LucyTuning Home Page
New to LucyTuning?
Academic & Research, John "Longitude" Harrison
Products & Services
LucyTuned Lullabies
Guitars & Frets
Midi, Keyboards & Composition
Colour & Mapping
Comparison to other Tuning Systems
Music Theory
Press Room
Listening Room
The Search for the Missing Harrison Manuscript




18th March 2005, London, UK

New Scientist Magazine have published a letter for me (with their cartoon) to spread the search for understanding New Scientist Letter . I have put the transcription of all Harrison's writings relating to Radical Numbers here in the hope that someone smart out there can untangle it for us.
Complete transcription in html format (big file)


NEWS; 4 September 2002, London, UK

A copy of the missing manuscript has arrived here in London and is currently being analysed. First appearances are that it gives details of the information which can be found in CSM. Up to page 14, Harrison explains that he has been unable to "solve" the problem of finding a mathematical or scientific justification for his choice of PI as a basis of his tuning system. He gives many musical and mathematical examples... Work continues on the transcription and research with the idea of publication towards mid-September 2002. A copy has been authenticated by Jonathan Betts, of the National Maritime Museum in Greenwich, as being the hand writing of John Harrison.

A true and (short, but) (*crossed out) full Account of the Foundation of Musick, or , as principally therein, of the Existense of the Natural Notes of Melody:

Wherein is shown the Absurdity of such imaginary stuff as was first crowded into the Scale of Musick by the Ancients, and has still been retained therein by our more modern Writers, in order to make the matter seem more Reasonable or Philosophical, whenas in reality it is even as hence a bereaved of all such Ornament, and as, when at the same time, its Foundation or basis as in another Sense tho' secret, is most strictly true or perfect in itself(?); and therefore, as being otherwise therefrom not only to a much higher degree than what we should think. or have thought to have been Mathematically Beautiful, or even as otherwise so Perfection itself, (fo) (*crossed out) 2. consequently it 1. (yet)(*crossed out) can have nothing to do with any such Arbitrary Conjectures: (via as intimated)(*crossed out):

And herein are also, (exhibited some)(*crossed out) very necessary Observations exhibited and as with Instructions about the highest, the most Important, or the most Undeniable life of the Subject:

As Experimented and Illustrated by John Harrison, Inventor and maker of the Time-Keeper for the Longitude at Sea: and who was for several years, Parish Clark [or Clark of the Psalmody] at Barrow near Barton upon Humber, in the county of Lincoln.

In left margin ---- a[ or would be as thence] bereaved.

History of the search for the missing manuscript

The following text appeared in the New Scientist Magazine in April 97 submitted by Charles Lucy. If you can help in any way with the quest for this document please contact Charles Lucy. We will be most grateful. It is our intention to publish information as it comes in relating to this search so please stay tuned !

It seems to me that we at at a crossroads in musical tuning, similar to that which mathematics passed, a couple of hundred years ago. Many still seem to judge the validity of a tuning system only by its proximity to integer frequency ratios and the harmonics, which are arrived at by this (to my mind) simplistic logic. From my readings, experiments, and observations, I am convinced that John Harrison had managed to break through this barrier in the mid-eighteenth century.

At the end of a very successful scientific career, during which he made three major new inventions, and "won" the prize for Longitude with his horological designs, he devoted his last years to the study of musical tuning. This is a subject very closely akin to his other particular areas of expertise, i.e.navigation, pendulums, harmonic motion, and the study of mechanical systems with regard to time..

In his book Concerning Such Mechanism, (after "slagging off" his contemporaries), he very clearly states his conclusions: The Natural Notes of Melody may be derived mathematically from pi. He gives no experimental details, except that he used monochords, and clearly understood and criticises WNR (whole number ratio) logic and practice. He seems to have been criticized for this work, in the same way that his tunings are criticised today.

[Not for their impracticabilities, tunelessness, or any musical reasons - (it works exquisitely for musical harmony, modulation, and transposition for all types of "ethnic" music which I have encountered to date); yet for its lack of scientific proof].

After CSM ..... was published he wrote a manuscript

HARRISON, John. A True and Full Account of the Foundation of Musick, or, as principally therein, of the Existance of the Natural Notes of Melody. An unpublished manuscript of 182 pp., which is cataloged as item 8961 in Bibliotheca Chemico-Mathematica issued by Messrs. H. Sotheran of London in 1921, but has since been lost.

I have seen only one page of this manuscript. It arrived at my London address from a horological researcher, about ten years ago. I hear that it was by way of a Folkestone antiquarian bookseller. The page was a diagram of a clockface, with the note names written around the circumference, and marks where later steps of fourths and fifths would arrive. It showed the Large interval at the angle of the radian i.e. 360/(2*pi) = 57.3 degrees.

C was at 6 o'clock and the other naturals were arranged ascending clockwise.

From this page and the title, I suspect that the missing manuscript revealed Harrison's experiments. I heard that the offices of Sotheran were destroyed during the London blitz by a direct hit.

I wish to attempt to reconstruct Harrison's experiments, for I believe that they will give us much greater insight into his thinking, and possibly provide us with "scientific proof".

Any help, pointers, or comments about this manuscript will be appreciated.

Should Harrison's "proof" be found to be valid, it will be necessary to re-examine the traditional scientific assumption that "harmonics" can only occur at integer frequency ratios.

That would really put the scientific "cat amongst the pigeons"!

Charles Lucy, March '97,



Related Pages
Transcription of Concerning Such Mechanism...(CSM)
Transcription of the mathematical parts of CSM
John Harrison - Biography by Heather Hobden
Information and extracts from Dava Sobel book Longitude
LONGITUDE film from Granada Films and Channel 4 broadcast January 2000 - The plot and details.
Robert Smith DD FRS comments on John Harrison's tuning ideas, from his book Harmonics or the philosophy of musical sounds Cambridge MDCCXLIV (1744)
Pictures associated with Harrison

National Maritime Museum webpages on John Harrison and the Longitude problem

NOVA Online - Lost at Sea: The Search for Longitude
Biographical notes on 17th and 18th century mathematicians. (Harrison's contemporaries)
Longitude - A Horizon 1999 special - about John 'Longitude' Harrison.
Recipe for homemade 3 dimensional Physical Modelling spiral for all meantone and similar tunings
Thoughts on PI and PHI
MusicAsEasyAsPi - Music, Ancient Greek Ratios, Geometry and Speculations.
Frequency to Wavelength Connection