Mathematicians and engineers gain insight into a system by examining its behavior at the extremes. Given a mathematical expression, we take limits as a variable approaches zero and infinity. This gives us insight that is helpful in between as well.
If it’s a filter (an electrical circuit), we get insights into the behavior of such a system, even one that may never be subject to extreme conditions, by calculating (or simulating) its impulse response (among other techniques).
We can also gain insights into social or cultural systems by exercising them with questions at the extremes. Here is one that can help in thinking about a cultural issue that I have been pondering for about thirty years, and reading and writing about since 2002.
Consider Bach, Beethoven, Mozart, Mendelssohn, and Rachmaninoff. You may not be a trained musician or a music professor; most people aren’t. You may not even know the music of these composers very well. However, I am willing to bet that you, the reader, hold at least some vague notion to the effect that these people have created the greatest music on Earth. Everyone seems to agree that they cannot be topped. Oddly enough, people who never listen to the music of these composers seem to hold that opinion rather more strongly.
Now consider Badenya, Babatunde, Muñequitos, Monobloco, and Rose. Do you believe that there is any measure by which not just you, but anyone in the world truly believes this group of five is comparable to the previous group of great Germanic and Russian composers?
If I had been nicer, and asked the question using The Beatles, Britney Spears, Michael Jackson, Madonna, and Rush, say, the politically correct instinct for diversity would likely kick in, and most people, at least in my collegiate, liberal, urban environment, would place the two groups on an equal footing. But I want to exercise the system of thought regarding “quality of music” to the extreme. Are you uncomfortable yet? Do you believe that the Afro-Latin B2M2R is really on par with the dead white European B2M2R? Do you want to, but cannot actually make yourself think or feel that way?
I think that is where most people are, or at least would be if they were interested in this question. I must admit this is much more of an old-world concern than a typical American one. Having been brought up in the old world, at the confluence of Asia and Europe, this question still matters to me after 26 years of American living. Perhaps it is my background that has given me this impression: Any Turkish person, even if they never listen to this type of music, will tell you that Bach, Beethoven, and Mozart made the greatest music in the world (closely followed by Queen . . . and who is this Mendel-something?), and that it is certainly of much better quality than what they listen to every day. This is the idea behind the differently attributed quotation, “Wagner’s music is better than it sounds.”
So, what am I doing about all this? As hinted at above, I have been compiling and researching scholarly material on value and judgment in music since 2002, and writing an article, a very early and embryonic version of which can be dug up by those of a worldy (wide web)-sleuth-like persuasion.
The article, in its current form, examines numerous music textbooks and reference books for qualitative and quantitative measures of the value attached to musics from different cultures, following a broad review of the musicology literature on quality, value, and sophistication. It establishes that there seems to be a cross-cultural baseline of expectation that the sophisticated cultivation of certain aspects of music are valued more highly than equally sophisticated cultivation of other aspects of music.
 “Impulse” sounds harmless, but it is a function that attains infinite magnitude in infinitesimal time, and as a direct result, contains all frequencies. (And yes, we can make use of such an abstract concept.)
 Perhaps it isn’t as popular as Beyoncé, The Beatles, Mariah Carey, or Lady Gaga, but we still, somehow, consider it the greatest.
 Badenya: les frères Coulibaly, a group of musicians from Burkina Faso
 Babatunde Olatunji, Nigerian (Yoruba) drummer influential on jazz and rock music of the last four decades
 Los Muñequitos de Matanzas, a famous rumba ensemble from Cuba
 Brazilian supergroup that pioneered a popular fusion of many traditional and popular styles
 Doudou N’Diaye Rose, Senegalese (Wolof) master drummer and ensemble leader