Theory of Harmony


I’m presenting my students with an anthology of 15 pieces. I’m not putting complete scores online but will include sample pages. (Sources are given at bottom of post. If you want the full PDF sign up for Transitional Technology and email me.)

Theory of Harmony (compiled by Ethan Iverson) 

Harmony is harmony; the same European information that goes back hundreds of years. Voice leading the twelve chromatic notes is voice leading the twelve chromatic notes.

Jazz performances include information from black music and the blues. Jazz masters learned European rules and then added in that other kind of aesthetic according to personal taste and style. Each greatest master is their own universe. Duke Ellington, Thelonious Monk, and McCoy Tyner all share the basic European information but their non-European information is harder to pin down. They all play blues riffs and relate harmony to rhythm in a “jazz” way but intellectual analyses of these procedures are rarely convincing. Indeed, “jazz harmony” books usually get it wrong by trying to reduce these black music and blues seasonings to a wholesale system disconnected from a master’s personal taste and style.

When jazz was popular there was a piano in most American homes. As a result there was a lot of sheet music generated by the major publishers. Some of that sheet music is frightfully banal and none if it is as great as classic jazz records. Still, the best of it can give an insight into the basic sound of jazz.

There is no reason to diligently practice any of the following selections. Just read through the pieces. Fool around and have fun. Learn some of the American seasonings to the European harmonic system by osmosis.

In approximate chronological order:

Heliotrope Bouquet — Scott Joplin and Louis Chauvin. Scott Joplin is the only jazz master who is mostly known through notated scores, but that’s not a good reason to treat Joplin like European classical music. Back when the music was fresh, experienced performers played ragtime with a hint of swing. Improvised elaboration and some swing is absolutely encouraged. Heliotrope Bouquet is a rare example of Joplin (or in this case, perhaps it’s Chauvin) using a left hand that connects to clave in addition to the march.

1. Heliotrope JPG

Pastime Rag No. 4 — Artie Matthews. Matthews was an important composer and arranger and also the teacher of Frank Foster. His clusters are famously “different” but many black pianists were playing like this in the first part of the twentieth century, they just weren’t writing it down. The clusters attempt to conjure a blues ethos just as Bartók’s clusters seek to conjure a Magyar folk ethos. All five Pastime Rags are beautiful; George Gershwin recorded Pastime Rag No. 3 for a piano roll in 1917.

2. Matthews JPG

The Man I Love — George Gershwin. Joplin and Gershwin are two crucial pillars to all American music. The earliest Gershwin song that has stayed in the repertoire is The Man I Love from 1924. Unlike the music of the black composers in this anthology, the use of rubato from the European tradition is appropriate in Gershwin. If you are comfortable playing Joplin like a good jazz pianist and Gershwin like a good classical pianist, then you’ve passed the exam.

3. Gershwin JPG

Organ Grinder Blues — Clarence Williams. Ragtime fit the idea of European notation much more easily than the blues: compare the scores of Joplin to those of W.C. Handy. Organ Grinder Blues is the most sophisticated early blues notation that I’ve seen. Williams was a prolific songwriter and this 1928 arrangement could easily be his work. If not, whoever prepared the score did a good job.

4. Clarence Williams JPG

In a Mist — Bix Beiderbecke. Beiderbecke recorded In a Mist and arranger Bill Challis figured out the notation. A legendary piece looked at by thousands of jazz pianists since. Like his obvious inspirations Debussy and Ravel, Beiderbecke often concludes his wild phases with pure triads.

5. Bix JPG

Willow Weep for Me — Ann Ronell. In 1932 Ronell is firmly interjecting the blues into a pop song. She was a white composer, but her solutions were accepted by Jimmy Smith, Stanley Turrentine, Ron Carter, and hundreds of other arbiters of the blues.

6. Ronell

While there aren’t any more original piano/vocal scores of standards in my anthology besides Gershwin and Ronell, I certainly encourage further exploration. Eubie Blake, Irving Berlin, Jerome Kern, Richard Rodgers, Harold Arlen, Cole Porter, Billy Strayhorn, and the rest were all masters of harmony who carefully chose every note they put on the page. The pop songs are also easier to sight read then many of these more pianistic pieces.

Modernistic — James P. Johnson. This is a comparative rarity, a “novelty rag” like Zez Confrey written by a black composer. It’s dead center between Jelly Roll Morton and Thelonious Monk (two geniuses relatively uninterested in publishing piano sheet music). The editing is terrible, some notes are definitely wrong. Johnson’s recording You’ve Got to Be Modernistic is famous. Playing a transcription of the record is a virtuoso affair, but the simplified sheet music is for a talented amateur.

7. James P. JPG

Never Heard of Such Stuff — Fats Waller. Folios of major artists were usually five or six pieces, later repacked in different ways.


