feat: add initial interval struct

I'm keeping the number an int this time around, but providing some
hard-coded constants for the intervals spanning two octaves for
convenience.

src/root.zig

@@ -14,4 +14,5 @@ test {
     // _ = @import("theory_v1/pitch.zig");
     // _ = @import("theory_v1/scale.zig");
     _ = @import("theory/note.zig");
+    _ = @import("theory/interval.zig");
 }

src/theory/interval.zig

@@ -0,0 +1,211 @@
+const std = @import("std");
+
+const c = @import("constants.zig");
+const Note = @import("note.zig").Note;
+
+pub const Interval = struct {
+    qual: Quality,
+    num: u7,
+
+    pub const Quality = enum { perfect, major, minor, augmented, diminished };
+
+    pub fn init(qual: Quality, num: u7) !Interval {
+        if (!isValid(qual, num)) {
+            return error.InvalidInterval;
+        }
+        return .{ .qual = qual, .num = num };
+    }
+
+    fn isValid(qual: Quality, num: u7) bool {
+        const simplified = @mod(num - 1, c.notes_per_oct) + 1;
+        const is_perfect = simplified == 1 or simplified == 4 or simplified == 5;
+
+        if (is_perfect) {
+            return switch (qual) {
+                .perfect, .augmented, .diminished => true,
+                .major, .minor => false,
+            };
+        } else {
+            return switch (qual) {
+                .perfect => false,
+                .major, .minor, .augmented, .diminished => true,
+            };
+        }
+    }
+
+    pub fn fromString(str: []const u8) !Interval {
+        if (str.len < 2) return error.InvalidStringFormat;
+
+        const qual = switch (str[0]) {
+            'P' => .perfect,
+            'M' => .major,
+            'm' => .minor,
+            'A' => .augmented,
+            'd' => .diminished,
+            else => error.InvalidQuality,
+        };
+        const num = try std.fmt.parseInt(u7, str[1..], 10);
+
+        if (!isValid(qual, num)) {
+            return error.InvalidInterval;
+        }
+        return .{ .qual = qual, .num = num };
+    }
+
+    // pub fn applyTo(self: Interval, note: Note) Note {}
+
+    // pub fn invert(self: Interval) Interval {}
+
+    // pub fn semitones(self: Interval) u7 {}
+
+    fn baseSemitones(num: u7) i8 {
+        const simplified = @mod(num - 1, c.notes_per_oct) + 1;
+        const oct_offset = (num - 1) / c.notes_per_oct * c.semis_per_oct;
+
+        const base = switch (simplified) {
+            1 => 0, // Unison
+            2 => 2, // Second
+            3 => 4, // Third
+            4 => 5, // Fourth
+            5 => 7, // Fifth
+            6 => 9, // Sixth
+            7 => 11, // Seventh
+            else => unreachable,
+        };
+
+        return @intCast(base + oct_offset);
+    }
+
+    // pub fn between(lhs: Note, rhs: Note) Interval {}
+
+    /// Unison.
+    pub const P1 = Interval{ .qual = .perfect, .num = 1 };
+    /// Perfect fourth.
+    pub const P4 = Interval{ .qual = .perfect, .num = 4 };
+    /// Perfect fifth.
+    pub const P5 = Interval{ .qual = .perfect, .num = 5 };
+    /// Octave.
+    pub const P8 = Interval{ .qual = .perfect, .num = 8 };
+    /// Perfect eleventh.
+    pub const P11 = Interval{ .qual = .perfect, .num = 11 };
+    /// Perfect twelfth.
+    pub const P12 = Interval{ .qual = .perfect, .num = 12 };
+    /// Perfect fifteenth, double octave.
+    pub const P15 = Interval{ .qual = .perfect, .num = 15 };
+
+    /// Minor second.
+    pub const m2 = Interval{ .qual = .minor, .num = 2 };
+    /// Minor third.
+    pub const m3 = Interval{ .qual = .minor, .num = 3 };
+    /// Minor sixth.
+    pub const m6 = Interval{ .qual = .minor, .num = 6 };
+    /// Minor seventh.
+    pub const m7 = Interval{ .qual = .minor, .num = 7 };
+    /// Minor ninth.
+    pub const m9 = Interval{ .qual = .minor, .num = 9 };
+    /// Minor tenth.
+    pub const m10 = Interval{ .qual = .minor, .num = 10 };
+    /// Minor thirteenth.
+    pub const m13 = Interval{ .qual = .minor, .num = 13 };
+    /// Minor fourteenth.
+    pub const m14 = Interval{ .qual = .minor, .num = 14 };
+
+    /// Major second.
+    pub const M2 = Interval{ .qual = .major, .num = 2 };
+    /// Major third.
+    pub const M3 = Interval{ .qual = .major, .num = 3 };
+    /// Major sixth.
+    pub const M6 = Interval{ .qual = .major, .num = 6 };
+    /// Major seventh.
+    pub const M7 = Interval{ .qual = .major, .num = 7 };
+    /// Major ninth.
