Evolving Arpeggios into Chords / (?)

Objective. To review how pitches of a scale become an arpeggio and how the arpeggio pitches are vertically stacked to become chords. To develop the ability to be able to spell out the letter name pitches of the seven diatonic triads of the major scale. Continue to expand our discussion of correlating theoretical complexity with our musical styles from a harmonic viewpoint.

A bit of history. With the emergence of the equal temper tuned piano in the early 1700's, composers began in earnest to support their melodies with stacked pitches of harmony, the chords generally struck in the left hand using lower pitches and the higher pitched melody in the right hand. This style of composition ushered in a new era of music termed the homophonic style. Defined as one main melody supported by chords, this approach to composition is by far and away what most of us we hear everyday and includes the European and American classical masters, blues, jazz, pop, folk, rock and the moderns of today. (1)

Evolving our scale into an arpeggio and into a chord. Thinking major tonality in the key of C, we can start by extracting the seven pitches of the C major scale from the twelve pitches of the chromatic scale. Example 1.

Next, we reconfigure the C major arpeggio from the two octave C major scale looping of pitches. Example 2.

By combining it all together, our numerical scale degrees, scale pitches, chord degrees and diatonic arpeggio pitches, the following chart for spelling out the pitches of chords emerges. (2) Example 3.

Spelling chords. To spell out the pitches of a three note chord we theorists term a triad, we simply find its root pitch from our major scale, locate that pitch in the arpeggio and read to the right to identify its other two pitches, its 3rd and 5th. Let's locate these three pitches of the C major chord in the chart above ( in bold type ), C, E and G, then on the treble staff and also on the piano keys. Example 4.

standard notation	at the piano

Easy enough eh? Or need help? Moving right along then, lets spell our Two chord, the chord built on the second scale degree of the major scale. Here is our chord spelling chart. Example 5.

The second scale degree of C major is the pitch D, this becomes the root of our chord. Finding the root pitch D in our arpeggio pitches then reading to the right of the arpeggio we see that the pitch F is the 3rd and A is the 5th. View the Two chord on the staff and locate it on the piano keys. Example 6.

Lets spell our Three chord, the chord built on the third scale degree of the major scale. Here is our chord spelling chart. Example 7.

Our third scale degree of C major is the pitch E, this becomes the root of our chord. Reading to the right of our root E in the arpeggio we see that the pitch G is the 3rd and B is the 5th. View the Three chord on the staff and locate it on the piano keys. Example 7.

Sounding these pitches together on any of our instruments or combinations of instruments sounds the E minor chord. In our present scheme of chordal theory, this E minor chord is also the "three chord in the key of C major." Cool?

Mini-review of the process of spelling chords.

(1) Determine the key of our music. C major.

(2) Spell out the pitches of its major scale. C, D, E, F, G, A, B, C.

(3) Convert this scale into its arpeggio by skipping every other note. C, E, G, B, D, F, A, C ... ( like our scales, the arpeggios are also perfectly closed loops of pitches yes?)

(4) Decide which chord needs spelling by its numerical degree within the scale. Find this pitch in the arpeggio, it becomes the root of our chord. Read the pitches to the right of the root for 3rd, 5th, and onward for other pitches within the chord. Spell the One chord: C, E, G. Two chord: D, F, A.

So your probably beginning to wonder about the rest of the pitches in the arpeggio after the root, 3rd or 5th of the chord? I thought so. First this chart, another idea or two and then more of the magic.

Spelling our seven diatonic triads. In this next chart, we work both horizontally across and vertically downward, spelling out all seven diatonic triads of the key of C major. At the top of the chart is the C chord scale or arpeggio that contains the pitches we need to spell each of the three note, diatonic triads. I expressly made this chart a bit tricky to read ... do search a bit for the theory within. Example 8.

