Maths and Music...

[Aeroplay]

Hey y'all!


Seems like the time has come for me, to share something with you - something I've been thinking about for quite a while, now...



Paraphrased in general, it has something to do with mathematics.

As you all know, we can't make music - like we do - by ourselves only, we need tools.

We can only make music as good as our tools - and therefor we try to make our tools as good as possible, and thats, what I'm trying to do as well.

I love what we have, but I think, we can still bring it to a whole new level!

Ever since I belive that, I have been wondering how it could be done...


Music, however, has a lot to do with mathematics, and I think the music of the future might have even more to do with it. I think especially counsciusness for that has to increase.


When I look all over my huge setup, I find a lot of crooked numbers, I don't really like...

All the numbers, we are using are following the tenner logarithm. But when I work in Live or other sequencers as well, it seems to me that the music is accely following an other one...

I hope you get me right...

Music is proportion, ratio, you know its like

1/4 ; 1/2 ; 1 ; 2 ; 4 ; ...

Its accely nothing but mathematical sense...


Also, I find it frustrating, that my controls only have a resolution, of 128 steps...

Why 128, by the way?

Because 128 is 2 to the power of 7

2*2*2*2*2*2*2 = 128


As you can see, our computers are't following tenner logarithm as well.

I would even go to the leght, of saying:



Nature in general does't seem to follow it.



If we would use for example the eighth logarithm, which means, that we only have 7 numbers, and count to eight instead of ten and then start again like:

1 ; 2 ; 3 ; 4 ; 5 ; 6 ; 7 ; 11 ; 12 ; ...

Then, we would have 128 beeing someting like 1000, maybe?



I don't know, for sure, what that would do, but who does?



I have done some different experiments - but didn't have a break trough yet. I wonder, if I'll ever have...



I'm accely at the very beginning of these thoughts myself...





Thank you a lot for your attetion...





And now, first of all:



Did you get me?

I will love trying to explain it in a different way...



Any thoughts on this are aprechiated very much!



Are there any mathematicians out there using Live? (since I have only a little idear what I'm talkin about..)





I wonder, what ideas a mathematic genius would have, if we showed Live to him...





All the best,

Felix

[sigabort]

maybe cos its early but this one went flying over my little head

[Aeroplay]

Hey, thank you a lot for answering so fast. Well, if you'll really try to understand it, you surely will. But it might not be worth the effort... It's always like this. You decide...


best to you, friend!

[chapelier fou]

Mathematics have always fascinated mucic composers. There are a lot of examples.
In the middle age, music was considered as a science. Check out Ockeghem's "Missa prolationum" for instance.
You should also take a look at Bartok's orchestral works for the use of the avogadro suite. Some Stockhausen too. The number Pi also have applications. Prime numbers are used to do non-repetitive sequences. Also check out the sequencers based on Conway's game of life.
These are only examples. This is so crazy. But I think playing an instrument without thinking is also a good thing...

[Aeroplay]

Thank you very much!

About some of the stuff you mentioned I've never heard yet. Sounds very interesting to me, will check it out soon...

What you say is true - just slammin' the keyboard is much more fun. But keyboards needed to be invented first, so I guess you need both.

To me it seems like this: To make great music, you first have to learn as much as you can, (theorie, techniques, practise, ...) - and then you can forget all about it and just go crazy...



cheers, mate!

(best to you aswell, for sure )

[krismkelley]

You should check out Automaton by Audio Damage.

http://www.audiodamage.com/effects/prod ... ?pid=AD020

It's a fantastic VST based on the Game of Life. It let's you take beats and really screw them up in random, or structured, ways. I've had a lot of fun with it and I am by no means a musician. But I really like the stuttery drum beats it lets me produce.

[Aeroplay]

Seems to be quite a nice vst - the game-of-life-thing is interesting... Thanx! I'm not gonna spent so much money on it, though...




best

[McQ714]

rambling what? it all starts at 1 and doubles from there.. the eighth number you get to using that logic is 128. a metronome is based on 4 counts to a bar and that's how music keeps it timing.. that doesn't mean you need to keep to 4 bars... there are a lot of guys that would be able to explain this better than i can as i never took a music history or theory class.

you want a more interesting theory on mathematics and life, read up on the fibonacci sequence. then do a search in the forums on that.

[Aeroplay]

Hey.

I know about the Fibonacci Sequence. But I'm sorry, I have no clue what you are trying to explain to me...

You are right, the most important proportion in music is 1 to 2 (and not only according to the timeline) ... So it doubles each time like you said, the problem is, that our way of counting in some way does't...

10 is not 2 to the power of a whole number... But if you start counting bars for exaple, you come to bar number nine and then there is ten, which is special, because from now on you will have two digits... If that would happen at, lets say 8 or 16 bars that would change something...

Not much according to bars for sure, since it really doesn't matter to the music what numbers you give to your bars...

But like I said music is proportion all over, and we always count to 10, which just doesn't seem to fit for music...

Ever wondered why a C3 is something like 130,81 Hz and not someting straight like 100? I know there are many reasons for this but it has something to do with it...


I know this sounds kind of strange and you might just think I'm a retarded one, but I think it's worth a try...


Thank you for your interest...

[turrican]

mhh.. I don't understand neither..

the logarithm of 128 to the base 2 is 7. But thats determined by the protocol, in case of midi it does explain the resolution.

The binary representation is based on the machinecode, which is needed at the very end to be translated to..
Do you mean we have to build something which is freed from the boolean thing?

By the way - I don't believe that the music we make is solely defined by the tools we have..

[Aeroplay]

Hello turrican!

mhh.. I don't understand neither..

the logarithm of 128 to the base 2 is 7. But thats determined by the protocol, in case of midi it does explain the resolution.

