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Boolean Sequencing
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Sam_Zen



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PostPosted: Thu Mar 13, 2008 10:20 pm    Post subject: Reply with quote  Mark this post and the followings unread

The ability to detect patterns-behaviour is a very basic one in our brain.
So the artist can make use of this.

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bachus



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PostPosted: Sat Mar 15, 2008 5:47 am    Post subject: Reply with quote  Mark this post and the followings unread

SamZen wrote:
The ability to detect patterns-behaviour is a very basic one in our brain.
So the artist can make use of this.


I'll accept that as self evident, note that my own experiments with retrograde have not been satisfying to me, and let it go at that as I don't know that I can hear everything others can hear.

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Sam_Zen



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PostPosted: Sat Mar 15, 2008 9:15 pm    Post subject: Reply with quote  Mark this post and the followings unread

Of course this is a matter of personal perception, training in interpretation, so it will be different to any listener.
The detection of something backwards of course starts with e.g. hearing the acoustical reflections before the sound itself.
Making use of it can be (which could be called a boolean sequence in some way):
~ Read a text, but reversed in letters, so "olleH" - record this, reverse the wav-file, and play it.

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PostPosted: Mon Mar 17, 2008 1:01 pm    Post subject: Reply with quote  Mark this post and the followings unread

MIDI makes experimentation with retrograde quite easy. I was inspired to use it by the serealists.
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bachus



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PostPosted: Mon Mar 17, 2008 3:11 pm    Post subject: Reply with quote  Mark this post and the followings unread

mosc wrote:
MIDI makes experimentation with retrograde quite easy. I was inspired to use it by the serealists.


Well it has been around awhile. Bach used in several places including The Musical Offering and many others before and after him made use of it. But in general these were written forward and backward simultaneously.

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Sam_Zen



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PostPosted: Mon Mar 17, 2008 8:48 pm    Post subject: Reply with quote  Mark this post and the followings unread

The idea may have been there already. But EM offers more than just being a station to make a reversion, like with tape.

We're talking about binary masks here. So an reversion of those bits would result in quite a different sequence of notes,
than Bach would have when inverting the phrase.

A total inversion of each bit could be another option.

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PostPosted: Tue Mar 18, 2008 5:17 am    Post subject: Reply with quote  Mark this post and the followings unread

SamZen wrote:
The idea may have been there already. But EM offers more than just being a station to make a reversion, like with tape.

We're talking about binary masks here. So an reversion of those bits would result in quite a different sequence of notes,
than Bach would have when inverting the phrase.

A total inversion of each bit could be another option.

Inversion and retrograde are not equivalent which make your post opaque to me.

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Sam_Zen



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PostPosted: Tue Mar 18, 2008 7:20 pm    Post subject: Reply with quote  Mark this post and the followings unread

You're quite right. I had a vague idea about 'retrograde'. Now I've checked the dictionary.
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PostPosted: Wed Mar 19, 2008 3:41 pm    Post subject: Reply with quote  Mark this post and the followings unread

I checked dictionary.com:

retrograde:
5. Music. proceeding from the last note to the first: a melody in retrograde motion.

inversion:
8. Music.
a. the process or result of transposing the tones of an interval or chord so that the original bass becomes an upper voice.
b. (in counterpoint) the transposition of the upper voice part below the lower, and vice versa.
c. presentation of a melody in contrary motion to its original form.

I don't quite follow what inversion really is, but retrograde seems clear. Some thoughts:

It is interesting that while the sequence is played backward in retrograde, the notes are still played forward. This gives us insight into the human mind: it is not working backward like a tape player or VCR, it is obtaining little chunks of forward music (notes) and doing pattern recognition on the reversed sequence.

Also, we can look at the amount of retrograde activity in our present and prehistoric lives to evaluate how well adapted we must be to it. Although there are many examples of retrograde in life experience (returning a stone tool to its original position to strike again, walking backward, climbing back down from a tree), retrograde is experienced much more rarely than forward patterns. From this I suppose that we must have much weaker ability to detect retrograde patterns compared to forward patterns.

