The Bohlen-Pierce scale

November 11, 2006 12:46 PM

The Bohlen-Pierce scale is a musical scale which has thirteen notes spread evenly across one and a half octaves, so that the highest note is three times the frequency of the lowest. Compare with the western twelve-tone scale, which has twelve notes spread evenly across one octave, where the highest note is twice the frequency of the lowest. Both are tempered scales, and both have close approximations to 'just intonations', meaning you could play the scales by plucking a string clamped at certain ratios like 1/2, 1/4, 5/3, etc. One of the independant co-inventors of the scale, John Pierce, was also a famous electrical engineer best known for inventing the communications satellite. You can listen to Pachelbel's Canon(midi link) rewritten in this scale.
posted by PercussivePaul (45 comments total)

I first heard of the scale through a story told by a well-known computer scientist who had been a personal friend of John Pierce. Pierce had been quite excited at his discovery and had said, only somewhat in jest, that if, despite his immense contributions to electrical engineering, he was remembered only for inventing this scale, then that would be okay with him.
posted by PercussivePaul at 12:46 PM on November 11, 2006

Well, then. I'm off to begin working on my Concerto in J flat.
posted by Baby_Balrog at 12:54 PM on November 11, 2006

Everyone knows Arthur C. Clarke invented the communications satellite without even machining anything!

At any rate, Pachelbel's Canon sounds horrible and I'm never, ever, never, writing a piece of music in this. It might be tempered, but it is ill-tempered and makes me so.
posted by Captaintripps at 1:03 PM on November 11, 2006

Wasn't that MIDI in Secret of Mana?
posted by Arcaz Ino at 1:10 PM on November 11, 2006

Arcaz, I think it's been in every Japanese RPG since the mid-80s. And that stage on Super Mario 64 where you were in the ghost infested merry-go-round.

And I, for one, welcome our creepy ghost overlords am not complaining.
posted by cerulgalactus at 1:14 PM on November 11, 2006

Turns a popular wedding processional into a horror movie sound track. What is the point?
posted by Cranberry at 1:20 PM on November 11, 2006

wow, this link explains a lot.

I've made music in my mind since I was a child that sounds a lot like that midi.

I always used to get so frustrated when I would try to play my music on our piano and the notes refused to match up. The music would sound so poignant in my mind but pedestrian and bland when I tried to force it into the notes available on the piano.

It doesn't sound like a horror movie to me at all, it sounds like a poignant but soothing & familiar lullaby.
posted by lastobelus at 1:28 PM on November 11, 2006

t doesn't sound like a horror movie to me at all, it sounds like a poignant but soothing & familiar lullaby

Oankali parents, I take it?
posted by Creosote at 1:36 PM on November 11, 2006

It doesn't sound like a horror movie to me at all, it sounds like a poignant but soothing & familiar lullaby.

Perhaps you are a sociopath who should seek help.
posted by Kwantsar at 1:36 PM on November 11, 2006

The Canon reminds me of music composed in some of Wendy Carlos' special scales. And especially this snippet from the Tron video game.

ENTER THE MCP CONE BEFORE TIME RUNS OUT
posted by ikkyu2 at 1:38 PM on November 11, 2006

OK, no hotlinks.

http://www.vgmusic.com/music/other/miscellaneous/arcade/Tron_Arcade_Success.mid
posted by ikkyu2 at 1:39 PM on November 11, 2006

There are lots of other examples linked on the site. For example,
one
two
three
four


From a review of work by Chalres Carpenter, also linked on the site (clips two and three above):

The resulting tonality shatters everything the well-tempered Western musical ear has spent a lifetime acclimating itself to. At first, it's extremely disconcerting—the music doesn't sound "in tune," but doesn't sound "out of tune" either, as there exist complex overtones and harmonies, consonances and dissonances as in any music, whether Western, microtonal Indian, or microtonal Muddy Waters. After all, the scale is based on mathematical relationships, and the notes do relate to one another in specific ways—it's not just random noise. Yet the Bohlen/Pierce tonality is literally alien, sounding nothing if not like music from another planet. After a while, you're ear stops focusing on the strangeness of the tonality, becoming drawn into the totality of the music, able to hear with a fresh perspective as a result of being liberated from the expectations of Western harmony, with its emphasis on "proper" chord progressions and "correct" harmonic resolution. The effect is, for me, liberating and exhilarating. For others, I'm afraid it will be too upsetting to listen to, perhaps almost physically so.

What is interesting for me to contemplate is why this music sounds so bizarre and why the 12-tone scale sounds so normal. They are both based on very similar mathematical structurs and there is no obvious reason why we should prefer one over the other. This suggests (to me) that our musical preferences are strongly shaped by our own culture, much more so than we may suspect.
posted by PercussivePaul at 2:11 PM on November 11, 2006 [1 favorite]

The Canon sounds awful, like a middle-school band of undead. But wouldn't it be remarkable if it sounded even remotely listenable? I think you'd get a similar result by "rewriting", however they did this, the Canon or anything else in a minor key rather than a major. It would sound awkward and wrong... just like this. There has to be something out there actually written in and for this scale? Can it possibly be inherently bad-sounding?
posted by StrangerInAStrainedLand at 2:21 PM on November 11, 2006

The Canon sounds awful, like a middle-school band of undead.

