any other interval (with the exception of the octave). They sound more "pure". Notes a minor second apart (like C and C#) "clash" when played together and that clashing or dissonance is often described as being an unpleasant sound.

So sure, if I were going to compose a rousing bit like the theme to Star Wars I would avoid using much dissonance which would mean gravitating toward perfect fifths, fourths, and octaves. That's not because I would assign these feelings to intervals but because I understand music theory and the ideas behind it and how people generally react to it all. But then if I were going to compose any piece of music that I want most people to think sounds "good" (regardless of the genre) I'm still going to gravitate to that interval and the harmonic relationship surrounding it. Just focusing on the perfect fifth might be a little too easy-going for most songs but that relationship is still the backbone of 99.999% of all Western European music.

I'm guess what I'm trying to get at is that A) there's no magic at work here -- music students learn all this in first semester Music Theory and B) it becomes so much a part of your normal thinking process that you do not ever have to stop and think "hmmm, what interval sounds majestic? What interval sounds scary?"

Still, like I said, it's a nice introduction even if a bit too breathless for what is being discussed.
posted by bfootdav at 6:20 PM on February 12, 2012 [3 favorites]

It goes like this, the 4th, the 5th...
posted by tspae at 6:57 PM on February 12, 2012 [3 favorites]

tspae, you beat me to that by about 7 minutes...
posted by HuronBob at 7:04 PM on February 12, 2012

It was OK but I was hoping for something that would more clearly distinguish Jerry Goldsmith music from the riff for "Sweet Child O' Mine" and every blues song.
posted by steinsaltz at 7:15 PM on February 12, 2012

A lot of good points in the article and comments above - here a few quick thoughts:

-regarding the hunting theme, there is a strong connection between 4ths/5ths and older music - the most commonly referenced pre-tonal western music is gregorian chant, which frequently harmonized in fourths and fifths (think that enigma song). There is also a strong tendency for us to hear music that predominantly features 4ths/5ths as 'exotic' (the intro to turning japanese is parallel fourths).

-Music with a lot of thirds sounds very harmonically 'safe' to us - think lullabies - while music that avoids the use of tertian harmony (basically, stacking thirds to build chords) will sound foreign, and the use of dissonant tones will make it sound more exotic. The battlestar galactic theme, for example, uses more dissonant intervals as well as instruments with complex harmonic series (which again sound foreign to western ears which are used to instruments with very simple overtone series) - so even though it tries to avoid the 4ths/5ths cliche it still evokes the sense of distance and otherworldliness that we associate with sci-fi.

-I always think there is a strong connection between sci-fi and fantasy, in lots of ways, and the 4th/5th connection with ancient and exotic music hints at that connection.

- The reason power chords are so popular is that because of the simple overtone series you can play them with heavy distortion (which adds a lot of harmonic overtones to the original tones) and they don't sound dissonant. I think the power comes more from the distortion aspect than the quality of the interval, but that's just my opinion.

- I fully agree with the mention of the 'open harmonic series' evoking vast spaces, whether in space or in nature

-Funny that they don't mention the original star trek, which starts with a series of ascending fourths. Actually, in jazz there was a movement towards quartal harmony around the same time - basically, harmony based on fourths - like the melodies and chords in the mccoy tyner tune here. Which is a really awesome tune, by the way - and the piano solo is killing.

-tspae, don't forget that the next lines are "the minor fall, and the major lift" which reveal that cohen was working well within western tonality, and the fourth and fifth refer to chord movements rather than harmonic material. Not that it's not a great reference. ;-)

-
posted by ianhattwick at 7:21 PM on February 12, 2012

The article tries to dismiss some common criticisms, particularly that a lot of these themes are similar because of plagiarism, particularly by John Williams. One composer I know criticized Williams as having plagiarized everything from Wagner.

