Math Becomes Music: What Pi Sounds Like
good.is
good.is
I always find it interesting when people say
"music is just like math!"
The scale is frustrating in music. Musicians think about it with the starting number being one, , whereas in maths we think of the starting number as zero.
When you're talking about different arrangements of a triad (example, major chor C-E-G) you can have three positions - root position (C-E-G), first inversion (E-G-C) and second inversion (G-C-E).
Anyone with a math/cs background would wish to express these as 0-2-4, 0-2-5 and 0-3-5 respectively. It would be easier to think about music and maths concurrently theory were it so. But the guys who built the rules of music didn't think like that, so instead it's 1-3-5, 1-3-6, 1-4-6. As a result, it's harder to reuse knowledge.
Timings are the same. First beat in a bar is 1, but it would be better if it were zero. As a result you have to get practiced at doing maths thinking offset by one. It's like having a C for-loop constantly on your back.
Could be a fun geek book geeks - to answer the question, if we redesigned the rules of music based on what we know now, what would we do differently? Interval expression would be top of the list.
Worth considering, I'd be tempted to express the scale as an expression of twelve (including half-tones) rather than what they do at the moment, an expression of 8. Because it gives you better fractions, and avoids conditioning.
I think the western tradition did do an awesome job of the important stuff. For example - the number of notes in the scale. Why twelve notes instead of 15 or 32? The reason is because you get a nice toolbox of frequencies (more than were available in strict pentatonic system, or the cool pentatonic-with-bending), without it getting too complicated. The basics of harmony theory are based around fractions of a halves and (fractional) thirds, which are easy to play with mentally, but give lots of scope for messing around.
I'd be interested from hearing from any Indians or other traditions what they think about the respective compromises. I notice in India that mainstream music has embraced the western scale.
Something like Jazz would be harder in other traditions becaues the internal maths would be harder. But there's still room for hacks like blues.
On youtube there's a great series of music videos by Howard Goodall on music theory. Coventry Carol is one of many Christmas songs that give us a link to the past and times before modern harmony. Say goodby to your Sunday :)
Another thing I've been thinking - there's room for a lot of development in music now that we can have direct manipulation of the waveform. This is a new power - something that has literally only been available for a few decades. Imagine if computer programming had started with high-level languages, and we had only recently discovered assembly language.
Pi in octal would be 3.1103755236215...
3.184809493b918664573a6211bb151551a05729290a7809a492742140a60a5
Where 0-B matches C, C#, D, D#, ..., A B.
I don't, however, agree that this is what Pi sounds like. The composer could easily have applied any one of an incalculable number of different rules, and come up with something which sounded completely different..
It is definitely a canon, meaning the same phrase played at different starting points. A round is a simple form of a canon. Think of the melody to Frere Jacques.
From a perspective of form, this song expands on the basic concept of a round by playing with double time, half time, quarter time, etc.
It has a lot of elements of serialist music, in which a musical pattern is subjected to a number of operations, although this song doesn't venture in to the more strict forms of twelve-tone composition. It is more along the lines of minimalist composers like Steve Reich and Phillip Glass, who took some of serialism's academic approaches to composition and made them hypnotic and rhythmic. In a sense, making fruit-of-the-earth pop music out of some sort of cerebral concept.
Overall the musical production is of pretty damn good quality. The performances sound good and the recordings were well made. The variation of instruments is impressive and the introduction of various pop styles keeps the concept novel.
One of my main gripes with "math music" is that it can be downright unenjoyable on an aesthetic level.
This song does a very good job of taking something inherently non-musical and making it pleasing to the ears, all while strictly adhering to a set of rules laid out before composition began.
What would really be interesting would be to express pi in base 12 and map the pitches of the chromatic scale to it. It might sound chaotic, but then again it's not pi's job to keep us entertained.
The video (by Keith Schofield) is also awesome.
On a related note, a tech metal band called "After the Burial" wrote a breakdown according to pi. The song is actually called "Pi (The Mercury God of Infinity)"... and for those of you who are unfamiliar with the term "breakdown" (in metal these days)... it's typically just chugging a certain pattern on a low note (sometimes a few more) with everyone in sync.
Here's After the Burial performing Pi live: http://www.youtube.com/watch?v=i_Msy-YUs4Y (The Pi pattern starts at 1:10 but I like the intro hehe...)
Forging a Future Self is such an amazing album all around. I listened to Fingers Like Daggers obsessively back a few years ago and always loved the deep complexity of their music. Not a fan of the rerelease of Rareform though, the sort of quieting/dulling of the vocals in Ometh (best song in that album IMO) killed it.