POSTLUDE: An Introduction to Music Theory (Fundamentals)
Chelsey Hamm
Key Takeaways
- Pitch in Western musical notation is designated by the letters A, B, C, D, E, F, and G, which repeat in a loop.
- Different clefs make reading different ranges easier.
- Each clef indicates how the lines and spaces of the staff correspond to pitch.
In Western musical notation, pitches are designated by the first seven letters of the Latin alphabet: A, B, C, D, E, F, and G. After G these letter names repeat in a loop: A, B, C, D, E, F, G, A, B, C, D, E, F, G, A, B, C, etc. This loop of letter names exists because musicians and music theorists today accept what is called octave equivalence, or the assumption that pitches separated by an octave should have the same letter name. More information about this concept can be found in the next chapter, The Keyboard and the Grand Staff.
This assumption varies withmilieu. For example, some ancient Greek music theorists did not accept octave equivalence. These theorists used more than seven letters of the Greek alphabet to name pitches.
TheNotation of Notes, Clefs, and Ledger Lineschapter introduced four clefs: treble, bass, alto, and tenor. A clef indicates which pitches are assigned to the lines and spaces on a staff. In the next chapter,The Keyboard and the Grand Staff, we will see that having multiple clefs makes reading different ranges easier. The treble clef is typically used for higher voices and instruments, such as a flute, violin, trumpet, or soprano voice. The bass clef is usually utilized for lower voices and instruments, such as a bassoon, cello, trombone, or bass voice. The alto clef is primarily used for the viola, a mid-ranged instrument, while the tenor clef is sometimes employed in cello, bassoon, and trombone music (although the principal clef used for these instruments is the bass clef).
Each clef indicates how the lines and spaces of the staff correspond to pitch. Memorizing the patterns for each clef will help you read music written for different voices and instruments.
The treble clef is one of the most commonly used clefs today. Example 1 shows the letter names used for the lines of a staff when a treble clef is employed. One mnemonic device that may help you remember this order of letter names is “Every Good Bird Does Fly” (E, G, B, D, F). As seen in Example 1, the treble clef wraps around the G line (the second line from the bottom). For this reason, it is sometimes called the “G clef.”
Example 2 shows the letter names used for the spaces of a staff with a treble clef. Remembering that these letter names spell the word “face” may make identifying these spaces easier.
The other most commonly used clef today is the bass clef. Example 3 shows the letter names used for the lines of a staff when a bass clef is employed. A mnemonic device for this order of letter names is “Good Bikes Don’t Fall Apart” (G, B, D, F, A). The bass clef is sometimes called the “F clef”; as seen in Example 3, the dot of the bass clef begins on the F line (the second line from the top).
Example 4 shows the letter names used for the spaces of a staff with a bass clef. The mnemonic device “All Cows Eat Grass” (A, C, E, G) may make identifying these spaces easier.
Example 5 shows the letter names used for the lines of the staff with the alto clef, which is less commonly used today. The mnemonic device “Fat Alley Cats Eat Garbage” (F, A, C, E, G) may help you remember this order of letter names. As seen in Example 5, the center of the alto clef is indented around the C line (the middle line). For this reason it is sometimes called a “C clef.”
Example 6 shows the letter names used for the spaces of a staff with an alto clef, which can be remembered with the mnemonic device “Grand Boats Drift Flamboyantly” (G, B, D, F).
The tenor clef, another less commonly used clef, is also sometimes called a “C clef,” but the center of the clef is indented around the second line from the top. Example 7 shows the letter names used for the lines of a staff when a tenor clef is employed, which can be remembered with the mnemonic device “Dodges, Fords, and Chevrolets Everywhere” (D, F, A, C, E):
Example 8 shows the letter names used for the spaces of a staff with a tenor clef. The mnemonic device “Elvis’s Guitar Broke Down” (E, G, B, D) may make identifying these spaces easier.
When notes are too high or low to be written on a staff, small lines are drawn to extend the staff. You may recall from the previous chapter that these extra lines are called ledger lines. Ledger lines can be used to extend a staff with any clef. Example 9 shows ledger lines above a staff with a treble clef:
Notice that each space and line above the staff gets a letter name with ledger lines, as if the staff were simply continuing upwards. The same is true for ledger lines below a staff, as shown inExample 10:
Notice that each space and line below the staff gets a letter name with ledger lines, as if the staff were simply continuing downwards.
