Oscar South Posted July 7, 2015 Share Posted July 7, 2015 I'm working on a ridiculous and overblown study at the moment: I'm attempting to exhaustively isolate, define and practically organise every possible harmonic combination of bass guitar overtones played over a fundamental root. I'll share the info in time, as it forms into something worthwhile (it's currently just a mass of scrawled out notes and half finished spreadsheets). Anyway this section of the study is easy enough, just methodical and time consuming. What I'm looking for assistance with is that I want to acknowledge and incorporate the research other players have done in this field, whether it be through teaching materials or through their practice as research. My request is: "Can anyone willing please share with me any players who explore this style, any materials teaching or expanding on it, any insights or considerations that you think are relevant, and so forth.." Thanks very much, and I'll post updates on the progress as I go! Oscar Quote Link to comment Share on other sites More sharing options...
alyctes Posted July 7, 2015 Share Posted July 7, 2015 Blimey Sorry, I can't add anything but good wishes. Quote Link to comment Share on other sites More sharing options...
3below Posted July 7, 2015 Share Posted July 7, 2015 [quote name='Oscar South' timestamp='1436268994' post='2816529'] I'm working on a ridiculous and overblown study at the moment: I'm attempting to exhaustively isolate, define and practically organise every possible harmonic combination of bass guitar overtones played over a fundamental root. [/quote] Can you explain in more detail what you mean by 'harmonic combination'. To my way of thinking as this stands it is a Physics / Maths problem. Quote Link to comment Share on other sites More sharing options...
JoeEvans Posted July 7, 2015 Share Posted July 7, 2015 Do you mean so that one string of four is just plucked to provide a root, then the other three are played with different harmonics? Quote Link to comment Share on other sites More sharing options...
leschirons Posted July 7, 2015 Share Posted July 7, 2015 Well, with the 1st reply being an apology, the 2nd and 3rd starting with "Can you explain?...... and "Do you mean?....... and me sitting here thinking "Eh?" It ain't looking good Quote Link to comment Share on other sites More sharing options...
HowieBass Posted July 7, 2015 Share Posted July 7, 2015 Unfortunately I'm also scratching my head here wondering what on earth this is supposed to be about. Are we talking Fourier transforms? Quote Link to comment Share on other sites More sharing options...
landwomble Posted July 7, 2015 Share Posted July 7, 2015 I'd be amazed if this wasn't a solved problem. Quote Link to comment Share on other sites More sharing options...
DaveFry Posted July 7, 2015 Share Posted July 7, 2015 [url="http://haakonthelin.com/multiphonics/multiphonics-on-the-double-bass/definitions/introduction-to-multiphonics-on-the-double-bass#Content-of-this-survey"]http://haakonthelin....-of-this-survey[/url] Quote Link to comment Share on other sites More sharing options...
HowieBass Posted July 7, 2015 Share Posted July 7, 2015 [quote name='DaveFry' timestamp='1436300079' post='2816937'] [url="http://haakonthelin.com/multiphonics/multiphonics-on-the-double-bass/definitions/introduction-to-multiphonics-on-the-double-bass#Content-of-this-survey"]http://haakonthelin....-of-this-survey[/url] [/quote] That's interesting, muting the partials to achieve colouration. I wonder if the OP is more interested in additive synthesis, adding partials to the fundamental to create timbre. https://en.wikipedia.org/wiki/Additive_synthesis Quote Link to comment Share on other sites More sharing options...
3below Posted July 7, 2015 Share Posted July 7, 2015 (edited) [quote name='HowieBass' timestamp='1436293542' post='2816853'] Unfortunately I'm also scratching my head here wondering what on earth this is supposed to be about. Are we talking Fourier transforms? [/quote] Fourier transforms +1 answer So much I have forgotten in the mists of time. Edited July 7, 2015 by 3below Quote Link to comment Share on other sites More sharing options...
