Welcome to Voices! Before you learn how to use the software to write great songs you’ll need to know, at a minimum, some music theory and sight-reading essentials. I believe you’ll also need to understand the principles which have made your favorite Western art music work for three hundred years and which are still the magic ingredients in popular music. These principles are embodied in the theory of tonal harmony which I intend to use the majority of this document to teach.
If you already know music theory then I still urge you to read through the Music Training section which follows because it will help you use the Voices software. As well as defining fundamental terms the next section explains ideas and visualizations which characterize the software’s user-interface.
This tutorial assumes no prior knowledge of the subject. It covers the essentials of music theory and sight-reading before moving onto tonal harmony. You will learn what notes are, how to represent them in written form, and how to make songs by combining notes both simultaneously and over time. This study is about composing music, not playing a musical instrument. Even so, it is my intention to leave you needing only a relatively small degree of additional instruction and effort in order to be able to make music with instruments. If any of the terms I use need clarification then please refer to Appendix A – Definitions.
If you’re learning music for the first time then you need to invest more than just reading time. Music is a whole new alphabet and a whole new arithmetic. Especially for adults, becoming fluent calls for prolonged mental training. That means reading and understanding the material, practicing it with the exercises until it is memorized, and then testing yourself. This can be done either with friends or alone, either using the Voices software, or written, or mentally. And you should practice any time you have a spare moment.
In the spectrum of human-audible sounds there are infinitely many frequencies. But musical instruments are not tuned arbitrarily; they are tuned to a relatively small set of discrete pitches or tones whose frequencies are related by simple ratios. It is these relationships, consistent from one octave to another, which enable tonal music.
There are 88 keys on a standard piano and pianos properly tuned relative to what is known as concert pitch will all produce the same 88 pitches to a high degree of accuracy. Of course, an instrument doesn’t have to be tuned to concert pitch to make music: it is the relative tuning of its tones to one another that matters. But multiple instruments played together do need to be in tune with one another; and concert pitch is the standard reference.
Figure 1. Piano keyboard.
The lower portion of a piano keyboard, beginning with its lowest key on the left, is shown in Figure 1. If at first glance the keyboard looks like so many black and white stripes then you need to look more carefully to see the subtle landmarks which orient the eye. The arrangement of black keys in groups of two and three breaks up the uniformity into a pattern. That leftmost exception is really the third of a group of three.
Of course the piano keyboard offers only a range of possible musical tones. It is merely an accident of history that its compass begins and ends where it does.
Figure 2. White key tones.
Each piano key plays a tone. As you see from Figure 2, seven of the twelve tones in an octave are named A-G and the remainder are unnamed. However, all tones have equal status whether named or not. By the way, it is not the piano but rather the history of tuning which dictates how the named tones are spaced-out: generally two tones apart, occasionally adjacent. The piano merely follows the same pattern followed by other instruments on many of which the pattern is less obvious.
The pattern is repeated a fraction over seven times across the standard keyboard which equates to a fraction over seven octaves. Because of this duplication, tone names need to be distinguished by their octave number. One convenient numbering convention is to say that octave 1 begins on the lowest C tone on the piano keyboard. Therefore the two lowest C tones marked in Figure 2. White key tones. are C1 and C2.
I’ve talked about the piano to give an example of how the twelve tones of the octave are arranged and named on a real instrument. But the form of the octave is common between instruments, so an illustration in an instrument-agnostic form is called for. Furthermore, tones of the same class in different octaves serve the same musical function, so the study of music can largely focus on the octave-in-general. Both these simplifications are achieved in a visualization which I will call the twelve-tone clock.
Figure 3. The twelve-tone clock.
Because the tones in Figure 3 map right onto the hour positions of a clock, you can equate each of the tone positions with an hour position. The position of the C tone can be thought of as either 12 or 0 (midnight in the 24-hour system) as you prefer. You can also think of the angular distance between any two tones as a ‘time’ in five-minute units. Use the clock analogy as a tool to help you picture the twelve-tone clock as a mental image.