But probably flexible, too. You could speed it up and use it for a soundtrack to a video featuring evil clowns.
posted by weston at 2:27 PM on November 11, 2006

Years ago there was a bit on "All Things Considered" on NPR about some guy who had just released an album of music composed in non-standard tonal scales (13 tones, 11 tones, 17 tones, etc.). As I recall these were non-standard subdivisions of the standard octave and not an extesion beyond like this seems to be. Anyone remember that?
posted by hwestiii at 2:31 PM on November 11, 2006

*Riots*
posted by dirigibleman at 2:40 PM on November 11, 2006 [2 favorites]

I definitely like the awkward, dissonant Canon better than the original.
posted by synaesthetichaze at 2:48 PM on November 11, 2006

I'd like to hear it on chamber instruments.
posted by found missing at 2:53 PM on November 11, 2006

I love how goofy most recent microtonal music sounds. There's something about the combination of unfamiliar intervals and corny synths that guarantees this music's inaccessability.

Thanks for the post...links two and three particularly.

(Partch 4 Lyfe)
posted by Monstrous Moonshine at 2:54 PM on November 11, 2006

The Ill-Tempered Clavier
posted by horsemuth at 2:54 PM on November 11, 2006

Horsemuth, I thought the same thing after reading Captaintripps's comment above... honestly, I like the creepy, unfamiliar dissonances and harmonies in this scale, but the MIDI makes it sound super cheeseball. I wonder if it's even possible to play this sort of thing on a violin (for example). Would you have to build a completely different instrument, or just play "between" the notes on a 12-note scale?
posted by synaesthetichaze at 3:13 PM on November 11, 2006

Moonshine: Yes, and there's enough of a history of bands and composers deliberately using the odd weird note or scale for wackiness purposes that to Western ears, most of this music will sound like Mr Bungle, or Danny Elfman/Oingo Boingo.

Not necessarily a bad thing, of course.
posted by Jon Mitchell at 3:21 PM on November 11, 2006

The Pachelbel's Canon midi, with the altered harmony and flutey/xylophoney instruments, sounds an awful lot like some kind of gamelan. Like, bad gamelan.
posted by rxrfrx at 3:30 PM on November 11, 2006

I wonder if it's even possible to play this sort of thing on a violin (for example).

Violins (and other fretless string instruments) aren't physically limited to 12 tone equal temperment...so yeah, for sure. Actually playing and intonating the pitches might be a little rough.

Other instruments require variants.
posted by Monstrous Moonshine at 3:34 PM on November 11, 2006

synaesthetichaze - I completely agree. I find it appealing, and with the right instrument, an album of music played on this scale, ala Switched on Bach, or The Well Tempered Synthesizer might be very pleasant (for the few people that this seems to appeal to)...
posted by horsemuth at 4:17 PM on November 11, 2006

That's the last bottle of scotch. Boy, Delbert's gonna be mad!"
"Hi, Mike. My name's Delbert. I'm a lawyer."
posted by Smart Dalek at 4:37 PM on November 11, 2006

Creosote--I get it!

I would pay good money to hear Europe's The Final Countdown converted to this.
posted by sourwookie at 4:44 PM on November 11, 2006

Of course Pachelbel's Canon doesn't work when it is mapped to the Bohlen-Pierce scale. A good mapping assumes there is some deep homomorphism (e.g. there are 2^nd order natural transformation) involved between the two scales and I don't think that is the case here. The cannon has

a simple chord progression, I-V-vi-iii-IV-I-IV-V

Bohlen-Pierce has an entirely different harmonic structure and if there is an analog progression it well may be that it contains more (or less) chords in the progression.

Instead of a Pachelbel's mapping, somebody should try a Pachelbel's translation. If I translate a phrase from English to Russian I do not expect that each word in English maps to a word in Russian.
posted by MonkeySaltedNuts at 5:43 PM on November 11, 2006 [2 favorites]

I don't know much about this stuff, but that Pachebel made my ears wish they had never been born.
posted by Kwine at 6:00 PM on November 11, 2006

The canon sounds like Slava Tuskerman (Liquid Sky) decided to score a movie about alien clowns.
posted by adipocere at 6:07 PM on November 11, 2006

it makes my cat meow; i'll call it the catatonic scale

(i like it too)
posted by sporobolus at 6:48 PM on November 11, 2006

I would pay good money to hear Europe's The Final Countdown converted to this.

