Guitar, Music

Estudio #1 para Guitarra

Here’s a short piece I’ve just finished writing for guitar; maybe it will become part of a series.  The style here is romantic and the texture is more homophonic than contrapuntal, a departure from the keyboard-oriented canons I’ve been working on recently.  It feels good to now be writing for the instrument I actually play.  This is in fact my first “composed” piece for guitar — my past guitar work has been improvisational and it’s taken me some time to move from a spontaneous to a planned approach to working with the instrument.   One thing I’ve learned is that writing for guitar involves a constant interplay between abstract musical thinking and a nut-and-bolts examination of the instrument’s possibilities and tendencies.  I suppose that’s true for any instrument, but it’s especially so for the guitar because the guitar is polyphonic, but not in the rational, orderly way the keyboard is polyphonic; instead, in a quirky, limited way, where the fingers of the left hand can quickly become immersed in a nightmarish game of Twister if the composer isn’t careful.  But one nice thing about being the author of the piece you’re playing is that if a certain note gives you trouble you have the authority to change it, and I did that several times in the course of practicing this!  In the clip, you’ll hear me playing my 2009 Connor guitar.  Feedback is welcome.


Major 3rds Fretboard Layout

This diagram shows the fretboard layout for a 6-string guitar in All Major Thirds tuning, assuming the open strings are tuned to E, G#, C, E, G#, C as recommended by Ralph Patt.  I made the diagram because I’m beginning to learn this nonstandard tuning and I wanted a study aid that emphasized the amazing regularity of the system.

Notice that because the three open bass strings are tuned the same as the three open treble strings (modulo an octave), the entire pattern of notes among the bass strings is repeated among the trebles — the left and right halves of the diagram are identical.

Each of the four colors used in the diagram indicates one of four possible augmented triads (modulo inversion and enharmonic respelling).  Notice, for example, that two copies the F Augmented triad (F A C♯) occur along the first fret and are shown with a light green background.  At the fifth fret the same set of notes occurs in a different inversion — now the notes are ordered A C♯ F; again they are shown with a light green background.   Finally, at the ninth fret, the notes occur in the order C♯ F A.

The “fret dots” on the left are positioned according to most common inlay pattern for standard tuning.  For simplicity, notes are always spelled using sharps instead of flats, though of course all the notes in the diagram could be written in multiple ways.

Major 3rds Tuning For Guitar: Fretboard LayoutAn intriguing property of this layout is that any block of notes spanning three strings and four frets can be considered as a “tile” that repeats across the entire fretboard, in a way where the tiles don’t overlap and also don’t leave any gaps.  In the image directly below, I started by drawing a box around the notes across the bass strings at frets zero through three; next, I placed boxes around all other instances of that same pattern.  (The notes with a gray background aren’t actually on the fretboard, of course — I included them to make the pattern clear.)


This next diagram is similar to the previous one, except I outlined a different block of notes:


Other regular tunings like All Fourths also give rise to tiling patterns like the ones above, but in the case of All Fourths, non-overlapping tiles won’t form nice, simple rectangles, and it’s not possible to “fit” as many complete tiles on the fretboard.  Here’s one way of tiling a fretboard tuned to E, A, D, G, C, F:


Guitar, Music

M3 Tuning For Guitar: A First Look

If you’ve followed my guitar posts here, you’ll know that I like the All Fourths tuning (E A D G C F) because it imposes a regularity on the fretboard that allows a player to shift chord and scale patterns across strings without fingering adjustments.  It’s also a comfortable tuning to explore if you’re familiar with standard tuning, since only the highest two strings are changed: you can reuse any chord or scale pattern that you’ve learned on the lower four strings, which are already tuned in fourths.

I had been cautiously avoiding other nonstandard tunings since switching to All Fourths around a year ago — I didn’t want to spread myself too thin.  But a blog visitor recently asked why I hadn’t considered All Major Thirds tuning here, and I couldn’t resist the invitation to experiment.  Now, after exploring M3 for a week, I’d like to share some initial observations.  (Alexandre, thanks again for the question that prompted this!)