Waller wrote out an extraordinary number of slight originals and quickie arrangements for the home pianist. Never Heard of Such Stuff offers a walking bass line and at least one harmonic progression straight from Schubert. It’s easy to imagine Benny Golson arranging this piece for a hard bop sextet.

8. Waller JPG

Diggin’ for Dex — Count Basie. Unlike the notation found in Duke Ellington folios, the notation in Basie folios can be somewhat representative of Basie’s big band. (It seems like Ellington actively fought to keep his music out of the hands of amateurs, perhaps as a way to secure his brand. Even if he liked the lunch money that came in from the folios, he didn’t give away any secrets in the process.) Although the piano writing in Diggin’ for Dex is reasonably convincing, I doubt the Count himself (or his arranger Eddie Durham) had much to do with the notation. At any rate, here we have the sixth chord in all its glory. The sixth chord is perhaps important to jazz because of how it relates to the pentatonic scale of some African musics. It’s a percussive sixth, not a coloristic sixth like in European music.

9. Basie JPG

Deuces Wild — Mary Lou Williams. Most of the masters didn’t sit down and notate arrangements of pop tunes or easy originals. However, publishers wanted product, so they had people play through a chorus of a standard or a few choruses of blues which were then transcribed. As far as I know, source recordings were never released. Undoubtedly some things were simplified in the process of getting the recording on to the page, and this inauthentic status means they are “for education only.” Perfect for jazz students! Whoever transcribed Deuces Wild knew what they were doing, this is really a good blues, completely written out, the scroll just unrolls.

10. Mary Lou JPG

Gang o’ Nothin’ — Art Tatum. Many transcriptions from the era were done by Frank Paparelli, an intriguing figure who shares compositional credit for Blue ’n Boogie with Dizzy Gillespie. Gang o’ Nothin’ is a Paparelli product, and in its way is a minor masterpiece. Mary Lou and Tatum both have folios of completely original pieces that were obviously improvised. Most of them are blues forms but Gang o’ Nothin’ is like a standard. With no Tatum recording to compare to, we can play as slowly as we want.

11. Tatum JPG

Blue Moon — Art Tatum. The fast figurations are challenging, but one can kind of fake around them while paying close attention to the marvelous harmonic information. Octaves or single notes (instead of wide-spaced tenths) work fine in the left hand. Blue Moon is one of the simplest of standards, but look what Tatum does with it!

12. Tatum blue moon JPG

Whispering — Teddy Wilson. The folios of Earl Hines and Teddy Wilson are terrific but quite difficult. (The Hines folios may be even harder to read through than the Tatum folios.) This is one of the easiest, just a delight to fool around with, and the tag is authentic. (Dizzy Gillespie based Groovin’ High on Whispering.)

13. Wilson Jpg

Just You, Just Me — Eddie Heywood. Heywood’s most familiar recording these days might be The Man I Love with Coleman Hawkins, although he also had a career in the 1950s creating gentle “moods” for easy listening. His folio is one of the most helpful as the left hand stride is beginning to lighten up and the phrasing is more like modern jazz.

14. Heywood JPG

How About You — George Shearing. Shearing’s arrangements were written out by Shearing himself. Both Cedar Walton and Herbie Hancock talked about playing though Shearing folios, and I’ve seen Lee Konitz read through them as well. At times the note choices are pleasingly avant-garde. In How About You there’s a real bebop ending. I remember playing it as a kid and thinking, “That can’t be right.” No, it’s right!

15. Shearing JPG

In my most recent DTM educational missive, “Received Wisdom,” I criticized Mark Levine’s famous educational text The Jazz Piano Book. Various corners of the internet yelped in outrage, so I bought the book and read it over the holidays to make sure I hadn’t missed something. (I took a class with Levine in 1990 at the Stanford Jazz Workshop.)

Levine begins with a table of intervals. On page nine he says, “One of the skills a pianist must have is the ability to invert intervals quickly.” I can invert intervals, sure, but the idea of telling a beginner to start with intervals seems wrong. Basic jazz is not twelve-tone music or anything else requiring advanced math.

Levine proceeds with a table of scales (of course: all jazz books have scales and more scales) before moving on to voicings. The song used to show these voicings in practice is “Just Friends” in G major.

“Just Friends” is a hard song to hear correctly and internalize on a student level because it starts on the IV chord. Incredibly, Levine does not explain anything about having a home key! He’s just involved in the rules of resolving independent tensions correctly. However, experienced musicians feel the first sustained chord of “Just Friends” as a kind of dissonance. It’s a subtle but very important detail.

