The Acoustic Guitar Forum

Go Back   The Acoustic Guitar Forum > General Acoustic Guitar and Amplification Discussion > PLAY and Write

Reply
 
Thread Tools
  #16  
Old 01-18-2018, 12:12 AM
rick-slo's Avatar
rick-slo rick-slo is offline
Charter Member
 
Join Date: Nov 2004
Location: San Luis Obispo, CA
Posts: 17,172
Default

Quote:
Originally Posted by Owen David View Post
Interesting point...and even with the same fret locations, different fingering will give a different sound...I know you definitely get a different sound if you bridge the A chord with one finger or if you use three or two fingers.
Different unique fret locations, not different fingering at the same locations.
__________________
Derek Coombs
Youtube -> Website -> Music -> Tabs
Guitars by Mark Blanchard, Albert&Mueller, Paul Woolson, Collings, Composite Acoustics, and Derek Coombs

"Reality is that which when you stop believing in it, doesn't go away."

Woods hands pick by eye and ear
Made to one with pride and love
To be that we hold so dear
A voice from heavens above
Reply With Quote
  #17  
Old 01-18-2018, 12:28 AM
SunnyDee SunnyDee is offline
Registered User
 
Join Date: May 2016
Location: Washington, DC
Posts: 1,031
Default

Quote:
Originally Posted by Owen David View Post
Well the article I quoted refer to gave over 2000 and that was just from what appeared to be a mathematical analysis of the chromatic scale with no allowance for octaves, doubled notes, inversions, harmonics etc etc.

If we are thinking about finger arrangements on a six string fretboard that sound clearly differentiated to the ear, I think we are talking at least in the tens of thousands and probably hundreds of thousands.
If you mean the Digging Deeper article, I looked at it. I'm not sure his reasoning actually answers your question, but, again, it all depends on your definitions.

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.
__________________
"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.
Reply With Quote
  #18  
Old 01-18-2018, 05:11 AM
M19's Avatar
M19 M19 is offline
Charter Member
 
Join Date: Dec 2009
Location: Land of 10,000 Lakes
Posts: 8,551
Default

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.
__________________
Marty
Twin Cities AGF Group on FB
Reply With Quote
  #19  
Old 01-18-2018, 06:57 AM
leew3 leew3 is offline
Charter Member
 
Join Date: Feb 2017
Posts: 2,953
Default

Quote:
Originally Posted by Looburst View Post
I just checked and it's 3,,,,,, if you're in the first month of learning.
and none of them are the dreaded first position F major!
Reply With Quote
  #20  
Old 01-18-2018, 11:24 AM
Owen David Owen David is offline
Registered User
 
Join Date: Jan 2018
Posts: 73
Default

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.

Quote:
Originally Posted by j3ffr0 View Post
I come up with 20,736. Ymmv of course and it is an approximation. Here’s the math:

6 strings raised to the power of 4 (the number of frets within usable reach for an average player). Multiply by the number of positions you feel like someone will play in. I choose 16... open position all the way up to 15th fret.

This doesn’t account for the extended reach many players can achieve or chords using open strings in higher positions. It also doesn’t account for alternate tunings, so 20k is probably a low estimate, but it may be balanced by some possibilities that probably just sound bad no matter the context. So let’s say at least 20,000.

Many will say they cannot memorize. 20,000 chords. Me neither! I took the easy way out and learned theory, so I can build whatever chord I want as long as I can reach the notes I choose.
Reply With Quote
  #21  
Old 01-18-2018, 11:34 AM
Owen David Owen David is offline
Registered User
 
Join Date: Jan 2018
Posts: 73
Default

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.

Quote:
Originally Posted by M19 View Post
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.
Reply With Quote
Reply

  The Acoustic Guitar Forum > General Acoustic Guitar and Amplification Discussion > PLAY and Write

Thread Tools





All times are GMT -6. The time now is 06:38 PM.


Powered by vBulletin® Version 3.8.11
Copyright ©2000 - 2024, vBulletin Solutions Inc.
Copyright ©2000 - 2022, The Acoustic Guitar Forum
vB Ad Management by =RedTyger=