It occurs to me that I never published any of my papers from the 20th Century Music Theory grad seminar I took during the past spring semester. I dug up a good one, submitted 15 Mar 2010, on Herbie Hancock's "Dolphin Dance." I was afforded a chance to apply the analysis tools we were learning to a jazz tune instead of the usual 19th/20th-century classical material. Enjoy.

An Analysis of "Dolphin Dance"

Herbie Hancock wrote "Dolphin Dance" in 1964, and it was first recorded for his seminal album, Maiden Voyage1, in 1965. While its melody is quite simple and motivically derived, it is among the most harmonically complex pieces of its time. The tools effecting tension and resolution are divided between traditional V-I motion in various temporary keys and a new level of abstraction in chromatic modal harmony. In the latter, tension is provided by dissonant, active-sounding chords, usually some form of dominant or altered chord. Release, outside the realm of V-I cadences, can be provided by more consonant, restful chords.


The main melodic motive is stated twice, repeated verbatim, in the four-bar intro to the song:


This motive is used extensively throughout the composition, in different keys, and with rhythmic and pitch contour variations, as in the first four bars of the form after the intro:


When comparing the motive introduced in the intro with the variations in the following four bars above, note that, while the pitch contours are identical, the intervals between the notes are not. The pitch-class set of the original motive is [F=0] [0, 2, 3, 5]. The pitch-class set of the variation is [D=0] [0, 1, 3, 5]. However, observing their applications over their designated chords, we find their functions to be identical. The first, over EbMa7, uses Eb major scale degrees 3, 4, 5, and 2. The second, over Cmi7, uses C minor scale degrees 3, 4, 5, and 2.

Bars 5-12 introduce and repeat a new ascending motive, increasing the energy of the piece:


Comparing these two, again we find identical pitch contours. Additionally, with the exception of the first note, all the intervals are identical; the second is a major third transposition of the first. Following this increase in intensity is an eight-bar repose over pedal points on G and F. The melody reverts to the main motive four times, from three different starting pitches:


In the second statement of the motive above, the descending interval is a tritone instead of the perfect fourth found in all the others. In the third statement, we see the same rhythmic variation introduced in the first two bars of the form. In the fourth statement, we see a pitch contour variation, continuing the ascent of the first three notes to complete a tritone between the outer notes.

This sets up the final motive and the imminent climax and high-note of the melody in bar 25:


The highest note in the piece, F# in bar 25, coincides with the climax in intensity in the tune's performance. Resolution is swift, as the most restful point of both melody and harmony lasts from bar 27 to bar 30.

The final four bars of the form serve as a turnaround to begin the solos at the start of the form. The main motive reappears twice, the second time exactly as it appeared in the intro:



The harmony of "Dolphin Dance" has proven to be problematic for transcribers. Lead sheets from different sources often show entirely different results. Attached to this document are lead sheets from four prominent and popular, if not always authoritative, sources: Jamey Aebersold's Play-A-Long series8, The Real Book: Fifth Edition9 (illegal), The Real Book: Sixth Edition10 (legal, Hal Leonard), and The New Real Book11. For the sake of this analysis, I have chosen Richard Helzer's transcription12 as an authoritative source for the harmony, and I have noted the primary deviations in the aforementioned lead sheets. All excerpts embedded in this document are from Helzer's lead sheet.

To begin a harmonic analysis of this tune, I first identify all the cells of traditional harmony in temporary key centers. This means looking for root movement up by perfect fourth, and chord qualities following major or minor II-V-I formulas, as well as any other implied key centers. The first 3 bars of the intro loosely establish a key of Eb major. In the fourth bar of the intro and first bar of the form, we move to the relative minor with a full II-V-I in C minor. Bars 2 and 3 remain in C minor, on the VI and back to I. Bars 4 and 5 modulate to the V with a II-V-I in G major. Bar 8 is usually played as a Bb7, and although not included in Helzer's lead sheet, an accompanist would likely include it as an embellishment anyway over two bars of Fmi9. This creates a IV-bVII-I progression in bars 7-9, known in the jazz world as a "backdoor turnaround," returning to the key of C minor. Bars 11-13 return to G major with another II-V-I. Bars 13-16 feature a pedal point on G with changing chord qualities in each bar. Bars 17-19 continue the pedal point a step down on F with changing chord qualities. Bar 20 contains a II-V in D that does not resolve immediate, but instead proceeds to the tritone substitution of the V, a bII, then to the I on D, but with a function change to a dominant chord. Note the similarities between the four-bar intro and bars 17-20. The first and third chords are the same in each case, while the chord between them completes a three-bar pedal on the same root. The final two chords in the fourth bar are of half diminished and altered dominant quality in both cases. All the chord roots in bars 17-20 are a whole step higher than those in the intro. Additionally, the main motive is used for the melody in both cases. Bars 23 and 24 contain another non-resolving II-V, this time in A. Bars 25 and 26 contain a II-V in B, but instead resolve to E9(sus4) on bar 27, starting the fourth multi-bar pedal point of the piece, on E. That's the last of the II-Vs in the piece, and the only remaining bit of traditional harmony is the V-I cadence in C minor in bars 34 and 1, effecting the turnaround to the beginning of the form.

The remaining chords in the piece, while non-functional in traditional harmony, can be described in more general terms of tension and release. Even if the root movement does not resemble V-I, and the chords have no relation within a key center, the effect of tension and release can still be provided through the use of dissonance and consonance, more broadly than the dissonance of a V (often altered) dominant chord to the consonance of a I major or minor chord. Additionally, non-functional chords can serve as passing chords without switching between tension and release, much as a II progresses to V or I progresses to IV.

