# Fingerboard Geometry

### Interval Shapes

## By Michael Manring

Those of use who play string instruments are lucky. There is a visual aspect to our instruments we can use to our advantage in learning to understand the musical options that are available to us. Musicians who play other instruments -- say winds for instance -- generally don't have a way to see the patterns they are playing as clearly as we can. By analyzing the shapes various patterns make on the fingerboard we can increase our knowledge of harmony and the musical possibilities in any particular situation. We bassists are especially lucky because our instrument is so symmetrical. Since all our strings are tuned a perfect fourth apart, geometric shapes repeat over the fingerboard without the kind of adjustments that guitarists deal with due to the major third interval between their second and third strings. Of course it's important to keep from relying too heavily on visual patterns in music because they are only a method for better understanding the instrument, but as long as you maintain a good perspective, fingerboard geometry can be a powerful tool for expanding expressive capability.

A good place to start examining fingerboard geometry is by looking at the shapes of intervals, so in this column we'll take a look at the ways that intervallic patterns appear on the fingerboard. In order to simplify things for the time being, we'll look at only the intervals in one-finger-per-fret fretting hand positions and avoid the use of open strings. If we accept these limitations it's possible to examine all the possible interval shapes; we can then use this understanding to make better fingering and phrasing choices. In one-finger-per-fret positions the fretting hand covers the space of four frets, or a minor third on one string. Doing this divides the fingerboard into symmetrical four-fret by four-string boxes with 16 notes in each box. These boxes can be a powerful tool to use in visualizing musical patterns on the bass. You may find the four-fret span to be too much of a stretch to use in the lower positions, so please only use it where you find it comfortable, but try visualizing these 4x4 boxes even if you are using a position that spans only three frets. I realize that restricting yourself to a "box" may seem a little confining at first, but please keep in mind that this is just one way of visualizing the fingerboard in an attempt to understand what's available to you. Ultimately you will use your sense of creativity to decide when and how to use this concept.

On a single string in the four-fret span position there are three interval shapes that can be played -- minor second, major second and minor third. Within this group there are three different minor seconds (between the first and second finger, the second and third finger and the third and fourth), two major seconds (1,3 and 2,4) and one minor third (1,4). This is pretty simple, but when we use multiple strings things get a little more interesting. Between adjacent strings there are 7 basic interval shapes. The smallest interval shape is played by using the pinky on a lower string and the index finger on a higher string (we'll call this 4-1). Between adjacent strings this fingering forms a major second, and this is the only way to play this double-stop interval in 4 fret span position. The next smallest interval will be the one played by either the third finger and the index (3-1) or the pinky and second finger (4-2). On adjacent strings this shape forms a minor third. Continuing on with this process we can play three major thirds (2-1, 3-2, 4-3), four perfect fourths (1-1, 2-2, 3-3, 4-4), three tritones (1-2, 2-3, 3-4), two fifths (1-3, 2-4) and a minor sixth (1-4). These are the seven successive interval sets available between adjacent strings in a four fret span position: the major second, the minor thirds, the major thirds, the perfect fourths, the tritones, the perfect fifths and the minor sixth.

If we use these same interval shapes between non-adjacent strings we get fourteen additional interval sets - seven skipping over one string and seven skipping over two. Skipping over one string we get the intervals ranging from a perfect fifth (4-skip-1) to a flat ninth (1-skip-4); when skipping two strings the range is from a perfect octave (4-double skip-1) to a sharp eleventh (1-double skip-4). If you're really paying attention you may notice that there is some overlap between these interval sets. There is more than one geometric identity for some intervals but not others. If you want to play a note a minor sixth above that given note for instance, you could play it either on the adjacent string with the 1-4 shape or you could play it on the string above the adjacent string with the 4-skip-1 shape. However, if you want to play a note a major third above any given closed tone, you can only play it on the higher adjacent string. In a four fret span position, most intervals will always look the same, but the following four intervals have two geometric identities: 5 (1-3 or 4-skip-1), #5/b6 (1-4 or 4-skip-2), octave (1-skip-3 or 4-double skip-1) and b9 (1-skip-4 or 4-double skip-2). Note that in a four fret span position on a 4-string bass without using open strings there is no way to play a double stop smaller than a major second or larger than a #11.

