Temperament: How Music Became a Battleground for the Great Minds of Western Civilization

by Stuart Isacoff

Few music lovers realize that the arrangement of notes on today’s pianos was once regarded as a crime against God and nature, or that such legendary thinkers as Pythagoras, Plato, da Vinci, Galileo, Kepler, Descartes, Newton and Rousseau played a role in the controversy. Indeed, from the time of the Ancient Greeks through the eras of Renaissance scientists and Enlightenment philosophers, the relationship between the notes of the musical scale was seen as a key to the very nature of the universe.

In this engaging and accessible account, Stuart Isacoff leads us through the battles over that scale, placing them in the context of quarrels in the worlds of art, philosophy, religion, politics and science. The contentious adoption of the modern tuning system known as equal temperament called into question beliefs that had lasted nearly two millenia–and also made possible the music of Beethoven, Schubert, Chopin, Debussy, and all who followed. Filled with original insights, fascinating anecdotes, and portraits of some of the greatest geniuses of all time, Temperament is that rare book that will delight the novice and expert alike.

Genres: Music, History, Nonfiction, Science, Classical Music, Art

288 pages, Paperback

First published November 13, 2001

Reviews

[Heather · Rating 4 out of 5]

I thoroughly enjoyed this book but found myself wishing for a companion CD with proper musical examples. YouTube was an utter failure as a resource.

[Dorai · Rating 3 out of 5]

Temperament is interesting enough that the author could have concentrated on it. However, he wants to talk about lots and lots of other things. The book does mention the arithmetic of temperament a bit, but I wish it had been more focused.

This isn't the only book with the following problem: Books that aren't primarily mathematical texts but nevertheless use the occasional math expression tend to have some pretty grievous math-typographic errors. I wish they'd follow perfectly valid linear typesetting. The fact that that this may be a bit more verbose is OK, because there aren't many such expressions, and I'd think it's more important to get them correct rather than pretty.

On page 147, for instance, the author refers to equal temperament's version of the fifth ratio (= 1.5). He means to say (the 12th root of 2) raised to the 7th power. However, his typesetter sets the 12th root of 2 (=~ 1.0595) as 12 times the square root of 2 (=~ 16.971), which would give a fifth ratio of over 400 million! The error happens because the typesetter put the 12 in front of, rather than in the bowl of, the root symbol. A very small rearrangement visually, but oh what a difference!

Now, it is perfectly reasonable to refer to the 12th root of 2 using the existing symbols of prose text as 2^(1/12), or 2**(1/12), if the caret is unavailable. So, the fifth ratio approximation becomes the not-too-unwieldy (2^(1/12))^7. Alas, authors don't seem willing to accept such "plain" syntax.

[Helen · Rating 4 out of 5]

Those of you who are budding Lennon-McCartneys, Gershwin-Porters, Cohen-Dylans, Cobains, Sheerans, Bach-Beethoven-Mozarts, Paganinis, forced to practice that detested piano every single goddamn day by your hated parents, passionate easy listening fans, or just like to sing in the shower: have you ever stopped to consider how each note came to be exactly where it is in a musical scale?

Think tuning is dry and boring, something only the white-haired piano tuner checked once a year back in the Dark Ages before electronic keyboards put a huge dent in the sale and maintenance of that dinosaur, the family upright piano? You couldn’t be more (up)wrong! This book explains the history, math, philosophy, and practicalities behind the intervals used in the modern tuning of all instruments – which includes western history beginning with Pythagoras; several wars; scientific inventions; various religious schisms; greed; the licentiousness of popes; the Age of Exploration; the Orient; architecture; too many musical factions to count; and several other kitchen sinks besides.

In the capable hands of Mr. Isacoff, the history of tuning – oh, the humanity! – turns out to be every bit as engrossing as a spy novel…and a true story to boot. If you have no music anywhere in your soul, then you can leave this one alone; otherwise, it’s not only instructive; it’s a lot of fun besides.

[Davis Smith · Rating 3 out of 5]

For the most part, an interesting if quite basic study of the Quadrivium and the Scientific Revolution. It would probably be better suited for neophytes of cultural history if not for the fact that there is a lot crammed between these pages that has the potential to be overwhelming. I admire the broad interdisciplinary scope, but it's almost too much. Also, some serious oversimplifications and mischaracterizations are present.

