On tempo

[Hexchild]

I find it interesting that eg. 180BPM* and 90BPM are essentially the same because the 90BPM beat will fit nicely with the twice as fast 180BPM one. By the same principle that makes overtones fit together, superimposing two rhythms where one is twice the tempo of the other will add some richness to the end result, but not really conflict in the tempo domain. I tend to use this a lot in my music, often toning down the faster of the two so that it only subtly brings a feeling of speed to the composite rhythm.

This can also work with factors other than 2, for example I've experimented with superimposing 4/4 rhythms and 3/4 ones, essentially creating a composite rhythm based on what I guess most closely becomes a 12/8 signature (in fact the "quarter notes" in the combined rhythms are of different length, so it's hard to define). So with signatures other than 4/4 the set of applicable factors can be different, but the principle remains. Still, the half/double tempo relationship tends to be the most prominent.

I tend to adopt a circular view of musical tempo rather than a scalar one. That is, I view eg. 75BPM and 150BPM as different versions of the same tempo rather than two compatible tempoes. Just like a C note is still a C even if set in a different octave.



On another note (npi), but still related to tempo, here's a quote from this thread (http://forums.intpcentral.com/showthread.php?p=210858#post210858):


I don't know...perhaps it is my mood when I listened to it, but this one doesn't really jive with me, timing-wise. My system either wants to go faster or slower than the tempo on this one. Always wondered about that, actually. Whether part of the reason why a song really grabs a person is if the tempo of it "clicks" with their particular heart rhythm or something.

TPol, I hope you don't mind that I "stole" this comment for the purpose of starting a creative theory discussion about the subject you mention. Now that you mention it I find it interesting. I've noticed the same kind of thing, but haven't really given it much thought. But in fact this is why I made the remix of that particular song faster than the original; it felt "too slow" for me.

I've noticed how with a few exceptions, anything between 100BPM and 120BPM tends to sound "too slow" or "too fast" for me (and likewise between 50BPM and 60BPM, and between 200BPM and 240BPM). So it would seem that there is a certain area of the aforementioned "tempo circle" that feels somewhat repulsive for some odd reason, but that the placement of this area depends on the individual. I've also noticed that this area has moved around for me during my lifetime. I used to make a lot of 4/4 signature songs with a tempo around 120BPM, but nowadays they often tend to be too slow for my taste.


Somehow I don't think it has much to do with your heart rhythm, though. :)

It does not seem unlikely to me that, just like you tend to like the genres you're used to listening to, tempo preference has a lot to do with the tempo of whatever music you're used to listening to.



Thoughts, anyone?



*Beats Per Minute

[SCARYdoor]

interesting take on it. I believe the band Dream Theater use these multiple rhythms quite a bit. I forget what they call it, but often they'll have different instruments using different time signatures or tempos. Meanwhile, the drummer has to drum out both these rhythms at the same time. I read that he would for example, be playing the rhythm, emphasizes the first beat of 4/4 (or whatever is it), then for the second beat, the emphasized beat would gradually moved further away from this, until it eventually comes full circle and lands on the same as the 4/4 again. And obviously the different instruments would be counting along with their respective time signatures.

I've often thought the same thing about 120bm and 60bpm etc, being exactly the same. I never thought about elborating on that further though. You would be able to write the exact same thing in both, however one might be better suited for how fast or slow the thing is. Or maybe you could have 90bpm over 60bpm. And other variations which just go to make it more complicated and interesting.

In my music class this year we had to listen to stuff, and identify what time signature it is. I would often identify 6/8 as 3/4 etc. But apparently this was wrong, because of the slightly different feel of each. That they have definite emphasized beats in this.

Anyway, this has been a rambling reply. I have to try some of these ideas. I had to write my first song a while ago, for school, it was very bad... I need to redeem myself.

[kuranes]

I've heard of composers who based their compositions on the Fibonacci series.

[SCARYdoor]

I've heard of composers who based their compositions on the Fibonacci series.

Oh yeah, I read that mozart used this once. I forget in which song, but he made the major change occur at the exact point in the song, so that the two sections were "golden proportions" to each other. One was 1.417 (whatever the number is) times longer longer than the previous/later section.

I've once tried writing songs in a purely mathematical pattern way, but they always end up sounding terrible. I think there is some creative, and imperfection elements that need to exist in any good song.

[The Mathemagician!]

I've once tried writing songs in a purely mathematical pattern way, but they always end up sounding terrible. I think there is some creative, and imperfection elements that need to exist in any good song.

Composing music using mathematics? Check this out:

http://us.metamath.org/mpegif/mmmusic.html

It all ends up sounding pretty similar, but I'm a pretty big loser and I find this stuff to be fascinating.

[stuck]

Composing music using mathematics? Check this out:

http://us.metamath.org/mpegif/mmmusic.html

O_o



It all ends up sounding pretty similar, but I'm a pretty big loser and I find this stuff to be fascinating.

It's pretty great.

I've messed around with many of what I call 'double time signatures'. The simplest one would be 6/4, which I think of as (3x2)/4. I've also tried to work in triple time signatures, like 30 (2x3x5), 60 (3x4x5), and 42 (2x3x7).

