11.6 Musical Notes

Calc can convert between musical notes and their associated frequencies. Notes can be given using either scientific pitch notation or midi numbers. Since these note systems are basically logarithmic scales, Calc uses the l prefix for functions operating on notes.

Scientific pitch notation refers to a note by giving a letter A through G, possibly followed by a flat or sharp) with a subscript indicating an octave number. Each octave starts with C and ends with B and the octave numbered 0 was chosen to correspond to the lowest audible frequency. Using this system, middle C (about 261.625 Hz) corresponds to the note C in octave 4 and is denoted C₄. Any frequency can be described by giving a note plus an offset in cents (where a cent is a ratio of frequencies so that a semitone consists of 100 cents).

The midi note number system assigns numbers to notes so that C_-1 corresponds to the midi note number 0 and G₉ corresponds to the midi note number 127. A midi controller can have up to 128 keys and each midi note number from 0 to 127 corresponds to a possible key.

The l s (calc-spn) [spn] command converts either a frequency or a midi number to scientific pitch notation. For example, 500 Hz gets converted to B_4 + 21.3094853649 cents and 84 to C_6.

The l m (calc-midi) [midi] command converts either a frequency or a note given in scientific pitch notation to the corresponding midi number. For example, C_6 gets converted to 84 and 440 Hz to 69.

The l f (calc-freq) [freq] command converts either either a midi number or a note given in scientific pitch notation to the corresponding frequency. For example, Asharp_2 + 30 cents gets converted to 118.578040134 Hz and 55 to 195.99771799 Hz.

Since the frequencies of notes are not usually given exactly (and are typically irrational), the customizable variable calc-note-threshold determines how close (in cents) a frequency needs to be to a note to be recognized as that note (see Customizing Calc). This variable has a default value of 1. For example, middle C is approximately ‘261.625565302 Hz’; this frequency is often shortened to ‘261.625 Hz’. Without calc-note-threshold (or a value of ‘0’), Calc would convert 261.625 Hz to scientific pitch notation B_3 + 99.9962592773 cents; with the default value of 1, Calc converts 261.625 Hz to C_4.