[Kelly · Rating 3 out of 5]

When I started piano lessons in the fourth grade, I clearly remember my piano teacher explaining the way the notes are organized on the piano and on sheet music, and it was like an explosion in my brain to learn that music is also math. I LOVED IT. I’ve always wanted to understand it better.

It took me seven months to read this book and I can barely describe anything about it, both because I don’t understand some basic thing about how music is organized that would have unlocked things for me (What is this missing piece?! Not sure!), and also because the book was all over the place. I feel like I should be a good audience for the book; I can read sheet music and play the piano, but didn’t study music any further. The book isn’t academic in style. It should be accessible, but there is a lot going on. It’s music and philosophy and math and science and religion. I did enjoy that *respected* scientists and philosophers sound completely insane describing their theories about connections between music/science/math/the spiritual world, insane and often intriguing. I haphazardly highlighted while I was reading. Why? Maybe I’ll come back to some things one day!

It is fascinating that pianos as we know them are a fairly recent invention and their modern tuning, which I always took for granted as just how it is, is something that was decided on (eventually) and fought over, it’s not the only way it could be, and people are still playing with tuning. That’s the main thing I gleaned from the book. Overall I had no idea what was going on, but I read it, it’s in my brain now, I’ll go from here.

[Jared Friedl · Rating 3 out of 5]

This book is… just ok. As a history, it falls into the traps of straying from its main topic (music) too often, including too many irrelevant quirky tidbits and asides, and making it difficult for the reader to identify the through-line of the temperament debate from era to era. I would often lose track of what century was being discussed and felt as if by the time the theory of temperament was paid any lip service, the chapter was about to end and the next chapter would start off establishing some new era, often by describing a popular historical figure only tangentially related to music. The author clearly has a passion for the subject, choosing to write on an under-appreciated conflict that we take for granted. The theoretical explanations were also a highlight. For the casually interested reader, the book just wasn’t “to the point” enough.

[Mark · Rating 2 out of 5]

Couldn’t finish it. The author includes an overwhelming and unnecessary amount of historical context. The development of tuning systems is addressed sporadically throughout the text. You lose the main thread. Try How Equal Temperament Ruined Harmony instead.

[R.K. Cowles · Rating 4 out of 5]

4 1/4 stars

[Ed Erwin · Rating 4 out of 5]

While he concept of equal-tempered tuning is a key point in this book, it actually discusses so much more. Though I initially regretted the absence of a deep dive into the math -- yes, I'm a nerd -- I did appreciate the more wide-ranging discussion.

Some of the facts included are quite obscure. For example, he mentions a keyboard called the "abacus enneacortus" of Juan Caramuel y Lobkowitz that had only 2 black keys. Intrigued -- and curious about which 2 black keys -- I turned to the internet and found only one single reference to that instrument, and only in Italian, but at least it had pictures. (The black keys were F# and B-flat.) (Lobkowitz is slightly more known for his organum panarchicum with 6 black and 6 white keys per octave, where the white keys make a whole-tone scale.)

[Thomas · Rating 2 out of 5]

This managed to give me some background in the temperament debate, but was not all it promised to be. The facts are remarkable enough - it seems every great scientist and thinker of the 17th and 18th century had something to say about this, which I never would have guessed. But Isacoff begins badly, spending the first 20 pages advertising the rest of the book - an annoying habit that also sets him up for a fall by promising the book of the century. In the spirit of the spate of books that attempt to tie all of civilization to salt or razor blades or what have you, he attempts to connect the whole train of western thought since the 1500s to keyboard tuning. Some of these connections, as you can imagine, are tenuous, and for all the breadth of his narrative, none of it ever catches fire. It never quite seems a LIVELY debate, particularly in the 19th century, when there is apparently reason to believe the issue remained quite lively, while for Isacoff modern tuning immediately became settled law. It is perhaps too expansive for a book of modest length. The author departs annoyingly from chronology without being explicit about it (apparently he decided or was advised to include as few dates as possible). He also repeats himself chapters apart, often using the same wording without any acknowledgement that he is doing so - a failure of editing that one can't help but find infuriating. In short, I would skip this one. If you want to know about the debate, read the wiki. The book is not worth it.

P.S. The second edition also includes a weirdly defensive - and egotistical - piece of apologetics of rather remarkable length.