Double time signatures are crazy because you can make anything you play sound different by switching between the two dominant pulses. *thinks of how to illustrate this*

ok. so, in 12/4, if you had a clave pattern, it'd be:

x-x-x--x-x-x

and then it repeats. you could play it against two main pulses (as shown by the red elements)

1.
x-x-x--x-x-x

2.
x-x-x--x-x-x

and they sound like you're playing the clave different when you've only changed the background. that's an example that I learned from malian djembe drumming. i got obsessed with this effect and extended it to higher number time signatures.

so those are the doubles. the triples are even crazier, because you end up with three different backgrounds which each have their own double time signature. 60 is my favorite. it's divisible into 3x20, 4x15, and 5x12. I've been trying to absorb it intuitively for the past decade or so, so that i can eventually make simple music around it.

yes i know that tool has a song in 60. messhugah uses some doubles, too.

[asperger]

There is an important distinction to be made between time signature and meter that hasn't been clarified. A single TS may be realized as more than one meter. Most obviously 5/4 which may decompose as either 3/4 + 2/4 or 2/4 + 3/4. 8/8 might be realized as 2/8 + 6/8 or 2/8 + 3/8 + 3/8 etc. These distinctions are either recognized implicitly by note lengths and distribution when all note lengths are > 1/8 or by how the beams parse when shorter notes are present. I.e. the formal rules of beam parsing reflect meter not TS

[asperger]

Another interesting thing about tempos is that as one increases the tempo for a given simple note pattern there reaches a point where the "ear" falls back to interpreting the tempo at half its notated value, there seems to be an attractor to beat rates that are in range of the human pulse.

[Rincon]

There is an important distinction to be made between time signature and meter that hasn't been clarified. A single TS may be realized as more than one meter. Most obviously 5/4 which may decompose as either 3/4 + 2/4 or 2/4 + 3/4. 8/8 might be realized as 2/8 + 6/8 or 2/8 + 3/8 + 3/8 etc. These distinctions are either recognized implicitly by note lengths and distribution when all note lengths are > 1/8 or by how the beams parse when shorter notes are present. I.e. the formal rules of beam parsing reflect meter not TS

I think how the meter of a given piece is interpreted depends on the phrasing, which can be uniform throughout the piece or vary locally within it. For example, you could write a phrase that is "atomic 5/4", in that it wouldn't naturally decompose into 3/4 + 2/4 (or 2/4 + 3/4) without losing some essential feel or quality of the phrase. It makes more sense (at least to me) to decompose into sub-meters when the component phrases themselves fit naturally into the sub-meters.

[asperger]

I think how the meter of a given piece is interpreted depends on the phrasing, which can be uniform throughout the piece or vary locally within it. For example, you could write a phrase that is "atomic 5/4", in that it wouldn't naturally decompose into 3/4 + 2/4 (or 2/4 + 3/4) without losing some essential feel or quality of the phrase. It makes more sense (at least to me) to decompose into sub-meters when the component phrases themselves fit naturally into the sub-meters.


Yes, meters encode accent groupings. Component phrases and phrase components are accent groupings. Meters provide a framework that defines the lowest level of temporal expectations within the domain of the meter. The rhythmic vitality of component phrases and phrase components derives from the way their accents conform to and violate(surprise) the temporal expectations established by the meter. But of course continued regular violations establish a new meter so there is a very plastic relation between the two.

Edit:

Beaming reflects accent group expectation while phrasing reflects the actual accent grouping of the music. Both are essential and interdependant.

[asperger]

I've heard of composers who based their compositions on the Fibonacci series.
I would wager that if temporal divisions based on the Fibonacci series are made in the vicinity of the human pulse the music feels entirely arrhythmic. This reduces a TS to simply a method of keeping track of where one is in the music rather than revealing something about the fine grain structure of the music. Just an observation.

[Resonance]

weird time signatures are silly just use 4/4 or 3/4

[Hexchild]

weird time signatures are silly just use 4/4 or 3/4

My faith in humanity diminished ever so slightly when they did this (http://www.youtube.com/watch?v=CnKzVo_V58Q).

[gps]

I've heard of composers who based their compositions on the Fibonacci series.


http://www.youtube.com/watch?v=wS7CZIJVxFY

[asperger]

I would wager that if temporal divisions based on the Fibonacci series are made in the vicinity of the human pulse the music feels entirely arrhythmic. This reduces a TS to simply a method of keeping track of where one is in the music rather than revealing something about the fine grain structure of the music. Just an observation.

Hey You were wrong!

[asperger]

Hey You were wrong!

Yea but I'd still like to see the score.

[asperger]

As shown below, taken literally a transformation of the Fibonacci numbers into note lengths yields an arrhythmic sequence.

However, any arbitrarily selected sub-sequence may be selected and repeated to produce a rhythmic pattern* as in the 6/8 sequence at the bottom of the image below.

However any repeated fixed length random sequence becomes rhythmic*. Thus I argue that to the extent the music observes the Fibonacci sequence it is arrhythmic.

*a repeated fixed length random sequence be comes rhythmic only over a fuzzy range of durations.

http://crhzfg.bay.livefilestore.com/y1pMz1K5N2RZfDkiD8v9Cn_yS5aUeWj7ZKiVITNc3PQYPkymI22DcEXCwnfh6v-xG2tQ8xVqTE2QSyBgZ3NHX3C0BwVN7puUN-Y/Fib%20fibbing.jpg?psid=1


This reduces a TS to simply a method of keeping track of where one is in the music rather than revealing something about the fine grain structure of the music. Just an observation.

This, however is a mind fart in the context of any non literal transformation of the Fibonacci numbers to note lengths .