Came up with an interesting one here. I wanted an easy way to be able to compute drop 2 and drop 3 inversions up the neck (if you're not familiar with drop 2 and drop 3 voicings, you'll have to google it, it's a technique for building chords used heavily at Berklee), so that if I forgot a seventh chord shape, I could easily figure it out. From there, I could add the 9th, change it to an open chord, whatever; the idea is to get to the base 7th chord quickly and then do the extensions or alterations.
There are 12 basic inversions of a drop 2 chord available --per octave--. Drop 2 voicing are across four consecutive strings (no skipped strings), so the root of the chord can be on the low D, A, or E strings, and there's four inversions per string; that's 12 shapes. If the B string was tuned consistently, you'd only have to remember four, because they'd repeat from string to string...but that's not the case, so you have to know all the fingerings.
There are 8 basic inversions of a drop 3 chord available per octave. Drop 3 have a set of top 3 strings, then skip a string, and the root is on the next string (the low string). So, the root can either be on the low A string (skipping the D in the chord), or the E string (skipping the A in the chord). Four inversions per string, 2 possible strings to put the root on; 8 shapes.
And that's PER CHORD QUALITY, and we're just talking seventh chords (so major 7, dom 7, minor 7, min 7 flat 5, dim 7). Do the math:
- Drop 2 7th chords: 12 inversions per octave, 5 chord qualities. 60 SHAPES.
- Drop 3 7th chords: 8 inversions per octave, 5 chord qualities. 40 SHAPES.
Technically, because diminished shapes are symmetrical, there's only three drop 2 shapes, and two drop 3 shapes, to memorize. Even then, you're still dealing with dozens of shapes to remember. That sounds really hard...and it is. Interestingly, this seems to be how most guitar players try to do it (ergo the haphazard chord knowledge of your typical guitar player).
There has to be a better way, and I came up with this: note there may be different ways to describe the steps, but these steps are the ones I find easiest to visualize.
Drop 2: 1573. Move second degree from top, to bottom. Move new top degree, to bottom.
Drop 3, 1735. Move the second degree from the top, to the bottom. Switch the order of the new top 2 degrees.
Let's try it:
The drop 2 first inversion voicing for any chord quality is 1,5,7,3 (your starting point). It can be any quality, it doesn't matter, so we'll use minor 7; In E, that'd be E, B, D, G. That's 1, 5, 7, 3.
Apply the formula (algorithm really): Move second from top, to bottom. Move new top, to bottom.
3-3-5
7-5-1
5-1-7
1-7-3
Do it again, second inversion (over the fifth).
5-5-7
1-7-3
7-3-1
3-1-5
Do it again, third inversion (over the 7th).
7-7-1
3-1-5
1-5-3
5-3-7
That's four inversions, which incidentally, you can call, "573 over 1, 715 over 3, 137 over 5, 351 over 7"...which reveals more relationships, like, the interval from the root of the inversion to the note on the top string in a drop 2, is always a 5th, and 5ths are always perfect unless they are altered, like a min7b5 or dim chord). Move the drop 2 form down a string (so start with first inversion voicing on A string) and start the formula all over again to get the four inversions on that string. Move down to the E string, repeat: 12 inversions.
For drop 3, let's start with the first inversion voicing of E minor 7 on the A string, and work the formula: move second-degree-from-the-top, to the bottom of the stack. Switch order of the new top 2 degrees. The starting degree order is 1, 7, 3, 5 (remember, drop 3...you are skipping a string).
5-5-7
3-7-5
7-1-1
1-3-3
Do it again to move from second to third inversion:
7-7-1
5-1-7
1-3-3
3-5-5
Do it again to move from third to fourth inversion:
1-1-3
7-3-1
3-5-5
5-7-7
Again, you could call these, "735 over 1, 157 over 3, 371 over 5, 513 over 7", which reveals relationships like, the interval from the root of the inversion to the note on the top string, is always a 7th of one kind or another).
Now...how do you remember exactly what fret each inversion starts on (what's the inversion root?).