There is no particular starting-point on the twelve-tone clock, and nor does it need to be oriented with C at the 0 (or 12) position. But, in the exercises which follow, work with the absolute positions of the tones as shown so that you absorb their relative positions. In time you will be able to visualize the circle rotated to any orientation. Incidentally, scales, which we will see later, do have a starting position; but the twelve-tone clock is not a scale.
The pitch distance between any two adjacent tones (a five-minute interval in the clock analogy) is called a semitone. Named tones are two semitones apart as a rule. B/C and E/F are the exceptions as they’re only a semitone apart. The shaded sectors in Figure 3 help you to imagine that the octave is divided into two groups – a group of three tones together and a group of four tones together – both of which follow the rule. At the borders of the two groups we see the pairs of tones B/C and E/F which are exceptions to the rule.
Visualization exercise 1) Quarters of the twelve-tone clock.
The purpose of this exercise is to commit the twelve-tone clock to memory so that you’re not dependent on the printed version. The named tones occur at positions 0, 2, 4, 5, 7, 9 and 11. In your mind’s eye divide the twelve-tone clock up into four quarters and memorize them. Be aware that in each quarter are two tones which are shared with neighboring quarters. Use these shared tones like printers’ registration marks to keep each quarter in context. What you should be visualizing is illustrated in Figure 4 through Figure 7.
Figure 4. First quarter.
Figure 5. Second quarter.
Figure 6. Third quarter.
Figure 7. Fourth quarter.
It’s now time to talk about notes. The term note is overloaded with meaning. Sometimes the physical divisions on an instrument (piano-key, fretted guitar-string) are referred to as notes. But also, like tone, the specific pitches produced by a tuned musical instrument are known as notes.
Each instrument tone corresponds to several possible notes, distinguished by their different note names and existing for different musical circumstances. So, although a note uniquely identifies a tone on the twelve-tone clock, the converse is not true. For example, C♯ and D♭ are different notes which identify the same tone in common tunings. In cases such as this, the choice of name – the tone’s spelling – depends on harmonic context. The semantic of note is more complex than that of a pitch or a tone. Tones are measured simply by their twelve-tone clock position, whereas a note’s clock position and name are found by adding an alteration to a named tone. So, a note’s name gives directions for how the clock position it occupies is reached.
A note takes the alphabetic part of its name from its named tone. The alteration, which can be zero, indicates the direction and distance in semitones the note’s clock position is relative to the named tone. Moving counterclockwise on the twelve-tone clock takes you lower in pitch – descending – and moving clockwise takes you higher in pitch – ascending. In music, lowering pitch is known as flattening, and raising pitch is known as sharpening. A note’s alteration, if it is not zero, is written as a series of either sharp (♯) or flat (♭) symbols known as accidentals.
A simple example is the note C whose named tone is C and which has no alteration. It is therefore at the same position as tone C at 12 o’clock. The path to the note C♯ also begins at tone C but is sharpened (raised a semitone in pitch, clockwise) once, so it occupies the 1 o’clock position. The note B and the flattened note C♭ both occupy position 11 and they identify the same tone but they are not the same note because they give different names, or spellings to the tone.
When its alteration is zero, you may optionally write a natural (♮) accidental in a note’s name to indicate that the note shares the natural name and position of its tone. For example, the note C can be called C♮ to make it clear you haven’t missed a symbol off a C♭ or a C♯. Another accidental is the double-sharp (x), which makes, for example, Cx a concise form of C♯♯.
It should be clear that the natural name, if any, of the tone identified by a note needn’t bear any relation to the note’s own name. For example, the note Cx occupies position 2, the same position as tone D, but D does not appear in the spelling of this note. What’s important is the name of the tone we begin from and the magnitude and direction of the alteration.
You will by now appreciate that, at least in theory, a number of note names can be given to each of the twelve tone positions. In practice, though, notes with more than one accidental are rare, so the note at position 2 is almost always D♮ and only very rarely Cx. Notes with natural names are no more nor less significant musically than notes with altered names. And, as I’ve said, all tones on the twelve-tone clock have equal status whether named or not.
