I always find it interesting when people say "music is just like math!" and then proceed simply to assign numbers to a scale like that. The relationship between C-D-E-F on a scale is nowhere close to 1-2-3-4. The stuff always ends up sounding like this, which is OK but it still bugs me.
When 1-2-3-4 is used in music to show degree, that is an ordinal representation, not a cardinal representation. That's sort of the key difference here.
I always find it interesting when people say
"music is just like math!"
It could be a lot more like maths, but for some unfortunate historical decisions.
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.
One of the first programs I ever wrote did basically this--took an expansion of pi and made midi files out of it. It took a scale parameter, so you could give it a minor or major key (or any of the modes). I found it interesting to listen to because my ear naturally looked for patterns, and occasionally found one only to have it ruined by the next bar.
Honestly, if this is considered as good-sounding music, then I don't think any combination of tones from the C major scale could be considered bad-sounding.
There is a fair bit of composition going on, albeit all based on a single melodic phrase, so it is far from just being any old random combinations of tones from the C major scale.
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.
I appreciate it for its good production value, and as an example of constrained composition. I question even the "mathiness" of it, since it's just based on a truncated decimalization of pi. If you're just looking for a quick and easy constraint to express yourself under, I suppose this is as good a constraint as any, but my main point is that, as you say, there is no aesthetic value to the piece, and definitely no true insight on mathematics or the nature of the constant known as pi.
I thought it sounded quite beautiful. Gave me chills.
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.
Hell yeah, never thought I'd see another tech death metal fan on HN, especially not a fellow ATB fan.
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.
Another option would be base 5 for a pentatonic scale [1], or using the decimal representation to cover 2 octaves. Might sound a bit more natural than base 12.
Pi IS pretty much random notes (digits). There's nothing about pi that says "express it in base ten". Probably in binary it would get pretty repetitive tho.
Great video and a beautiful composition using very simple rules. I'd have liked to have seen more about the circle of fifths and harmonic structure though, because this is where the relationship between music and mathematics starts to get really interesting.
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..
Well I liked this... but I know nothing about music. All the posts griping about "math music" -- can anyone point to something like "intro to music for math people" ?
The major scale has 7 notes: do, re, mi, fa, sol, la, and ti. The 8th note is just another do.
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.
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[ 3.1 ms ] story [ 76.0 ms ] threadhttp://en.wikipedia.org/wiki/Degree_(music)
http://en.wikipedia.org/wiki/Pythagorean_tuning
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.
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.
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.
Pi in octal would be 3.1103755236215...
3.184809493b918664573a6211bb151551a05729290a7809a492742140a60a5
Where 0-B matches C, C#, D, D#, ..., A B.
[1] http://en.wikipedia.org/wiki/Pentatonic_scale
http://tauday.com
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..
The video (by Keith Schofield) is also awesome.
http://en.wikipedia.org/wiki/Overtone_series
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.