Western theory

Shared foundations for pitch, intervals, scales, keys, modes, harmony, and rhythm. Next layer: Advanced theory. Rooms apply these ideas — Piano, Guitar, Ukulele, Bass. Mirror: theory.md. Companion: Eastern · East ↔ West.

Pitch

Pitch is how high or low a tone sounds. Western tonal music builds from a 12-tone chromatic octave. An octave is the span where frequency doubles (A4 = 440 Hz → A5 = 880 Hz) — same letter name, higher register.

Twelve tones in an octave

Every adjacent step on a piano (including black keys) is a half step (semitone). One octave holds 12 half steps:

• Whole step (W) = 2 half steps · Half step (H) = 1
• Sharps (♯) raise a letter by one half step; flats (♭) lower it.
• Enharmonic spellings name the same sounding pitch (F♯ = G♭ on the piano) — the spelling you choose depends on key and voice-leading.
• There is no black key between E–F or B–C — those pairs are already a half step apart.

Equal temperament

Modern fretted instruments and pianos usually use 12-tone equal temperament: the octave divides into 12 equal ratios. Pure “just” intervals are slightly compromised so every key is usable and you can modulate freely. (Eastern śruti maps often keep just ratios against a drone — different job, same ear.)

Octave and register

Scientific pitch labels the octave number: Middle C = C4. Same letter in the next octave = same pitch class, different height. Guitar TAB and bass often count frets instead of octave numbers — the pitch idea is the same.

Intervals

An interval is the distance between two pitches. Count the letter names inclusive for the number (C–E is a third), then check half-steps for the quality (major, minor, perfect, diminished, augmented).

Why fifths matter: a perfect fifth (7 half steps) is the step the circle of fifths is built on. Stack fifths and you visit every pitch class once before returning home. Interval = distance; scale degree = that pitch’s numbered seat once a tonic is chosen.

Interval inversion

Turn an interval upside-down: keep the same two pitch classes, but put the lower note on top (or move the upper note down an octave). Number + quality swap so the pair still adds to a ninth: 2nd ↔ 7th, 3rd ↔ 6th, 4th ↔ 5th, unison ↔ octave.

Quality rule: major ↔ minor, augmented ↔ diminished, perfect stays perfect. Half-steps in the pair always add to 12 (an octave).

Scales

A scale is an ordered set of pitches — the palette a melody or chord progression draws from. The tonic (degree 1) is home.

Major and natural minor

Major follows W–W–H–W–W–W–H on the chromatic row. From C: the scale lands only on the filled cells — it jumps over C♯ to reach D, over D♯ to reach E, then steps half to F, and so on.

Start the same pattern on another tonic and accidentals appear (G major needs F♯ to keep W–W–H…).

Natural minor = W–H–W–W–H–W–W. Parallel to C major is C natural minor (♭3, ♭6, ♭7). Compared with C major, E / A / B drop a half step to E♭ / A♭ / B♭ — so the half steps sit in different places.

Scale degrees

A scale degree is a pitch’s address in a scale — which step of this scale it is, counting from the tonic as 1. An interval is only the distance between two pitches, with no scale required.

Relative vs parallel

• Relative major/minor — same seven notes, different tonic (C major ↔ A minor).
• Parallel major/minor — same tonic, different formula (C major vs C minor).

Beyond major / natural minor

Each of these is a small edit of major or natural minor — change a degree or drop a couple of notes, and the colour shifts.

Circle of fifths

Yes — that’s exactly what it shows. Each slice is a major key. The little label under the key name is its key signature: how many sharps or flats you need to build that major scale.

• C = 0 (no sharps or flats)
• G = 1♯ (only F♯) · D = 2♯ (F♯ and C♯) · and so on clockwise
• The other way: F = 1♭ · B♭ = 2♭ · …

Moving one step clockwise = up a perfect fifth = add one sharp. One step counter-clockwise = add one flat. The inner ring is the relative minor that shares that same signature (G major and E minor both use 1♯).

How to read the wheel

Read any outer slice as: “This major key’s scale needs this many sharps or flats.” Example: find G → label 1♯ → G major = G A B C D E F♯. Find D → 2♯ → D major keeps F♯ and adds C♯.

• Clockwise (sharps): C (0) → G (1♯) → D (2♯) → A (3♯) → E (4♯) → B (5♯) → F♯/G♭ (6)
• Counter-clockwise (flats): C (0) → F (1♭) → B♭ (2♭) → E♭ (3♭) → A♭ (4♭) → D♭ (5♭) → G♭/F♯ (6)
• Sharps appear in order F C G D A E B; flats reverse B E A D G C F.
• Bottom of the circle: F♯ (6 sharps) and G♭ (6 flats) are the same piano keys spelled two ways.