So, what can we accomplish with this little bit of knowledge? Well, one aspect of bass playing that it might help open up is playing fifths. We typically play perfect fifths on bass using the 1-3 or 2-4 shape on adjacent strings, but try playing them using the 4-skip-1 shape. This version of fifths isn't quite as apparent and it may open up some melodic possibilities you hadn't thought of. It also may help you to avoid shifting positions so often, thus allowing you to play smoother lines. Considering how much we bassists have to play fifths, this can be a very useful idea.

I very much recommend familiarizing yourself with all the intervals in a four fret span position, but the task may seem a little daunting at first. Here's one way to simplify it: Given any note in a four fret span position there are 15 possible interval shapes to choose from without shifting -- three additional notes on the same string and four on each of the three other strings. If you are holding a note with your third finger on the E string for example, you could move to any of three other notes on the E string or four each on the A, D and G strings. Since there are 16 notes in a four fret span position and 15 intervals available from each note, that means there are 240 possible intervals in a four fret span position (15 X 16 = 240). These can be practiced in a short time, and this provides an excellent warm up -- one that I like to do everyday, in fact. I begin by playing all of the 15 intervals that start from the lowest note in a four fret span position -- the index finger on the E string -- and then all fifteen from the middle finger on the E string, then 15 from the third finger and so on. This exercise takes about three minutes at a slow tempo.

However, there are many other ways to practice this material. Simply playing the fifteen interval shapes from any one note is a valuable exercise, as it contains all the basic material. The difference is that this way you aren't practicing the shapes on all the possible string combinations. For instance, if you choose to practice only the fifteen interval shapes starting with the index finger on the E string you will only be playing the 4-1 shape on the E and A strings, not on the A and D or the D and G strings. Alternatively, you could practice all the interval shapes, but only in one direction. The exercise with 240 shapes includes 4-1 and 1-4 as two separate shapes. By eliminating these doublings the total number of interval shapes is brought down to 120 (because you are removing the reverse of each interval, or half of the original 240). You can do this exercise with the same method as the 240-shape exercise; just eliminate either all the upward moving shapes or all the downward moving ones. The advantage of using these shortcuts is that you can spend more time focusing on each of the shapes; the disadvantage is that you are practicing a less complete set of movements. Try to determine for yourself what works best for you in any particular practice session.

Having a complete understanding of interval shapes will give you a powerful tool to use in creating smoother lines. I find that one of the problems that challenges students the most is an incomplete awareness of the possibilities in one position. Unnecessary shifting tends to cause inconsistent, awkward phrasing. By being aware of the possibilities that exist in one position you can greatly increase your facility and fluidity and ultimately build skills that can help you make more engaging music.

A good place to start examining fingerboard geometry is by looking at the shapes of intervals, so in this column we'll take a look at the ways that intervallic patterns appear on the fingerboard. In order to simplify things for the time being, we'll look at only the intervals in one-finger-per-fret fretting hand positions and avoid the use of open strings. If we accept these limitations it's possible to examine all the possible interval shapes; we can then use this understanding to make better fingering and phrasing choices. In one-finger-per-fret positions the fretting hand covers the space of four frets, or a minor third on one string. Doing this divides the fingerboard into symmetrical four-fret by four-string boxes with 16 notes in each box. These boxes can be a powerful tool to use in visualizing musical patterns on the bass. You may find the four-fret span to be too much of a stretch to use in the lower positions, so please only use it where you find it comfortable, but try visualizing these 4x4 boxes even if you are using a position that spans only three frets. I realize that restricting yourself to a "box" may seem a little confining at first, but please keep in mind that this is just one way of visualizing the fingerboard in an attempt to understand what's available to you. Ultimately you will use your sense of creativity to decide when and how to use this concept.

On a single string in the four-fret span position there are three interval shapes that can be played -- minor second, major second and minor third. Within this group there are three different minor seconds (between the first and second finger, the second and third finger and the third and fourth), two major seconds (1,3 and 2,4) and one minor third (1,4). This is pretty simple, but when we use multiple strings things get a little more interesting. Between adjacent strings there are 7 basic interval shapes. The smallest interval shape is played by using the pinky on a lower string and the index finger on a higher string (we'll call this 4-1). Between adjacent strings this fingering forms a major second, and this is the only way to play this double-stop interval in 4 fret span position. The next smallest interval will be the one played by either the third finger and the index (3-1) or the pinky and second finger (4-2). On adjacent strings this shape forms a minor third. Continuing on with this process we can play three major thirds (2-1, 3-2, 4-3), four perfect fourths (1-1, 2-2, 3-3, 4-4), three tritones (1-2, 2-3, 3-4), two fifths (1-3, 2-4) and a minor sixth (1-4). These are the seven successive interval sets available between adjacent strings in a four fret span position: the major second, the minor thirds, the major thirds, the perfect fourths, the tritones, the perfect fifths and the minor sixth.