Fortunately, the answer lies in something you probably already know if your still reading, and it applies to both drop 2 and drop 3 voicings: interval stacks.
All interval stacks for 7th chords (chords are built in intervals of thirds, so these are stacked thirds):
- Maj7: maj, min, maj.
- Dom7: maj, min, min.
- Min 7: min, maj, min.
- Min 7 b5, min, min, maj.
- Dim: min, min, min (symmetrical).
In terms of frets:
Any major third is 4 frets away (5, if you include the start fret).
Any minor third is 3 frets away (4, if you include the start fret).
Take E maj 7, which is E, G#, B, D#. Start on first inversion; your are playing chord/root (chord over root). You want to:
- Start on E.
- move to second inversion (chord/3rd). The first interval in a major chord is major third...four frets away. You'll be on G#
- move to the third inversion (chord/5th). The second interval is a minor third....three frets away. From G#, you'll be on B.
-move to the fourth inversion (chord/7th). The third interval is a major third...four frets away. From B, you'll be on D#.
Take diminished chords. The interval stack is minor 3rd, minor 3rd, minor 3rd (symmetrical). Start with first inversion voicing (chord/root).
- Start on E.
- Move up a minor third. G.
- Move up a minor third. Bb
- Move up a minor third. Db.
Put it all together, let's take A maj 7, which is A, C#, E, G#:
- Start with a drop 2 first inversion, 1573. This is chord/root (so you should be fretting an A on the bottom string).
- First interval of a maj 7 chord, is a major third. Move up four frets (C#). The formula for drop 2 gives you 3715. So you've already got the third fingered, and you know what string to find the root on, so finger that A. Now just work out the 7th and 5th.
- Second interval of a maj7 chord, is a minor third. Move up three frets (E). The drop 2 formula gives you 5137. You already have the fifth fingered, you know what string the root belongs on, so finger that A, then work out the 3 and 7.
- Third interval of a maj7 chord, is a major third. Move up four frets (G#). The drop 2 formula gives 7351. You already have the 7th fingered, and know what string the root is supposed to be on, so finger that A, and work out the 3rd and 5th.
For improvising, say you can't work out the "remaining two" quickly; you still have the fundamental tone of the inversion you want to hit, and the root. You can comp that all the way up and down the neck over a given chord voicing. That's snazzy.
Anyway, I've been working with this, and it's paying off, so I decided to write it out, and if you find it helpful, cheers. Chords are starting to naturally look like collections of intervals with harmonic possibilities. And of course the more I do it, the more automatic the fingerings will get, and I'll internalize the order of degrees instead of having to apply the formula. This seems to be a path to where I want to get; seeing the neck as one pattern that applies to everything.
As always, thanks for visiting.
Sunday, July 18, 2010
Work out all drop 2 and drop 3 7th chord inversions of any quality (maj, min, min7b5, dim) without remembering shapes.
Came up with an interesting one here. I wanted an easy way to be able to compute drop 2 and drop 3 inversions up the neck (if you're not familiar with drop 2 and drop 3 voicings, you'll have to google it, it's a technique for building chords used heavily at Berklee), so that if I forgot a seventh chord shape, I could easily figure it out. From there, I could add the 9th, change it to an open chord, whatever; the idea is to get to the base 7th chord quickly and then do the extensions or alterations.
There are 12 basic inversions of a drop 2 chord available --per octave--. Drop 2 voicing are across four consecutive strings (no skipped strings), so the root of the chord can be on the low D, A, or E strings, and there's four inversions per string; that's 12 shapes. If the B string was tuned consistently, you'd only have to remember four, because they'd repeat from string to string...but that's not the case, so you have to know all the fingerings.
There are 8 basic inversions of a drop 3 chord available per octave. Drop 3 have a set of top 3 strings, then skip a string, and the root is on the next string (the low string). So, the root can either be on the low A string (skipping the D in the chord), or the E string (skipping the A in the chord). Four inversions per string, 2 possible strings to put the root on; 8 shapes.
