Evolution of Chords

Objective. To understand the theoretical transformation process that takes place when the pitches of a scale are reconfigured into an arpeggio and how the sequence of pitches of an arpeggio are stacked to become chords. To develop the theory skills to be able to spell out the letter name pitches of the seven diatonic triads of the major scale. Continue to expand our understanding of the relationship that exists between musical pitches and theoretical numbers. To continue our discussion of correlating theoretical complexity with our musical styles from a harmonic viewpoint.

A bit of history. About 300 years ago, the genius of the equal temper method of tuning and the creation of the piano combined to begin to give to composers the ability to equally create any chord or melody from any of the 12 pitches of the chromatic scale, all of this music within one instrument, and all of it in tune. Talk about YIPEE ! This enthusiasm here is not intended to suggest that prior to the emergence of the piano and equal temper tuning, that something was "missing" from the musician's palette of the day. Those folks got along just fine, wrote lovely, lasting music, some of which is still played everyday in our own times today. Lest we forget that their ways of doing things evolved and improved on the ways of those before them. Just as the piano was the "new" instrument during the middle 1700's, in modern times, the "electric" and "synthesizer piano" evolved from the acoustic piano. This process of improving or creating new instruments from existing ones is simply the way of the world and can apply to just about everything. Maybe there is always a better way for everything, and we just haven't dreamed of it yet.

With the emergence of the equal temper tuned piano, composers now paired their chords with their melodies. The chords generally struck in the left hand using lower pitches and the higher pitched melody in the right hand, composers began ushering in a new era of music termed the "homophonic style." Defined as one main melody supported by chords, this homophonic style of composition is still way in vogue today. That 99% of everything we usually listen to and perform, from European and American classical masters from the 1750's through the American blues, jazz, pop, folk, rock and the "moderns" of right now today, is all written in this homophonic style of composition, one distinct melody line supported by background chords or other aural textures. All good?  (1)

A theory for spelling chords. Thanks to all of the knowledge and skilled effort that goes into placing equal temper tuning into a well built piano, or even a guitar for tat matter, creating nice sounding chords is now quite a simple task. The following discussions describe a method to spell out the letter names of the pitches of chords. Thinking major tonality in the key of C, we can start back at our original beginning point simply 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 C major scale. Example 2.

By adding our numerical scale and chord degrees to our C major scale and it's diatonic arpeggio, the following chart emerges. (2) Example 3.

Spelling chords. To spell out the pitches of a three note chord, we simply find it's root pitch from our major scale, locate that pitch in the arpeggio and read to the right to identify it's other pitches. Let's locate the 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.

  at the piano 

Easy enough eh? Or need help? 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.

Our 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 it's major scale. C, D, E, F, G, A, B, C.

(3) Convert this scale into it's 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 it's 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. Mmmm ... 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 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 it's chords? That is indeed the case.

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

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 it's major or minor quality. Example 10.

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 in to it's 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, just creative solutions to express our ideas.

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 the major sale. Do note the slight change in the charting of the numbers and pitches so as to allow for all of the G arpeggio to be included. The theory is still the same. Example 11.

O.k. with the spelling of the pitches yes? The root G is followed by it's 3rd B, then it's 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, it's 7th is added. 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.

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. 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 it's tension and release function within elementary "dominant / tonic" cadential motions, we can build from it's triad by adding it's "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 styles of American and European music we love.

So, thinking C major, our tonic One chord is C major, it's dominant chord is built on the fifth scale degree of the major scale, the pitch G. Let's spell out it's 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 it's 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 and figure out all of the coolness they created.

Back to the theory, here are the pitches of the extended arpeggio for G 7, the dominant 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 it's complexity and where we often find, or not, it 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 it's 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, it's 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. 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.

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" 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 will non-diatonically alter the 9th 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 it's 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 Copeland and beyond to the moderns, generally not a "core" chordal color of most of the popular classical music we hear on the radio. Thus, perhaps used more for it's different effect of the V 7 than 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.

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 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 and 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. It's softer hue "planes" well, meaning it slips and slides chromatically up and down with more ease than V7. The !3th / 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 it's ability to sweeten up their cherished V 9 chord, the main 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 major triad, it's 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 it's 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 classical literature.

G 15. As the 15th degree pitch is the same as our starting pitch, though two octaves up, we usually don't think of it in terms of being a color tone. Things get thick enough in a hurry with sorting out color tones without additional pedantics. I must note here that in my own theoretical perspective, raising the diatonic 15th by half step to #15, plays a rather crucial role in the theory, but as a component in a different part of the story. You'll have to write to me for more information on this or search through the Tonal Resources text for the "Overtone Series Experiments" for more information about this #15 rascal. ( I'll link this up better for ya soon as I can. )

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 it's harmony. This we could partially determine by use of upper extension pitches to the triad called color tones as well as complexity of it's 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 ...!

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 it's vast and perfectly tuned system of harmony. Mmm ... Prior to it's 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 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 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, one distinct melody line supported by chords, each of which is available from any of the 12 pitches of the chromatic scale, and now all of it available on one instrument. Talk about a composers dream come true ! (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 a harmonic analysis of a J.S. Bach Chorale. 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 ! 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. Needless to say I've never forgotten it, probably because I've written it out for friends about a gillion times.

(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.

(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