diff --git a/Cargo.lock b/Cargo.lock
index bbc5385..f26cc09 100644
--- a/Cargo.lock
+++ b/Cargo.lock
@@ -1695,6 +1695,15 @@ version = "1.17.0"
 source = "registry+https://github.com/rust-lang/crates.io-index"
 checksum = "6f61fba1741ea2b3d6a1e3178721804bb716a68a6aeba1149b5d52e3d464ea66"
 
+[[package]]
+name = "ordered-float"
+version = "3.4.0"
+source = "registry+https://github.com/rust-lang/crates.io-index"
+checksum = "d84eb1409416d254e4a9c8fa56cc24701755025b458f0fcd8e59e1f5f40c23bf"
+dependencies = [
+ "num-traits",
+]
+
 [[package]]
 name = "owned_ttf_parser"
 version = "0.18.1"
@@ -1761,6 +1770,7 @@ dependencies = [
  "flate2",
  "gd_plist",
  "home",
+ "ordered-float",
  "rodio",
 ]
 
diff --git a/Cargo.toml b/Cargo.toml
index b4724d4..61dca13 100644
--- a/Cargo.toml
+++ b/Cargo.toml
@@ -13,3 +13,4 @@ base64 = {version = "0.21.0"}
 flate2 = {version = "1.0.25"}
 gd_plist = {git = "https://github.com/Syudagye/gd-plist.git", version = "1.4.0"}
 chrono = {version = "0.4.23"}
+ordered-float = {version = "3.4.0"}
diff --git a/src/music.rs b/src/music.rs
index cc826f8..2f0b89a 100644
--- a/src/music.rs
+++ b/src/music.rs
@@ -3,16 +3,21 @@
 
 use chrono::Duration;
 use std::collections::BTreeMap;
+use ordered_float::OrderedFloat as Float;
+
+pub type BeatPosition = Float<f32>;
 
 /// Like BPM, but not necessarily represented in terms of minutes
 /// Only BPM jumps for now; no smooth accel/decel
 pub struct BeatRate {
     initial: StaticBeatRate,
-    changes: BTreeMap<Duration, StaticBeatRate>,
+    changes: BTreeMap<BeatPosition, StaticBeatRate>,
 }
 
+#[derive(Clone, Copy, PartialEq, Eq, PartialOrd, Ord, Debug)]
 pub struct StaticBeatRate(Duration);
 
+
 impl StaticBeatRate {
     pub fn from_bpm(bpm: f32) -> Self {
         Self(Duration::microseconds(60_000_000 / bpm as i64))
@@ -27,3 +32,55 @@ impl From<StaticBeatRate> for BeatRate {
         }
     }
 }
+
+impl BeatRate {
+    pub fn at_beat(&self, pos: BeatPosition) -> StaticBeatRate {
+        match self.changes.first_key_value() {
+            Some((first_change, _)) => {
+                if &pos < first_change {
+                    self.initial
+                } else {
+                    *self.changes.iter().rev().find(|&el| el.0 <= &pos).unwrap().1
+                }
+            },
+            None => self.initial,
+        }
+    }
+    
+    pub fn add_change(&mut self, new_pos: BeatPosition, new_rate: StaticBeatRate) {
+        self.changes.insert(new_pos, new_rate);
+    }
+}
+
+#[cfg(test)]
+mod tests {
+    use super::*;
+    #[test]
+    fn rate_when_no_changes() {
+        let rate: BeatRate = StaticBeatRate::from_bpm(100.0).into();
+        assert_eq!(rate.at_beat(5.0.into()), StaticBeatRate::from_bpm(100.0));
+    }
+
+    #[test]
+    fn rate_before_changes() {
+        let mut rate: BeatRate = StaticBeatRate::from_bpm(100.0).into();
+        rate.add_change(5.0.into(), StaticBeatRate::from_bpm(120.0));
+        assert_eq!(rate.at_beat(3.0.into()), StaticBeatRate::from_bpm(100.0));
+    }
+
+    #[test]
+    fn rate_after_change() {
+        let mut rate: BeatRate = StaticBeatRate::from_bpm(100.0).into();
+        rate.add_change(5.0.into(), StaticBeatRate::from_bpm(120.0));
+        rate.add_change(10.0.into(), StaticBeatRate::from_bpm(140.0));
+        assert_eq!(rate.at_beat(6.0.into()), StaticBeatRate::from_bpm(120.0));
+    }
+
+    #[test]
+    fn rate_at_change() {
+        let mut rate: BeatRate = StaticBeatRate::from_bpm(100.0).into();
+        rate.add_change(5.0.into(), StaticBeatRate::from_bpm(120.0));
+        rate.add_change(10.0.into(), StaticBeatRate::from_bpm(140.0));
+        assert_eq!(rate.at_beat(5.0.into()), StaticBeatRate::from_bpm(120.0));
+    }
+}