{"id":1205,"date":"2016-07-07T20:43:14","date_gmt":"2016-07-08T01:43:14","guid":{"rendered":"http:\/\/android-originals.com\/tulsasound\/?page_id=1205"},"modified":"2016-07-07T20:43:14","modified_gmt":"2016-07-08T01:43:14","slug":"how-many-useful-outputs-from-five-coils","status":"publish","type":"page","link":"http:\/\/android-originals.com\/tulsasound\/tutorials\/humbucking-pairs\/how-many-useful-outputs-from-five-coils\/","title":{"rendered":"How Many Useful Outputs From Five Coils?"},"content":{"rendered":"

How Many Useful Pickup Combinations Can You Get From 5 Coils?<\/strong><\/h3>\n

\u00a9 2016 Don Baker dba android originals LC<\/p>\n

How many possible connections, musically meaningful or not, can you get from 5 electromagnetic coil pickups?\u00a0 More specifically from two humbuckers, one each at the bridge and neck, with a single coil in the middle.\u00a0 If you are going to sell something based upon the many choices you offer, what choices in what order did you pick to offer, and what musical sense to they make?\u00a0 For a simple example, a clear progression from warm to bright, like a tone pot.<\/p>\n

There’s a simple calculation for how many unique combinations you can get of N things taken M at a time, without regard for order of choice: N!\/(M!*(N-M)!), where N! = N*(N-1)*…*2*1.\u00a0 So if you take 5 pickups 2 at a time, you get 5!\/(2!*3!) = 10.\u00a0 Note that the 3! term cancels out of the numerator and it can be written as (5*4)\/(2*1) = 10.<\/p>\n

You can pretty much figure that any odd number of coils is going to have hum.\u00a0 If you restrict your choices to humbucking, only the even number of coils matter.\u00a0 And BTW, if you do contra-phase right, it can be just as rich and bright as any single coil at the bridge.\u00a0 But just for the sake of argument, let\u2019s try to find as many musically meaningful combinations as possible, hum or not.<\/p>\n

For 5 coils taken 1 at a time, there are only 5\/1 = 5 unique combinations, all producing hum.\u00a0 For 5 coils taken 2 at a time, there are 10 unique combinations.\u00a0 Does order matter?\u00a0 No, but the topologies of connections do.\u00a0 Two pickups can only be connected together in two different topological electric circuits, serial and parallel, as shown below.<\/p>\n

\"2016-07-07<\/a>It makes no electrical difference in the signal if pickups A and B are switched in position in the circuit.\u00a0 Because of the differences in magnetic polarity and phase, it does make a difference if the connections of A are reversed or B are reversed, but we\u2019ll pass on that for now, assuming that the connections will be made in whatever way best cancels hum, whether it produces an in-phase or contra-phase signal.\u00a0 So now we have 5 coils taken two at a time with 2 different topologies and no order (or one order only), for 5*2*2 = 20 unique tonal combinations, all capable of humbucking if connected correctly.\u00a0 As noted previously<\/a>, using two humbuckers and a single coil pickup reduces the number of useful humbucking pairs to 16, because the two coils in each humbucker are so close together.<\/p>\n

For 5 coils taken 3 at a time, or (5*4*3)\/(3*2*1) = 10, I found four 3-coil topologies shown below: all serial, all parallel, one in series with a parallel pair, one in parallel with a series pair.<\/p>\n

\"2016-07-07<\/a><\/p>\n

Order does not matter in the first two, nor in the parallel or serial pairs in the other two.\u00a0 For example, it does not matter electrically if you interchange B with C in the Topology 3 drawing.\u00a0 But it does matter if you interchange B or C with A.\u00a0 That gives the three orders, with A, B and C in the A-position in topology 3.\u00a0 The same for topology 4.\u00a0 This means 8 different configurations where topology and order matter.\u00a0 So 10*8 = 80.\u00a0 With hum.<\/p>\n

For 5 coils taken 4 at a time would have just 5 combinations, and a lot more topologies.\u00a0 I found 9 different electrical topologies, shown below, but may have missed something.<\/p>\n

\"2016-07-07<\/a><\/p>\n

In topologies 1 and 2, order does not matter.\u00a0 In topologies 3 and 4, order does not matter within each serial pair and each parallel pair, but the combinations of AB, AC, AD, BC, BD and CD do, but only in one of the pairs, because the same combinations in the other pair are mirror images or repetitions.\u00a0 In other words, AB in the series pair produces the same result as CD in the parallel pair.\u00a0 So the combinations are 4 things taken 2 at a time, 4*3\/(2*1) = 6.\u00a0 In topologies 5 and 6, mirroring means that the only combinations which are unique are AB, AC and AD in one of the pairs.\u00a0 In topology 7, the D position controls the number of combinations, leaving just 4 orders, with D, A, B and C in that position.\u00a0 The same thing occurs in topology 9, with 4 orders.\u00a0 Topology 8 is controlled by the A and D positions, 4 things taken 2 at a time, or 6 different orders.<\/p>\n

