Pitch Theory

Physics in the Cambridge of the 1890s was bubbling with ideas that spilled over into biology. It is likely that William Bateson had every opportunity to discuss them with his St. John's College colleague, the physicist Joseph Larmor (see biography p. 226). The vortex theory of atoms had been advanced by the Scotsmen Peter Tait and William Thomson (Lord Kelvin) and we find "vortex" quite often in Bateson's writings. Likewise, the mathematicians and philosophers (e.g. Alfred North Whitehead) were toying with continuous and "discontinuous" functions, and it is possible that Whitehead drew Bateson's attention to William James' thoughts on the role of "exceptional" observations ("exceptions") and the "unclassifed residue" of observations that do not seem to fit in with the rest (see 3rd edition of Evolutionary Bioinformatics, p. 397). These words recur in Bateson's writings. Thus, it is perhaps not surprising that he struggled to relate music to his biological interests, especially speciation mechanisms. An unpublished "Pitch Theory" was found among his papers (see below). A century later, Forsdyke drew on radio wave transmission for a similar metaphor (Click Here) . For more on the Whitehead-Bateson relationship Click Here .


Pitch Theory of Reproductive Cells

Bateson's Notes on a Pitch Theory of Reproductive Cells [probably early 1890s; Queen's University Archive]







Reproductive cells (units from which species start)

Keynotes. Units of vibration from which melodies


start. Definite units of vibration, bearing definite


relation to all other notes in the melody.




Relation of reproductive cells of one species to

Relation of a Tone to its Overtones

reproductive cells of another species of same genus





Relation of reproductive cells of one species to

Relation of Tone to its nearest overtones

those of another with which it can be cooped and


yield fertile offspring.





Hybrids can be obtained from the reproductive cells

Chords in harmony can be formed from 

of two species which yield fertile offspring

fundamental notes struck with their nearly


altered overtones, and further two melodies may


be worked together if their fundamental tones


are in simple relations to each other to form a






Hybrids are for the most part obviously compounded

Two voice Counterpoints are obviously composed

of their parents. Often (usually?) definite pieces of

of two melodies. Pieces have sometimes to be

each parent appear, (though sometimes intermediate

interpolated or left out to make the parts fit

between the two in part at all events)

together (?) yet the 2 melodies are still apparent.




[empty, but the spacing and numbering is 

The figures made by sand on glass plates when

maintained, so that the two sets of sheets can be

made to sound to certain tones. Their outward

aligned for comparison. DRF]

resemblance to appearance of segmenting eggs,


transverse sections of stems, veins in leaves, etc.




Often an hybrid can be produced, between 2

No counterpoint can be made of two voices 

outwardly very similar species

singing the same melody in unrelated or distant






Nature abhors a hybrid

Musical students abhor counterpoint




A species may be varied to any extent, yet as a rule

A melody may be varied to any extent yet remain

varieties breed with their parent species no matter

the same melody and stand in the same relation

how varied they have become. Yet some species[,]

to other melodies unless its ground tone is altered

though more nearly allied to all appearances[,] as a

in pitch[.]then though it is still the same melody it

rule will not or do not breed together

does not bear the same relation [to] its original


melody nor to other melodies.




Reciprocal hybrids (such as mules and hinnies)

Twisted intervals, or inverted counterpoints (?are


there such things)




The power which a male cell has of making a female

The power which vibrations from one tuning fork

cell of same species segment

have of making another of the same pitch originally


at rest sing out its note




Entire prepotency of one parent over another. Direct

The power which a swinging pendulum possesses

effect of male over female (as in oranges).

of coercing one swinging beside it, into its own


period of oscillation




The power which certain species of the same genus

The power which tones not of the same pitch as 

have of breeding together

the resonant body have of throwing resonant 


bodies into vibration, if they contain the right tone


amongst their upper partials (overtones)




The fact that certain species are more fertile with

The power which certain resonant bodies 

pollen of other species than their own (i.e. dimorphic

(circular membranes) possess of responding only

plants and self-sterile plants)

to sounds more acute than their own note




Species of the same genus

Notes on a diatonic scale




Possible varieties filling in between species

Chromatic or not "well-tempered" intervals in sound




A variety cooped with its parent reproduces within

A melody played with its variation forms a unison

itself or its parent (although are said by Darwin to be

of melody and variation not a counterpoint

not different from hybrids in kind. ? Is that so ? They


do seem different really)





Any number of varieties may cross with each other

Any number of instruments of different Timbre may

yet the original species remains the same, with 

play the same melody together, yet there is only

perfect fertility.

unison, no counterpoint.





Compatibility of pitch





Incompatibility of pitch




Hybrids are either totally sterile or reproduce one

Two melodies started in different keys and played

or other of the parents, but not the hybrid form; do

together in counterpoint have still two different

not seem capable of producing intermediate

keynotes, not a keynote intermediate between

reproductive cells. The means of reproduction are

the two

present as a rule the cells only are wanting.





Species are thought to be derivable one from the

Diatomic intervals are derived one from the other

other. Should there be anything in this pitch theory

There are definite overtones belonging to every

of reproductive cells, it is conceivable that a change

fundamental tone. Certain instruments make

in what corresponds to timbre in living things may

overtones more apparent to our senses than

occasionally take place suddenly right through an 

others (this is a matter of timbre in the instrument

organism, whereby their reproductive cells should

itself). Also if the lowest tone of a resonance box

change in timbre also and "synchronize"[?] with the

does not correspond with the prime tone but with

cells of their equally changed brethren? (Rather wild!)

some of the upper partials, the corresponding


upper partial predominates

Go to: Bateson Biography (Click Here)

Go to: Bateson & Saunders 1902 (Click Here)

Return to: Bateson Papers Catalogue (Click Here)

Return to: Evolution Index (Click Here)

Return to: Bioinformatics Index (Click Here)

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This document was prepared from William Bateson's handwritten notes, which probably date from the early 1890s, placed in these webpages in Nov 2008 and last edited on 05 Feb 2018 by Donald Forsdyke.