So when we listen to retrograde, we must be using some part(s) of the mind that is not nearly as well developed as the forward-biased part(s). This would make retrograde a strange, quirky stimulator; somewhat like a right handed person using the left hand.

Perhaps a psychology experiment might be to play retrograde music of various complexity and having the subjects match it to the forward sequences. Skill in retrograde pattern recognition might be correlated with intelligence or music ability or emotional/social IQ, etc.

Does that make sense or am I rambling nonsensically yet again?
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bachus



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PostPosted: Wed Mar 19, 2008 7:00 pm    Post subject: Reply with quote  Mark this post and the followings unread

Again, until the "modern" era forward and retrograde lines were always written simultaneously. That is, the line was constructed from the get-go so that it made sense in context going in both directions. Without this kind of very careful construction little relationship is detectable between them -- at least to me.

"Uncalculated" retrograde, however, might be used to create recognizable figures. Blue Hell's suggestion that two notes would not be good may be exactly wrong (even though he's usually right). If one retrogrades over just a few of the immediately past notes a figure, a small unit of musical coherency might be generated.

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Sam_Zen



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PostPosted: Wed Mar 19, 2008 7:48 pm    Post subject: Reply with quote  Mark this post and the followings unread

Don't worry, I'm quite capable of following your considerations, I think.
Quote:
I don't quite follow what inversion really is, but retrograde seems clear.

I can understand why 'inversion' stays fuzzy, because this dictionary approaches this from the academic music view.
It's confusing because retrograde clearly has an element of inversion too. In time that is.
From a physics point of view (EM), looking at a song as a waveform, it will stay more clear.
As in a wav-editor, inversion can be done in 2 different dimensions : X or Y.
X (time) would mean playing backwards, Y (phase) would mean a 180 degrees flip.
If looking at the song as a binary representation, more types of 'inversion' are possible.
Quote:
while the sequence is played backward in retrograde, the notes are still played forward.

A nice observation. This is the difference between the score-inversion and the sound-inversion.
Quote:
a psychology experiment might be to play retrograde music of various complexity and having the subjects match it to the forward sequences.

There are tests with retrogrades. I've seen several tv-quizzes where a song was played backwards with the question
which song it is. Sometimes it's difficult, sometimes not. I think it's dependent of the personal skill of listening.
The training of sound-imagination. The ability to ignore artifacts and focus on the real content.
So I don't agree to couple such abilities directly to intelligence, etc.
An example of using retrograde in a compo can be found here

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PostPosted: Thu Mar 20, 2008 10:45 am    Post subject: Reply with quote  Mark this post and the followings unread

Academic definitions are pretty important if one is to communicate effectively with one's peers about any subject in depth. I would say that while certainly related, reversing the audio is not retrograde. Retrograde is reversing the order of the notes. Notes is a musical term. While audio can produce notes, notes are understood to be part of music.

Anyhow, the perception of reversed audio and retrograde music is quite different, but it is possible to combine both. For example, play a melody. Play the retrograde (easy in MIDI DAWs). Then play the new audio backwards.

I was watching a program on the Discovery Channel about the intelligence differences between humans and the great apes. It turns out surprisingly that chimps have much better short term memory than humans. Maybe the ability to identify retrograde would be better in chimps, I don't know.

I'm not saying it is easy to identify retrograde in a composition by listening, but retrograde melodies have a certain relatedness in feeling to the non-retrograde version, so it makes a very nice compositional tool.

Here is an example of perfect retrograde. I wrote this in 1992. It is called 2andFro. It is retrograde by taking a MIDI file and concatenating the same file but retrograde. Thus, exactly 50% though the composition, the notes begin to be played in reverse order. I call this trick arching for lack of a better term. If you listen carefully, you'll hear some strange effects caused by the retrograde of the sustain pedal. I like the effect so I didn't try to correct it. (Correction, I did try to correct it but didn't like it as much).

