Sitting in with the 8 Mile Band

Another first: first, er, "public performance" since arriving in Alaska.

Larry Staehle and the 8 Mile Band graciously tolerated my sitting in with them as they played for KPC's holiday gathering, and it was a good time. Repertoire was mostly cover tunes in I-IV-V type progressions--you know, all the stuff I have next to no experience with. There might have been one tune I had actually played before in a similar context, so I spent most of my time decorating and hoping like hell I would stay out of the way of whoever was in front. Instrumentation was two guitars, violin, flute/sax, bass, and percussion, with me on mandolin, mostly in the second octave. I brought my SWR California Blonde amp but ended up running mostly through the mains anyway, using the old DOD AcousTEC for a little slapback delay and feedback control.

It was the usual array of terrors. If I can hear myself, am I too loud? Am I in tune? Okay, I've found some nice phrases here but am I treading on someone else's toes? Can I try a little chromaticism here before they change chords--and when is that going to be, anyway? Larry seemed encouraging (he was gracious enough to call out keys for every tune) and everyone was friendly to me, but it definitely felt like I had just started to get comfortable by the time it was winding down. I am so happy to understand how to find triads and sevenths anywhere on the board, else I'd have been totally lost!

Probably the best moment of the night (for me, at least!) was when folks started to pack up, and Larry just started a little noodly riff on his own, D centric. I reacted instantly and a minor 'something' happened. I walked all over Dm territory, relishing a couple of nice setups for hanging on a big fat major-seventh, and Larry said, "let's do that again, call a key." I immediately said Gm and started incorporating a few favorite chords (diatonic sevenths and alterations), and at some point I realized that the sax player was joining. Nice! I apologized later as I was ranging considerably over several different scales and she could not have had an easy time figuring out where I was. I went back to a couple of chords that should have settled things down (Ebmaj7 and Bbmaj7) but things broke down about then and the moment passed. Dang. I'm scared witless of the I-IV-V and triadic stuff but give me improv in Gm, with enough space to really hear each other, and I'll go!

It sounds like this band plays area venues quite commonly, and I hope I might get another chance to sit in, even if it's a practice. Going so far out of my comfort zone and into unfamiliar territory is good for me, and I might even get better at learning how to fit in with tunes people know. I'm crossing fingers.

Thanks, Larry, and everyone in the band, for letting me sit in. If we get to do this again, I guarantee I learned some things that should make my next contributions better!

Fretless revision 1

The fretless guitar has been revised to cure the high spot on the fingerboard. A bit of judicious time with sandpaper has proven fruitful and educational.

The diagnosis was a high spot in the region of "frets" 14-18, for the first and second strings. On careful inspection, the bottom lip of the fingerboard was partly the culprit, it was also partly the general slope of the board above the octave. These tolerances are tight!

The diagnostic sanding (60-grit and 150-grit) was done with strings in place; once all notes were ringing clear, I took strings off and more gratuitously sloped off the end of the board. When satisfied, I finished up with 220, 400, and 600-grit paper. The board is certainly not perfect, you can see that right away, but since this is a bit of work in progress and an experiment to begin with, I'm pretty happy with progress thus far. Before restringing, I did manage to get a couple of photos of the fingerboard, which I'd meant to do before:

Yeah, 600-grit sandpaper is pretty nice. I'd never seen unfinished wood shine before these projects. (It was after these photos that I wiped on the linseed oil.)

Restringing this time was another experiment. The first iteration had a marvelous warm buzz (what Dave Sweeney called the "mwah" sound, which is exactly right), but the top two strings were so light (.012 for the E and .010 for the G) that I thought I should try some heavier ones to see if I could get a little more sound. What I did, so as not to risk overtensioning my little kit's system, was to go to heavier gauge strings all around, and then tune everything down a whole step. So, I used the following for this experiment

• 6th string: .059 bronze wound, tuned to Bb1
• 5th string: .048 bronze wound, tuned to F2
• 4th string: .038 bronze wound, tuned to C3
• 3rd string: .022 nickel wound, tuned to G3
• 2nd string: .014 plain, tuned to D4
• 1st string: .012 plain, tuned to F4

Boy, interesting observations there. First: the .059 for the Bb is floppy, and the instrument does seem to have a hard time responding to it. Curiously, the .054 string seemed to work fine for the low C previously. Quite a difference. Next, those first two strings really do sound better being a little thicker. That point is well-taken. Finally, I noticed that a lot of the "mwah" was missing, at least the first time the strings were brought up to pitch.

I started thinking about this, and it's quite possible that multiple things are at work. First, the thicker strings may simply ride a little higher in the nut/saddle notches, and be enough higher off the board that the natural buzzing is affected by it. Probably it's also that the fingerboard has indeed been relieved by the sanding.

