The other day I watched a great video about playing melodies around arpeggios.

What struck me is that there seemed to be insanely many ways to play arpeggios. Of curiosity I calculated it.

Take a regular three note chord, for instance Cm7, consisting of the notes C-E-G-Bb.

This could be rearranged to inverted chords, so that E or G would be the lowest note instead of C. The number of possible combinations can be calculated by the expression

4! = faculty of four = 4*3*2*1 = 24

The number four is the number of notes in the actual chord.

If the guitar had an equal interval between each string we would be done here, but that isn't the case. If we consider standard tuning each of these six chord could be grabbed in three ways right?

Grip one = all with a 4th's (strings E-A-D-G)
Grip two = third on the last (strings A-D-G-B)
Grip three = third in the middle (strings D-G-B-E)

This means it seems we could do the same four note arpeggio in 4! * 3 = 24*3 = 72 ways.

A three note chord would be a bit more merciful, as it could be done in "only" 3! * 3 =3*2*1* 3 = 18 ways.

All this is provided that the lowest note is on the lowest string, because it probably wouldn't make sense to put the highest note on the lowest string and such. But if that is possible to, the number of possible combinations would be multiplied by a faculty of the number of notes again.

This could be dismissed as mathematical mambo-jambo not even worthy for the pit. But, the result could show once again that playing shouldn't be based on learning combinations by heart but rather by ear and rules.

A person who can regonize inverted chord by ear and/or know the intervals of it can soon do all 72 combinations without even thinking much about it, I believe. Learning these combinations by heart would be a waste I think. I however have met many people that sure can play, but they don't really have a clue about what they're doing when I ask. Is that a waste of talent that could be something more, or would higher levels of understandning not fit everybody in this area perhaps?

What do you guys think?

EDIT: When I mean number of ways and combinations, I mean number of grips that reasonably could be used when doing these arpeggios on a guitar with regular tuning.
Last edited by Guitarxor at Jun 26, 2014,
This is the reason I teach my students to simply learn the same scale in 5, or sometimes 7 different positions; then you can play the same arpeggio in 7 positions, and it doesn't particularly matter where you start. This greatly reduces the number, and it's easier to see the greater perspective over the fretboard as a whole. It's a broader take on it, but more easy to incorporate and more easily recognizable.
Wise Man Says: The guitar is obviously female, she's got hips, breasts... and a hole.
UG's Flamenco Club
FretboardToAsh: Would that also include inversed arpeggios in some way (for instance G-E-C), or just "straight chord" arpeggios?
Um...ok. That's great. But what does knowing this fact do in regards to you actually 1) being able to play arpeggios AND 2) how does it help you get the sound in your head?

What I'm getting at is, your mathematical stuff here doesn't actually mean a whole lot, beyond "we have tons of possibilities". It doesn't help you learn to use your ear, so that you can decide when to use this inversion of Cm7 over that other inversion. It doesn't actually give you the technical skills to play arpeggios. So...what purpose does it serve, beyond "HEY, THIS IS COOL! (to you, TS)"?
Quote by Guitarxor
The other day I watched a great video about playing melodies around arpeggios.

What struck me is that there seemed to be insanely many ways to play arpeggios. Of curiosity I calculated it.

Take a regular three note chord, for instance Cm7, consisting of the notes C-E-G-Bb.

cm7 = c eb g bb

i organize my fretboard with 5 positions. i know the arps that fit into each position so i just need 5 mental images of Cm7 for every possibility
Quote by crazysam23_Atax
Um...ok. That's great. But what does knowing this fact do in regards to you actually 1) being able to play arpeggios AND 2) how does it help you get the sound in your head?

What I'm getting at is, your mathematical stuff here doesn't actually mean a whole lot, beyond "we have tons of possibilities". It doesn't help you learn to use your ear, so that you can decide when to use this inversion of Cm7 over that other inversion. It doesn't actually give you the technical skills to play arpeggios. So...what purpose does it serve, beyond "HEY, THIS IS COOL! (to you, TS)"?

Exactly why I wrote this in the original post:

Quote by guitarxor
This could be dismissed as mathematical mambo-jambo not even worthy for the pit. But, the result could show once again that playing shouldn't be based on learning combinations by heart but rather by ear and rules.

What it shows me is that learning a lot of arpeggios by heart probably isn't worth it, as there are to many combination. Therefore another focus of learning probably should be adopted. But I'm not sure so I invite for discussion. A lot of playing has got to be prelearned patterns off course.

Quote by SuperKid
cm7 = c eb g bb

i organize my fretboard with 5 positions. i know the arps that fit into each position so i just need 5 mental images of Cm7 for every possibility

Oops, my typo.

That sounds rational. But, that won't give you any inverse chords by default right? I don't really know if the inverse ones are necessary either and in that case how many, opinions appreciated. That the bottom three strings form an inverse minor chord when fretted equally is something that I've found useful though.
Quote by SirSixString
FretboardToAsh: Would that also include inversed arpeggios in some way (for instance G-E-C), or just "straight chord" arpeggios?