When people like Louis Armstrong, Lester Young or Charlie Parker improvised, they played in the home key of a song. For “Just Friends,” they would play in G major. They certainly wouldn’t move scales around in order to spell the harmony out on every chord. (Lester Young didn’t like chord charts. At rehearsal or a jam session, he’d just ask what key the song was in.) Compared to Pops or Prez, Bird plays considerably more material to imply passing chords, but on his famous version of “Just Friends,” most of the phrases are still in the home key. By the time we get to John Coltrane, it’s a little different: Coltrane could move scales around and spell out all the vertical harmony. But Coltrane is incredibly advanced. Coltrane internalized everything that came before him and then curated his supersonic style from a place of deep knowledge. That knowledge included lots of harmony and technical information about pitches, but all those fast and fancy note choices weren’t more important than the blues, swing, and Afro-American sonority.

The next composition Levine offers with a chordal realization is Wayne Shorter’s “Infant Eyes,” a song so difficult that good versions of it (besides the original on Speak No Evil) are hard to come by. I can’t imagine a beginning jazz pianist succeeding with “Infant Eyes.”

All this stuff in Levine so far is very technical, very intellectual. There’s no blues, no stomp, no stride, no dance, no folkloric repertoire.

The tree of Mary Lou Williams should be on the wall of all jazz classrooms everywhere:

Mary Lou tree

Mary Lou suggests that “Exercises” and “Classical books” are dead branches. In my view, the kind of technical information offered in many jazz harmony books might foster a dead relationship to the basic aesthetic of jazz.

Ok. Let me slow up my ranting and note that Levine’s book runs nearly 300 pages. With that many words, naturally some of them are valuable. It was fun to consider some of the points Levine raises and look at some of the worthy examples. Also, I truly admire the selection of photos of the jazz masters. The first page has Duke Ellington, on page ten there’s an astounding photo of Thelonious Monk. There’s certainly an argument that jazz students should ignore all words about jazz and just look at the photos. (Duke and Monk sure didn’t use many words.)

Levine’s book may have been a notably strong entry compared to what came before. I also looked through a pirated copy of Jazz Voicings for Keyboard by Frank Mantooth, which was a reasonably popular text a couple of generations ago. (I had a class with Mantooth at a Jamey Aebersold camp in the late 1980s.) Mantooth spends page after page defining “Generic Voicings,” “Miracle Voicings,” and “Polychord Fractions.” (These things don’t exist outside a Frank Mantooth treatise, by the way.) Finally he’s writing about comping on the blues:

Frank Mantooth 1

What the hell? Is a “Dan Haerle handout” our source for the blues? How about just showing us some blues music?

Mantooth doesn’t include a blues piece by a master, but he does include a bebop tune. He misspells Tadd Dameron’s name and misspells the title of “Ladybird.”

Mantooth 2.jpg

Mantooth continues:

Mantooth 3
Mantooth 4
Mantooth 5

Mantooth was a good jazz pianist and arranger. I just don’t believe he thought about the music this way in his own creative space. All this blather (“Generic major constructions  from either the tonic or the fifth descending would have worked equally well”)  is a way to create an artificial system that can be taught in order to sell a book. The blather sounds impressive, a rube can be tricked into thinking you can learn jazz like algebra or computer programming, the carnival barker gets the money.

While I’m throwing Mantooth under the bus (and, for the record, I think his voicing choices for bars 13 and 14 are profoundly unmusical), his realization of “Ladybird” is a perfect illustration of another pet peeve of mine: Chords without a root in the bass.

Of the many recordings of “Ladybird,” two stand out as especially important: The first one by Dameron/Fats Navarro and the Art Blakey with Horace Silver. These great and popular recordings must be a big part of why the tune became a jam session classic.

Both Dameron and Silver are extraordinary compers. They both play the root in the bass on the first bar of every chorus “Ladybird.” Naturally. If there’s any song that needs a “C” in the basement at the top of the form, it’s “Ladybird.”

Here’s a list of pianists that regularly play a root in the bass whether a bass player is present or not:

Duke Ellington
Teddy Wilson
Earl Hines
Art Tatum
Bud Powell
Mary Lou Williams
Horace Silver
Ahmad Jamal
Oscar Peterson
Herbie Nichols
Randy Weston
McCoy Tyner
Jaki Byard
Geri Allen

Here’s a list of pianists that never play a root in the bass:

Bill Evans
jazz students

Ok, that’s not entirely fair. The piano chair of the Miles Davis band grew into being a situation where the bass dictated the harmony as much as the piano. Red Garland to Bill Evans to Wynton Kelly to Herbie Hancock to Chick Corea: It’s a glorious tradition.

Those Miles Davis pianists play a root in the bass when there’s no bass — except Bill Evans, at least some of the time.  The Evans duos with Tony Bennett can be strangely “empty” sounding in places. The accompaniment for the Bennett vocals couldn’t be better — the instrument sounds like it is lit from within — and then the piano improvisations sound like they need a bass player.

