michelez

I have two phasor~ objects used as sampled ramp and trigger in a "sample and hold” (sah~) object. I get variable samples based on the frequencies of the two phasor~. (The sah works by outputting the value of the sampled ramp only when the trigger ramp crosses a certain threshold, say 0.5).

Example: If the trigger has frequency 4Hz and the sampled oscillator has frequency 2Hz the sah will output 4 values per second, but the first couple of values is equal to the second couple since the two oscillators align halfway through. So far so good.

My problem is that I am trying to build an algorithm to calculate the period of the pattern given the two oscillators frequencies. In other words: how long will it take the pattern generated by the two phasor~ to start over?

The solution is pretty is easy when the two frequencies are integers, it is enough to use a lcm function. But I encounter problems when the two frequency values are not integers.

I also tried to work with least common multiple function multiplying each value by 100 to get rid of the decimals and the dividing the result again by 100. It didn’t work. At this point I am very confused and could use an expert’s input.

I have two phasor~ objects used as sampled ramp and trigger in a "sample and hold” (sah~) object. I  get variable samples based on the frequencies of the two phasor~. (The sah works by outputting the value of the sampled ramp only when the trigger ramp crosses a certain threshold, say 0.5).
Example: If the trigger has frequency 4Hz and the sampled oscillator has frequency 2Hz the sah will output 4 values per second, but the first couple of values is equal to the second couple since the two oscillators align halfway through. So far so good.

My problem is that I am trying to build an algorithm to calculate the period of the pattern given the two oscillators frequencies. In other words: how long will it take the pattern generated by the two phasor~ to start over?
The solution is pretty is easy when the two frequencies are integers, it is enough to use a lcm function. But I encounter problems when the two frequency values are not integers. 

I also tried to work with least common multiple function multiplying each value by 100 to get rid of the decimals and the dividing the result again by 100. It didn’t work. At this point I am very confused and could use an expert’s input.
Michele


patterns-with-sah-period

interesting subject, but I can't help...


@Enrico Wiltsch He uses the lcm which is what I mention in my original post. Like I said it's not a problem when the two patterns are integers, the problem is when they are not.

I actually figured way to work with fractional lengths patterns, I call it Nonlinear sequencer and is now a package in Max if you want to look it up. this is a video explanation of it

NLS is a generative algorithm that creates rhythms using a music sequencer that behaves in ways other than linear. It is an algorithmic composition technique I invented and developed in MaxMsp (Max 8). An interesting generative tool for electronic musicians as well as experimental or electroacoustic music. The paper was first published at the SEAMUS 2020 virtual conference in Charlottesville, VA.

Download Nonlinear Sequencer Package as a zip file here:
https://github.com/michelezaccagnini/Nonlinear_Seq_Package

To install: drag the folder in Documents-Max 8-Packages, then from the Extras tab select NLS-launch

To read the paper:
https://michelezaccagnini.blog/wp-content/uploads/2020/05/Non-Linear-Sequencing-05_05_2020-2.pdf

Paper abstract:
Since the early developments of the MIDI protocol, electronic musicians have been making use of sequencers and keyboards to playback MIDI data. In its most basic form, a sequencer triggers events by reading through a list of performance information, such as pitch, duration, and velocity. In this paper, I discuss how the core time function at the base of the sequencer can be manipulated and turned into a compositional parameter. In particular, the paper explores ways of breaking away from the linear nature of the sequencer’s time function, one that has characterized it from its inception. The procedures and tools presented in this paper are part of an evolving compositional practice that goes under the name of Nonlinear Sequencing. 

Support me on Patreon!
https://www.patreon.com/michelez

Nonlinear Sequencer: Max package and theory

@Enrico Wiltsch He uses the lcm which is what I mention in my original post. Like I said it's not a problem when the two patterns are integers, the problem is when they are not.
I actually figured way to work with fractional lengths patterns, I call it Nonlinear sequencer and is now a package in Max if you want to look it up. this is a video explanation of it


isnt the lcm calculation for floats the same as ints? i.e. you needed to transform the float into an int first? 

of course the majority of 64 floating point numbers will not match into a 64 bit int number beause they become to long when multiplying them, haha.

but if you have, say, 2.5 and 4.75 ... you could multiply by 100 and then their "lcm" is 750/100. the values in milliseconds or bpm are only other representations for "bars and beats" anyway, and they are lawfully ints.

and you dont need an ultrahigh precision either, when in the end you only want to know in about which next sample something happens. (aka rounded sr*2)

i dont even know how to lcm() in max, my beloved expr doesnt do it, so i have to use wolfram alpha.


isnt the lcm calculation for floats the same as ints? i.e. you needed to transform the float into an int first? 

of course the majority of 64 floating point numbers will not match into a 64 bit int number beause they become to long when multiplying them, haha.

but if you have, say, 2.5 and 4.75 ... you could multiply by 100 and then their "lcm" is 750/100. the values in milliseconds or bpm are only other representations for "bars and beats" anyway, and they are lawfully ints.

and you dont need an ultrahigh precision either, when in the end you only want to know in about which next sample something happens. (aka rounded sr*2)

i dont even know how to lcm() in max, my beloved expr doesnt do it, so i have to use wolfram alpha.


Yes, I tried that back then but you can't really harness floats like that if you want synchronization to really happen. I worked on this issue for some time and I did find a solution which is the Nonlinear sequencer. It can be found in the package manager now or watch the video (I should make a shorter video just to give the general idea of it)

Yes, I tried that back then but you can't really harness floats like that if you want synchronization to really happen. I worked on this issue for some time and I did find a solution which is the Nonlinear sequencer. It can be found in the  package manager now or watch the video (I should make a shorter video just to give the general idea of it)

oops, of course i was overlooking the fact that not both values for speed in BPM are always ints, only for one of them it can be made sure.

but when you have 2,34776090871456 and 7,0247109911123, they will not be in sync again during your lifetime, the max DSP chain will run out before they meet again.


oops, of course i was overlooking the fact that not both values for speed in BPM are always ints, only for one of them it can be made sure.

but when you have 2,34776090871456 and 7,0247109911123, they will not be in sync again during your lifetime, the max DSP chain will run out before they meet again.


Patterns with sah~: period?