The Circle of Fifths The Circle of Fifths Tony R. Kuphaldt A G F E D C B A A G A G F G F E F# E D E D C D C C The Circle Bb B A A G G F F# E E D D Why Theory? C C C major F G major major Purpose A A G G F F# Eb E D D C C# Bb B A A G G Assumptions F F# Eb E D b D C B D C# Intervals major major Scales Ab A G G# F F# Eb E D b D C C# Bb E A B Tension and Ab A G G# F major major F# Eb E D D Resolution C C# Keys Ab E Ab A Building the G G# F major major F# Eb E Db D# C C# Circle Bb B Ab A G G# F F# Eb E Db D# C C# So What? C#/Db B/Cb major major F#/Gb Ab A# Circle of tones Gb G# F major F# Eb E Db D# C C# Bb B Ab A# Gb A# G# F G# F# Circle of Eb F# E Db E# D# C D# C# C# A# B Ab chords G# A# Gb F# G# Fb E# F# Eb D# E# Db C# D# Cb B# C# Bb A# Ab G# Ab Gb F# Gb Fb Circle of keys E# F Eb D# Eb Db C# Db Cb Bb Ab Gb F Eb Db Practice Ideas Cb Glossary Copyright The Circle of Fifths Tony R. Kuphaldt The Circle Why Study Music Theory? Why Theory? Purpose Many extremely proficient musicians play quite well with little Assumptions or no knowledge of music theory, so why study it? Intervals Scales The answer is very practical and very simple: music theory Tension and saves you from having to learn by trial and error, and that Resolution makes the learning process faster! Keys Building the Circle This tutorial begins with a review of intervals, scales, and keys. So What? After that, it explores how the Circle of Fifths is constructed Circle of tones and what it means. Circle of chords Circle of keys Practice Ideas Glossary Copyright The Circle of Fifths Tony R. Kuphaldt The Purpose of This Tutorial The Circle Why Theory? This tutorial will teach you to understand the meaning of the Purpose Circle of Fifths. Mastering these concepts will enable you to: Assumptions Intervals • More easily find the right tones when playing by ear Scales • Identify the “key” of a tune or song from the number of Tension and Resolution sharps or flats in the key signature Keys Building the You will maximize your learning by experimenting with all these Circle So What? concepts on your instrument(s) while you read the tutorial. Circle of tones Any text set in italicized red denotes an exercise recommended Circle of for immediate application or a question for you to answer. chords Circle of keys Practice Ideas Glossary Copyright The Circle of Fifths Tony R. Kuphaldt The Circle Why Theory? Starting Assumptions Purpose Assumptions This tutorial assumes prior knowledge of certain music theory Intervals topics, including intervals, scales, and keys. A review of these Scales topics precedes the main tutorial on the Circle of Fifths. Tension and Resolution This tutorial also assumes a context of Western music, Keys particularly the common genres of folk and classical. In other Building the Circle words, nothing too crazy . So What? Circle of tones Circle of chords Circle of keys Practice Ideas Glossary Copyright The Circle of Fifths Tony R. Kuphaldt Intervals The Circle 1 Why Theory? A musical interval is the difference in pitch between two Purpose tones. The basic unit of measurement for intervals is the step. Assumptions Intervals One half-step is the difference in pitch between two successive Scales frets on a guitar, or between two immediately adjacent keys on Tension and a piano. When we modify a natural tone to make it either Resolution “sharp” or “flat” we are applying a half-step interval. Keys Building the Circle One whole-step is equal to two half-steps: a distance of two So What? frets on a guitar, or two keys on a piano with one key in Circle of tones between. Circle of chords Whole- and half-steps are alternatively referred to as Circle of keys whole-tone and semi-tone intervals. Practice Ideas Glossary 1 Copyright Mathematically, an interval is a ratio of pitch frequencies. The Circle of Fifths Tony R. Kuphaldt Half- and whole-step examples The Circle Why Theory? Whole Purpose step Piano Whole step Assumptions keyboard Intervals Guitar fretboard Scales Tension and Resolution Half Half Whole Keys step step step Half Half Whole Building the step step step Circle So What? Try playing half-step and whole-step intervals on your Circle of tones instrument to explore what they sound like! Circle