Studies in A for Diatonic and Chromatic Mountain Dulcimer

[For a reference starting point to this series, please visit the link for Studies in C for Diatonic and Chromatic Mountain Dulcimer.]





A Diatonic Scales.pdf



A Chromatic Scales.pdf


A Chromatic Scale Harmonizations.pdf

As we continue our study of the 15 Major keys and their relative minors (30 keys in all!) this year, I'd like to point out that the traditional Appalachian mountain dulcimer is not stuck in the key of D Major like some folks think. In fact, when tuned to dd-A-D (also written DAD or known as 1-5-8 tuning), performers of mountain dulcimer can easily play in six different keys without ever re-tuning or applying a capo. Beyond that, some fudging is necessary (such as barring and bending to omit or find missing notes.) In creating the worksheets for each of the keys, I was hesitant to include some of the more difficult-to-attain notes, chords and scales for diatonic (standard) mountain dulcimer, but decided to do so anyway. On the diatonic dulcimer scale sheet for each key, I show both Major and minor scales plus some scale harmonization. You'll notice that with the minor scales, there are some half-frets that you probably don't have on your instrument. For instance, in the A minor scale tablature, you'll find a 4+ to indicate the F natural. Whenever you see a + next to a fret number, you can bend that particular note to get the tone that's missing from your fretboard. It'll sound funky, but at least you'll be able to still join in on the studies (and bending notes is a good technique to have in your toolbox.)

In fact, diatonic players, it's not a bad idea to go ahead and download the chromatic worksheets as well, as they are chock full of extra information.

For example, harmonic minor scales are listed with the chromatic sheets as well as ascending and descending melodic minor scales. I figured that might be a little too much information for diatonic students, which is why that's not covered in the diatonic materials.



As we begin exploring the key of A Major, I'll give a rundown of the characteristics of each scale here. First off - the key of A Major has three sharps: F, C and G.

A  B  C#  D  E  F#  G#

Remember how to build chords from these notes? Begin with the root (A) and skip every other letter to form triads. Some chords will be Major, others will be minor and one chord will be diminished:

A C# E = A Major

B D F# = B minor

C# E G# = C# minor

D F# A = D Major

E G# B = E Major

F# A C# = F# minor

G# B D = G# diminished

In any Major scale - chords or scales built from the 1st, 4th and 5th degrees are Major. Chords or scales built from the 2nd, 3rd and 6th degrees are minor. Chords or scales built from the seventh degree are diminished.

Begin the Major scale from the sixth note and use the same notes (just in a different order) and you've got the relative minor scale. In this case, that scale would be F# minor. This is also known as the natural minor.

F#  G#  A  B  C#  D  E

Same chords are formed when skipping every other letter.

Now, what happens when we keep the same root and switch to a minor scale? Let's go from A Major to A minor. What's the difference? We take the 3rd, 6th and 7th notes of the Major scale and flatten them; take them down a half step.

A  B  C#  D  E  F#  G#

becomes

A  B  C  D  E  F  G

If you've been following along with our studies since the beginning of the year, this scale should look familiar to you. Why is that? Because A minor is the relative minor scale to C Major, which is the very first scale we took a look at! (No flats and no sharps.)

This is an important distinction to make: relative minor scales are the same as natural minor scales, no matter what. However - when you are comparing a Major scale and its relative minor, none of the notes change - only their order changes. When you are comparing Major and minor scales that share a root, then three of the notes will be flattened. Does that make sense? Let's recap what keys we've looked at so far:

Major keys and their relative minors:

C Major -> A minor (no flats/sharps - both share the same notes in different orders)

G Major -> E minor (1 sharp - F# - both share the same notes in different orders)

D Major -> B minor (2 sharps - F#/C# - both share the same notes in different orders)

Major and minor keys that share a root:

C Major (no flats/sharps) - C minor (3 flats - Bb/Eb/Ab)

G Major (1 sharp - F#) - G minor (2 flats - Bb/Eb)

D Major (2 sharps - F#/C#) - D minor (1 flat - Bb)

So now, we're at A Major - the relative minor is F# minor. Both have three sharps. F#/C#/G#. When changing A Major to A minor, the result is no flats or sharps. Do you see a pattern here?

