Haekel's Law of Recapitulation - sometimes stated as ontogeny repeats phylogeny - was an early attempt to relate biological development to the then new theory of Darwinian evolution.

It passed into 19^th century intellectual orthodoxy through the door opened by Herbert Spencer and other Social Darwinists and became influential in education theory.

Haekel's Law is reflected in the conventional approach to musical education which is founded on immersion in the Old Masters.

How does an autodidact acquire musical knowledge?  Afro-American music offers an interesting insight into what happens when the development of musical understanding (music ontogenesis) occurs outside the formal structure set by historical progression (music phylogenesis).

What's so special about jazz and its offspring styles in this respect?

One factor is the short span of its own history as a discipline separate from Western art music - about a century from birth to its present condition.

Another is the learning pathway which, despite the growth of jazz studies as an academic discipline in recent decades, remains largely a matter of self-education.

And an important further issue is the aspirant musician's low exposure rate to jazz through the mainstream media that, while not reducing environmental influences to quite the level of some of the historical experiments on language deprivation, is in some cases close to a state of nature.

A case-study: here’s a characteristic harmonic motif that represents one of the versatile tools in the jazz musicians workbag (click on the notation to hear an mp3).

Consider the example of the first 8 bars of Duke Ellington's In a sentimental mood (1935).  The motif comprises four instances of the same minor chord with a moving added note, respectively the octave, major 7, minor 7 and sixth relative to the root.

Such harmonic movement in the hands of a skilled practitioner often comes across as quite sophisticated and "jazzy"; but looked at in another way, it has characteristics that link it directly with an older, even ancient, era of western harmony.

Upper movement above repetition of root-and-fifth is strongly reminiscent of the drone-based harmonic conventions of early music.

Arguably, a musician of the era of Bach would consider conveying the sense of stepwise harmonic movement through the use of chord inversions.

But inversions are a relatively recent feature of conventional jazz harmonic practice.

The term "rootless voicing" is widely employed, particularly in educational materials (for example in Mark Levine's jazz musicians' bibles The Jazz Theory Book and The Jazz Piano Book), indicating that inversions are not usually thought of as agents of harmonic mobility but as anchored to root notes either overtly stated by the bassline or mentally filled in by the listener.

[Incidentally, the issue of rootless phylogenetic trees is of contemporary concern to systematists engaged in cladistic analyses of organism interrelationships].

Another example of inversion-denial in jazz harmony is the (relatively recent arrival of the) slash chord.

It could be argued that, in this sense, jazz harmony has got stuck in a kind of evolutionary (pre-Baroque era) eddy, within which it has evolved its own conventions and understandings off the mainstream of Western-type musical history.

How did this come about?  There are many contributing factors:

An absolute requirement for, and reliance on, a bassline (why? too complicated to go into here); the relationship between technological advances and the environment in which jazz evolved (acoustics of venues such as outdoors, clubs, bars etc, frequency responses of microphones and PAs, volume of front line instruments); self-taught instrumental technique; the limitations of conventional jazz chord notation; the role of Tin Pan Alley in mass-production of accessible (sometimes even downright rudimentary) published copy; the influence of the blues tradition and other contributing musical forms outside that of classical European culture.

Nevertheless, as with any evolutionary outcome, the adoption and development of these non-canonical conventions fulfil fitness-for-purpose needs.

For example, relatively simplified or intuitive harmonic principles are more compatible with improvisation and communal jamming.

This has allowed the sophistication of the improvised line (driven by the great creative soloists) to lead the development of harmony, rhythm etc.

These harmonic and rhythmic innovations rapidly became fixed and further elaborated by the celebrated arrangers of jazz history, such that evolution of the music flows in two great interconnecting streams, those of the soloists and the arranger/composers.

All in all, this looks less like Haekel's Law in its original naive form, and more like the post-Haekelian concept of heterochrony, in which previously embryonic characteristics (pre-Baoque harmony in this case) are retained at maturity, with the loss of previously adult traits.

In conclusion, careful and critical analysis of how a vibrant and complex musical tradition like jazz rapidly developed and flourished in a historical backwater could conceivably give insights into the interrelationships between ontology, phylogeny and heterochrony in musical education and biological evolution.