# Circle of Fifths Practice: Rebuild Key Signatures Without the Chart

*2026-10-08*

E major is the fourth key after C on the sharp branch of the circle of fifths. Its fourth sharp is D♯. Those are two different sequences, and mixing them up can produce a signature with the right number of sharps on the wrong notes.

For this **circle of fifths practice**, take a blank sheet and build each answer in three parts: the route from C, the accidental count, and the spelled signature. Then repair a few deliberately wrong answers. A finished wheel makes a useful answer key; keep it covered while you work.

The exercises cover the 15 ordinary Western major-key signatures, from no accidentals through seven sharps or seven flats. They practice written spelling. Staff placement, listening, and identifying the key of a real passage need separate work.

![A woman compares a cream tile with a gap in the border of a circular blue and cream mosaic](/blog/circle-of-fifths-practice.png)

## Keep the two orders apart

The **tonic** is the note that names the key. The **key signature** gives its default sharps or flats. Starting at C major, follow one of these tonic routes, reading down the chosen column:

| Steps from C | Sharp-branch tonic | Flat-branch tonic |
| --- | --- | --- |
| 0 | C | C |
| 1 | G | F |
| 2 | D | B♭ |
| 3 | A | E♭ |
| 4 | E | A♭ |
| 5 | B | D♭ |
| 6 | F♯ | G♭ |
| 7 | C♯ | C♭ |

Each step away from C adds one accidental of that branch's type. Moving toward sharps goes up a perfect fifth; moving toward flats goes down a perfect fifth, or up a perfect fourth. The [University of Puget Sound's major-key lesson](https://musictheory.pugetsound.edu/mt21c/MajorKeySignatures.html) shows this relationship and the three enharmonic overlaps between branches.

The accidentals inside the signature follow their own orders:

- **Sharps:** F♯, C♯, G♯, D♯, A♯, E♯, B♯.
- **Flats:** B♭, E♭, A♭, D♭, G♭, C♭, F♭.

Take the first *n* entries for a signature with *n* accidentals. [Open Music Theory's major-scale chapter](https://viva.pressbooks.pub/openmusictheory/chapter/major-scales/) gives these orders and the major-scale pattern: whole, whole, half, whole, whole, whole, half. A whole step is two semitones; a half step is one.

Write the tonic route on one line and the accidentals on another. E is fourth on the sharp route; D♯ is fourth in the sharp list. Keep those two sequences separate when filling the row.

## Build a row before checking it

Copy this template for each attempt:

```text
Requested major key:
Branch and route from C:
Number and type of accidentals:
Signature, in standard order:
Check using the scale:
First wrong step, if any:
```

Start with the requested spelling. B major belongs to the sharp branch; B♭ major belongs to the flat branch. Keep every sharp or flat in the tonic's name. C major stays at step 0 and has no accidentals.

If you need to construct the next tonic, [count letters and pitch distance separately](https://musictheory.pugetsound.edu/mt21c/HowToIdentifyIntervals.html). A perfect fifth up spans five letter names, counting the starting note, and seven semitones. From B, the letters are B–C–D–E–F; the pitch seven semitones higher is F♯. Writing G♭ would land on the same equal-tempered piano key but use the wrong letter for that fifth. For the flat direction, a perfect fourth up spans four letters and five semitones: F–G–A–B gives B♭.

Count the route's arrows from C. Then copy that many accidentals from the appropriate list. To check independently, write the scale's letters from the requested tonic, using each letter once before repeating the tonic. Add accidentals to make the major-scale step pattern, then compare them with your signature.

### Worked row: A♭ major

```text
Route: C → F → B♭ → E♭ → A♭
Count: four steps, so four flats
Signature: B♭, E♭, A♭, D♭
Scale: A♭–B♭–C–D♭–E♭–F–G–A♭
```

The signature lists accidentals in flat order; the scale lists notes from A♭. Starting the signature with A♭ would confuse those jobs. The scale's half steps fall between C–D♭ and G–A♭, at degrees 3–4 and 7–8.