Each time we've added a sharp, we've removed a flat. I won't go into detail on this yet (in fact, I'll save a look at the harmonic minor scale and melodic minor scale for two posts from now), but how in the world can you keep track of it all without having to memorize every single key? That's where the Circle of Fifths comes in.



The Circle of Fifths shows all of the relationships between the 12 notes of the chromatic scale. It can be quite handy as a visual or mental tool (which is why I highly recommend memorizing this simple version of it and then discovering what it's good for along the way.) At the top of the circle is C, with no flats and no sharps. Then, as you move clockwise around the circle, you are moving in fifths; each of the notes around the edge of the circle are a distance of a fifth as you travel clockwise. What's more, beginning with G, you add a sharp for each note name (up to seven sharps total.)

Now, if you move counter-clockwise around the circle, let's start from C again, then all of those notes are a fourth apart. In addition, beginning with F, you add a flat for each stop around the circle in a counter-clockwise motion, up to seven flats. Some people call this image the Cycle of Fourths but it works out to be six of one and a half-dozen of the other!

So, someone calls a tune in the jam that's in the key of A. Flip around the circle in your head clockwise until you come to A. Remember not to count C, since it has no flats or sharps. Counting G, that's three total "clicks" around the circle. So, three sharps are in the key of A.

Also, notice the interior of the circle. There, you have all of the relative minor keys right next to their relative Majors. There's another way of finding this. First, choose the Major key on the outside of the circle and then move "fifteen minutes" (four total note names) clockwise around the circle. The note you arrive at, simply call it minor and there you have it! See how that works counting from D Major (you arrive at B - so call it minor.) Remember to count the note that you start with.

A couple more things to mention. This is a simplified version of the Circle of Fifths, but I wanted to introduce it to you (if this is, indeed, your first encounter with it) without it being too terribly intimidating. One thing that you'll need to know about music theory is that some notes, intervals and key signatures are exactly the same as other notes, intervals and key signatures but spelled differently. For example, take a look at the Circle of Fifths and find Db. That's D flat Major. It's the same thing as C# or C sharp Major. We'll get more into that later on.

Also, it's not a bad idea to memorize the order of sharps and flats as they appear on the musical staff.

Sharps = F, C, G, D, A, E, B

Flats = B, E, A, D, G, C, F

If you look at the Circle of Fifths, you may see some patterns emerging. Look closely.

This is where it gets interesting.

I know that there are many musicians out there who have been studying along with us and they play other instruments besides diatonic and chromatic mountain dulcimer. This broad overview of music theory applies to the general musical language. However, diatonic instruments are somewhat limited by design, so after this particular pair of key studies, I'll be taking a slightly different approach to materials for the mountain dulcimer. You may have noticed in the initial workshop materials for each Major key, I've presented the scales and harmonizations in a straightforward manner, although sometimes I've switched up a chord shape or two here and there. For diatonic, that has been necessary to make up for the lack of available notes within immediate range, so you'll see a little zig or a zag instead of a perfect staircase of notes, in the case of harmonization. Also, with the chromatic worksheets, I have been using a couple of different general chord shapes. Some, as you can see, are tightly bunched together. Some are spread out with spaces in between the next closest note. These are alternately known as closed voicing and open voicing. Again, we'll get more into that as we go along.

It's my sincere wish that you'll plug along with me in this general study of keys. Along the way, there are lots of music theory bits and bites that will come into play. What I've discovered in my years of study is that what seems confusing at first will slowly begin to fade into understanding, light bulbs will go on, patterns will emerge and once you've got a toe hold there - the world of music unfurls itself before you and you simply cannot get enough. Thanks for taking the journey with me!

Go Ahead: B minor.

I hope you hung out in the key of D Major for awhile and had some fun exploring! I've been exploring the joys of spring cleaning here at the studio (and in the guest room and in the bedroom.) So sorry about the delay in posting the follow-up to our Major key study by delving into the relative minor key:

For every Major scale there is a relative minor or natural minor scale that shares the same notes, albeit in a different order. To find it within the Major key, simply begin on the sixth note of the scale and play the seven notes in sequence:

Major

D  E  F#  G  A  B  C#
1  2  3   4  5  6  7

minor

B  C#  D  E  F# G  A
1  2   3  4  5  6  7 

Though we keep the scale degrees the same, the character of each tone remains the same as it was in the Major scale.

