This post is part of a series of notes and exercises for a summer camp on making musical instruments with Arduino and Pure Data.
There are several ways to map an instrument’s “inputs” to the pitch that it “outputs”:
We’re about to make an instrument that’s a member of the one-to-many family. We’ll activate a single input and it will produce many outputs. Before we get to it, however, we need to be talk a bit about combining multiple notes at a time. For you see, not every combination of notes produces a pleasing sound.
Musicians have cataloged many sequences or scales of notes that can be used to produce pleasing sounds. Scales start at a root note and jump up from the root in a particular pattern. Because the scale is defined in terms relative to the root, it is not an exact sequence of notes. Rather, it a relative sequence, built up from the root chosen by the musician.
One of the most common scales in Western music is the major scale. A C major scale is rooted at C, an F♯ major scale is rooted at F♯, and so on. Let’s see how the major scale progresses using the MIDI number table we saw earlier.
The universal definition of the major scale goes like this:
root in octave i +2 +2 +1 +2 +2 +2 +1
Using this table, answer the following questions:
60 +2 = 62 +2 = 64 +1 = 65 +2 = 67 +2 = 69 +2 = 71 +1 = 72
54 +2 = 56 +2 = 58 +1 = 59 +2 = 61 +2 = 63 +2 = 65 +1 = 66
When we start writing code, you will find it useful to know exactly how far from the root each note is. The third note, for example is +2 +2, or 4 half-steps from the root.What are the distances from the root for each of the notes in the major scale?
0 2 4 5 7 9 11 12
Many other scales exist, but they only differ in their list of offsets. We’ll see others later.
Play any note in the major scale. Play the note two offsets beyond that note. Play the note two more offsets beyond. Play all three of those notes at the same time and you have a triadic chord, or a triad. It will sound pleasant.
Musicians name the triads that you can play using their starting note. If you pick the root, you are playing a I chord (read “one chord”). If you pick the second note, you are playing the ii chord (read “two chord”). Here’s the whole list:
I ii iii IV V vi vii
They are written in Roman numerals, but some are capitalized and some are not. The uppercase chords are called major chords, and the lowercase chords are called minor chords. Let’s figure out the offsets of these chords from the root. The I chord consists of:
So, the I chord is comprised of offsets 0, 4, and 7. Let’s work through the offsets for the rest of the chords:
Our instrument will play triadic chords in the major scale, so keep your list of offsets around. The qualitative differences between the two (or three) types of chords will be audible once it is built.