- The Staff, Clefs, and Ledger Lines (musictheory.net)
- Flashcards for Treble, Bass, Alto, and Tenor Clefs (Richman Music School)
- Printable Treble Clef Flash Cards (Samuel Stokes Music) (pages 3 to 5)
- Printable Bass Clef Flash Cards (Samuel Stokes Music) (pages 1 to 3)
- Printable Alto Clef Flash Cards (Samuel Stokes Music)
- Printable Tenor Clef Flash Cards (Samuel Stokes Music)
- Paced Game: Treble Clef (Tone Savvy)
- Paced Game: Bass Clef (Tone Savvy)
- Paced Game: Alto Clef (Tone Savvy)
- Paced Game: Tenor Clef (Tone Savvy)
Easy
Medium
- Worksheets in Treble Clef (.pdf)
- Treble Clef with Ledger Lines (.pdf)
- Worksheets in Bass Clef (.pdf, .pdf)
- Bass Clef with Ledger Lines (.pdf)
- Worksheets in Alto Clef (.pdf, .pdf)
- Worksheets in Tenor Clef (.pdf)
Advanced
- All Clefs (.pdf)
- Writing and Identifying Notes Assignment #1 (.pdf, .mscx)
- Writing and Identifying Notes Assignment #2 (.pdf, .mscx)
definition
Key Points
In this chapter we learn about the minor mode, how it evolved in tonal music and how we might best use it.
We will cover the following:
- Seventh Chords in the Major Mode
- Preparation and Resolution of the Dissonance and the Chord Progression Schema for Seventh Chords
- Inversions of the Seventh Chord
- Connecting Seventh Chords to One Another
Until now, our study of tonal music has focused on materials and techniques using only one of the seven diatonic modes: the major mode. However, in tonal music, we also have another mode available to us: the minor mode. The modern, tonal minor mode slowly evolved through compositional and performance practices, using the Aeolian mode as a foundation, borrowing elements from the other two minor-like diatonic modes of Dorian and Phrygian. One might reasonably ask why it was necessary to wait until now to begin our study of the minor mode but, as you will see, because it shares characteristics of all the diatonic minor-like modes, it contains peculiar features and characteristics which need more care and attention in practice to use and understand the mode effectively, and to obtain the unique sound and flavor of minor to which it offers.
As mentioned above, the modern, tonal minor mode evolved through compositional and performance practice over several centuries in Western music to incorporate aspects of each of the diatonic minor-like modes. As you may recall from your fundamentals study, there are three possible configurations of the tonal minor mode: Natural, Harmonic, and Melodic. These three terms refer to the ways in which each variation is deployed within a musical setting. First, let us first quickly review each one.
Natural Minor (Aeolian)
So-called "natural" minor is simply the unaltered version of the diatonic Aeolian mode.
Figure 1. Natural Minor, in scale order, built on pitch class A.
Harmonic Minor
The first variation of natural minor is known as "Harmonic" minor. It is the natural minor mode with a raised seventh scale degree.
Figure 2. Harmonic Minor, in scale order, built on pitch class A.
As you likely learned in your study of music fundamentals, the natural minor mode does not contain a leading tone but rather a subtonic with [latex](\hat7)[/latex] a whole step below the tonic. This is one of a few important differences between the major mode and the minor mode. In Harmonic minor, the [latex](\hat7)[/latex] is raised by a half-step, creating an artificial leading tone which then gives us the ability to have a strong tonal harmonic progression in cadences, similarly to how the major mode behaves intrinsically (as we will learn more about shortly). It this use of the artificially created leading tone in harmonic progressions that give this variation its name ("harmonic").
Melodic Minor
The second variation of natural minor is known as "Melodic" minor. It is the natural minor mode with a raised seventh scale degree, just as we have in Harmonic minor, but also contains a raised sixth scale degree.
Figure 3. Melodic Minor, in scale order, built on pitch class A.
