Interval API Reference

Complete API documentation for the Interval class.

Class Definition

namespace MusicTheory;

public sealed class Interval : IEquatable<Interval>
{
    public IntervalQuality Quality { get; }
    public int Number { get; }
    public int Semitones { get; }
}

Constructors

Interval(IntervalQuality, int)

Creates a new interval with the specified quality and numeric value.

public Interval(IntervalQuality quality, int number)

Parameters:

quality: The interval quality (Diminished, Minor, Major, Perfect, Augmented)
number: The interval number (1-15 typically)

Exceptions:

ArgumentException: If the quality is invalid for the given interval number
ArgumentOutOfRangeException: If number is less than 1

Validation Rules:

Perfect quality is only valid for unison (1), 4th, 5th, and octave (8)
Major/Minor quality is only valid for 2nd, 3rd, 6th, and 7th
Diminished/Augmented can be used with any interval

Examples:

var majorThird = new Interval(IntervalQuality.Major, 3);
var perfectFifth = new Interval(IntervalQuality.Perfect, 5);
var minorSeventh = new Interval(IntervalQuality.Minor, 7);

Properties

Quality

public IntervalQuality Quality { get; }

Gets the quality of the interval.

Number

public int Number { get; }

Gets the numeric value of the interval (1 = unison, 2 = second, etc.).

Semitones

public int Semitones { get; }

Gets the number of semitones (half steps) in the interval.

Calculation: The semitone count is calculated based on:

The diatonic interval (based on the number)
The chromatic adjustment (based on the quality)

Examples:

Major 3rd = 4 semitones
Perfect 5th = 7 semitones
Minor 7th = 10 semitones

Instance Methods

IsEnharmonicWith(Interval)

Determines if this interval is enharmonically equivalent to another.

public bool IsEnharmonicWith(Interval other)

Parameters:

other: The interval to compare with

Returns: True if both intervals span the same number of semitones

Example:

var augFourth = new Interval(IntervalQuality.Augmented, 4);
var dimFifth = new Interval(IntervalQuality.Diminished, 5);
bool same = augFourth.IsEnharmonicWith(dimFifth); // true (both 6 semitones)

Invert()

Inverts the interval.

public Interval Invert()

Returns: The inverted interval

Inversion Rules:

Number: 9 - original number (for simple intervals)
Quality:
- Major ↔ Minor
- Augmented ↔ Diminished
- Perfect remains Perfect

Examples:

var major3rd = new Interval(IntervalQuality.Major, 3);
var minor6th = major3rd.Invert(); // Minor 6th

var perfect5th = new Interval(IntervalQuality.Perfect, 5);
var perfect4th = perfect5th.Invert(); // Perfect 4th

ToString()

Returns a string representation of the interval.

public override string ToString()

Format: "{Quality} {Number}{Suffix}"

Examples:

Perfect Unison → "Perfect Unison"
Major 3rd → "Major 3rd"
Perfect 5th → "Perfect 5th"
Minor 7th → "Minor 7th"
Augmented 4th → "Augmented 4th"

Equals(Interval?)

Determines if this interval equals another interval.

public bool Equals(Interval? other)

Note: Compares by quality and number, not by semitones.

GetHashCode()

Returns the hash code for the interval.

public override int GetHashCode()

Static Methods

Between(Note, Note)

Calculates the interval between two notes.

public static Interval Between(Note lower, Note higher)

Parameters:

lower: The lower note
higher: The higher note

Returns: The interval from lower to higher

Algorithm:

Calculate the numeric interval based on note names
Calculate the exact semitone distance
Determine the appropriate quality

Example:

var c = new Note(NoteName.C, 4);
var e = new Note(NoteName.E, 4);
var g = new Note(NoteName.G, 4);

var third = Interval.Between(c, e);  // Major 3rd
var fifth = Interval.Between(c, g);  // Perfect 5th

FromSemitones(int)

Creates an interval from a semitone count.

public static Interval FromSemitones(int semitones)

Parameters:

semitones: Number of semitones

Returns: An interval (prefers standard spellings)

Note: This method returns the most common spelling for the given semitone count.

Example:

var majorThird = Interval.FromSemitones(4);   // Major 3rd
var tritone = Interval.FromSemitones(6);      // Augmented 4th

Operators

Equality Operators

public static bool operator ==(Interval? left, Interval? right)
public static bool operator !=(Interval? left, Interval? right)

Compare intervals by quality and number.

