Allow adding intervals together

src/intervals.jl

@@ -112,6 +112,15 @@ function Base.:+(p::Pitch, interval::Interval)
 end
 
 
+function Base.:+(i1::Interval, i2::Interval)
+    bottom = C[4]
+    top = bottom + i1 + i2
+
+    return Interval(bottom, top)
+end
+
+
+
 const Minor_2nd = Interval(2, Minor)
 const Major_2nd = Interval(2, Major)
 

src/scales.jl

@@ -1,10 +1,18 @@
-# Represents a musical scale
-# I.e. an object that repeats each octave
+"""
+    struct Scale{T<:Union{PitchClass, Pitch}}
+
+A musical scale divides up an octave.
+A scale is represented as an iterator.
+"""
 struct Scale{T<:Union{PitchClass, Pitch}}
     tonic::T
     steps::Dict{PitchClass, Interval}
 
     function Scale(tonic::T, steps::Vector{Interval}) where {T}
+
+        # steps must add up to an octave:
+        @assert sum(steps) == Interval(8, Perfect)
+
         steps_dict = Dict{PitchClass, Interval}()
 
         current = tonic

test/intervals.jl

@@ -17,4 +17,17 @@ end
 
     @test C[4] + Interval(2, Major) == D[4]
     @test B[4] + Interval(2, Major) == C♯[5]
+end
+
+@testset "Sum of intervals" begin
+    @test Interval(3, Major) + Interval(3, Minor) == Interval(5, Perfect)
+    @test Interval(3, Major) + Interval(3, Major) == Interval(5, Augmented)
+    @test Interval(3, Major) + Interval(4, Diminished) == Interval(6, Minor)
+    @test Interval(4, Perfect) + Interval(5, Perfect) == Interval(8, Perfect)
+
+    major_scale = let M = Major_2nd, m = Minor_2nd
+        [M, M, m, M, M, M, m]
+    end
+
+    @test sum(major_scale) == Interval(8, Perfect)
 end