What is the minimum amount of information necessary to describe all chords?

dendy

@u0421793 said:

@dendy said:
easiest dedcription of any chord:

"just fucking hit any number of notes between 2 and 8 (including) until it sounds pleasant to yourl ears"

What if we don’t want pleasant? Is it still a chord? Is a harmonically complex single-note sound that happens to have high enough harmonic peaks in other areas actually a chord (ie, a dual VCO synth where the VCOs are tuned to a fifth, or a 3 VCO synth where they’re tuned apart as root third fifth)? Is a harmonically complex single-note sound that just happens to invoke a lot of peaky sideband stuff that you’d mistake for lying at harmonically meaningful intervals actually a chord? Is a single-note sound that is pretty much filtered white noise actually a chord? Is an explosion a chord? A cannon fire? A fart? A cough?

If we only qualify harmonic combinations that are pleasant, and exclude a lot that aren’t pleasant, that’s a bit unfair on the whole chord world.

And pleasant to whom? What if they change their mind?

pleasant to creator.. who wants to make music unpleasant to himself ? Would call that masochism, not creativity :-))))

Of course i thpuht we're talking about chord in original meaning of his world.. if you want consider farting as chord, your creative choice :-))) But son't be surprised other people will look at your in weird way :-))

McD

@TonalityApp said:

@McD said:
This is so much fun... everyone that tries to narrow the answer to a precise criteria gets a more expansive problem statement that even includes the infamous "raspberry" (the Fart chord).

Computer scientists measure the complexity of a problem using this language:

An NP-complete problem is a problem for which the correctness of each solution can be verified quickly and a brute-force search algorithm can actually find a solution by trying all possible solutions.

Your question and the solution is NP-Hard. The idea of a "minimum" for something so vast is an exercise in contemplating the infinite which can conveniently be found in the lower portion of your abdomen.

This chart does an excellent job of making the concept even harder to understand. It looks like a basketball playbook to me. Your problem lives near the net.

https://forum.audiob.us/uploads/editor/hn/0a2cmwa5ncwb.png

When considering a finite amount of chord types, the problem certainly isn’t NP-hard. It takes a minimum of log2(n) bits to uniquely encode each, where there are n possibilities total. Even if you allow infinitely many chord types, I’m not convinced the minimal representation is an NP-hard problem. There are tons of infinite spaces from which points can be described in a provably minimal finite representation.

Very astute analysis... I was using the concept of NP-Complete as an analogy for the way the OP changes the definitions of chord to expand the numerical domain of "minimal" descriptions. Loki (the trickster) comes to mind. Get close to an answer and the problem is re-defined to keep the conversation moving down the rabbit hole to the Tea Party.

But there are some good app ideas coming from the discussion like the "Fart Harmonic Analyzer"...
the spread spectrum approach. Thankfully the concept is virtual and no hand sanitizers are required.

u0421793

Well, in the modular synth example I gave earlier, you’d have a pitch CV as we currently do, but if we wanted some hypothetical and independent ‘chord’ signal that perhaps you could pipe down a patch lead into a jack socket, what would that signal be? I’m suggesting it probably isn’t a scalar dimension such as a single voltage that [does something to some module to make what we interpret as a chord], but possibly more axes. Getting down to what those are is the thing of this.

McD

@u0421793 said:
Well, in the modular synth example I gave earlier, you’d have a pitch CV as we currently do, but if we wanted some hypothetical and independent ‘chord’ signal that perhaps you could pipe down a patch lead into a jack socket, what would that signal be? I’m suggesting it probably isn’t a scalar dimension such as a single voltage that [does something to some module to make what we interpret as a chord], but possibly more axes. Getting down to what those are is the thing of this.

I can't believe you haven't even mentioned Fourier Transforms since they can break down a note into
the harmonic content inherent. But it does require oscillatory input and has no benefit for random noise
like many categories of flatulence... but some flatulence can having a nice trumpet like quality.

Overtones are the ultimate basis for most chordal structures that have coherence sonically.

How many pages are we shooting for here?

u0421793

@McD said:

@u0421793 said:
Well, in the modular synth example I gave earlier, you’d have a pitch CV as we currently do, but if we wanted some hypothetical and independent ‘chord’ signal that perhaps you could pipe down a patch lead into a jack socket, what would that signal be? I’m suggesting it probably isn’t a scalar dimension such as a single voltage that [does something to some module to make what we interpret as a chord], but possibly more axes. Getting down to what those are is the thing of this.

I can't believe you haven't even mentioned Fourier Transforms since they can break down a note into
the harmonic content inherent. But it does require oscillatory input and has no benefit for random noise
like many categories of flatulence... but some flatulence can having a nice trumpet like quality.