Figure out the pathways? Probably by this point you've got it, but still it's a pretty neat process huh? Help? The "A ..." at the right of the top line is the clue. Hmmm ... Remember our loops of pitches? How all of our groups of pitches will always eventually close back at our starting point? And could we place the pitches of any of our other 11 relative major / minor scales in the above chart and spell their chords in exactly the same way? ABSOLUTELY ! So we can basically plug any of the pitches of our scales into the above chart and spell its chords? That is indeed the case.

Here's the sound of the 7 diatonic triads of C major. Example 9. (3)

I ii iii IV V vi vii VIII

Sound familiar? Tis a very common chord progression. Notice the Roman numerals above each chord? We theorists will use these symbols to denote diatonic scale degree in relation to the tonic, as well as using the upper and lower case symbols to denote whether the triad is major or minor. As with our scales, it's the 3rd of the chord which determines its major or minor quality. Example 10.

C major to C minor by lowering its 3rd by half step D minor to D major by raising its 3rd by 1/2 step

Starting to hear these two distinct colors? Starkly presented as in the above idea, the major / minor shading is not all that obvious. When listening to music it's a lot easier to make this major / minor distinction. So often the overall tonality of the tune is unmistakable, especially if we're tuning into its theory elements. A sad and reflective sounding song? Usually in the minor tonality created by minor chords. Joyous and uplifting? Major chords and thus major tonality. Can we mix the major and minor colors together? Of course, were artists, were creative and our inner muse is our guide. There is no right or wrong, we are the "musical mixmasters" of the local universe, we find creative solutions to express our ideas and the art in our hearts.

More of the magic. So what about the other pitches of the arpeggio past the root, 3rd and 5th of the triad? Turns out we often need them to help define our unique musical styles. First the theory and then the art.

The dominant 7th chord. Familiar with this critter? Here's the theory in the key of C major. Our dominant chord is always built on the 5th scale degree of either the major sale or minor scales. Do note the slight change in the charting of the numbers and pitches so as to allow for all of the diatonic G arpeggio to be included. The theory is still the same. We simply designate the pitch G to be #1, as it is the root pitch of the dominant chord in C major. Example 11.

O.k. with the spelling of the pitches yes? The root G is followed by its 3rd B, then its 5th D. This creates the G major triad built on the 5th scale degree in the key of C major. So often in many of our styles of music, when the Five chord comes in to play, its 7th is added. It becomes a "dominant seventh." We do this to simply create a greater degree of urgency to "resolve" back to our One chord. It makes our dominant chord a wee bit more dominant in directing harmonic traffic. Compare the cadences or resolving motions towards C major, first by G triad then the triad with an added 7th. Example 12.

G triad      C major triad      G 7      C major triad

Feel the "oomph ..." of the G 7 to C major? Keep trying, it's in there for sure. Find these changes at the piano and feel the push of the 7th in the lead, the pitch F in bar 11 wanting to move down by half step to E, the 3rd of the C major triad in bar 12. And how about the pitches past the 7th in the arpeggio? Can other chords beside the dominant have a 7th? Is there a 9th? 11 or 13th? What's beyond the 13th or what's practical?

Now the art. Interestingly enough, correlating musical style and theoretical complexity in regards to the harmony is a very easy task. With the emergence in this chapter of the dominant 7th chord and getting a glimpse of its tension and release function within elementary dominant / tonic ( Five to One ) cadential motions, we can build from its triad by adding its color tone (4) pitches and correlate these extended chords to musical style and theoretical complexity along the way. For as second in command to our tonic or One chord, we so often find the dominant chord as our harmonic "traffic cop", directing the flow and direction of the music, in all of the homophonic styles of the American and European music we love.

