How Equal Temperament Ruined Harmony

by Ross W. Duffin

A captivating look at how musical temperament evolved, and how we could (and perhaps should) be tuning differently today. Ross W. Duffin presents an engaging and elegantly reasoned exposé of musical temperament and its impact on the way in which we experience music. A historical narrative, a music theory lesson, and, above all, an impassioned letter to musicians and listeners everywhere, How Equal Temperament Ruined Harmony possesses the power to redefine the very nature of our interactions with music today.

For nearly a century, equal temperament―the practice of dividing an octave into twelve equally proportioned half-steps―has held a virtual monopoly on the way in which instruments are tuned and played. In his new book, Duffin explains how we came to rely exclusively on equal temperament by charting the fascinating evolution of tuning through the ages. Along the way, he challenges the widely held belief that equal temperament is a perfect, “naturally selected” musical system, and proposes a radical reevaluation of how we play and hear music.

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

208 pages, Hardcover

First published November 17, 2006

Reviews

[Imogen · Rating 5 out of 5]

When I was a little kid, I'd always shoot straight through the book store to the humor section, to suck down easy, unchallenging, y'know, bullshit. (Not that comics are necessarily bullshit; just that, at that point in my life, what I wanted was something easy that I didn't have to think critically about, which Ziggy or Garfield... can be.) Then, when I decided I was older and more mature, I started heading to the music section of the book store for my unchallenging bullshit. THEN now that I am older, the fiction section- or, sometimes, the gender studies or cultural criticism sections- seems most inviting, and both the humor section and the music section seem like they are totally for stupid little babies.

Which they are! Kind of, I guess. I don't know. I'm trying to draw a picture of the falseness of this hierarchy of seriousnesses I've made up in my head so I can explain how much it feels like, instead of internalizing challenging music theory, I've been COMPLETELY DORKING OUT for the last couple months I read this in quick little stolen moments. But I have been *so* into it.

I mean, okay, I am going to state at my navel- I will set the navelgazing between blocks of asterisks so you don't have to read it. Ready? Okay.

***I have been playing guitars for something like twenty (literally, seventeen, which also is a lot) years, and I am pretty good at it. And I think about it all the time. I don't talk about it that much because really who wants to hear it? "That's an interesting inversion of the d major power chord in that Minor Threat song," I'd say, to which people would stare blankly at me and then ask me to turn off Minor Threat. Y'know? So I stew on guitar stuff kind of all the time, and I figured out at some point that mostly I play weird, complicated chords up and down the neck of the stupid thing to avoid playing anything other than octaves, fourths and fifths. I remember the moment in high school when I decided, Oh shit, fourths are a great interval! Partly 'cause it made me feel smart, to know so much about an interval, and just partly because, I mean, fourths ARE a weird interval- they're weirdly parallel, static- they move, but not with the tension of a fifth, y'know? There isn't that resolution, that sense of finishedness.

Anyway, early in this book, when duder explained that fourths and fifths and octaves are going to be in tune in any kind of temperament- whereas other intervals would only be kind of (or not) in tune depending on the temperament, and that therefore the thirds I tend not to play mathematically are totally fucked with regard to being in tune, 1. I felt smart for intuiting it but also, 2. felt justified in playing guitar the way I do, even if Sonya's trying to make a rule where I don't play octaves any more because she is bored of it.***

So yeah. I think it's interesting that he doesn't mention the guitar at all, but I guess his focus is on classical (or probably "classical") music, which tends not to feature guitars too prominently. I was mostly surprised that they didn't show up in the chapter about why Equal Temperament became the hegemonical maniac overlord it is today, because it seems like- in the 20th century, when everybody was internalizing that other temperaments were stupid- the rise of the guitar happened maybe a little bit after the rise of Equal Temperament zealotry, but not far enough after that they're unrelated.

Anyway, yeah. This was fascinated and I'm a little sad it's over and that all the sources probably only exist in academic libraries at music schools, because while I am a loud dumb rocknroller and therefore probably not that best person to put it into practice, I would like to dork out even harder on music theory. Or music theory theory- meta music theory- which I guess this is. Five stars!

