Fibonnaci in music...

There have been some really good threads on ATS lately in general and there have been 2 or 3 relevant to music, maths and our relationship with it, so I'm going to stick my hand in too as I've not seen (or been able to find) this covered on ATS...

As it happened I stumbled across something on 4chan (of all places) about the band TOOL TOOL and their musical relationship with mathematics, now being a musician myself I find this sort of stuff fascinating and would be very interested to see if any of my fellows with more mathematical leanings had any thoughts on this and how it might bear relevance to anything...

Anyway, here's the youtube link, it's a cool song and I've personally got a thing for "non-standard" time signatures and how they feel when played or listened to, certainly from a performance point of view playing in these time signatures is a "weird" experience for me, it's like a meditative thing.



I like this a lot lyrically too and the lyrics also fit into the Fibonacci sequence - I've not included them here because the youtube is pretty comprehensive in its explanations.

From good old wikipedia...

Signatures that do not fit into the usual duple or triple categories are known as complex, asymmetric, or irregular, although these are broad terms, and usually a more specific description is appropriate. Most often these can be recognised by the upper number being 5, 7, or a larger prime number. The earliest examples of irregular signatures are found in instrumental music by Giovanni Valentini (1582–1649), written in 5/4, 9/8, etc.[citation needed] Although these more complex meters were common in non-Western music, they were rarely used in formal written Western music until the late 19th century . The waltz-like second movement of Tchaikovsky's Pathétique Symphony is an example of 5/4. Examples from the 20th century include Holst's "Mars, the Bringer of War," (5/4) from the orchestral suite The Planets, and the ending of Stravinsky's Firebird (7/4). Examples from the Western popular music tradition include the Allman Brothers Band's "Whipping Post" (11/4), Nick Drake's "River Man" (5/4), Soundgarden's "Outshined" (7/4), Alice In Chains' "Them Bones" (7/8 in the verse and 4/4 in the chorus), Radiohead's "15 Step" (5/4), "2+2=5" (7/8 then 4/4) and "Paranoid Android" (includes 7/8),[3] Metallica's "Blackened" (7/4 pre-verse, 6/4 verse and 4/4 chorus), "Smile" by The Fall (10/4), Sufjan Stevens' "A Good Man is Hard to Find" (5/4), and Incubus' "Make Yourself" (main verse riff is a bar of 7/8 followed by a bar of 4/4). Progressive rock music made large use of unusual time as a defining characteristic; examples include "Money" (mostly 7/4, with the guitar solo in 4/4), from Pink Floyd, and "Metropolis Pt. 1: The Miracle and the Sleeper" by Dream Theater. Beginning of instrumental section in 13/8, broken down as 6/8 + 7/8, and later as 4/4 + 5/8. A 9/8 meter is used in the song "Jambi" by Tool. Unlike a traditional 9/8 signature, which is divided into three triplets, the main riff of "Jambi" is broken into a quadruplet and a quintuplet. The jazz composition "Take Five," written in 5/4 time (or more correctly 3+2/4), was one of a number of irregular-meter experiments of The Dave Brubeck Quartet, which also produced compositions in 11/4 ("Eleven Four"), 7/4 ("Unsquare Dance"), and 9/8 ("Blue Rondo à la Turk"), expressed as (2+2+2+3)/8, this last being a good example of a work in a signature which, despite appearing to be merely compound triple, is actually more complex. It should be pointed out that such time signatures are only considered unusual from a Western point of view. In contrast, for example, Bulgarian dances use such meters extensively, including forms with 5, 7, 9, 11, 13, 15, 22, 25 and other numbers of beats per measure. These rhythms are notated as additive rhythms based on simple units, usually 2, 3 and 4 beats, though the notation fails to describe the metric "time bending" taking place; or as compound meters, for example the Bulgarian Sedi Donka, consisting of 25 beats divided 7+7+11, where 7 is subdivided 3+2+2 and 11 is subdivided 2+2+3+2+2 or 4+3+4. See Variants below.