So, thinking C major, our tonic One chord is C major, its dominant chord is built on the fifth scale degree of the major scale, the pitch G. Let's spell out its color tones, using the same method used above and create an abbreviated chart to zero in on the dominant's triad and color tone extensions. Note the bottom row of the chart now includes chord symbols, simply a shorthand way to designate a chord in sheet music, especially for guitar part. We can then discuss each of the dominant chords, from the triad upward into its arpeggio, in regards to theoretical complexity and the musical style or settings we often find them. What we must always remember in these type of art discussions, is that the composer has the final say as to what goes where and when in their music. That anything can be anywhere. Just one of the many cool aspects of composing. As theorists, we simply come along after the fact and figure out all of the coolness they created, then find ways to use the sounds in our own artistic creations.

Back to the theory, here are the pitches of the extended arpeggio for G 7, the dominant chord or Five chord in the key of C major. Example 13.

Nice chart huh? The following discussions simply illuminate various aspects of the dominant chord as we add the color tone pitches one by one, gradually increasing its complexity and where we often find it, or not, in the musical styles we love. Remember that stylistically, anything can be anywhere and that we each must often accept a chordal color as sounding right, to then begin to incorporate it into our own creations.

G triad. Usually just noted as the chord symbol "G" in a musical score, we often find the G triad functioning as a dominant chord in children's songs and some of the more basic folk music, in songs that tell stories. I think a part of this is due to the easy guitar shapes for the G chord, as well as the softer color of the triad without its 7th. In these styles, the melody of the song is almost always in the vocal part. The harmony is subtle, so often the rhythms of strumming the guitar motor things along, allowing the story to unfold. Instrumental improvisation is minimal if present at all, although vocal elaboration of the melody can be boundless. So cool is knowing that these basic musical elements, which in all probability go all the way back to our musical origins, can create any degree of emotional intensity, artistic beauty and musical fun.

G 7. Adding the 7th to the triad we create the dominant 7th chord. With the addition of this one pitch to the triad, its stylistic range expands dramatically. From children's songs into folk songs, which with the added 7th may take on a distinctive Mixolydian flavor, a favorite color for jammers of all musical stripes. Keep in mind here that a traditional American folk / bluegrass sound from early America days was created by the Scotch / Irish group of folks, and that their musical heritage and traditions are so often based in the Mixolydian pitches. Tunes like "Old Joe Clark" capture this dominant 7th coloring.

The tritone bearing, V 7 chord is the key director of harmonic motion in all of the European classical music we love. Everyone from Handel, through Haydn, through Mozart, through Beethoven and into Brahms and beyond to the "moderns" used this simple four note chord to modulate or direct the key schemes of their music. The V 7 chord is among the core colors for American Blues, especially after mixing with the rock n' roll sounds of the 1950's and 60's. The rocking classic "Twist and Shout" uses the dominant 7th arpeggio to great effect in the vocal line. So anything with even a dash of the blues flavor will often include this combination of pitches. The jazz players will use this inner tritone tension of the V7 chord to "theoretically" create "substitutions" that will resolve the G 7 chord not only to C major / minor, but the Eb, Gb and A major / minor key centers as well. The jazz cats totally exhaust the traffic cop concept of this dominant 7th chord to direct harmonic and melodic motion.

G 9. Not usually found in children's songs or folk music, both the blues and jazz cats dig the dominant 9th chord. I think a big part of this love is simply due to the fact that there is a rather easy chord shape for guitar for this color, that holds up well to even the most complex rhythmic poundings. Blues and rock artists will use the dominant 9th in all of the funk musical styles of the 70's and 80's, or think of the G 9 as a B -7b5 voicing, which with no root, is lighter in texture but darkly colored by the 9th. This G 9 is not a folk or bluegrass color, it's too dark for these lighter hued styles. Jazz players abuse this color on a regular basis and will also non-diatonically alter the 9th by half step both sharp and flat, borrowing pitches from other keys. The G 7#9 is a blues color too, while the G 7b9 is jazz or sometimes, though rare, in contemporary pop music. American pop runs a wide range of complexity. And lest we forget that jazz was the American "pop" or popular music from the early 1900's to the 1950's when rock n' roll came along. Pop king Stevie Wonder's music is anything but theoretically simple. Of course his writing is so fluid one might never know of its complexities until we try to recreate his sound with our own instruments. In the Euro / American classical music tradition, we find the dominant 9th chord as far back as Scarlatti and forward to Wagner through Copland and beyond to the moderns, though generally not a core chordal color of most of the popular classical music we hear on the radio. Thus, perhaps used more for its different effect than the more basic V 7 structure. (5)