[Danielle · Rating 1 out of 5]

First, I read this book on Kindle. The Kindle version (which has apparently been taken off the "shelves") is disastrous. None of the figures are there (although I didn't miss any of them. They seemed useless anyway). Footnotes are in the middle of pages without warning. It is a mess to navigate. Symbols, such as flats and sharps, when they are not simply omitted, disfigure the layout.
Now about the content... The author argues that we should use other tunings besides equal temperament (ET). I was expecting an historical argument, a philosophical argument, a psychological argument, an acoustical argument, and an unpredicted surprising argument I had not thought of. Instead, all I got was an historical argument that is not very convincing. Basically, the thesis is: Since Mozart didn't use ET, we shouldn't either. This is an exaggeration of course, but honestly, not a big one. Needless to say, there are a lot of problems with this argument. He also mentions that we should make our major thirds smaller because "it sounds better" (yes, that is a quote). There is no defense of this statement. Again, a psychological or acoustical approach as to why we might prefer a just third would be helpful. He argues at the beginning that the beats should not be there, but the temperaments he proposes all include beats in them, as the just intervals are not the ones he prefers either. In summary, his arguments are weak and contradictory.
Another big flaw, is the lack of mention at ANY point in the book of the compositional aspect. His argument is for performance only, which adds to the overall weakness of his point. Before reading this book, I was a fan of the use of various temperaments. Reading this book just sparks this reaction "I'm not convinced. Despite already being convinced." That's how weak the arguments are.
Finally, if someone purchases a book called "How equal temperament ruined harmony", you can safely assume that they have SOME interest in temperament and that they probably know about the octave being a 2:1 ratio. Dedicating pages and pages to the explanation of the interval ratios was useless. Parentheses over-explaining simple concept are on every page. Moreover, since the author uses music theory lingo, it is assumed that basics of theory are known. The intended audience of the book is very unclear because of this.
A good side to the book is the historical aspect. It is a decent refresher on the history of temperament, although I have seen better. However, Duffin could write a decent book if he stuck with history and stopped trying to make arguments, as he is obviously not gifted in the rhetorical.

[Rachel · Rating 5 out of 5]

What an important work for every professional musician to read! As an instrumentalist I have always preferred just temperament but felt that equal temperament was a necessary evil for instruments such as the piano. Through the years, I simply avoided playing with the piano & relished in the flexibility that orchestral rehearsals/performances provided me with tuning closer to just temperament. Tuning was always a hot topic in music school & later in professional musician circles, but the details of “why” were never truly explored. I applaud Duffins effort in making us aware of the how & why in the temperament debate.

[Erik Moore · Rating 5 out of 5]

This was an eye opening work for me regarding how the standard scale of music came to be today. Key is how Duffin lays out the mathematical issue with scales, how when one multiplies a frequency by halves, thirds, or fifths, you will not get overlapping notes along those progressions, and how those harmonics of tone are what we find beautiful about music. That incongruity for me was something I hadn't considered in all my years of playing tuba in band and orchestra. From their, laying out the different temperaments of history that reconciled this problem, and how they both defined and were chosen by style of music was great. Then how Duffin lays out the competition between the coherence of the scale of notes in any one time with the coherence of the melody over time was beautiful, particularly how this is naturally handled by string quartets of a high caliber. The keyboard instruments were of course a huge move to standard fixed scales, early on with organs setting the scales for towns, and then the pervasiveness of the piano that made an equally tempered scale with fixed notes just darn convenient. Duffin's survey of history here provides enlightenment for both historical instruments and for modern musicians (digital or otherwise) who are looking for ways to think outside the box of the standard scale and discover new beauty in ancient variety. A great revelation, and link to science, for me was Duffin's review of the work of William Braid White around 1917. White was the one who used electronic measurement to point out that "the emperor (of the world's preeminent tuners)had no clothes" when it came to what temperaments they were tuning, versus what they were purporting to tune. Duffin goes on to suggest that it was more than the resignation of convenience and accountability that led to the diminished use of our broad heritage of diverse tempered scales, that it was Positivist philosophy, and that perhaps we should musically challenge such philosophies. I would disagree here, glad that with scientific understanding that we can better understand those choices and make them with eyes wide open rather than by falling into preferences of habit or affiliation that Duffin brings up so eloquently in his example of George Bernard Shaw's change in hard regarding Joseph Joachim's music. All in all, I could not even make such subtle conjectures though if Duffin had not led me down that path of understanding. What a fun read and what an amazing body of knowledge to share and preserve. I've recommended to the author that he consider making smart phone apps that can help folks hear the subtleties he describes, about beat, about variance in temperament, and about chord versus progression of melody. I'm hoping to see more from this author in print and in the digital world.

