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Final Post The Last Post in Len’s Current Music Blog (entry for 2/7/2025) We’ve come to the end of this current series. By popular request, Len will soon launch a music blog aimed at beginners, or at musicians with no exposure to music theory who want to learn about why music works the way it does. (The current series of posts was aimed at people who already had some exposure to music notation, theory, and harmony, to correct some myth-conceptions running around out there.) Summaries are often useful things, so here’s a summary of what we covered in this series: 1. In the first six posts, we talked about where traditional music notation came from, including its method of showing pitch and rhythm, and how all of the current features of notation grew out of a concept developed by a monk named Guido. In particular, we talked about how clefs define pitch, and why a clef without a staff is like a kettle without a stove. 2. In the next two posts, we discussed why and how the Italian language...
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     The Wedge for Minor Keys (entry for 1/31/2025) Most printed Circle of 5 th  Charts that you can buy, and most of the printable ones you can find online, have one fatal flaw in common: They assume that the Roman numerals for Minor Keys are the same as for Major Keys. This simply cannot possibly be true. Think about it: if the Roman Numeral is the number of the note value in the scale in that key, then the ‘home note’ for the key you’re in must be a ‘one.’ To be sure, it’s a lower case ‘i’ rather than a capital ‘I,’ because the chord is minor, but it still has to be a ‘one,’ not a ‘six,’ because it’s the home note of the scale. For example, let’s say we’re in the key of d-minor. The circle layout is the same, but the wedge isn’t. If the wedge for the key of one-flat is at eleven o’clock on the wheel, and if the key is d-minor rather than F major, then the ‘home chord’ for the d-minor key is where the ‘vi’ would be if we were in major. But it has to be the numeral ...
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  Substitutions (entry for 1/24/2025) We’ve talked in the last couple of posts about some of the principles that need to be followed in using the Circle of 5ths and the associated Wedge. As we’ve said before, there are actually no ‘rules’ for harmony, but our ears do expect certain guidelines to be followed. One of these guidelines is that ‘leaping out of the wedge’ sounds OK if that is done cloackwise, say, from G major to B major. Our ear expects us then to ‘walk back’ one step at a time, that is, by having each chord that follows the leap have a root a fifth lower than the leap chord, and then each following chord to have a root a fifth lower than that. To use the example we just invented, G to B, we would then expect that the root of each chord be a fifth lower than the one before: in other words, B, then E, then A, then D, and finally back to G. (If you look at your completed circle from the post on that subject, you’ll see that this is indeed ‘walking back,' one ‘notch at a t...
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      Leaving the Wedge (entry for 1/17/2025) Last post we covered the fact that there are six different chords you can use in any major key, without leaving that key. For example, if you are in the key of B-flat major, you can visit the IV chord (E-flat major), the V chord (F major), the ii chord (c minor), the vi chord (g minor), or the iii chord (d minor). You can do all this without leaving the key you are in, and you can visit any of the six in any order without violating any rules. Ordinarily, you will end on the I chord, and just as ordinarily you will usually precede that I chord with either a IV or a V chord (usually the V), but there are exceptions. Some popular folk songs end on the V chord for example. We also mentioned that most simple songs are either two-chord or three-chord, and when the song falls into that category, the two chords in a two-chord song are almost always the V and the I. In most three-chord songs, the three chords are the IV, and V, and the...
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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...
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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 ...
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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...
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