Like Harmonic minor shown above, Melodic minor also contains an artificial leading tone by way of a raised [latex](\hat7)[/latex] for the purpose of strong tonal cadential progressions. However, unlike Harmonic minor, the Melodic minor variation adds a raised [latex](\hat6)[/latex] which now smooths out the awkward interval of an augmented second (A2) between [latex]\uparrow\hat6[/latex] and [latex]\uparrow\hat6[/latex] that we find in Harmonic minor[1]. Now, instead of the augmented second between 6 and 7, we have a smoother melodic interval of a whole step. Hence, the name "melodic" simply refers to this smoothing out of the augmented second we find in Harmonic minor.
As with triads, seventh chords are labeled with both a Roman numeral analysis designation and a lead-sheet chord symbol. For scale degrees [latex](\hat1)[/latex] through [latex](\hat6)[/latex] we use upper and lower case to denote major or minor quality, and place a superscript figure number 7 to the right to indicate that the chord is a seventh chord. The differentiation of specific seventh quality is inferred by context and no further information is necessary. However, some texts try to differentiate a major-major seventh with a superscript "MA" versus a major-minor seventh, the "Dominant" seventh which often only contains the number. For scale degree [latex](\hat7)[/latex], the Roman numeral label will have a circle with a diagonal slash , the sign for "half" diminished which is a very specific type of seventh chord: a diminished triad with a minor seventh as a chord tone in relationship to the root. In all cases, the figure number will change with inversions, explained a bit more below.
Lead sheet chord symbols are a bit more specific with regard to specifying the quality of the seventh chord. First, as we would do with a triad, the pitch class of the chord's root is written. This is then followed by a triangle and a superscript seven 7 for a major-major seventh chord, a minus sign with a superscript 7 for a minor-minor seventh chord, a superscript 7 alone for a major-minor seventh chord (also called the "Dominant Seventh"), and a half-diminished sign with a superscript 7. to indicate the half-diminished seventh chord. This particular quality of seventh chord is also referred to as a "minor seven, flat five", particularly in the world of jazz and pop music, and is sometimes preferred. To label in this manner we write the lead sheet symbol the same way as we would a minor-minor seventh but add a superscript 5 in parentheses after the 7 to indicate that the chord has its fifth chord tone is lowered by a half-step (colloquially speaking, "flatted"). These types of symbols, such as a flat 5 (5), are known as alterations. We will encounter more of these types of symbols as we continue to dive deeper into the world of harmony.
The Major-Major Seventh
The major-major seventh is a major triad with a major seventh chord tone in relationship to the root. This chord is colloquially referred to simply as a "major seventh" chord and is labeled in lead sheet notation with a triangle and a superscript seven 7. It has a strong, robust sound which, despite the strong dissonance of the major seventh (minor second in an inversion) with the root, it has a remarkably stable and grounded sound. In the world of jazz harmony, this chord is often substituted for any primary or secondary major triad.
The Minor-Minor Seventh
The minor-minor seventh chord is a minor triad with a minor seventh chord tone in relationship to the root. Colloquially the chord is often referred to simply as a "minor seventh" chord and is labeled in lead sheet notation with a minus sign with a superscript 7. It has a softer and somewhat darker sound quality than that of the major-major seventh, but, similarly, has a stable and grounded sound. As with the major-major seventh chord, in jazz it is often substituted for any primary or secondary minor triad.
The Major-Minor Seventh ("Dominant Seventh")
The major-minor seventh chord is a major triad with a minor seventh chord tone in relationship to the root. It is almost always referred to colloquially as a "dominant seventh" chord as it is built naturally on the dominant scale degree (scale degree [latex](\hat1)[/latex] ). It is labeled in lead sheet notation simply with a superscript 7. The sound quality is quite a bit less stable and more uneasy than either the major-major seventh chord or minor-minor seventh chord owing primarily to the presence of an unstable tritone interval between the third and seventh chord tones. In tonal music, this chord, has a strong dominant function that feels a need to resolve. In jazz is often used wherever a dominant tonal function is desired.
