#16
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Different unique fret locations, not different fingering at the same locations.
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#17
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What he does is calculate how many possible unique 3 note combinations of 12 notes there are, meaning the first note is established and you have 11 possibilities for the second note and then 10 possibilities for the third note. In his calculation, order is not a factor. In other words, CEG and EGC are the same. This is how he gets 220. Then he does this for 4, 5, and 6 note combinations. He then adds those numbers for 3, 4, 5, and 6 note combinations together which should be 2431, but he types 2341, which, I assume, is just a typo. So, even if all those were possible chords on the fretboard, the number of combinations in playable shapes would have to be a subset of that number, iow, smaller, but using combinations doesn't take into account at all what forms chords actually take, how many frets there are to play them on, or even that notes are repeated across six strings rather than each note in a 6-string chord being a unique note. In other words, the calculation does not reflect reality. What, I assume, you are referring to when you mention hundreds of thousands of possibilities are permutations rather than combinations. In case anyone doesn't know, "permutations" are combinations that do take order into account so that CEG and EGC are counted as two different things. We do not usually name different voicings/inversions as different chords, but... well... I've mentioned that it depends on your definition. If you just calculated permutations and added them together the way he did, you'd get 773,520, a large number, yes, but, probably, a meaningless one. It doesn't take into account how chords are actually formed. It answers as if once you have a root note any of the other 11 notes are possible, then any of the 10 remaining ones, etc. then counts each group of possible notes in each order as a different unit. It wouldn't take into account how many frets there are for you to play these combinations on or the fact that 6-string chords are not made of 6 unique notes, or ... you get the idea. I don't think that makes much sense. If you wanted to know how many potential voicings of 3 note chords there are, you could use permutations and get 1320, which is correct, but, again, not very useful. Really, for any given scale there are 18-20 useful chord types, less depending on your genre, and there are 5 shapes to play them in, but a good many of those are too hard to reach, and these shapes are all the same for all the keys. So, really, it's entirely doable.
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"Militantly left-handed." Lefty Acoustics Martin 00-15M Taylor 320e Baritone Cheap Righty Classical (played upside down ala Elizabeth Cotten) Last edited by SunnyDee; 01-18-2018 at 01:01 AM. |
#18
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In just the first four frets you have 6 possibilities per string (mute, open and 1-4) and 6 strings which leads to 6 ^ 6 or 46,656. A LOT (majority?) of those would be unplayable of course.
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#19
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and none of them are the dreaded first position F major!
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#20
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Oh yeah - alternative tunings! There's a virtually infinite number via that route...but your figure of 20,736 with standard tuning looks credible to me.
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#21
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Interesting observation...of course, with 19 or more frets in total, on that basis we would be into the hundreds of thousands and of course the playable options should get easier (in the sense of hand stretch) as you go up the fretboard, where the distance between the frets is so much smaller! Maybe something like 300,000 on the basis of your calculation, and taking into account the ease of hand stretch further up.
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