Semitone, Octave

When one frequency is double another, these two are an octave apart.   Any octave divides into 12 semitones. On piano, key N+1 creates a frequency 1.059 times that of  key N.  These frequencies are a semitone apart.  Key N and N + 12 are an octave apart.  On guitar, on the same string, the notes created at frets N and N+1 are a semitone apart.  Frets N and N+12, an octave apart.

Natural minor scale

Starting at some arbitrary note, natural minor scale notes are 0, 2, 3, 5, 7, 8, 10 semitones above it .   If that note is A2 (or maybe F4), all octaves of each of these seven notes implicitly belong to A (or F) natural minor.

New intervals appear that aren’t found in the major scale:

• notes 1 and 3 are 3 semitones apart, called minor 3rd, with a symbol “b3” (pronounced “flat 3”) appearing in chord and scale diagrams.
• notes 1 and 6 are 8 semitones apart, called minor 6th (“b6”)
• notes 1 and 7 are  10 semitones apart, called minor 7th (“b7”)

Click this icon to see two octaves of A natural minor along the 5th string (starting at A2).  Drag the anchor to the 1st fret on the 1st string (F4) to see two octaves of F natural minor along the 1st string (starting at F4)

The notes are different between A and F natural minor, but if we listen to one of these scales, then the other, we hear the same sound flavour, just “higher”.  Your brain recognises these distances from a note that stands out from all the others. Making one note stand out is discussed in section “Using the scale”.

Fundamentally, music theory is about semitone relationships between groups of notes. Emuso has a clock-face tool and a relationship explorer tool for visualising these relationships, and note labelling can show the relationship of a note to a scale tonic, or to a chord root.

We’ll use this to find the intervals of natural minor within the major scale, and its chords.

Click this icon to create C major.

Now follow these steps

1. Enter the Toolkit
2. Click “Rel-X” in the toolkit button block.  This gadget can be dragged.
3. Repeat-click “Labels” on the interval strip until you see the numbers in the range 0 – 11  in the scale shape.
4. Select “Harmonic” on the Play Construct gadget.
5. Hold down ALT (opt on Mac) and move mouse over string 5, fret 3.  The generated tonic triad appears on both “guitar” and “clock face”.
6. Hold down ALT (opt on Mac) and move mouse over string 3, fret 5.  The generated tonic triad appears on both “guitar” and “clock face”.
7. Notice clock times 0 AM, 2, 4, 5, 7, 9 and 11 AM are occupied by circles coloured the same as on “guitar”.  Notice that clock times 0, 4, and 7 swell up regardless of which octave is involved on guitar.
8. Drag the anchor at string 5, fret 3 (C3) to string 5, fret 4 (C#3).  All the notes change, but the semitone relationships, the intervals made with the tonic don’t change. This is the secret to reducing the memorisation effort, and building a mental framework to tie music concepts together.
9. Drag the anchor back to C3.
10. If needed, repeat-click “Labels” on the interval strip until you see the numbers in the range 0 – 11  in the scale shape.
11. Click “Explorer” in Rel-X.
12. Select “from Scale menu” using the “Choose search” dropdown. Click “Scale” button in the toolkit button block and select “Minor”.  This loads the intervals for minor scale onto the coloured spokes.  Click “Rotate -” several times until all the occupied spokes turn orange (at time 9 AM).  This means a match has been found, when the minor scale tonic aligns with the major scale note at 9 AM (9 semitones above the major scale’s tonic at 0 AM).  In this situation, we call this the relative (natural) minor of the major scale it is found in.

Now let’s check out the chords of natural minor.

1. Click “Reroot” on the interval strip, and click string 6, fret 5 (A2). This results with the natural minor intervals (aka descending melodic minor) on the clock, starting at 0 AM.  A scale’s tonic is always at 0 AM.
2. Select “Harmonic” on the Play Construct gadget.
3. Hold down ALT (opt on Mac) and move mouse over string 6, fret 5.  The generated tonic triad appears on both “guitar” and “clock face”.
4. Notice above the “guitar”, you can see the scale name and the generated triad name “(I) min”.
5. Repeat this with the other six minor scale notes.  You get minor triads rooted at I, IV and V, major triads at bIII and bVII, and one diminished triad at II.
6. Choose “generate sevenths” from the “Gen” dropdown in the toolkit button block, and repeat the above with ALT.  You get minor seventh chords rooted at I, IV, and V;  major seventh chords rooted at bIII and bVI; a dominant 7th chord rooted at bVII; a minor 7 flat 5 chord rooted at II.

Finally, let’s use Chord-X to explore some chord voicings from natural minor.

1. Click Rel-X to turn it off.
2. Click Chord-X.
3. Use Labels, to show semitones in range 0 – 11, or to show theory-based interval symbols, like “b3”.
4. Click each scale note, and a voicing for that chord will appear.

Intervals that determine the tonic for the scale, and its basic minor”flavour”

To establish the sound flavour as major scale, notes chosen from the pitch classes of note 1 (tonic) need the most emphasis, along with notes chosen from the pitch classes of notes 3 (“b3”) and 7 (“5”)  semitones above the tonic.

For A minor, emphasise notes in the pitch classes for A, C, E.