The Half-Diminished Seventh Chord ("Minor Seven, Flat Five")
Built naturally on the leading-tone scale degree, scale degree [latex](\hat7)[/latex], the half-diminished seventh chord is a diminished triad with a minor seventh chord tone in relationship to the root. As outlined above, the chord is often referred to as a "minor seven flat five" chord. Both terms are interchangeable. It is labeled in lead sheet chord notation with either a half-diminished sign with a superscript 7 or like a minor seventh chord (a minus sign with a superscript 7) adding a superscript 5 in parentheses after the 7 to indicate that the chord has its fifth chord tone is lowered by a half-step. This chord is literally a minor-minor seventh chord with a lowered fifth. Like the major-minor ("dominant") seventh chord, it also contains a tritone (between the root and fifth chord tones) and has a similarly unstable sound. However, unlike the major-minor ("dominant") seventh, the lack of a stable perfect fifth between the root and fifth of the chord serves to soften the need for immediate resolution and as a result the chord feels more ambiguous and cloudy. It is often used as a predominant chord, especially in the minor mode for reasons we will explore later.
We may invert seventh chords just as we are able to invert triads. As we know from fundamentals, a seventh chord has three possible inversions:
Figure 2. The inversions of the seventh chords with a C Major-Major (C7) seventh used for example.
The figure above shows a C Major-Major seventh chord (C7) in each possible inversion from root position to third inversion. As with triads, we label the inversions of each seventh chord with both a lead-sheet style chord symbol and a figured-bass number in relation to the Roman Numeral analysis. For the lead-sheet symbol, we label the chord as we do in root position and then use the slash "/" followed by the pitch class of the sounding bass tone. For the Roman Numeral figure, we use a superscript "7" for root position, "[latex]_5^6[/latex]" for first inversion, "[latex]_3^4[/latex]" for second inversion, and simply a "2" for third inversion. The figures (known as figured bass), as with triads, tell us where the other chord tones are in relationship to the bass--notably the root and the third of the chord in each of the inversions. A good way to remember these numbers is to think of them as part of a count down from the number seven: 7, 6-5, 4-3, 2.
Unlike the triad, we do not need to consider any additional voice-leading guidelines when using inversions of seventh chords and this includes the second inversion where we have the fifth of the chord in the bass. In a triad, this tone still needs to be handled carefully, but the seventh, owing to the dissonance that is already inherent in the chord, we need not be so careful. In short: we can use any of the inverted seventh chords anywhere we can use a root position seventh chord so long as we are fulfilling all the other voice leading requirements know to us, i.e. handling the dissonance(s), making sure we have good melodic motion with the voices, making sure our voices are properly spaced and in the proper ranges, and we aren't engaging in perfect parallel motion between the voices, etc.
The dissonance, the harmonic seventh as a chord tone that sounds against the root, is handled in the same way as the diminished fifth chord tone in the diminished triad. We must first choose a chord that contains the pitch class that will become the dissonant seventh chord tone in the chord preceding. Then, after sounding the seventh chord in question, we resolve the dissonance by moving the voice containing the seventh chord tone downward by step into a chord that contains the resolving pitch as a consonant chord tone. In the case of the half-diminished seventh chord, where we have two dissonances (the seventh and the diminished fifth chord tones in relation to the root), we need to doubly prepare and doubly resolve each dissonance. Later these strict guidelines will be relaxed as our ability to enrich our harmonic phrases will increase.
Unlike the diminished triad which occurs on only the leading tone, we have the opportunity to build and use seventh chords on all seven scale degrees of the major mode. Thus, to accomplish the successful handling of the dissonant seventh, we need to locate appropriate preparation chords and resolution chords which will work with any of the available seventh chords. The chart below summarizes each of the different possible preparation and resolution schemes for each of the seventh chords we have available to us in the major mode. Later we shall adapt and modify this chart for the minor mode.
Seventh Chord Preparation and Resolution Schema
PREPARATION | SEVENTH CHORD | RESOLUTION |
|---|---|---|
Dominant (V) Mediant (iii) | Tonic (I7) | SubDominant (IV) |
SubMediant (vi) SubDominant (IV) | SuperTonic (ii7) | Dominant (V) |
Leading-Tone (vii) Dominant (V) | Mediant (iii7) | SubMediant (vi) |
Tonic (I) SubMediant (vi) | SubDominant (IV7) | Leading-Tone (vii) |
SuperTonic (ii) Leading-Tone (vii) | Dominant (V7) | Tonic (I) |
Mediant (iii) Tonic (I) | SubMediant (vi7) | SuperTonic (ii) |
SubDominant (IV) SuperTonic (ii) | Leading-Tone (vii7) | Mediant (iii) |
Summary
We may summarize what we learned above in three step process as follows:
- Prepare the dissonant seventh chord tone by sounding it first in a preceding chord as a consonant tone and then tying it over as a common tone. For the leading tone half diminished seventh, we need to prepare both the seventh and the diminished fifth dissonances. Use the chart above to refer to chords that could be used to prepare a seventh on any given scale degree in the major mode.