Oscar South Posted July 8, 2015 Author Share Posted July 8, 2015 Thanks for the couple of links guys, very interesting stuff to read and take on board. Correct that I'm essentially figuring out every possible variation of three natural overtones in combination with a stopped tone (on any of the four strings) and defining what harmonic structure it forms. I'll also organising them into keys and plan to touch on expanding the practicalities of the shapes.. all you have to do to blow the roof off harmonically is introduce the possibility of moving one of the natural tones using an artificial harmonic, so I'll see how much depth I can get into with that. I don't expect it to be as exhaustive as the other areas! I've found various 'chord dictionary' type things for natural harmonics and plenty of online lessons and things like that which touch on it. Lots of players that have pieces written using some of the structures. I've never found anything exhaustive however. Either way, the real purpose of this for myself is the process.. the level of detail I'm going into means that I've got a whole lot of overtone shapes and their harmonic implication imprinted into my brain and under my fingers!! (and everything else on paper should I need it) I'll share some of the work as I get into it, I've done most of the deriving and am just filling in (many) blanks on spreadsheets currently. Quote Link to comment Share on other sites More sharing options...
jazzyvee Posted July 8, 2015 Share Posted July 8, 2015 Off the cuff, the only player I can think of who might be into that stuff is Michael Manring. Quote Link to comment Share on other sites More sharing options...
3below Posted July 8, 2015 Share Posted July 8, 2015 [quote name='Oscar South' timestamp='1436316504' post='2817072'] Thanks for the couple of links guys, very interesting stuff to read and take on board. Correct that I'm essentially figuring out every possible variation of three natural overtones in combination with a stopped tone (on any of the four strings) and defining what harmonic structure it forms. I'll also organising them into keys and plan to touch on expanding the practicalities of the shapes.. I've done most of the deriving and am just filling in (many) blanks on spreadsheets currently. [/quote] As far as my understanding goes (and I am still not sure I fully understand) you are looking at the combination of a plucked string (the stopped tone) and combination of the available harmonics? The availability of harmonics is presumably limited by finger reach. I would be interested to know the methodology you have developed to find solutions. My first step would be to start with the available harmonics since these are defined both in frequency and position by the the frequency and length of the string. I would then mathematically define what frets (and thus frequencies) are physically available in the proximity of the harmonic. It would then be possible to program a solution to generate the combinations. These would have to be limited to sane (physical number of fingers, location of fingers etc.) conditions. An interesting problem Quote Link to comment Share on other sites More sharing options...
Norris Posted July 8, 2015 Share Posted July 8, 2015 Are you just talking about harmonics of root, third & fifth? Major/minor keys? Other modes? Quote Link to comment Share on other sites More sharing options...
Oscar South Posted July 8, 2015 Author Share Posted July 8, 2015 (edited) I'm looking at the combination of 3 open overtones and one stopped tone acting as a root. I'm not considering what stopped notes/overtones are reachable because the harmonics occur in multiple points on the string and don't need to be stopped, so you can just leave them ringing and then hit the root (5+ string basses also have more stoppable notes available under a hand span). I'm considering the first 5 overtones above the fundamental in this study (so up to the b7 of the fundamental). I do plan to expand to 6 string guitar and 6 string bass later, but for the purposes of this first exploration I'm looking at EADG and EAEGB (the solo tuning I perform in) [attachment=195888:20150708_114512.jpg] [attachment=195889:20150708_114655.jpg] [attachment=195890:20150708_114726.jpg] Eventually I'll collate all this info into a coherent format that documents the process and results! Edited July 8, 2015 by Oscar South Quote Link to comment Share on other sites More sharing options...
3below Posted July 9, 2015 Share Posted July 9, 2015 [quote name='Oscar South' timestamp='1436354187' post='2817345'] I'm looking at the combination of 3 open overtones and one stopped tone acting as a root. I'm not considering what stopped notes/overtones are reachable because the harmonics occur in multiple points on the string and don't need to be stopped, so you can just leave them ringing and then hit the root ... [/quote] A good point about not being concerned about reachable root notes - obvious really, don't know how I missed that. I am getting the mathematical problem solving itch Quote Link to comment Share on other sites More sharing options...
TimR Posted July 9, 2015 Share Posted July 9, 2015 (edited) Why don't you just list the overtones on each string so you have three sets nG, nD, nA where n is the number of tones in each set. The total number of chordal tones will be 12 x nA x nD x nG. Only a limited number of them will be traditional western chords. I don't see a mathematical solution to this you'll just have to solve it by brute force. Edited July 9, 2015 by TimR Quote Link to comment Share on other sites More sharing options...