You'll have to forgive my english not being quite broad enough to fully comprehend what you mean. By your example, do you mean playing the larger intervals than simple thirds in a 7th chord, or playing such an arpeggio not starting from the root note, I could be misinterpreting something? In either case the answer would be yes. The patterns span all (6) strings always, so that when an opportunity is presented, they have both the sound and visual in mind already and can take it from there. If they wish a certain rhythmic pattern, or going through the arpeggio with different intervals... I suppose some of them practice this less than others.
Wise Man Says: The guitar is obviously female, she's got hips, breasts... and a hole.
UG's Flamenco Club
Quote by Guitarxor
The other day I watched a great video about playing melodies around arpeggios.

What struck me is that there seemed to be insanely many ways to play arpeggios. Of curiosity I calculated it.

Take a regular three note chord, for instance Cm7, consisting of the notes C-E-G-Bb.

This could be rearranged to inverted chords, so that E or G would be the lowest note instead of C. The number of possible combinations can be calculated by the expression

4! = faculty of four = 4*3*2*1 = 24

The number four is the number of notes in the actual chord.

If the guitar had an equal interval between each string we would be done here, but that isn't the case. If we consider standard tuning each of these six chord could be grabbed in three ways right?

Grip one = all with a 4th's (strings E-A-D-G)
Grip two = third on the last (strings A-D-G-B)
Grip three = third in the middle (strings D-G-B-E)

This means it seems we could do the same four note arpeggio in 4! * 3 = 24*3 = 72 ways.

A three note chord would be a bit more merciful, as it could be done in "only" 3! * 3 =3*2*1* 3 = 18 ways.

All this is provided that the lowest note is on the lowest string, because it probably wouldn't make sense to put the highest note on the lowest string and such. But if that is possible to, the number of possible combinations would be multiplied by a faculty of the number of notes again.

This could be dismissed as mathematical mambo-jambo not even worthy for the pit. But, the result could show once again that playing shouldn't be based on learning combinations by heart but rather by ear and rules.

A person who can regonize inverted chord by ear and/or know the intervals of it can soon do all 72 combinations without even thinking much about it, I believe. Learning these combinations by heart would be a waste I think. I however have met many people that sure can play, but they don't really have a clue about what they're doing when I ask. Is that a waste of talent that could be something more, or would higher levels of understandning not fit everybody in this area perhaps?

What do you guys think?

EDIT: When I mean number of ways and combinations, I mean number of grips that reasonably could be used when doing these arpeggios on a guitar with regular tuning.

It's best not to over-think things.

seriously
I dont think you need to memorize anything if your figuring out a run of melody in arpeggios you do it once and muscle memory that sequence, if your on about improvising best stick to basics any of the caged and dim shapes you know where the intervals are in those shapes and how to get your 2's, 4's and 7's if any of them are relevant to your style
I agree with all the responses above so have nothing new to add on those points.

There are flaws in your reasoning though; too much theory not enough practicality.

Many of those "possibilities" are impossible due to the physical limitations of the human hand.

Try "gripping" the chord Eb7 in the order (from lowest to highest) Eb Db Bb Gb where the bass note is on the D string.

e-14
b-11
g-6
d-1
a---
e---

........
Quote by Guitarxor
That sounds rational. But, that won't give you any inverse chords by default right? I don't really know if the inverse ones are necessary either and in that case how many, opinions appreciated. That the bottom three strings form an inverse minor chord when fretted equally is something that I've found useful though.

Yes it will give you all the inversions you want...all the following chords are tabbed in the same way as above i.e. in this string order...
e
b
g
D
A
E

So...
This A Major chord shape is in first inversion with a bass A on the 5th fret low E string:
5
5
6
7
7
5

The same shape without that bass note on the low E string...
5
5
6
7
7
-
is an A major in second inversion (the lowest note in that chord is the fifth (E) of the A major chord). Similarly, voice the same chord shape using the third of the a major chord (C#) as the lowest note...
5
5
6
-
-
-
and this is an A major in first inversion.

We can play the same chord shape in root position but use a different voicing such as...
-
5
6
7
-
-
Which is an A major triad (A C# E) and is pretty much the same chord shape but gives a different chord voicing.

_______

Similarly...

3
5
4
-
-
-
is an Em in second inversion and if you add a bass note on the second fret of the D string...
3
5
4
2
-
-
It's a regular Em chord in root position.

______
speaking of Em chords...If you play
0
0
0
-
-
-
you have an Em in first inversion which comes from the open Em shape:
0
0
0
2
2
0

If you play
7
8
9
-
-
-
you have an Em in root position which comes from the 7th fret Em barre chord shape:
7
8
9
9
7
-

So yes, if you know those five shapes then through partial fingerings of those five shapes or joining a couple of partial fingerings of some of those shapes together you have every possibility of a triad and it's inversions. If you know where to find the seventh then you have those too.

