What defines “good” design in the composition of music and the tuning of musical instruments?

[advanced IDCS topics for students of music and philosophy of art]

“Bad design” is one of the most formidable arguments against intelligent design. I’ve responded to the “bad design” arguement by saying that what constitutes “good design” depends on the goals of the designer.

If fuel efficiency is the criteria of good design, then a motorcycle is a better design than an SUV. But some will argue the SUV is a better design for snowy and icy conditions when transporting babies, thus an SUV is a better design. The problem is what constitutes “good design”, and who decides the criteria for good?

We also have the paradoxical situation where good drama needs a bit of “bad” designed into it. If a great novel told a story with no problems, will it be a good drama?

“Once upon a time there were no problems…there were never any problems or difficulties….they lived happily ever after”.

And for those familiar with music theory, one can appreciate the importance of incorporating “bad notes” in making beautiful designs.

Here is a table of musical intervals. The list contains intervals that are called “perfect”. The label of perfect implies the other intervals are considered less than perfect, even the extreme opposite of perfect, such as the tritone interval “musica diabolica (the devils’ music)“.

The “musica diabolica” interval is featured in the first two notes of the melody known as “Maria” by Leonard Bernstein. When the word “Ma-ri-a” is sung to Bernstein’s music, the “musica diabolica” interval can be heard in the “Ma-ri” part. But then Berstein transforms the two harsh sounding notes of “Ma-ri” into a 3 beautiful notes of “Ma-ri-a”. We have two imperfect dissonant intervals (“Musica diabloica” combined with a minor-2nd) to make something beautiful. The whole is greater than the sum of the parts in the final effect. Bernstein figured out how to incorporate two imperfect parts into a heavenly design that would not have been otherwise possible using only perfect parts.

By way of contrast, if musical culture enforced the convention of Gregorian chants using harmonies with only “perfect” intervals, we’d be stuck singing Gregorian chants rather than richly harmonized Christmas carols at Christmas. The resulting music would be sterile and lacking variety and contrast, much like a novel with no drama (where all the characters are perfect and the plot free of drama from start to finish).

Thus a little “bad design” may allow us to experience a greater good that would otherwise not be possible, it just takes a greater level of intelligent design to make that possible.

Here is a nerdy treatment of the topic of “good” design in relation to tuning of musical instruments and personal tastes. It may be insufferably boring to most readers here, so I leave it as a post script.

Greeks found the notion of irrational numbers shocking, and this is reflected by the cultural myth that Hippasus drowned for divulging the secret of irrational numbers, a secret which came from the gods.

The Greeks loved whole numbers. In quantum mechanics and harmonics we see whole numbers to describe certain things. For example, we have quantum numbers that are whole numbers or integers. So what the Greeks perceived in their philosophy is echoed even a the atomic level.

The notion of sounds with small whole number ratios in pitch was very satisfying to the Greeks. Hence, a lot of the way instruments were tuned in the past relied heavily on small whole number ratios (like 2-to-1 and 3-to-2) .

The Ancient Greeks probably would have had a fit if they lived to see how musical tuning evolved in western culture toward “equal temperament”. Equal temperament is based on the 12th root of 2 which is an irrational number. So which design is bad or good for tuning of musical instruments? It seems the question of “good” or “bad” is somewhat in the ear of the beholder.

I like the “irrational” tuning of equal temperament better. It is where western music has evolved. What defines perfection in tuning in my book? A little irrationality…

Unfortunately, videos available on the topic aren’t so good. I link to the best URLs I could find. In the video below, the piano on the left was tuned in meantone temperament. It sounded awful to my ears except when pieces were played in C major.

The piano in the middle I presume was tuned in well temperament (“new” temperament). It wasn’t so bad. No wonder Bach liked it. It approaches equal temperament, but isn’t exactly equal temperament.

The piano on the right is tuned in the “irrational” equal temperament. It was the one I liked, but he only played a few notes on it. Irrational equal temperament is how most western music is tuned.

Equal temperament allows melodies to express themselves in different keys effortlessly, whereas in mean tone temperament (closer to the Greek conception of good) the same melodies in another key would sound out of tune. Equal temperament also made it easier for a diverse number of instruments to participate in music production such as in symphony orchestras.

Even though the presenter in the video obviously loved the more “rational” Greek-like modes of tuning, it just didn’t sound right except for pieces played in certain keys. The Bach C# prelude sounded way out of tune on the piano on the left (mean tone temperament), so did the Chopin sonata. He liked it, I didn’t. Ugh!

The reason he liked these old tuning schemes is that music played in the old tuning schemes were possibly those used by the composers. Thus performances using such tunings are more authentic and thus (in his view) more beautiful — but that is subject to debate. Only goes to show, some notions of good and bad design are in the ear of the beholder.

The tuner gives another lecture. The video was a bit confusing, but I’m sure it was clearer for those in the audience who saw the talk in context and with their handouts. He tries to clarify the fact that “equal temperament” in the 18th century isn’t what it means in the 20th century.

As a total aside, I was surprised at the interest physicists had in the question of tuning.

I have heard it said that an A cappella choir will tend to sing in non-equal temperament modes because they have no (irrationally-tuned) musical instruments to reference their tuning with. This makes sense in that it is easier from a physics standpoint to sense frequencies with certain simple whole number relationships rather than the irrational relationships in equal temperament.

From wiki Perfect Fifth

The justly intoned pitch ratio of a perfect fifth is 3:2 (also known, in early music theory, as a hemiola[9][10]), meaning that the upper note makes three vibrations in the same amount of time that the lower note makes two. In the cent system of pitch measurement, the 3:2 ratio corresponds to approximately 702 cents, or 2% of a semitone wider than seven semitones. The just perfect fifth can be heard when a violin is tuned: if adjacent strings are adjusted to the exact ratio of 3:2, the result is a smooth and consonant sound, and the violin sounds in tune. Just perfect fifths are employed in just intonation. The 3:2 just perfect fifth arises in the C major scale between C and G.[11]

Kepler explored musical tuning in terms of integer ratios, and defined a “lower imperfect fifth” as a 40:27 pitch ratio, and a “greater imperfect fifth” as a 243:160 pitch ratio.[12] His lower perfect fifth ratio of 1.4815 (680 cents) is much more “imperfect” than the equal temperament tuning (700 cents) of 1.498 (relative to the ideal 1.50). Helmholtz uses the ratio 301:200 (708 cents) as an example of an imperfect fifth; he contrasts the ratio of a fifth in equal temperament (700 cents) with a “perfect fifth” (3:2), and discusses the audibility of the beats that result from such an “imperfect” tuning.

In keyboard instruments such as the piano, a slightly different version of the perfect fifth is normally used: in accordance with the principle of equal temperament, the perfect fifth is slightly narrowed to exactly 700 cents (seven semitones). (The narrowing is necessary to enable the instrument to play in all keys.) Many people can hear the slight deviation from the idealized perfect fifth when they play the interval on a piano.

einstein violin