One way to implement M3 is to keep the guitar’s lowest string at E and tune major thirds above that, giving E, G#, C, E, G#, C.  This is the 6-string setup recommended by Ralph Patt, who is considered to be the originator of M3 tuning.  Notice that while P4 tuning expands the guitar’s range by a semitone, M3 narrows it by a major third (the highest string drops from E down to C), which is why some M3 players prefer a 7-string guitar.  And while P4 only requires two strings to be retuned, M3 requires five retunings, which makes it a very different beast from standard tuning.

One of the first observations people make about M3 tuning is that you can play an entire 12-note chromatic scale in a span of four frets, with the same finger always playing the same fret, without shifting hand position.  Since any octave-repeating scale is a subset of the chromatic scale, this means you can play any scale you want without a position shift or stretch.  (If you’ve grown up adjusting to the shifts and stretches of standard tuning, it’s worth taking a moment to consider how remarkable this is.)

A nuance I haven’t seen emphasized elsewhere is that all this holds true regardless of which finger you use for the root note.  You can start the scale with your index finger or your pinky, and in each case there’s no need to move your hand or stretch beyond four frets.  The diagram below shows four different fingerings of the chromatic scale, corresponding to the four fingers you could use to play the root.  The numbers indicate which finger is used to play the notes at the corresponding fret — in the first example we play the root with the index finger (1), in the second example we play it with the middle finger (2), and so on.

M3ChromaticFingeringsJust as the chromatic scale can be played with any starting finger, without a position shift, so too can any scale be played with any starting finger, without a position shift.  What’s more, the four single-position fingerings of any given scale bear noticeable similarities to each other, as they are composed of the same building blocks — it’s easy to learn all four fingering patterns at the same time!  In the remainder of this post I’ll elaborate on this point with the major scale as an example.

In working out 7-note scales in M3 tuning I’ve found it useful to think of these scales as stacked tetrachords.  For our purposes a tetrachord is any sequence of four notes spanning a fourth (alternatively you could think of a tetrachord as a sequence of three intervals that add up to a fourth); here we’ll only look at tetrachords that span a perfect fourth but in a followup post we’ll consider tetrachords that span an augmented fourth.  The major scale is nicely regular in that it can be seen as two stacked copies of the same whole-whole-semi tetrachord pattern.  Starting at the root, say C, and traversing a whole tone, another whole tone, and finally a semitone gives us C, D, E, F.   Starting at the fifth, G, and applying the whole-whole-semi pattern again gives us G, A, B, C.  Put them together and you have the entire major scale: C, D, E, F, G, A, B, C.  The diagram below shows how the whole-whole-semi tetrachord pattern is fingered in M3 tuning, with all possible starting fingers.  Notice that the first two examples have the same shape though they employ the fingers differently.

M3WholeWholeSemiFingeringsNow we’re ready to finger the major scale itself, not just in one way but in four ways that are interrelated.  Since the major scale consists of two copies of the whole-whole-semi tetrachord, each single-position fingering of the major scale can be understood as a pairing of two of the whole-whole-semi fingerings we saw above.  Let’s say we want to play the major scale starting with our index finger on the root.  First we’d play the whole-whole-semi tetrachord pattern starting from the index finger (I’ve colored this pattern dark blue in the diagrams).  Notice how the pattern ends with the second finger playing the fourth degree of the scale.  Next we need to skip a whole step up to the fifth degree of the scale, which falls under the pinky.  Keeping the hand position fixed and applying the whole-whole-semi fingering starting from the pinky (I’ve colored this patten cyan) completes the scale.  What if we wanted to start playing the major scale with the pinky instead of the index finger on the root?  The reasoning is similar: first play the whole-whole-semi tetrachord pattern starting from the pinky; then, since the pattern ends on the first finger, skip a whole step up to the third finger and play the tetrachord patten that starts from the third finger (green). The diagram below shows all four fingerings of the major scale as combinations of the whole-whole-semi tetrachord fingerings from the previous diagram:

