pitch

Overview

440Hz Phase Increments pitch is determined by its position on the chromatic scale, which is a system of 12 notes that repeat in octaves. The distance between each pitch on the chromatic scale is a semitone, and each pitch represents a specific frequency measured in hertz (Hz).

pitch is an interval with a base frequency of 8.1757989156437 Hz that correspond to MIDI note 0 (which is an octave below F#0). pitch is represented by the MIDI value. Therefore, only positive values are valid.

pitch includes construction from frequency as well as numeric values representing the absolute position in the chromatic scale from the base frequency. pitch also includes conversions to frequency.

Conversions to and from frequency utilize fast log2 and pow2 computations using fast math functions.

Include

#include <q/support/pitch.hpp>

Declaration

struct pitch : interval
{
   constexpr static auto base_frequency = frequency{8.1757989156437};

   constexpr            pitch();
   explicit             pitch(frequency f);

   constexpr bool       valid() const;

   // These operations do not make sense and are not allowed.
   pitch&               operator+=(pitch) = delete;
   pitch&               operator-=(pitch) = delete;
};

// Free functions
frequency         as_frequency(pitch n);
float             as_float(pitch n);
double            as_double(pitch n);

constexpr pitch   round(pitch n);
constexpr pitch   ceil(pitch n);
constexpr pitch   floor(pitch n);

// These operations do not make sense and are not allowed.
pitch operator+(pitch, pitch) = delete;
pitch operator-(pitch, pitch) = delete;

Expressions

In addition to valid expressions for interval, pitch allows these expressions.

Notation

p, a, b

Objects of type pitch

f

Object of type frequency

Constructors

Expression Semantics

pitch(f)

Construct a pitch from frequency f.

pitch()

Default construct a pitch. The result is an invalid pitch by default where p.rep == -1.0.
C++ brace initialization may also be used.

Conversions

Expression Semantics Return Type

as_float(p)

Convert pitch to a float.

float

as_double(p)

Convert pitch to a double.

double

as_frequency(p)

Convert pitch to a frequency.

frequency

Functions

Expression Semantics Return Type

p.valid()

Returns true if p is valid. p is valid if p.rep >= 0.0

bool

round(p)

Rounds p to the nearest non-fractional pitch.

pitch

ceil(p)

Returns the smallest non-fractional pitch that is greater than or equal i

pitch

floor(p)

Returns the largest non-fractional pitch that is less than or equal i

pitch

Deleted Functions

These valid expressions for interval do not make sense for pitch and are no longer allowed.

Expression

a += b

a -= b

a + b

a - b