  

Major

D    E    F#    G    A    B    C#
I   IIm  IIIm  IV    V   VIm  VII°

minor

B    C#    D    E    F#   G    A
Im   II°  III   IVm  Vm   VI  VII 

This is as good a time as any to talk about more complex scale harmonization. As discussed in the last post, one of the foundations of harmony is taking a Major or minor scale and then adding a second note and then a third note on top to form a chord. For each note of the scale comes a full three notes played at the same time or a triad. You play one chord for each scale note and this creates harmonies all the way up the scale. To get the chord tones, just look at the scale and skip every other note.

Based off of the 1st minor scale degree, a B minor chord would be B (skip a letter), D (skip a letter) and F# as the notes. G Major would be G, B and D. See the pattern?

I'm going to write something in B minor, just to play with some chords a bit:

i - iv - VII - III

VI - iv - III - VII | ii°

which translates into:

Bm - Em - A - D

G - Em - D - A | C#dim

Okay, there are the changes. Eight measures with that final measure being three counts of A and then one count of C#dim as a passing chord. Passing chords can be viewed as "filler chords" to assist you in getting from one chord to another. Chords built off of the Major seventh scale degree (the same as the minor second in this minor scale) carry an inherent tension that leads naturally to the roots of these two scales. (6 1/2 - 6 - 8 will form a C#dim chord for you. Try playing that and then going to Bm. Then play the C#dim and go to D Major. Hear the resolution?

Quick review on chord building:

Major chords consist of a root - Major third - perfect fifth

In the case of D Major - skip every other letter from the root:

D - E - F# - G - A - B - C#

D - F# - A = D Major

Minor chords consist of a root - minor third - perfect fifth

In the case of D minor - skip every other letter from the root.

D - E - F - G - A - Bb - C

D - F - A = D minor.

Another way to do that is to use the Major scale and simply take the Major third (F#) down a half-step (F).

Diminished chords are like minor chords but you also take the perfect fifth down a half step as well.

If you have a 8+ fret on your dulcimer, you can play a 6+ - 6+ - 8+ chord, which is C# Major. Then flatten, lower the third and fifth a half-step. What was C# - F - G# becomes C# - E - G. C# diminished!

In this exercise, play through the above chord progressions and then work out a melody that will fit neatly over the top. Generally speaking, when writing melodies, you should select notes that can be found within the scale of each chord. For example - melody notes for Bm should come from the B minor scale. Melody notes for A should come from the A Major scale and so on. Some of your melody notes will obviously be found in many different scales, which makes it easy to sustain melodies through the chord progressions. When you're ready to end your song, be sure to end it on the root of B minor.

For my tune, I've chosen a 3/4 time signature:

Go Ahead, B Minor.tef

Go Ahead, B Minor.pdf

Fun With 7th Chords

As promised, we'll have a quick look at 7th chords, of which there are a few. Please refer to the .pdf for D Scale Harmonization.

So, we've got Major chords and minor chords plus the odd-sounding diminished chord. What else is there? The answer to that question is "plenty." But for starters, we'll look at the different types of 7th chords.

When you see D7 - you're looking at the fundamental 7th chord, known as a dominant seventh. Is it bossy? Perhaps a little. I don't want to get into all of the scary music theory terms too early here, but suffice it to say that each of the scale degrees have names associated with them that are descriptive of their strengths and weaknesses. The fifth note of any scale is often referred to as the "dominant."

If you build a major triad starting with the fifth note of the scale and add a fourth note to the mix, you'll get a naturally occurring dominant seventh. Let's do this with D Major:

D - E - F# - G - A - B - C#
    *        *   *       *

So, we're skipping every other letter, beginning with A, which is the fifth note of the D Major scale.