Beside note, the other fundamental idea in music is interval, which is the distance between two notes. This is not the same idea as the distance between two tones. Tones are measured by their twelve-tone clock position – a scalar value – and the distance between them is measured as a number of semitones – also scalar. But, as we’ve seen, notes are complex, consisting as they do of a named tone and an alteration. And the distance between them is also complex because intervals consist of both a quantity and a quality.
An interval’s quantity is counted from the first note in the sequence and named for the last. So C up to D is called a second because D is the second of the sequence. And G up to B is a third. If you know an interval’s quantity then you know the general interval. If you also know the interval’s quality then you know the specific interval. By way of analogy you could say that knowing a note’s alphabetic name is knowing the general note; and also knowing its alteration is knowing the specific note. Any C to any D is a general second. If we can be specific about the C and the D then we can be specific about the second. For example if the C and the D are natural then we have a major (which means larger, or greater) second. Major seconds are two semitones in size. Any B to any C is also a general second, and if the B and C are natural then we have a minor (which means smaller, or lesser) second. Minor seconds are one semitone in size.
You can think of the interval between two natural notes as the natural interval between them. Of the seven natural seconds on the twelve-tone clock, five are major and two (E-F and B-C) are minor. Therefore the varieties of second which occur naturally are major and minor.
It’s important that all visualization exercises are done mentally, in your mind’s eye. If you find you’re struggling to do this without looking at the printed figures then do more training with Visualization exercise 1.
Visualization exercise 2) General seconds ascending.
Starting on any natural note on the twelve-tone clock, read off natural seconds ascending for at least two full circuits. Use this exercise to train in the ascending alphabetic sequence of seconds; don’t concern yourself with quality yet.
· B C D E F G A B C D E F G A B
· C D E F G A B C D E F G A B C
Visualization exercise 3) General seconds descending.
Starting on any natural note on the twelve-tone clock, read off natural seconds descending for at least two full circuits. Use this exercise to train in the descending alphabetic sequence of seconds; don’t concern yourself with quality yet.
You’ll notice the mnemonic ‘bagfed’ in the descending sequence. Use it if it helps.
· B A G F E D C B A G F E D C B
· D C B A G F E D C B A G F E D
Visualization exercise 4) Natural seconds ascending.
Repeat Visualization exercise 2 but this time be aware of the quality, and therefore the semitone size, of the intervals.
You may find it useful to use the clock analogy and think of a minor second as a five-minute interval, and a major second as a ten-minute interval.
· B, five minutes therefore a minor second up to C, ten minutes therefore a major second up to D, ten minutes therefore a major second up to E, etc.
· C, ten minutes therefore a major second up to D, ten minutes therefore a major second up to E, five minutes therefore a minor second up to F, etc.
Visualization exercise 5) Natural seconds descending.
Repeat Visualization exercise 3 but this time be aware of the quality, and therefore the semitone size, of the intervals.
· B, ten minutes therefore a major second down to A, ten minutes therefore a major second down to G, etc.
· D, ten minutes therefore a major second down to C, five minutes therefore a minor second down to B, etc.
If one, or both, of a pair of notes is not natural but altered then the otherwise natural interval between them is also altered. An example of an altered second is C♮ to D♭ (altered to a minor second from the major second which would naturally occur between C♮ and D♮). Another example is B♮ to C♯ (altered to a major second from the minor second which would naturally occur between B♮ and C♮). Altered or natural, an interval’s semitone size is determined by its quantity and quality.
Visualization exercise 6) Natural and altered seconds.
Starting on any natural note on the twelve-tone clock, ascend to each natural note in turn. For each object note, find the target notes at intervals of: a major second lower, a minor second lower, a minor second higher and a major second higher.
Build on your training in Visualization exercises 4 and 5. You already know the natural seconds which provide half the answers. For the rest, alter the natural seconds by altering the target note. For example, when finding the seconds below C, you already know that B is a minor second; to make a major second you need to flatten B.
· C (maj2 down to B♭, min2 down to B, min2 up to D♭, maj2 up to D), D (maj2 down to C, min2 down to Cc, min2 up to E♭, maj2 up to E), etc.
