Ear Training & Practice
Ear Training for Intervals: A Method You Can Practise Daily
Interval recognition comes faster with a method: three intervals tied to a tonic, sung before they are named, and a short daily routine you can keep.
Search
Type a chord symbol or a scale name and go straight to it, or search tools, glossary terms and every article. Results are ranked by where the words appear.
Glossary
- IntervalThe distance between two pitches, measured by the number of letter names it spans and by the number of…
- Interval inversionReversing an interval by moving its lower note up an octave, which turns a third into a sixth and a fifth…
- Augmented intervalAn interval one semitone wider than a major or perfect interval with the same letter names, such as F to B.
- Compound intervalAn interval larger than an octave, such as a tenth or twelfth, made of a simple interval plus one or more…
- Diminished intervalAn interval one semitone narrower than a perfect or minor interval with the same letter names, such as B to F.
- Major intervalA second, third, sixth or seventh that spans the number of semitones found in the major scale on its lower…
- Minor intervalA second, third, sixth or seventh one semitone smaller than the major interval with the same letter names.
- Perfect intervalA unison, fourth, fifth or octave, which has one standard size and becomes augmented or diminished when…
Articles
Tuning & Temperament
Just Intonation, Beating and Why Intervals Sound in Tune
Pure intervals come from small whole-number ratios, and beating is what stops them sounding pure. What just intonation gives, and what it cannot fix.
Fundamentals
Reading Intervals at Sight: Generic and Specific
Naming an interval at sight takes two passes: count the staff positions first, then judge what the accidental does to the size.
Harmony
Figured Bass: Reading Intervals Above the Bass Line
Figures name intervals above the bass, not chords. What each shorthand means, how accidentals override the key, and what the player decides.
Tuning & Temperament
Equal Temperament: What It Costs and What It Buys
Twelve equal semitones solve the problem pure intervals create. The cost is small in fifths, large in thirds, and paid by every fixed-pitch instrument.
Counterpoint
Parallel Fifths and Octaves: Why the Rule Exists
Parallel fifths and octaves are voices that move together and keep a perfect interval. Here is why strict voice leading forbids them and where the rule bends.
Tuning & Temperament
Pythagorean Tuning: How Stacked Pure Fifths Build a Scale
Pythagorean tuning builds every interval from pure 3:2 fifths. Here is the seven-note scale it produces, its whole tones and semitones in cents, and the wolf fifth it leaves behind.
Orchestration
Transposing Instruments Explained: Written and Sounding Pitch
A transposing instrument sounds a different pitch from the one on the page. The intervals for common instruments, and how to transpose a part.
Tuning & Temperament
What Are Cents? The Unit That Measures Small Pitch Differences
A cent is one hundredth of an equal-tempered semitone. Here is the formula, what the common intervals measure in cents, and what a tuner is showing you.
Counterpoint
Canon Types and Techniques: Rounds to Crab Canons
Strict and free canon, interval and time distance, inversion and crab canons: how canons work and how to write a singable one.
Fundamentals
The Major Scale Formula: Whole and Half Steps Explained
The major scale is seven notes spaced whole, whole, half, whole, whole, whole, half. Here is the formula, four scales built from it, and the sharps and flats it forces.
Acoustics & Sound
The Harmonic Series: Why Octaves, Fifths and Thirds Come First
A vibrating string or air column sounds a fundamental and a set of partials at whole-number multiples of it. Here are the first sixteen, their cents, and where they differ from equal temperament.
Counterpoint
Types of Motion in Voice Leading: Parallel, Contrary, Oblique
Parallel, similar, oblique and contrary motion defined between two voices, what each does to their independence, and which one counterpoint prefers.
Counterpoint
First Species Counterpoint, Rule by Rule
Species counterpoint isolates one compositional decision at a time. First species isolates the hardest one: how to make two voices sound like two voices.
Counterpoint
Fugue Subjects and Answers
A fugue's opening notes commit the piece to more than a tune. The subject's shape and the answer's adjustment decide what can happen next.
Counterpoint
Imitation and Invertible Counterpoint
Imitation makes one idea serve two lines. Invertible counterpoint makes those lines interchangeable, and the arithmetic behind it is small enough to check.
