Serial alignments

Recently, I have been so busy that I overlooked the blog a bit too much. Even if I had no time to post anything, I didn’t put my ideas on the back burner and now I am ready to share a few of them. Let’s start considering the first three hexachord of the mirrored palindromic series that I showed in this post: <5,8,9,7,6,3>, <2,5,6,4,3,0>, and <1,4,5,3,2,11>. If we consider the pitch class integers (C=0, C#=1 … A#=10, B=11) of a hexachord as units of linear distance (with C=0 defined as 12 units) and align the resulting three distance sequences one after the other in a proportional way, we obtain a multiple alignment like the following.

Note that every unit (the space between two blocks) is meant to describe the temporal extent of some event (e.g., a sound, or a silence). Thus the very last three blocks of such a multiple alignment are actually the starting points of the first three units of a new alignment. Moreover, the number of units between two positions of the alignment depends on the metric choice. For instance, considering a quarter note as unit, the distance between the sixth block of the first sequence of distances (position 160 in the alignment) and the third block of the second sequence of distances (position 76 in the alignment) is a half note and 5 thirty-second notes (2 + 5/8) according to the metric of the first sequence of distances (i.e., 5 units between position 1 a 160). The distance between the same two blocks is approximately 2 + 1/5 according to the metric of the second sequence of distances, and approximately 1 + 2/5 + 1/7 according to the metric of the third sequence of distances.

Of course it is possible to measure the linear distances between all points of the alignment but it is also necessary to introduce some kind of approximation to avoid complex musical notation. We can approximate those distances using the closest option available on a preordered table of note values and derive three different patterns starting from the original multiple alignment.


After converting all the linear distances into note values, we can decide which kind of event (sound, silence, dynamics, etc.) must be bound to the fundamental elements of each pattern. In the following example, I used the third pattern as template and assigned dynamics, articulations and rests respectively to the elements of the distance sequences derived from the third (blue blocks), the second (red blocks), and the first (black blocks) hexachord. By way of information, the serialization of these three parameters were obtained from the diagonals of the matrix of permutations of the generating row.

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The well intentioned amateur enthusiast: Oban 14yo

Then comes the Oban. 14 years old Oban Scotch malt whiskey is made in the Western Highlands, one of the most sparsely populated region in Europe. Oban is not exactly a gem, as the saying is. It is a ‘clean’ malt that misses its mark somehow. It has a flimsy, spiritous smell, by no means spreading throughout the tumbler after pouring. The taste is dry and clean, but fresh, with citrus and licorice tips. It quickly turns to salty and bitter keeping a sharp almost metallic acidity. Its harshness is balanced by the pleasant long finish of mature fruits and pervasive burn-out feeling. It gives a fresh breath too! My overall opinion is quite contrasted. For sure, Oban doesn’t stand comparison with the excellent Lagavulin. Now I can’t wait to taste the remaining four Classic Malts and make comparisons as well.

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The well intentioned amateur enthusiast: Lagavulin 16yo

While digging through my family liquor cabinet last week (hey I’m not an alcoholic!), I noticed two noble looking bottle packages down inside. Oban 14 and Lagavulin 16! Do we have two such top-notch malts and nobody told me?! What an amazing discovery!

As you might know, there are three categories of Scotch: malt, grain and blended whisky. Blended whisky (Johnnie Walker, Ballantine’s, J&B, etc.) is a mixture of 1/3 single malt and 2/3 grain whiskies from several distilleries. The wide success of those international brands is probably due to the common compliance of their conformed tastes. Sadly, the less distinctive, the more successful. Grain whisky is made from a mash of cereal grains (usually malted and unmated barley, wheat and maize). There are not so many different grain distilleries. Indeed bottled grain whisky is still a bit of an odd choice! Finally malt whisky is made from 100% malted barley. Malts are divided in single (no blends) and vetted (blends of malts). Lagavulin and Oban are two out of six so-called ‘Classic Malts’ marketed since 1988 by Diageo. The other four are Dalwhinnie, Cragganmore, Talisker e Glenkinchie.