[Bruno · Rating 3 out of 5]

This book provides a rather technical and historical overview of Equal Temperament. It's very interesting and valuable, but not so much for the non-musician or the uninitiated. Amongst other things it made me understand that indeed there is a difference between an augmented second and a minor third, and between a G# and an Ab.

(If G# and Ab mean nothing to you, this book is definitely not intended for you.)

[Meara]

This book is dorky and deeply satisfying.

[Emiel Vertongen · Rating 3 out of 5]

Goei leesvoer.
Zet goed aan tot dieper nadenken over intonatie, en prikkelt de nieuwsgierigheid om meer informatie over andere stemmingen op te zoeken.
Op een beargumenteerde manier toont de auteur aan dat muziek die voor 1917 gecomponeerd is vaak niet met gelijkzwevende stemming voor ogen werd geschreven, en waarom.
Vaak wel een storende opbouw met te veel irrelevante biografieën die de gedachtegang onderbreken.
Een toegankelijke eye-opener, maar niet volledig genoeg als je er ook echt mee aan de slag wil.

[Louis Headley · Rating 5 out of 5]

I devoured this book in one day. Duffin makes his case with precision and sensitivity, providing source material and references throughout. I was also impressed that he's not afraid to offer opinions of those who disagree with him.

I don't think I'll quite use a non equal tuning system for my piano, but if I ever own two I'll now consider it.

The only thing I find fault with is the extremely low quality publication. The cover doesn't line up with the pages and the formatting within the book is sometimes done in a strange way with footnotes going over multiple pages and some text boxes occupying a strange space. But I can hardly fault the author for that.

[Jordon Gyarmathy · Rating 5 out of 5]

This exploration of temperaments other than the now standard Equal Temperament was very helpful in my research on historical temperaments. I enjoyed the historical accounts, the measuring of tuning in historical recordings, and the analysis of the other literature released on the subject. I do not mind the author's bold campaign for unequal systems, because he openly admits to his agenda in the title of the book. Quite a nice light read that manages to be pretty extensive and thought provoking.

[Rebecca · Rating 4 out of 5]

It was a mind-bending struggle for long stretches to grasp - or attempt to grasp - the physics at core of the author's commentary on the history of western tuning systems and how we got to ET (equal temperament) for not only fixed-pitch instruments like the keyboard family, but an extended agreement out to ALL modern instruments.

However, I feel the challenge was definitely worth it. As an amateur musician foraying into Baroque music performance, I believe I'm now a little better prepared for those moments of tuning chords across voices in an ensemble, knowing that there's a history of disagreement on what the objective should be. I'll still end-up bending to the keyboard, as that poor instrument is incapable of adjusting to the harmonics of the moment, but I now know why I have to indulge it for the sake of the whole.

Secretly, however, I'll take comfort in the book's closing admonition taken from Pablo Casals:

"Do not be afraid to be out of tune with the piano. It is the piano that is out of tune. The piano with its tempered scale is a compromise in intonation."

I feel better already!

[Joe · Rating 3 out of 5]

EVERYTHING YOU KNOW IS A LIE

OK, maybe that's not true. But the musical scale that you take for granted? There's a lot more to it than you might expect.

