## Wednesday, March 7, 2012

### How Many Guitar Chords Are There? by Shawn Persinger

By the author of

So how many guitar chords are there? Well I need to clarify and be more specific. What I really want to know is how many chords are there period, on all instruments. The issue with sticking to just guitar chords is the fact that you can only play six notes at a time on the guitar (yes I know some guitars have seven strings and you can even retune a 12 string guitar to have all 12 pitches but I’m talking about the most common variety of guitars, in standard tuning) and we all know there are 12 different pitches in music, not counting the different octaves.

Here are my parameters: How many different chords are there, using the 12 different notes found in one octave and playing each note only once? One other qualification/definition: you need at least three different notes to make a chord, no two-note chords allowed, sorry.

As turns out there is actually an easy answer to this question that can be solved with a math equation. Now I am horrible at math but I have a couple of friends, Nick Didkovsky (another guitarist as well as software programmer and professor at NYU) and John Charpie (who is a physicist), who are great at math. To them this equation is simple, to me not so much but the basic idea makes sense. I thank them from the bottom of my heart for helping me out with this chart.

Using the 12 note chromatic scale here are the combination available to us.

1 note = 12 ways (not a chord)
2 notes = 66 (not a chord)

3 notes = 220
4 notes = 495
5 notes = 792
6 notes = 924
7 notes = 792
8 notes = 495
9 notes = 220
10 notes = 66
11 notes = 12
12 notes = 1

Total = 4017 Chords

Playable Guitar Chords = 2431

But this is not correct! Because for every chord there are several ways to play, voice, finger, etc. the chord (depending on the number of notes the number of ways change). These options multiply our base number of 4017 by...well I don't know. I'm sorry. But 4017 is a good place to start.

This perfunctory, almost trivial, musical concept could be viewed as little more than a list of musical statistics. These are nothing more than some mathematical figures (I do not make the claim that music is math, I don’t believe this). But they can give you a sense of how many possibilities musical notes have to offer us and to suggest that very little has actually been done by humans so far. I haven’t even bothered to offer the rhythmic possibilities, as these are infinite.

Below is a chart of the 35, three note chords, available from a seven-note scale (in this case C Major). Here is the disclaimer: I think there are too many chords on this page! It has been proven that the more options humans have the more difficult it is to make a decision. It is highly likely you will play through this chord chart and then never look at again because its practical application is vague at best. I don’t want that too happen. Play through all the chords and then pick one you like and start using it in your everyday playing. Heck play through the first five chords and pick one you like and start using it. Don’t let this chart overwhelm you. While it can be fun, it can also be a lot like reading the dictionary.

Disclaimer 2: This chart contains only one voicing and fingering possibility for each three note chord. For every three note chord there are six different ways to voice them e.g.: 1. C E G, 2. E G C, 3. G C E, 4. C G E, 5. E C G, 6 G E C. You also have the option to duplicate notes in different octaves. While this does not make our options infinite the computation to figure this out is practically useless.

SOME MORE NUMBERS

• Number of three note “chord” combinations available from a seven note diatonic major scale, e.g.: C D E F G A B = 1. C D E, 2. C D F, 3. C D G, etc.

Total number of three note diatonic chords = 35

• Number of four note “chord” combinations available from the seven note diatonic major scale, e.g.: C D E F G A B = 1. C D E F, 2. C D F G, 3. C D G A, etc.

Total number of four note diatonic chords = 35 *

• Number of three note “chord” combinations available from the 12 note chromatic scale, e.g.: C C# D D# E F F# G G# A A# B = 1. C C# D, 2. C C# D#, etc.

Total number of three note chromatic based chords = 220

• Number of four note “chord” combinations available from the 12 note chromatic scale, e.g.: C C# D D# E F F# G G# A A# B = 1. C C# D D#, 2. C C# D# E, etc.

Total number of four note chromatic based chords = 495

• Number of seven note “scale” combinations available from the 12 note chromatic scale, e.g.: C C# D D# E F F# G G# A A# B

Total number of seven note scales = 462

This is simply a list of possible musical alternatives. 99% of all music, and not just Western music but Earth music, is derived from essentially the same half dozen scales and harmonic theory. Ultimately these lists are a topic that require a longer conversation, and more complex theoretical understanding to do them justice, but I wanted to share it to let you, the reader, understand that there is more than one way to carve an octave, melodically and harmonically. And while it is open to question whether these alternative “sound good” I think that is a question that should be answered with an understanding that listeners and players have only experimented with a handful of these options.

* Note: There is a basic mathematical reason that there are the same number of three note chords and four note chords. Given seven notes, every time you choose three, you leave behind four others. So in the process of writing down all of the 3-note combinations, we also leave behind the 4-note ones. If it is not obvious they are different combination, thus equaling 70 different chords.

For more music and numbers and possibilities please visit: The Musical Scale Enumerator

The End.

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