Why each step adds one accidental

Build a major scale on a root a fifth higher than the previous tonic. Six notes stay the same; one must rise to keep W–W–H–W–W–W–H:

• C major = C D E F G A B — none.
• Up a fifth → G major = G A B C D E F♯.
• Up again → D major = D E F♯ G A B C♯ (F♯ carries over).

Going the flat way (down a fifth / up a fourth) flattens one note each step: C → F adds B♭; F → B♭ adds E♭; and so on.

Relative minors — the inner ring

Every major key shares its seven notes with a minor key on degree 6 (or down three half steps from the major tonic): C ↔ Am, G ↔ Em, F ↔ Dm. Same key signature; only home changes.

Neighbours = IV and V

For any major key, the neighbour counter-clockwise is IV and clockwise is V. Those neighbours (plus the relative minors on the inner ring) are the backbone of the diatonic chords in a key — I, IV, V and vi, ii, iii. Strong cadences (V→I, ii→V→I) move toward home along the circle — often felt as falling fifths (full labels on Advanced · cadences).

How to read a key signature

A key signature is the cluster of sharps or flats at the start of the staff. You do not need the circle every time — two glance rules name the major key:

• Sharps: the major tonic is a half step above the last sharp (the rightmost sharp = Ti / scale degree 7). Example: last sharp is F♯ → tonic is G. Last sharp C♯ → tonic D.
• Flats: the major tonic is the second-to-last flat (the last flat = Fa / degree 4). Example: B♭ E♭ → second-to-last is B♭ → tonic B♭. One flat only (B♭) → tonic F.

Relative minor = same signature, home on degree 6 of that major (or down a minor third). Order of sharps F C G D A E B; flats B E A D G C F. See also the circle of fifths.

Modes

A mode is a seven-note scale with a characteristic colour. Two ways to meet the same seven mode formulas:

• Relative — keep one parent major’s notes; move home to a different degree.
• Parallel — keep the same tonic (e.g. always C); change which degrees are sharp/flat vs major.

Relative modes (parent = C major)

Same seven notes C D E F G A B; only the starting pitch changes.

Parallel modes (all on C)

Same tonic C every time. Compared with C major (C D E F G A B), the formula says which degrees to raise or flatten. That is usually the easier way to build a mode on an instrument.

Same formula, two stories: “D Dorian” in the relative table (notes of C major starting on D) uses the same pattern as “C Dorian” here (1 2 ♭3 4 5 6 ♭7) — only the tonic letter changes. Parallel is “fix the root, edit the major scale”; relative is “keep the white keys, move home.”

Chords

A chord is three or more notes sounded together — usually stacked thirds from a root. Harmony is how chords move; melody often outlines chord tones.

Triads

Also common: sus2 R–2–5, sus4 R–4–5 (no third — ambiguous major/minor), power chord R–5 (rock / metal).

Sevenths (essentials)

Qualities alone are not enough for songs — next: which chords belong together in one key.

Chords in a key — Roman numerals

The chords that use only the notes of a scale are the diatonic (or relative) chords of that key. Label them with Roman numerals so the same progression works in every key: I–V–vi–IV in C is C–G–Am–F; in G it is G–D–Em–C.

How to build them

Write the major scale. On each degree, stack every other note (root–3rd–5th) using only scale tones — that triad is the chord “of” that degree:

Those stacks are not the same quality. In a major key the pattern is always:

• Uppercase = major triad (I, IV, V)
• Lowercase = minor triad (ii, iii, vi)
• ° (diminished) = vii° (tense; often skipped in beginner song charts)

Full map — C major

Primary chords: I, IV, V (enough for folk, blues, many hymns). Secondary / relative chords: ii, iii, vi (and vii°) — still in the key, used for colour and common loops. “Relative” here means relative to the key, not a new accidental set.

Same chords, relative minor

A minor shares C major’s seven notes — so it shares the same seven triads. Only home changes: Am becomes i, C becomes III, and so on. Beginner charts often stay in major numerals first; minor-key spellings (and the raised leading-tone V) are on Advanced theory · Roman numerals in minor.

Any key — same pattern

Keep the numeral qualities; rename the roots. Example G major (one sharp: F♯):

Drill: pick a major key from the circle, write its scale, stack thirds on each degree, check that you get maj–min–min–maj–maj–min–dim. Neighbours on the circle are again IV (counter-clockwise) and V (clockwise).

Common loops (major)

Numbers travel; letter names do not. Learn progressions as numerals, then plug in the key. Next: how bass position changes the same chord (inversions). Phrase endings and chord “jobs” live on Advanced · cadences and function (short teasers below).

Chord inversions

Same three (or four) chord tones; a different note is in the bass. Pop/jazz write this with a slash: chord / bass note.

Seventh chords also have a 3rd inversion (7th in the bass), e.g. G7/F. Inversions smooth bass lines and keep common tones between chords — the ear still hears the same harmony if the upper notes spell the chord.

