How come a guitar has more chords than a piano?

Question

A typical guitar has just 6 strings while a piano has 88. Yet, there are websites claiming to be able to find you as many as 86 MILLION different guitar chords, while for a piano it's only in the thousands. What's going on?

http://www.gootar.com/folder/guitar.html

Answer 1

The piano has every note that can be played on a guitar plus additional notes as well.  So any chord that can be played on a guitar can be played on a piano also.

Answer 2

From a MATHEMATICAL point of view, yes there are more combintions of 88 keys than 6 strings. But also remember you only have 10 fingers. Even if you consider unmusical combintations of notes, each string can play one of 12 unique notes. 12^6 < 3 million. Not even close to 86 million.

Anyway, from a MUSICAL point of view, there is no difference. Any chord (combination of 3 or more notes) that you can play on a guitar, you can also play on the piano. Guitar chords can only consist of a maximum of 6 notes, while you can play much more complicated chords on the piano.

Look at the middle scroll down menu on your link. That gives a list of 48 different chords for each key signature. There are a total of 12 key signatures. That would lead to a total of 576 different chords, not taking into account different cadences and octaves for the same chords. A piano will allow for more variations of a particular chord, because of the ease of fingering and the wider range of octaves.

The misleading thing about that link though is that  a guitar can't really play all those chords. A 13th chord for instance requires 7 notes. How are you doing that on the guitar?

And in addition, the G13 on that site only uses 5 notes. The C and the F are both missing from the Q3 variation which robs the G13 chord of its suspended and dominant 7th effects. The G13 can be played on the piano by playing all 7 white notes. So when you press your forearm on the keyboard, you are actually  playing G13.

See http://ezinearticles.com/?Piano-Lesson-U...

Answer 3

This questions interests me both as a musician and a math geek....

..................

First I'll ignore the practical considerations of having hands of limited size and limited numbers of fingers.

With 88 keys, a piano has a possibility of playing (2^88 - 88*87*86) chords (if we consider a chord to contain at least 3 notes), or exactly

309,485,009,821,345,068,724,122,640 chords.

Needless to say, only a tiny fraction of those chords would be "consonant."

The rest would sound roughly as if one had pushed the instrument down the stairs.

Most guitars have 22 frets and 6 strings. if we also consider the additional possibilities of an open sting, and not playing the string at all, that makes the net number of chords to be 24^6 - 24^3, or

191,089,152.

Since we only have six notes playing at once, these chords wouldn't sound quite as bad as most of the piano chords, some might be quite interesting.

OK, now I'll imagine that a *human being* is actually playing these chords.

The largest interval on a piano that can be played by most people is an octave, or 12 keys. (Rachmaninoff is said to have been able to play larger, and to have written large intervals into his music, but he had HUGE hands...)

Then the number of possible chords on just the left hand, as a rough estimate is...

88*11*10*9*8 = 696,960.

In realistic terms, however, many of those chords would require a superhuman ability to stretch and extend one's fingers, it's probably something more like  

88*11*6*5*3 = 87,120 ,

give or take a few thousands....

if we make the further stipulation, that the hands don't overlap, nor come within an octave of each other. (I'll ignore such "advanced" techniques as using one's elbows, forehead, or feet...or playing more than one key with one finger....) Using both hands, the total comes to perhaps

87,120 * (76*11*6*5*3) = 6,554,908,800?

Keep in mind that there are many more practical considerations here, than the ones I've mentioned... I wouldn't be surprised if the *real* number was smaller by  4 or 5 orders of magnitude....

On a guitar, one can only use 4 fingers, and probably, one can only use a length of the neck about 4 frets from were the pinky is.  You can press down on multiple strings at once with one finger, though....

On second thought, the number of meaningful guitar fingerings is a problem I just don't want to deal with right now.....

~WOMBAT

EDIT:

Obviously, with only six strings, 4 fingers, and a limited number of fingerings, the chordal and musical possibilities on a guitar are much less than a piano. This might explain why guitars tend to sound so banal and pedestrian, while pianos sound so lively, bright, and expansive.... (piano > guitar, lol)

Answer 4

Well, that's a trick question. There are more notes on a guitar because you have about 18 frets for each string giving you about 20 more notes to form 'chords' with than a piano.

That said, it's all nonsense becaus those chords would sound terrible....:-( There are actually only about 50 chords on the guitar that are worth playing and that goes for piano, too.

The books are talking about 1 chord being played in 12 different positions and being 12 different chords etc., etc. Many chords have  4 or 5 names (same chord) so it's easy to come up with 'thousands' of  chords.....:-)

But 50 will cover about everything.