The binary representation is based on the machinecode, which is needed at the very end to be translated to..
Do you mean we have to build something which is freed from the boolean thing?

No, I don't mean that... Sorry, it is really hard to explain!

Let me try it this way:


Why is ten the "special" first number, to have two digits?

Obviously, because we have ten fingers, and people used to count with them, I'd say.

But that is arbitrarily - like randomly. It's not given by nature, that our "special" number is 10. We could choose any other one and already have a second digit at 8 for example... If we would use the 8th logarithm instead of the tenner.

And that would be useful, according, to the binary system, to what sounds harmonically, and as I'd say nature in general...

It's because the proportion 1 to 2 ( or 2 to 4, if you like) is in general the by far most important one!

So it goes like:

1 , 2 , 4 , 8 , 16 , ...

Ten does NOT appear here...

And we don't use 1/10 notes, because it just makes no sense, we have 1/8 and 1/16 notes...


So WHY do we use the tenner logarithm for all our mathematical opperation, for example in Live ???

What it does is leading to croocked numbers, that don't make sense!

We are just so used the tenner logarithm, that we don't see it...





My only point according to midi is: I'd like to have a resolution of lets say 1024, instead of 128, because that would be better for sure...

By the way - I don't believe that the music we make is solely defined by the tools we have..

Not solely defined, but the tools give us the frame we can be creative in...




I aprechiate your answer a lot!

Please feel free to ask other questions, if this doesn't help you...



peace

[turrican]

Hi there Aeroplay,

I agree that the decimal system is commonly used because its easy to count
but there are a lot more representations than to the base of 10.
I think its basic concept is a axiomatic one. When is one thing equal one?
What does one mean?

The nature doesn't speak, just humans do.

To me its more social-historical question: why has the decimal-system (indo-arabic)
prevailed in a greater bandwith and other didn't?
The evidence thats the base of 10 isn't something a priori implemented in our DNS is based
on the simply existence of other systems, even if they have already disappeared.

If you take the roman latin representation you
have characters and even the number two is already expressed by II (2 times capital(i)).
and I'd say that X is not more important than V or C..

For instance the hexadecimal System the base is 16, there the 10 is a Char(A). Of course this is not a commonly used
system in means of interaction but in terms of computer science its indispensible.

In musical terms i'd say it depends on the definition of a whole bar. If you are used to 4-4 measure it's quite normal
to work with exponents of 2, there you can accomlish all needed values, 2 to the power 0f 0 eq. 1, 2 ttpo 1 eq. 2 so on.. but if you take triplets, tripple eight notes, a 4th note equals 3 eight notes or
if you take the quintole, tow quarter-notes equal 10 eights! - there you got a 10, for instance - TEN DOES APPEAR.
If you got an ten-eighths-bar, you need to filled the bar with 10/eighths - somehow- that means 5 times quarter-notes do fit as well as 10 eights.

to conclude this- I think its more what we are used to through our musical development.
Something a lot discussed between modern and traditional musicians.
Can you explain why the interval of one semi-tone is classified disharmonic? Why are micro-steps in other cultures sounding wanted and nice while in traditional western music no less than semi-steps are typical for scores?

[McQ714]

ok then in a logical sense, the only way you could accomplish what i think you are getting at is to count as follows...

1,2,3,4,5,6,7,8... 11,12,13,14,15,16,17,18... 21,22,23,etc.

But the problem with that is that when you look at a timeline, what we would've known to be the 65th bar is now the 81st bar but if you were to count the number of bars up to that point it would only be 64 bars and that's where the theory would fuck everyone up. leave well enough alone.

[Aeroplay]

Hi !



Well, seems like this is reeeeeeally fuckin' hard to explain!

I'm so sorry, guys!


Maybe it really would't change much or isn't even right the way I imagine it, I can't be sure, for sure.

Then I would just be bullshitting you poor people, which would be absolutely embarrassing to me.


- But I bet it is right and does change something!

I'm quite sure that it would make a huge difference...


I guess it's hard to imagine, since you have to think in a mathematical way you are not familiar with.

You first have to forget, what you know about numbers, and then learn it again, using some kind of octalsytem...

As I said I've really been thingking about this for quite a long time, and it wasn't easy to me either...




I will give it one last try, according to what you wrote, McQ714 since you are on the right way:

The point we know from our sequencer to be the 65th bar, which are accely only 64 whole bars counted in the way we are used to, would in my system be something similar to the number 100 in the number system we are using now...

You know, when you zoom out the timeline, there are some bar-numbers that disappear, and some that stay...

In the system I imagine the ones staying would be 10; 20; 30; 40; ... and later 100; 200; 300; 400; ...

But they would for sure no longer be what you know as 10; 100; and so on...



But really interesting it only gets, when you use that system on semitones, milliseconds, ... accely everything, where numbers occure...



By the way: I posted a link to this in a math forum, but didn't recieve any replys yet...

http://www.mymathforum.com/viewtopic.php?f=40&t=8886



I'll definetly stick to this, since now I really need to know...

Next thing I'll do will be a picture of a timeline, the way I imagine it...



@ turrican:

I can't know weather nature "speaks" or not, and so can't you. But if we ever meet (in Odonien, maybe?) I'm sure we can have a good conversation about it.





Thank you very much for your feedback again, at this point, it was really important for me to talk about it to somebody... I love the Ableton community!

[Aeroplay]

By the way, I really threw myself away on that one:

... what we would've known to be the 65th bar is now the 81st bar but if you were to count the number of bars up to that point it would only be 64 bars and that's where the theory would fuck everyone up.

Hilarious!


( Not laughin about your thoughts at all - they were very helpful - I just love that formulation, especially out of context...)



Respect!