I. Fundamentals

Chelsey Hamm and Bryn Hughes

Key Takeaways

  • A major 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.
  • are syllables notated by with above them. The scale degrees are [latex]\hat1-\hat2-\hat3-\hat4-\hat5-\hat6-\hat7[/latex].
  • 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 : tonic, supertonic, mediant, subdominant, dominant, submediant, and leading tone.
  • , consisting of either or , 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 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 is an ordered collection of half and whole steps (see Half and Whole Steps and Accidentals to review).

Major Scales

A 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  apart, 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 1 and Example 2.

Example 2. A B-flat major scale.

Scale Degrees, Solfège, and Scale-Degree Names

Musicians name the notes of major scales in several different ways. are syllables notated by with 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 3 shows 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. (a system of 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. Because do ([latex]\hat{1}[/latex]) changes depending on what the first note of a major scale is, this method of solfège is called This is in contrast to a 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 : 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 id=37 /]

Example 4. Scale-degree numbers, solfège syllables, and scale-degree names.

Example 5 shows 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 music.
  • The word mediant means “middle,” and refers to the fact that the mediant 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  instead 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.)
Lines show that a fifth relates D♭–A♭ and A♭–E♭; a third relates F–A♭ and A♭–C, and a second relates G–A♭ and A♭–B♭.
Example 6. The notes of the A♭ major scale arranged to show the derivation of scale-degree names.

Key Signatures

, consisting of either or , 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.

A bass clef is shown on a staff, followed by a three-flat key signature, and a 4/4 time signature.
Example 7. A key signature goes after a clef, but before a time signature.
There are 2 Bbs in different octaves, Bb2 and Bb3
Example 8. Both Bs are flat, regardless of octave.

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 9 shows the order of sharps and flats in all four clefs that we have learned:

The order of sharps and flats in treble, bass, alto, and tenor clefs.
Example 9. The order of sharps and flats in treble, bass, alto, and tenor clefs.

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 10 shows three sharp key signatures in different clefs. Here’s how to identify each with this method:

1. A one-sharp key signature in treble clef, 2. a three-sharp key signature in bass clef, and 3. a six-sharp key signature in Alto Clef
Example 10. Three different sharp key signatures in treble, bass, and alto clefs.
  1. The last 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.
  2. The last sharp, G♯, is a half step below the note A. Therefore, this is the key signature of A major.
  3. 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 11 shows three flat key signatures in different clefs. Here’s how to identify each with this method:

1. A two-flat key signature after a bass clef, 2. a four-flat key signature after a treble clef, and 3. a six-flat key signature after a tenor clef.
Example 11. Three different flat key signatures in bass, treble, and tenor clefs.
  1. The second-to-last flat in this key signature is B♭. Therefore, this is the key signature of B♭ major.
  2. The second-to-last flat is A♭. Therefore, this is the key signature of A♭ major.
  3. The second-to-last flat is G♭. Therefore, this is the key signature of G♭ major.
A treble clef is shown with a blank key signature, and a one-flat key signature is shown after a bass clef.
Example 12. The key signatures of C major (top) and F major (bottom).

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 13 shows 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 14  first 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.

All of the flat key signatures, first in treble, bass, alto, and tenor clefs.
Example 14. The key signatures of C, F, B♭, E♭, A♭, D♭, G♭, and C♭ in all four clefs.

Example 14 first 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 13 or 14. If a or  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

The 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 16 shows the circle of fifths for major key signatures:

Major key signatures are placed around a circle in order of the number of their accidentals
Example 16. The circle of fifths for major keys.

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 . 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.

Online Resources
Assignments from the Internet
  1. Writing Major Scales (.pdf), from Tonic and Other Scale Degrees (.pdf)
  2. Writing Major Key Signatures (.pdf)
  3. Identifying Major Key Signatures (.pdf)
  4. Major Keys Worksheets for Children (.pdf)
  5. Scale Degrees or Solfège (.pdf.pdf)
Assignments
  1. Writing Major Scales (.pdf, .mscx)
  2. Key Signatures: Major (.pdf, .mscx)

Media Attributions

  • scale degree names derivation
  • Key Signature
  • Key Signature Application
  • Order of Sharps and Flats
  • sharp-sigs
  • flat-sigs
  • cmajfmaj
  • Sharp Key Signatures
  • Circle of Fifths

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OPEN MUSIC THEORY by Chelsey Hamm and Bryn Hughes is licensed under a Creative Commons Attribution-ShareAlike 4.0 International License, except where otherwise noted.

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