### Worked row: F♯ major

```text
Route: C → G → D → A → E → B → F♯
Count: six steps, so six sharps
Signature: F♯, C♯, G♯, D♯, A♯, E♯
Scale: F♯–G♯–A♯–B–C♯–D♯–E♯–F♯
```

E♯ belongs here. Replacing it with F natural would repeat the letter F and omit E. On an equal-tempered piano they sound alike, but the written scale requires E as its seventh letter. The half steps are A♯–B and E♯–F♯.

For a quick major-key check, move a half step up from the last sharp, keeping the next letter: E♯ leads to F♯. With at least two flats, the second-to-last flat names the major tonic. A♭ is second-to-last in A♭ major's four-flat signature. Handle the two small cases directly: **F major has B♭; C major has no accidentals**.

## Why the circle has 12 positions but 15 signatures

This worksheet has C major, seven sharp signatures, and seven flat signatures: **15 written major-key signatures**. Three pairs share pitch-class positions in equal temperament:

| Sharp spelling | Flat spelling |
| --- | --- |
| B major: five sharps | C♭ major: seven flats |
| F♯ major: six sharps | G♭ major: six flats |
| C♯ major: seven sharps | D♭ major: five flats |

Counting both spellings gives 15 signatures across 12 pitch-class positions. The overlap doesn't make the written signatures interchangeable in a spelling exercise.

At that edge, **choose the branch explicitly**. From B major, one more step toward sharps gives F♯ major with six sharps. From G♭ major, one more step toward flats gives C♭ major with seven flats. Keep the requested spelling even when the other branch names the same piano pitches.

Stop the sharp branch at C♯ and the flat branch at C♭ for this worksheet. Continuing those spellings would require double accidentals. Changing branches is a separate respelling decision, so don't do it silently to make the count smaller.

## Circle of fifths quiz: construct and repair

Cover the reference above and the answers below. Write the route, count, and ordered signature for every construction. For repairs, mark the **first incorrect entry or decision** before rewriting the answer. The wrong examples below are intentional.

1. Start at D major and take one step toward sharps. Give the destination and its complete signature.
2. Build E♭ major from C, then spell its scale to check the signature.
3. A draft says: “E major: four sharps, F♯, C♯, G♯, A♯.” Find the first incorrect accidental and repair the signature.
4. A draft says: “D♭ major: five flats, B♭, E♭, A♭, D♭, C♭.” Find the first incorrect accidental and repair the signature.
5. A flat-branch route reads “C → F → B♭ → D♯ → G♯,” and its final key is labeled “four-flat G♯ major.” Mark the first spelling error, then repair the route and final signature.
6. A B-major row gives the route “C → G → D → A → E → B,” counts six steps, and lists F♯, C♯, G♯, D♯, A♯, E♯. Find the first wrong step and repair the row.
7. Start at G♭ major and take one step toward flats. Keep the flat spelling. Name the destination, list its accidentals, and spell its scale.
8. A request asks for C♯ major, but the answer gives “D♭ major; B♭, E♭, A♭, D♭, G♭.” Explain why the answer fails the request, then write the requested signature.
9. A seven-sharp row ends “F♯, C♯, G♯, D♯, A♯, E♯, C natural.” Repair only the wrong entry. Which major scale does the repaired signature support?
10. A passage has B♭, E♭, and A♭ in its signature. In a major/minor task, give both candidate keys. Can the signature alone select one?