I think you'll agree that the piece has a unified feeling. I got the idea to do this from studying the music of Anton Webern. I know Bach, Mozart and others used retrograde too, but those uses weren't what inspired me. I don't use this much anymore because I've moved away from MIDI.

http://mosc.com/~mosc/2andFro.mp3

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PostPosted: Thu Mar 20, 2008 12:49 pm    Post subject: Reply with quote  Mark this post and the followings unread

mosc wrote:
Here is an example of perfect retrograde. I wrote this in 1992. It is called 2andFro. It is retrograde by taking a MIDI file and concatenating the same file but retrograde.

Nice sample, Howard! One thing I noticed in several places is that the normal tension->release pattern became release->tension, which I guess one should expect in applying retrograde to music with tension->release.

I wonder if there are other dynamic, second order structures like tension->release that are also reversed or otherwise changed in structure by techniques like retrograde and inversion.

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PostPosted: Thu Mar 20, 2008 1:54 pm    Post subject: Reply with quote  Mark this post and the followings unread

Since we're discussing retrograde, I thought I'd give my new up/down counter a try and make us a simple retrograde sequence using my new program, Synth Lab. I'm not sure if I have implemented it properly though, so maybe this will be a good test.

I made a 19 second sequence that has three repetitions of the foreward pattern followed by some repetitions of the forward/retrograde pattern (about 3). There are brief moments of silence between the first three patterns so you can tell beginning from end, then the forward/retrograde sequence begins with no silence between repetitions. Here is the link:

http://www.freedomodds.com/music/songs/Chimp_Retrograde.mp3

I cannot make sense of this retrograde pattern very well at all, really, so it's likely that I've been outsmarted by a chimp! I know I don't have the "ear" for music because I was tested once, so maybe that's why I can't hear it. Either that or my program is not coded properly and the sequence isn't really retrograde. Can you hear it?
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Low Note



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PostPosted: Thu Mar 20, 2008 3:14 pm    Post subject: Reply with quote  Mark this post and the followings unread

When people ask me what retrograde/inversion mean i normally say:

Retrograde is reading a musical idea right to left.

Inversion is taking a note in a musical idea and using it as a pivot point to spin all the other notes around. So if you have three notes: C D E. You spin it around the note C, it becomes: C Bb Ab. (Of course you can have diatonic and real/chromatic inversions. A diatonic inversion of that idea in C major would be C B A).

Webern's use of retrograde is really interesting. He dealt with it so deliberately that it can be really powerful. It took a while, but once I was able to get excited about Webern's very short gestures, it all took off. Hindemith's use of retrograde can be just as interesting, but he's normally a lot busier of a composer, and I can never really hear the retrograde unless I've also analyzed the piece.

One idea that jumped out at me here was the idea of retrograding "bits" of information. I'm not sure if this is what the person was getting at, but it might be interesting to take the motivic ideas that make up a piece and reverse their order, instead of the entire melody. Instead of the notes A B and C, if you had the ideas A B C, and then performed them C B A.

That might be something for me to explore. Almost like a concentrated Arch Form.
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PostPosted: Thu Mar 20, 2008 3:23 pm    Post subject: Reply with quote  Mark this post and the followings unread

Low Note wrote:
I'm not sure if this is what the person was getting at, but it might be interesting to take the motivic ideas that make up a piece and reverse their order, instead of the entire melody. Instead of the notes A B and C, if you had the ideas A B C, and then performed them C B A.


Yup that's it. Though I was thinking A B C => A B C B A, which creates a prominent figure.

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PostPosted: Thu Mar 20, 2008 3:36 pm    Post subject: Reply with quote  Mark this post and the followings unread

Low Note wrote:
Inversion is taking a note in a musical idea and using it as a pivot point to spin all the other notes around. So if you have three notes: C D E. You spin it around the note C, it becomes: C Bb Ab. (Of course you can have diatonic and real/chromatic inversions. A diatonic inversion of that idea in C major would be C B A).


Inversion has several meanings in music. The one you describe is more precisely designated as melodic inversion though context can make the modifier irrelevant. It is pretty clear in this conversation but as some are not familiar with it's various forms it might be best to be specific.

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PostPosted: Thu Mar 20, 2008 3:46 pm    Post subject: Reply with quote  Mark this post and the followings unread

Inventor wrote:
I cannot make sense of this retrograde pattern very well at all,


Me neither but it's well established that's a week point for me.

