Gene Gajewski

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Taking a break, but not really…

So yes, I’ve really been absorbed working with the score to Gustav Holst’s The Planets in Cubase. It’s quite fascinating, but tonight, I need to go to bed early. I have an incredibly early appointment at the radiologist for my annual lung screening (I’m an ex-smoker). So, no Cubase today. I thought I’d do some light reading – but you know me better than that.

Since I am running into tons of enharmonic respelling issues in the score, I decided to dig into the history of these two-named notes. Turns out there’s good reasons for it in a historical context, just not as much in a modern one.

You know, as a child I played a full-sized piano accordion (that felt like it weighed a ton) from first up through the fifth grade, and the cornet through eighth grade. I never really considered the whys and wherefores of those sharps and flats, just that you needed to know about them in case you ran into an accidental. We just took them for granted that that was the way of the world. Music instructors love to get their students young – you’re just not smart enough yet to notice the contradictions inherent in music. Pay no attention to the man behind the curtain the fact that a written C comes out a Bflat on that cornet…

No pesky questions son, just do as you are told. Fine. But eventually you do get curious, usually much later as an apprentice player and you are comfortably good at playing your instrument. You find out the names are based on Pythagorean tuning intervals which is based on the concept of perfect fifths. This is a 12-tone tuning system based on the ratio of 3:2, between notes with an interval of 7 half tones. But here’s the kicker as Wikipedia puts it, “no stack of 3:2 intervals (perfect fifths) will fit exactly into any stack of 2:1 intervals (octaves).” Uh oh!

These so-called enharmonic notes were not the same tones then, the frequencies are different depending on whether you were ascending or descending these intervals within an octave. A perfect ascending fifth (7 half tones) turns out to be a fourth in the opposite direct (-7 half tones). See the green dots here.

Pythagorean scale (3:2)

Modern music (and the piano) uses equal temperament (the black dots) which dispenses with these anomalies so that these intervals converge in either direction, and thus the sharps and flats all fall on the same frequency. We keep both spellings for these notes despite the fact they are the same now.

So, I guess if you ever perform music from the 15th century, you’re going to need those extra names…heh. 

So, analysis done. Conclusion: we’re stuck with them. Instructor: no questions, shut up and play!


It just occurred to me the interval names (Major, Minor, etc.) only have significance in ascending order (per Pythagorean tuning). Notice the major seventh interval is the same physical distance from the root (octave), as the minor second interval is from the root. But one interval is minor, the other interval is major, but both are the same distance. But have a look at the augmented fourth and diminished fifth. The diminished fifth is the only key named for a yet-to-be encountered (fifth) key. Did I mention that music is full of inconsistencies…?

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