Some of that "mwah" is coming back as things settle in, or perhaps it's because of how I'm playing it. I also have considered the roundwound strings. Ultimately, I am still interested in either flatwound electric strings, or possibly the original idea, nylon. (That would really require some more work on nut and saddle!) But...I wonder how much of this buzzing sound is actually coming from the roundwound strings. I've heard that the "Jaco growl" may have been partly due to his use of roundwound strings, and I'll admit, that's not a bad sound to have available...

One way or the other, it's given me a lot to think about. Current plan is to play like this for a while, and then at my next string change, polish up the fingerboard once again and put on the "light" electric flatwounds to see what they sound like. The plan there is for the following:

• 6th: .056 flatwound, tuned to C2
• 5th: .042 flatwound, tuned to G2
• 4th: .024 flatwound, tuned to D3
• 3rd: .018 plain, tuned to A3
• 2nd: .013 plain, tuned to E4
• 1st: .011 plain, tuned to G4

I figure that if the action/setup sounds good with the lightest strings, I'll have done with the instrument what I am capable of doing as a luthier, and by then I'll have enough evidence to decide how I want to string in the longer term.

For now, we'll try whole-step-down, heavy strings, and see how it goes!

The NST fretless acoustic guitar

The big project, the one I'm the most excited about, is the fretless acoustic. This project is still one or two steps away from being "really done", but these are definitely in the spirit of small refinements. I am psyched about this one.

The concept

I was after several things here. I had for a while been intrigued by the concept of a fretless guitar, having loved the sounds of Jaco, Percy Jones, Kai Eckhardt, Michael Manring, and Tony Levin for some years now. But it was running into Neil Haverstick, who served as a marvelously patient and charmingly idiosyncratic "theory teacher" for Dave Cialone and I (after Nathan left for Illinois), that really inspired this project. In addition to teaching us an approach to tonal music theory (read the theory posts on this blog and you'll see the product of a lot of that), Neil was personally in the midst of exploring alternative tuning options for his microtonal music, and was himself just beginning to perform with a fretless guitar. It was compelling.

So, I had identified that I wanted to build a guitar from a Musicmakers kit, and their "Guit-along" teardrop shaped mini-guitar (which is not a currently available kit, it appears) seemed like the right design for compact size and complete access to the upper register. It is designed to be a steel-string, fretted acoustic guitar in standard tuning with a small floating bridge and no electronics. So, naturally, I decided I'd build it as a nylon-string, fretless acoustic guitar in Guitar Craft standard tuning (aka New Standard Tuning or NST to Crafties*) with the addition of an onboard pickup and preamp for amplifying and recording. This would involve coming up with a solution for the provided fretboard, which was already slotted for fretwire, fabricating my own bridge and saddle, and selecting and adapting electronics.

You know, for building my first guitar. :-)

I'm happy to say that I am pleased with the end result. There were certainly headaches in there, but the result is good as it is, and will get better with a couple more refinements.


The tour

The kit came with pre-bent wood for the guitar body, and sound- and backboards. The wood turned out much prettier than I'd expected it to be, but I didn't find that out until the finish (clear lacquer) went on. The plainest piece of wood on the thing is the Sitka spruce laminate soundboard!

Note in the pic on the left, above, the battery box, and look closely inside the far side of the soundhole and you'll see the volume and tone pots supplied with the LR Baggs undersaddle transducer (I got one specifically calibrated for nylon strings). In the pic on the right, you can see the battery box through the other side of the soundhole. Note too that the bridge in these shots is the first-phase bridge, fabricated from a plank of padauk wood from Rockler's in Denver whose color was pretty close to the kit's supplied padauk fingerboard. The saddle in this first iteration is a plastic saddle from an old dreadnaught and was being used as a placeholder; I had not even started work on the bone saddle at this point.

Here's a look at the fingerboard and the headstock. It's a shame that I wasn't able to capture the almost mirror shine that 600-grit sandpaper put on the fretless surface.

To solve the problem of the fret slots, the staff at Musicmakers suggested I glue light-colored wood veneer into the 18 fret slots, and then sand the board flat. This was a great idea; it looks really nice and the reference is very useful for someone getting started with fretless playing!

Of interest: despite my using a drill press to cut the peg holes for the tuning machines, I still managed to get one of them off-center. Doesn't affect how it plays, I know, but it still makes me grumpy. I'm much happier with the bone nut (from Stewart-MacDonald, along with the bone saddle, battery box, and electronics) I substituted for the plastic one provided with the kit.

Here's a look at the neck, and a closeup of the volume/tone pots in the soundhole:

In hindsight, I probably should have shaped the neck a little differently, as this one feels a little thick, but it is my first time shaping a neck (the kit's neck was bandsawn, so it wasn't a complete neck blank; essentially the rounding is mine), and I was conservative.