Overtones are the ultimate basis for most chordal structures that have coherence sonically.

Sure, but these analyses don’t give you a compact pitch-independent single ‘qualia’ that no matter where it is applied impart that flavour that is of that denoted chord. In effect they do the reverse – generate far more information.

How many pages are we shooting for here?

180

McD

@u0421793 said:
Sure, but these analyses don’t give you a compact pitch-independent single ‘qualia’ that no matter where it is applied impart that flavour that is of that denoted chord. In effect they do the reverse – generate far more information.

How many pages are we shooting for here?

180

If we are shooting for 180 pages it seems we would want to expand the production of information...
while seeking some minimal boundary implied by the original problem statement. Can we entertain any
concepts of "Chaos Theory" or "Fractal Geometry" to open additional avenues of obfuscation and
convergence towards some form of agreement? These are fertile areas of mathematics that tend to produce more words than they do equations. I'm sure that a real mathematician could explode this discussion into multiple dimensions and leverage the concepts of String Theory which I assume would
have analogs beyond strings for columns of air or oscillating membranes.

The mind reels at the possibilities and we seem to be in an expanding universe of areas to investigate.

Still... 180? We will have to repeat ourselves and hope no one calls us out for it.

u0421793

@McD said:

@u0421793 said:
Sure, but these analyses don’t give you a compact pitch-independent single ‘qualia’ that no matter where it is applied impart that flavour that is of that denoted chord. In effect they do the reverse – generate far more information.

How many pages are we shooting for here?

180

If we are shooting for 180 pages it seems we would want to expand the production of information...
while seeking some minimal boundary implied by the original problem statement. Can we entertain any
concepts of "Chaos Theory" or "Fractal Geometry" to open additional avenues of obfuscation and
convergence towards some form of agreement? These are fertile areas of mathematics that tend to produce more words than they do equations. I'm sure that a real mathematician could explode this discussion into multiple dimensions and leverage the concepts of String Theory which I assume would
have analogs beyond strings for columns of air or oscillating membranes.

Actually that’s a good point – if you consider chaos theory as basically being about stability, or the causes of the opposite - asymptotic excursions to who knows where at a moments notice. And what sort of pretty pattern you get when it does the same or similar things over a long monte-carlo of time (ie phase space). A phase space plot might turn out to be basically a chord flavour. But (and it’s a big but) it doesn’t give you compact information you can shove down a minimum number of patch cords. Or does it?

Still... 180? We will have to repeat ourselves and hope no one calls us out for it.

We will have to repeat ourselves?

TheOriginalPaulB

Ignoring differences between inversions, all chord types playable on a piano keyboard can be described as a 12 bit numerical value. If you go microtonal, the possibilities become infinite and descriptions become approximations.

TonalityApp

@McD said:
Very astute analysis... I was using the concept of NP-Complete as an analogy for the way the OP changes the definitions of chord to expand the numerical domain of "minimal" descriptions.

Ah

@TheOriginalPaulB said:
Ignoring differences between inversions, all chord types playable on a piano keyboard can be described as a 12 bit numerical value. If you go microtonal, the possibilities become infinite and descriptions become approximations.

Exactly... and even if you allow "standard" inversions you can just add another few bits to describe inversion offset from the lowest one possible on the keyboard. It only gets slightly harder if you allow completely arbitrary voicings. Even then, however, there is a minimal scalar representation.

Just like what @TheOriginalPaulB mentions and I described earlier, we can encode any chord as an integer. To allow the full space of voicings we just need 88 bits now instead of 12, one for every key on the piano.

This allows 309,485,009,821,345,068,724,781,056 possible chords, including any arbitrary voicing playable on the piano, which I think is plenty. It even includes what I suspect @McD would call the "ultra-fart chord". And it's still a single scalar value, albeit a fat one.

If this still meets @u0421793 requirements, you could just split this bit set into two integers, say 64 bits each. One would encode the lower half of the keyboard and the other the upper. You'd even have 40 bits left over to encode whatever extra information you want (note velocity anyone?)

Over 300 octillion possibilities and only two scalars.... the magic of combinatorics.

@u0421793 said:
I’m suggesting it probably isn’t a scalar dimension such as a single voltage that [does something to some module to make what we interpret as a chord], but possibly more axes. Getting down to what those are is the thing of this.

Depending how precise your voltages can get (a potentially big caveat), the above could still work for an analog system (especially if you just split the value up into a few CVs). You effectively get 88+ "axes", but squashed into a few scalars by treating each bit as an "axis". Or, if you greatly limit the number of chord types/inversions, just have one CV for the root note and one for the quality.

u0421793

That sounds like it could get feasibly close to being an actual buildable module in the modular synth domain (which we all know is a bit crazy and experimental anyway). And, if slew is applied to one or both scalars, you can get portamento not only between notes but also between chord flavours. Maybe.