A (skip) C# (skip) E (skip) G

So, take A - C# - E - G and play them all simultaneously, you've got an A7 chord. Another way of thinking about this: take a Major chord and add the seventh note of the scale, flattened a half-step. In the case of D7 - we'd build a D Major chord:

D - F# - A and then add the seventh note of the D Major scale, which is C#. Then take that down a half-step to C. D - F# - A - C is a D7 chord.

As dulcimer players, we are often playing on three string courses, so how do we add a fourth note? By playing a rootless voicing. That is, taking the root out of the picture and playing only the remaining three notes. Believe it or not, it still works! Let's play an A7 chord this way.

Play 1 - 2 - 4 on your diatonic dulcimer. Now drop the A on the melody string down to the third fret, which is G. You're now playing, from bass to melody, E - C# - G which is enough to play the A7. Cool, huh?

Now, let's suppose you see this note: GMaj7. This is a Major seventh chord. Begin the same, with a Major chord. But now add the seventh note of the Major scale. In the case of G:

G - A - B - C - D - E - F#

Skipping every other note: G - B - D - F#

Try this - Play a 3 - 1 - 0 chord, your G Major in diatonia. You're playing, from bass to melody, G - B - D. Now, on the melody string, replace D with F# at the second fret. Voila! You're playing a GMaj7! It's got a distinctly jazzy sound and a great chord substitution for G Major.

A minor seventh chord takes, you guessed it, a minor triad and adds the minor seventh to it. Let's take a look at Em7:

Beginning with the E minor scale which has, remember, one sharp (F#) - 

E - F# - G - A - B - C - D

Skipping every other letter we get E - G - B - D

Play 8 - 6 - 5 and you've got E minor. Now play 8 - 6 - 7 and you've traded the B on the melody string for the flat seventh (D) and you've got an Em7! Remember that when the number 7 is there by itself, always use the flat/minor seventh.

So, what happens when you see AmMaj7? You play a minor triad and add the seventh note of the major scale, in other words, the Major seventh.

A minor scale

A - B - C - D - E - F - G

A Major scale

A - B - C# - D - E - F# - G#

Play 6 - 7 - 8 and you've got your A minor chord. (A - C - E) Now, switch out the root (A) for the G#. 6 - 6+ - 8 (A - G# - E) and you've got an AmMaj7 chord. Sort of mysterious sounding, isn't it?

Of course, not all of these chord options are going to be available for diatonic dulcimer players, but it helps to know how to build these chords. If you're looking down at your fretboard asking "what are my options?" The best way to proceed is to know what scales you can play from every root spot on the fretboard. And once you know those scales, you can build chords and begin working with extensions, "color chords", etc. If you're playing four-string equidistant, you'll get even more benefit out of these exercises.

Okay then! We've explored the key of D Major and its relative key of B minor. Coming up next, we'll get into the key of A Major and I'll introduce the Circle of Fifths as a way of keeping all of this stuff together. Happy Playing! And thank you to all who have been donating through PayPal. I appreciate it very much!

Studies in D for Diatonic and Chromatic Mountain Dulcimer

[UPDATED: If you've already downloaded the .pdf for D Diatonic Scales, please download the correct version for D Diatonic Scales again. Inadvertently left the setting on CAPO 3, which effects fingering. Thank you!]

For a reference starting point to this series, please visit the link for Studies in C for Diatonic and Chromatic Mountain Dulcimer.




• Download the .pdf for D Diatonic Scales



• Download the .pdf for D Chromatic Scales



• Download the .pdf for D Scale Harmonization

As we continue along on our journey through the 15 Major keys (and their relative minors), we reach the key of D - D for dulcimer. Since most mountain dulcimer players begin playing the instrument with a tuning of DAD (dd-A-D) this should be fairly familiar to many. Once again, chromatic players need not retune for any of these explorations.

Where the key of C had no flats (b) or sharps (#) and the key of G has one sharp, which is F# - we now add to that one sharp for the key of D. In addition to F#, we've also now got C#. Remember, flats and sharps effectively mean to lower (flatten) or raise (sharpen) notes a half step. Following the seven-note pattern, the D Major scale looks like this with its corresponding scale degrees:

D  E  F#  G  A  B  C#
1  2  3   4  5  6  7

A note by itself is simply that: a note.

