{"id":1215,"date":"2016-07-10T13:03:12","date_gmt":"2016-07-10T18:03:12","guid":{"rendered":"http:\/\/android-originals.com\/tulsasound\/?page_id=1215"},"modified":"2016-07-10T13:04:25","modified_gmt":"2016-07-10T18:04:25","slug":"on-changing-the-personality-of-a-guitar-part-2","status":"publish","type":"page","link":"http:\/\/android-originals.com\/tulsasound\/tutorials\/humbucking-pairs\/on-changing-the-personality-of-a-guitar-part-2\/","title":{"rendered":"On Changing the Personality of a Guitar \u2013 Part 2"},"content":{"rendered":"

How Many Ultimate HB Pair Combinations Do K Pickups Have?<\/strong><\/p>\n

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

\u00a0Notes on Humbucking Pair Placement<\/strong><\/a> showed how the ratios of in-phase to contra-phase humbucking pairs among 4 pickups could be changed by changing the number of the same poles up.\u00a0 On Changing the Personality of a Guitar \u2013 Part 1 <\/strong><\/a>suggested that pickups, plugged into fixed positions, with different poles could be moved from spot to spot for other pole arrangements.\u00a0 And that the pickup switching could be rearranged using a cross-point board or switch to maintain a switching progression from warm timbres (tones) to bright.\u00a0 On other words, just like a tone pot.<\/p>\n

Applying Humbucking (HB) Pairs Analysis to the Music-Man St. Vincent Guitar<\/strong><\/a> and Applying Humbucking (HB) Pairs Analysis to the Paul Reed Smith 513 Guitar<\/strong><\/a> showed that using standard humbucker pickups in a humbucking pairs switching system can result in effectively equivalent tones for different HB pairs.\u00a0 How Many Useful Pickup Combinations Can You Get From 5 Coils?<\/strong><\/a> showed a number of different electrical circuit topologies for 2, 3, and 4 coil systems.<\/p>\n

If you have K matched single-coil pickups in fixed positions, we know from combinatorial math and empirical testing that you get K*(K-1)\/2 different combinations of two coils each, which can be either of two topologies, series- or parallel-connected, for a total of K*(K-1) different timbres.\u00a0 But if you start moving the poles around changing the ratio of N to S poles, how many different timbres are actually possible, and how many are equivalents?\u00a0 How many are in-phase?\u00a0 How many are contra-phase?<\/p>\n

K = 2<\/strong><\/p>\n

For the lack of a better term, let\u2019s call that the ultimate number of combinations for K pickups, UK<\/sub>.\u00a0 For the moment, let\u2019s ignore the question of circuit topology.\u00a0 For HB pairs, you just take the number of unique combinations and multiply by 2.\u00a0 For K = 2, the answer almost trivial.\u00a0 You can have either two poles the same (contra-phase) or two poles different (in-phase).<\/p>\n

So U1<\/sub> = 2, and the total number of possible timbres is 2*U1<\/sub> = 4.\u00a0 And because it doesn\u2019t matter if you change the poles of both pickups at the same time, only one of them in one physical position needs to be changed to the opposite pole to change from in-phase to contra-phase and back.\u00a0 Note that this could be done by putting a standard humbucker in place of one of the single coils, and using either one pole or the other.<\/p>\n

K = 3<\/strong><\/h3>\n

K = 3 is a bit more complicated.\u00a0 The math may exist for predicting UK<\/sub>, but it isn\u2019t immediately apparent.\u00a0 For K = 3, only one pole can be different, if any, and it doesn\u2019t matter for this discussion if it is N or S.\u00a0 We know that for K = 3, we can have 3*2\/(2*1) = 3 different HB pairs for each pole setup.\u00a0 We can have either 0 poles different or 1 pole different, since having either 2 N poles or 2 S poles still leaves just 1 pole different.\u00a0 The different pole an be in each of the 3 physical positions, so with that and 0 poles different, we have 4 different pole setups.<\/p>\n

So we start by drawing out all the combinations, and striking out the ones that are effectively the same from the first pole setup in which they appear, to their appearance in the next setup(s).\u00a0 In the tables below, the black rectangle shapes represent pickups with N poles up, and the white, S poles up.\u00a0 Instead of the possibly confusing position designation N, M, B for neck, middle and bridge, we will use A, B and C, with AN meaning A position, N-up, BS meaning B position, S-up, etc.\u00a0 In\u00d8 means in-phase, and con\u00d8 means contra-phase.\u00a0 We take the pairs in the order, AB, AC, & BC, and placed the in-phase and contra-phase pairs in the proper column.<\/p>\n