I really would have liked to sum up the Fibonacci sequence a little better so please excuse my poor mathematical knowledge or language here - it's been at least 16 years since I did math at school.

Basically the Fibonacci sequence is sequence of numbers that crops up in nature and is based on the (relatively) simple process of taking a starting number - say 1 and then adding the previous number to it, so 1 + 0 = 1, 1 + 1 = 2, 2 + 1 = 3, 3 + 2 = 5, 5 + 3 etc... when plotted on paper you get this...



It makes more sense to look at the image than cope with my poor math/language.

Here's a couple of other nice examples...




Wiki Fibonnaci Page

An example of the spiral ratio in nature...



Here's a couple of threads I've found really interesting lately that might bear relevance.

Adventures in Prime Number Land:
Adventures in prime number land:

Mozart Effect:
Mozart Effect:

If anyone would like to chip-in and help with my shakey math knowledge, that would be great.



Replaced 'code' tags with 'ex' tags for external content

[edit on 23/9/09 by masqua]

i remember a couple years ago finding out about the fibonacci in that Tool song and thought it was awesome. The way the song starts is a great way to set up how the song peaks and ends with the music 'spiralling' away... its funny though how the final riff of the song ends right on the note that your ear tells you it should, bringing a sense of completion to the riff and the song, but in doing so breaking the infinite spiral.

Music is of course just math and shapes but expressed in sounds, but when a band goes out of their way to include and use bizarre time signatures it can add a secondary message to the music itself. Meshuggah ia an example of how every instrument diverging in a different time signature can still work, and often times sound evil as f##k. My friend had a camel spider, and if you've ever met one in person you will know it seems like evil incarnate, and Meshuggah sounds like the soundtrack to its brain.

That same friend, who is a member here though dont know if he posts any more, is really into math in music and has been working on morse-code beats worked into discordant time signatures.. pretty interesting.

Wish your wikipedia excerpt wasnt so hard to read, haha

reply to post by jokei

You know, artforms are subjected to a personal and mostly intuitive appraisals. I would prefer a situation where a song hits #1 on the chart, and since the business part of music production always prompts other artists to figure out why certain songs are so popular, the song gets under musicological scrutiny and guess what . . . there are catchy changes in the the beat based on Fibonacci sequence. But the composer doesn't have the slightest idea that it is so!

I mention this example, coz the flow of that song you put out seems to be mercilessly restricted by the math; it doesn't feel natural and invokes the image of a kid who wants to play but it's time for bed. I think it is just a musical curio, but you never know what the future holds.

It just ocurred to me: the Fib sequence starts this way: 1, 2, 3, 5, 8 . . .
So you can use "Fibonacci" pentatonic diatonic scale C, D, E, G, C; or start with the F note, coz the name Fibonacci starts that way as well: F, G, A, C, F. Or you can use a chromatic version F, F#, G, A, C to avoid the octave and play genuine pentatonic. Sounds weird, though.

reply to post by kidney thief


Yeah, sorry about the wiki link, not sure what I did wrong there...

I was thinking about morse code in music the other day actually, I wonder if it's been done "commercially".

I totally get what you mean about the cyclical nature of that particular song, I've a somewhat limited frame of reference for music along those lines, but the stuff they play always resolves itself really well and doesn't sound/feel unnatural as some pieces in non-standard time signatures can.

There's an odd osrt of pull to the music, I find it virtually impossible to have on in the background, it constantly draws my attention to it and I think that actually it has a lot to do with the construction of the songs, I know that the drummer especially has a lot of influences from occult sources...
anyone know anything about this - www.dannycarey.org...
?

His drums are set up in accordance with the Universal Hexagram and the rules of Sacred Geometry...