A third is the interval spanned by two consecutive seconds. Two major seconds make a major third (e.g. C♮ to E♮). Major thirds are four semitones in size. A major second and a minor second in any order make a minor third (e.g. A♮ to C♮). Minor thirds are three semitones in size. Of the seven natural thirds on the twelve-tone clock, three (C-E, F-A and G-B) are major and four are minor. Therefore the varieties of third which occur naturally are major and minor. Thirds can also be altered.
Visualization exercise 7) General thirds ascending.
Starting on any natural note on the twelve-tone clock, read off natural thirds ascending for at least two full circuits. Use this exercise to train in the ascending alphabetic sequence of thirds; don’t concern yourself with quality yet.
This exercise visits each natural note (there is an odd number of them). You’ll notice the mnemonic ‘face’ in this sequence. Use it if it helps.
· B D F A C E G B D F A C E G B
· C E G B D F A C E G B D F A C
Visualization exercise 8) General thirds descending.
Starting on any natural note on the twelve-tone clock, read off natural thirds descending for at least two full circuits. Use this exercise to train in the descending alphabetic sequence of thirds; don’t concern yourself with quality yet.
· B G E C A F D B G E C A F D B
· C A F D B G E C A F D B G E C
Visualization exercise 9) Natural thirds.
Starting on any named note on the twelve-tone clock, ascend to each natural note in turn. For each note visited be aware of the quality, and therefore the semitone size, of the natural thirds below and above it. Do this for at least two full circuits.
You may find it useful to use the clock analogy and think of a minor third as a fifteen-minute interval, and a major third as a twenty-minute interval.
· B (20m/maj3 down to G, 15m/min3 up to D), C (15m/min3 down to A, 20m/maj3 up to E), D (15m/min3 down to B, 15m/min3 up to F), E (20m/maj3 down to C, 15m/min3 up to G), etc.
Visualization exercise 10) Natural and altered thirds on natural notes.
Starting on any named note on the twelve-tone clock, ascend to each natural note in turn. For each object note, find the target notes at intervals of: a major third lower, a minor third lower, a minor third higher and a major third higher.
Build on your training in Visualization exercise 9. You already know the natural thirds which provide half the answers. For the rest, alter the natural thirds by altering the target note. For example, when finding the thirds below C, you already know that A is a minor third; to make a major third you need to flatten A.
· C (maj3 down to A♭, min3 down to A, min3 up to E♭, maj3 up to E), D (maj3 down to B♭, min3 down to B, min3 up to F, maj 3 up to F♯), etc.
Visualization exercise 11) Natural and altered thirds on natural and altered notes.
Starting on any named note on the twelve-tone clock, ascend in semitones. For each clock position, consider whether sharpened, natural, and flattened notes can occupy it. For each object note that applies at each clock position, find the target notes at intervals of: a major third lower, a minor third lower, a minor third higher and a major third higher.
You will find 21 object notes in total. Visit them in this order: B♯, C, C♯, D♭, D, D♯, E♭, E, F♭, E♯, F, F♯ ... B, C♭. Build on your training in Visualization exercise 10. You already know the answers for the natural notes. For the altered notes, 1) consider what the target note would be if the object note were natural. Then, 2) re-apply the object note’s alteration to both notes. For example, to find the minor third above C♯, 1) find the minor third above C which is E♭. Then 2) sharpen both notes to give the answer C♯ up to E. To find the minor third above F♭, 1) find the minor third above F which is A♭. Then 2) flatten both notes to give the answer F♭ up to A♭♭.
· B♯ (maj3 down to G♯, min3 down to Gx, min3 up to D♯, maj3 up to Dx), C (maj3 down to A♭, min3 down to A, min3 up to E♭, maj3 up to E), C♯ (maj3 down to A, min3 down to A♭, min3 up to E, maj3 up to E♯), etc.
I suggest that you don’t proceed with the tutorial until you are fluent in all the preceding exercises. In time you will be able to sense intervals without counting the semitones between notes nor relying on their absolute positions. Rather than merely memorize the fact that, for example, the note a major third below C is A♭; I encourage you to practice until you have some strong sense or visualization of the size of an interval, particularly in proportion to the octave. To test that you have this fluency, try performing the exercises with your visualized twelve-tone clock rotated some random amount.
Copyright (c) Steve White 2005