And that's PER CHORD QUALITY, and we're just talking seventh chords (so major 7, dom 7, minor 7, min 7 flat 5, dim 7). Do the math:
- Drop 2 7th chords: 12 inversions per octave, 5 chord qualities. 60 SHAPES.
- Drop 3 7th chords: 8 inversions per octave, 5 chord qualities. 40 SHAPES.
Technically, because diminished shapes are symmetrical, there's only three drop 2 shapes, and two drop 3 shapes, to memorize. Even then, you're still dealing with dozens of shapes to remember. That sounds really hard...and it is. Interestingly, this seems to be how most guitar players try to do it (ergo the haphazard chord knowledge of your typical guitar player).
There has to be a better way, and I came up with this: note there may be different ways to describe the steps, but these steps are the ones I find easiest to visualize.
Drop 2: 1573. Move second degree from top, to bottom. Move new top degree, to bottom.
Drop 3, 1735. Move the second degree from the top, to the bottom. Switch the order of the new top 2 degrees.
Let's try it:
The drop 2 first inversion voicing for any chord quality is 1,5,7,3 (your starting point). It can be any quality, it doesn't matter, so we'll use minor 7; In E, that'd be E, B, D, G. That's 1, 5, 7, 3.
Apply the formula (algorithm really): Move second from top, to bottom. Move new top, to bottom.
3-3-5
7-5-1
5-1-7
1-7-3
Do it again, second inversion (over the fifth).
5-5-7
1-7-3
7-3-1
3-1-5
Do it again, third inversion (over the 7th).
7-7-1
3-1-5
1-5-3
5-3-7
That's four inversions, which incidentally, you can call, "573 over 1, 715 over 3, 137 over 5, 351 over 7"...which reveals more relationships, like, the interval from the root of the inversion to the note on the top string in a drop 2, is always a 5th, and 5ths are always perfect unless they are altered, like a min7b5 or dim chord). Move the drop 2 form down a string (so start with first inversion voicing on A string) and start the formula all over again to get the four inversions on that string. Move down to the E string, repeat: 12 inversions.
For drop 3, let's start with the first inversion voicing of E minor 7 on the A string, and work the formula: move second-degree-from-the-top, to the bottom of the stack. Switch order of the new top 2 degrees. The starting degree order is 1, 7, 3, 5 (remember, drop 3...you are skipping a string).
5-5-7
3-7-5
7-1-1
1-3-3
Do it again to move from second to third inversion:
7-7-1
5-1-7
1-3-3
3-5-5
Do it again to move from third to fourth inversion:
1-1-3
7-3-1
3-5-5
5-7-7
Again, you could call these, "735 over 1, 157 over 3, 371 over 5, 513 over 7", which reveals relationships like, the interval from the root of the inversion to the note on the top string, is always a 7th of one kind or another).
Now...how do you remember exactly what fret each inversion starts on (what's the inversion root?).
Fortunately, the answer lies in something you probably already know if your still reading, and it applies to both drop 2 and drop 3 voicings: interval stacks.
All interval stacks for 7th chords (chords are built in intervals of thirds, so these are stacked thirds):
- Maj7: maj, min, maj.
- Dom7: maj, min, min.
- Min 7: min, maj, min.
- Min 7 b5, min, min, maj.
- Dim: min, min, min (symmetrical).
In terms of frets:
Any major third is 4 frets away (5, if you include the start fret).
Any minor third is 3 frets away (4, if you include the start fret).
Take E maj 7, which is E, G#, B, D#. Start on first inversion; your are playing chord/root (chord over root). You want to:
- Start on E.
- move to second inversion (chord/3rd). The first interval in a major chord is major third...four frets away. You'll be on G#
- move to the third inversion (chord/5th). The second interval is a minor third....three frets away. From G#, you'll be on B.
-move to the fourth inversion (chord/7th). The third interval is a major third...four frets away. From B, you'll be on D#.