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In humbucking pairs, AS,BN will produce the same tone as AN,BS, so the second is stricken from the tables, as are all the other similar tones.\u00a0 This leaves U3<\/sub> = 6, with 3 in-phase, and 3 contra-phase.\u00a0 So with the series and parallel topologies, this means that the 4 pole setups can produce 2*U3<\/sub> = 12 unique timbres with humbucking pairs.<\/p>\n

Note that in the last figure, no unique humbucking pairs have been added.\u00a0 So if one were going to replace any single-coil pickups with dual-coil humbuckers, to switch the poles electronically, it would be sufficient to place them in the A and B positions only.\u00a0 Then they would add the 2 in-phase humbucking pairs in those positions, for a total of 8 unique pairs, or 16 humbucking pair timbres, consistent with the analysis in Applying Humbucking (HB) Pairs Analysis to the Paul Reed Smith 513 Guitar<\/strong><\/a>.\u00a0 Which also applies to the Music-Man Game Changer guitar with two humbuckers and a single.<\/p>\n

K = 4<\/strong><\/h3>\n

For K = 4, we use matched single-coil pickups in positions A, B, C and D.\u00a0 The pairs, numbering K*(K-1)\/2 = 6, will be listed in the tables below in the order AB, AC, AD, BC, BD & CD.\u00a0 We start with the pole setup (S,S,S,S); then add one pole and shift it to each position: (N,S,S,S), (S,N,S,S), (S,S,N,S) & (S,S,S,N); then add another pole and shift the two poles to other positions: (N,N,S,S), (N,S,N,S) & (N,S,S,N); until no more unique pairs can be added.\u00a0 Note that these 8 setups suffice, as anything with 3 N poles up will merely mirror the setups with 1 N pole up.<\/p>\n

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Now we see the mathematical pattern for K number of matched single-coil pickups.\u00a0 The total number of possible in-phase pairs is K*(K-1)\/2, and the total number of possible contra-phase pairs is K*(K-1)\/2.\u00a0 So UK<\/sub> = K*(K-1) and the total number unique humbucking tones or timbres is 2* UK<\/sub> = 2* K*(K-1).\u00a0 So for K = 2,3,4,5,\u2026, UK<\/sub> = 2, 6, 12, 20, \u2026, and the number of possible unique timbres is 2* UK<\/sub> = 4, 12, 24, 40, …<\/p>\n

It also appears that it takes only K sets of different pole configurations to obtain UK<\/sub>.\u00a0 Which K sets?\u00a0 It probably doesn\u2019t matter.\u00a0 For K = 2, the possible different sets with unique pole configuration (excluding those mirrored in exchanging N and S), is (S,S) and (N,S), or 2 sets.\u00a0 For K = 3, the possible different sets with unique poles configurations is (S,S,S), (N,S,S), (S,N,S) & (S,S,N), or 4 sets.\u00a0 For K = 4, the possible unique pole configurations are (S,S,S,S), (N,S,S,S), (S,N,S,S), (S,S,N,S), (S,S,S,N), (N,N,S,S), (N,S,N,S) & (N,S,S,N), or 8 sets.<\/p>\n

K = 5<\/strong><\/p>\n

For K = 5, the unique configurations are (S,S,S,S,S), (N,S,S,S,S), (S,N,S,S,S), (S,S,N,S,S), (S,S,S,N,S), (S,S,S,S,N), (N,N,S,S,S), (N,S,N,S,S), (N,S,S,N,S), (N,S,S,S,N), (S,N,N,S,S), (S,N,S,N,S), (S,N,S,S,N), (S,S,N,N,S), (S,S,N,S,N), (S,S,S,N,N), or 16 sets.\u00a0 For 3 N poles of 5, it only mirrors 3 S poles of 5.\u00a0 So the mathematical pattern appears to\u00a0 be for K coils, there are 2^(K-1) or 2 raised to the (K-1) power, K = 2, 3, 4, 5, \u2026 \u00e8 2, 4, 8, 16, \u2026 unique sets of pole configurations.<\/p>\n

