1. **Tones and Semitones:**
- A **tone** is the distance of two keys on a piano where there's exactly one key in between. For example, C to D is a tone.
- A **semitone** (also known as a half step) is the distance of two keys on a piano where there's no key in between. For example, C to C# or C# to D is a semitone.
2. **Sharps and Flats:**
- A **sharp** raises a note by a semitone. For example, C# is one semitone higher than C.
- A **flat** lowers a note by a semitone. For example, Db is one semitone lower than D.
3. **Roots:**
- The **root** of a chord is the note on which the chord is built. For example, in a C major chord (C-E-G), C is the root.
4. **Octaves:**
- An **octave** is the interval between one musical pitch and another with double its frequency. On a piano, this means going from one key to the next key of the same name (e.g., from one C to the next higher or lower C).
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**Symbols:**
- **Sharp**: # (e.g., C#)
- **Flat**: ♭ (e.g., Db)
- **Natural**: ♮ (e.g., C♮ to represent a natural note, not sharped or flatted)
- **Root Symbol**: Usually indicated by the letter of the root note (e.g., C for a C major chord)
- **Octave Symbol**: Sometimes represented by an apostrophe (') above the note name to indicate a higher octave (e.g., C') or a comma (,) below the note name to indicate a lower octave (e.g., C,).
**Example:**
- Let's take a C major scale on the piano: C-D-E-F-G-A-B-C. Here, the distance from C to D is a tone, from D to E is a tone, from E to F is a semitone (as there's no black key between them), and so on.
- If we want to play a C# major chord, we would use the notes C#, E#, and G# (which are each raised by a semitone from the C major chord).
- The root of a chord is usually the bottom note when the notes are stacked in thirds. In the chord C-E-G, C is the root.
Understanding tones, semitones, sharps, flats, roots, and octaves is fundamental to playing and understanding music, especially on instruments like the piano.
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