TonalityApp

@u0421793 said:
That sounds like it could get feasibly close to being an actual buildable module in the modular synth domain (which we all know is a bit crazy and experimental anyway). And, if slew is applied to one or both scalars, you can get portamento not only between notes but also between chord flavours. Maybe.

Yeah, the only problem (back to my discussion of embedding chords as points in some kind of space) is that this particular space is very non-musical, at least with linear traversal. For example (using 12 bits again for simplicity), if you apply a digital "slew" from CM to FM you'd travel from 145 (CM) to 545 (FM) and get way too many chords in between. Further, they amount to some weird changes: bits added or removed as you increment by one would mean a completely variable number of pitches per chord.

You'd get CM, C#dim, C#dim(M7), Em7, C(add9), (cluster), (even grosser cluster), Em(M7), etc. for 400 chords until you hit F. At some point along the way you'd even hit 000111111111, a lovely cluster of every note between C and Ab.

I'd argue that the question is no longer the minimal representation of chords, but instead "can I find a traversal of the integers which results in a musical-sounding sequence?" or alternatively, "can I find a space isomorphic to the integers modulo [that large number from before] which lends itself to morphing between chords?"

zedzdeadbaby

@u0421793 said:
This might seem a strange question. It might not have an answer.

What is the minimum set of parameters that can describe a chord - all chords. I’m guessing perhaps a vector, or perhaps a curve? I’m also thinking it should avoid mention of discrete note numbers, instead focusing on a description of a way of getting to them, using the minimum set of info necessary.

Obviously a triad can be described as only three discrete note numbers, which isn’t a lot. But this doesn’t apply to all chords. Is there a single set or structure of information that can describe all chords (by varying the parameter values)?

Everytime I see the header for this question it immediately puts me in a good mood. You my friend will have a good life ahead of you with this mentality, including all who have tried to answer this question with good intention.

Cheers

McD

Wait... @u0421793, are you willing to accept a digital "encoding" of a chord as a "description"?

u0421793

@McD said:
Wait... @u0421793, are you willing to accept a digital "encoding" of a chord as a "description"?

Well… it’s not really continuous is it – it’s not something you can represent with a patch cord or two, and I think the scenario alluded to whereby integrating from one position to another involves going through a whole load of confusing undergrowth might be an indication that although it’s in the correct general direction, we shouldn’t stop there.

u0421793

What if we had a joystick where the side-to-side axis was ‘major to minorness’ or even more extreme than that, beyond at each end so that actual major and minor were within the range. And the other axis, the ‘away-to-toward’ axis was another significant characteristic of chord flavour distinct from major/minorness.

zedzdeadbaby

If I might add a couple thoughts to this. First if you look towards Michael Gerzons white papers this questions comes up often and there is much gold within his research in the early days of propogation. Many reverb dsp developers know this mans work very well.

2nd the matrix we live in must be respected in that our preception of harmonics overtones and all things that make beautiful and ugly sounds are a by product or function of "TIME" sounds simple. well yes and no. But one experiment is to record a guitar/ and a bass/ and a drum and basically anythings that makes music. For this experiment make sure to pluck or play any of the instruments on the same note and also the same beat repeatedly as to anonymize each instrument for a AB comparison. Now take a really high quality low pass filter and get down as close to DC as possible. Youll be amazed what you find!! Now with this knowledge we can read some literature and things become clearer.

Related mind blowing side-note on guitar/synth FX (because this too is a function of time) As amazing as man has become with all of the cool flangers choruses delays reverbs equalizers or anything that we collect so dearly. Its all exactly the same technology.. Its all based on a single time delay line.

1.Parametric EQ 4-band: Duplicates input signal 4 times each with its own variable "Q or quality"potemtiometer.. After a little time offset or delay on each band it restructures each copy.back onto the original thus creating a phase shift in each respective band.

2 Flanger... basically delay line modulated onto orig copy thus creating phase shifts

3. chorus Same as flanger just longer delays

4 delay pedal...Well this doesnt need an explanation... except sometimes.the delays never are reintroduced to the original signal unless the effect is desired.

5. Reverb.... just a bunch of tiny quick delays that flop the polarity on every other succsesive delay..

6 wah pedal...band pass filter modulated in time over the input signal..

7. Even tubes in an amp can be thought of in this way.. usualy a Negative Feedback design creates the most desirable phase shift or what most consider smooth.

The list goes on and on and on. Its all just a dragon eating itself within its self within itself.

Cheers