It is not immediately apparent how to prove that any K different pole configurations out of 2^(K-1) possible unique pole configurations can produce the maximum number of humbucking pairs and humbucking pair timbres.\u00a0 Other than by writing out all the tables and demonstrating that likelihood by induction, as was done here for UK<\/sub>.\u00a0 This exercise is left to the reader.<\/p>\n

Purpose – a Whole New Universe of Customization
\n<\/strong><\/p>\n

This article only means to show how many different timbres can be expected from K number of single-coil pickups that can each be switched out independently for opposite poles.\u00a0 If for example, you have a guitar with K = 4 pickups, switching between humbucking pairs and serial and parallel connections will give you 12 different timbres for each pole arrangement, and 24 different timbres across all the pole arrangements, of which you probably need only 4 different pole arrangements of the possible 8.<\/p>\n

If the humbucking pair switching is set up to go from warm to bright, the 8 different pole arrangements will give you different progressions from warm to bright.\u00a0 As noted in Part 1<\/strong><\/a>, it is feasible to put a cross-connection board or cross-point switch in between the pickups and the switching to compensate for the pole arrangement to produce switching that goes progressively from warm to bright.<\/p>\n

If you can switch out the poles in this manner, and the switching compensates to produce a progressive order from warm to bright, you have a 4-pickup guitar with 4 to 8 different personalities in timbre.\u00a0 You can go from all contra-phase outputs (with all 4 N poles up, or 4 S poles up), serial and parallel, to 2\/3 in-phase and 1\/3 contra-phase (with 2 N and 2 S poles up), as noted in Notes on Humbucking Pair Placement<\/strong><\/a>.<\/p>\n

If you can further shade the timbres by moving the pickups physically, as in Patent U.S. 2016\/0027422 A1<\/strong><\/a>, then that opens up a whole new universe in customizing the guitar to the guitarist.\u00a0 One that will require a great deal more study and experimentation.<\/p>\n

Take, for example, a decision not to use plug-in pickups, but to place standard humbuckers in positions A, B, and C or D for K = 4, switching the poles electrically instead of physically.\u00a0 This adds a new wrinkle or two.\u00a0 First, that\u2019s 7 coils in the space between the neck and bridge.\u00a0 That\u2019s a lot of coils in a small space.\u00a0 Second, the humbuckers themselves add 6 new timbres (3 each with parallel and serial connections of their 2 poles) to the 24 they can produce in the analysis above for a total of 30.<\/p>\n

Third, let\u2019s say the humbuckers are all mounted with their N poles closer to the neck.\u00a0 That means the NN & SS (and to a lesser extent the NS and SN) connections of single poles between them now have slightly different physical positions than if they had be constructed of single-coil pickups.\u00a0 Are the differences tonally significant, or even audible enough, to nullify the previous strikeouts in the tables above for K =4?<\/p>\n

Only experimentation and verification can tell.<\/p>\n

Legal Notice<\/strong> \u2013 Copyright and patent law (Patent Pending US 2016\/0027422 A1, filed July23, 2014; an undisclosed U.S. Provisional Patent Application, filed June 28, 2016) protection covers the material you see and read here.\u00a0 Here\u2019s how to avoid getting sued:<\/p>\n

    \n
  1. Build it with your own hands for your own personal use, at your own risk<\/li>\n
  2. Do not sell it or make it for sale<\/li>\n
  3. Do not take any money to do it for someone else (unless you are working for a guitar company and making it for evaluation only)<\/li>\n
  4. Do not reproduce it for any and all public distribution<\/li>\n
  5. Provide only links to this site with personal descriptions of how it worked for you<\/li>\n
  6. Do not try to profit from it in any manner, shape or form<\/li>\n
  7. Do not import any guitars containing this technology into the S. without licensing these patents.<\/li>\n<\/ol>\n","protected":false},"excerpt":{"rendered":"

    How Many Ultimate HB Pair Combinations Do K Pickups Have? \u00a9 2016 Don Baker dba android originals LC \u00a0Notes on Humbucking Pair Placement showed how the ratios of in-phase to contra-phase humbucking pairs among 4 pickups could be changed by … 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\/1215"}],"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=1215"}],"version-history":[{"count":14,"href":"http:\/\/android-originals.com\/tulsasound\/wp-json\/wp\/v2\/pages\/1215\/revisions"}],"predecessor-version":[{"id":1238,"href":"http:\/\/android-originals.com\/tulsasound\/wp-json\/wp\/v2\/pages\/1215\/revisions\/1238"}],"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=1215"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}