diff --git a/.travis.yml b/.travis.yml
index d312762..bd0b6c1 100644
--- a/.travis.yml
+++ b/.travis.yml
@@ -4,11 +4,11 @@ os:
 language: generic
 sudo: required
 dist: trusty
-osx_image: xcode10
+osx_image: xcode10.2
 install:
   - eval "$(curl -sL https://swiftenv.fuller.li/install.sh)"
 env:
-  - SWIFT_VERSION=4.2
+  - SWIFT_VERSION=5.0
 script:
   - swift package update
   - swift test
diff --git a/Package.resolved b/Package.resolved
index 19c8740..616bfbf 100644
--- a/Package.resolved
+++ b/Package.resolved
@@ -5,9 +5,9 @@
         "package": "Math",
         "repositoryURL": "https://github.com/dn-m/Math",
         "state": {
-          "branch": null,
-          "revision": "075ebb5a934251ed7acbe4feace925ed7e322d0f",
-          "version": "0.6.0"
+          "branch": "swift-5",
+          "revision": "51f8032aa2aea3e8a88b44dcc858c4551b855478",
+          "version": null
         }
       },
       {
@@ -23,9 +23,9 @@
         "package": "Structure",
         "repositoryURL": "https://github.com/dn-m/Structure",
         "state": {
-          "branch": null,
-          "revision": "11e920b1b883fe169c5ebb58e6489c0f28e9ad90",
-          "version": "0.20.0"
+          "branch": "swift-5",
+          "revision": "8f67514cba950f60ee992a8d0996d4f11d9654b0",
+          "version": null
         }
       }
     ]
diff --git a/Package.swift b/Package.swift
index e823da3..da6ea5e 100644
--- a/Package.swift
+++ b/Package.swift
@@ -13,8 +13,8 @@ let package = Package(
         .library(name: "MusicModel", targets: ["MusicModel"])
     ],
     dependencies: [
-        .package(url: "https://github.com/dn-m/Structure", from: "0.19.0"),
-        .package(url: "https://github.com/dn-m/Math", from: "0.6.0")
+        .package(url: "https://github.com/dn-m/Structure", from: "0.23.0"),
+        .package(url: "https://github.com/dn-m/Math", from: "0.7.0")
     ],
     targets: [
 
diff --git a/Sources/Duration/Rhythm/ProportionTree.swift b/Sources/Duration/Rhythm/ProportionTree.swift
index aec5c61..8687295 100644
--- a/Sources/Duration/Rhythm/ProportionTree.swift
+++ b/Sources/Duration/Rhythm/ProportionTree.swift
@@ -137,7 +137,7 @@ public func * (duration: Int, durations: [Int]) -> ProportionTree {
 
 /// Tree recording the change (in degree of power-of-two) needed to normalize a 
 /// `ProprtionTree`.
-typealias DistanceTree = Tree<Int,Int>
+public typealias DistanceTree = Tree<Int,Int>
 
 extension Tree where Branch == Int, Leaf == Int {
 
@@ -178,7 +178,6 @@ extension Tree where Branch == Int, Leaf == Int {
             default:
                 fatalError("Incompatible trees")
             }
-            return propagatedUp
         }
 
         return propagatedDown(self, propagatedUp(self), inherited: nil)
diff --git a/Sources/Duration/Tempo/Tempo.swift b/Sources/Duration/Tempo/Tempo.swift
index 9966851..6dbecc8 100644
--- a/Sources/Duration/Tempo/Tempo.swift
+++ b/Sources/Duration/Tempo/Tempo.swift
@@ -464,7 +464,7 @@ public extension Tempo.Interpolation {
 
     /// An ordered, contiguous collection of `Tempo.Interpolation.Fragments` indexed by their
     /// fractional offset.
-    public typealias Collection = ContiguousSegmentCollection<Tempo.Interpolation>
+    typealias Collection = ContiguousSegmentCollection<Tempo.Interpolation>
 }
 
 /// A class which encapsulates the stateful incremental building process of
diff --git a/Sources/MusicModel/Data Structures/IntervalSearchTree.swift b/Sources/MusicModel/Data Structures/IntervalSearchTree.swift
index fb026a9..f50f1ed 100644
--- a/Sources/MusicModel/Data Structures/IntervalSearchTree.swift	
+++ b/Sources/MusicModel/Data Structures/IntervalSearchTree.swift	
@@ -17,7 +17,7 @@ import Math
 public struct IntervalSearchTree <Metric: Comparable, Value> {
 
     /// Underlying `AVLTree` augmented for interval searching purposes.
-    typealias Base = AVLTree<Metric,Node>
+    public typealias Base = AVLTree<Metric,Node>
 
     public struct Node {
 
diff --git a/Sources/Pitch/NoteNumberRepresentable.swift b/Sources/Pitch/NoteNumberRepresentable.swift
index f72f2e9..5866b1b 100644
--- a/Sources/Pitch/NoteNumberRepresentable.swift
+++ b/Sources/Pitch/NoteNumberRepresentable.swift
@@ -54,8 +54,8 @@ extension NoteNumberRepresentable {
     // MARK: - Hashable
 
     /// - Returns: The hash value of a `NoteNumberRepresentable` type.
-    public var hashValue: Int {
-        return value.hashValue
+    public func hash(into hasher: inout Hasher) {
+        hasher.combine(value)
     }
 }