As for being out smarted by a chimp, don't feel bad. I've been out smarted by a pig several occasions Laughing

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PostPosted: Thu Mar 20, 2008 4:14 pm    Post subject: Reply with quote  Mark this post and the followings unread

Inventor wrote:
I made a 19 second sequence that has three repetitions of the foreward pattern followed by some repetitions of the forward/retrograde pattern (about 3).


It sounds like three repetitions of the foreward pattern followed by four repetitions of the retrograde/forward pattern. It seems to end on forward.

bachus wrote:
Low Note wrote:
I'm not sure if this is what the person was getting at, but it might be interesting to take the motivic ideas that make up a piece and reverse their order, instead of the entire melody. Instead of the notes A B and C, if you had the ideas A B C, and then performed them C B A.


Yup that's it. Though I was thinking A B C => A B C B A, which creates a prominent figure.


From using lots of combinatorics in places like path searches in computer science, I've gotten almost half good at improvising some transitions where there is more than one path from point 1 to 2 in a piece, and just running the combinations. For example, if path A and path B both get me from the same start to finish, and I need to fill out 8 bars, then it might be

B, A
A, A
B, B,
A, B

A and B could also have opposite start and end point in this example.

As natural as eating or farting to a CS person, although not at the same time!

eat, fart
fart, fart,
eat, eat,
fart, eat

Reminds me of my beagle rendeer

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Sam_Zen



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PostPosted: Thu Mar 20, 2008 6:58 pm    Post subject: Reply with quote  Mark this post and the followings unread

For a moment I was afraid that this discussion was going a bit off-topic, because the main 'Boolean' aspect
was somewhat lost, in the arguments about what exactly is inversion or retrograde.
But Inventor introduces an up/down counter and I see some lists looking like a binary truth table from AI.
So that's reassuring.
As bachus states, inversion has several meanings in music.
So even much more meanings if electronics are involved.
It depends on which variable within which field it's applied. Inversion of sound, of a sequence, a waveform, a bit,
a byte, a filter, a formula, etc.
And inversion is just one of the boolean functions. More : AND - OR etc. Binary masks can be used.

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PostPosted: Fri Mar 21, 2008 10:10 pm    Post subject: Reply with quote  Mark this post and the followings unread

Acoustic Interloper wrote:
Inventor wrote:
I made a 19 second sequence that has three repetitions of the foreward pattern followed by some repetitions of the forward/retrograde pattern (about 3).


It sounds like three repetitions of the foreward pattern followed by four repetitions of the retrograde/forward pattern. It seems to end on forward.



Thanks, yes that is what I recorded. Now I know that my attempt at programming a retrograde-ready up/down counter thingie works properly, good news.

I should mention that although I cannot specifically detect the retrograde, I can enjoy the sequence created by the retrograde, so maybe I'm not totally deaf to it.
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PostPosted: Sat Mar 22, 2008 6:41 pm    Post subject: Reply with quote  Mark this post and the followings unread

Bachus and LowNote are talking about retrograde with multi-note structures.

Since this topic is about Boolean Sequencing (not sure that's defined, but that's OK with me), it seems very difficult to make structures by those means that build such extended forms. This is why I do most of my algorithmic composing with analog components on a G2 virtual analog machine. Step sequencers, LFOs, multi-segment envelopes, etc.

I'm very interested to hear if anyone has made much headway in this larger scale aspect of sequencing.

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PostPosted: Sat Mar 22, 2008 9:12 pm    Post subject: Reply with quote  Mark this post and the followings unread

I'll try to create a definition for Boolean Sequencing:

Boolean Sequencing: A technique for creating music sequences by forming logic expressions from a binary counter. The outputs of the binary counter drive a logic network and a note is played whenever the logic output is true. Note frequency is specified by an algebraic expression of the counter bits and/or logic terms. Random bits and retrograde sequences can also be incorporated in the composition. Base-N counters may be used along with a chosen definition of Base-N logic expressions.

That's a bit wordy but I got it all in there. Now for your listening pleasure, a 52 second piece that I created tonight using Boolean Sequencing in Synth Lab, attached.