When I was a student at jazz camp, many of my fellow students couldn’t play songs with a root in the bass, probably because they were looking at jazz harmony books by people like Frank Mantooth. Mark Levine doesn’t make this error in quite this way, thank goodness, although there’s one Levine sentence I cannot forgive: “Don’t worry about the lack of a root in a chord,” which is sort of like saying, “Don’t worry about whether your body’s heart is pumping or not.” Still, Levine doesn’t start in that abstract place, his “Just Friends” and “Infant Eyes” examples include proper bass motion, and if you read everything else in The Jazz Piano Book, there’s a lot of important context for “rootless” voicings. Now that I’m teaching, most of my students generally seem to understand they need a root, so perhaps Levine actually helped out on this specific issue.

At any rate, one of the reasons I compiled Theory of Harmony is to encourage learning repertoire. Discovering what the masters actually played always offers the right path. A transcription of a chorus of Dameron or Silver on “Ladybird” has value. The abstract Mantooth realization does not.

Sources and footnotes for Theory of Harmony:

The Joplin is anywhere and everywhere. Artie Matthews used to be harder to find, but now the five Pastime rags are just up at IMSLP. James Scott was another black ragtime composer who published a lot of worthy music; Joseph Lamb was a white ragtime composer who unashamedly loved Chopin. (Skipping decades ahead into the future, I also dig the 70’s ragtimes of William Bolcom and William Albright.)

Jazz, Blues, Boogie & Swing for Piano (1985, Hal Leonard) is a big anthology that was a kind of bible for me when I was a kid. Has Tatum’s Gang ‘o Nothin, Waller’s Never Heard of Such Stuff, James P’s Modernistic, and the Clarence Williams Organ Grinder Blues.

We could really use a collection of James P. Johnson. He published so much music in single sheets, and some of it might already be lost.

The easy-to-find Eubie Blake collection has some good things. Jelly Roll Morton’s published scores are very simple and relatively uninteresting; the big anthology of Jelly Roll transcriptions by James Dapogny is a must.

Gershwin’s anthologies are also essential for the American piano library. Other standards by composers like Ronell are a click away in the internet age; various song collections in libraries always have a few items of extraordinary interest. I stole this “In a Mist” from a file-sharing platform but as a kid I had it in a “Best of the Big Bands” anthology of some sort.

I also still have a few books called Giants of Jazz (Alfred Music) with selections from the folios of improvisations by Mary Lou Williams, Earl Hines, Art Tatum, Teddy Wilson, Eddie Heywood, and others. Some of the Shearing arrangements are in those, but standalone collections of Shearing are also easy to find. Interesting and reasonably accurate anthologies of Marian McPartland, Dave Brubeck, Bill Evans, and Stan Kenton are also readily available.

Ebay and other online stores might have original folios from the 30’s and 40’s. I myself tracked down the selections of Tatum and Mary Lou original material, as not all of these pieces have been republished since the first edition.


Waller transcriptions, original notated arrangements, and original compositions all exist. His recordings are vastly more important, but these pieces of paper have at least some value as well. Again, it would be good to have fresh anthologies of this material before it vanishes off the earth forever.

In that era Boogie Woogie was a huge commercial success, which is why there are so many “standards done as a boogie” folios, for example Duke Ellington Boogie Woogie Piano Transcriptions. In small print at the beginning of the book there is the comment, “Edited by Billy Strayhorn.” Huh. Well, playing through the folio didn’t give me a whole lot of insight into Duke, Strayhorn, or boogie. (As I write above, I have a theory that Duke liked to keep his secrets.)  However, the easy-to-find Strayhorn anthology is a worthy purchase.

Bonus track:

Another reason I compiled Theory of Harmony: I’ve been telling students to play through Bach and Chopin but obviously that’s not as relevant to jazz as the music in Theory of Harmony. Still, I maintain that the European repertoire is important. Indeed, since most of the greatest American music is too rhythmically sophisticated for the page (and therefore requires a recording for finest realization), most of the canonical European classical repertoire is more masterful than the sheet music anthologized in Theory of Harmony (with the exception of the Joplin).

For fun I collect examples of Afro-American jazz greats playing European classical music on tape in a “straight” fashion. There are many more bits and pieces around, but these five seem especially telling:

Erroll Garner: Debussy Clair de Lune
Phineas Newborn: Ravel Sonatine
Roland Hanna: Bach C# Major Prelude (on Mingus Let My Children Hear Music)
Kenny Kirkland: Brahms Rhapsody in G Minor (in Sting documentary Bring on the Night)
Jason Moran: Brahms Intermezzo in A Op. 118