If we use these same interval shapes between non-adjacent strings we get fourteen additional interval sets - seven skipping over one string and seven skipping over two. Skipping over one string we get the intervals ranging from a perfect fifth (4-skip-1) to a flat ninth (1-skip-4); when skipping two strings the range is from a perfect octave (4-double skip-1) to a sharp eleventh (1-double skip-4). If you're really paying attention you may notice that there is some overlap between these interval sets. There is more than one geometric identity for some intervals but not others. If you want to play a note a minor sixth above that given note for instance, you could play it either on the adjacent string with the 1-4 shape or you could play it on the string above the adjacent string with the 4-skip-1 shape. However, if you want to play a note a major third above any given closed tone, you can only play it on the higher adjacent string. In a four fret span position, most intervals will always look the same, but the following four intervals have two geometric identities: 5 (1-3 or 4-skip-1), #5/b6 (1-4 or 4-skip-2), octave (1-skip-3 or 4-double skip-1) and b9 (1-skip-4 or 4-double skip-2). Note that in a four fret span position on a 4-string bass without using open strings there is no way to play a double stop smaller than a major second or larger than a #11.

So, what can we accomplish with this little bit of knowledge? Well, one aspect of bass playing that it might help open up is playing fifths. We typically play perfect fifths on bass using the 1-3 or 2-4 shape on adjacent strings, but try playing them using the 4-skip-1 shape. This version of fifths isn't quite as apparent and it may open up some melodic possibilities you hadn't thought of. It also may help you to avoid shifting positions so often, thus allowing you to play smoother lines. Considering how much we bassists have to play fifths, this can be a very useful idea.

I very much recommend familiarizing yourself with all the intervals in a four fret span position, but the task may seem a little daunting at first. Here's one way to simplify it: Given any note in a four fret span position there are 15 possible interval shapes to choose from without shifting -- three additional notes on the same string and four on each of the three other strings. If you are holding a note with your third finger on the E string for example, you could move to any of three other notes on the E string or four each on the A, D and G strings. Since there are 16 notes in a four fret span position and 15 intervals available from each note, that means there are 240 possible intervals in a four fret span position (15 X 16 = 240). These can be practiced in a short time, and this provides an excellent warm up -- one that I like to do everyday, in fact. I begin by playing all of the 15 intervals that start from the lowest note in a four fret span position -- the index finger on the E string -- and then all fifteen from the middle finger on the E string, then 15 from the third finger and so on. This exercise takes about three minutes at a slow tempo.

However, there are many other ways to practice this material. Simply playing the fifteen interval shapes from any one note is a valuable exercise, as it contains all the basic material. The difference is that this way you aren't practicing the shapes on all the possible string combinations. For instance, if you choose to practice only the fifteen interval shapes starting with the index finger on the E string you will only be playing the 4-1 shape on the E and A strings, not on the A and D or the D and G strings. Alternatively, you could practice all the interval shapes, but only in one direction. The exercise with 240 shapes includes 4-1 and 1-4 as two separate shapes. By eliminating these doublings the total number of interval shapes is brought down to 120 (because you are removing the reverse of each interval, or half of the original 240). You can do this exercise with the same method as the 240-shape exercise; just eliminate either all the upward moving shapes or all the downward moving ones. The advantage of using these shortcuts is that you can spend more time focusing on each of the shapes; the disadvantage is that you are practicing a less complete set of movements. Try to determine for yourself what works best for you in any particular practice session.

Having a complete understanding of interval shapes will give you a powerful tool to use in creating smoother lines. I find that one of the problems that challenges students the most is an incomplete awareness of the possibilities in one position. Unnecessary shifting tends to cause inconsistent, awkward phrasing. By being aware of the possibilities that exist in one position you can greatly increase your facility and fluidity and ultimately build skills that can help you make more engaging music.