- Sound the seventh chord by holding over the dissonance(s) and any other common tones, then moving the other voices to the next nearest chord tones to complete the chord. As we are sounding a seventh chord, no doubling is necessary. However, we do need to make sure we have a complete chord. For now, do not omit any chord tones (later we will be able to relax this condition).
- Resolve the dissonance(s) by moving to the resolution chord and moving the voice containing the dissonant seventh chord tone (or both the seventh and the diminished fifth) downward by step, holding over any tones in common, and moving the other voices to the nearest available chord tones. Again, mindful of trying to double the root when possible when moving to a triad.
- When resolving to a triad, move to the resolution chord found in the chart which is, for now, always found a root motion of a fourth upward from the scale degree on which we sounded the seventh chord. The concept of relative root motions of chords in harmonic progressions is a very important one and will become more and more important as we move further in our study.
- It is possible, and sometimes desirable, to connect sevenths to one another. There are no special additional guidelines for this so long as you are able to properly prepare and resolve the dissonance(s) and also satisfy quality voice leading with all of the guidelines we've covered and discussed thus far.
Now that we have added seventh chords to the mix, we can add and adjust our tonal harmony progression flowchart:
Common Tone Chord Chart (Major Mode)
| Chord | Has common tones with... | |||
|---|---|---|---|---|
| I | iii | IV | V | vi |
| ii | IV | V | vi | vii |
| iii | I | V | vi | vii |
| IV | I | ii | vi | vii |
| V | I | ii | iii | vii |
| vi | I | ii | iii | IV |
| vii | ii | iii | IV | V |
Seventh Chord Preparation and Resolution Schema
PREPARATION | SEVENTH CHORD | RESOLUTION |
|---|---|---|
Dominant (V) Mediant (iii) | Tonic (I7) | SubDominant (IV) |
SubMediant (vi) SubDominant (IV) | SuperTonic (ii7) | Dominant (V) |
Leading-Tone (vii) Dominant (V) | Mediant (iii7) | SubMediant (vi) |
Tonic (I) SubMediant (vi) | SubDominant (IV7) | Leading-Tone (vii) |
SuperTonic (ii) Leading-Tone (vii) | Dominant (V7) | Tonic (I) |
Mediant (iii) Tonic (I) | SubMediant (vi7) | SuperTonic (ii) |
SubDominant (IV) SuperTonic (ii) | Leading-Tone (vii7) | Mediant (iii) |
EXAMPLES: Seventh Chords in the Major Mode
If the score above is not displaying properly you may CLICK HERE to open it in a new window.
RWU EXERCISES
Mixed Triads and Seventh Chords in Short Phrases
Using the templates below, do the following:
A) ROOT POSITION SEVENTH CHORDS
- Realize the given harmonic progression (the Roman numeral analysis is provided). You may choose inversions of the triads as you wish within the guidelines.
- Compose three harmonic progressions of your choice, at least 8 to 12 chords in length, one may be in C Major, and the other two any major key of your choosing.
- Follow the guidelines set above.
- You must have at least two seventh chords per phrase, but not more than three. Try, across your three attempts, to use one of each possible seventh chord found on each of the seven scale degrees.
- You must have at least one instance of a leading tone diminished triad OR half-diminished seventh chord in each of your phrases, properly prepared and resolved according to the guidelines above.
- Use triad inversions wherever you wish according to the already established guidelines for voice leading. Strive for a decent mixture of root, first, and second inversion triads to complement the seventh chords.
B) INVERSIONS OF SEVENTH CHORDS
- Compose three harmonic progressions of your choice, at least 8 to 12 chords in length, one may be in C Major, and the other two any major key of your choosing. Follow the guidelines above except this time, when using the seventh chords, you may use inversions. Strive for a good mixture of different inversions and root position for both practice and variety. You may also try to connect seventh chords to one another--you should have at least two instances across your three phrases.