Two notes comprise an interval: the measured distance between two notes.

Three notes officially becomes a chord or triad. You can also have more than three notes in a chord, but more on that later.

Begin building chords out of each note in the D Major scale by first choosing the root note and then skipping every other letter in the scale like this:

D  F#  A = D Major
E  G   B = E minor
F# A  C# = F#minor
G  B   D = G Major
A  C#  E = A Major
B  D  F# = B minor
C# E  G  = C# diminished

Major = root, Major third, perfect fifth
minor = root, minor third, perfect fifth

diminished = root, minor third, diminished fifth (or "flat fifth" or b5 or 5b)
augmented = root, Major third, raised or "augmented" fifth (or #5 or 5#)

Remember that even though we are dealing with seven-note scales, there are notes in between some of these steps that can be found by raising or lowering the notes a half-step.

According to Christian Schubart's "Ideen zu einer Aesthetik der Tonkunst", published in 1806, D Major is the key "triumph, of Hallejuahs, of war-cries, of victory-rejoicing. Thus, the inviting symphonies, the marches, holiday songs and heaven-rejoicing choruses are set in this key."

The key of D is certainly a preferred key for mountain dulcimer players, Old-Time performers and Celtic session musicans.

For every Major scale there is a relative minor or natural minor scale that shares the same notes, albeit in a different order. To find it within the Major key, simply begin on the sixth note of the scale and play the seven notes in sequence:

Major

D  E  F#  G  A  B  C#
1  2  3   4  5  6  7

minor

B  C#  D  E  F# G  A
1  2   3  4  5  6  7 

I know I'm repeating things quite a bit, but that's one of the fundamental rules of learning - repeat, rinse, repeat (okay, maybe not the rinse part) until it's locked into your memory.

Speaking of repeating, you'll notice in the Major and minor diatonic and chromatic studies that are available for download on each of our key studies blog posts, I have not touched upon the relative (or natural) minor for each of the Major keys. Rather, I've dealt with Major and minor scales coming out of the same root. (C Major - C minor - G Major - G minor, etc.) This is to help you with playing Major and minor examples in the same areas of the fretboard. Nevertheless, the construction of both types of scales is the same:

Major

Whole Step - Whole Step - Half Step - Whole Step - Whole Step - Whole Step - Half Step

minor

Whole Step - Half Step - Whole Step - Whole Step - Half Step - Whole Step - Whole Step

(Did you figure out what the relative Major key of G minor was? How about the relative Major key of D minor?)


Scale Harmonizations

I figure now's as good a time as any to begin covering some of the extra materials in the .pdf files you're hopefully downloading. Along with Major and minor scales (and there are a few different types of minor scales, which we'll get into with the next post) for diatonic and chromatic fretboards, I've also included scale harmonizations. Scale harmonization can be described as using each note of a scale as a root note for a chord and then adding other notes within that scale to form a chord.

So, instead of playing a scale of seven notes, you're playing a scale of seven chords in sequence. This can be effectively viewed as a chord progression and it's the foundation upon which most music in the western world is based.

By the way - notice how the term "notes" is an anagram for "tones"? Cool, huh? They are one and the same.

Also, notice how I've been capitalizing the term "Major" and spelling "minor" with a lower-case letter. This has been by design, leading up to a better understanding of reading scale degrees.

Let's take our D Major and minor scales with their Arabic numerals (1-7):

Major

D  E  F#  G  A  B  C#
1  2  3   4  5  6  7

minor

B  C#  D  E  F# G  A
1  2   3  4  5  6  7 

Now, let's replace the Arabic numerals with Roman numerals (I-VII)

Major

D   E   F#   G   A   B   C#
I  II  III  IV   V   VI  VII

minor

B   C#   D   E   F#  G   A
I   II  III  IV  V   VI  VII 

Now, remember, when we build chords off of each of these notes, skipping every other letter, the result is a mixture of 3 Major, 3 minor and 1 diminished chord. That's just the way the math works out.

