<pre>thanks chaps, chuck, yeah, i'd been thinking with this one to use the larger numbers as is (instead of chopping them to 8 beat length), so that the original part loops every 8 beat, and part 4 for instance, is much longer... i've had some success with using prime numbers as the lengths for sequences, i got the tip from a flash book years ago, with animation it works well with several elements looping at the same time, it creates longer sequences that don't repeat the same way twice... at least not for a long time in sound terms i like using clock dividers set to prime amounts, then feeding both signals into a logic gate, with a bit of care this can make really nice rhythms (using several such units) the bitwise gates in pd don't really lend themselves to this, but more straightforward gates do... i've had a quick look at your tribalhaus generator andy, looks really good from here (didn't get much joy sound-wise from this machine, pd audio in win98 isn't all that great anyway, i'll hopefully try it on a mac at some point, should be much better)... i had been thinking about using mathematical whatsit to create wavetables that could be kind of morphed or reshaped easily, what you've done there looks quite similar to what i had in mind. i had been wondering how primitive beatboxes store their rhythms, i assumed it was all hard-wired... all the best adam </pre>
To help you stay safe and secure online, we've developed the all new Yahoo! Security Centre. http://uk.security.yahoo.com
On Tue, 27 Jun 2006 19:47:30 +0100 (BST) adam armfield adamairmailed@yahoo.com wrote:
in sound terms i like using clock dividers set to prime amounts, then feeding both signals into a logic gate, with a bit of care this can make really nice rhythms (using several such units) the bitwise gates in pd don't really lend themselves to this, but more straightforward gates do...
For polyrythmnic combinations it's all about common factors. Using primes means that there are none, so your sequence zeros at the LCM of the two two primes, for 7 and 11 it's at 77 beats. That's why we use primes for delay times in reverbs to get a sound that doesn't seem too coloured by common modes.
Check out the work of these drummers
Pantera - Vinnie Paul Gong - Pierre Mouerlen Tool - Daney Carey
Carey and Mouerlon are both known for fibonacci based syncopations. It seems there are indeed many useful rythmnic applications contained in the fib sequence, off the top of my head I haven't a clue why, one to research. This is most definitely not "house" though. :)
The easy way into this territory is using the [mod] and [%] operators with [change] and [select]. You might like to check the other drum unit (the jazz one) at http://www.obiwannabe.co.uk/toys.html and see how I used remainders and modulo to make that work.
i've had a quick look at your tribalhaus generator andy, looks really good from here (didn't get much joy sound-wise from this machine, pd audio in win98
Yes, sorry but some of more recent patches really need pd-extended to work. Not because they use strange externals just because the they use very common and important units that aren't in the very mean (imho) build of vanilla Pd right now. ;)
all best, Andy
Hallo, padawan12 hat gesagt: // padawan12 wrote:
i've had a quick look at your tribalhaus generator andy, looks really good from here (didn't get much joy sound-wise from this machine, pd audio in win98
Yes, sorry but some of more recent patches really need pd-extended to work. Not because they use strange externals just because the they use very common and important units that aren't in the very mean (imho) build of vanilla Pd right now. ;)
Attached is a version of TribalHaus, where I replaced ead~ with an abstraction called vead~.pd that is a clone of ead~ built using only core objects. This will run on any recent Pd without any externals.
Thanks to vline~ it even has much tighter timing so it better rocks the house, Anna. ;)
Ciao
Frank Barknecht _ ______footils.org_ __goto10.org__
On Wed, 28 Jun 2006, padawan12 wrote:
Carey and Mouerlon are both known for fibonacci based syncopations. It seems there are indeed many useful rythmnic applications contained in the fib sequence, off the top of my head I haven't a clue why, one to research. This is most definitely not "house" though. :)
The Fibonacci sequence has this peculiarity that any two consecutive numbers are coprime.
_ _ __ ___ _____ ________ _____________ _____________________ ... | Mathieu Bouchard - tél:+1.514.383.3801 - http://artengine.ca/matju | Freelance Digital Arts Engineer, Montréal QC Canada
-----BEGIN PGP SIGNED MESSAGE----- Hash: SHA1
Mathieu Bouchard wrote:
On Wed, 28 Jun 2006, padawan12 wrote:
Carey and Mouerlon are both known for fibonacci based syncopations. It seems there are indeed many useful rythmnic applications contained in the fib sequence, off the top of my head I haven't a clue why, one to research. This is most definitely not "house" though. :)
The Fibonacci sequence has this peculiarity that any two consecutive numbers are coprime.
and also: if you divide any fib number by its preceeding number, you get the "magic" number (the one of Pitagora's sectio aurea)
(this works better with numbers > 100)
try it yourself. here is an old post of mine: http://lists.puredata.info/pipermail/pd-list/2005-02/025822.html
Federico
It is an approximation, and gets closer and closer, and it works if you start with ANY 2 positive numbers and make a Fibonacci-esque series from them. You could start with 2 and 417, then 419, 836, 1255, etc, and gradually the ratios of consecutive members of the series start to approach the golden ratio.
