Notes, Intervals and Scales

Physics hands you a continuous ribbon of frequency with nothing marked on it. Music cuts it into steps you can name, find again tomorrow and describe to another player. Notes are the steps, intervals are the distances between them, and scales are the small repeatable patterns of distance — the ones most songs are built out of.

Players tend to assume theory is a rulebook imposed on musicians from above, and that you need to read notation before any of it reaches you. Both are backwards. Theory is a description of what people were already doing, written down later by people trying to explain it. A guitarist who slides a chord shape up two frets and knows it still works has already used the idea this article is naming.

Twelve Notes Is a Decision, Not a Discovery

One interval is beyond argument, and the physics lesson already established it — an octave is a doubling of frequency, 440Hz up to 880Hz. Two pitches an octave apart sound so alike that every musical tradition treats them as one note. How many steps you put inside that doubling is where the traditions stop agreeing.

The harmonic series supplies the next piece, and the physics lesson has already laid it out — harmonics riding along at whole-number multiples of the fundamental. The third of those sits an octave plus a fifth above the note you played, which puts a 3:2 relationship inside a single plucked string before anyone has tuned anything. Stack fifths and you keep generating fresh pitches. Stack twelve and you arrive just past seven octaves, overshooting by about 23.5 cents, roughly a quarter of a semitone. Twelve is where the miss gets small enough to sweep away.

So twelve is a very good bargain rather than a law of nature. Arabic tone systems are commonly described in twenty-four divisions of the octave, and Indonesian gamelan tunings sit outside the twelve altogether, with each ensemble carrying a tuning of its own. Western instruments hide the leftover error by sharing it out evenly — in equal temperament every semitone is the same ratio, the twelfth root of two, about 1.0595. Be honest about the cost, because this is where theory writing most often goes wrong: the fretted fifth runs about 2 cents flat of a pure 3:2, and the fretted major third about 14 cents sharp of a pure 5:4. Nobody hears the fifth. The third is why a fretted major chord can sound faintly restless beside a singer tuning by ear.

A Semitone Is One Fret, and a Tone Is Two

A semitone is the smallest step the system contains. On a guitar it is one fret on one string. On a piano it is the very next key in either direction, black or white — black keys are not extras, they are the steps that land between the lettered ones. A tone, or whole step, is two semitones: two frets, or one key skipped.

Twelve semitones return you to where you began, an octave higher. Play an open string, then that string at the twelfth fret, and you are hearing one note at two frequencies. Everything else here is counting semitones out from somewhere.

Tuners talk in cents, and you have read one on a display. An octave is 1,200 cents, so an equal-tempered semitone is exactly 100 of them — a tuner reading −8 says you are eight-hundredths of a fret flat.

An Interval Is a Distance You Can Already Recognise

Learn these by sound before the names — you have heard all of them thousands of times.

• The octave, 12 semitones — the same note in two sizes. Two singers an octave apart read as one thicker voice rather than as harmony.
• The fifth, 7 semitones — open, hollow, hard to pin a mood on. Root plus fifth is the power chord, and that refusal to commit is why it sits over major and minor songs alike.
• The fourth, 5 semitones — a fifth turned upside down. Most adjacent string pairs in standard guitar tuning are a fourth apart, so your fretting hand already lives inside it.
• The major third, 4 semitones — bright and settled, the sound of a chord that has made up its mind.
• The minor third, 3 semitones — the same distance minus one fret, and noticeably darker.

The third earns the most attention, because it is the single note deciding whether a chord is major or minor while root and fifth stay put. Move one finger one fret and the character of the chord flips — a lot of leverage for a very small movement.

Be careful with the emotional vocabulary. Bright, dark, happy and sad are conventions of a listening culture, not properties of the air. Researchers played major and minor melodies to communities in Papua New Guinea with differing exposure to Western tonal music, and the major-sounds-happier response tracked that exposure rather than turning up everywhere — useful shorthand among players who share the habit, not physics.

The Major Scale Is a Pattern of Steps, Not a List of Notes

The major scale is seven steps in a fixed order — tone, tone, semitone, tone, tone, tone, semitone, which counted in semitones is 2-2-1-2-2-2-1 and sums to twelve, landing you back on the octave. The two small steps fall between the third and fourth degrees and between the seventh and the octave — that last one is why the seventh leans so hard toward home.

Because it is a pattern of distances rather than a set of names, it does not care where it starts. Begin on C and the spacing works out with no sharps or flats, the only reason C major gets called the easy one. Begin on G and one note has to move up a semitone to preserve the spacing. That is all a key is — the same seven-step shape planted on a different starting pitch.

On a fretted instrument this is the whole reason shapes are moveable. Frets are uniform semitones, so a major-scale fingering played two frets higher is still a major scale in a key two semitones up, and chord shapes behave the same way. Dropping a song three frets for a singer who cannot reach the top note is arithmetic, not a rewrite.

Minor Is the Same Notes With a Different Centre of Gravity

Natural minor uses the same twelve-note alphabet with the steps rearranged: 2-1-2-2-1-2-2. The small steps arrive earlier, between the second and third degrees and between the fifth and sixth, and that early flattened third is most of what your ear catches.

Here is the relationship worth internalising: every major scale already contains a natural minor built from exactly the same pitches, starting on its sixth degree — three semitones below the major root, or three frets down. C major and A minor are the same seven notes. Nothing is added or removed; only the note the music treats as home has moved.

A second route to minor keeps the root fixed and moves the notes instead. Lower the third, sixth and seventh of a major scale by a semitone each and you have the minor scale on that same starting pitch. Guitarists do this constantly without naming it — every time a major chord shape turns minor by lifting one finger back a fret.

What to Do With This on the Instrument

• Count frets, not letters — every interval here is a fret distance first. Note names are a labelling system you can add later.
• Learn the fifth and third by ear before the names — play a root, add the note seven frets up, then four, then three.
• Move one shape instead of memorising twelve — a scale or chord shape shifted up two frets is the same thing in a key two semitones higher.
• Look three frets down for the relative minor — the minor key sharing your major key's notes starts there, the cheapest place to find a darker section.
• Check the third when a chord sounds sour — root and fifth are forgiving, and the third is usually what is fighting the vocal or the other guitar.
• Never expect an interval to carry a mood alone — tempo, dynamics and timbre do as much work, and the emotional labels are learned.