(you must be logged into your Noteflight account to open the activity templates above)
Schoenberg Theory of Harmony Examples
Further Reading
- Schoenberg, Arnold: Theory of Harmony
- Schoenberg, Arnold: Structural Functions of Harmony
Core sections comprise the main musical and poetic content of a song. Core sections include strophe (AABA and strophic form only), bridge, verse, chorus, prechorus, and postchorus.
A single step within a scale; usually indicated by either a solfège syllable or an Arabic numeral with a caret.
[["Chord","Has common tones with...","#colspan#","#colspan#","#colspan#","#colspan#","#colspan#","#colspan#","#colspan#"],["i","III","III+([latex]\\uparrow\\hat7[/latex])","iv","IV ([latex]\\uparrow\\hat6[/latex])","v","V ([latex]\\uparrow\\hat7[/latex])","VI","vi\uea97 ([latex]\\uparrow\\hat6[/latex])"],["ii\uea97","iv","","v","I ([latex]\\uparrow\\hat6[/latex])","VI","","VII","vii\uea97 ([latex]\\uparrow\\hat7[/latex])"],["ii","","","","","","","",""],["iii ","I","","V","","vi","","","vii\uea97"],["III+","","","","","","","",""],["iv","I","","ii","","vi","","","vii\uea97"],["IV","","","","","","","",""],["v","I","","ii","","iii","","","vii\uea97"],["V","","","","","","","",""],["VI ","I","","ii","","iii","","","IV"],["vi\uea97","","","","","","","",""],["VII ","ii","","iii","","IV","","","V"],["vii\uea97","","","","","","","",""]]
Key Takeaways
- A major scale is an ordered collection of half and whole steps with the ascending succession W‑W‑H‑W‑W‑W‑H.
- Major scales are named for their first note (which is also their last note), including any accidental that applies to the note.
- Scale degrees are solmization syllables notated by Arabic numerals with carets above them. The scale degrees are [latex]\hat1-\hat2-\hat3-\hat4-\hat5-\hat6-\hat7[/latex].
- Solfège solmization syllables are another method of naming notes in a major scale. The syllables are do, re, mi, fa, sol, la, and ti.
- Each note of a major scale is also named with scale-degree names: tonic, supertonic, mediant, subdominant, dominant, submediant, and leading tone.
- Akey signature, consisting of either sharps or flats, appears at the beginning of a composition, after a clef but before a time signature.
- The order of sharps in key signatures is F, C, G, D, A, E, B, while the order of flats is the opposite: B, E, A, D, G, C, F. In sharp key signatures, the last sharp is a half step below the tonic (the first note of a scale). In flat key signatures, the second-to-last flat is the tonic.
- The circle of fifths is a convenient visual for remembering major key signatures. All of the major key signatures are placed on a circle in order of number of accidentals.
A scale is an ordered collection of half and whole steps (see Half and Whole Steps and Accidentals to review).
A major scale is an ordered collection of half- (abbreviated H) and whole steps (abbreviated W) in the following ascending succession: W-W-H-W-W-W-H. Listen to Example 1 to hear an ascending major scale. Each whole step is labeled with a square bracket and “W,” and each half step is labeled with an angled bracket and “H.”
Example 1. An ascending major scale.
A major scale always starts and ends on notes of the same letter name, one octaveapart, and this starting and ending note determines the name of the scale. Therefore, Example 1 depicts a C major scale because its first and last note is a C.
The name of a scale includes any accidental that applies to the first and last note. Example 2 shows a B♭ (B-flat) major scale—not a B major scale, which would use a different collection of pitches. Note that the pattern of half and whole steps is the same in every major scale, as shown in Example 1and Example 2.
Example 2. A B-flat major scale.
Musicians name the notes of major scales in several different ways. Scale degrees are solmization syllables notated by Arabic numerals with carets above them. The first note of a scale is [latex]\hat{1}[/latex] and the numbers ascend until the last note of a scale, which is also [latex]\hat{1}[/latex] (although some instructors prefer [latex]\hat{8}[/latex]). Example 3shows a D major scale with each scale degree labeled with an Arabic numeral and a caret.
Example 3. A D major scale.