As a woodworking project, it was fun. I learned a great deal about gluing, sanding, and the use of router attachments for Dremel tools, and enjoyed it. The electronics scared the shite out of me, though, as I am no electrician, and I was continually petrified that I'd build the whole thing, plug in and then get...nothing.

The pickup is an undersaddle transducer, which meant that I could not use the kit's supplied bridge--which simply floats on top of the soundboard with no provision for a separate saddle to transmit vibration to the transducer. So...I fabricated a bridge, from a plank of padauk wood from Rockler's, with a Dremel tool and hand sanding, using the Dremel plunge router attachment to fashion a workable but far from perfect channel for the saddle, and then just sanding that thing square with the aid of my shooting micrometer. In the end, I managed to build a little compensation into the saddle, with the bass strings slightly longer than the trebles (this may be somewhat academic on a fretless instrument, but I'm happy I did it).

The preamp is built into the endpin jack, so a giant hole went into the tailblock of the guitar, and instead of using the battery bag included with the pickup, I rewired the battery to Stew-Mac's battery box, which I fitted on the top side of the guitar in the only "flat" spot on the teardrop's curve. I think that will work out rather nicely; the box is much more elegant than trying to negotiate a battery bag through that reduced-size soundhole.

I assembled the whole thing up, mostly to see if the electronics would even work, and strung it up and plugged it in. To my total astonishment, it sounded fabulous through my SWR California Blonde. To my ears, at least.

My thoughts now turned to the guitar's action. For the initial test, I used "throwaway" strings, and acoustic steel roundwounds at that, just to provide a starting point. The action was sky-high, which I kind of expected as I had just fabricated a bridge from scratch, used a placeholder saddle, and had not done anything to reduce the height of the nut. Check out these shots of the initial action. (For reference, note the how thick the bridge is in the first three pictures in this post.)

Measured with my reloading micrometer, string heights at the nut were .130" for the sixth string down to .085" for the first string. (A general rule of thumb is that 1/16", or .063", is appropriate for this measurement, for guitars, and this measurement is from the crown of the first fret to the bottom of the string.) At the 18th "fret", the heights were .345" for the sixth string and .290" for the first. In general, the lower the action the better, especially for a fretless instrument, and my goal was to get to 1/32", or .0313", at the nut. (My Fender Stratocaster's action, set up for me by a luthier, measures .025" at the first fret and .100" at the 18th, and it is the easiest action I currently own.)

So, I thickness-sanded the bottom of the bridge, sanded down the top of the bone saddle (both to reduce height, and also to observe the "50/50 rule" that you want at least 50% of the saddle to be down in the slot, not above it, to avoid excessive tilt), and filed deeper slots in the nut for the strings I have on, to hit my target.

I was careful, and the result was extremely gratifying. These pics are of the revised bridge with the bone saddle fitted and notched:

And these last pics are of the revised action. Compare them to the ones above!

In the end, the numbers were a little better than my target. The revised action has .021" - .030" gap at the nut, and .071" - .080" at the 18th "fret". What a difference!

The revision did highlight a small high spot in my fingerboard, in the area of "frets" 16-18 on the first and second strings. I'm no luthier, but I would think this is an encouraging place to have a minor high spot, and my intent is to sand this area slightly to take care of that, put a final nice polish on the whole fingerboard again, and re-string with my next experiment: flat-wound electric guitar strings (which have the primary advantage of not needing to be purchased; I already have a set of them, in NST gauges, from my previous experiment with the Stratocaster).

When I tuned up and plugged in again, I played for a while for Sabre, who seemed to enjoy the new sound. For me, the sound of the instrument is intoxicating, and I suspect I will learn a number of new techniques to allow me to take advantage of what I've got. (Those will certainly get posted here...)


Now what?

The purpose of this was to experiment with a fretless instrument; hell, mostly it was to see if I could build something worth playing! It started with the idea of "hey, let's try building a guitar" and steamrolled with the additions of the fretless fingerboard and the onboard electronics.

It's got its warts, and I'm sure I'll find things to dislike about it. But I have to say, I'm pleased at the result, and I intend to see what the application of a Crafty mindset to a completely new instrument might yield. (I am certainly treating it as a new instrument!)



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* For those who do not know it, the Guitar Craft Standard Tuning is C2 - G2 - D3 - A3 - E4 - G4, from sixth to first strings. This gives an expanded range over the fourths-based standard tuning, broader chords in general and an orchestral approach to music theory (the CGDA pitches of strings 6-3, are the same pitches as a cello is tuned). I like this tuning, and being a blowhard, all my guitars are tuned this way; I've even brought the intervals of the top four strings to my new kit banjo. Anything to be difficult! :-)

The kalimba

Another kit from Musicmakers, the first one I did, got completed along with the banjo by virtue of my finally putting a finish on it. The kalimba (thumb piano) is now ready to go, finished in the same clear lacquer that went on the banjo and fretless guitar.