G 11. Not generally a folk color, the G 11 could be theoretically viewed as a type of suspension, popular with the rockers and pop guys. So often we hear this dominant 11th chord resolving to the tonic major or minor triad. Jazzers often use this color also as a "sus" or suspended chord, in the popular Bossa Nova styles from the 1960's and all of the popular Latin styles that evolved from this beginning. Jazz artists will also sharp the eleventh (#11), above the ninth, to bring in a wee bit of the whole tone color or think polytonally, floating two key centers together at the same time. And as with the V9 chord, we do find the 11th chord in classical music, although harmonies with this many pitches stacked up are rare indeed, thus it appears as more of a 4 / 3 suspension.

G 13. The dominant 13th chord is reasonably complex. It carries the tritone within of course, that's what makes it a truer dominant chord, but the added 13th is somewhat reminiscent of the pentatonic color, so the 13th adds a bit of the carefree, joyous pentatonic magic while still having a blue hue core and dominant function. Blues players will use it as a tonic chord as there are some great sounding, yet relatively easy guitar shapes they use to bring it to life. With the added 13th, which is the 6th scale degree up an octave, the V 7 chord takes on a bit of a softer hue. So it's a wee bit lighter and thus perhaps better for telling a funny or more carefree story than the dragout, crash and burn of many of the darker blues tunes. "Jump" tunes, with either rhythm or 12 bar blues changes from the 1940's onward, used the lighter 6th / 13th color to help get the dancers on their feet. Jazz cats love the 13th for tons of reasons. Its softer hue "planes" well, meaning it slips and slides chromatically up and down with more ease than V7. The 13th / 3rd relationship between dominant and tonic makes for an easy common tone between the chords, smoothing out the cadential motion. The 13th degree alters easily by half step down to b13 or #5, creating a nice "passing tone" line. Funksters crave the 13th for its ability to sweeten up their cherished V 9 chord, the main harmonic pillar of their musical citadel. The softer color of the dominant 13th allows us more easily to hang other color tones onto it, b5 / #5, b9 / #9, the # 11. All of these are jazz colors and provide nice, embellished ways to do simple, cadential functions. With the 13th being, the 3rd of the tonic major triad, its inherent strength within the tonal gravity of a key center also makes it a popular polytonal chord member, allowing players to take it a bit further "out" while still having the solid "anchor" of the 3rd of the tonic triad in its color. Of course we do find this dominant 13th color in classical music, but like the 9th and 11th, it's a bit of a rare bird and gets a bit tippy when the pitches are stacked so high, it's just not too common in the traditional classical literature.

Here is the sound of the above dominant seventh chords. Example 14.

G 7 G 9 G 11 ( G 7 sus 4 ) G 13

Review. Equal temper tuning is what allows us to create the in tune, full spectrum chords from our modern piano. Earlier, pre equal temper melodic scales became known as the church modes. In polyphony, each instrument plays a melodic line. In homophonic music, composers create stacks of vertical pitches that we call chords. Chords are created from arpeggios, a hybrid chord scale, built in major and minor 3rds. A root, 3rd and 5th pitch is needed to create the three note triad. Of the three notes in the triad, it is the quality of the 3rd interval above the root that determines the major or minor color of the triad. In further discussions we could begin to correlate the various styles of Western music with theoretical complexity of its harmony. This we could partially determine by use of upper extension pitches to the triad called color tones as well as complexity of its chord progressions. The true genius of equal temper tuning is that every scale, chord, alteration and extension we can devise can be equally projected from each of the 12 pitches of the chromatic scale. And it's all in tune! Talk about yipee ...!

