There are many ways to start an argument with someone, but one of the easiest is to ask a musician to define music–and often more interestingly, what is not music. For our purposes, we will use the broad definition of “organized sound”. This is a common way to define music in its simplest form, and we can use this definition as a launching point for study without setting one style or genre above others. Throughout this course, we will focus on the concept of how music functions in order to create a common ground for discussion, and to do so, we will spend time working through a variety of ways to communicate our thoughts about musical fucnction separate from our biases toward and against certain styles. If you can differentiate between your personal preferences from the functional aspects of music, you will be able to reach more people as a teacher, performer, or composer.
If we accept that music is “organized sound”, then the methods used to organize sound will define all aspects of its composition. For this course, the majority of music that we’ll study will be tonal music, meaning music that is organized around a central pitch called the tonic.
When we build a tonality around a tonic pitch, every pitch in the tonality can be considered to have a set distance, or interval, between it and the tonic. It is these intervallic relationships that differentiate one pitch collection from another, and we can categorize each pitch collection by studying their commonalities and differences.
As we begin our study of measuring the distances between pitches, we could begin by counting the smallest possible distance between two pitches and then using that as a unit to measure. (And we will do exactly this later in this unit.)
But most people first learn music as part of performing; not as some esoteric counting and numbering system. You already do this instinctively when you listen to music. If you have participated in any amount of musical performance, you can likely tell the difference between a major and minor tonalities–even if you don’t know the names–simply by hearing the piece. People will often reduce these concepts to a relatable emotion such as “happy” versus “sad”, but these tonalities encompass a wide variety of musical styles and responses. You don’t need to know the exact pitches, nor do you need to know the name of the primary pitch of the key. Instead, you intuit the relationships in pitch collection by hearing the relative distance between pitches. We will discuss our system for labeling intervals in the next unit, but to do so, we need a system that demonstrates the distances between pitches in relation to a tonal center, without having to refer to the letter system and a key name.
This clip of Bobby McFerrin working with a crowd of scientists demonstrates our ability to intuit musical scales beautifully. Notice that he never needs words to explain the relationships, but instead builds a relationships to the first pitch in the spontaneous composition.
There are multiple methods that define music in relative terms, but for this textbook, we will use moveable-“do” solfege, a system that evolved from some of the earliest methods of notation. In this system, we assign the tonic of the key (or in simpler terms, the first note of the key), to do, and then we assign each note above that pitch a similar Latin name based on its distance from do. For those of you familiar with the musical The Sound of Music, you probably already know the basic seven solfege. “Do (doe), a deer, a female deer…and so on.
We will discuss this system in detail in the unit on scales, but until then, it will be helpful for you to refer to the following chart when necessary.
| Scale degree | Solfege syllable | Raised | Lowered |
|---|---|---|---|
| ^1 | do | di | N/A |
| ^2 | re | ri | ra |
| ^3 | mi | N/A | me |
| ^4 | fa | fi | N/A |
| ^5 | sol | si | se |
| ^6 | la | li | le |
| ^7 | ti | N/A | te |
Moveable-do solfege allows us to look at the relationships between a group of pitches that are organized around a central pitch. As a byproduct of examining these relative distances, we create a scale. A group of any number of pitches is called a collection, but an ordered pitch collection by the frequency of each pitch–or more simply stated, arrange the pitches from low to high–you is a special subset of a collection called a scale. So a scale is a collection of pitches that are organized in an ascending or descending form, and consequently create a fixed intervallic pattern. A scale can encompass any tuning system or style of composition.
Certain scales are at the core of all common practice harmony, and as a music student, you are likely already familiar with these: major, minor, modal, pentatonic, and chromatic. Below, we discuss the diatonic scales (i.e. major and minor) and Topic 2b details the others. We will explore even more types of scales in Unit 22.
For the majority of this course, we will be discussing diatonic music, which is a subset of tonal music. The term diatonic can have a variety of meanings depending on context, but for this course, we will be using this term to refer to music that:
Put simply, our musical hierarchy is:
As you listen through the examples below, you should:
The following examples demonstrate how the tune of Happy Birthday would be written if only using the notes from a particular scale. In most examples, scale degrees are numbered below each pitch as well as solfege using movable “do”. Additionally, scale degrees are named above the pitches for the examples in major and melodic minor. You goal is to find the scale from which the melody is derived, so you should start by arranging the pitches in an ascending order based on the scale degrees. When determining your pitch collections, pay particular attention to the differences of the sixth and seventh scale degrees.
(Because ABC notation does not support scale degrees, I have placed a ^ in front of each scale degree. In normal scale degree notation, the ^ would appear above the numeral for each scale degree, not before it.)
There are three forms of the minor scale, and each has a specific role. As you listen to these three melodies, only one of them will sound as if it has no surprising pitches. Once you have found the example that doesn’t have a “surprise moment”, consider the name of the mode. Does it give you some insight into why it sounds best playing this melody?