The unicursal hexagram is used to express a high level of self-confidence and belief that one can achieve the highest of goals and become a divine figure.[citation needed] Aleister Crowley's adaptation of the unicursal hexagram placed a five petaled rose, (symbolizing the divine) in the center; the symbol as a whole making eleven (five petals of the rose plus six points of the hexagram), the number of divine union. It is also used in the Greek and Hindu mythologies. as a symbol of dedication to the divine rulers.[citation needed] A unicursal hexagram is also seen as a symbol of the solar system in some Pagan philosophies, with the central intersection representing the sun and the outer intersections and points representing the celestial bodies

wiki - again

A contemporary usage of the term sacred geometry describes assertions of a mathematical order to the intrinsic nature of the universe. Scientists see the same geometric and mathematical patterns as arising directly from natural principles. Some of the most prevalent traditional geometric forms ascribed to sacred geometry include the sine wave, the sphere, the vesica piscis, the 5 platonic solids, the torus (donut), the golden spiral, the tesseract (4-dimensional cube), and the merkaba (2 oppositely oriented and interpenetrating tetrahedrons).

It's worth reading the entire piece on Sacred Geometry...
Wiki Link

If anyone could enlighten me any more on any of these subjects I'd really appreciate it.

reply to post by stander


To be honest, I think it was a purposeful use of the Fibonacci sequence, the song worked for me, but that's neither here nor there really.

I like what you said about the use of scale... I couldn't find a "nice" example, but here's one with some not so great audio quality.



I quite liked the scale, I was trying to find a better example on bass, it's more "ethnic" sounding to my ears...

I like the way the Tool piece resolves itself, I find it draws me in.

Nice thread thanks for the invite!
This is very interesting stuff, I have heard that Rivers Quomo from the band Weazer uses mathematical equations to predict and produce a pop hit.
As for me I use math to create my art but I hate math! I seem to visualize things in 3-D but unfortunately I must use math to create them in the real world.

Once like 25 years ago (while musician-flavored on my writer-artist-musician Bermuda Triangle - it's cyclical, like El Niño) I did this one song that had, say, call it a "found vocal track", and I wanted to include it in the piece but I didn't just want to play it straight through, I wanted it to develop and build in a way that would be simultaneously mysterious yet give the impression it was conforming-to-some-rule...so I broke that tape up into segments by the little (what was it? tape feet?) counter on this one tape deck I was using...start it at beginning, go to 1, stop, rewind to beginning, go to 1, stop, rewind to beginning, go to 2, stop>go to 3>5>8>13 etc. and so on.
It came out really good oddly effective and disruptive...I don't know whether it has anything to do with subconscious Fibonacci appreciation or just the good effect of submitting to some arbitrary rule and thus getting my-usual-monkey-self-him-again halfway out of the driver's seat...Or both, hmm...

reply to post by nine-eyed-eel


Link? I'd be interested to hear that...

Was it a conscious thing on your part, do you use or reference Math in any of your other artisitic endeavours?

reply to post by nine-eyed-eel


id imagine what you did with the sample sounded awesome, cool idea.. would make a great experiment with other tracks/effects

Interesting thread. I hate YouTube though, it never works properly for me, so trying to count time while the video keeps sticking is just a no-no.

Personally I'm not keen on odd time signatures for their own sake, although people now use them a lot more naturally than they used to. I'm surprised no-one has mentioned Frank Zappa, whose polyrhythmic subdivisions remain unsurpassed to this day. Drummers still learn "The Black Page" as a rite of passage. Zappa also did a tune called "Five-Five-FIVE" which had a recursive construction using the number five.

And, like him or not, Sting actually uses odd time signatures in a clever and unobtrusive way. For me, that's much more interesting than arbitrary divisions of time. Zappa's use of odd time almostalways flowed from the melodies he heard, rather than a pre-arranged idea (although Five-Five-FIVE is an example of the latter.

Most of the attempts to use complex time sound strained to me. I prefer to feel something visceral: and there's so much you can do against a regular pulse that's surprising and fun.

reply to post by rich23


I agree that using anything in music for the sake of it is a bad idea, it happens a lot though. Zappa and Sting are good examples, I also think Soundgarden managed to use non-standard time signatures and make them sound natural.