This is the kit that showed me that I enjoyed the woodworking and detail work enough, to inspire me to go with the more challenging projects. Learned about my Dremel tool and accessories, a little about sanding, and certainly about patience. I was pleased with this one.

And of course, the kalimba has a bit of extra meaning to a Crimhead by virtue of its being featured on Larks' Tongues in Aspic.

For those who know me, don't worry, I did manage to do something different with it. The thumb piano is commonly tuned to a major scale, but I decided I'd try tuning it to the augmented scale for grins. This piano comes with 12 keys, and since the augmented scale is a six-tone scale (C-Eb-Fb-G-Ab-B) I can cover two octaves, although I'd like to have a thirteenth key for another root at the second octave). One thing that's kinda cool about this tuning, with the keys arranged with the bass keys at the center, alternating outward as they rise in pitch, is that you can swipe the keys one way from the center and get stacked major thirds (augmented chord), and then swipe the other way and get stacked major thirds a semitone higher. Playing either side sounds just like whole-tone, because, well, it kinda is whole-tone!

Anyway, I do envision this being a novelty instrument, but who knows? If the right use for it flies in my face, I'll be loath to ignore it. And it may have created a monster, judging from how much I like my "big" project...

The NST banjo

Well, it's finally here, and mostly done. I now have a working banjo, with a twist (those of you who know me don't need to snicker so loudly). Instead of the standard banjo tuning, I have employed the intervals of the top four strings of the Guitar Craft (New Standard) tuning, so I'm dubbing this the NST banjo.

(Click to enlarge any picture!)

The brief history

A "Cumberland Banjo" kit was ordered about two years ago, from Musicmakers in (Stillwater, Minnesota, of all places), and it was early last year that I started to work on it. The design intrigued me--it's a small, open-backed banjo with a couple of nifty features including a cleverly adjustable angle on the neck, and an interchangeable insert in the fingerboard that allows you to use either the standard first three frets, or a fretless insert. It seemed something that I could try my hand at to see if I enjoyed the woodworking, and if I could actually make a playable instrument from the kit!

Things didn't start out so well. While trying to shape the peghead, I put too much stress on the joint where the nut is glued in (the kit's neck came rough-fabricated, with the fingerboard already glued on, truss rod in place, 5th-string peghole pre-reamed and tapped, and nut already in place, with the neck rough-shaped) and put a telltale hairline crack in it using an inappropriately underpowered jigsaw. I was not pleased, and put the kit away, disgusted with myself. About along that time, the move to Alaska started up, and I didn't resume building the kit until June of this year. I sheepishly got on the horn with Musicmakers, described the problem, and got the encouraging opinion that I could probably try to force a little glue in there and just glue the hairline back together, proceeding as normal. Because of the specific place the crack was located, the tension of the strings will tend to pull it closed, not open, and between the wood glue, re-epoxying the nut in place, and the strings pulling the crack closed, it seemed to be a good risk (and so far, so good!).

And so, while I assure you I am no sort of nascent Dan Erlewine or Ken Parker, I did manage to build the banjo, learning a great deal in the process. It was a lot of fun.

In this picture, note how the tone ring tensions the (8") plastic drum head. Six cap screws abut directly on the tone ring--simple but effective. The angle in this pic is a bit tough (I'm no photographer either), but you can just see two screws at the bottom of the black plastic tone ring.

The "tailpiece" is another ingeniously simple design, five pins sunk into the banjo's body and draped over a leather strap.

How's this for a first-timer's gaffe: notice anything unusual about this photo of the neck and headstock?

If you look closely, the eagle-eyed may notice that I managed to put the tuning machines on backwards! (Thank you, thank you.) I was so careful about shaping the peghead, after almost destroying it initially, that I just fit those machines on it in the manner most conducive to how they fit, and I got lefts and rights backwards without even realizing it! (The little "point" on the machines is supposed to point down, not up.) How's that for a truly customized banjo? I foresee continual amusement while playing the tuning song on this one...

Next pic is of the body. Eight-inch drumhead, and a standard five-string banjo bridge. Of interest is that this picture was taken before intonation. It became clear very quickly that the bridge was set too far forward, and after about 10m of work intonating, I've got a good position for it, very slightly compensated with the traditional bias towards longer bass strings.

Below, a shot of the banjo back. Note the two cap screws holding the neck joint. The top one is the tension screw; the bottom one abuts against a brass plate on the neck itself. To adjust the angle of the neck, loosen the top screw, then set the angle with the bottom one, retightening the top when finished. That was the fastest "action job" I've ever seen!