Notes are frequencies of vibration; certain ratios of vibrations work well together. The most basic ratio is 2:1 -- if you pluck a string, then pluck a string of 1/2 the length, you'll get a vibration of twice the frequency and hear the same note as the first time, but transposed one octave higher.

Other basic ratios work well: that is, they sound especially pleasing to our ear when played together. A ratio of 4:3 is called a perfect 4th, and is the relationship between a C and an F; a ratio of 3:2 is called a perfect 5th, and is the relationship between a C and a G.

That's a great start, but to make a song you'll need more notes than that. Conveniently, if you split an octave starting with C into twelve even intervals, you'll end up with a good number of notes, and two of those notes will almost exactly correspond to that F and G. Great: we have a full set of notes, those notes allow us to play the pleasing 4th and 5th, and the regular relationship lets us transpose music in a simple, flexible, powerful manner to any key.

Well, not quite. Notice how I said that splitting the octave into twelve intervals ends up giving us notes that *almost* correspond to F and G? They're close, but they're not perfect. Ultimately, we have to make a choice: do we want to maintain the ability to play exact harmony with perfect 4ths and 5ths, or do we want a scale that is flexible, not fixed to a single scale, and works pretty well? That decision -- how to adjust the scale to handle those cases -- is temperament. Musicians and composers throughout history have made different choices, and there are good arguments for either way. In recent times, though, virtually everything only uses equal temperament (equal intervals between notes), to the point where trained musicians, people who have played for years and decades, don't realize that there is another choice.

Some aspects of this are simply fascinating. This book does a decent job of covering them. Unfortunately, it spend the vast majority of its space describing the history of how different musicians and composers have chosen different temperaments, and not all that much space covering the music theory that's necessary for really understanding temperament. I absolutely enjoyed the first few chapters, where Duffin describes the basic problem and gets into a little theory. However, he doesn't really go deep enough. The history of scales and temperaments is somewhat interesting, but it becomes overwhelming: one composer felt one method was better, a different composer preferred another type, and so on.

In the end, the beginning chapters were great, but they only began to whet my appetite; the majority of the book was not nearly as interesting. Someone that is more interested in the history for history's sake would definitely appreciate this book more much than I did.

[Mangoo · Rating 4 out of 5]

Duffin's thesis is pretty straightforward: 1) equal temperament is not the best temperament in all occasions, as compared to its many alternatives, and 2) it was known long ago (long before its almost universal adoption as a standard) and still dismissed by most musicians for a long time because of its impure tunings.
The issue of musical temperament is old and unsolved. ET came as a practical and reproducible solution to the issue, and by 1917 it was assumed essentially as a standard. To the point that the physics of acoustics is only taught in advanced musical courses, the difference between major and minor semitones has no real value, and above all hardly anyone has ever listened to music played in a different temperament, so it has simply become a second nature to us. It is just like we have eaten pizza since we are born but never knew about its original neapolitan taste.
Many might say, ok the difference between just intonation and ET is so small that the latter's convenience for keyboards and fixed tuning instruments is more than legitimate. Duffin claims that today we are beyond this simplistic matter, and it's time to use temperaments as close to nature as possible wherever possible.
Duffin reconstructs the history of the matter, the many proposal of solutions, the opinions of many distinguished musicians about temperament, the philosophical underpinning of the acceptance of ET (interestingly connected to the rise of positivism, if not communism) and particularly the late disposal of precise measurement tools that finally allowed the temperament to be precise.
A rather academic book perhaps, but definitely interesting and provocative for what matters, thin and well documented. Pythagoras is still concerned about the issue. Duffin's proposal of using notes as close as possible to natural acoustics makes sense, given the constrainst on horizontal and vertical musical dimensions.

