Possible Coil Combinations

[ChrisK]

Taken in the full context of ALL possible combinations of 2 coils sans OFF and PHASE, there are 4 variants.

Taken in the full context of ALL possible combinations of 3 coils sans OFF and PHASE, there are 17 variants.


Taken in the full context of ALL possible combinations of 4 coils sans OFF and PHASE, there are 97 variants.

[col]

Hi Chris,

Skimming over your list of possible 4-coil arrangements, I think you missed 3. I do not fully follow your table (a legend would help), but there is a four-coil arrangement, and its three permutations missing from your list.


..^
._|_
|...|
1...2
|___|
._|_
|...|
3...4
|___|
..|
..G

..^
._|_
|...|
1...3
|___|
._|_
|...|
2...4
|___|
..|
..G

..^
._|_
|...|
1...4
|___|
._|_
|...|
3...2
|___|
..|
..G


Col.

[sbgodofmetal]

Welcome to the nutz house. Were truly sorry to say but chrisk is no longer with us anymore. He has left us with many great articles concepts and ideas many with charts and diagrams. and a few schematics here and there. But feel free to ask any of us about his works a lot of members have been here long enough to explain anything of his to you.

R.I.P. Chrisk.

[newey]

col-

Hello and Welcome to G-nutz2!

I do not fully follow your table (a legend would help)

Somewhere, ChrisK is having a chuckle. This is a logic puzzle, and I don't fully understand his notation either. But I'll guarantee you, the failure to include a key was a purposeful omission.

He was challenging us to figure it out for ourselves, hoping to get us to "see" the logical sequence.

ChrisK never handed anything out on a silver platter, as he felt no one would learn anything that way. "Teach a man to fish", as the old saw goes- that was one of his favorites.

If I can decipher your notation, col, you are suggesting that Chris forgot the arrangement of 4 coils whereby two series pairs are joined in parallel- and the permutations of that arrangement, i.e., (1 X 2) + (3 X 4), (1 X 3) + (2 X 4) and (1 X 4) + (2 X 3).

Look in the second column, 4th diagram down, and I think you'll find that Chris has not, in fact, omitted these possibilities . . .

BTW, I have built a guitar that realizes all those series pairs, joined in parallel- the "4Caster":



It does not, however, do all 4 coils in series, nor does it do 3 in series, in parallel with the fourth. The structure is based on pairs of coils.

Of course, two pairs of coils in series, which are then joined in parallel represents the standard wiring for most two- HB guitars such as SGs and LPs, if we further assume that the pairs of coils are close enough together to "co-habit" one pickup frame.

[ashcatlt]

col's diagram looks to me like parallel pairs in series with one another - (1+2)x(3+4), etc.

I'm not actually seeing that represented in chrisk's table. I want to say that this is because it's mathematically the same as the parallel combination of series pairs, but I can't make that work unless all four coils are the same.

[using our standard notation of + for parallel and x for series, don't try to just do normal math here.]
(1+1)x(1+1)=1=(1x1)+(1x1)
but
(1+2)x(3+4)=(50/21)!=(1x2)+(3x4)=(21/10)

But maybe I'm missing something...

[reTrEaD]

Apr 18, 2012 10:02:10 GMT -5 ashcatlt said:

I want to say that this is because it's mathematically the same as the parallel combination of series pairs, but I can't make that work unless all four coils are the same.

Right.

Let's compare these two similar configurations...




..^
._|_
|...|
1...3
|___|
._|_
|...|
2...4
|___|
..|
..G


..^
._|_
|...|
1...3
|...|
|...|
2...4
|___|
..|
..G


Let's arbitrarily assign values for the resistance (or inductance) of each coil as 1, 2, 3, and 4, respectively. Then solve for the total in each circuit.

In the first case we would have:
(1//3) + (2//4) = (3/4) + (8/6) = 0.75 + 1.33 = 2.08
(product over sum for parallel)

In the second case we would have:
(1+2) // (3+4) = 3//7 = 2.1

Similar, but not exactly the same.
If the coils are not identical, there will be a slight difference in the total resistance (or inductance).

Is that the end of the story? Maybe not...

Even with identical coils, each coil is sensing a different region of the string. So the amplitude and ratio of fundamental to various harmonics will be quite different on each coil. And we are combining them in a slightly different way. So I would expect a small disparity of tone between the two configurations.