Interestingly, the action is limited on this instrument by the string height of the fifth string. At the neck joint, it is dramatically lower than the other four strings. I may at some point try to lower the action more, both by taking the main four strings down at the nut and filing slightly deeper notches in the ebony bridge for strings 1-4, but first I'm going to take some time to learn how to play it as it is!

This last picture doesn't really show this string height disparity, but it does give you an idea of the fifth string peg, individual "nut" (machine screw) and fingerboard. The fingerboard is made of padauk wood, a beautiful African hardwood with a lovely red color. (The rest of the banjo is of cherry wood, finished with plain clear lacquer.)

All in all, I'm reasonably pleased with my work. Doing the dot-inlays was an educational task, but I got it figured out and sanded that puppy to glassy smoothness with a final pass of 600-grit sandpaper. Fretwork turned out all right, with decent bevels and a minimum of sharp edges. The Dremel drum gave me one "oops" on the side of the fingerboard; otherwise I am pretty happy with it.

I learned a number of lessons, in addition to the ones noted above:

• The Dremel is your friend, but there's nothing like hand-sanding for final shaping and detail work.
• I do seem to enjoy the work with details--polish sanding, intonation, action setup, etc.
  
• That 5th string tuning machine is not geared (the main string machines are 14:1). So far it has not been a problem, but I can envision getting excited and working that one too far either way at some point!
• What to do with the string-end on the 5th string. Since it's a very light-gauge string (.010), the cut end is sharp, and although one should not have one's hand in a position to contact it during normal play, if it does end up making contact, there's gonna be a hole in your hand. I think I'll find a way to trim the string end so that the end loops back into the hole, presenting a smooth surface. Just seems smart!

So now what?

I got this banjo because I love the sound of the instrument, and of course I have a love of bluegrass-related musics. Being essentially a resounding mutt by disposition, I envision trying to use this instrument in bluegrass/newgrass, jazz, Crafty, and other contexts that haven't occurred to me yet. So, the fact that it's not a "bluegrass banjo" doesn't bug me (the sound is rather cool, actually) nor that I've adopted a different tuning for it.

Learning to play the banjo will be an interesting journey. The right hand clearly has a lot to learn, as I have thus far used a flat pick in Guitar Craft style, and my physical programming runs pretty deep. My intent is to apply a Crafty approach to it and see what happens.

The tuning, from strings 5-1, is:

G4 - C3 - G3 - D4 - F4

The main four strings (4-1) are the same intervals as the top four strings of the Guitar Craft tuning: a perfect fifth, a perfect fifth, and a minor third. (The standard banjo is tuned G4 - D3 - G3 - B3 - D4, with intervals over the main four strings being a perfect fourth, a major third, and a minor third.) My thought here is that it would allow me to use the same music theory on the banjo that I am learning for the guitar, and avoid me having to learn another set of intervals. (It will certainly also have the effect of giving this banjo a different voice, with chords very broadly spaced in the bass register and closely spaced on the top...and, duh, it's bound to be a PITA for someone else to figure out, which is always good for a larf. :-)

Anyway, the instrument is essentially done, with leeway for a little refinement on setup. I've got a strap fixed to it now (buttons at two and eight o'clock on the rim) and am ready to start the learning process!

A preliminary chord dictionary for the 'NST banjo'

Stringing up the new kit banjo (writeup coming soon) with NST intervals for the main 4 strings, I finally sat down and worked through the basic library of chord forms that I had long ago wanted to get around to. For NST guitar players this may look a little funny, with everything down a whole step and a 5th string that I haven't even considered yet, but since I'm after closed forms anyway, this will certainly serve as my own reference for these intervals. For this library, I have operated within the following constraints:

• The banjo is tuned, from strings 5-1, thus: G4-C3-G3-D4-F4. Diagrams should be read accordingly.
  
• I'm looking for closed forms.
• I want one working form for each possible chord inversion. In general, this means each form has a unique bass and treble note; occasionally they swap out interior notes.
• I approached the problem like I did when working through the "all-fifths" four-string group, trying to increment each note on each string first, and only amending a given form if the fingering started to look superhuman.
• Whenever possible, each chord contains all constituent tones (no omitted notes)...this is obviously a limitation on the number of available chords, but I am looking both for a working library, and an approach to chord construction that I can use as a basis for on-the-fly alteration.
• Finally, I used all four strings for each form, simply for the purposes of thinking in a useful box.

Okay then, here's the initial library; it only gets better from here! First, there are the fifths, which are pretty easy to figure out:


Then, there are the four triads. (NOTE: I have not been happy in my search for viable three-string triads on the first three NST strings. Fingerings get ugly; it's just not as elegant as straight fifths or fourths. In the end, I have returned to the four-string model, which obviously works fine.)