[John · Rating 4 out of 5]

I was very happy to read this book as I've never liked equal temperament (except for music post-Debussy that is non-tonal). It's great to discover that J.S. Bach's famous Well-Tempered Clavier was written for a "well-tempered" and not an "equal-tempered" keyboard. The possibility of discovering different character for the different musical keys is tantalizing, rather than being stuck with same-old boring grey equal temperament. I would have liked a little more discussion beyond Western music. At the end of the book he begins a discussion of monodic music, and, in a footnote reveals that a 40-year old scientific study showed that listeners – both musically-trained and not – preferred the "expressive intonation" of raised major thirds and leading tones. Since Persian music, for example, has a quite sharp major third, the whole topic of whether there is an acoustical reason for the separate western harmonic traditions and the monodic traditions of the Silk Road would be fascinating to explore – in another book of course.

I recommend this book for any musician and enthusiast that would like to understand more about the hegemony of the way music sounds today and consider why great tunes are increasingly a rare breed these days.

[David Dines]

If the full text can be characterized by the first half, it's a fairly breakneck tour through the modern history of the adoption of equal temperament tuning. Coming into it I was aware that there were different tunings outside of ET, but I had no real idea what benefits over it they provided. Duffin, I think, does a good job of picking out clear, or at least less than murky, quotes from historical texts to illustrate his point, but I find the most value from the illustrative musical examples he discusses as they provide the best evidence for the practical reasons for using any tuning over another. It's clear that there will be no tuning in Western music, with its great emphasis placed on the modulation between keys within a piece of music, that will allow for "pure" intonation, but I am coming away from this book hoping to find recorded examples (or performances near me) that show how non-ET tunings can be used for expressive and creative ends in a piece (assuming my mushy ears could even tell the difference).

[Terry · Rating 4 out of 5]

The opening paragraph of this book comments on how equal temperament is viewed as a "solution" and that the theory was explained and the world moved on happily. That happens to be a reference to the book on temperament I had just finished beforehand so I found this particularly funny. In contrast to "Temperament", this book focuses on the fight over temperament. NOtable players, music historians, musicologists, and composers who put particular thought into tuning and how that changed how music was heard. The author quotes heavily from sources and has extensive biographical sidebars. I found these distracting and sometimes hard to follow as the book is small and these asides often spil over pages.

The book does a good job of showing that the issue of temperament being "settled" is a side effect of the dominance of the piano and the fact that most people are never taught anything besides equal temperament.

[Nina · Rating 3 out of 5]

I was hoping more for a historical view on temperaments and why they changed and why equal temperament became the standard. While Duffin does address those issues, this is really more of an argument against modern musicians automatically using equal temperament. Since (I admit) I do not have a lot of music theory, some of what he said went over my head...I wanted to hear the differences in tuning he was discussing. However, he did raise a number of issues that I know will resonate in the future (pardon the pun). I am still digesting some of the points he raised

[Ameliedanjou · Rating 4 out of 5]

I am re-reading this little gem - he really succinctly explains the math in an easy to understand manner. Now what it needs is a companion CD with snippets of music played in the different temperaments so that we can truly grok it.

[James Klagge · Rating 2 out of 5]

To a non-expert like me, it just didn't seem very significant. The book's website gives examples you can listen to. But I can't really hear much difference.

[Acer Pseudoplantatus · Rating 1 out of 5]

While the author is clearly passionate (and opinionated), sadly his writing is badly structured and despite having promised to keep it short, he spends about half of the book providing irrelevant information, repeating himself verbosely ad nauseam (sometimes in very short intervals; making a statement, providing a quote to back it up and then repeating the whole thing just to 'explain' it) or filling space with badly drawn and unfunny comics.
Unfortunately to top this off, the author argues fallaciously most of the time, using strawmen, exaggerations, appeals to authority, appeals to emotion, mistaken issues, speculation and conjecture as well. In one of his appeals to authority he even admits that no recording of the quoted remark exists.