Tuning & Temperament
Meantone and Well Temperament: Why Keys Used to Sound Different
Quarter-comma meantone, the wolf fifth and the well temperaments in between: what keyboard tuning did to each key before equal temperament settled the argument.
Music History
After Tonality: What Composers Replaced It With
When chromatic harmony outgrew the tonal hierarchy, composers tried serial rules, rhythm, folk modes, and sound mass. What each method actually solved.
Fundamentals
Scale Degrees Explained: Numbers, Names and Solfège
Scale degrees number each note of a scale from its tonic, and solfège names the same positions do, re, mi. Degree names, movable and fixed do, and why degrees travel between keys.
Fundamentals
Pentatonic and Blues Scales: Patterns With a Purpose
Major and minor pentatonics plus the blues scale: the patterns, the blue notes, and why five notes carry so much melody.
Fundamentals
Clefs and Transposition: What Players Actually Read
A clef fixes one pitch and the staff follows. Transposing instruments move it again, so the same written note reaches the audience at different pitches.
Harmony
Roman Numeral Analysis: How to Label a Chord Progression
Roman numerals label each chord by the scale degree of its root and its quality. Here is a step-by-step method, with I vi IV V worked in C and G.
Harmony
Seventh Chords and How They Resolve in Tonal Harmony
The chordal seventh falls, the leading tone rises, and the tritone at the centre of V7 resolves by step. What each diatonic seventh chord is for.
Jazz & Popular Harmony
Chord Extensions Explained: Ninths, Elevenths and Thirteenths
Ninths, elevenths and thirteenths are chord tones stacked above the seventh. Which of them fit a chord depends on its quality, and some clash with the third.
Songwriting & Composition
How to Write a Melody Over Chords, Note by Note
Put chord tones on strong beats, approach tension notes by step, and keep the line singable. A worked melody over C, G, Am and F shows each choice.
Jazz & Popular Harmony
Jazz Chord Voicings: Shell and Rootless Voicings Explained
Shell and rootless voicings keep the third and seventh of each chord and leave room for a bass player. Worked examples use Dm7, G7 and Cmaj7.
Harmony
Borrowed Chords: Modal Mixture in Practice
Mixture borrows chords from the parallel mode. What the common borrowed chords do to a phrase, how they resolve, and where labelling fails.
Orchestration
Voicing a String Quartet: Registers, Doublings, Weight
The quartet is four registers, not four violins. What each instrument can sustain, where the texture muddies, and which double stops lie under the hand.
Harmony
Voice Leading: Why the Rules Exist in Four-Part Writing
Parallel fifths, tendency tones, spacing and doubling, read as solutions to one problem: keeping four lines heard as four lines.
Guitar & Fretboard
Capo and Transposition: How a Capo Changes the Key
A capo raises every open string by one semitone per fret, so a G shape played at fret 2 sounds in A. This shows how to find the sounding key and how to choose a capo position.
Pages
Intervals
- Major secondThe major second is a whole tone of two semitones, with a just ratio of 9:8, and it is the step between most neighbouring degrees of the major scale.
- Major seventhThe major seventh spans eleven semitones with a just ratio of 15:8, a sharp dissonance that the ear hears as a leading tone pulling toward the octave.
- Major sixthThe major sixth spans nine semitones with a just ratio of 5:3, an open imperfect consonance that sounds bright and lifted.
- Major thirdThe major third spans four semitones with a just ratio of 5:4, the bright imperfect consonance that gives major chords their sound.
- Minor secondThe minor second spans one semitone with a just ratio of 16:15, the narrowest step used in Western tonal music.
- Minor seventhThe minor seventh spans ten semitones with a just ratio of 9:5, a dissonance that sounds unresolved at the top of the dominant seventh chord.
- Minor sixthThe minor sixth spans eight semitones with a just ratio of 8:5, a dark imperfect consonance that inverts to the major third.
- Minor thirdThe minor third spans three semitones with a just ratio of 6:5, the darker of the two thirds and the interval that gives minor triads their colour.