So for 5 pickups chosen 4 at a time, there are (1+1+6+6+3+3+4+6+4) = 34 orders, making ((5*4)\/(2*1))*34 = 340 unique combinations.\u00a0 We can safely suppose that topologies 1 to 6 are humbucking.\u00a0 Not so much for topologies 7 to 9.\u00a0 That means 10*(1+1+6+6+3+3) = 200 safe choices out of those 340.\u00a0 It\u2019s not so easy to say that all those choices sound different.\u00a0 Not without testing and verification.\u00a0 The mix of in-phase and contra-phase pairs will likely make the most difference.\u00a0 And the switches necessary to produce these combinations probably won\u2019t be cheap.<\/p>\n

5 coils taken 5 at a time has just 1 unique combination, but I didn’t even try to figure out how many topological variations are possible, as I don’t have any systematic way to produce solutions.\u00a0 But 5 in series should be about 5x the volume of 5 in parallel, maybe.\u00a0 And I don’t doubt they all have some hum.<\/p>\n

Staying with safe humbucking choices of pairs and quads, that leaves 220 choices.\u00a0 Using 2 standard humbuckers for the five coils cuts those down to about 16 choices of humbucking pairs with possibly unique timbres.\u00a0 The number of possibly unique humbucking quads of that 200 is left as an exercise for the reader.\u00a0 Even if all those choices have different timbres, that\u2019s probably more choices that most guitarists would care to fool with.\u00a0 Unless you can create an order to the switching that makes musical sense in musical theory (which I don’t have).<\/p>\n

In my 2014 patent<\/a>, I put an extended fret scale to the sides of the movable pickups<\/a> to assist any calculations of musical theory.\u00a0 The neck pickup sits at the 24th virtual fret, the next is 5 frets down from that, the next 7 frets down from that, and the bridge 12 frets down from that, which turns out to be almost equal spacing.\u00a0 If you pluck a fundamental, you might be able to say something from those spacings about the timbre of the result.\u00a0 But that changes in ways I don’t understand as soon as you finger another fret.<\/p>\n

Furthermore, the way you pick the string makes a difference.\u00a0 I’ve watched strings vibrate in an elliptical orbit (about the relative position of the string at rest), with a rotating major axis that changes amplitude over time in relation to the minor axis.\u00a0 You can see it going from a flat vibration at an angle to the guitar top to a full circle and back.\u00a0 The results of which you can even see in the pickup signal shown on an oscilloscope.\u00a0 I’ve seen strings picked carefully produce and almost perfect triangle wave (well, maybe that was with a non-magnetic sensor).\u00a0 But the research papers I’ve seen tend to reduce string vibration to simple Fourier components, without ever touching on this behavior.\u00a0 I think it’s still an open question.<\/p>\n

Even the calculations here are open to some debate, but only on the merits of the math.\u00a0 If you can demonstrate that I\u2019ve missed something by the math (entirely possible), you win – three points in the competition dunking for toilet paper.<\/p>\n","protected":false},"excerpt":{"rendered":"

How Many Useful Pickup Combinations Can You Get From 5 Coils? \u00a9 2016 Don Baker dba android originals LC How many possible connections, musically meaningful or not, can you get from 5 electromagnetic coil pickups?\u00a0 More specifically from two humbuckers, … Continue reading →<\/span><\/a><\/p>\n","protected":false},"author":1,"featured_media":0,"parent":1179,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"","meta":[],"_links":{"self":[{"href":"http:\/\/android-originals.com\/tulsasound\/wp-json\/wp\/v2\/pages\/1205"}],"collection":[{"href":"http:\/\/android-originals.com\/tulsasound\/wp-json\/wp\/v2\/pages"}],"about":[{"href":"http:\/\/android-originals.com\/tulsasound\/wp-json\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"http:\/\/android-originals.com\/tulsasound\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"http:\/\/android-originals.com\/tulsasound\/wp-json\/wp\/v2\/comments?post=1205"}],"version-history":[{"count":4,"href":"http:\/\/android-originals.com\/tulsasound\/wp-json\/wp\/v2\/pages\/1205\/revisions"}],"predecessor-version":[{"id":1209,"href":"http:\/\/android-originals.com\/tulsasound\/wp-json\/wp\/v2\/pages\/1205\/revisions\/1209"}],"up":[{"embeddable":true,"href":"http:\/\/android-originals.com\/tulsasound\/wp-json\/wp\/v2\/pages\/1179"}],"wp:attachment":[{"href":"http:\/\/android-originals.com\/tulsasound\/wp-json\/wp\/v2\/media?parent=1205"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}