The author makes grand assertions without any quotation, reference or evidence and in fact only provides quotes that agree with his statements; Even in the section where he states that he could "hardly argue that ET was not being used or advocated by the second quarter of the nineteenth century", he only provides quotations where the supposed champions and proponents of ET admit that enharmonic notes are in fact different and thus ET is a distortion of musical reality.
Not just that, fails to mention that ET had plenty of proponents, including Rameau, Neidhardt and Marpurg or the fact that the nature of the Lute and Viol (or guitar, mandolin,...) requires semi-equal to equal temperament and ET has been used for lutes at least since Vincenzo Galilei. This is more than a little oversight, given the importance of both Lute and Viol as not only solo but also ensemble and accompaniment instruments.
I shall not hazard a guess weather this is due to ignorance or done to deceive.

His arguments against ET boil down to the following
1) it is "unnatural" (appeal to nature)
2) it was not widely used in earlier periods (appeal to tradition, appeal to authority, semi-false)
3) it sounds bad

Most of the book is spend dwelling on the second reason and providing several interesting historic examples and an interesting history of ET and the challenges in tuning.
The third reason, however, the author argues against himself; while banging on about how terrible ET major thirds are, he himself admits that nobody notices.
The assertion is made that this is due to conditioning and an experiment with a signal generator and sinus waves is used (which can actually be dismissed, as those signals are vastly different from the complex musical sounds and as the attack, amplitude and decay influence the perception of pitch as well).

Sadly the author additionally fails to mention that 'just intonation' is and has always been fiction: Even if singers had incredible control and perception, just intonation would require the pitches of a note to shift and 'perfect' harmony could (and often would) require out of tune melodic intervals.
For instrumentalists this would be possible only for fretless string istruments with fretboards and even for them it would severely limit the use of open strings.
I have to assume he is unaware of this lack practicality, as he boasts in the book of having written polemic about the adoption of 'just intonation' for Renaissance vocal music.

Add to that ridiculous remarks politicising ET, linking it to the Russian revolution and remarking how "Democracy and capitalism are also reflected in the use of ET in wind instrument design." and attempts to explain the general ignorance towards temperaments through the supposed prevalence of certain philosophical schools of thought.
Not to mention historical inaccuracies such as asserting musical instruments were forbidden by the Church in the medieval period, assertions of the wolf-fifth in Pythagorean tuning being discovered or dealt with only because of the rise of keyboards and so on or ridiculous assertions such that ET does not favour "harmonic performance, much less harmonic thinking".

Sadly what could have been an intriguing exploration of historical attitudes to temperament and myth-buster concerning the spread and adoption of ET has been severely marred by one-sidedness, moralising and bad argumentation.
And while I considered the title bait (which becomes quite obvious when one considers that ET enables incredible modulations and complex harmony), as a musician interested in historical performance practice who loves experimenting with different tunings, I wanted this book to be good. To be that, it would have needed to be much better, though.

[Samathy Barratt · Rating 5 out of 5]

This is a perfect introduction to non-ET western musical systems. It does not require much knowledge of ET music theory to enjoy.

How Equal Temperament Ruined Harmony ruined my confidence that I understand musical theory at all.

By that I mean, it opened my eyes and expanded my horizons past the common understanding of how music works that we're taught in the west.

The book goes into depth about how the western Equal Temperament system works, and what problem it exists to solve.
Followed by discussing many of the temperament systems ( mostly western ) that came before ET, which composers may have used them, which musicians might have used them and the benefits and disadvantages of each.

Completely surprising to me is the excellent presentation of the argument for using non-ET temperaments in the current day, especially for historical music ( music we call 'Classical', from Renaissance to Modern ) but also for new music.
ET is not the perfect solution to making harmonious music, as we are lead to believe nowadays. Other systems exist and can, apparently, be beautiful in their own way.

I particularly enjoyed the frequent humorous comics to illustrate a point, as well as the regular sections covering a brief life-and-times of a specific composer being discussed.

This book is very approachable to those interested in music theory, historical music and probably mathematics.
Its not very long, a short read.