Imagine two identical HBs that have traditional (internal) series connections placed the bridge and neck positions, in parallel with each other. Now connect the two series links together. Will this sound different than when the series links were not joined together? I think so. Will the difference amount to much? Probably not.

[sumgai]

col,

Nice eye, almost a good catch. But, as usual, the devil is in the details.

It so happens that various members of this board have had this discussion, often, in the dim and distant past. Here's the nutshell breakdown:

Without getting into any kind of math, all we need is simple arithmetic for this excercise. Look at the numbers in the small boxes below the count (for each possibility) - those represent the impedance ratios for a given combo, as compared to one single pickup. (Assuming that all four coils are identical.) As a starting point, it's interesting to note that the "standard" combo of two coils in series (one standard pup) in parallel with another such also comes out to "1".

Now, if I can guide your attention to the lowest row, second column, you'll find this exact combo, with the "1" as I've described. Look at all the other combos, you'll not find another ratio of "1". (I'm describing combinations here, not single pups.)

Let us now turn to your diagrams.... Your assignment is to determine what the ratio of inductance will be for each of the three combos, as relative to the standard "1".

For extra credit, explain how they will deliver a different tonality to the output, and thence on to the amplifer/speaker.



This is exactly what newey was speaking to, the fact that Chris never gave anything away without a fight. Well, he did once give some free Unobtanium to JohnH, but that's a story for another day! ;D

HTH




sumgai

[ashcatlt]

Umm...sg? retread and I have covered that. If all the coils are the same then all of these combos come out the same. But that's rarely the case. More often (ie - typical HH configs) we'll have two pairs of coils which are internally close enough to identical but signicantly different between the pairs. Worse, consider newey's 4caster, where (I think) all four coils are different.

There are proofs above.

[col]

Apr 17, 2012 23:24:55 GMT -5 sbgodofmetal said:

Welcome to the nutz house. Were truly sorry to say but chrisk is no longer with us anymore. He has left us with many great articles concepts and ideas many with charts and diagrams. and a few schematics here and there. But feel free to ask any of us about his works a lot of members have been here long enough to explain anything of his to you.

R.I.P. Chrisk.

Hello sbgodofmetal,

I am sorry to learn that ChrisK passed away. I see that he contributed/compiled a hell-of-a-lot of data - it seems he was an interesting guy.

[col]

Hi,

I've read the replies with interest.

I think that there will be little difference between many of the possible configurations already outlined by Chris. Since this was supposed to be an exhaustive list, I just thought I'd point the missing configurations.

I am not an electronics guy, but I understand a few basics. I get the gist about there being little difference between the two circuits if the pickups are (near) identical (the circuit pointed out by me; and a standard in-series pair of coils, and the two pick-ups wired up in parallel, as is common across most HH setups with a three way switch). However, I do question if 'there is little difference in the two examples', for this reason: even if the pickups were theoretically identical, the signal generated by each pickup will be different (since they each sense a different part of the guitar string, or at a different distance from the string). Wouldn't these different signals combine quite differently in the two given arrangements? Just a thought.

Thanks for the replies and detailed information about how to make the calculations, and how to read Chris's tables.

[col]

Apr 18, 2012 12:25:13 GMT -5 reTrEaD said:

Is that the end of the story? Maybe not...

Even with identical coils, each coil is sensing a different region of the string. So the amplitude and ratio of fundamental to various harmonics will be quite different on each coil. And we are combining them in a slightly different way. So I would expect a small disparity of tone between the two configurations.

Imagine two identical HBs that have traditional (internal) series connections placed the bridge and neck positions, in parallel with each other. Now connect the two series links together. Will this sound different than when the series links were not joined together? I think so. Will the difference amount to much? Probably not.

Sorry, I see that my point was already covered by reTrEaD.

[newey]

OK, we're debating apples and oranges here.

ChrisK's original post was detailing all possible combinations of 2, 3 and 4 coils. Certainly, different positions along the strings and differences in the coils will allow for different tones- but Chris' post doesn't have anything to say about tones, only about combinations of coils. He expressly omits "all off" and phasing from consideration, meaning we're talking about explicating all possible series and parallel variants.

I did misread col's diagrams. So we're clear here, we're talking about parallel pairs of coils which are then joined in series- I had it the other way around.