[Carol · Rating 4 out of 5]

This short book was surprisingly fun, given its esoteric and nerdy subject matter. Isacoff examines the tuning of the Western diatonic scale, the problem of obtaining pure, harmonious intervals across the scale and across keys, and the development of equal temperament. This examination puts these things into context, relating developments in tuning to concurrent developments not only in music, but in science, art, philosophy, and religion. Although this book didn't have much in the way of things I didn't already know, it did an amazing job of delving into relationships between music and other disciplines, which proved fascinating. Isacoff also did a great job of taking a potentially dry subject and making it incredibly interesting and even exciting.
(I should note that the text is not very technical at all - the reader does not need to read music or have any background in music theory.)

[Rebecca Rebecca · Rating 3 out of 5]

This book is an interesting introduction to the development of equal temperament in European music. Its best usefulness is a resource that will send the reader to primary sources and scholarship on the topic; a bibliography is included. The author relates musical developments to painting, literature, political and intellectual developments in a way that isn't really satisfying. He does not go into enough depth on any one theme, preferring to suggest connections and move on. The book is also marred by a few sexist jokes.

If you're an amateur musician beginning to explore the history of temperament, this book is a possibly useful resource to get the lay of the land.

[MICHAEL · Rating 2 out of 5]

This book has been on my shelf for years, it was one of a long line of these narrative history type books (Longitude, Brunellesci's Dome, etc.). This one fell far short of the two mentioned. It is full of historical and technical information, but never got into a narrative, and lacked a protagonist that I could relate to, and I was never drawn into it.

If you are really into music, and the history of music, you may find it compelling, but, otherwise it was a struggle.

[Estott · Rating 2 out of 5]

Interesting if you like the subject and have some musical knowledge - and know your way around a keyboard. If you don't have these things this book will be incomprehensible. As someone else mentioned, this should have come with a CD of examples as the subtleties of character ascribed to various keys on various tuning systems are meaningless on the page and a modern keyboard won't help antirely.

[Wesley Toler · Rating 3 out of 5]

For those of us that were introduced to musical intervals as perfect fractional intervals (3/2 ratio of frequencies in a fifth, 4/3 in a fourth, etc.), the reality that the modern Western tuning violates these perfect ratios is a bit shocking. The Pythagorean / Keplerian "music of the spheres" has such aesthetic and philosophical appeal that it resisted alteration, even in the face of its glaring practical issues for musicians. This book marches through the history of the development of "equal temperament" (the modern scale), and the musical and cultural developments that helped shape the transition.

The material itself was interesting and informative, but I found the overall tone to be snarky and irreverent, which is not typically my cup of narrative tea. This work also (in my opinion) falls into the trap that a lot of popular history books fall into, of connecting wide swaths of culture together in a cohesive whole whether they actually fit or not. I understand the need to craft a narrative, but the world is a complicated place, and the narrative of old-fashioned geometrical purists vs. the revolutionary practical iconoclasts unfettered by religious pretense seems reductionist to me.

But I may have fallen into the same trap of reductionism by trying to summarize and criticize a 230-page book in a couple of paragraphs. :)

[Roberto Pieraccini · Rating 3 out of 5]

While the book offers a broad overview of general world history, centered around the main developments if music theory evolution, it devotes disproportionately little attention to the very topic it promises—scales and tuning. Readers seeking an in-depth exploration of tuning systems and their evolution will likely find the coverage too brief and lacking in analytical depth. This imbalance between contextual history and the book’s stated focus makes it feel more like a general history survey than the specialized study implied by its title

[John · Rating 4 out of 5]

Scientists, engineers, composers and musicians wrestle in acoustic mud for 2,000+ years. Fascinating and hilarious.

[Heather Parks · Rating 5 out of 5]

My friend loaned me this book, promising that I would love it. He knows me all too well. Read it in two days and thoroughly enjoyed it.

The book is primarily a historical narative that follows the development of the Western musical scale from Pythagorus's early theories to the adoption of equal temperament at the beginning of the classical era. Along the journey, Isacoff weaves together the varied threads of scientific discovery, philosophy, musical theory, socio-political movements, artistic and musical fads and fashions in such a way to paint a fascinating picture of how our modern intonation came to the accepted standard.

The book never gets too technical and should be easy to understand for musicians and music lovers alike. Not a lot of theory involved, as the book really focuses on the historical narative rather then the technical aspects, while accessibly explaining the significance of each development.