The golden ratio is defined by x=1/x + 1
when you take, for instance, 13/8, that is 1 + 5/8... or 21/13 is 1 + 8/13... 34/21 is 1 + 13/21, because of the way you obtain each number. Always 1 + the reciprocal of the previous ratio. So you will never quite reach the golden ratio, but you alternately go slightly higher and slightly lower, getting gradually closer.
On 6/29/06, Federico xaero@inwind.it wrote:
-----BEGIN PGP SIGNED MESSAGE----- Hash: SHA1
Mathieu Bouchard wrote:
On Wed, 28 Jun 2006, padawan12 wrote:
Carey and Mouerlon are both known for fibonacci based syncopations. It seems there are indeed many useful rythmnic applications contained in the fib sequence, off the top of my head I haven't a clue why, one to research. This is most definitely not "house" though. :)
The Fibonacci sequence has this peculiarity that any two consecutive numbers are coprime.
and also: if you divide any fib number by its preceeding number, you get the "magic" number (the one of Pitagora's sectio aurea)
(this works better with numbers > 100)
try it yourself. here is an old post of mine: http://lists.puredata.info/pipermail/pd-list/2005-02/025822.html
Federico -----BEGIN PGP SIGNATURE----- Version: GnuPG v1.4.2.2 (GNU/Linux) Comment: Using GnuPG with Mozilla - http://enigmail.mozdev.org
iD8DBQFEpEzWxlXK3KziJfcRAvqKAJ4jcpaJMOx6XQQwuIb/92Uo/1P3egCbBcbc p/zP0nrY6rX8WDUu4ko2RXs= =NzDu -----END PGP SIGNATURE-----
PD-list@iem.at mailing list UNSUBSCRIBE and account-management -> http://lists.puredata.info/listinfo/pd-list
-----BEGIN PGP SIGNED MESSAGE----- Hash: SHA1
Chuckk Hubbard wrote:
It is an approximation, and gets closer and closer, and it works if you start with ANY 2 positive numbers and make a Fibonacci-esque series from them. You could start with 2 and 417, then 419, 836, 1255, etc, and gradually the ratios of consecutive members of the series start to approach the golden ratio.
yes, with fibonacci serie it is an approximation. but you now discovered the rule:
The golden ratio is defined by x=1/x + 1
that is:
1/1.618 = 0.618 and 1/0.618 = 1.618
you could write that formula as a 2nd grade equation:
1/x = x - 1
x*(1/x) = (x - 1)*x // multiply by x 1 = x^2 - x
then write as:
x^2 - x - 1 = 0
so, applying the formula for solving 2nd g eq:
x[1,2] = (1 ± sqrt(5))/2
you got *THE* magic ratio:
x1 = 1.618033989... x2 = -0.618033989...
(and the approximation depends on your calculator... hehe ;)
1.61803398874989484820458683436563811772030917980576286213544862270526 is enough?
when you take, for instance, 13/8, that is 1 + 5/8... or 21/13 is 1 + 8/13... 34/21 is 1 + 13/21, because of the way you obtain each number. Always 1 + the reciprocal of the previous ratio. So you will never quite reach the golden ratio, but you alternately go slightly higher and slightly lower, getting gradually closer.
On Fri, 30 Jun 2006, Chuckk Hubbard wrote:
It is an approximation, and gets closer and closer, and it works if you start with ANY 2 positive numbers and make a Fibonacci-esque series from them. You could start with 2 and 417, then 419, 836, 1255, etc, and gradually the ratios of consecutive members of the series start to approach the golden ratio.