Examining the remainder of the chords in this context of tension and release/repose, we can categorize each chord and better understand the progression of the piece's harmony. The tritone is generally the source of dissonance within a chord, so any non-suspended dominant chord can be labeled as a tension point. Major 7 chords, minor 7 chords, and suspended chords are generally consonant, depending on context, and considered points of repose. Beginning with the intro, the first three bars are restful and consonant. I view the Abmi9 chord in bar 6 as a passing chord in repose, between the GMa7 in bar 5 and the Fmi9 in bar 7. Helzer refers to the movement from the Abmi9 to the Fmi9 as "harmonic parallelism," consecutive chords of the same quality with different roots. This provides some familiar territory to the listener while letting go of the current key center. Root movement in this case is down a minor third. The concept is repeated four bars later, at the same point in the second motive, in its second statement. Although the bass line is descending from Bb to A, the root of the Cmi7 chord descends a minor third again to the Ami9 in bar 11. The pedal point on G in bars 13-16 provides a vehicle for increasing tension, beginning with consonant chords over the first two bars, and increasing dissonance with a G dominant and an EbMa9(+5) in first inversion. Bars 17-19, over the F pedal point, alternate between repose and tension. Contextually, this section embodies more suspense than is evident in the lack of dissonance in the two F9(sus4) chords, as the listener anticipates how this new pedal point a whole step down from the previous one will be handled, setting up the climax of the tune in bars 21-26. The Dmi7 in bar 24 would be consonant out of context, but contributes to the tension of the climax, being unrelated to its preceding chord, an E altered dominant. Following the Dmi7 is another example of harmonic parallelism, this time descending a minor second to C#mi11. The big release after the climax occurs in bars 27-30, in which the melody holds a single note throughout, and the harmony alternates between two consonant chords on an E pedal, an E9(sus4) and a CMa7 in first inversion. The final four chords, while not part of the climax, are the most harmonically dense and most dissonant moments of the piece. The first three are over an Eb pedal, starting in repose on a suspended chord, increasing tension with a Bb13(-9) with its 4 in the bass, and culminating with the outlandish voicing Helzer transcribed from Hancock's original recording: an Eb major triad over an Ab augmented triad, all over an Eb in the bass, slightly simplified to an AbMa7(+5) over Eb. The final chord, a G altered dominant, maintains the tension while directing the harmony back to Cmi7 at the beginning of the form. Note the similarities between the pedal points on G and F in bars 13-20 and the pedal points on E and Eb in bars 27-34. In both cases, the first is maintained for four bars while the second lasts for three before moving to a turnaround to the next section. Both cases end in tension and suspense, as the first leads to the climax of the tune and the second turns around back to the start of the form.


The complex harmonies and progressions in "Dolphin Dance" present a unique challenge to the improvisor, who must spontaneously create melodies in the context of these chord changes. To help my own approach to soloing over this tune, I wrote out all the scales most likely to be used over each chord, outlined here:

| Eb Lydian (Lyd) | Eb Mixolydian (Mix) | Eb Lyd | D Locrian Natural 2 (Loc 2), G Altered Dominant (Alt) ||
|| C Dorian (Dor) | Ab Lyd | C Dor | A Dor, D Lydian Dominant (Lyd Dom) |
| G Lyd | Ab Dor | F Dor | / |
| C Dor | / | A Dor | D Alt |
| G Lyd | G Mix | G Lyd Dom | Eb Lydian Augmented (Lyd Aug) |
| F Mix | F Symmetrical Diminished (Sym Dim) | F Mix | E Loc 2, A Alt |
| Eb Lyd Dom | D Sym Dim | B Dor | E Alt, D Dor |
| C# Dor | F# Sym Dim | E Mix | C Lyd | E Mix | C Lyd |
| Eb Mix | Eb Major | Ab Lyd Aug | G Alt ||

Works Cited

Aebersold, Jamey. Play-A-Long Book & Recording Set, Volume 11: Herbie Hancock. New Albany, IN: Jamey Aebersold, 1978.
Bain, Reginald. "Analysis: Hancock, Dolphin Dance." University of South Carolina School of Music. (accessed 11 Mar 2010).
Hancock, Herbie. Maiden Voyage. Blue Note BST 84195. CD. 1965.
Helzer, Richard. Transcription of "Dolphin Dance."
Real Book, The: Fifth Edition.
Real Book, The: Sixth Edition. Milwaukee: Hal Leonard Corporation, 2004.
Sher, Chuck. The New Real Book, Volume 3. Petaluma, CA: Sher Music Co., 1995.


1 Herbie Hancock, Maiden Voyage, Blue Note BST 84195, CD, 1965.
2 Richard Helzer, Trascription of "Dolphin Dance."
3 Ibid.
4 Ibid.
5 Ibid.
6 Ibid.
7 Ibid.
8 Jamey Aebersold, Play-A-Long Book & Recording Set, Volume 11: Herbie Hancock (New Albany, IN: Jamey Aebersold, 1978), 10-11.
9 The Real Book: Fifth Edition, 122.
10 The Real Book: Sixth Edition (Milwaukee: Hal Leonard Corporation, 2004), 119.
11 Chuck Sher, The New Real Book, Volume 3 (Petaluma, CA: Sher Music Co., 1995), 108.
12 Richard Helzer, Trascription of "Dolphin Dance."