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Compare Pitches in an Octave
Calculator for the comparison of two tone pitches with a given distance of semitones. An octave has 12 semitones or half steps. When two tones have the distance of one octave, one tone has twice the frequency (pitch) of the other. The first tone of an octave here is labeled 1, the last 12. So 13 is the first tone of the next octave. The ratio between two neighboring tones is roughly 1.06.
Please enter two values, the third will be calculated.
Example: a fifth spans 7 semitones, e.g. tone 1 to tone 8. Tone 8 is almost 1.5 times higher than tone 1.
The term octave comes from Latin, octava meaning the eighth, and originally refers to the eight degrees of a diatonic scale. In Western music, however, an octave comprises twelve semitones: C - C-sharp (or D-flat) - D - D-sharp (or E-flat) - E - F - F-sharp (or G-flat) - G - G-sharp (or A-flat) - A - A-sharp (or B-flat) - B - C.
C, D, and so on are the fundamental notes. C-sharp, D-sharp, and the like are altered notes. With the five altered notes and seven fundamental notes, there are the 12 semitones of an octave, from C to the next C, which already belongs to the next octave. There are no additional notes between two degrees, E-F and B-C.
Mathematically, an octave describes a frequency ratio of two to one. If you double the vibration frequency of a note, it sounds the same note one octave higher. Each semitone corresponds to a frequency ratio of the twelfth root of two, which is approximately 1.05946. Thus, the pitch of C-sharp is 1.05946 times higher than that of the C below it. So the tonal system is also logarithmically structured, because the intervals grow exponentially, not linearly.
The discovery that harmonic intervals arise from simple numerical relationships goes back to Pythagoras.
Last updated on 10/06/2025. Author: Jürgen Kummer
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