M3MajorFingeringsOf course it’s possible to conceive of scale fingerings in terms of tetrachords in other tuning systems, but M3 is the only system I know where it works so well — where you can mix and match tetrachord fingerings as we’ve seen to build scales that stay entirely within four frets.  In a followup post we’ll take a look at other tetrachord patterns (like semi-whole-whole, whole-semi-whole, etc.) and how they can be used in M3 to finger the natural minor scale, the melodic minor scale, and pretty much any scale you could imagine.


String Buzzing Exercise For Left Hand Pressure

In guitar playing, it’s easy to fall into the habit of applying more pressure with your left hand fingers than you really need.  You might not be aware that you’re pressing too hard until find your left hand becomes tired or strained.  This habit is hard to diagnose because it doesn’t always come with visual or auditory cues: you might not be able to see signs of excess pressure when you look at your left hand in the mirror, and you can’t hear it either. Here’s an exercise/experiment that can help you build control over left hand pressure and ultimately find the minimum level of pressure needed to get a clear tone. The idea is simple: play a scale and try to make every note buzz. That’s right — while buzzing is usually considered a mistake, in this exercise it’s the goal. Try to make the string just barely touch the fret, so that it rattles against the fret when you strike the note. You should be able to hear the note along with the buzzing: don’t press hard enough that the buzzing goes away and you get a clear tone, but don’t press so lightly that the string never comes into contact with the fret and you get a muted sound. You’ll probably find that it’s easy to create buzzing for one note in isolation, but it will take some practice to be able to achieve buzzing consistently as you play up and down the scale of your choice. That’s because buzzing only occurs within a narrow pressure range, and the right level of pressure differs slightly for each note (it depends on where the note is on the fretboard, on your guitar’s action, on the shape and height of the fret in question, and possibly also on the strength of your right hand stroke). So, by learning to achieve a consistent buzz as you play up and down the fretboard, you force yourself to pay close attention to left hand pressure and you learn to control that pressure in very precise way. (Remember, by “consistent buzz” I mean that every single note should buzz: no note should be clear, and no note should be fully muted. If you find yourself playing too many clear notes, keep practicing!) The next step, once you’ve learned to achieve a consistent buzz, is to increase the pressure very, very slightly so that the buzz goes away. Instead of doing this all at once, you could try playing a scale in alternating fashion, where one note buzzes, then next is clear, the next buzzes, and so on. Spend some time with this, and you’ll get a good sense of how it feels to play with no more left hand pressure than you need.

Guitar, Music

Note Neighborhoods II

This post is a follow-up to my article about Note Neighborhoods, a technique I developed for navigating the guitar fretboard.  In this post I’d like to provide charts that can be used for practicing this approach — these are the charts I use myself.

First, a recap of the Note Neighborhood concept.  In guitar playing it’s common to practice ascending and descending scale patterns that start from the root of a scale or mode and stretch across all six strings (for example, see my post on Guitar Modes Unified).  In the Note Neighborhood approach, you dispense with the idea of ascent and descent from a starting point, and you focus on smaller patterns that extend outward from a central note.  You practice one pattern for each scale degree, taking that scale degree as the center and learning to find all of the other notes that surround it physically on the fretboard (within a three-string/three-note-per string circumference).   If you’re playing in major, melodic minor, harmonic minor, or any of the their modes, each scale degree will have a unique neighborhood pattern, a unique “geography” including eight notes around the center.  Once you’ve memorized all seven neighborhoods, you can play freely in your chosen scale anywhere on the fretboard, as long as you recognize what degree you’re playing at a given time and can recall its neighborhood pattern.  This approach works particularly well in All Fourths tuning because you don’t need to memorize variants of each neighborhood pattern for different string sets; however, it can be applied to Standard Tuning as well.  I find it particularly useful when working in Melodic Minor and its modes, since the six-string patterns for Melodic Minor lack the regularity of the Major patterns and (for me at least) are harder to internalize.  This approach also frees you from always searching for the root as the anchor of your fingering because you learn to be equally comfortable taking any scale degree as your “anchor” — that’s helpful if you’re improvising music that’s not “root-centric” but moves back between different points of modal focus within an available pool of notes.