On researching my OP I've become a lot more interested in the "sacred geometry" - if anyone can help out with a little more insight into that, in layman's terms I'd greatly appreciate it. I think music can be very healing and a useful learning tool that can overlap into different spheres of education/aspects of life - it just seems to be something these days taken for granted and not really payed much heed, I know in UK schools it's given a lot less emphasis on the syllabus these days.

Here's an article I found that's a little interesting:

heart.bmj.com...

I remember reading somewhere about the reason most pop songs are around 120bpm and in 4/4 time is that this excites us, as it correlates to the heart rate of someone doing moderate exercise - damned if I can find a link for that anywhere. What I'm heading to though, is that some songs seem to have this effect upon me, where you get hairs standing up on the back of your neck, I'm sure we've all got at least 1 of these, maybe something you put on before going out to get ready for a good night with.

Although it's not an example of a band I'm fond of I find the song "Everlong" by Foo Fighters does this to me - I'm picking this as I guess a lot of us will be familiar with it...

I don't really want to use a youtube video for this example as they never sound great (at best), so if you've got this on cd or VINYL - we'll come to that later - stick it on at home at a reasonable volume.

Listen at the beginning and when the first power chord comes in note the effect...


Now, (for me) here's where it gets interesting and relates to the OP - there are other pieces of music that make my brain feel different, the example in the OP is one of them. There are albums I have that are just fun, or things I appreciate think are cool - whatever... there's nothing I have that I don't think is "cool" in some way - ABBA I find makes me feel happy and upbeat (aside from "Winner takes it all" which is heart-rending)...

BUT!!! There are some albums/songs that seem to have this "other" effect where I feel more alert, focused, sharper - smarter! I'll list a few, but I'm trying to steer this away from being a music/band appreciation thread and focus on the actual "process/mechanics" of the how and why, anyway...
Mars Volta
Ornette Coleman
Sun Ra
Pink Floyd
Gong
King Crimson
Alice Coltrane
are a few examples - I think it's the complexity, timings, layers and how the instruments are interacting with the overall piece that trigger something that makes me more alert, some pieces do this more than others and a lot is relevant to my current state of mind at the time.

This may be a good time to link back to this thread...
www.abovetopsecret.com...
as my current thoughts are drifting towards pieces of music that don't "overtly" have beats - by which I mean drums or percussion, so the timing and tempo of the piece are perhaps more subtle and how this may affect the ways in which people listen to them. As that thread states there is a link between brain activity and listening patterns, I think there is - I think as well, certainly with a lot of the pieces mentioned there that with the lack of an "overt beat" the brain will pick it up anyway, but in a sense it's focusing you more on what's going on, you're attuning to the piece in your head as opposed to a physical sense.

I hope this all seems clear and any thoughts on this are much more than welcome, if anyone can add to things with relevance to Sacred Geometry I would be very keen to hear.

Originally posted by jokei
I remember reading somewhere about the reason most pop songs are around 120bpm and in 4/4 time is that this excites us, as it correlates to the heart rate of someone doing moderate exercise - damned if I can find a link for that anywhere. .

The pop music descended from folk music which was meant mostly for dancing. Folk dances were lively, as opposed to the way the aristocracy span around. But the folk dances were popular, so the aristocrats modified some of the styles to serve their needs to be told from the commoners and so you can hear some baroque dances written by J.S. Bach, like gigue, going at around 120 BPM. You never hear this rate during traditional funerals. So I think it's the psychology that favors faster going music.

There is really not much on the fusion of sacred geometry and music on the web. Originality sells, but originality is a well with a deep bottom, so many folks are looking for an alternative source of inspiration. But history tells you that very popular songs usually appeared "out of nowhere." It just happened -- pretty quickly.

Fantastic post, I have to say.

Originally posted by jokei
reply to post by rich23

 

... I also think Soundgarden managed to use non-standard time signatures and make them sound natural.