Then there are the basic suspended forms:


Then, the meat and potatoes--diatonic sevenths from the Western major and minor keys:


And to round things out, major and minor sixths:


There is a lot more work to be done, for sure, but this should serve as a basis.

Tertian arithmetic - the basics

This post lays out the example of looking at extended chords (ninths, elevenths, thirteenths) as the product of two simpler chords. The philosophical idea behind this is discussed here.

Okay, so think in the box of a seven-note scale and its diatonic, tertian chords. I'll stick with the Western major scale for simplicity--the example will be good old C major.

Our givens:

Diatonic triads are built by stacking two thirds on top of one another. The sequence and nature of the component thirds determines the type of triad: a diminished triad is two minor thirds (BDF), a major triad is a minor third on top of a major third (CEG), a minor triad is a major third on top of a minor third (DFA), and an augmented triad is two major thirds (unavailable in the Western major scale, this would be CEG#). In C major, then, the diatonic triads are C major (CEG), D minor (DFA), E minor (EGB), F major (FAC), G major (GBD), A minor (ACE), B diminished (BDF).

Diatonic sevenths take these triads and add another diatonic third onto each one. The combinations become much more complex, and C major only yields four of the possible variants. The diatonic seventh chords for C major, then, are Cmaj7 (CEGB), Dm7 (DFAC), Em7 (EGBD), Fmaj7 (FACE), G7 (GBDF), Am7 (ACEG), and Bm7b5 (BDFA), also known as the "half-diminished seventh".

Ninths add another diatonic third onto the seventh, making them a stacking of four thirds. Elevenths add a fifth third, and thirteenths are six thirds stacked together. (At this point, you are playing every note in the scale simultaneously, so there is no such thing as a fifteenth or beyond.) The possible permutations quickly get ridiculous here, and so does the harmonic density. After a few too many of these chords, even the most diehard jazz lover can appreciate the clarity and resolution of a triad or power chord.

Great, so where is all this going?

Consider C major: C-E-G. Now, consider E minor: E-G-B. What happens if you get your buddy to play a C major at the same time you play an E minor? Together, you're playing Cmaj7, C-E-G-B, and are overlapping on the E and the G. Huh.

You may also have heard that Em is a good "substitute chord" for C major. The logic goes that the bass player is probably covering the root note, so if you play an Em somewhere in the upper register, it should sound "right", and a little fuller. What you're doing is extending the basic chord by another diatonic third, making a more complex chord in the process - Cmaj7.

Now, what makes Em a suitable substitute chord for C? Here is the simple, master-key answer: it's a diatonic third up from C.

From here, everything starts to fall into place. If you understand diatonic triads in your scale, you can easily create sevenths by playing two triads a third apart. If you understand diatonic sevenths in your scale, you can easily create diatonic ninths by playing a "root" seventh chord and the diatonic seventh one-third above it. (Three tones will overlap.) That is, you can easily create Cmaj9 by playing Cmaj7 and having your buddy play Em7 over it. C-E-G-B plus E-G-B-D equals C-E-G-B-D, or Cmaj9. Work up the scale: Dm7 + Fmaj7 = Dm9, Em7 + G7 = Em7b9, etc.

Now, here's the real kicker: consider those overlapping tones. In the case of Cmaj9, the notes are C-E-G-B-D. If you start to break apart the ninth into constituent chords, do you notice that you could also play the G triad over the C triad, and come up with Cmaj9? C-E-G plus G-B-D equals C-E-G-B-D. The G triad is two thirds up from C, and now you're playing a ninth from two triads with one note still overlapping. Why not go a step further? Three thirds up from C is the B diminished triad, B-D-F. C major (C-E-G) plus B diminished (B-D-F) yields C-E-G-B-D-F, or Cmaj11. Imagine playing eleventh chords simply from knowing your triads, and knowing how to go up three diatonic thirds up from a root chord. Not bad!

Now, combine a seventh with a triad. Hold down your Cmaj7 and have your buddy play a D minor (D-F-A). Poof! Cmaj13 (C-E-G-B-D-F-A), no overlapping notes. You could do the same playing a Bm7b5 over a C major triad.

There will be practical limits to this, of course, but this is a powerful concept, and once you have mastered triads and are comfortable with sevenths, these extended chords are almost instantly available to you. Commit these ideas to immediate recall:

Look at complex chords as a series of thirds stacked together in the scale. That is, for Cmaj13, look at the chord as C-E-G-B-D-F-A. Do you suddenly see all the triads in there? Just break them up, assign them and play them!

To extend a chord by one "factor" (triad to seventh, seventh to ninth, ninth to eleventh, eleventh to thirteenth), you need to add a third. You can do that by creating a polychord from a root chord of appropriate complexity and a chord a third above of appropriate complexity. (Here, we start to get limited by terminology. I'm working on this!)