Below the scale degrees, Example 3 also shows another method of naming notes in a major scale: solfège solmization syllables. Solfège (a system of solmization syllables) are another method of naming notes in a major scale. The syllables do, re, mi, fa, sol, la, and ti can be applied to the first seven notes of any major scale; these are analogous to the scale degrees [latex]\hat{1}[/latex], [latex]\hat{2}[/latex], [latex]\hat{3}[/latex], [latex]\hat{4}[/latex], [latex]\hat{5}[/latex], [latex]\hat{6}[/latex], and [latex]\hat{7}[/latex]. The last note is do ([latex]\hat{1}[/latex]) because it is a repetition of the first note. Becausedo ([latex]\hat{1}[/latex]) changes depending on what the first note of a major scale is, this method of solfège is called movable do. This is in contrast to a fixed do solmization system, in which do ([latex]\hat{1}[/latex]) is always the pitch class C.
Each note of a major scale is also named with scale-degree names: tonic, supertonic, mediant, subdominant, dominant, submediant, leading tone, and then tonic again. Example 4 shows how these names align with the scale-degree number and solfège systems described above.
[table “37” not found /]
Example 4. Scale-degree numbers, solfège syllables, and scale-degree names.
Example 5shows these scale-degree names applied to an A♭ major scale:
Example 5. An A♭ major scale with scale-degree names.
Example 6 shows the notes and scale-degree names of the A♭ major scale in an order that shows how the names of the scale degrees were derived. The curved lines above the staff show the intervallic distance between each scale degree and the tonic.
- The word dominant is inherited from medieval music theory, and refers to the importance of the fifth above the tonic in diatonic music.
- The word mediant means "middle," and refers to the fact that themediant is in the middle of the tonic and dominant pitches.
- The Latin prefix super means “above,” so the supertonic is a second above the tonic. This is the only "super-" interval.
- The Latin prefix sub means “below”; the subtonic, submediant, and subdominant are the inverted versions (i.e., below the tonic) of the supertonic, mediant, and dominant respectively. (Note that in this text, we prefer the term leading toneinstead of "subtonic" when referring to the scale-degree that is a half step below tonic, so named because it is often thought of as “leading” toward the tonic.)
Akey signature, consisting of either sharps or flats, appears at the beginning of a composition, after a clef but before a time signature. You can remember this order because it is alphabetical:clef,key,time. Example 7 shows a key signature in between a bass clef and a time signature.
Key signatures collect the accidentals in a scale and place them at the beginning of a composition so that it is easier to keep track of which notes have accidentals applied to them. In Example 7, there are flats on the lines and spaces that indicate the notes B, E, and A (reading left to right). Therefore, every B, E, and A in a composition with this key signature will be flat, regardless of octave. In Example 8 both of these Bs will be flat because B♭ is in the key signature.
Flat key signatures have a specific order in which flats are added, and the same is true of the sharps in sharp key signatures. These orders apply regardless of clef. Example 9shows the order of sharps and flats in all four clefs that we have learned:
The order of sharps is always F, C, G, D, A, E, B. This can be remembered with the mnemonic "Fat Cats Go Down Alleys (to) Eat Birds." The sharps form a zig-zag pattern, alternating going down and up. In the treble, bass, and alto clefs, this pattern "breaks" after D♯ and then resumes. In the tenor clef, there is no break, but F♯ and G♯ appear in the lower octave instead of the upper octave.
The order of the flats is the opposite of the order of the sharps: B, E, A, D, G, C, F. This makes the order of flats and sharps palindromes. The order of flats can be remembered with this mnemonic: "Birds Eat And Dive Going Copiously Far." The flats always make a perfect zig-zag pattern, alternating going up and down, regardless of clef, as seen in Example 9.
There are easy ways to remember which key signature belongs to which major scale. In sharp key signatures, the last sharp is a half step below the tonic (the first note of a scale). Example 10shows three sharp key signatures in different clefs. Here's how to identify each with this method:
- Thelast sharp (in this case the only sharp), F♯, is a half step below the note G. Therefore, this is the key signature of G major.
- The last sharp, G♯, is a half step below the note A. Therefore, this is the key signature of A major.
- The last sharp, E♯, is a half step below the note F♯. Therefore, this is the key signature of F♯ major.
