Yesterday I began Ross W. Duffin’s book How Equal Temperament Ruined Harmony (and Why You Should Care). It is one of the several books on my summer reading list, but the first to be read out of the music-related books so far. It seems that just starting this book has begun to get some of the gears turning again, as recommended by Brittany Chase in one of my recent posts.
I wrote down the title of this book a while back after I noticed it on a shelf in the gift shop at Disney Hall. The provocative title caught my eye–I had never thought that equal temperament ruined harmony. I simply assumed that it made it better, since it was commonplace, universal, and easy to transpose. It also facilitates performing with other instruments in tune, especially ones that can’t be tuned during performance (i.e. keyboard instruments). The “joys” of equal temperament remind me of how harsh-sounding some of the period recordings were in my music history class, especially in pieces that were more chromatic than their predecessors.
However, writing my microtonal, multi-movement string quartet piece (tentatively titled Embers) has made me realize how much my harmonic thinking is still inside of the box, so to speak. It has been a lot more difficult for me to imagine how it would sound, given that microtonal ear training has not been a priority. (Perhaps I should find a way to work on that. I surely can’t sing microtones–well, not intentionally.)
I just finished chapter two of the book this morning. One of the shocking assertions that I read about is that major thirds in equal temperament are extremely harsh compared to pure thirds (which are at a ratio of 5:4) because they have been widened significantly. Ironically, major thirds are supposed to be one of the sweeter consonant intervals in our music. Less shocking is the overly narrow temperament of the perfect fifth, which I have realized as a result of being a violinist and violist. Years ago, I had noticed the differences in tuning when using an electronic tuner for all four strings instead of using a tuner solely for the A. When using my ears alone, all of the strings below A would be slightly flat in comparison to my tuner. On the other hand, the E would run a bit sharp. Now I know that pure fifths (at a ratio of 3:2) are wider than equally tempered fifths. Narrowing fifths is necessary for equal temperament because stacking them would sharpen the note at octave–a tragedy for the pianist.
Another surprising point that Duffin made is that due to the physics of equal temperament, string players should flatten the leading tone, not sharpen them, as they tend to do in expressive intonation. The reverse applies for the minor second above the tonic, which string players tend to flatten. All of this is amazing to realize, but totally screwing with my mind!