of chords Circle of keys How many steps are in one octave (i.e. the point at which the Practice Ideas tone-letters repeat)? Prove it by playing a one-octave interval Glossary on your instrument! Copyright The Circle of Fifths Tony R. 2 Kuphaldt Intervals through one octave The Circle Each octave is a doubling of pitch, which is why you get an Why Theory? octave tone when you fret a string at half-length. Purpose Assumptions Steps Interval name Symbol Approximate pitch ratio Intervals (none) Perfect Unison P1 20/12 = 1.000 or 1:1 H Minor Second m2 21/12 = 1.059 ≈ 16:15 Scales W Major Second M2 22/12 = 1.122 ≈ 9:8 Tension and W+H Minor Third m3 23/12 = 1.189 ≈ 6:5 Resolution 2W Major Third M3 24/12 = 1.2599 ≈ 5:4 Keys 2W+H Perfect Fourth P4 25/12 = 1.335 ≈ 4:3 Augmented Fourth Building the aug4 6/12 3W (a.k.a. "tri-tone") 2 = 1.414 ≈ 17:12 Circle Diminished Fifth dim5 7/12 ≈ So What? 3W+H Perfect Fifth P5 2 = 1.498 3:2 4W Minor Sixth m6 28/12 = 1.587 ≈ 8:5 Circle of tones 4W+H Major Sixth M6 29/12 = 1.682 ≈ 5:3 Circle of 5W Minor Seventh m7 210/12 = 1.782 ≈ 9:5 chords 5W+H Major Seventh M7 211/12 = 1.888 ≈ 15:8 Circle of keys 6W Perfect Octave P8 212/12 = 2.000 or 2:1 Practice Ideas Glossary 2Pitch ratios vary slightly according to how the instrument is Copyright constructed and tuned, an advanced concept called temperament. The Circle of Fifths Tony R. Kuphaldt Intervals define melodies The Circle Why Theory? The defining tonal characteristic of any melody are the Purpose intervals between successive tones. The actual tones don’t Assumptions Intervals matter so long as the intervals remain unchanged. Scales Try playing the first few tones of “Mary Had A Little Lamb” Tension and Resolution beginning with E: E-D-C-D-E-E-E Keys Building the Now try playing the same sequence of intervals beginning with Circle B instead of E: B-A-G-A-B-B-B So What? Circle of tones In either case the melody is still “Mary Had A Little Lamb” Circle of chords despite using completely different tones because the same Circle of keys intervals (whole-steps) are used in each case! Practice Ideas Glossary Copyright The Circle of Fifths Tony R. Kuphaldt Scales The Circle Why Theory? Purpose A scale is a particular sequence of tones played in either Assumptions ascending or descending order of pitch. Any such sequence is Intervals fair to call a “scale,” but some scales are more common than Scales others. Tension and Resolution Keys Examples of common scale types include major, natural minor, Building the and harmonic minor. Circle So What? The pattern of intervals between scale-tones defines the quality Circle of tones (major, minor) of that scale. Every major scale, for example, Circle of chords exhibits the exact same interval pattern between its tones. Circle of keys Practice Ideas Glossary Copyright The Circle of Fifths Tony R. Kuphaldt Major scales The Circle Major scales follow the interval3 sequence W-W-H-W-W-W-H. Why Theory? C major and F-sharp major are shown as examples: Purpose Assumptions C major scale: Intervals Scales CDEFGABC Tension and Resolution Whole Whole Half Whole Whole Whole Half Keys step step step step step step step Building the Circle # So What? F major scale: Circle of tones F# G# A# BC# D# E# F# Circle of chords Circle of keys Whole Whole Half Whole Whole Whole Half step step step step step step step Practice Ideas Glossary 3 Copyright W = Whole step ; H = Half step The Circle of Fifths Tony R. Kuphaldt Natural minor scales 4 The Circle Natural minor scales follow the interval sequence Why Theory? W-H-W-W-H-W-W. Again, C and F-sharp are shown as scale Purpose examples: Assumptions Intervals C natural minor scale: Scales C DEb FGAb Bb C Tension and Resolution Keys Whole Half Whole Whole Half Whole Whole step step step step step step step Building the Circle So What? F# natural minor scale: Circle of tones # # # # Circle of F G ABC DE F chords Circle of keys Whole Half Whole Whole Half Whole Whole Practice Ideas step step step step step step step Glossary 4 Copyright W = Whole step ; H = Half step The Circle of Fifths Tony R. Kuphaldt Harmonic minor scales 5 The Circle Harmonic minor scales follow the interval sequence Why Theory? W-H-W-W-H-(W+H)-H.