In flat key signatures, the second-to-last flat is the tonic (the first note of a scale). Example 11shows three flat key signatures in different clefs. Here's how to identify each with this method:
- The second-to-last flat in this key signature is B♭. Therefore, this is the key signature of B♭ major.
- The second-to-last flat is A♭. Therefore, this is the key signature of A♭ major.
- The second-to-last flat is G♭. Therefore, this is the key signature of G♭ major.
There are two key signatures that have no "tricks" that you will simply have to memorize. These are C major, which has nothing in its key signature (no sharps or flats), and F major, which has one flat: B♭ (Example 12).
Example 13shows the key signature for C major (no sharps or flats) followed by all of the sharp key signatures in order in all four clefs: G, D, A, E, B, F♯, and C♯ major.
Example 13. The key signatures of C, G, D, A, E, B, F♯, and C♯ in all four clefs.
Example 14first shows the key signature for C major (no sharps or flats), then all of the flat key signatures in order in all four clefs: F, B♭, E♭, A♭, D♭, G♭, and C♭ major.
Example 14first shows the key signature of C major (with no sharps or flats), and then the key signatures of F, B♭, E♭, A♭, D♭, G♭, and C♭ in all four clefs.
There is one other "trick" that might make memorization of the key signatures easier: C major is the key signature with no sharps or flats, C♭ major is the key signature with every note flat (7 flats total), and C♯ major is the key signature with every note sharp (7 sharps total).
Major keys are said to be "real" if they correspond to one of the key signatures in Examples 13or 14. If a double sharp ordouble flat would be needed for a key signature, then that key signature would be "imaginary." Occasionally, you may encounter music in an imaginary key. Example 15 shows an F♭ major scale; an F♭ major key signature is imaginary because it would need a B𝄫.
Example 15. An F♭ major scale in treble clef.
The circle of fifths is a convenient visual. In the circle of fifths, all of the major key signatures are placed on a circle in order of number of accidentals. The circle of fifths is so named because each key signature is a fifth away from the ones on either side of it. Example 16shows the circle of fifths for major key signatures:
If you start at the top of the circle (12 o'clock), the key signature of C major appears, which has no sharps or flats. If you continue clockwise, sharp key signatures appear, each subsequent key signature adding one more sharp. If you continue counter-clockwise from C major, flat key signatures appear, each subsequent key signature adding one more flat. The bottom three key signatures (at 7, 6, and 5 o'clock) in Example 16 are enharmonically equivalent. For example, the B major and C♭ major scales have different key signatures—five sharps and seven flats, respectively—but they sound the same because the notes B and C♭ are enharmonically equivalent.
- Major Scales Tutorial (musictheory.net)
- Major Scales (Practical Chords and Harmonies)
- Major Scales (YouTube)
- Scale Degree Names (musictheoryfundamentals.com)
- Scale Degree Names (musictheory.net)
- Solfège History and Tutorial (Earlham College)
- Scale Degrees, Solfège, and Scale-degree Names (YouTube)
- Major Key Signatures (musictheory.net)
- Sharp Key Signatures (YouTube)
- Flat Key Signatures (YouTube)
- Major Key Signature Flashcards (music-theory-practice.com)
- The Circle of Fifths (YouTube)
- The Circle of Fifths (Classic FM)
- Writing Major Scales (.pdf), from Tonic and Other Scale Degrees (.pdf)
- Writing Major Key Signatures (.pdf)
- Identifying Major Key Signatures (.pdf)
- Major Keys Worksheets for Children (.pdf)
- Scale Degrees or Solfège (.pdf,.pdf)
- Writing Major Scales (.pdf, .mscx)
- Key Signatures: Major (.pdf, .mscx)
A core section of a popular song that is lyric-invariant and contains the primary lyrical material of the song. Chorus function is also typified by heightened musical intensity relative to the verse. Chorus sections are distinct from refrains, which are contained within a section.
Notes whose exact pitch sounds somewhere between the flat and regular versions of a scale degree, particularly 3̂ and 7̂.
Sections that are lyric-variant and often contain lyrics that advance the narrative.
Sections that are lyric-variant and often contain lyrics that advance the narrative.
One-twelfth of an octave; generally considered to be the smallest interval in Western musical notation.
The process by which a non-tonic triad is made to sound like a temporary tonic. It involves the use of secondary dominant or leading-tone chords.