I'm afraid I don't know much of their stuff. But the standard in rock music generally has got really much higher - things have moved on, there's the whole hundredth monkey thing... so I hear a lot of bands doing things in interesting time, these days, and doing it well, for the most part. I think since the "democratisation" of music, in that it's no longer taught exclusively as an academic subject and that computer tools can let any idiot put something random together... I think all this is adding up to people starting to hear time in a different way, in fact a rather more natural way than many people other than say, Zappa, Monk or Stockhausen, who each at times phrased their music according to human speech patterns. Actually, a master of this is Hermeto Pascoal, whom I think you'd like if you don't know him already. A Brazilian Zappa. Need I say more?

On researching my OP I've become a lot more interested in the "sacred geometry"...

Google Video "David Wilcock's 2012 lecture" and there's some good stuff in there. Whether or not you go down the whole path with him (I don't) there's some stuff you'll find useful. And surprising.

...I think music can be very healing and a useful learning tool that can overlap into different spheres of education/aspects of life - it just seems to be something these days taken for granted and not really payed much heed, I know in UK schools it's given a lot less emphasis on the syllabus these days.

Funnily enough I was a peripatetic music teacher in the South of England a couple of years back. Packed it in before I started to really hate it. The boss, Bob rot his socks, was an oily backstabber who constantly sung the praises of the government policy to make sure every child could learn an instrument.

The trouble is, not every child wants to learn an instrument. Or, not infrequently, they think they want to learn, but the real motivation is to be (insert current Noel Gallagher here). When they find out they have to put time in on the instrument, it's not so cool. There were one or two kids who were really getting into it, and they were almost worth all the BS that stank up the job... but it was only one or two, out of maybe 150.

I'm not being elitist here, don't get me wrong. I'm completely self=taught, and got put off piano lessons by a terrible teacher, who got very ratty when I didn't practice his crappy exercises. The other thing is that the kids who spend any practice time they bother to do alone with just their instrument (unless they're part of the keen and/or talented crowd) don't do so well. The best kids I taught were already playing in bands. I teach guitar, so that's what's going to happen. At any rate, having to make a good noise as part of a group effort instils first responsibility and then groove.

Here's an article I found that's a little interesting...

heart.bmj.com...

Thank you so, so much for posting this. Excellent reading. Interesting passage about entrainment of breathing going in cycles of four and eight beats. It's really hard to tell about how much our response to music is determined by culture. I've heard some jolly-sounding Javanese funeral music that apparently sounds pretty sad. On this point, you might be interested in an observation of the rather wonderful human being and awesome slide guitarist Bob Brozmann... (I'm paraphrasing here)

There are really only two types of music, the music of the oppressors and the music of the oppressed, and this holds true everywhere, in the islands of Japan, in Africa... Oppressors like to march, so their music has a lot of emphasis on the one. With the oppressed peoples, it's the opposite. Think of Cuban rhumbas where the accent comes on the end of beat 4.

There's also an odd-time tradition in Central Europe, come to think of it. If you want to hear post-Parker sax over Bulgarian odd-meter "dance" music, check out Ivo Papassov and his Bulgarian Wedding Band. (I kid you not. I've seen them live at WOMAD, and watching hippy girls trying to dance to it and give up into formless swaying was a tiny guilty pleasure.)

Does this mean that the entrainment of breathing of an oppressed person, say, from the countryside of Cuba, would be differently aligned? Would it change according to whether it was Cuban music or more Western, pumping, music?

These are questions I suspect may never be answered (gets out onion).

It's also interesting that although the researchers checked for breathing entrainment, they don't seem to have done the same for heartbeat. They checked for heart rate but that's not the same thing.

I remember reading somewhere about the reason most pop songs are around 120bpm and in 4/4 time is that this excites us, as it correlates to the heart rate of someone doing moderate exercise - damned if I can find a link for that anywhere.

It wouldn't surprise me, although I'm not sure that the scientists concerned might not have mistaken correlation for causality. There's a lot of it about, I understand. Dancing to a consistent pulse is also a feature of many trance rituals.

Going back to sacred geometry in music, you might also consider the idea that each bpm will have different harmonics. In theory, harmonics go on forever, or at least as fast as the material world can vibrate, which I guess counts in atoms and plasma. So... if you vary the bpm you're also varying the harmonics, which might have all sorts of effects. Who knows?

