Octave

As explained in Learn Haskell by Example

An octave is a musical interval spanning a frequency ratio of two to one.

An octave is a pitch interval in which frequency doubles when ascending or halves when descending. In 12-tone equal temperament, it spans 12 semitones. section 10.4.1

Checking octave calculations

Using the semitone representation, concert A is 440 Hz: 12 semitones higher is 880 Hz, and 12 semitones lower is 220 Hz. A note 12 semitones above another retains the same frequency ratio. section 10.4.1

Figure 10.8 Formula to compute the frequency (f) from a given semitone distance to concert A (s) in 12-tone equal temperament

The frequency formula connects a semitone distance from concert A with octave doubling in 12-tone equal temperament. section 10.4.1

How Learn Haskell by Example covers it

How deep it goes

Defines octave doubling and halving, then checks it through semitone calculations and a proposed QuickCheck property.

Examples

Uses concert A at 440 Hz, semitone offsets of 12 and −12, and GHCi frequency calculations.

What it assumes

Assumes basic musical pitch terminology while teaching semitone-based frequency conversion from concert A.

What you can do after

Apply octave relationships through Haskell frequency calculations and test them as formal properties.

How it connects

Connects octaves with semitones, frequency, chromatic notes, pitch, and 12-tone equal temperament.

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Also explained in

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  Learn Generative AI with PyTorchThe distance between one level of musical pitch and the next, where frequencies double from one octave to the next.

Compare how 2 books explain octave →

This explainer was generated by Manning's knowledge graph from the text of Learn Haskell by Example. The section links point to the parts of the book it draws on.