### Answers with the first wrong step

1. **A major; three sharps: F♯, C♯, G♯.** The route is C → G → D → A. One step toward sharps adds G♯ to D major's two-sharp signature.
2. **E♭ major; three flats: B♭, E♭, A♭.** The route is C → F → B♭ → E♭. Its scale is E♭–F–G–A♭–B♭–C–D–E♭. Check half steps at G–A♭ and D–E♭.
3. **The fourth entry is wrong: replace A♯ with D♯.** E major's count is correct. The ordered signature is F♯, C♯, G♯, D♯; the draft skipped the fourth sharp and used the fifth.
4. **The fifth entry is wrong: replace C♭ with G♭.** D♭ major has B♭, E♭, A♭, D♭, G♭. C♭ belongs at position six in the flat order.
5. **The first error is D♯ after B♭; write E♭.** The repaired route is C → F → B♭ → E♭ → A♭. Its final signature is four flats: B♭, E♭, A♭, D♭. D♯ matches E♭ on an equal-tempered piano, but B♭ to D♯ does not spell the required fourth up. The final tonic must also become A♭.
6. **The route is correct; counting six steps is the first error.** It has five arrows, so B major needs five sharps: F♯, C♯, G♯, D♯, A♯. Remove the extra E♯. The six-sharp list follows sharp order correctly, but belongs to F♯ major.
7. **C♭ major; seven flats: B♭, E♭, A♭, D♭, G♭, C♭, F♭.** The route is C → F → B♭ → E♭ → A♭ → D♭ → G♭ → C♭. Its scale is C♭–D♭–E♭–F♭–G♭–A♭–B♭–C♭. All seven letters are flat, including C and F. Check half steps at E♭–F♭ and B♭–C♭.
8. **The answer changed the requested spelling.** D♭ major's five-flat signature is internally correct, but it doesn't answer a C♯ spelling task. C♯ major needs seven sharps: F♯, C♯, G♯, D♯, A♯, E♯, B♯.
9. **Replace C natural with B♯; the key is C♯ major.** The corrected list ends E♯, B♯. B♯ is the scale's seventh degree: C♯–D♯–E♯–F♯–G♯–A♯–B♯–C♯. C natural would repeat C and leave out B.
10. **E♭ major or C minor; the signature alone cannot choose.** Relative keys share a signature. Phrase endings, harmony, and the note that sounds settled help establish the tonic in a passage. [Open Music Theory's minor-scale chapter](https://viva.pressbooks.pub/openmusictheory/chapter/minor-scales/) explains the relationship and why identifying a key needs musical context.

## Make a repair card, then try a different key

Check your worksheet from top to bottom: requested spelling, route, count, ordered signature, scale. Mark the earliest mismatch. A later error may simply follow from it: question 6's extra sharp came after a wrong count, while question 3 had the right count and a wrong entry.

Correct the paper answer first, then make a small card only for a rule you couldn't retrieve. You don't need to turn every row into another card.

| First wrong step | Possible repair card | Fresh paper task after correction |
| --- | --- | --- |
| Put the next sharp on the wrong letter | After F♯, C♯, G♯, which sharp comes next? **D♯.** | Rebuild B major and identify its newly added sharp after E major. |
| Lost count on the tonic route | When counting from C major, does C count as step 1? **No; C is step 0. Count arrows.** | Build D♭ major from C. |
| Replaced a requested spelling | Does a C♭ major task accept B major's signature? **No; preserve C♭ and use seven flats.** | Write separate rows for G♭ major and F♯ major. |

Try the fresh tasks before reading these checks:

- B major adds **A♯** after E major.
- D♭ is step **5**, with B♭, E♭, A♭, D♭, G♭.
- G♭ uses **B♭, E♭, A♭, D♭, G♭, C♭**; F♯ uses **F♯, C♯, G♯, D♯, A♯, E♯**.

In your next study session, mix the prompts so their order doesn't reveal which rule to use. Nibomo's [Circle of Fifths flashcards](/catalog/packages/circle-of-fifths-flashcards/) provide text-based recall practice for these relationships. Use them alongside construction on paper. The [music theory flashcard guide](/blog/music-theory-flashcards/) covers spelling-aware cards and choosing what deserves review.

Keep minor transfer limited at first: reconstruct a major signature, then identify its relative minor while keeping that signature. For example, E♭ major and C minor share three flats. Use the [relative versus parallel minor lesson](/blog/relative-vs-parallel-minor/) when you need to distinguish a shared signature from a shared tonic. Minor-scale alterations in a passage don't automatically replace its key signature.

Once the letter lists are reliable, move to a staff. Use [musictheory.net's key-signature exercise](https://www.musictheory.net/exercises/keysig) to practice reading signatures in notation, and write them in the clefs your course uses. Text reconstruction won't teach their staff positions or how a key sounds. Return to a score, instrument, or listening exercise to practice those parts.

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