sourwookie FTW.
posted by Devils Rancher at 7:02 PM on November 11, 2006

At first, it's extremely disconcerting—the music doesn't sound "in tune," but doesn't sound "out of tune" either, as there exist complex overtones and harmonies, consonances and dissonances

Sounds like the first ten minutes of any sitting of gamelan.
posted by dreamsign at 7:12 PM on November 11, 2006

Pachelbel's Canon really does sound remarkably like gamelan. Anybody know what kind of scale gamelan instruments are tuned to?
posted by Quietgal at 7:15 PM on November 11, 2006

http://en.wikipedia.org/wiki/Gamelan#Tuning
Seems there are many possible tunings.
posted by PercussivePaul at 7:19 PM on November 11, 2006

Speaking of Gamelans, I wouldn't mind hearing the "Star Blazers" theme song played in the Bohlen-Pierce scale.
posted by emelenjr at 8:36 PM on November 11, 2006

The Canon's not that bad after the beginning, but I would never be able to identify it for what it was originally.
posted by smackfu at 10:27 PM on November 11, 2006

The last third is the best part, which ain't saying much.

hwestiii,

Yes, I remember the story about the composer writing and recording music in a completely non-traditional scale. It was fascinating to hear it, and opened my mind to the possibility of music played in scales other than our regular twelve note one. It did not, however, make me want to play music in those alternate scales...or listen to it, particularly.
posted by wsg at 11:08 PM on November 11, 2006

@found missing
I'd like to hear it on chamber instruments.

Yes. Or some more suitable synth timbres. But just plugging MIDI into an unchanging sound for 4 minutes always sucks.

What was that band that did that amazing thing by reworking Aphex Twin with acoustic instruments? Oh yea, Acoustica - "Alarm Will Sound"

This CD is a major sleeper.
posted by Twang at 12:00 AM on November 12, 2006

Alternative tuning: The wanky jazz of art music
posted by tylermoody at 9:09 AM on November 12, 2006

I wonder if it's even possible to play this sort of thing on a violin (for example). Would you have to build a completely different instrument, or just play "between" the notes on a 12-note scale?
Take it from a violinist - it's all too easy to play between the notes. Especially in precarious situations like jumping up from first to say, sixth, position.

I can't seem to open the Pachelbel file now, and I'm sure it'll kill my ears anyway. (So sensitive that singers just slightly off and noise from leaf blowers/ jet skis make me want to curl up and scream.)

But as pointed out, what's the point of trying to play a piece of music written for "our" scale here. And I don't think Mr. Pierce should count on lasting fame from even if someone else composes original stuff.

Because its creation is filling a geeky need of his, not an urgent need in the musical world as was the case with the 12-tone well-tempered scale.

Still, an interesting topic!
posted by NorthernLite at 9:53 AM on November 12, 2006

I think you'd get a similar result by "rewriting", however they did this, the Canon or anything else in a minor key rather than a major. It would sound awkward and wrong... just like this.

I don't think that would be analogous at all. It would be easy to rewrite a major-key piece as minor and still have it sound good/normal.

What is interesting for me to contemplate is why this music sounds so bizarre and why the 12-tone scale sounds so normal. They are both based on very similar mathematical structurs and there is no obvious reason why we should prefer one over the other. This suggests (to me) that our musical preferences are strongly shaped by our own culture, much more so than we may suspect.

Of course it's cultural. Not every culture uses the western tempered scale. What else would it be, biological?
posted by ludwig_van at 11:31 AM on November 12, 2006

Yeah, Here Comes The Sun is a good example of a song sounding just fine in major & minor keys... although, the original shifts between major and minor from time to time, it's mostly in Dmaj. Putting it in Dmin just makes it sound melancholy, but not like crap.
posted by synaesthetichaze at 12:24 PM on November 12, 2006

I don't think that would be analogous at all. It would be easy to rewrite a major-key piece as minor and still have it sound good/normal.

Too-simple analogies are things that I always regret in the morning. What I was trying to get at is that any song composed in a certain scale is constructed from the inherent harmonies and tonalities in whatever scale this is; particularly I would say, western classical music. So if you take such a song, say the Canon, and try to make it happy in another tonal environment, outlandish or not, Results May Vary.
posted by StrangerInAStrainedLand at 5:27 PM on November 12, 2006

I emailed Charles Carpenter and got the following reply:

Hi xxxxx,

Nice to hear from you. Regarding Pachelbel and Bohlen-Pierce, I do not see any reason to try to re-write the piece in BP tuning. It was not written for Bohlen-Pierce tuning. I certainly would not take any of the pieces I have written for BP tuning and re-write them in standard ET tuning. It would serve no purpose other than perhaps a game.

While all tunings follow certain laws, each is unique in itself. My advice would be to explore BP tuning and understand how it works and what makes it unique.

Best,

Charles Carpenter

posted by MonkeySaltedNuts at 7:51 AM on November 15, 2006