The reading experience is greatly enhanced by searching youtube and google for the all the cited musical examples, composers and innovators throughout the book as you read. The perfect soundtrack.

[Johnny Bookworm · Rating 3 out of 5]

Oh boy this was a weird one. I was certainly a bit disappointed with the lack of in-depth musical talk but I suppose I can’t criticize it too much for that since it was intended for the general public. I was looking for an introduction to the musical world of temperaments, however this book provides more of a recount of artistic and philosophical developments over the years and often times the chapters don’t really have much to do with temperament. This was sometimes interesting but sometimes boring. I certainly learned a lot but ultimately this book missed the mark of my tastes.

[Bill Dearth · Rating 5 out of 5]

Absolutely fascinating

This is one of the most compelling books on music that I have ever read! The author takes through the art, architecture, philosophy, theology, science and everything else behind the tempered scale. It completely blew me away, the breadth and depth of the long history of temperament. I was totally engaged throughout the book, and appreciated the extensive bibliography, which has given me many more roads to explore.

[Marc Heyvaert · Rating 2 out of 5]

A wealth of cultural and historical background but lacking in technical detail. After reading the book I was happy to find that information on the internet, it helped me to make sense of some parts of the book, but that should have been unnecessary.

[Tweedledum · Rating 5 out of 5]

Fascinating history of the piano -how and why it came to be just so....

[Ivan · Rating 5 out of 5]

This was an amazing book. It is a musical book, but not a textbook on temperament, so no long dry passages to worry about that in regard.

The history covered is spiraling and complex, and the way its written as intertwined thorough that period makes the book seem to project, in a bizarre and beautiful sense, that the world is just a frame to hold the debate on temperament and its journey to its current position.

The renaissance approach the author takes with including the different philosophers and schools of thought to temperament, brings a deep richness to the book. Though, I'll provide a fair warning, with the richness of the added philosophers, is a brief passage or two where the philosophers describe their viewpoint in analogy to more corporal form.

Having said that and set aside, I can give an unreserved recommendation of this book to my friends.

I loved the discourse on the ratios and how those ratios appear all around us in life. I've been made aware of those connections through various math and biology courses, however, as I traveled through the book, the experience of how I arrived at those points made the rediscovery awe inspiring. Especially, the chapter that ended with Kepler. I found the journey to that point of the book incredible. The tie in to string theory was good too, and while I appreciate string theory, the fact Kepler's discovery ties into the ratios so beautifully makes it that much cooler.

Rousseau makes an appearance. Luckily the book didn't include any passages where we have to read him describe himself at length. It was focused on his part as a wave in the foaming sea that was the debate on temperament (and art in general).

I also really enjoyed the exploration on how the freedom of art vs discovery of art embedded in nature played out across the various mediums (not just temperament), when considering that and combing it with the discourse on the ratios, it really draws in the depth of mathematics. And while the book wasn't broad enough to include more math, it really brought to mind the same debate that mathematics faced. Is math created (art) or discovered (nature)? The parallels between the difficulty in advancing math compared to the difficulty with changing art (due to Roman Catholic Church) was interesting to me. For instance, the concept of zero or negative numbers used to be dangerous or even heretical. Though the zero controversy was a good bit earlier than the debate of temperament, it still took till the 12th century to get a copy of a zero from Arabia.... Faxing the negative numbers proved slower and took another 300 years to arrive in the west and longer still before its meaning was clearly defined.

This book was a very good read, and I'm getting a copy of it for myself.

[Terry · Rating 3 out of 5]

Instrument temperament is something that even music dorks consider something out there even by music dork standards, but Temperament attempts to put the debates over how to tune an instrument into historical context. For a little background: All of the common intervals can be expressed as a ratio of frequencies of small whole numbers. An octave is twice the frequency of the initial pitch and an fifth is 3/2nds the frequency of the initial pitch. There's a problem, though, if you take 12 fifths, you don't wind up with the same pitch as if you took seven octaves. The two differ by about a percent. This gap is called the Pythagorean comma and is quite audible. The same problem pops up if you want 3rds (4:3) to add up to 5ths (3:2). Historically, there have been differing ways of modifying these intervals to deviate from these pure ratios in such a way to hopefully minimize dissonance. For instruments with variable tuning like string instruments, the human voice, and some woodwind/brass instruments, you adjust the written pitch so that it fits the part in the chord. For instruments where tuning is non-trivial like the harpsichord then the piano, a tuning needs to be set. The supposed answer to the problem of "best" tuning is offered by the author to be equal temparament which was widely known by the end of the 18th century. In equal temperament, each semitone is the 12th root of 2 higher than the previous, so 12 semitones gives you a doubling of frequency or a perfect (just) octave.