I wouldn't put it past him. I met John Williams and he is a monumental asshole. I met a lot of assholes in Hollywood, but he is the only one who ever screamed at me, "don't you know WHO I AM?"
posted by charlie don't surf at 7:32 PM on February 12, 2012 [1 favorite]

One composer I know criticized Williams as having plagiarized everything from Wagner.

Ridiculous. Some of it is obviously stolen from Gustav Holst.
posted by straight at 9:22 PM on February 12, 2012 [1 favorite]

One composer I know criticized Williams as having plagiarized everything from Wagner.

Ridiculous. Some of it is obviously stolen from Gustav Holst.

I don't hear any Wagner in Williams either. The abundant use of leitmotif is something they're both known for but as straight states above, musically Williams seems to borrow from Holst.
posted by bfootdav at 9:41 PM on February 12, 2012

My sense here is that McCreary (one of my favourite suppliers of faintly Celtic space-music) has some engaging and nuanced things to say, which mostly don't make it though the filter of this post's author, who doesn't seem to get too much further than "fifths! There are fifths! Listen to the fifths!"

So, as usual, I blame the media.
posted by bicyclefish at 9:58 PM on February 12, 2012 [1 favorite]

I met a lot of assholes in Hollywood, but he is the only one who ever screamed at me, "don't you know WHO I AM?"

Let me guess, you were trying to explain to him that the kinescope would be vastly enhanced by the addition of musical accompaniment, perhaps one employing orchestral instrumentation to lend a certain gravitas to the proceedings.
posted by anigbrowl at 10:29 PM on February 12, 2012 [1 favorite]

While we're in this 'why does it sound good' vein, I have lately become a fan of a small imprint called Wooden Books, and their publication Elements of Music is by far the best introduction to music theory I have come across. I keep a copy of their Quadrivium next to the keyboard and find it a very reliable source of inspiration.
posted by anigbrowl at 10:48 PM on February 12, 2012

If you take "physics" to mean "music theory" this actually makes sense.
posted by madcaptenor at 11:58 PM on February 12, 2012

What do all of these iconic scifi music themes have in common? Bear McCeary discusses the physics behind them.

I missed "music themes" and was expecting the article to be comparing and contrasting the physics of each series' space battles. And was therefore kind of bummed out at the actual article.

For the record someone should write that article.

Also I prefer the "naval battle in space with broadsides" BSG reboot physics with small fighters displaying lots of inertia style of space battle.
posted by nathancaswell at 4:42 AM on February 13, 2012

Perhaps I misremembered the accusation of Williams' plagiarism as being from Holst. You are probably right. It has been a while since I heard that criticism. But anyway..

Let me guess, you were trying to explain to him..

More mundane than that, but a good story, so I'll tell it. I used to work at a computer store near all the movie studios. One day probably around 1984, a guy came in and looked around, then stopped in front of our top end Compaq 386 machine. I asked if I could help him, he abruptly said, "Yes, I'd like you to give me this computer for free." Um.. what do you say to a request like that? I was a bit taken aback, but our store was well known for handling celebrities with care, no matter how outrageous their demands were. So I deflected his outrageous demand, "You have a good eye, if I could have any computer in this store for free, this would be the one." Apparently he didn't like that answer, he started roaring "don't you know WHO I AM?" and explained that he was the most important composer in Hollywood, Star Wars, blah blah blah. How the hell would I know who he was on sight? It's not like anyone ever sees his face on screen. He was quite insistent that I should give him a free computer, and in particular, this loaded machine which cost over $4000, since he was so influential and whatever computer he owned would become the standard in his field. This was utterly ridiculous, since PCs were pretty much all alike, and there wasn't even any music composition software for the PC yet. But he persisted. So I told him, I can't just give him a computer for free, someone has to pay for it. But Compaq had a seed program and would provide computers to influential people. I could make a phone call and I could probably arrange it for him, but it would take a couple of days to deliver a computer. He became angry and insisted I should give him THIS computer NOW. I asked if he could wait for a moment, and I'd call my Compaq rep and see how fast I could arrange a seed computer, perhaps she could arrange it this afternoon. I picked up a phone to call her, and he yelled that he didn't have time to wait, and stormed out of the store. OK, good luck finding your free computer, Mr. John Asshole Williams.
posted by charlie don't surf at 4:57 AM on February 13, 2012 [3 favorites]