And of course there's the whole subject of brainwave entrainment as well... but that's getting way off-topic indeed.

What I'm heading to though, is that some songs seem to have this effect upon me, where you get hairs standing up on the back of your neck...

So... what is it about the song? BPM? Doubt it. Performance level? Very likely, but not necessarily: "Autobahn" anyone? If we could bottle what you're talking about we'd be rich, I tell you, rich! And, er, we can't. Or perhaps I'm being defeatist...

There's also the fact that some songs have a real impact and then six months later, you think, "why was I so keen on that? And then a few years later it might be more "jFC, what the hell was I thinking?" Music is an ephemeral thing because it happens inside people's heads.

Couldn't watch the video, I'm afraid. It might be my computer... youtube stuff never works properly for me, though Google video does. So I miss out on a lot of stuff, really... I went round to a friend's recently and we just surfed the music on YT for a while, picking out people we know.

Music has all sorts of effects. Certain pieces, for a while, were guaranteed to make me cry, others to make me shake my booty, others to play air guitar, others to lie on the floor... but I do know what you mean by feeling alert. Good list btw. There's a track from "You" by Gong that does that for me. It's a funk tune but it moves from four to five to seven and back again, and with each time changes the key moves up by a minor third. Combine that with the most crucial ingredient of all, which is a really good rhythm section playing a very taut groove (without this all is wasted) and you have a track that, even in the background, makes you sit up a bit.

But much of this stuff - Ornette, Zappa and King Crimson in particular, are not really suited to background music, though it would be cool to hear them in Asda.

I'll have to get back to you on the Mozart effect...

as my current thoughts are drifting towards pieces of music that don't "overtly" have beats - by which I mean drums or percussion,

Just thought I'd mention a piece that kind of has both. Gyorgy Ligeti wrote an avant-garde piece for (iirc) 30 metronomes. It was kind of an early satire on the stuffiness of classical music: it was written in the fifties and Ligeti wanted everyone in full evening fig to very solemnly go on stage, set their metronomes (to specific tempi), at the conductor's signal, let them go... and then retire from the stage. The resulting sound is amazing, and the effects as each metronome starts to run down and the sound becomes thinner and fhythms come and go... very cool.

...so the timing and tempo of the piece are perhaps more subtle and how this may affect the ways in which people listen to them. As that thread states there is a link between brain activity and listening patterns, I think there is - I think as well, certainly with a lot of the pieces mentioned there that with the lack of an "overt beat" the brain will pick it up anyway, but in a sense it's focusing you more on what's going on, you're attuning to the piece in your head as opposed to a physical sense.

As a musician, I have a particular direction and that kind of music isn't it: it's not that I don't like it, it's just that my focus is elsewhere so I don't hear much of it. A friend of mine has an extraordinary music collection ranging from Tuvan throat-singing to "just intonation" music. He was telling me about a piece that's just one note all the way through, but different instruments play it so the sound changes according to the balance of whichever instruments are playing at any given time. That's pretty fearsomely minimalist.

And I can't separate my head from my body when it comes to music. Even if it's a piece by Ligeti with no audible pulse, I'll still move with the ebb and flow of it. I suspect that separating the mind and body on this is.. hmm... suspect, though this could easily be the bias of someone who's spent a l

i'm so glad someone mentioned zappa and the black page.
frank has numerous songs that are in odd metres...

reply to post by rich23


Excellent, thanks for the links... I will investigate.

The Soundgarden stuff is possibly worth you checking out if you're partial to a bit of Led Zeppelin, if you have Lastfm or Spotify, you'll be able to find it easily, try tracks like: Never The Machine Forever, Fell on Black Days and Spoonman are good examples.