This is because defining Newfib(1)-Newfib(0)!=1 just multiplies Fibonacci by a constant, which cancels out when taking ratios; and redefining Newfib(0) != 0 only shifts it like Newfib(n) = Fib(n+c), though c might be fractional (you normally have to use the formula i gave in the previous mail to get Fibonacci values on the positive real domain)
The golden ratio is defined by x=1/x + 1
More usually like x^2 - x - 1 = 0, which is really the same thing. Note how it looks like Fib(n+2) - Fib(n+1) - Fib(n) = 0 ! You may consider Fib(n+c) = x^c for extra fun.
when you take, for instance, 13/8, that is 1 + 5/8... or 21/13 is 1 + 8/13... 34/21 is 1 + 13/21, because of the way you obtain each number. Always 1 + the reciprocal of the previous ratio. So you will never quite reach the golden ratio, but you alternately go slightly higher and slightly lower, getting gradually closer.
BTW, Euclid's way of simplifying fractions (greatest common divisor) is slowest with consecutive Fibonacci numbers. Its average and worst running times are multiples of log((a+1/a)*n)/log(a), where a is the golden ratio.
_ _ __ ___ _____ ________ _____________ _____________________ ... | Mathieu Bouchard - tél:+1.514.383.3801 - http://artengine.ca/matju | Freelance Digital Arts Engineer, Montréal QC Canada
Interesting stuff, so it's a very useful sequence for seeking non coincidence. A fib sequence based reverb algorithm is immediately desirable.
On Fri, 30 Jun 2006 00:23:47 -0400 "Chuckk Hubbard" badmuthahubbard@gmail.com wrote:
It is an approximation, and gets closer and closer, and it works if you start with ANY 2 positive numbers and make a Fibonacci-esque series from them. You could start with 2 and 417, then 419, 836, 1255, etc, and gradually the ratios of consecutive members of the series start to approach the golden ratio.
The golden ratio is defined by x=1/x + 1
when you take, for instance, 13/8, that is 1 + 5/8... or 21/13 is 1 + 8/13... 34/21 is 1 + 13/21, because of the way you obtain each number. Always 1 + the reciprocal of the previous ratio. So you will never quite reach the golden ratio, but you alternately go slightly higher and slightly lower, getting gradually closer.
I forgot, what's the name for a curve that oscillates (asymptotically?) around a value converging on it, in the purest mathspeak?
And I was thinking about this when playing with your microtone stuff Chuck, computing arbitary arithmetic sequences (as expressions) in Pd to some depth, like is [expr] the best way to think about that iyho?
Andy
On 6/29/06, Federico xaero@inwind.it wrote:
-----BEGIN PGP SIGNED MESSAGE----- Hash: SHA1
Mathieu Bouchard wrote:
On Wed, 28 Jun 2006, padawan12 wrote:
Carey and Mouerlon are both known for fibonacci based syncopations. It seems there are indeed many useful rythmnic applications contained in the fib sequence, off the top of my head I haven't a clue why, one to research. This is most definitely not "house" though. :)
The Fibonacci sequence has this peculiarity that any two consecutive numbers are coprime.
and also: if you divide any fib number by its preceeding number, you get the "magic" number (the one of Pitagora's sectio aurea)
(this works better with numbers > 100)
try it yourself. here is an old post of mine: http://lists.puredata.info/pipermail/pd-list/2005-02/025822.html
Federico -----BEGIN PGP SIGNATURE----- Version: GnuPG v1.4.2.2 (GNU/Linux) Comment: Using GnuPG with Mozilla - http://enigmail.mozdev.org
iD8DBQFEpEzWxlXK3KziJfcRAvqKAJ4jcpaJMOx6XQQwuIb/92Uo/1P3egCbBcbc p/zP0nrY6rX8WDUu4ko2RXs= =NzDu -----END PGP SIGNATURE-----
PD-list@iem.at mailing list UNSUBSCRIBE and account-management -> http://lists.puredata.info/listinfo/pd-list
-- "Far and away the best prize that life has to offer is the chance to work hard at work worth doing." -Theodore Roosevelt
PD-list@iem.at mailing list UNSUBSCRIBE and account-management -> http://lists.puredata.info/listinfo/pd-list
On 7/3/06, padawan12 padawan12@obiwannabe.co.uk wrote:
On Fri, 30 Jun 2006 00:23:47 -0400 "Chuckk Hubbard" badmuthahubbard@gmail.com wrote:
Always 1 + the reciprocal of the previous ratio. So you will never quite reach the golden ratio, but you alternately go slightly higher and slightly lower, getting gradually closer.
I forgot, what's the name for a curve that oscillates (asymptotically?) around a value converging on it, in the purest mathspeak?
Got me. Curious if you find out.