The author outlines the path from music without harmony to equal temperament tracking the developments in both theory and technology along the way. The author outlines how other arts shifted over time, particularly painting and theater, as well as the various responses to tunings from the church. These strands are interwoven but in reading, the crossovers felt haphazard. Things move roughly chronologically but sometimes things jump around in time or space. Additionally, the author treats equal temperament like it's "right"; the obvious and nearly self-evident solution to the problem of tuning which is far from true. The author ignores the persistence of chromatic and microtonal tunings as well as the historical music movement which saught to recreate pieces as first consumed.

The book is a good introduction to the problem of equal temperament as well as the history of fashion in some of the arts. As for a definitive treatment on temperament, far from.

[Forrest · Rating 4 out of 5]

Isacoff tries to tell parallel stories here, comparing the intellectual progress through the Renaissance and the Enlightenment with the "progress" from just intonation to equal temperament. Here's a quote that illustrates the general tone:

After Newton, earlier philosophers of nature seemed, like the residents of Laputa in Gulliver's Travels, prisoners of of a rigid, geometric fantasy. [ ... ] Newton's universe was a different sort of place: [ ... ] His descriptions of things as they are overwhelmed the old picture of what they logically ought to be.

He proceeds with the attempt to force this analogy, even when it doesn't really work. Of Newton, he was later forced to concede

Nevertheless, his solution to the temperament problem was, in the end, unremarkable. [ ... ] Newton remained convinced that the simple ratios governing musical concords had indeed been consecrated by nature.

After praising Newton's ability to value his faculties of observation over theory, it doesn't seem to occur to him that perhaps Newton actually listened to musical intervals and found that just intonation actually sounded better.

After continuing to tell the tale until, at the end of the Enlightenment, equal temperament is almost universally accepted, he ends by talking about modern composers who still haven't accepted it, describing his delight at a special concert by Michael Harrison he was privileged to attend. (So, maybe his entire thesis didn't work? He doesn't conclude this.)

Then, there is another chapter, which he added to the paperback edition, responding to his many critics. He states that he's surprised that everyone who read the book thought he was such an advocate for equal temperament. Duh, that was the conceit around which the entire book was structured! Equal temperament is "progress". Yet, as his critics pointed out to him (some not so nicely, I take it), that's not really the case.

Yet, despite the fact this book is structured around a failed thesis, I still have to recommend it. The only other sources for this information are dry and academic; Isacoff manages to keep things interesting with all sorts of anecdotes about the very colorful characters who had a part in this development, and descriptions of the different keyboards that tried cramming more and more keys into the octave in quest of perfect harmony.

[Chris · Rating 3 out of 5]

A decent look at the concept of musical temperament from a perspective that is more favorable to 12TET than some other books written on the subject. Isacoff generally does a good job explaining the conceptual foundations of differing tuning systems, though I take issue with some of the diagrams and mathematical formulas used.

The biggest issue with Temperament is that, at times, it seems resistant to actually discussing temperament. The book certainly picks up as at moves along, but I found certain chapters in the first half so frustrating that I considered returning the book to the library without finishing it. Analogies are useful for explaining abstract concepts, but in a book about temperament, I don't want to read entire chapters about what was going on among physicists, or painters, or architects. I get the sense that these passages were included to make the book more interesting to a general audience, but to be blunt, nobody save for hardcore music nerds was ever going to read a book about temperament, of all things.

The writing could have undergone some additional revision, too. Isacoff uses uncommon and frankly distracting words such as "lapidary," yet he misuses more common words such as "comprised." While I understand the historical necessity of naming so many figures, the number of names in the book is a bit dizzying as well.

Temperament is a fascinating subject, and I'm glad that this book exists, but a more focused text would have been better. While neither book is perfect, the flaws of Isacoff's book make me appreciate How Equal Temperament Ruined Harmony more than I did previously. The two books complement each other decently for a reader who'd like a variety of perspectives on the subject.