But I still think Chris didn't omit these- they're included as a subset of the series pairs. He indicated that, when we're considering combinations involving all 4 coils, that these number 49 total. If you look at the diagrams he has which show all four coils in various configurations each one has a red number in the second box shown next to each 4-coil diagram. Add all those numbers together, and you indeed get 49 combos.

Mathematically, this is an exercise in matrix algebra, permutations and combinations- and that's about the point where my limited math talents ran head-on into a brick wall.

But if you look at those diagrams which show some coils in series with others in parallel, I don't see how we get to 49 unless the 4 noted by col are included in one of the diagrams which indicates 12 combinations.

Anyway, I can't do the math and I haven't got time to write out 49 combos, but I'll have to do so eventually since col now has me curious!

[ashcatlt]

I personally am talking only about the action of the filter created by the interaction of the resistance, inductance, and self capcitance of this set of coils.

If we start to get into the harmonic content transducer from the strings it gets out a little beyond me. I'm not sure how the different circuits change the way each individual coil contributes to the overall mix. Is the voltage calculation the same as the R calculations? I suppose some leasing with Ibm's law might explain it, but no time right now.

[col]

Hi,

I have a total of 52 possible arrangements with 4 pickups (not including out-of-phase configurations).

The below figures indicate the number of possible arrangements as they relate to the positions in Chris's second table. I created these figures independent of Chris. The three arrangements I described are in addition to the below.

xx xx xx 01
xx xx 04 xx
xx 06 12 04
01 03 06 12

Chris's table indicates three possible arrangements for the "series pairs" - this is correct. This does not include the three possible arrangements for parallel pair of coils, then placed in series, as I described. My and Chris's numbers tally, except the for the missing arrangement I described in my opening post.

[reTrEaD]

Apr 18, 2012 18:55:37 GMT -5 ashcatlt said:

Is the voltage calculation the same as the R calculations?

Good question. I suppose I should plug in some values for disparities in E while holding series R the same for each coil, then compare with and without the series links being bridged. But I'm feeling lazy atm.

[sumgai]

ash,

As noted, we're talking idealized here, nothing real world about the tonality... except that you then went on to ponder the potential differences in potential (sorry, couldn't help that ) for having each coil in a structure located in a different position along the string.

As we concluded many years ago, the overall difference is not noticible to the ear, and likely not to any kind of spectrum analyzer you and I are likely to get our hands on. IOW, the coil sensing the signal at X inches along the string will sense the same amount of energy, and convert it to the same amount of voltage/current, regardless of which way it's connected to the other coils, be it parallel then series, or the other way around.

But I do stress, we're speaking of idealized exactitude in our theoretical coils and pickups here, not what we'd ordinarily find in the real world.

---

All,

I do take it that Chris meant to display all possible combinations here, not just those that are unique in some way. For that reason, I must surmise that he did indeed "miss" some of them. One can only wonder now at his reasoning for this omission.

But then again, this is how Legends are born, right? ;D


+1 to col for making everyone shake their heads in wonder and disbelief at how we could've missed that for so long....




sumgai

[reTrEaD]

Apr 19, 2012 21:25:19 GMT -5 sumgai said:

I do take it that Chris meant to display all possible combinations here, not just those that are unique in some way. For that reason, I must surmise that he did indeed "miss" some of them. One can only wonder now at his reasoning for this omission.

It's possible that it was not an oversight, but was an intentional omission.

DC loop analysis suggests my earlier speculation was WRONG, regarding a difference between parallel pairs in series and series pairs in parallel, based on identical coils and different harmonic structure at each coil. UNLIKE the case where the resistance/inductance is different for each coil, having a different signal on each coil will not produce a disparity in output when the series links are bridged. Even though you can have different voltages at the two "series link" nodes, the output will NOT change when the series links are tied together.

I'll stop short of saying there is no difference between the two, allowing for the possibility that there is something that has been overlooked. But I suspect Chris may have considered this to be a redundancy and intentionally omitted the series combination of parallel pairs.

[col]

From what I've read, there is some disagreement, or argument, as to whether or not there is any theoretical difference between the two circuits, assuming that that the pickups are identical, and the signal generated by the four pickups are identical. But, of course, even if the two arrangements are electronically identical, in reality the signal generated by each pickup will vary quite considerably - I can only surmise that the interplay of the four pickups in the two arrangements will also vary significantly enough to be of interest.

Maybe someone might like to test this is the real world?

What free software is available for testing out these kind of circuits?

Col.