Take diminished chords. The interval stack is minor 3rd, minor 3rd, minor 3rd (symmetrical). Start with first inversion voicing (chord/root).
- Start on E.
- Move up a minor third. G.
- Move up a minor third. Bb
- Move up a minor third. Db.
Put it all together, let's take A maj 7, which is A, C#, E, G#:
- Start with a drop 2 first inversion, 1573. This is chord/root (so you should be fretting an A on the bottom string).
- First interval of a maj 7 chord, is a major third. Move up four frets (C#). The formula for drop 2 gives you 3715. So you've already got the third fingered, and you know what string to find the root on, so finger that A. Now just work out the 7th and 5th.
- Second interval of a maj7 chord, is a minor third. Move up three frets (E). The drop 2 formula gives you 5137. You already have the fifth fingered, you know what string the root belongs on, so finger that A, then work out the 3 and 7.
- Third interval of a maj7 chord, is a major third. Move up four frets (G#). The drop 2 formula gives 7351. You already have the 7th fingered, and know what string the root is supposed to be on, so finger that A, and work out the 3rd and 5th.
For improvising, say you can't work out the "remaining two" quickly; you still have the fundamental tone of the inversion you want to hit, and the root. You can comp that all the way up and down the neck over a given chord voicing. That's snazzy.
Anyway, I've been working with this, and it's paying off, so I decided to write it out, and if you find it helpful, cheers. Chords are starting to naturally look like collections of intervals with harmonic possibilities. And of course the more I do it, the more automatic the fingerings will get, and I'll internalize the order of degrees instead of having to apply the formula. This seems to be a path to where I want to get; seeing the neck as one pattern that applies to everything.
As always, thanks for visiting.
There are 12 basic inversions of a drop 2 chord available --per octave--. Drop 2 voicing are across four consecutive strings (no skipped strings), so the root of the chord can be on the low D, A, or E strings, and there's four inversions per string; that's 12 shapes. If the B string was tuned consistently, you'd only have to remember four, because they'd repeat from string to string...but that's not the case, so you have to know all the fingerings.
There are 8 basic inversions of a drop 3 chord available per octave. Drop 3 have a set of top 3 strings, then skip a string, and the root is on the next string (the low string). So, the root can either be on the low A string (skipping the D in the chord), or the E string (skipping the A in the chord). Four inversions per string, 2 possible strings to put the root on; 8 shapes.
And that's PER CHORD QUALITY, and we're just talking seventh chords (so major 7, dom 7, minor 7, min 7 flat 5, dim 7). Do the math:
- Drop 2 7th chords: 12 inversions per octave, 5 chord qualities. 60 SHAPES.
- Drop 3 7th chords: 8 inversions per octave, 5 chord qualities. 40 SHAPES.
Technically, because diminished shapes are symmetrical, there's only three drop 2 shapes, and two drop 3 shapes, to memorize. Even then, you're still dealing with dozens of shapes to remember. That sounds really hard...and it is. Interestingly, this seems to be how most guitar players try to do it (ergo the haphazard chord knowledge of your typical guitar player).
There has to be a better way, and I came up with this: note there may be different ways to describe the steps, but these steps are the ones I find easiest to visualize.
Drop 2: 1573. Move second degree from top, to bottom. Move new top degree, to bottom.
Drop 3, 1735. Move the second degree from the top, to the bottom. Switch the order of the new top 2 degrees.
Let's try it:
The drop 2 first inversion voicing for any chord quality is 1,5,7,3 (your starting point). It can be any quality, it doesn't matter, so we'll use minor 7; In E, that'd be E, B, D, G. That's 1, 5, 7, 3.
Apply the formula (algorithm really): Move second from top, to bottom. Move new top, to bottom.
3-3-5
7-5-1
5-1-7
1-7-3
Do it again, second inversion (over the fifth).
5-5-7
1-7-3
7-3-1
3-1-5
Do it again, third inversion (over the 7th).
