Intervals · Exhibit
Hear every interval
in the octave.
Pick an interval. How far pure ratio sits from equal steps changes from one to the next.
Reading P5 and m3
The number counts letter names from the lower note, both ends included. The letter in front, m or M or P, names the size.
Perfect fifth
The switch above plays bare test tones in the tuning you press. A reedy tone carries partials, so the two notes can share one. Listen for the width, and for beating when pure ratio and equal steps differ.The tuning switch uses bare test tones. Listen for width and for beating when pure ratio and equal steps differ; that gap is the keyboard compromise.
This 3:2 tuning sounds 1.96 cents above written E4. Cents split the octave into 1,200 equal parts, so a step between neighbouring keys measures 100. The notehead leaves that tuning gap to your ear.
Reading the labels
How the names work
C up to E covers C, D and E, so that pair makes a third. Thirds, sixths, seconds and sevenths come in major and minor, a wider form and a narrower one. Unisons, fourths, fifths and octaves have one form each, and medieval theory called them perfect because they were the blends it counted as stable. The name outlived the theory. The tritone is named for its width, three whole tones, and it is the one interval that splits the octave in half. Its code on the rail is A4 for augmented fourth, or d5 for diminished fifth.
Pure ratio and Equal steps name both systems on the switch and the notes rail. Pure upper and Equal upper give the higher note in each system. Pure ratio uses whole-number interval ratios (just intonation). Equal steps split the octave into twelve equal parts (12-TET), and each part is a semitone. Two cents is a fiftieth of a semitone and slips past most ears. A pure major third sits 13.69 cents under its keyboard neighbour. The Hear both tunings at once button sounds both upper notes together, which turns that gap into audible beating.
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