Recently, I got this inquiry from an interested reader:
I read your interesting articles on key colour. Since you seem
to know a lot about equal temperament and tuning, I was
wondering if you could take a look at my site: http://www.skytopia.com/project/scale.html
Basically, I'm considering the possiblity that equal
temperament isn't a compromise after all. What would
you say about this?
I looked up his website and read through it, not entirely sure of his premise but I wrote him a detailed answer anyway which I hope you'll find interesting.
"Thank you very much for your interest. I have read your website and I think I understand where you are coming from. In a sense, you might consider the theoretical values of the 12 toned Equally Tempered scale and all of its multiples as being a framework or paradigm from which all artful tuning may be measured. As such, it is not at all a compromise but something we can all depend upon.
All tuning today uses that standard as far as I know (I'm afraid I don't know much about the notation of other scales which contain more than 12 notes). As you well know, I am a piano technician which means I earn my daily bread by tuning pianos. I have to do what pleases my customers or I am out of business. Many people in my profession show little interest in exploring better ways to tune the piano. They just accept what they're taught and often use an electronic tuner and accept the information it provides without questioning it.
Clearly, we can't use either the Pythagorean or Just Intonation scales as a frame of reference. I firmly believe that a person like Helmholtz, who I believe is the first one to produce the figures for all of the theoretical pitches of the equally tempered scale thought he had the idea to end all others. In the early 20th Century, a piano technician named William Braide White wrote a definitive book on the subject of tuning and maintenance of the piano called, Piano Tuning and Allied Arts.
It is quite evident from reading White that he firmly believed in the concept of Equal Temperament (which I usually abbreviate as ET). But take a look at the period from which this line of thinking came. There were other ideas that claimed to be the ultimate answer: Darwin's Evolution Theory, the Communist Doctrine, Utopian Societies, Freud's Psychology. All of these concepts had merit but today we all know that they didn't have a full and complete understanding and therefore, the ideas themselves we reject as unworkable, there is more information needed, the problem is more complex than what was originally believed.
Many people today however, still seem to firmly cling to the idea that a note is a note and that's that. You're either on that exact pitch or you're off, therefore, you're either right or you're wrong. You're either "in tune" or "out of tune". People have a way of wanting to know what is right and do what is right and once they think they have the answer, want to maintain and enforce that policy.
So today, there are strong emotions and entrenched ideas about ET that are nearly unshakable. But believe me, if all music were nothing but these theoretical pitches, the sounds produced in the world would be a crashing bore. Have you ever noticed how tinny and how much of a facsimile music produced from a computer or electronic keyboard which is limited to theoretical frequencies sounds?
It sounds dull and uninteresting because it has none of the true grit which real music has. The piano can never be tuned in a completely satisfying way. While trying satisfy one type of desire, another undesirable consequence is the inevitable result. For this reason, most Piano Technology professionals believe that the smoothest, most equalized scale which takes into account and compromises for the confounding and compounding factor of Inharmonicity is the best compromise.
I challenge that notion. Tuning the 6 string guitar has the same dilemma, only on a much smaller scale. There are many piano technicians and pianists who use what are called the Historical Temperaments but the general consensus is that none of them could ever have that universal acceptability that ET has, therefore, there is reason to reject and even suppress knowledge and use of them.
This has lead to what some believe to be the "Conspiracy of ET". While I don't believe there was ever a conspiracy as such, the effects of what some have believed and imposed on others has lead to the same result as if there truly had been one and that one still exists. The recent book, Temperament by Isacoff goes a very long way in supporting this "conspiracy" by mixing in a few things which are not true and never were with a lot of well documented history.
What I believe is that the piano may be tuned in a variety of pleasing and satisfactory ways but that there should also be a general way which could suit all music which might be played upon it. The many other ways can be decided upon depending on the circumstances but the general way should be otherwise used. This is a lot like the "default" settings one uses when ignorant of any better or custom setting.
My studies have lead me to believe that a nearly but not quite ET creates a better "default" tuning than does strict ET. The same for the guitar. I have some material I have written on guitar tuning which I'll eventually have posted on my website but will send upon request if you are interested. It has the same idea. You can deviate from ET a little, just a little, and come up with a very pleasing sound but going any further will make it sound worse, not better.
So, in no way would I ever expect the exact scale I create when tuning any particular piano to become the standard of the music industry, after all, each piano is different, having different amounts of Inharmonicity, so each one is and should be, "tuned to itself" in order to be most musically compatible with all others.
What may still trouble some people is the idea that if the piano or other instruments are not always tuned to some very exacting and same standard each time, then how could they ever be compatible with others? The answer is that to sound "in tune" or be musically pleasing to the listener, there will always be an envelope of tolerance. This is how such techniques as "vibrato" (where the pitch oscillates within a certain envelope) and "note bending" are purposefully used to create musically pleasing effects. Without these, music would be quite dull, indeed.
In tuning the piano, I try to set up that envelope within which each individual pitch is placed so that in all possible and probable combinations with other pitches, the piano will produce the most pleasing and satisfying artistic results. The numerical analysis of what I do shows that some of the pitches will be the same as they are in ET and others will vary just slightly but each one will have a different value depending upon the properties of the piano itself and other artistic choices made while effecting the tuning.
I hope you found my response interesting and if so, I would be interested in including a link to your website in my own since I value the opinions of others who think along entirely different lines than my own."