Cadences (teaser)

A cadence is how a phrase ends — harmonic punctuation. Four everyday labels (in C): V→I authentic (strong close), …→V half (hangs open), IV→I plagal (“Amen”), V→vi deceptive (expects I, gets vi).

PAC vs IAC, hearing tips, minor cadences, and how phrases use them belong on Advanced theory · Cadences — they sit with form and secondary dominants, not the foundations map.

Functional harmony (teaser)

Once you know the Roman-numeral map, each chord has a job: tonic (I · vi) = home · predominant (IV · ii) = leave home / set up V · dominant (V · V7 · vii°) = tension that wants I. Classic sentence: tonic → predominant → dominant → tonic (I–IV–V–I).

Why V pulls, substitutions, and mapping pop loops to jobs live on Advanced theory · Function.

Note values

Rhythm is how long sounds and silences last. In 4/4, the quarter note is one beat and a bar holds four beats.

• A dot after a note adds half its value (dotted half = 3 beats in 4/4).
• A rest is silence for the same length as the matching note.
• A tie joins same-pitch notes across a barline or beat.
• Count: 1 2 3 4 · eighths 1 & 2 &… · sixteenths 1 e & a….

Syncopation & ties

Syncopation accents a weak beat or the “and” of a beat — off the expected pulse. A tie holds a pitch across a beat or barline so the attack lands early and the sound continues into a strong beat (common in pop, jazz, and funk).

• In 4/4, accents on & of 2 and 4, or a tied note into beat 1, feel syncopated.
• Count aloud while you clap the written rhythm; then play it.
• Room drills: strumming / groove pages teach this by feel — theory just names it.

Time signatures

• Top = how many beats in a bar · Bottom = which note gets one beat (4 = quarter note).
• Simple meters (beat divides in two): 4/4, 3/4, 2/4, 2/2 (cut time).
• Compound (pulse felt in three): 6/8, 9/8, 12/8 — often counted as two/three/four dotted-quarter pulses.
• Odd meters: name the grouping (5/4 as 3+2 or 2+3; 7/8 often 2+2+3).

Solfège (movable Do)

Optional bridge to the singing room: name scale degrees with syllables so the ear learns function, not only letter names.

Movable Do: Do = whatever tonic you chose (like Sa in Eastern theory). Fixed Do: Do always means the pitch C — useful in some classical training, less common in pop pedagogy. Accidentals get altered syllables (Fi = ♯4, etc.).

Reading notation

Western music is written on a staff of five lines and four spaces. The clef at the start tells you which pitch each line/space means. Rhythm (how long) lives in note shapes and rests — covered under note values and time signatures. This section is where the pitch sits and the common expression marks.

Staff, clefs, Middle C

• Lines and spaces are counted from the bottom up.
• Treble clef (G-clef) — curls around the second line = G above Middle C. Higher melody / right-hand piano / guitar written pitch.
• Bass clef (F-clef) — two dots around the fourth line = F below Middle C. Lower register / left-hand piano / bass.
• Middle C sits on a short ledger line: one line below the treble staff, or one line above the bass staff. Same pitch.
• Grand staff = treble + bass joined by a brace (piano). Read the clef of each staff before naming the note.

Mnemonics help at first (“Every Good Boy…”, “FACE”); drop them once your eye knows landmarks (treble G line, bass F line, Middle C). C clefs (alto / tenor) are on Advanced theory.

Ledger lines & accidentals

• Ledger lines extend the staff one note at a time above or below — same spacing as staff lines. Count from the nearest staff edge.
• A sharp ♯, flat ♭, or natural ♮ before a notehead alters that pitch for the rest of the bar (unless cancelled). The key signature at the start applies to every bar.
• Letter name = line/space + clef; accidental = which piano key of that letter.

What sits at the start of a piece

1. Clef — which pitch map.
2. Key signature — which notes are always ♯ or ♭ (how to read it).
3. Time signature — beats per bar (meter).

Then the music: noteheads on lines/spaces, stems, beams, rests, barlines. Duration is the note-value system you already learned — reading is “pitch location + duration + expression.”

Dynamics, tempo, articulation

Barlines & common road signs

• Barline ends a measure; double bar often ends a section; final bar (thin + thick) ends the piece.
• Repeat signs ‖: :‖ — play the enclosed music again.
• 1st / 2nd endings — first time take ending 1; on the repeat, skip to ending 2.
• D.C. / D.S. — return to the beginning / to the sign; often with al Fine (end at Fine) or al Coda.

TAB vs staff

TAB (guitar, bass, ukulele) shows where to put fingers — one line per string, numbers = frets. It does not by itself show rhythm or that the same pitch can be fretted in several places. Staff shows pitch and duration and works across instruments. Best habit: read both when a method book prints them together; use TAB for speed in room drills, staff when you need portable pitch.

How to practise reading: name one note at a time (clef first) → add rhythm counting → then hands/frets. Room pages below are the interactive drills.

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