Len's Music Blog

How to Use the Circle (entry for 1/10/2025) Last post we talked about the Circle of 5ths and how to construct one. This time we’re going to talk about how to use it and why it’s important to the study of harmony. We’ve already mentioned that keys arranged a fifth apart have either one more sharp or one more flat than the key before, depending on which way we go around the circle. (Remembering that adding a sharp is the same as subtracting a flat, and vice versa.) The next thing to notice is that keys which are only one signature element away from each other are more closely related than other pairs of keys. For example: The key of D major (two sharps) is more closely related to G major (one sharp) than it is to E major (four sharps). Another example: The key of D-flat Major (five flats) is more closely related to A-flat Major (four flats) than it is to B-flat major (two flats). Etc. In fact, you can go temporarily to a chord from a key that is only one sharp or one flat away from the k...

Circular Reasoning (entry for 1/3/2025) If you’ve been around music much, particularly if it’s music theory rather than mere performance, I’m sure you have by now run into the idea of the  Circle of 5ths . If you’re a typical musician, you’ve also been bewildered, confused, and perhaps even angered, by the concept. The reason for this is that a lot of theory teachers think that the Circle is the answer to everything, and it simply isn’t. But their promotion of that notion is what sets off the negative reactions. The Circle is important, but not for the reason the typical theory teacher thinks it is. The mistaken idea is that the Circle somehow  drives  harmony. It doesn’t. It’s the other way around.   Harmony drives the circle.  By that I mean that the way harmony works is most easily explained by using concepts from the circle. But the way harmony works would be true, whether there was such a thing as the circle or not. The circle just helps explain and ...

Ranking the Intervals (Still More About Series) (entry for 12/27/2024) You may have already noticed, but whether or not you have, there’s a strange feature about the idea of Partials or the Overtone Series that we’ve talked about for the last two posts: namely, that as you go up the ‘steps’ of the series, each interval involved is smaller than the one before. Go back to the Partials of the note A110 that we already covered extensively. (An illustration of the intervals involved is at the head of this post.) The distance from the first partial (the fundamental) to the second one (the first overtone) is exactly one octave. To be more precise, the next partial up from the fundamental A110 is A220, an octave higher. The next ‘step’ is from A220 to E330, which is a perfect fifth (in ‘pure’ tuning). The next one up is from E330 to A440, which is a perfect fourth. Then from A440 to C-sharp 550 is a major third. And from C-sharp 550 to E660 is a minor third. In other words, each subsequent ste...

The Seventh Partial (entry for 12/20/2024) Two posts ago, we mentioned that the 7 th  partial of the Series of Partials, that is, the 6 th  overtone of any fundamental, was not involved in the tuning system used in Western Music, that is, the music of Europe and the Americas. There are a couple of reasons for this state of affairs, but first I need to clarify something: countries such as Greece, Romania, and Bulgaria are all part of Europe, but it turns out that nowadays their music is heavily influenced by that of Turkey and the other regions of what we call the Middle East. This makes sense, because those areas are ‘right next door.’ So their music is not strictly ‘Western’ in the same way that the music of, say, Germany or France is. The difference is the importance, or lack of it, of the 7 th  partial. Now if you think back to the principle of ‘diminishing importance in tone quality’ of each higher partial, where the 6 th  partial was only 1.5625% of the total so...

More About Series (entry for 12/13/2024) Last post we talked about the Overtone Series: how its third, fourth, and fifth steps create the major triad, which is contained within every note that we ever hear. There are a couple of other important points to get to regarding intervals as defined by the Overtone Series, but before we get there, this would be a good spot to clear up some confusion about the whole ‘Series’ concept. Namely, the difference between the Series of Partials and the Overtone Series. They’re really the same thing, but they’re numbered differently. Remember back to the idea that each tone in the series is half as loud as the tone before? And remember that we said the first tone, the fundamental, accounts for 50% of the total sound? Well, the Series of Partials starts with that fact. Each step in the series is Part of the whole sound, so each step is a Partial. And Partials include every step in the sound, including the Fundamental (the 50% part). So in the illustratio...

Series (entry for 12/6/2024) One important aspect of music we haven’t touched on yet is the notion of the Harmonic Series, or Overtone Series, or Series of Partials. (All of these refer to the same sonic phenomenon, though the definitions used in each are a bit different.) We have needed to cover some other concepts first, like the idea of ‘intervals’ and the meaning of ‘chords’ and ‘triads,’ but we’re now (finally!) ready to get to one of the most fundamental ideas of all. Every musical note you hear contains other notes that you aren’t aware of.  (Well, there’s one exception to that fact, but we’ll get to it later.) It turns out that this fact is the entire basis of what we call ‘harmony,’ so it’s extremely important. High time, then, that we explore it in some depth. Let’s take a very familiar pitch, for example: the note ‘middle C.’ When you hit that note on a piano, you are not hearing just the C sound for that pitch. You are also hearing the C an octave above that, the G...