Then it's just a matter of imagination on how you put it all together.
Si
Sean0913: How?

Quote by FretboardToAsh
You'll have to forgive my english not being quite broad enough to fully comprehend what you mean. By your example, do you mean playing the larger intervals than simple thirds in a 7th chord, or playing such an arpeggio not starting from the root note, I could be misinterpreting something? In either case the answer would be yes. The patterns span all (6) strings always, so that when an opportunity is presented, they have both the sound and visual in mind already and can take it from there. If they wish a certain rhythmic pattern, or going through the arpeggio with different intervals... I suppose some of them practice this less than others.

It's not your english but more likely my question that is vague.

Are your approach similar to that of 20Tigers or what is your method?

Quote by 20Tigers
Many of those "possibilities" are impossible due to the physical limitations of the human hand.

You're right there, good point. I feared that there probably would be some special cases like that. Note that I only wrote that there "appears" to be so and so many combinations But I guess there are still quite many variations available, especially if we consider that we want to be able to do each chord in at least major and minor variations.

All regular chords should be fine though I think.

Quote by 20Tigers
So yes, if you know those five shapes then through partial fingerings of those five shapes or joining a couple of partial fingerings of some of those shapes together you have every possibility of a triad and it's inversions. If you know where to find the seventh then you have those too.

That seems like a great way to learn and memorizing many positions of a triad. I like that is based on prior knowledge, so we won't have to learn everything from scratch. Apparently it's also quite easy to add variations. We also get quite a good overview over what we're doing it seems. Awesome

However, the inversion third - root - fifth can't be extracted via this. Simillarily we cant get that many variations from a varied chord like a 7th chord. Would there be another good method for getting those ones, or do we have to learn it as a special case? Or do we simply not need that many more ways to pluck and arpeggio, perhaps we got enough material already?
You can get every variation and possibility.

Third Root Fifth voicing?

No worries...

Chord shapes have optional fingerings. To keep it simple take the G Major chord shape...

3
3
0
0
2
3

Where the 3 on the B string is optional and it could also be voiced like this...

3
0
0
0
2
3

However if we voice this chord the first way and use just the A G and B string we get...

-
3
0
-
2
-

Which is a G major in first inversion, voiced from low to high Third (B), Root (G), Fifth (D).

We could also find this voicing an octave higher...
10
8
-
9
-
-
Which is of course a G major in first inversion voiced Third (B), Root (G), Fifth (D). If we move this down seven frets we get this...
3
1
-
2
-
-
Which is a C major in first inversion voiced Third (E), Root(C), Fifth (G).

A typical Open C major chord is voiced as follows...
0
1
0
2
3
-

But has an optional chord tone (5th) on the third fret high e string abd can be voiced as follows:
3
1
0
2
3
-
But it's still the same C major chord shape.

So we can see that voicing can be extracted from the CAGED chords.

You want a seventh chord? Sure what type of seventh? A major seventh? Usually achieved by replacing one of the two root notes in the chord shape with a note a half tone lower but you could also replace the fifth in the voicing with a note four frets higher.

Want a dominant seventh? Either lower one of the root notes a whole tone or replace the fifth with a note three semitones higher. Done.
Si
Aha, I'm not that famililar with open string chords but I should probably get going on those soon too. Until now I've only focused on lead playing and barre chords, as I like the generality I get from those. The term CAGED was new to me. I found some guides here on UG, I should probably do some study on this.

Today I played around with inverse chords on a piano (which is sometimes the best instrument to learn guitar playing and music in general I think) and found that two of the minor/major inversions can be found stacking a fourth and minor/major thirds.

As I like to learn fast pull off / hammer on arpeggios on one string I think this can be useful to me. In addition to knowing that a regular major/minor chord is consisting of two thirds, I can now get six chords. I just have to remeber that I have to stack either two different thirds, or a fourth and a third in any combination. For instance, take the C major/minor chords:

C-E-G

C - E - G
major third minor third

E - G - C
minor third - fourth

G - C - E
fourth - major third

C-Eb-G

C - Eb - G
minor third major third

Eb - G - C
major third - fourth

G - C - Eb
forth - minor third

If the lowest note is kept the same (as it will if I do hammer on / pull off arpeggios on one the same string that is ringing open between other notes), I can get many proper chords doing this. Off course, just playing around and taking chances can generate some quiet cool licks but knowing the simple fact above could be of help I think.
there are many ways to play the same note combinations..check out George van Eps..Harmonic Mechanisms for Guitar-this should make you want to burn your guitar...ted greene studied with van eps and likewise shows many possibilities for exploring 3 and 4 note combinations of any chord or melodic patterns for any chord quality in all positions and octaves

but the mechanical memorization of this type of work is in vain unless it is used in a vehicle such as a song structure or improvised solo against a given melody..to do such takes a great deal of time and dedication to achieve this goal..in all keys..van eps and greene did such .. a study of their work is worth the time and effort if your wanting to explore the many possibilities in melodic playing

play well

wolf