New Book on tuning and scales by Bruce R. Gilson

Back in 1993, Bruce R. Gilson published an article in Xenharmonikon 15
titled "A Numerical Theory of Scale Invention." Recently Bruce
contacted me to let me know that he had expanded this article into a
book called "Construction of Musical Scales, A Mathematical Approach"
which is available from Createspace, a publish-on-demand site for
books, music and video, that is affiliated with Amazon Books. It may
be visited at the URL below: https://www.createspace.com/3353001.

I've been far too busy to write a formal review, but the Table of
Contents looks comprehensive, to say the least. A novel aspect of this
book is that it uses millioctaves rather than cents and contains a
very large table of intervals expressed in Monzos, ratios, decimals
and MO's as an appendix. As I recall, there was a recent discussion on
the advantages of MO's on this or the tuning math list recently. The
book also has a comprehensive index, making it quite easy to locate
topics quickly.

The mathematical level is rather elementary, being limited to ratios
and logarithms, and advanced techniques such as the predicate
calculus, matrices, and Grassman algebra that are to be found on the
Tuning Math list are avoided, so it should be readily accessible to
anyone who wishes to learn about tuning and scales.

I've appended the TOC below. Alas, it appears that his careful
formatting seems to have been mostly lost in going from PDF to email.

--John

Table of Contents
Chapter 1. Introduction: What this book is
about...................................................................................1
Chapter 2. What is a musical tone?
........................................................................................4
Chapter 3. Octaves and
fifths..................................................................................7
Chapter 4. Measuring
intervals...............................................................................9
Chapter 5. The circle of fifths; the Pythagorean
scale...................................................................................14
Chapter 6. Modes and
keys....................................................................................19
Chapter 7. Naming of
intervals...............................................................................21
Chapter 8. The (Pythagorean) chromatic
scale...................................................................................24
Chapter 9. Thirds and sixths; just
intonation..............................................................................28
Chapter 10. Properties of just-intonation
scales..................................................................................35
Chapter 11. Temperaments, part 1. Meantone
temperament.............................................................................37
Chapter 12. Temperaments, part 2. Twelve-tone equal
temperament.............................................................................41
Chapter 13. Some properties of regular
temperaments............................................................................44
Chapter 14. General properties of diatonic
scales..................................................................................46
Chapter 15. Generalizations of the just
scale...................................................................................48
Chapter 16. Other equal
temperaments............................................................................51
Chapter 17. Other scales extracted from chromatic
scales..................................................................................62
Chapter 18. General comments on regular
temperaments............................................................................65
Chapter 19. Non-octave-based
scales..................................................................................66
Appendix A. Binary logarithms for computation of millioctave
intervals...............................................................................67
Appendix B. Named musical
intervals...............................................................................68
Appendix C. Frequency ratios for various fractions, and millioctave
equivalents.............................................................................105
Appendix D.
Bibliography............................................................................140
Index...................................................................................141

correct link:
https://www.createspace.com/3353001