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Re: J.R Pierce paper

An interesting idea. Following from the statement:

Our previous work demonstrated that chords with frequency ratios 3:5:7: and 5:7:9: have many perceptual harmonic properties of major triads (4:5:6 ratios). The traditional diatonic scale can be constructed from three major chords, the tonic, the dominant, and the subdominant chords. 

I took some liberties with names and numbers to simplify the results.

Build a 'C major triad' , C  E  G.  ratio  4:5:6
The 'C' is the 5th of the subdominant chord, F, and G is the root of the dominant.

Using this ratio to build the F and G triads, and using foldover octave equivalence, the C 'major' scale, [starting on the arbitrary frequency of 400 Hz], seems to come out as follows:

  C  400
  D  450
  E  500
  F  533
  G  600
  A  666
  B  750
  C  800

This scale may already have a name. The three primary major triads would  be beat free. I think that melodies constructed from here might be quite interesting for the general population.

By extension up and down, F# and Bb would be introduced. Built on the D, the notes would be D, 450Hz, F# 562Hz and A 675. This A is higher than that in the F major triad. Maybe the solution would be to split the difference and tune A to 670Hz. It would be about equally inharmonic with both triads . . . 


On 2012, Jun 11, at 3:32 PM, Richard F. Lyon wrote:

It does show up at their site, but it's only an abstract from a meeting; there is no corresponding paper.


At 10:02 AM -0700 6/11/12, richard duckworth wrote:
Hi all, does anyone have this? I even have a JASA sub. but it doesn't show up on their site!!
Four new scales based on nonsuccessive-integer-ratio chords
J. Acoust. Soc. Am. Volume 75, Issue S1, pp. S10-S10 (1984); (1 page)
M. V. Mathews1, L. A. Roberts1, and J. R. Pierce2

Thanks, Rich

Rich Duckworth
Lecturer in Music Technology
Department of Music
House 5
Trinity College
Dublin 2
Tel 353 1 896 1500

It's the most devastating moment in a young mans life, when he quite reasonably says to himself, "I shall never play The Dane!"