[megi]

I'm thinking it's possible that he has just listed all the types of configuration, and deliberately not shown every arrangement within each type? So for example, with one pickup in series with 2 others in parallel, there would be 3 ways of doing that, but he only shows one diagram. The numbers on the left may then fill in the details re number of ways the diagram can be realized.

[col]

Apr 20, 2012 5:12:05 GMT -5 megi said:

I'm thinking it's possible that he has just listed all the types of configuration, and deliberately not shown every arrangement within each type? So for example, with one pickup in series with 2 others in parallel, there would be 3 ways of doing that, but he only shows one diagram. The numbers on the left may then fill in the details re number of ways the diagram can be realized.

No, ChrisK listed all the permutations for each four-coil configuration. Check the table in my last post; ChrisK's corresponding figures are shown in red and underscored in his diagrams/tables.

[sumgai]

Chris's usual modus operandi was to announce when he was leaving something out, and for what reason. Or sometimes he'd test us with "find the missing combo....." types of postings.

I had first replied that Chris quite possibly laid the 'standard' scheme as the basis for col's "redundant" schemes, and therefore abbreviated the chart. reTrEaD now thinks so too. But I've changed my mind, and I now wonder if Chris really frain-barted and forgot either to list those combos, or to give a reason for not doing so (as he did with the phase option). After all, he stated in all caps the word ALL.... not once, but three times!

Besides, I edited that post, what, five years ago. And do you think I could possibly remember why I did that? Nah, don't bother - I don't know either, anymore.

Growing old with CRS is like a fish with a bicycle - we could both do a lot better without it!





sumgai

[newey]

Well, since no one has shown a matrix-based proof, and since I don't understand that math anyway, I started trying to work it out manually, just by diagramming all the possible combinations.

And, I can't even get to 49, much less to 53, so clearly I'm missing some somewhere- stay tuned, hopefully I can work it all out one way or another.

[col]

Hi Newey,

If you look at Chris's diagrams, and the red underscored figure, this indicates the possible permutations for the given arrangement of four coils.

To work out the number of different permutations, you must discount similar arrangements (parallel or serial two, three or four coils). And such instances should be counted only once, unless other coils in the arrangements can be swapped to create a different circuit, such as the last diagram in Chris's table (I think that's the only one, actually).

So, if you look at my three arrangements, it is the individual pairings that would be counted.

Strictly, from a mathematical point of view, we are not talking about permutations, but combinations within a given four coil arrangement. It is quite difficult to explain. If you try out some pure mathematical examples for calculating combinations and permutations, my explanation will hopefully become more clear.

[newey]

If you look at Chris's diagrams, and the red underscored figure, this indicates the possible permutations for the given arrangement of four coils.

That much I got. And his numbers match up with his total, for the 49 exemplars.

The question is, are there 49 or 53? Or, perhaps, some other number?

It's myself I have to convince, so the math won't help- I understand the problem can be mathematically solved that way, but that won't really help me to understand it as I won't understand the math, at least not without having to revisit some very old math textbook that I never mastered back in the day . . .

[ashcatlt]

It's as simple as looking at the table and asking yourself "is there a picture here which looks like col's?" The answer is "No!"

I didn't want to believe that he had made an error...

[col]

Apr 11, 2008 18:27:27 GMT -5 ChrisK said:

Taken in the full context of ALL possible combinations of 2 coils sans OFF and PHASE, there are 4 variants.

Taken in the full context of ALL possible combinations of 3 coils sans OFF and PHASE, there are 17 variants.


Taken in the full context of ALL possible combinations of 4 coils sans OFF and PHASE, there are 97 variants.

Retrieved these images. Probably not permanent*. Are we going to organise systemic retrieval and saving of these old images? After all, Chris was one (if not, the most) important contributor to Gnuts before his demise, and probably no chance of us getting these images from anywhere else.

* I wonder if these images are from a ProBoards cache? That would make sense. If so, they will certainly go bye-bye at some stage.

[Yogi B]

Nov 28, 2017 12:18:03 GMT -5 col said:

I wonder if these images are from a ProBoards cache? That would make sense. If so, they will certainly go bye-bye at some stage.

No, they are still from Photobucket.

What modifying the URL does is avoid Photobucket redirecting to the "PLEASE UPDATE YOU ACCOUNT..." image, and I can't think of a good reason why they haven't countered this already -- it's likely just an oversight on their part.