If I was John Williams I would have asked you for a freebie like this:

[Please sing to the tune of the Indiana Jones March]

This computer - that I see,
This computer - give to me, me, me!
Don't you know just who I am?
I'm John Williams!
John Williams!
John Williams!
John Williams, I am!

[/Indiana Jones March]
posted by the quidnunc kid at 6:13 AM on February 13, 2012 [1 favorite]

With regards to valved instruments without valves, the progression of notes fallows the harmonic series (which by the way is the same for strings and winds), which is roughly: octave, 5th, 4th, maj 3rd, min 3rd, 2nd.

Trumpets don't usually get the first octave interval, which has more to do with the mouthpiece I think than anything else as I can get the first octave on a flugelhorn.

I say "roughly" because these intervals are close, but a little bit off and get more off the higher you get. Way up in the nosebleed range of trumpet you don't really even need valves anymore except they help in articulation somewhat.

There is a cool shepherd's flute called a tlinca. It is essentially a meter long tube with a diameter of about 1.25 cm. It was made from willow, IIRC, but you can make one out of PVC. You blow across one end and plug the far end to drop the pitch an octave. You think, "great - all I can get out of this is the harmonic series (bugle calls) in two octaves," but then you find out that where the upper series overlap, you find a diatonic scale with horrible intonation, yet still a diatonic scale. And hell, you're just watching sheep and they don't care.

All this has to do with how things want to vibrate in their natural modes.
posted by plinth at 9:41 AM on February 13, 2012

To understand mathematically which intervals are the most basic/powerful, one simply looks at the corresponding frequency ratios. The corresponding physical explanation relies on the fact that string and wind instruments have essentially the one-dimensional vibration modes of a line segment, and hence contain only frequencies (overtones) which are integer multiples of the root. Furthermore the miracle of 12-tone scales is that the 5th and 4th intervals come out so close to integer semitones, with maj 3rd and min 3rd less so. The tritone, with an irrational algebraic ratio is maximally dissonant. However, one should note that bell-like instruments do note have overtones in the harmonic series (integer multiples), and lend themselves to alternate scales and harmonies, as in Indonesian gamelan music.

Interval    Ratio    Semitones = 12 log_2 (ratio)
octave     2/1      12
5th          3/2      7.01955
tritone      √2      6
4th          4/3      4.98045
maj 3rd     5/4      3.86314
min 3rd     6/5      3.15641
posted by metaplectic at 10:08 AM on February 13, 2012 [2 favorites]

or what plinth said, with numbers
posted by metaplectic at 10:10 AM on February 13, 2012

metaplectic:
with all due respect, that stuff about "irrational ratios" is nonsense held over from the cult of Pythagorus. Dissonance is analogous to red/green scintillation in the eye, and is caused by combinations of frequencies within a critical band. The critical bands have different widths in different ranges of the audible spectrum (this is why chords are less dissonant in the bass register). If our ears were more finely tuned, previously dissonant tones would become consonant, and combinations we now hear as unisons would become dissonant.

A pair of harmonically rich notes playing a diminished fifth or a minor second contain frequencies within a critical band, so are dissonant (a cool trick: without the overtone series present, the minor fifth is consonant - with a good hifi audio setup (bad amps and speakers add harmonics) you can hear this yourself with a pair of sine waves).
posted by idiopath at 11:11 PM on February 13, 2012

s/minor fifth/diminished fifth/ in the above, no need to muddy things up with microtonality.
posted by idiopath at 11:13 PM on February 13, 2012

Critical bands are an important part of the theory of auditory perception, and for understanding consonance/dissonance, but they only help to explain why small integer ratios and just intonation sound so good to us. It is because two notes (with harmonic overtones) that have root frequencies related by a small integer ratio will have many overtones overlapping exactly, and the rest well separated.

