Temperament: The Idea That Solved Music's Greatest Riddle

I have paraphrased the author but annoyingly he always leaves out any exponentiation or even ordinary manipulation of fractions where appropriate. You will see the ratios mentioned seperately, all the relevant discussion is accompanied by the piano keyboard drawing (redrawn and remarked in several pages, in various tuning attempts, very pedagogically and clearly set out), but the mathematically inclined reader with a passion for vulgar fractions such as the syntonic(80/81) (and even the fourth root of (80/81) to distribute the comma over four intervals), can do the math for himself ( aided by the author's text) and make marginal notes for additional edification and erudition.

Contrary to someone's negative review, I found the accomanying history, and the running theme of culture and musical tuning very thought-provoking if not completely convincing. For the amount of ground covered and for the respect the author shows for his facts historical, and for his facts musical. The author's love for his subject and care for exposition are evident. This book is enjoyable and one to keep.

I, for one, being more a math-head than a western-music-head, would only have wished for a few more fractions and decimals if only as an appendix. And "cent" the 1/1200 of the logarithmic ratio is not even mentioned.

Another point where math might have made things clearer, while its omission makes for a little more obscurity is why (in Chapter 11) 749/500 worked out better as a fifth. The author informs us that in the East, in China, Prince Chu-Tsai-Yu, a descendant of a Ming emperor found this ahead of the discovery of equal temperament in the west. I saw at least one reviewer perplexed. Stuart Isacoff correctly says that closure after the twelve-cycle of fiths was ALMOST there. In equal-temperament, it would be 749.153538, pretty close!


Not so fast, please.   January 2, 2002
 12 out of 13 found this review helpful

Mr. Isacoff has managed to skip a hugely important period in the development of tuning, specifically the era between 1700 and 1900, in which he believes equal temperament was in use on pianos. The evidence from Jorgensen and Barbour would indicate otherwise. It is also naive to believe that tuning went from the restrictive Meantone to today's Equal Temperament in one step.
ET requires certain tests, checks, and balances to occur, and we know that those were not widely available before at least 1830.
I have tuned ET on pianos for many years, I know exactly what it sounds like, but by following the pre 1800 instructions that purportedly create equality, I find something far different than what we call ET today. Given the recalcitrant nature of piano tuners,(whose trade didn't really exist before the early 1800's), adoption of this more difficult temperament certainly didn't happen overnight.
It is one thing to simply say that people started using ET, but quite another to show that it was possible From the various Kirnberger tunings to Thomas Young, there was a generic shape to the tuning that caused the progression of "color" to be universally recognized. This common genre provided a basis for "key character". It is also interesting that in 1885, Ellis found that the master tuners at Broadwood's were not using ET.
Making a temperament "non-restrictive" does NOT make it "equal". There is far more harmonic activity in the work of these composers than ET will create but a "well-tempered" piano is required to hear it. To gloss over everything from Bach onward with modern tuning is to miss a huge part of the art. The book misses the basic and the finer of these points. Interesting read for the context, but it missed describing the true art of tuning.