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.
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Glossary
Articles
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.
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.
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
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.
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.
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
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.
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
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.
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.
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
Suspended Chords: Sus2 and Sus4 Explained
A sus chord swaps the third of a triad for the second or fourth. Here is what Csus2 and Csus4 contain, why neither is major or minor, and how they resolve.
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.
Music History
From Ars Nova to the Renaissance: How Notation Changed Music
Rhythm took two centuries longer than pitch to notate. Mensural notation solved it with ratios, and the Renaissance then replaced black ink with white.
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.
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.
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.
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.
Harmony
Cadences: How Phrases End in Tonal Music
Authentic, half, plagal and deceptive cadences, and the real reason a close sounds strong: what happens in the bass, the top voice and the metre.
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.
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.
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.
Fundamentals
Circle of Fifths Explained: Keys, Signatures, Changes
The circle of fifths organizes every key by signature and closeness. How to read it, memorize it, and use it for modulation and chord choice.
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
Instrument Ranges for Arrangers: Playable, Comfortable, Usable
A playable range and a usable register are different facts. Transposition arithmetic, endurance, doubling, and the notes that are another instrument.
Guitar & Fretboard
Guitar Fretboard Note Names: Learn the Neck String by String
Every fret is one semitone, so the fretboard is a grid of note names. This covers standard tuning, the landmark frets and a two-week routine for learning the whole neck.
Orchestration
Reading an Orchestral Score: Layout and a Method for First Reads
An orchestral score stacks every part on one page. This covers the standard order of the families, the brackets and clefs, and a first-read method.
Fundamentals
Church Modes From Dorian to Locrian: A Practical Guide
Dorian, Phrygian, Lydian, Mixolydian, Aeolian and Locrian explained by pattern and color, with hearing tips and modern uses.
Intervals
- Perfect fifthThe perfect fifth spans seven semitones with a just ratio of 3:2, an open, stable interval at the core of major and minor triads.
- Perfect fourthThe perfect fourth spans five semitones with a just ratio of 4:3, an open interval whose stability depends on which note sits in the bass.
- Perfect octaveThe perfect octave spans twelve semitones at the ratio 2:1, and the two notes share a name, making it the most stable interval after the unison.
- Perfect unisonThe perfect unison is two notes at the same pitch, with zero semitones and a ratio of 1:1, and it is the baseline for measuring every other interval.