For Major scales, you can always count on 1, 4 and 5 being Major chords (or scales), 2, 3 and 6 being minor chords (or scales) and the 7th being a diminished chord (or scale.)

For minor scales, you can always count on 1, 4 and 5 being minor chords (or scales), 3, 6 and 7 being Major chords (or scales) and 2 being a diminished chord (or scale).

If we use all uppercase Roman numbers, then we just add a lowercase "m" to those scale degrees that are minor. We then add a degree symbol "°" (like what is used to denote temperature in Celsius or Fahrenheit) to the degrees that are diminished. Nothing is changed with the Major degrees. So we get this for the Major and minor scales:

Major

D    E    F#    G    A    B    C#
I   IIm  IIIm  IV    V   VIm  VII°

minor

B    C#    D    E    F#   G    A
Im   II°  III   IVm  Vm   VI  VII 

Notice how in either scale, the characteristics of each scale degree don't change between Major and minor scales. D remains Major, B remains minor, C# remains diminished, and so on. The order changes, but that's it.

Though this method is perfectly acceptable, there is also another way of going about this, and it's considered easier to read by many. You simply make the minor and diminished scale degrees lower-case. But be sure to keep the degree symbol on the diminished:

Major

D    E    F#    G    A    B    C#
I   ii   iii   IV    V   vi   vii°

minor

B    C#    D    E    F#   G    A
i   ii°   III   iv    v   VI  VII 

WHY is this important? Well, by using the scale degrees, we can talk about the progression of chords without having to specify the key.

For example, one of the most popular chord progressions of all time is:

I - IV - V

What does that mean? Well, at first glance, we can see that they are all Major chords. So, let's assign a key: D.

If we're using a D Major scale, that means that:

D  -  G  -  A
I  - IV  -  V

The chords built off of the first, fourth and fifth scale degrees. Try playing it on your mountain dulcimer (or whatever instrument you've got with you.) Sound familiar?

So, what if we see this?:

i  -  VII   -  VI

Our first clue that something is different is that our root chord is minor (lowercase.) So we're dealing with something in a minor key, even though it has Major chords as well. If we are in the key of Bm (B minor) then:

B  -   A    -  G
i  -  VII   -  VI

Of course, you can also write it out as Bm - A - G, but our focus now is on identifying Major, minor and diminished chords by looking at the scale degrees.

Next up: we'll get into the relative minor key from D Major and also dip into a look at chroma or extended chords.

Dulcimerica 158 - "Dulcimer Blues Pt. 2"

Eternal Cabbage

Jerry Rockwell is the mad scientist/genius of the mountain dulcimer, applying music theory to this simple instrument and exploding/exploring the possibilities within/without its structure. His "Eternal Cabbage" chordal exploration is a great exercise for playing and recognizing partial chords up and down the fretboard.

While you're over at his site, poke around and investigate some of the other pages too. Do it till your head hurts - then bookmark where you left off and come back for more. It's guaranteed to get you playing better/smarter in a heartbeat/New York Minute.

I have no idea what this/that is all about. Some kind of hidden theme - need more coffee to suss that out.

Hands-On Training

You may not be familiar with Mike Casey, the performer - he's a wizard on mountain dulcimer, limber like a gymnast on the fretboard. His book "Hands-On Dulcimer" is like spring-training for serious players.

Chock full of exercises for the left and right hands, this book is something I use to warm up before launching into playing or working out tablature or studying music theory. It consists of a number of targeted modules that help to develop and firm up strumming, flat and finger-picking, melody and chordal development as well as strengthening finger and hand muscles to do the work.

Great for all skill levels, it's either a great introduction to techniques such as hammer-ons, pull-offs and slides or it's a rigorous work-out for those familiar with those ornaments. It's probably a good thing to face; you don't just learn all of this stuff and then automatically "have it" for the rest of your life. Nay - even seasoned professionals need to crack away at scales, chords, various rhythms, picking patterns and studies in order to, as I call it, "stay on the horse." The moment you stop learning is the moment that your music starts to go south (and I don't mean Key West, either.)

I highly recommend this book to not only my students, but also anyone who is serious about stepping up their game on mountain dulcimer!

Amazon coupons are available for this book.