And I was thinking about this when playing with your microtone stuff Chuck, computing arbitary arithmetic sequences (as expressions) in Pd to some depth, like is [expr] the best way to think about that iyho?
Like to modulate continuously? I think the best way to do that would be to change the base frequency and keep the ratios simple, imho, provided you don't intend to modulate back. I don't know how it affects the sound, but trying to modulate the way my patch does, with numerator/denominator stored separately, sometimes leads quickly to strange floating point errors in both that will never go away. Or if you mean to sequence higher harmonics, then yeah, expression seems like it would work well. $f1 could be base frequency, and $f2-$fn harmonics of it, outputting midi note numbers or frequency. Either of those what you are thinking?
Andy
On 6/29/06, Federico xaero@inwind.it wrote:
-----BEGIN PGP SIGNED MESSAGE----- Hash: SHA1
Mathieu Bouchard wrote:
On Wed, 28 Jun 2006, padawan12 wrote:
Carey and Mouerlon are both known for fibonacci based syncopations. It seems there are indeed many useful rythmnic applications contained in the fib sequence, off the top of my head I haven't a clue why, one to research. This is most definitely not "house" though. :)
The Fibonacci sequence has this peculiarity that any two consecutive numbers are coprime.
and also: if you divide any fib number by its preceeding number, you get the "magic" number (the one of Pitagora's sectio aurea)
(this works better with numbers > 100)
try it yourself. here is an old post of mine: http://lists.puredata.info/pipermail/pd-list/2005-02/025822.html
Federico -----BEGIN PGP SIGNATURE----- Version: GnuPG v1.4.2.2 (GNU/Linux) Comment: Using GnuPG with Mozilla - http://enigmail.mozdev.org
iD8DBQFEpEzWxlXK3KziJfcRAvqKAJ4jcpaJMOx6XQQwuIb/92Uo/1P3egCbBcbc p/zP0nrY6rX8WDUu4ko2RXs= =NzDu -----END PGP SIGNATURE-----
PD-list@iem.at mailing list UNSUBSCRIBE and account-management -> http://lists.puredata.info/listinfo/pd-list
-- "Far and away the best prize that life has to offer is the chance to work hard at work worth doing." -Theodore Roosevelt
PD-list@iem.at mailing list UNSUBSCRIBE and account-management -> http://lists.puredata.info/listinfo/pd-list
PD-list@iem.at mailing list UNSUBSCRIBE and account-management -> http://lists.puredata.info/listinfo/pd-list
On Mon, 3 Jul 2006, Chuckk Hubbard wrote:
On 7/3/06, padawan12 padawan12@obiwannabe.co.uk wrote:
I forgot, what's the name for a curve that oscillates (asymptotically?) around a value converging on it, in the purest mathspeak?
Got me. Curious if you find out.
I don't think that there's a name for such a sequence.
Even if every term is on the opposite side of the limit than the preceding one, then I don't know any word for that. The corresponding series would then have every term be of opposite sign than the previous one, which is called an alternating series, but this would be only one kind thereof, because there are alternating series that don't alternate sides of the limit.
_ _ __ ___ _____ ________ _____________ _____________________ ... | Mathieu Bouchard - tél:+1.514.383.3801 - http://artengine.ca/matju | Freelance Digital Arts Engineer, Montréal QC Canada
Mathieu Bouchard wrote:
On Mon, 3 Jul 2006, Chuckk Hubbard wrote:
On 7/3/06, padawan12 padawan12@obiwannabe.co.uk wrote:
I forgot, what's the name for a curve that oscillates (asymptotically?) around a value converging on it, in the purest mathspeak?
Got me. Curious if you find out.
I don't think that there's a name for such a sequence.
A limit cycle? http://mathworld.wolfram.com/LimitCycle.html
Martin
On Tue, 4 Jul 2006, Martin Peach wrote:
Mathieu Bouchard wrote:
On Mon, 3 Jul 2006, Chuckk Hubbard wrote:
On 7/3/06, padawan12 padawan12@obiwannabe.co.uk wrote:
I forgot, what's the name for a curve that oscillates (asymptotically?) around a value converging on it, in the purest mathspeak?
Got me. Curious if you find out.
I don't think that there's a name for such a sequence.
A limit cycle? http://mathworld.wolfram.com/LimitCycle.html
No, a LimitCycle not only doesn't (generally) have a single Limit (the concept exists for the case where an ordinary Limit is not enough), it also can apply to cases where values don't "oscillate" around the Limit points.