When first determining your basic rules for melodic minor, you may want to choose to ignore ‘le’ in measure 6. That pitch serves a harmonic goal as part of a cadence, rather than a melodic function.
In diatonic music, each scale has seven pitches. All seven letters can be used once, and no letter can be used more than once. This creates a series of intervals that we will label as half steps, whole steps, and augmented steps for now–until we formally define intervals in Topic 2c. Half steps are intervals between two consecutive letters with no pitches between them (e.g. C to D-flat), whereas whole steps have one pitch between them (e.g. C to D has D-flat between them). Augmented steps are intervals between two different letters and have two pitches between them (e.g. C to D-sharp has D-flat and D-natural between them). These are much rarer than whole and half steps and only occur in one commonly-used diatonic scale. Of note, the letter names must be different, or it is not a half-step (e.g. B-flat to B-natural).
Major scales have an intervallic pattern of:
(W = whole-step, H = half-step, A = augmented step)
W - W - H - W - W - W - H
Natural minor scales have an intervallic pattern of:
W - H - W - W - H - W - W
Harmonic minor scales have an intervallic pattern of:
W - H - W - W - H - A - H
Melodic minor scales have both an ascending and descending form. The intervallic pattern for descending melodic minor is identical to a descending natural minor scale. (The necessity of this seemingly redundant pattern is discussed below under “Why we need three minor scales”.) The intervallic pattern for 4ascending melodic minor is:
W - H - W - W - W - W - H
Similar to solfege, there is another commonly-used system in which you can label the pitches in a scale without referencing a specific tonic. Instead of solfege names, you can instead use scale degree numbers. We denote these by placing a caret ^ above the scale degree number. For example, the note that is five letter names above the tonic of a scale would be called fifth scale degree and written as ^5–although the caret would be above the numeral, not to the side.
The scale degree system functions similarly to the solfege system that we discussed in the Unit 1b, with the added benefit of not requiring someone to memorize a bunch of Latin terms. The two systems can be used mostly interchangeably, at least if you are comparing it to moveable-do solfege. Of note however, the solfege system is much more useful in sight-singing because each note designation uses only one syllable, whereas some scale degrees have two syllables and there is no simple way to show alteration to a scale degree without adding further syllables.
You can review the chart below showing all seven scale degrees next to the solfege syllables and the altered solfege for raising and lowering pitches. If a solfege symbol is marked as “N/A”, this alteration is non-functional in tonal harmony. You should be fluent in both of these systems if you plan to have a career in music, because both are widely used in a variety of contexts.
| Scale degree | Solfege syllable | Raised | Lowered |
|---|---|---|---|
| ^1 | do | di | N/A |
| ^2 | re | ri | ra |
| ^3 | mi | N/A | me |
| ^4 | fa | fi | N/A |
| ^5 | sol | si | se |
| ^6 | la | li | le |
| ^7 | ti | N/A | te |
A final method for labeling scale degrees is to use the names of the functions of each pitch as it relates to tonic. These names evolved over centuries of theory treatises from scholars such as Rameau, Riemann, Secther, Schoenberg, and Schenker. We will not use these names often in this course, but knowing them can help understand harmonic function when that concept is introduced.
They are:
Notice the relationship between any term and its counterpart as denoted by the prefix sub. The dominant is the fifth pitch above the tonic; the subdominant is the fifth pitch below the tonic. The mediant is the third above the tonic; the submediant is the third below the tonic.
The supertonic is the second pitch above the tonic, but because of the importance and function of the leading-tone, its scale degree name changes to reflect the difference between a whole step below the tonic versus a half-step below the tonic. This is true in both major and minor.
Most intermediate music students learn multiple forms of the minor scale, but they do not often give much thought as to why these forms exist.
Natural minor is the most intuitive. It uses all of the naturally occurring notes from the key signature.
We will discuss the role of harmonic minor more when we begin analyzing chords, but as the name implies, it is a form of minor that emphasizes the most common scale degrees from a harmonic standpoint.
The “Happy Birthday” examples above are perfect for exploring the importance of melodic minor. By keeping the interval sizes from “Happy Birthday” but changing the pitches to fit the various forms of minor, you can hear three similar but distinct versions of “Happy Birthday”. When a student first listens to the natural minor version, they often feel that the first te does not work with the rest of the tune, and in the harmonic minor version, the augmented 2nd that occurs between ti and le is jarring. On the other hand, the melodic minor version sounds entirely correct, although some may not like the darker tone of a traditionally “happy” song!
This clarifies the role of melodic minor–to create melodies in minor. By having both an ascending and descending version, we can resolve the sixth and seventh scale degrees upward and downward by relying on the tendency of those scale degrees. Te and le both have a strong downward pull and almost always resolve downward. Ti and la both have a strong upward pull and tend to resolve upward. These are general rules and are occasionally broken, but I encourage you to play with the example below to hear how “strange” the piece becomes if you do not allow the sixth and seventh scale degrees to account for their resolutions. (Try putting la in for every sixth scale degree for the most jarring version.)