I don’t see the Neighborhood concept as competing with other approaches for understanding the fretboard; it can be used to complement them.  In fact, if you know the three-note-per-string fingering patterns for the major and melodic minor modes, you’ll see that the Neighborhoods are just fragments of those patterns, labelled in a different way (focusing on the center as opposed to the lowest note).  If you’re an experienced player, you might think of the Neighborhood concept as a different way of organizing fretboard knowledge that you already have, so you can apply it differently and see new possibilities.  Or if you’re just starting out with scale patterns, you might find that Neighborhoods cut down on the amount of rote memorization you have to do the first time around.

Here are the seven neighborhood patterns for Major.  (If you’re playing in standard tuning, these will work on the bottom four strings as shown, but you’ll have to shift things up by a half-step when you cross from the G string to the B string.)

Major Note Neighborhoods (guitar)

And here are the neighborhood patterns for Jazz Melodic Minor:

Melodic Minor Note Neighborhoods (Guitar)

To get started with these, try playing the notes of C major up the A string, focusing on C, then D, then E, etc., and using the patterns for 1, 2, 3, etc. to give you the neighboring notes.  Then do the same for C melodic minor.  As for fingering, try placing your middle finger on the central note of the neighborhood you’re playing–keep it there and explore all the intervals you can play between that central note and the other notes in the neighborhood.

Addendum I: Comparing The Neighborhoods

One way to get to know the neighborhoods is to compare them–to notice what they have in common and how they differ.  A great way to do this for the Major neighborhoods is to lay them out side-by-side in Circle of Fifths order: 4, 1, 2, 5, 6, 3, 7.  When you do this you’ll notice that each neighborhood differs from the previous one by only one relationship, as shown in the diagram below.  For example, look at the 5 and 2 neighborhoods: 5 has a major third above it, while 2 has a minor third above it.  This means the finger position in the top right region of those two neighborhoods is different; otherwise, the fingering patterns are identical.  Now compare the 2 and 6 neighborhoods, and you’ll spot only one difference, this time in the bottom left corner.  Note that between the 4 and 1 neighborhoods, and also between the 3 and 7 neighborhoods, you’ll spot two finger positions that are different.  That’s because each neighborhood contains some doubled notes, and when you go from the 4 to the 1 neighborhood, or the 3 to the 7 neighborhood, it’s one of these doubled relationships that changes.  Take a closer look and you’ll see that the two positions that shift are an octave apart.  (As always, click on the image for the full size version.)

Major Note Neighborhoods in Circle Of Fifths Order

Addendum 2: Theory Behind The Comparison

What’s the theory behind the diagram above?  Well, anyone who’s looked at the circle of fifths knows that two major keys a fifth apart differ by one accidental.   A slightly less common observation is that the formulas for modes of the major scale based on degrees a fifth apart differ by one sharp or flat as well.  As we progress from Lydian to Ionian to Mixolydian, all the way to Locrian, we pick up natural 4, then flat 7, then flat 3, then flat 6, then flat 2, and finally flat 5:

  • Lydian: 1 2 3 #4 5 6 7
  • Ionian: 1 2 3 4 5 6 7
  • Mixolydian: 1 2 3 4 5 6 b7
  • Dorian: 1 2 b3 4 5 6 b7
  • Aeolian: 1 2 b3 4 5 b6 b7
  • Phrygian: 1 b2 b3 4 5 b6 b7
  • Locrian: 1 b2 b3 4 b5 b6 b7