The irrational ratio nonsense is also well justified (again, for harmonic instruments only). No matter how precise your ear is (tiny critical bands), the tritone will never sound consonant, since √2 has poor rational approximations. (Quadtratic irrationals have eventually periodic continuted fractions, while algebraic irrationals are the subject of Roth's theorem.) In reality, where our ears have finite precision, it is enough just to use a ratio with poor approximations like 1.41 = 1 + 1/(2 + 1/(2 + 1/(3 + 1/(1 + 1/(1 + 1/2))))).

And as I pointed out before, all bets are off for non-harmonic notes, like bell tones. This is discussed extensively in Tuning Timbre Spectrum Scale.
posted by metaplectic at 10:23 AM on February 14, 2012 [1 favorite]

As I said before, the rational vs. irrational issue is nonsense. It has nothing to do with it.

For every pair of rational numbers, no matter how close, there are an infinite number of irrational numbers between the two. Most of the numbers, and most of the ratios, in nature are irrational.

If you have an irrational ratio that is close enough to 1.0, 1.5, or 2.0, it will be perfectly consonant to a human ear. A rational ratio that approximates the twelfth root of two will be dissonant despite being rational.

At one time the irrationality or rationality of a scaling factor may have been a helpful rule of thumb for approximations, but it is less scientific than epicycles - at least epicycles had predictive power.

The critical band is not just useful for explaining just intonation, it is the only mechanism by which the human ear experiences dissonance. Period.
posted by idiopath at 11:29 AM on February 14, 2012

Almost forgot the citation for my above comment: the physiological basis of dissonance.
posted by idiopath at 11:48 AM on February 14, 2012

Also, I have been making claims about perceptual experiments. Here is the csound source code to demonstrate some of those claims:

ton.orc:

sr	=	44100
ksmps	=	1024
nchnls	=	2

iun	ftgen	1, 0, 32768, 10, 1
iun	ftgen	2, 0, 32768, 10, 1, 1/2, 1/3, 1/4, 1/5

	instr	1
aamp	linen	ampdbfs(p5), .1, p3, p3/3
asig	oscil3	aamp, cpspch(p4), p6
	outs	asig, asig
	endin

	instr	2
aamp	linen	ampdbfs(p5), .1, p3, p3/3
asig	oscil3	aamp, cpspch(p4), p6
asig2	oscil3  aamp, cpspch(p4)*sqrt(1.01), p6
	outs	asig*ampdb(-5)+asig2, asig2*ampdb(-5)-asig
	endin

pitches are converted using cpspch, which takes input in octave.degree format, (.0 is c, .02 is d, .03 e, .05 f, .07 g, .09 a, .11 b) and converts it to a frequency in hz.

The first instrument makes a simple tone, either sine or bandlimited sawtooth.

The second instrument plays the frequency asked for, along with a second frequency, higher than the original by a ratio approximating the square root of 1.01 (computers cannot do true irrational numbers, but this should be close enough given csound's 64 bit float precision).

d_fifth.sco

i 1 0  10  7   -10 1
i 1 0  10  7.06 -10 1
i 1 11 10  7   -10 2
i 1 11 10  7.06 -10 2

this demonstrates the diminished fifth without and then with overtones present

unison.sco

i 2 0  10  7      -10 2

this demonstrates an approximation of a very small irrational interval.
posted by idiopath at 2:29 PM on February 14, 2012

One day probably around 1984, a guy came in and looked around, then stopped in front of our top end Compaq 386 machine. I asked if I could help him, he abruptly said, "Yes, I'd like you to give me this computer for free."