You can extend a chord by more than one "factor" at a time (thereby keeping constituent chords simpler and fewer notes overlapping) by going up two or three thirds for your "upper" component of the polychord, and/or by extending the upper chord by one or more "factors".

In general, you can cover any diatonic ninth, eleventh or thirteenth chord with one seventh and one triad.

Hopefully I will get clearer with this each time I explain it. For now, here are some practical examples that illustrate the explanation. Try these things!

Cmaj9 (CEGBD) = C (CEG) + Em7 (EGBD) (also w/ Cmaj7)
Cmaj9 (CEGBD) = C (CEG) + G (GBD) (also w/ Cmaj7)

Cmaj11 (CEGBDF) = C (CEG) + G7 (GBDF) (also w/ Cmaj7)
Cmaj11 (CEGBDF) = C (CEG) + Bdim (BDF) (also w/ Cmaj7)

Cmaj13 (CEGBDFA) = Cmaj7 (CEGB) + Bm7b5 (BDFA)
Cmaj13 (CEGBDFA) = Cmaj7 (CEGB) + Dm (DFA)

Note that in each of those pairs of examples, the first suggestion goes up the minimum number of thirds and uses a seventh form; the second suggestion goes up an additional third from the root, but simplifies the upper chord form.

There is a little arithmetic involved here, sure, but it is very logical, and I imagine that mastering it would make one a very powerful improviser. I can envision a situation in which I'm playing mandolin and reading a chart which vamps on a dominant chord for a few bars. The band has the G7 covered, and I want to add tension on top of the mix. For the first bar I play G7, then I play Dm (making a G9), then F (making a G11), then cap it off with Am (G13)--just by knowing to go up in thirds.

I know I'm a geek, but that's cool.

Tertian arithmetic - the idea

Okay, this has been stewing around in my head for a little while now, and I think there's something significant in it, but I have not yet found the pow! way to explain it. So, please forgive me if this discussion still seems a bit formative--it is.

The topic is looking at extended complex chords (ninths, elevenths, thirteenths) as polychords. The intent here is to come up with a deliberate device to understand these complex chords better, by viewing them as the products of multiple simpler chords (triads, sevenths) that one may already have in the hands. What I like is that there is a very simple logic at work that makes this daunting subject rather easy to grasp--at least in a practical way.

And that is my goal. Many of us find ourselves in a group context in which we are one voice among several, and so this concept of reducing a complex chord into two simpler chords, each to be played by a separate person, has a great deal of appeal. And for the improvising musician, the ability to add harmonic complexity spontaneously (without having to know where, say, a G13 or an Am11 is) is a real bonus.

You've probably heard the phrase "chords are built in thirds", and the term "tertian chords". It turns out that there's a lot more to this than you might think. Most of our chords are indeed built from stacked thirds, but the stacking can be applied further to whole chords a diatonic third apart. Somewhere in there is a sort of "tertian arithmetic" that can be described, that just unlocks the whole mess like a master key. It is the description of this arithmetic that I continue to struggle with; I can see it by permutation, but the teacher in me wants to be able to distill out the best way to 'splain it. (I'll get there.)

So, here we go. The next post will lay out the examples.

Finding sevenths from the triad

Continuing this theme of using the three-string triad as a template to alter into other chords, I'm starting to see forms I'd never thought of before. I was noodling around for Sabre this evening, trying to think on three-string triads, and wound up making another accidental "duh" discovery.

For those of you who can appreciate stream-of-consciousness thinking, here's how the sequence went: I started by revisiting the first suggested "alter the first-inversion triad to get a dominant seventh" suggestion, on G major. On the mandolin and other fifths tunings, that looks like this:


Well, what about going the other way? If we can take that root down a whole step to get G7, what about going up a whole step to get the ninth? It's probably fudging the point a bit from a Juilliard/Berklee point of view, but that could probably serve as both Gadd9 and as Gmaj9, depending on what notes others are holding down.


And that's got to be so much easier to think of doing, at speed, in an improvisational context. If we consider the mandolin (or the Guitar Craft guitar, for that matter) as but one voice among other instruments, this would promise to be a very effective way of adding color notes with less risk of bumping into others' territory.

From here, it can start to get pretty fast and furious. On that first-inversion triad (third in bass), I just started permuting:


That rather neatly covers those*; then, you could start walking the fifth around as well (for this diagram, read down, not across, to see the permutations):


This could get out of hand in a hurry, but on the other hand (and with apologies to Frank Zappa), great googly-moogly! And that is just the first-inversion triad...I'll try my hand at root-inversion and second-inversion next time, and holy cow, then there's ninths.

