Interval

Overview

An interval is the distance between two pitches, measured in semitones. It is the basis for melody and harmony as well as all musical scales and chords. The basic_interval<T> is a template class, parameterized by the underlying type T.

Include

#include <q/support/interval.hpp>

Declaration

struct interval_unit;

template <typename T>
struct basic_interval : _unspecified_base_type_
{
   using base_type = _unspecified_base_type_;
   using base_type::base_type;
   using unit_type = interval_unit;

   constexpr explicit   basic_interval(concepts::Arithmetic auto val);
};

// Free functions
template <typename T>
constexpr int as_int(basic_interval<T> i);

template <typename T>
constexpr float as_float(basic_interval<T> i);

template <typename T>
constexpr double as_double(basic_interval<T> i);

template <typename T>
requires std::floating_point<T>
constexpr basic_interval<T> round(basic_interval<T> i);

template <typename T>
requires std::floating_point<T>
constexpr basic_interval<T> ceil(basic_interval<T> i);

template <typename T>
requires std::floating_point<T>
constexpr basic_interval<T> floor(basic_interval<T> i);

Template Instantiations

There are two basic type aliases: interval and exact_interval, which are template instantiations of the basic_interval template class:

interval

Fractional interval. Can represent microtones —intervals smaller than a semitone.

exact_interval

Exact, whole number intervals.

using interval = basic_interval<double>;
using exact_interval = basic_interval<std::int8_t>;

Expressions

basic_interval<T> is a model of Unit. In addition to valid expressions for Unit, Intervals allow these expressions.

Notation

i

Object of type basic_interval<T>.

Conversions

Expression Semantics Return Type

as_int(i)

Convert an interval to an int.

int

as_float(i)

Convert an interval to a float.

float

as_double(i)

Convert an interval to a double.

double

Functions

Expression Semantics Return Type

round(i)

Rounds i to the nearest non-fractional interval.

basic_interval<T>

ceil(i)

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

basic_interval<T>

floor(i)

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

basic_interval<T>
The round, ceil and floor functions require T to be a floating point type.