### The boundaries between the Trojan symbols

Posted:

**Wed Feb 12, 2020 11:07 am**In Figure 10 of http://sagittal.org/sagittal.pdf we give a number-line marked in cents showing the approximate boundaries between the Trojan symbols, but we do not give precise numerical values. Here they are as fractions of a semitone plus or minus epsilon, where epsilon stands for an infinitesimal quantity, or the smallest change available in the number system being used.

Note: As first published, the boundary between and was as follows:

Symbol Common Boundary Boundary semitone semitone cents fraction fraction -------------------------------------- -3.999999999 -(1/25-ϵ) no symbol, natural 3.999999999 1/25-ϵ 1/12 9.090909101 1/11+ϵ 1/10 11.99999999 3/25-ϵ 1/6 16.66666668 1/6+ϵ 1/5 22.22222223 2/9+ϵ 1/4 28.57142856 2/7-ϵ 1/3 33.33333334 1/3+ϵ 3/8 38.88888888 7/18-ϵ See note below 2/5 42.85714285 3/7-ϵ 7/16 48.00000001 12/25+ϵ 1/2 51.99999999 13/25-ϵ 9/16 57.14285715 4/7+ϵ

Note: As first published, the boundary between and was as follows:

2/5 40.00000001 2/5+ϵ obsolete 5/12But when working with 60-edo in 2012, Graham Breed made a case for the new 38.88888888 cent boundary, which George and I agreed was convincing.