[Ceena · Rating 3 out of 5]

I'm a bit hesitant of how to rate the book. The book is a good read all in all and the historical background is quite interestin. But I feel there's just too much redundancy at the first half of the book. The style of writing is a bit awkward in my opinion. The biographies could have easily been put at the end of the book to make the body smaller and to the point. The author provides a long background on the tuning systems in an effort to convince the reader that equal temperament is not the absolute go to tuning system. As a violin player the idea of temperament scale and uts compromiseis is nothing new and indeed a good player knows how to adjust the intonation depending on the situation; whether to use the high leading Pythagorean intonation or the just intonation for chords to get the most out if the harmony.
I think the most interesting part of the book start at chapter 8 which is more relevant. But what in my opinion the author fails to answer is precisely the title of the book. He never argues how it is that the equal temperament doesn't sound as good as others. After all, the time has proven well that it has worked quite well.

[Amelia · Rating 2 out of 5]

I've read better music-adjacent books in my life. I think there is a real need for what Duffin sought to accomplish with this book, especially in classical music. However, I struggled to get past the crass and borderline distracting writing. It would not have been so bothersome if the conclusion of all the temperament discussions had not been something slightly more detailed than "it depends what you are playing."

This topic is fascinating and very important for what I do. However, I don't feel the content of this book warrants an argumentative perspective. It may have been better received by myself and others if it had been more about the different tuning systems and less about why equal temperament is just so terrible.

[Dobiasz · Rating 3 out of 5]

Nie tak odkrywcza ani kompleksowa, jak zapowiadały recenzje i wstęp. Zupełnie zbędne noty biograficzne rozmywają zasadniczy tekst, i tak obfitujący w powtórzenia, de facto czyniąc go jeszcze krótszym niż sugeruje skromna objętość książeczki. Główna teza również nie jest ani tak odkrywcza ani radykalna, jak zdaje się sugerować Duffin. Ze szczegółów: tu i ówdzie zdarzają się (jemu albo tłumaczowi) mało profesjonalne wpadki typu "trytony i kwinty zmniejszone" albo ewidentne językowe trudności ze zwięzłym i precyzowanym tłumaczeniem szczegółów technicznych.

W telegraficznym skrócie — warto, ale szału nie ma.

[Tony Bittner-Collins · Rating 5 out of 5]

An amazingly useful book! I loved the various explanations regarding enharmonic notes especially the difference between minor semitones vs major semitones. For example, G-G# is minor because it's chromatic while G-Ab is major because it's diatonic. G# is one comma lower than Ab. Late 19th century composers deemed Equal Temperament as 'the only correct one' dismissing Just Intonation, Meantone, etc. which are actually better temperaments to perform early music repertoire on period instruments as discussed in many music treatises from pre-classical/romantic composers such as Pier Francesco Tosi, J.J. Quantz, L. Mozart, et al.

[Tom Blurbgess · Rating 4 out of 5]

The first I read on equal temperament, and indeed a solid entry-level book I'd recommend. Its brevity and flow make it surprisingly engaging, or more so than most books on the topic, but becomes immediate what is lacking when you dive into the rabbit hole. While generally positive to have a personal touch, Duffin can occasionally be overbearing in his opinions.

[Dan Vine · Rating 5 out of 5]

It took a little while to get the hang of the author's somewhat quirky style but it is a good read and I found his argument compelling. I think I will need to read it again when I have a bit more theory under my belt.

[Aaron · Rating 2 out of 5]

This is mildly interesting, but it’s really not aimed at a general audience, and it requires at least a basic knowledge of music. It doesn’t answer the question of why *I* as a non-musician should care. The cartoons and biographical notes are distracting and unhelpful.

[Bruno · Rating 5 out of 5]

An homage to the tuning diversity of the old western world. This book is for nerds like me that have a deep interest in the history of tuning systems but also for musicians who seek to learn more about the old compositions they play and the musical world of the composers who wrote them.

[FS · Rating 3 out of 5]

An interesting read for those who are already well-versed in classical music, but requires much background knowledge for those who aren't. The topic is very niche, so ease of understanding depends significantly on how much you already know about the topic.

[Andrew Litfin · Rating 5 out of 5]

Essential reading for all musicians interested in tuning.