Al's Music Tidbits - Volume 2
by Al Shank
In the Introductory Edition, I described my musical journey from square one (little talent, no knowledge) to whatever square I now occupy, which is for others to determine. Along the way, one of the most useful concepts I picked up was the idea of the scale. Now, hearing the term “scale” is enough to send some people off in the opposite direction. How many of you were forced to sit at the piano playing do-re-mi-fa-sol-la-ti-do until you couldn’t stand it any more? Well, I wasn’t; maybe that’s why I took to scales eagerly later in life. The one thing I held against my parents was that they didn’t make me take music lessons when I was a kid (my big brother Erik gave them so much hassle about practicing his clarinet that they didn’t want to go through that with me), but, who knows, if I had taken violin lessons maybe I would have been turned off to music for life. The scale, for me, was the key to answering the question, “What notes should I play (sing)?” I was amazed to find out that there are only seven distinct notes in the scale most Bluegrass songs are based on.
The key to that statement above is something called “octave equivalency”, the somewhat strange fact that we hear two notes, one of which vibrates twice as fast as the other, as “the same”, even though we can clearly hear that one is higher than the other. Why is that? Well, according to Wikipedia, “…its biological basis is apparently an octave mapping of neurons in the auditory thalamus of the mammalian brain…” Whatever. The result is that in almost all tonal systems the basic scale patterns fill in the space between two tones an octave apart.
So, how do we fill in that space? Here, too, nature gives us a hint in the natural series of overtones. If you take a string on a guitar, divide it in half and make one half vibrate, you get a note one octave higher than the “fundamental”, the note you get when you make the whole string vibrate. Any further halving of the string length produces another octave note. On a guitar, if you place your finger lightly over the 5th fret of the low E string and pluck that string simultaneously with the high E string open, you will hear the same note (if your guitar is in tune, of course), because the 1st string is two octaves above the 6th string. However, if you divide the string into thirds and make one third vibrate, you get a note that is not an octave, but that still has a certain similar sound. In vibrations, it is halfway between the octave and the double octave of the fundamental. You can produce this on a guitar or other fretted stringed instrument by placing your finger lightly on the string just above the 7th fret and plucking the string lightly. Of course, dividing the string in fourths produces a double octave; any time you halve or double the length you have “octave equivalency”. If you divide the string in fifths and make one fifth vibrate, you get another “new” tone; this can be obtained by the above method at the 4th fret. Of course, this applies to every string, but it is easier to hear these “harmonics” on the fatter strings.
So, we have produced two “new” notes, as well as a few “octave equivalents”. Try playing the harmonic on the 7th fret, then the 4th fret, then the 5th fret; hey, it’s the old “N B C” tune, isn’t it? Now, if you can get three people with guitars, have one of them play the harmonic at the 5th fret, another the harmonic at the 7th fret and the third the harmonic at the 4th fret, all at the same time, making sure the three low E strings are all in tune. (You may have to feel around for the exact spot on the string to produce these harmonics, because, as we shall see, the frets are not in exactly the right places.) What you will hear is one of the most beautiful sounds in nature, the “major triad”, about which much more, in a later edition. The ratios of the vibrations of these two “new tones” to the fundamental one are 3:2 and 5:4. As with octave equivalency, our ears seem to have a natural tendency to hear simple ratios as beautiful and correct sounds. How fortunate for us!
Many attempts have been made to construct scales using these simple ratios, like 3:2, 5:4, 4:3, etc., but they all come upon a problem: a note derived as the third harmonic of a fundamental note will be very close to, but not quite the same as, a note derived as the fifth harmonic of a different fundamental. It’s sort of like having a puzzle where one piece just will not quite fit. Anyone interested in further study of this problem (“just intonation”) can find a good discussion at:
In order to play keyboard instruments and fretted stringed instruments in different keys, that is, using different notes as the “tonal center”, a “compromise” system was derived in which each octave is divided into 12 equal parts; this is called “twelve-tone equal temperament”, and you can read all about it at:
In this scale, which is used for almost all “Western” music, including Bluegrass, none of the chords created using notes from this scale sounds as beautiful as that “major triad” you got from the different harmonics on the guitar. Every “interval”, the “sonic distance” between notes, in this scale is a “little off” from the corresponding natural harmonic interval, but none is as far off as some of the intervals in the various “just intonation” scales. On a piano or a fretted stringed instrument, you can take any note as the “tonal center” and the scale will sound the same.
Hey, but I said “seven notes”, didn’t I? How do we get from twelve down to seven? Tune in next month!
Here’s hoping that this mini-treatise on scales will be helpful, and that many of you will be “working for scale” soon. Any questions or suggestions for subject matter may be sent to: firstname.lastname@example.org.
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