Example:

var int1 = new Interval(IntervalQuality.Major, 3);
var int2 = new Interval(IntervalQuality.Major, 3);
var int3 = new Interval(IntervalQuality.Minor, 3);

bool equal1 = int1 == int2;  // true
bool equal2 = int1 == int3;  // false

Interval Reference Tables

Simple Intervals (Within an Octave)

Number	Perfect	Diminished	Minor	Major	Augmented
1	0	-1	-	-	1
2	-	0	1	2	3
3	-	2	3	4	5
4	5	4	-	-	6
5	7	6	-	-	8
6	-	7	8	9	10
7	-	9	10	11	12
8	12	11	-	-	13

Compound Intervals (Beyond an Octave)

Number	Common Name	Semitones	Simple Equivalent
9	Ninth	14 (Major)	2nd
10	Tenth	16 (Major)	3rd
11	Eleventh	17 (Perfect)	4th
12	Twelfth	19 (Perfect)	5th
13	Thirteenth	21 (Major)	6th
14	Fourteenth	23 (Major)	7th
15	Fifteenth	24 (Perfect)	Octave

Common Patterns

Creating Common Intervals

// Perfect intervals
var unison = new Interval(IntervalQuality.Perfect, 1);
var fourth = new Interval(IntervalQuality.Perfect, 4);
var fifth = new Interval(IntervalQuality.Perfect, 5);
var octave = new Interval(IntervalQuality.Perfect, 8);

// Major/Minor intervals
var majorSecond = new Interval(IntervalQuality.Major, 2);
var minorThird = new Interval(IntervalQuality.Minor, 3);
var majorSixth = new Interval(IntervalQuality.Major, 6);
var minorSeventh = new Interval(IntervalQuality.Minor, 7);

// Altered intervals
var augmentedFourth = new Interval(IntervalQuality.Augmented, 4);
var diminishedFifth = new Interval(IntervalQuality.Diminished, 5);

Working with Interval Collections

// Major scale intervals from root
var majorScaleIntervals = new[]
{
    new Interval(IntervalQuality.Perfect, 1),    // Root
    new Interval(IntervalQuality.Major, 2),      // Major 2nd
    new Interval(IntervalQuality.Major, 3),      // Major 3rd
    new Interval(IntervalQuality.Perfect, 4),    // Perfect 4th
    new Interval(IntervalQuality.Perfect, 5),    // Perfect 5th
    new Interval(IntervalQuality.Major, 6),      // Major 6th
    new Interval(IntervalQuality.Major, 7),      // Major 7th
    new Interval(IntervalQuality.Perfect, 8)     // Octave
};

// Build scale from intervals
var root = new Note(NoteName.C, 4);
var scaleNotes = majorScaleIntervals
    .Select(interval => root.Transpose(interval))
    .ToList();

Interval Analysis

public class IntervalAnalyzer
{
    public static string DescribeInterval(Interval interval)
    {
        var consonance = interval.Semitones switch
        {
            0 or 12 => "Perfect Consonance",
            5 or 7 => "Perfect Consonance",
            3 or 4 or 8 or 9 => "Imperfect Consonance",
            1 or 2 or 6 or 10 or 11 => "Dissonance",
            _ => "Unknown"
        };
        
        return $"{interval} ({interval.Semitones} semitones) - {consonance}";
    }
}

Error Handling

Invalid Quality for Number

try
{
    // Invalid: can't have a major 5th
    var invalid = new Interval(IntervalQuality.Major, 5);
}
catch (ArgumentException ex)
{
    // "Major quality is not valid for interval number 5"
}

Interval Calculation Edge Cases

// Handling enharmonic notes
var c = new Note(NoteName.C, 4);
var bSharp = new Note(NoteName.B, Alteration.Sharp, 3);

var interval = Interval.Between(bSharp, c); // Diminished 2nd (0 semitones)

Performance Notes

Semitone calculation is performed once in constructor
Interval comparison uses cached semitone values
String representation is generated on demand
Static factory methods use lookup tables for efficiency

Thread Safety

The Interval class is immutable and thread-safe. Multiple threads can safely:

Read all properties
Call all methods
Share Interval instances

No synchronization is needed.

MusicTheory Help

Interval API Reference

Class Definition

Constructors

Interval(IntervalQuality, int)

Properties

Quality

Number

Semitones

Instance Methods

IsEnharmonicWith(Interval)

Invert()

ToString()

Equals(Interval?)

GetHashCode()

Static Methods

Between(Note, Note)

FromSemitones(int)

Operators

Equality Operators

Interval Reference Tables

Simple Intervals (Within an Octave)

Compound Intervals (Beyond an Octave)

Common Patterns

Creating Common Intervals

Working with Interval Collections

Interval Analysis

Error Handling

Invalid Quality for Number

Interval Calculation Edge Cases

Performance Notes

Thread Safety

See Also