[Daniel Winnick · Rating 2 out of 5]

I admit I read this hurriedly, in one sitting, so “savoring” wasn’t really the goal…still, I found it extremely exasperating. If I had tried to read more patiently, I wonder if the frustrating effect of Isacoff’s many—innumerable—digressions (in the service of “context”…telling the entire story of Western civilization?!) would have been even more potent in diluting the narrative of a book that is, nominally, about the history of temperament in the Western musical scale.

As a musician, that was all I was really interested in. Am I really going to remember the likely-over-half of the book devoted to illuminating the margins around the main text? (What Isacoff describes in his postscript essay as “spark[ing] in the reader a profound sense of wonder and discovery—to provoke a little of the awe that lives in the hearts of true artists and great thinkers” PLEASE!) For the most part, no.

But part of the problem is that Isacoff was aiming this book at general readers. I do appreciate his attempt to demystify the musical scale for those with little or no musical training. (Keyboard diagrams help.) But ultimately, I wonder if anyone really, truly needed this book to be as bloated with hyperventilating historical detail as it is. It certainly ruined for me what could have been a fascinating book on a subject of real import for musicians up to the present day.

[MIke Coldewey · Rating 3 out of 5]

I enjoyed the tone of the book: the author mixed a lot of technical information about intonation and what it means in terms of the diatonic scale, key modulations, and the acoustic properties of overtones with anecdotes and stories about the arguments and discussions arising from the different methods of tuning. That said, it's hard to imagine this facet of music creating so many conflicts outside of performance circles, composers and instrument creators (and I think that "Battleground" is a little over the top). It may be that people's attention and hearing were more closely aware of the intonation of the instruments they were hearing than today, because my experience is that the vast majority of listeners don't notice instruments that are out of tune, let alone tuned in other than equal temperament.
I do think that the author presents the various methods of tuning well, or as well as can be done outside of a live demonstration with a guitar or violin. Any more technical or mathematical discussion might have been overkill.
I did appreciate the idea the "well-tempered" (as in the Bach Well Tempered Clavier) didn't necessarily mean "equal temperament", although I'm not sure now which tuning Bach was using or wanting to illustrate with that work.

[• Lulù • · Rating 5 out of 5]

"Temperamento. Il termine deriva dal latino temperare, ovvero unire nelle giuste proporzioni. […] Temperare può significare adattarsi alle contingenze, addolcire le difficoltà trovando una soluzione intermedia o accettando un compromesso."


Quando personaggi del calibro di Pitagora, Platone, Newton, Keplero, Galileo, Leonardo Da Vinci, Rosseau, Diderot e molti altri si sono battuti tutti nel corso della storia al fine di trovare un'accordatura "perfetta", il cosiddetto "temperamento equabile" il lettore capirà immediatamente, fin dalle prime pagine, di essere stato coinvolto in uno dei più grandi enigmi, non soltanto musicali, ma altresì filosofici, scientifici e perfino religiosi.

Ricchissimo di particolari storici, scientifici e filosofici, la lettura non risulta mai pesante, ma al contrario, invoglia il lettore al proseguimento.

Testo portante di uno dei miei esami di storia della musica, mi sento di consigliarlo a chiunque, osservando la tastiera del proprio pianoforte, si sia mai chiesto quale fosse il trascorso dietro quelle proporzioni che oggi, erroneamente, si danno per assolute.

"L'eufonia - la bellezza sonora - era riassumibile in un numero."

[Kiersten · Rating 2 out of 5]

I really wanted to like this, but unless you've graduated with a degree in music, this is VERY murky reading. After finishing the book, I'm still not sure what the difference is between equal temperament, mean-tone tuning, and perfect tuning. Isacoff, while thorough, wanders off on a myriad of historical tidbits which are perhaps related to temperament in loose ways. In the beginning of the book, wonderful tuning occurs due to the vibrations matching up at particular coordinated times, and yet later in the book he claims that this can't be true because notes that begin at different times STILL ring true. And later, he says that the overtones and surrounding vibrations somehow get in sync with the original initiation of the sound. So is THAT what's happening? I really wanted an easy-to-digest explanation of the physics of sound and tuning, and I wanted a bit of backstory on the history of tuning. I really didn't want to slog through all the debate and characters surrounding the problem for centuries. To be honest, it doesn't sound like we've really solved music's greatest riddle at all.