To condense some of your points, I think that the democratisation has been a great thing, at the age of 14 I picked up a "not bad" 2nd hand bass for £100 - which was affordable on a paper-round. As for teaching, I also had a couple of great music teachers at secondary school, but if you try to make kids learn something they don't want, they'll just resent it, I think for the kids that wanted to learn great - but those that didn't, perhaps should be geared towards a "critical study", write about songs they like etc, something that won't require practice AND there's also the Embarrassment factor, some kids feel really awkward about playing/performing in front of others.

As to the sacred geometry, I've read up on bits on the Tool Drummers webiste dannycarey.org and whilst interesting, it's to "esoteric" for me to believe, but I do find it very interesting, I'd also link in the film Pi at this point as a reference and how I believe that the patterns in nature, whilst not necessarily harnessable, could be influence or worked with - it's hard to put into words, but some of the feelings accessible through music seem to defy rational explanation.

AND!!! Considering that this must be a fairly cheap field to research, plus the potential benefits of such an easy "healing" tool it flabbergasts me as to why there hasn't been more research into this subject, I guess though, like many other things, it isn't profitable...

Think you're hitting the nail on the head with regard to breathing entrainment, it would be interesting to look at from a cultural/geographical perspective and any correlation to heart patterns, I think we're fully aware of the effects of depression and mental state on the body and it's wellness, so this would be fascinating research.

The X-Factor in music, what gives it that Oomph (in whatever way you get it)?
If only...

P.S.

Hermeto Pascoal is excellent.

Amazing thread Jokei

Uber S&F,

I'm a huge Tool fan, but I'd never looked at that song or even that album in that way!

Opened my eyes to a whole new way of looking at it, and it makes so much sense!

Gonna go back and read these other interesting posts!

Well, thanks.

It's a really interesting subject, that I seem to be running out of good material for, certainly in the way of hard research that's been done, there just seems to be a lot of anecdotal stuff out there.

It's really worth checking out the Mozart Effect thread too...

I'm a massive Tool fan too and find a lot of their ideas fascinating, one of my mates is re-working Lateralus in ProTools to get all the over laps correct and everything...

Originally posted by jokei

As to the sacred geometry, I've read up on bits on the Tool Drummers webiste dannycarey.org and whilst interesting, it's to "esoteric" for me to believe, but I do find it very interesting, I'd also link in the film Pi at this point as a reference and how I believe that the patterns in nature, whilst not necessarily harnessable, could be influence or worked with - it's hard to put into words, but some of the feelings accessible through music seem to defy rational explanation.

Speaking of drums . . . I became curious what would happen if you incorporated the beginning of the Fibonacci series -- 1, 2, 3, 5, 8 -- into the drum beat. Like playing wholes, halves, triplets, quintuplets and eighths. So I made a sample:
crop720.tripod.com...

It kinda sounds like Jeff Porcaro's glasses falling into a food processor, though. LOL. But if you play wholes, halves and eights with the triplets and quintuplets as techno tom fills, then it shouldn't sound weird.

Originally posted by jokei

It's a really interesting subject, that I seem to be running out of good material for, certainly in the way of hard research that's been done, there just seems to be a lot of anecdotal stuff out there.

It's really worth checking out the Mozart Effect thread too...

It just hit me that the beginning of the Fibonacci series 1, 2, 3, 5, 8 corresonds with whole, half, triplet, quintuplet, eight notes, but they can be handled the "classic" way. For example, contrabass plays quintuplets in space of two halfs taking care of numbers 5 and 2. Violoncello plays the same, but adds a triplet in the space of whole taking care of numbers 1 and 3. Then the second violin adds two halfs and the first violin joins the club with triplets -- all in smooth 120 BPM:

[atsimg]http://files.abovetopsecret.com/images/member/7956962ba7c8.jpg[/atsimg]
[atsimg]http://files.abovetopsecret.com/images/member/3f64001b956f.jpg[/atsimg]
[atsimg]http://files.abovetopsecret.com/images/member/0635263fdb06.jpg[/atsimg]
crop720.tripod.com...

I used one eight and one whole to bring it to an abrupt end.
You can experiment with Fibonacci series in music when you score a movie scene where the music is subordinate to the visual effect. So, here's that dude on his way to have the root canal done . . .