Padawan is talking about something that does always converge. E.g. he might be thinking about exp(t)*sin(t) or sin(t)/t, neither of which have a limit cycle bigger than 1 element, which means that they have a single limit, and then calling that a limit cycle doesn't imply anything about oscillations.
_ _ __ ___ _____ ________ _____________ _____________________ ... | Mathieu Bouchard - tél:+1.514.383.3801 - http://artengine.ca/matju | Freelance Digital Arts Engineer, Montréal QC Canada
On Thu, 29 Jun 2006, Federico wrote:
and also: if you divide any fib number by its preceeding number, you get the "magic" number (the one of Pitagora's sectio aurea) (this works better with numbers > 100)
This is because if a is the golden section and b=-1/a, then:
Fib(n) = (a^n - b^n)/(a-b)
so:
Fib(n+1)/Fib(n) = (a^(n+1) - b^(n+1))/(a^n - b^n)
and because |b|<1, b^n converges towards zero, so:
lim n->infinity Fib(n+1)/Fib(n) = lim n->infinity a^(n+1)/a^n = a
_ _ __ ___ _____ ________ _____________ _____________________ ... | Mathieu Bouchard - tél:+1.514.383.3801 - http://artengine.ca/matju | Freelance Digital Arts Engineer, Montréal QC Canada
I found a closed ofrm of fib which goes
fib(n) = (phi^n - (1-phi)^n)/sqrt(5) but when I patch it up I get an error.
It seems to be with the second numerator term, the Pd [pow] doesn't like non integer negatives. Anyone know how I get around this?
THe attached patch "works", only those aren't all fib numbers at the output, every few are rounded to an error because of the effect of the broken second term.
On Fri, 30 Jun 2006 20:40:56 -0400 (EDT) Mathieu Bouchard matju@artengine.ca wrote:
On Thu, 29 Jun 2006, Federico wrote:
and also: if you divide any fib number by its preceeding number, you get the "magic" number (the one of Pitagora's sectio aurea) (this works better with numbers > 100)
This is because if a is the golden section and b=-1/a, then:
Fib(n) = (a^n - b^n)/(a-b)
so:
Fib(n+1)/Fib(n) = (a^(n+1) - b^(n+1))/(a^n - b^n)
and because |b|<1, b^n converges towards zero, so:
lim n->infinity Fib(n+1)/Fib(n) = lim n->infinity a^(n+1)/a^n = a
_ _ __ ___ _____ ________ _____________ _____________________ ... | Mathieu Bouchard - tél:+1.514.383.3801 - http://artengine.ca/matju | Freelance Digital Arts Engineer, Montréal QC Canada
At 06:00 07.07.2006, padawan12 wrote:
I found a closed ofrm of fib which goes
fib(n) = (phi^n - (1-phi)^n)/sqrt(5) but when I patch it up I get an error.
It seems to be with the second numerator term, the Pd [pow] doesn't like non integer negatives. Anyone know how I get around this?
use [expr].
sven.
On Fri, 7 Jul 2006, padawan12 wrote:
Mathieu Bouchard wrote:
This is because if a is the golden section and b=-1/a, then: Fib(n) = (a^n - b^n)/(a-b) so: Fib(n+1)/Fib(n) = (a^(n+1) - b^(n+1))/(a^n - b^n)
I found a closed ofrm of fib which goes fib(n) = (phi^n - (1-phi)^n)/sqrt(5)
That's the same, cause a=phi, b=-1/a=1-a, a-b=sqrt(5)
It seems to be with the second numerator term, the Pd [pow] doesn't like non integer negatives.
It's not well-defined to compute a negative number to a non-integer power. "Not well-defined" means that there are several possible answers, or no answer, or even both (depending on the way of looking at it).
(1-phi)^n for even n is a positive value.
(1-phi)^n for odd n is a negative value.
(1-phi)^n for noninteger n would be a value for which the sign is unknown, but for which you know the absolute value. In another way, it can be argued that it should be a complex number, and in yet another way it can be argued that it can be a set of complex numbers.
If any other object actually gives an answer for that, I can't guarantee that your results will make sense.
_ _ __ ___ _____ ________ _____________ _____________________ ... | Mathieu Bouchard - tél:+1.514.383.3801 - http://artengine.ca/matju | Freelance Digital Arts Engineer, Montréal QC Canada
-
adam armfield -
Chuckk Hubbard -
Federico -
Frank Barknecht -
Martin Peach -
Mathieu Bouchard -
padawan12 -
sven