3below Posted July 9, 2015 Share Posted July 9, 2015 (edited) [quote name='TimR' timestamp='1436447391' post='2818220'] Why don't you just list the overtones on each string so you have three sets nG, nD, nA where n is the number of tones in each set. The total number of chordal tones will be 12 x nA x nD x nG. Only a limited number of them will be traditional western chords. I don't see a mathematical solution to this you'll just have to solve it by brute force. [/quote] Agree there may not be a full mathematical solution, but partial solutions which will help devising algorithms to aid brute force solutions. On the initial boundary condition of 5 harmonics, using your calculation give 12x5x5x5 = 1500 possibilities, some of which will be duplicates. With a bit of internet research the following emerges, 'Michael Keith "From Polychords to Polya: Adventures in Musical Combinatorics," computed that for the equal tempered scale there are 351 essentially different chords'. I just wonder if set theory might provide solutions but my mathematics is not that sharp any more. Off to think a bit more, reaching for brute force implement which will be the quick way. Edited July 9, 2015 by 3below Quote Link to comment Share on other sites More sharing options...
TimR Posted July 9, 2015 Share Posted July 9, 2015 You can't have 5x5x5 possibilities. As that would imply that you have 15 tones. There are only 12 so there must be tones used twice. Possibly you could have 12x5x4x3 If including octaves. Otherwise you'd have 12x4x3x2 = 288. Quote Link to comment Share on other sites More sharing options...
3below Posted July 9, 2015 Share Posted July 9, 2015 Gets better and simpler all the time In my defence I did mention duplicates (which would emerge in computation) however you have expressed it much more elegantly and succinctly. Quote Link to comment Share on other sites More sharing options...
TimR Posted July 9, 2015 Share Posted July 9, 2015 (edited) If you're also looking at tritones you might be only considering pairs that make up 3rds and flattened 3rds in the A string and 5ths and aug5ths on the D string. But that may be restricting it too much. Edited July 9, 2015 by TimR Quote Link to comment Share on other sites More sharing options...
Oscar South Posted July 9, 2015 Author Share Posted July 9, 2015 (edited) Cheers for the input guys!! There's so much interesting info here to digest and think about and it's great to see that people are interested. As far as actually figuring out all the possibilities to analyse, I just approached it logically and methodically. Right now I'm working through defining what harmonic implication all the possible structures imply (see the preview of the start if the spreadsheet above!). Any anyone who mentioned it is absolutely correct.. There is no 'mathematical' solution to a problem like this, it's more of a process. Here is the opening statements from the work attached (it's a little tongue in cheek ): Edited July 9, 2015 by Oscar South Quote Link to comment Share on other sites More sharing options...
lojo Posted July 10, 2015 Share Posted July 10, 2015 42? Quote Link to comment Share on other sites More sharing options...
BlueJazz Posted November 1, 2015 Share Posted November 1, 2015 Hi Guys, You might like to watch the video below. All the harmonic combinations possible were comprehensively codified by Slonimsky in his book, which you can find here: http://www.u.arizona.edu/~gross/Slonimsky/Thesaurus.of.Scales.And.Melodic.Patterns.Nicolas.Slonimsky.pdf for free. The video below shows you how to make use of just one of these harmonic patterns for a 7b9 scale over a major dominant scale e.g. G7 Fascinating but a life's work of practicing and soloing Happy harmonising ... BlueJazz [color=#EAE2EE][font=Roboto, Arial, Helvetica, sans-serif][size=2][url="https://youtu.be/-Pr68duMGn4"][color=#EAE2EE]https://youtu.be/-Pr68duMGn4[/color][/url][/size][/font][/color] Quote Link to comment Share on other sites More sharing options...
JapanAxe Posted November 1, 2015 Share Posted November 1, 2015 I remember reading something by Robert Fripp, many years ago (1980s?), where he says something along these lines: 'Every note on the guitar produces a harmonic of an octave, a 5th above that, a 4th above that, etc. When you play 2 notes together, each of those notes produces such a harmonic series, and many of the harmonics will clash. With a 3-note chord, things could get seriously out of hand.' Is that what you mean? Quote Link to comment Share on other sites More sharing options...
Recommended Posts
Join the conversation
You can post now and register later. If you have an account, sign in now to post with your account.