28: Real and Tonal Sequences

 

Sequences are a critical part of helping music move along. It helps to think of them framed by the mathematical constant of an arithmetic sequence, given by the rule that any number in the sequence is some starting number, plus a multiple of another.

For example, you might have a sequence 2n+3—starting with 3, going up by 2 each time: 3, 5, 7, 9, 11, and so on. Sequences start somewhere, move by a fixed amount, and have a certain number of “legs” (what mathematicians would call “terms”).

There are two kinds of sequences: real ones and tonal ones. Real ones don’t happen very often because they get out of hand, harmonically speaking, very quickly; tonal sequences, therefore, are much more common.

Look for example, at this first phrase of this Bourree written by Handel:
A sheet music with notes and a square box AI-generated content may be incorrect.

In bars 6 and 7, we see a 4-legged sequence.

1.       B C# D B

2.       C# D E C#

3.       D E F# D

4.       E F# G E

Notice that the intervals between them, broadly speaking, are the same: go up a second from note 1 to 2, another second from note 2 to 3, and then descend a third from note 3 to 4. Do this for four legs, moving up a second each time.

This is a tonal sequence, since we obey at all times the constraints of D major (really, overall, G major, but D major in this sequence that closes out the first phrase). The first, second, and fourth legs’ descents are by minor thirds, but leg number 3 descends by a major third.

If we had made it a real sequence, it would look like

1.       B C# D B

2.       C# D# E C#

3.       D# E# F# D#

4.       E# Fx G# E#

A sheet music with musical notes AI-generated content may be incorrect.

Technically, my software didn’t even let me spell the sequence correctly (but I wrote it in the numbered list correctly) because I tried to get it to accept—but it would not—that I needed double sharps and the like. Regardless, look how far away we are by point D from where the sequence started at point A, if we’re treating the sequence in real terms: start B C# D B, and then each leg is the previous one, transposed up by a whole step each time

Comments

Post a Comment

Popular posts from this blog

35: Figured Bass

Image
  There’s a system of notating harmonies that’s rather unique to the Baroque era, but which is so frequently used there, and so important to it, that no discussion of theory would ever be complete if we did not cover it. This is the notation of figured bass: “figured,” in the sense of using figures (numbers) to notate the bass. Figured bass was, in a sense, its own notation completely separate from the five lines and four spaces of the staff, which was nearly exclusively the purview of cellists, bassists, harpsichords, and organists.  Figured bass, fair warning, can be intimidating at first. But, just as with anything else we’ve covered so far, the more you practice reading it, the better you’ll get.  In this system, we use numbers to indicate intervals above the bass. We stack them, and this is how we build chords. If you can’t stack them, nowadays, it’s perfectly fine to use slashes and write the numbers horizontally.  Let’s start with the easiest figured bass nota...
Read more

58: Swell pedals and swell shades

There’s one pedal that we haven’t discussed on the organ because it isn’t one of the “note” pedals—in fact, it’s the only one that doesn’t have a pitch. Instead, the missing pedal is the swell pedal. Look at the body of the organ (the assembly of where all the pipes are, as opposed to the “console”, where the organist sits and plays the instrument—these may or may not be physically close to each other), and you’ll probably see what kind of look like plantation shutters. (If you know where my parish is, then this feature of the organ is very clearly visible on ours. Your local organ might not be so obvious.) These shutters, called “swell shutters/shades,” show or hide the pipes of the organ. Organs have instantaneous dynamic control—the amount of pressure you put on a key dictates how much air flows through the pipes, just like a piano allows you to adjust dynamics on the fly by changing the amount of pressure with which the hammer hits the string(s) given the pressure on the key. Thes...
Read more

54: Trills in the Baroque vs. Classical Periods

Image
Baroque music is known for its incredibly technical and ornamented style. The most common and fundamental of those ornaments is our focus today: the trill. Most simply, a trill is a very fast, repeated alternation of two notes. In the vast majority of cases, those notes are adjacent, but that is not a requirement. Given how fast and common they are, regardless of what you play—whether it’s a string, wind, or keyboard instrument, or your voice—they have a reputation for being quite tiring to play. The period matters when considering a trill. Classical and later composers treat trills, in a sense, in the opposite manner than Baroque composers do. Let me show you two examples: First, the Baroque way of thinking. This is a PAC:   and especially in the Baroque era, when the plucked harpsichord dominated over the hammered piano, it was hard to sustain sounds for long since the sound of the plucking decays quickly. The trill was developed in response, out of a need both to ornam...
Read more