The short song was created by driving three SinOsc VCOs with logic terms from the counter logic, then sending the VCO outputs into a ring of three band pass filters. A little reverb adds some depth to the output, which is taken from one of the filter ring nodes. I have been playing around with rings of oscillators, filters, delays, and gain blocks in various geometric topologies. It's a good learning experience.


Synth_Lab_Ring_LPF.mp3
 Description:
A light melody created in Synth Lab with Boolean Sequencing and a ring of filters, 52 seconds.

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PostPosted: Sun Mar 23, 2008 9:16 am    Post subject: Reply with quote  Mark this post and the followings unread

mosc wrote:
Since this topic is about Boolean Sequencing (not sure that's defined, but that's OK with me), it seems very difficult to make structures by those means that build such extended forms. This is why I do most of my algorithmic composing with analog components on a G2 virtual analog machine. Step sequencers, LFOs, multi-segment envelopes, etc.

I'm very interested to hear if anyone has made much headway in this larger scale aspect of sequencing.


In CS formal language and automata jargon, there are four basic categories of phrase structured languages & machines:

1. Regular expressions (finite state automata)

In these the current state + the next input generates the next output and moves you to the next state. Think of regular expressions in places like 'grep' or Perl (or Awk, Howard!), or wildcards at the end of a query string.

So, everything you've heard and played is consolidated in your current state, and some input makes you play the next note (or whatever sound granularity you are at) and move on to the next state.

2. Context free grammars (pushdown automata)

Like (1), but now you can push your current state onto a stack and go into a sub-machine to play its music, maybe even sending down some parameters when you make the call. Just like a subroutine/function/method call in a programming language.

This is good for having phrases appear at various places embedded in the piece, (not just at the tail as with 1), perhaps with variations in those phrases driven by their input parameters.

3. Context dependent grammars (linear-bounded automata)


Like (2), but you can save pieces of state in registers (notes, scales, chords, transformations, whatever you like) from one phrase "subroutine" and use it in another. Phrases (subroutines) that would be unrelated in (2) become related in (3) by passing messages in registers. That is the "context dependence."

4. Turing machines (unbounded automata) -- anything goes.

I think Boolean Sequencing is probably (1), unless it makes use of a stack to push and pop the current state.

If Inventor adds a stack (pushdown automaton), he'll be able to push into phases and then pop back out to where he invoked them.

If he adds registers that are preserved across pushes/pops (context), he'll be able to pass notes in class (so to speak).

After a while, it will (and should) start to be impossible to hear a 1-to-1 match between algorithm and generated sound.

I've tried ad hoc chunks of (2) and (3) in MIDIME, based on traces of my own phrase playing and then later improvisation in real time, with mixed results, but I really don't have enough time to devote to this. "Maybe in the next life I'll be able to hear myself think," to quote Bob Dylan from about 11 years ago (time flies).

Most of the academic studies of mechanisms related to (2) and (3) seem to be non-real-time score matching and the like, not performance.

A fair number of Minimalist pieces seem to use mechanisms (1) (2) and (3) to some degree in structuring the (at times glacially slow) transitions. Of course phrase structuring shows up in most music.

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PostPosted: Sun Mar 23, 2008 1:09 pm    Post subject: Reply with quote  Mark this post and the followings unread

Well, if we allowed flip-flops to be part of the decoding logic, then we would have the context-dependent grammars situation. This would mean that the decoder logic would be a state machine instead of just logic, what an excellent idea. We've just expanded on Boolean Sequencing, AI. Now, what that state machine would do remains a mystery, but obviously the possibilities are extensive.

Hmm... if we have logic (or state machine) that plays a sequence, then a state machine could control that sequence. If there were multiple sequence generators, the state machine could be coded with inversion or retrograde of sequences, then make each sequence happen at the right time.

In fact, another generalization is to replace the counter with a state machine so that instead of just counter followed by logic, we have a full state machine in its place. Well, a counter is a type of state machine anyway so I guess that is what we have now.

This is exiting, through forum discussion we have generalized Boolean Sequencing to a more useful concept.
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