I suspect that there are a couple of goals with going further down this approach:

• The real goal here is not just to build a library of chords to memorize, but to become competent at finding a triad and altering it on the spot (and herein is where the value of reducing from four strings to three becomes obvious, saving what must be a fairly staggering amount of complexity)
• With the enharmonic equivalents starting to pop off the page (with just three strings to keep track of, it's much easier, isn't it?), it seems that using this approach will also underscore the need to better understand polychords, both from the standpoint of deliberate construction of polychords by multiple members of the group playing simple chords, and also from the standpoint of reduction of polychords into smaller constituent pieces that a player can grab onto either at speed, or to allow a humane fingering. (I think I'm going to have to chew on that one for a while.)
• One nice thing about using three strings instead of four is that it does leave the player more room to wander about the registers, in effect "playing his harmony with more melody". I suppose that a complete player would want both full voicings and the three-string variants at his disposal, but the potential for improvisation here is pretty huge.
  

Note to self: don't sit down to write the bit on ninths until you have a lot of time. :-)

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* How about the bender of the enharmonic equivalents, as well? That three-string Gmaj7 is also known as Bm, which is a standard third-up substitution...also check out Bb augmented aka Gm/maj7, Bb major aka Gm7 (diatonic third up and relative major).

Finding dominant sevenths from the triad

On the mandolin, my "guerrilla" learning style has thus far been focused on constructing four-string chords, both for a fuller voicing and (let's be honest) to allow the right hand to cruise sloppily.

Structurally, it's been about regular permutations deliberately limited to moveable forms. So, for triads, I carried over what I'd learned on the Guitar Craft-tuned guitar, from a California Guitar Trio exercise: one form per inversion, root, first (third in bass), and second (fifth in bass), with the other strings advancing diatonically up the neck as well. So, for A major, the three inversions with A, C#, and E in the bass would be:

This proved to be so helpful in my learning that I sweated out the same thing for the diatonic sevenths...again, one form per possible inversion, advancing up the neck, moveable forms. Translating directly from the guitar, for Amaj7 as an example, the forms for A, C#, E, and G# in bass, are: The really geeky may notice that in first inversion I altered the triad, flatting the root to the major seventh; this allowed me to use the root on the top string, keep all four component notes in the chord, and have each form truly advance the bass and treble strings up the neck each time. It was an arbitrary choice, but it helped me construct a box that really helped me to "see" the chord forms advancing up the neck.

On the mandolin, I ran into another problem: some of these forms are simply too tight to work well on the smaller instrument. (By contrast, stretches like the second-inversion maj7 voicing are very workable on the mandolin while being a real workout on the guitar.) I realized that I would eventually need to find other convenient voicings for the mando.

Somewhere in there I ran across Jethro Burns' outstanding book, which advocates the concept of the three-string chord (even for chords with more than three tones) on the basis that it can be altered more easily than a four-string chord. True, but that introduces an unintended problem for the beginner: how can you understand what chord tones you can omit, before you've got a good grip on where the possibles are? I ignored the three-string approach at the time, staying with my fours and developing some confidence (this was a good decision, at least for me), but how funny what comes back in due time. With a good grounding in where all those notes actually are, and watching Mike Marshall articulate the same advantage of alteration in one of his excellent video resources, I actually started to "get it". In working with a couple of David Grisman tunes, the three-string chord really started to show its value, and with that came another revelation: the three-string chord is much, much easier on the tightest fingerings.

Great. So I've started to explore the three-string chord concept, with an eye to building a library of chords for my own use. And, quickly enough, the "omit tones" problem rears its head, to wit: how does one intuitively know where to find a three-string chord that omits the root?

As with many things I've learned about music so far, at least one example turned out to be a "duh" moment. I was playing around with the four suggested inversions of a three-string dominant seventh, as noted by Burns. Going up the neck, this is A7 with G (7th), A (root), C# (3rd), and E (5th) on top:

Now you may notice that the note A only appears once in those four chords, as the top note of the seventh-in-bass inversion. So: how the heck do I quickly find an A7 that doesn't even have an A in it?

I found myself noodling a bit on this, and stumbled on creating the seventh out of each triad inversion, by flatting the root note by a whole tone. Whoa, there they are!


Then, what really bent me is that suddenly I also recognized that these root-omitted dominant seventh chords are enharmonically the same as the diminished triad build on the chord's third--in each inversion. That is, A7 with no root (C#-E-G) is also a C# diminished triad. This makes complete sense, of course, since a dominant seventh is nothing more than two minor thirds stacked on top of a major third, and if you omit the major third, what you're left with is two minor thirds--or a diminished fifth. Quo erat duhmonstratis. (Okay, maybe it takes a geek to appreciate that, but sue me, I love this stuff.)

Excepting the form with root on top, then, which kind of lives "in between" the third inversion and the first, I can now find any dominant seventh by finding the appropriate triad and altering it. This three-string chord thing may have some value yet!