+    pub const M9 = Interval{ .qual = .major, .num = 9 };
+    /// Major tenth.
+    pub const M10 = Interval{ .qual = .major, .num = 10 };
+    /// Major thirteenth.
+    pub const M13 = Interval{ .qual = .major, .num = 13 };
+    /// Major fourteenth.
+    pub const M14 = Interval{ .qual = .major, .num = 14 };
+
+    /// Diminished first.
+    pub const d1 = Interval{ .qual = .diminished, .num = 1 };
+    /// Diminished second.
+    pub const d2 = Interval{ .qual = .diminished, .num = 2 };
+    /// Diminished third.
+    pub const d3 = Interval{ .qual = .diminished, .num = 3 };
+    /// Diminished fourth.
+    pub const d4 = Interval{ .qual = .diminished, .num = 4 };
+    /// Diminished fifth.
+    pub const d5 = Interval{ .qual = .diminished, .num = 5 };
+    /// Diminished sixth.
+    pub const d6 = Interval{ .qual = .diminished, .num = 6 };
+    /// Diminished seventh.
+    pub const d7 = Interval{ .qual = .diminished, .num = 7 };
+    /// Diminished eighth.
+    pub const d8 = Interval{ .qual = .diminished, .num = 8 };
+    /// Diminished ninth.
+    pub const d9 = Interval{ .qual = .diminished, .num = 9 };
+    /// Diminished tenth.
+    pub const d10 = Interval{ .qual = .diminished, .num = 10 };
+    /// Diminished eleventh.
+    pub const d11 = Interval{ .qual = .diminished, .num = 11 };
+    /// Diminished twelfth.
+    pub const d12 = Interval{ .qual = .diminished, .num = 12 };
+    /// Diminished thirteenth.
+    pub const d13 = Interval{ .qual = .diminished, .num = 13 };
+    /// Diminished fourteenth.
+    pub const d14 = Interval{ .qual = .diminished, .num = 14 };
+    /// Diminished fifteenth.
+    pub const d15 = Interval{ .qual = .diminished, .num = 15 };
+
+    /// Augmented first.
+    pub const A1 = Interval{ .qual = .augmented, .num = 1 };
+    /// Augmented second.
+    pub const A2 = Interval{ .qual = .augmented, .num = 2 };
+    /// Augmented third.
+    pub const A3 = Interval{ .qual = .augmented, .num = 3 };
+    /// Augmented fourth.
+    pub const A4 = Interval{ .qual = .augmented, .num = 4 };
+    /// Augmented fifth.
+    pub const A5 = Interval{ .qual = .augmented, .num = 5 };
+    /// Augmented sixth.
+    pub const A6 = Interval{ .qual = .augmented, .num = 6 };
+    /// Augmented seventh.
+    pub const A7 = Interval{ .qual = .augmented, .num = 7 };
+    /// Augmented octave.
+    pub const A8 = Interval{ .qual = .augmented, .num = 8 };
+    /// Augmented ninth.
+    pub const A9 = Interval{ .qual = .augmented, .num = 9 };
+    /// Augmented tenth.
+    pub const A10 = Interval{ .qual = .augmented, .num = 10 };
+    /// Augmented eleventh.
+    pub const A11 = Interval{ .qual = .augmented, .num = 11 };
+    /// Augmented twelfth.
+    pub const A12 = Interval{ .qual = .augmented, .num = 12 };
+    /// Augmented thirteenth.
+    pub const A13 = Interval{ .qual = .augmented, .num = 13 };
+    /// Augmented fourteenth.
+    pub const A14 = Interval{ .qual = .augmented, .num = 14 };
+    /// Augmented fifteenth.
+    pub const A15 = Interval{ .qual = .augmented, .num = 15 };
+
+    pub fn format(
+        self: Interval,
+        comptime fmt: []const u8,
+        options: std.fmt.FormatOptions,
+        writer: anytype,
+    ) !void {
+        _ = fmt;
+        _ = options;
+        try writer.print("{s}{d}", .{
+            switch (self.qual) {
+                .perfect => "P",
+                .major => "M",
+                .minor => "m",
+                .augmented => "A",
+                .diminished => "d",
+            },
+            self.num,
+        });
+    }
+};

src/theory/note.zig

@@ -33,7 +33,7 @@ pub const Note = struct {
             .double_sharp => 2,
         };
         const midi = base + offset + (oct + 1) * c.semis_per_oct;
-        if (midi < 0 or c.midi_max < midi) {
+        if (midi < 0 or midi > c.midi_max) {
             return error.NoteOutOfRange;
         }
         return .{ .midi = @intCast(midi), .name = .{ .let = let, .acc = acc } };
@@ -51,6 +51,8 @@ pub const Note = struct {
         return .{ .midi = midi, .name = spellWithSharps(midi) };
     }
 
+    // pub fn fromString(str: []const u8) !Interval {}
+
     pub fn frequency(self: Note) f64 {
         const a4_freq = 440.0;
         const a4_midi = 69;
@@ -117,6 +119,8 @@ pub const Note = struct {
         };
     }
 
+    // pub fn respell(self: Note, ???) Note { }
+
     pub fn format(
         self: Note,
         comptime fmt: []const u8,