16 years old Lagavulin is made on Islay, “the Queen of the Hebrides”. Its rubbish color is warm like its taste. When you nose it, you get scent of leather and wood on fire. The taste is way smokey but gentle and sweet, like an old cask cellar in winter or a mild cigar’s aroma. Smooth peaty tones return in the end. Unfortunately the design of the bottle suggests that it was realized after 1999 (the royal seal has been replaced with a sailing ship drawing on the label). I was told that the late 1980’s batches were the best. Anyway, that dram of Lagavulin has been a revelation for me being used to bourbon. Now I am curious to try out Oban. I will report my impressions here later.

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Somewhere beyond the se…ries! [Pt. 3]

The method of serial composition that I showed you earlier is not the most immediate to deal with but it’s turning out to be very versatile and prone to improvements. Here I am going to explain a solution to avoid the rhythmic monotony of just superimposing patterns having the same meter, such as those I used in previous posts. As an illustrative example, consider the following three patterns

A   x . . x
B   x x .
C   . . . x . x

First, I assign a specific combination of them to the voices I want to overlap

B     C           B
x x . . . . x . x x x .

A       A       B     A
x . . x x . . x x x . x . . x

At this point, there are several ways to align the two strings. I could fix the beat and scroll one string upon the other, like this

|x x . |. . . |x . x |x x . |<============
======>|x . . |x x . |. x x |x . x |. . x |

This kind of approach doesn’t rescue from the risk of rhythmic monotony. As an alternative, I could stretch or shrink one string proportionately to the length of the other string




or partially in its length

|x x . . . |.         x         .         x         x         x         .         |
|x . . x x |.      .      x      x      x      .      x      .      .      x      |

Here we go! It now appears that the method gained a broadened applicability. It would be interesting to apply this kind of musical pattern transformations to simulate a mosaic tessellation like the following “Maya-ish” example, where I used just two patterns (. x x and . x x x).

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Drafts limbo

I was cleaning out my room today and came across four binders crammed with hand-written sheet music. 10,5 kg of sketches! I stored up all this stuff almost since the beginning of my first meeting with written music in late primary school. It was a very sad moment for me as I became aware of all the huge amount of music that have been noted down over the years and put to the side though. I must admit that it’s my greatest regret that I dropped my musical vocation down the hole. I was younger and naive. Nowadays music is my main diversion and I still can’t help composing tons of snippets and drafts. I see over time it’s increasingly difficult to find the time for carrying out a complete and exhaustive work indeed. What’s more, I’m a perfectionist. So at the moment I’m forcing myself not to start anything new before finishing the current projects. Maybe there will be a day when I’ll take that heap of memories into my hands again and try to get the best from it.

Everything’s composed—but not written yet.
W. A. Mozart

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Bricks

Here is the method I developed to compose an intricate corrente as part of a wider piano piece. First of all I chose a musical unit consisting of two superimposed pentachords (A and B).
The inversion of the harmonic intervals of this unit and of its inversion provided two further pentachords (C and D).

At this point it’s possible to arrange the four non-standard rows according to the preferred scheme. I followed an outline that I had projected in consideration of the requirement of an overall irregular rhythmic structure.

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Symmetric compulsion

Recently I’ve had a lot to do with a very special tone row. It’s a mirrored palindromic row derived from the trichord {5, 8, 9}. The three notes after the prime trichord are its retrograde, the next three are its inversion, and the last three are its retrograde inversion. The clock-diagram of this row has a clear mirror simmetry.

This row is its own transposed retrograde inversion just like the row from the fifth movement of Schoenberg’s Serenade, Op. 24. Thus the second hexachord is the retrograde inversion of the first one, which summarizes the feature of the entire row (see the green square in the matrix). The matrix is symmetric along the red diagonal in the figure below, being P0 = RI9 and I0 = R3, P9 = RI6 and I3 = R3, and so on.

Moreover, the middle eight notes of the row compose an octatonic scale.

Not so bad for just three notes!

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