Vocabulary for this chapter.

Go on and ace the quiz, then onto a discussion of how we notate and motor all of this theory stuff in real music, i.e., the Rhythm. Remember as you take the quiz, you can always "google" any term for more information.

Second quiz. Spell out the letters for each of the seven diatonic triads in the key of D major.

Easy enough huh? Have a sense of where our harmony comes from? Do you have the ability to play chords on your chosen instrument? Sense how musical complexity correlates with harmonic densities? Comments or questions? info@jacmuse.com On to our next topic but first ... a question and musings and then a quote.

Is equal temper tuning's greatest contribution to the overall evolution of Western music in its vast and perfectly tuned system of harmony. Hmm ... Prior to its emergence and acceptance, players had a varied assortment of "groups of pitches" and corresponding ways to tune their string and brass instruments, all of which is said to have worked just fine. Today we often refer to these early groups of pitches as the church modes. These modes were later assimilated to become the essence of the equal temper system of tuning, which then to a certain degree applied to all of the instruments. This new tuning and way of hearing the pitches was a somewhat radical departure from what musicians were using during those times. From archived records we know of this early, pre equal temper music was polyphonic, described as music with two or more melodic lines played simultaneously. While oftentimes thematically and rhythmically independent, these melodies would often momentarily converge to create vertical pairings of pitches. This sounding of two or more pitches together must have created a semblance of the harmony that was still yet evolving in the continued evolution of music that began with the early Pythagorean ideas. With the creation of the piano and acceptance of equal temper tuning in the early 18th century, we see the emergence of a new style of composition called homophonic, one distinct melody line supported by chords, each of which is available from any of the 12 pitches of the chromatic scale and all of it available on one instrument. This style of composition is roughly 300 years old now and still going strong! What style do you compose in? (6)

"The future belongs to those who believe in the beauty of their dreams." Eleanor Roosevelt

rhythm

(1) This is a combined footnote that includes the historical reference to equal temper from the Isacoff work and the definition of the homophonic style of composing from the Harvard Dictionary of Music.

(2) I've yet to see this combination of elements in chart form in any music theory book I have or have ever seen. Very early in my collegiate career I was tasked with doing harmonic analysis of a J.S. Bach Chorales. With little theory knowledge and zero piano skills, I simply had no way to "crack" the code. Like the "Far Side" comic ... "look at all the black dots", I was completely at a loss and had spent part of an evening just staring at the music. Going over for coffee the next morning at our campus cafeteria, I ran into classmate alto saxophonist, jazz improvisational extraordinaire Larry Tuttalamundo, who also wanted a cup of coffee. Tutt was a bit tight on dough, but that luckily I had, but he was pretty loose with his knowledge of chords, their progressions and overall theories of modulation, substitution and most importantly at that time to me, how to simply identify them by spelling out their pitches! So for the price of a cup of coffee, Larry drew this chart for me in pencil on the back of a paper napkin and explained how it worked. I probably still have it somewhere after these near 30 years. If I can find it needs to be framed! Needless to say I've never forgotten it, probably because I've written it out and explained it about a gillion times to help new musical friends just as Larry Tutt did for me three decades ago.

(3) Ottman, Robert. Elementary Harmony, Theory and Practice, Second Edition, p. 233. New Jersey: Prentice-Hall, 1970.

(4) I cannot find this term in any of my theory books. I learned and use this term as how it was taught to me by my college professor Dr. James B. Miller, at the State University of New York at Plattsburgh, Plattsburgh, N.Y., 1980.

(5) Ottman, Robert. Advanced Harmony, First Edition, p. 17. New Jersey: Prentice-Hall, 1970.

(6) To get a sense of the historical drama of the emergence and acceptance of equal temper tuning, one book to read is Isacoff's "Temperament ... The Idea That Solved Music's Greatest Riddle." U.S.A. Alfred A. Knopf, New York. 2001