7-7-1
3-1-5
1-5-3
5-3-7
That's four inversions, which incidentally, you can call, "573 over 1, 715 over 3, 137 over 5, 351 over 7"...which reveals more relationships, like, the interval from the root of the inversion to the note on the top string in a drop 2, is always a 5th, and 5ths are always perfect unless they are altered, like a min7b5 or dim chord). Move the drop 2 form down a string (so start with first inversion voicing on A string) and start the formula all over again to get the four inversions on that string. Move down to the E string, repeat: 12 inversions.
For drop 3, let's start with the first inversion voicing of E minor 7 on the A string, and work the formula: move second-degree-from-the-top, to the bottom of the stack. Switch order of the new top 2 degrees. The starting degree order is 1, 7, 3, 5 (remember, drop 3...you are skipping a string).
5-5-7
3-7-5
7-1-1
1-3-3
Do it again to move from second to third inversion:
7-7-1
5-1-7
1-3-3
3-5-5
Do it again to move from third to fourth inversion:
1-1-3
7-3-1
3-5-5
5-7-7
Again, you could call these, "735 over 1, 157 over 3, 371 over 5, 513 over 7", which reveals relationships like, the interval from the root of the inversion to the note on the top string, is always a 7th of one kind or another).
Now...how do you remember exactly what fret each inversion starts on (what's the inversion root?).
Fortunately, the answer lies in something you probably already know if your still reading, and it applies to both drop 2 and drop 3 voicings: interval stacks.
All interval stacks for 7th chords (chords are built in intervals of thirds, so these are stacked thirds):
- Maj7: maj, min, maj.
- Dom7: maj, min, min.
- Min 7: min, maj, min.
- Min 7 b5, min, min, maj.
- Dim: min, min, min (symmetrical).
In terms of frets:
Any major third is 4 frets away (5, if you include the start fret).
Any minor third is 3 frets away (4, if you include the start fret).
Take E maj 7, which is E, G#, B, D#. Start on first inversion; your are playing chord/root (chord over root). You want to:
- Start on E.
- move to second inversion (chord/3rd). The first interval in a major chord is major third...four frets away. You'll be on G#
- move to the third inversion (chord/5th). The second interval is a minor third....three frets away. From G#, you'll be on B.
-move to the fourth inversion (chord/7th). The third interval is a major third...four frets away. From B, you'll be on D#.
Take diminished chords. The interval stack is minor 3rd, minor 3rd, minor 3rd (symmetrical). Start with first inversion voicing (chord/root).
- Start on E.
- Move up a minor third. G.
- Move up a minor third. Bb
- Move up a minor third. Db.
Put it all together, let's take A maj 7, which is A, C#, E, G#:
- Start with a drop 2 first inversion, 1573. This is chord/root (so you should be fretting an A on the bottom string).
- First interval of a maj 7 chord, is a major third. Move up four frets (C#). The formula for drop 2 gives you 3715. So you've already got the third fingered, and you know what string to find the root on, so finger that A. Now just work out the 7th and 5th.
- Second interval of a maj7 chord, is a minor third. Move up three frets (E). The drop 2 formula gives you 5137. You already have the fifth fingered, you know what string the root belongs on, so finger that A, then work out the 3 and 7.
- Third interval of a maj7 chord, is a major third. Move up four frets (G#). The drop 2 formula gives 7351. You already have the 7th fingered, and know what string the root is supposed to be on, so finger that A, and work out the 3rd and 5th.
For improvising, say you can't work out the "remaining two" quickly; you still have the fundamental tone of the inversion you want to hit, and the root. You can comp that all the way up and down the neck over a given chord voicing. That's snazzy.
Anyway, I've been working with this, and it's paying off, so I decided to write it out, and if you find it helpful, cheers. Chords are starting to naturally look like collections of intervals with harmonic possibilities. And of course the more I do it, the more automatic the fingerings will get, and I'll internalize the order of degrees instead of having to apply the formula. This seems to be a path to where I want to get; seeing the neck as one pattern that applies to everything.
As always, thanks for visiting.
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