The note neighborhoods in the diagram are just different ways of expressing the information in these modal formulas.  A modal formula looks at the notes in an ascending sequence from the root, whereas a neighborhood pattern considers how the notes are situated around the given center, but the underlying relationships are the same.  It’s a remarkable property of the major scale that the modes can be arranged in such a clean progression, where one modal formula differs from the next by only one sharp or flat.  That’s to say, it’s remarkable that when you look at the interval relationships that one note forms with other notes in the major scale, and then you do the same analysis for its fifth, there’s only one difference.  I call this “remarkable” because it’s not true for many other scales, namely melodic minor.  You can’t arrange the modes of melodic minor so that successive formulas differ by one accidental, and you can’t arrange the neighborhood patterns in a clean progression like what’s shown in the diagram above for Major.  For example, try comparing 1 and 5 in melodic minor and you’ll see two relationships that are different: 1 has a minor third and a major sixth above it, while 5 has a major third and a minor sixth above it!  You can try other comparisons too–1 with 4, 1 with 7, etc.–and in each case you’ll find at least two differences in the neighborhoods.

Guitar, Music

Fingerings Derived

In my post on the three-note-per-string fingerings for the major modes on guitar, I showed how those fingerings all stem from a pattern we can write as XXXYYZZ.  In this notation, X means that we play two whole tones on a given string, Y means we play a semitone followed by a whole tone, and Z means we play a whole tone followed by a semitone.  If you looked over my post, you had to trust that I put the dots in the right places in my fingering diagrams, or else you had to check the positions for yourself.  Here, I’d like to show that this XXXYYZZ pattern can be obtained directly from the “formula” for a major scale, using some simple variable substitution.  Remember that the pattern of semitones and whole tones in a major scale is whole-whole-semi-whole-whole-whole-semi or 2212221. If we start at the fifth note of the scale and keep ascending over several octaves, we’ll play a pattern like this:


If we’re playing exactly three notes per string on the guitar, then we’ll always traverse two intervals on one string, and one interval when we cross strings. We can use parentheses to group the intervals that would fall on the same string like this:


Now we can replace (22), meaning “play two whole tones,” with X, our abbreviation for the two-whole-tones-on-one-string fingering pattern.  Similarly, we can replace (12) with Y and (21) with Z, giving this:


Finally, we can reveal the pattern by replacing the 2’s (meaning “play a whole tone when you cross strings”) with a space, and the 1’s with no space, giving this:


Here it is again:


And now a follow-up regarding the Jazz Melodic Minor scale.  If you’ve ever worked out the 3-note-per-string fingerings for melodic minor and its modes, you know those fingerings are not as “nice” as the major mode fingerings.  But how can we characterize the difference?  One way to explain what makes the major mode fingerings “nice” is that the single-string shapes appear in distinct groups: three X’s, then two Y’s, then two Z’s.  If we do a similar derivation for the melodic minor fingerings, starting with 2122221 as our scale formula, the pattern we arrive at is XZ X YX Z Y.  In other words we have to switch from X to Z, then back to X, then to Y, and then to X again (and so on) as we’re playing. This interleaving of single-string shapes is one thing that makes the melodic minor fingerings harder to work with.  Here is the derivation for the melodic minor 3-note-per-string pattern:

XZXYXZY Derived From Melodic Minor Formula

(By the way, I expect this post to make sense to people who are interested in mathematical music theory and who have studied guitar and read my previous post on modal fingerings.  If this doesn’t make sense and you want to know more about it, please ask me a question as I’d be happy to provide more of an explanation.)

Guitar, Music

Fourths vs. Standard Tuning

This diagram shows where the notes of C major fall on a guitar fretboard in Fourths Tuning (EADGCF) versus a fretboard in Standard Tuning (EADGBE). I’ve extended the main pattern across the boundaries of the two fretboards so you can see how it repeats in space.  The red dots show how the pattern is pushed up a fret on the two highest strings in Standard Tuning.

All Fourths vs. Standard Guitar Tuning