Given I have a 20 fret, six-string guitar, and I can play with four fingers, allowing for barring, if my finger span is 5 frets and I can play any combination notes within this span, also, counting harmonics and open strings, how many different notes and combinations of notes (chords of otherwise) can I make on a guitar?
Um … all of them?
Go here and start counting. Don’t forget to get all the variations of each chord.
If you are willing to embrace different tunings this site will generate over 3,000,000 chords although it will be less with your span restriction.
The number of notes is easy enough. The way most guitars are tuned, you have 20 notes on each string (22 on my guitar but yours has a different number of frets), but most of them overlap. You have 20 notes on the bottom string, 20 notes on the top string, and 5 notes on the second to the top string that aren’t also on the top string, for a grand total of 45 unique notes. With some creative tuning you’d have 20 x 6 or 180 different possible notes but don’t ask me how you’d play much practical music with a setup like that.
Harmonics go out to infinity, but as a pracitcal matter I just tried and I can really only get about 8 or 10 per string. Harmonics sound different than plucked notes, so I don’t know if you want to count these all as seperate notes, in which case you’d add maybe 60 notes to your original count. It’s also possible to hold down the string with one finger then pluck it and hit the string with your thumb to make a harmonic, and that’s really going to add a huge number of notes to your total.
I find statistics unpleasant enough that I have no desire to calculate the possible combinations thing. 99 percent of those “chords” are going to be very unpleasant to the human ear.
None of these chords will sound unpleasant because of its construction. They are all valid chords containing only valid notes. Pick up a guitar and try all the variants of say C major. They will all contain C G and E. Convention is to have C as the lowest note but it is not essential.
I remember reading that there are 42,000 or so possible chord combinations, but in light of don’t ask’s total, this seems rather low. The article must have been referring to a particular tuning.
You are talking about inversions of chords. I thin he means more or less random tones played together. Many will be dissonant.
By “chords” I meant combinations of notes, like what the OP was asking for, not all published lists of chords and their variations like 7ths and 9ths and such which may or may not be a valid chord depending on what style of music and culture you are talking about.
Note that with the use of string bending, you can play chords between the notes. It’s easy enough to play an open D-major-shape with bending to get a chord that’s between Dmajor and D#major. Given this, the answer is inifinity.