cycle of fifths

If the vast majority of melody and all of the harmony of recent American music ( the past 150 years or so ) is created from within the equal temperament system scheme of tuning, and by adding a heaping amount of the blues spice to equal temper, is there an "organic way" to organize this vast musical resource? Absolutely. There are many n'est pas?

Based on theoretically dividing the octave into 12 equal parts, which in turn become the 12 pitches of the chromatic scale, from this equal temperament system we can create the two main tonal / artistic environments which we term the relative major / relative minor tonalities. These emotional environments are basically created from the major and minor scales and their variations. Is all of the harmony we hear in American music is based in this equal tempered system? Totally, the equal tempering of the pitches allow chords to happen from each of the 12 pitches. Are there more than 12 pitches within equal temper? Nope.

So where are we going with all this? Well, organizing this vast but finite resource is potentially an important step for the emerging creative artist, providing an overview of the entire system and it's resources. One essential way to organize the 12 equal divisions of the octave and the tonalities they create is to create a picture like the hours on the face of a clock. As theorists, we can call this picture the "cycle of fifths." Example 1.

Let's try to create a sound on this loop of pitches. Example 1a.

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Oh well not too much music there eh? So, why that name, cycle of fifths? Well, the fifth is the first partial, after the octave, as produced in the naturally occurring overtone series. To explore this just a bit, one way to describe this phenomena of nature is by thinking of a stringed instrument. The sound created when the entire length of a string is plucked theorists call the fundamental pitch. Divide this string in perfectly in half and we create a pitch one octave higher than the fundamental. Divide this string into three equal parts and we create a pitch whose sound is the interval of a perfect fifth above the fundamental pitch of the string. Cool? Thus, the name cycle of fifths is organically derived from the overtone series, and this interval of a perfect fifth we use to organize the 12 key centers of equal temperament. Cool with this?

So, based on the naturally occurring overtone series, this convenient key clock is created by the motion by perfect fifths. C at 12 o'clock. Moving clockwise to the right, what is the fifth degree of the C major scale? Count out the letter names of the C major scale on your fingers.  1,2,3,4,5, the fifth is G. Yes? G is at 1o'clock. What is the fifth degree of G? D right? Fifth degree of D? A right? Round and round. Example 1b.

Cycle of fourths. Must we always go clockwise? Of course not, this is art right? Moving counterclockwise of the cycle of 5th's, to the left, the key centers move by perfect fourth. What is the fourth scale degree of C major? F, right? Fourth degree of F major? Bb, n'est pas? Bb? Are you hip to the "b" of Bb? Theorists call it an accidental. So, round and round until the loop of 12 keys closes upon itself by motion of ascending perfect 4th's. Here's the picture, recreating the cycle of pitches in perfect 4th's. Example 2.

Here is the sound of this loop. Example 2a.

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So why is this cycle of fifths / fourths important for the creative musician? Well, for many reasons. First, that the cycles are a pictorial representation of how the key centers of the equal tempered system are organized. It provides a mathematical way of understanding the theory of the 12 tone system and creates an initial "foundation" upon which new theoretical information may be placed in an organized manner. With the idea that one way to learn the theory is to understand the concept in one key and then simply project that theoretical principle from any of the 12 tonal centers available, the cycles are an easy way to organize the whole structure of equal temper.

Is that is why so much of this text presents the theoretical ideas in one key, usually C for the major environment, or A for the minor tonality, because of their simple notation, i.e., no sharps or flats? Once the idea is understood, we simply project the identical theory to the other tonal centers. The cycle of fourths / fifths provides a solid representation of the "big picture" key wise and can thoroughly organize our shedding of the theory and resources.

Secondly, that the chord progressions we so often use to create American music uses the root motion of a perfect fourth / perfect fifth, which are said to be "inverted" of each other. These two intervals are by far and away the most common root motions for our chords regardless of style. When the dominant resolves up to the tonic from, the motion is up the interval a perfect fourth. When we reverse or invert this cadential motion, the resolution of the roots of the chords is from a fifth above. Examine the bassline in the following idea. Example 3.

resolving up a perfect 4th

G up to C

resolving down a perfect 5th

G down to C

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Within a given key, these root motions of the fourth and fifth are oftentimes used to encompass all of the diatonic chords. This next idea cycles all of the 7 diatonic chords using the common root motion of the perfect 4th. Example 4.

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Sound familiar? Although we do not generally create our songs of American music using all of the chords used above, we do often extract segments of the above cycle of 4th's progression to create our music. Check out the following idea. Example 5.

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The above chord progression is commonly termed a "Two / Five / One." Looking at the graphic of the cycle, we see the counterclockwise root motion of D moving to G moving to C. Players call this backpedaling. This Two / Five One harmonic "cell" of example 4 is a very common chordal feature in jazz standards. Examine the music of tunes such as "Tune Up", "Round Midnight", "Satin Doll", "End of a Love Affair", "Joy Spring" for the Two / Five / One harmonic cadential motion. Depending on which way you go artistically, this 2 / 5 / 1 harmonic cell may become a big section on your palette.

Third, the cycle of 5th's provides a pictorial representation of the 12 major / minor tonal centers and by it's mathematical layout, displays how closely one key is related to another. Keys that are said to be closely related simply share more pitches in common. How important this is to each player is hard to say, but just the picture itself puts all the keys on the musical "map" so to speak and perhaps makes the understanding of the whole system a bit easier, by providing a glimpse of it's "big picture." The "relatedness" of one key to another is an important aspect in music composition and also in the theoretical analysis of musical pieces. A quick reference for how closely one key is related to another is achieved by looking at their key signatures, which simply shows us what pitches are used to create a given key. Here is a picture of the cycle of major keys with their signatures. Example 6.

So, is the key of C and G closely related? How about C and Ab? Even though the key of G and Ab are only a half step apart, from the chart above we can see by proximity that C and G are closer than G and Ab. In writing tunes, these relationships between keys can create some dramatic effects and this cycle of keys graphically lays it all out so very conveniently. Is this part of the color of keys thing? Yep.

Fourthly, that the cycle of fourths provides a pathway to cover all 12 keys, that becomes an exercise format for the improvising musician. For example, we learn the theoretical concept of the major triad based on the root C. It is comprised of the first, third and fifth degree of the C major scale. So, the pitches C, E and G. To cement this new knowledge and get it under our fingers on our chosen instrument, we can simply run it through the cycle to expand this knowledge over the entire resource provided by our equal temperament system. Here we run the major triad through the cycle of 4th's to cover all of the 12 major keys. Example 6a.

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Conceptually easy enough eh? Got these 12 major triads under your fingers? In practice, it's a cool and potentially important challenge for the aspiring jazz artist. If this is a new idea for you, give it a try, even one time though the cycle in this manner will change your playing and concept dramatically. And like many things in life, it's easier the second time around. At many points throughout the text the reader will be prompted to run an idea through these cycles, future editions will include such exercises written out. Do please keep in mind that for the improvising musician, the ability to "run the cycle" directly off the internal "harddrive" in our head is the ultimate goal!

So, can we build a major scale from each of the 12 pitches? Absolutely. Minor scales? Absolutely. Any scale from any pitch? Totally. Chords too? Absolutely, 100% correct. Is this like the anything from anywhere concept? Exactly. Comments / questions?

Where to next?
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I find television very educating. Every time somebody turns on the set I go into the other room and read a book. Groucho Marx