I can see why you'd be ticked off after that, actually! Could it have been an imposter, do you think? I ask only because tech companies seem to work pretty hard to get their products into the hands of leaders in the creative field...'have this on us, oh and if you wouldn't mind us showing it in your studio in this print ad we're running next quarter...'
posted by anigbrowl at 4:05 PM on February 14, 2012

idiopath, I agree with most of what you said, but you really seem to be missing my point about small integer ratios. I certainly do not believe and did not say "irrational = dissonant", which is obviously wrong for the reasons you gave. But it is absolutely true that small integer ratio intervals = consonant (with harmonic timbres), and likewise for intervals that are close enough to such ratios as to be indistinguishable to human hearing. Furthermore, as you perturb the interval enough to be detectable, it turns dissonant very quickly.

What I was trying to get at about algebraic irrationals, like √2, is that such numbers have the worst Dirichlet approximations, according to Roth's Theoerem. In general, the irrational roots of simple polynomials are the best candidates for not being close to any small integer ratio, and hence to be floating in a sea of dissonance. Of course you can still find particular algebraic irrationals as close as you want to any given number, but they probably come from complicated polynomials.

Your csound experiments look interesting. I won't have time to play with it for at least a week, but here is what I want to try:

1) On a pure sine tone at 440Hz, determine the width of the critical band by superimposing a second tone and shifting its frequency until it becomes detectable, and then continue shifting to find local maximum of dissonance. I would expect detection within .05 semitones.

2) Repeat the previous using sawtooths at 440Hz. Detection might occur sooner, say within .02 semitones, because the audible overtones should have smaller critical bands. (If I tune my guitar using open strings, it is noticeably off from 12tET, and this is a .02 semitone difference.) It's not clear to me what should happen with local max dissonance; it might get spread out by the overtones.

3) Similarly perturb an octave dyad with the sawtooth, and a 5th dyad, and compare the ranges.

4) Finally, compare dyads for the first four convergents of √2, which are 1, 3/2, 7/5, 17/12. I am really interested to hear how consonant or dissonant these sound -- I would guess 7/5 is only moderately consonant, and 17/12 barely at all.
posted by metaplectic at 11:47 PM on February 14, 2012 [1 favorite]

Here is where I agree with you:
if the audience only wants to hear consonance and will riot at dissonance, in the real world with imperfect physical instruments that frequently go out of tune, instruments which even in tune have harmonic series that go out of tune with their own fundamental, and musicians that are prone to hitting the wrong note, tell musicians to make intervals that are ratios of small whole numbers because their attempts to follow that instruction will get the best average case outcome and the least-worst disastrous outcome.

What you still don't seem to get is that when you leave the realm of prescriptive craft, and into the realm of scientific description, irrationality of an interval is not a predictor of dissonance because the human ear does not have an irrationality sensor in it. Do you know what the following have in common?

choirs, voice doubling, string sections, vibrato, tremolo, leslie speakers, tremelo pedals, phasor pedals, flanger pedals, chorus pedals, reverb pedals (plus more that I am forgetting, I am sure)

They all help to create or simulate the acoustic phenomenon of shifting phase interference caused by irrational intervals. Because phase interference sounds pretty!

Below a certain threshold of frequency, human listeners tend to find phase beating quite pretty.
Go a bit higher, and they find it extremely ugly.
Go a bit higher, than that, and it is beautiful.
Go a bit higher again, and they can't perceive it any more (but it is still there).

I understand and respect that a musician or composer has a specialized knowledge of how to make sound that listeners can find pleasure in.

SImilarly, architects and carpenters have specialized knowledge about using triangular and rectangular solids to build durable domiciles.

But those best practices are too often mistaken by their practitioners for transcendental truths. We shouldn't take a carpenter at his word when he pretends to be an expert of geometry while reciting obvious falsehoods. Similarly we shouldn't simply trust a musician that makes demonstrably false claims about the nature of sound and hearing.
posted by idiopath at 10:54 AM on February 15, 2012 [1 favorite]