diff --git a/modules/juce_audio_devices/audio_io/juce_SampleRateHelpers.cpp b/modules/juce_audio_devices/audio_io/juce_SampleRateHelpers.cpp
new file mode 100644
index 0000000000..ce8c6b1ec1
--- /dev/null
+++ b/modules/juce_audio_devices/audio_io/juce_SampleRateHelpers.cpp
@@ -0,0 +1,48 @@
+/*
+  ==============================================================================
+
+   This file is part of the JUCE library.
+   Copyright (c) 2020 - Raw Material Software Limited
+
+   JUCE is an open source library subject to commercial or open-source
+   licensing.
+
+   The code included in this file is provided under the terms of the ISC license
+   http://www.isc.org/downloads/software-support-policy/isc-license. Permission
+   To use, copy, modify, and/or distribute this software for any purpose with or
+   without fee is hereby granted provided that the above copyright notice and
+   this permission notice appear in all copies.
+
+   JUCE IS PROVIDED "AS IS" WITHOUT ANY WARRANTY, AND ALL WARRANTIES, WHETHER
+   EXPRESSED OR IMPLIED, INCLUDING MERCHANTABILITY AND FITNESS FOR PURPOSE, ARE
+   DISCLAIMED.
+
+  ==============================================================================
+*/
+
+namespace juce
+{
+namespace SampleRateHelpers
+{
+
+const auto& getAllSampleRates()
+{
+    static auto sampleRates = []
+    {
+        std::vector<double> result;
+        constexpr double baseRates[] = { 8000.0, 11025.0, 12000.0 };
+        constexpr double maxRate = 768000.0;
+
+        for (auto rate : baseRates)
+            for (; rate <= maxRate; rate *= 2)
+                result.insert (std::upper_bound (result.begin(), result.end(), rate),
+                               rate);
+
+        return result;
+    }();
+
+    return sampleRates;
+}
+
+} // namespace SampleRateHelpers
+} // namespace juce
diff --git a/modules/juce_audio_devices/juce_audio_devices.cpp b/modules/juce_audio_devices/juce_audio_devices.cpp
index c76663a1e7..b9e29b1ad4 100644
--- a/modules/juce_audio_devices/juce_audio_devices.cpp
+++ b/modules/juce_audio_devices/juce_audio_devices.cpp
@@ -45,6 +45,8 @@
 
 #include "juce_audio_devices.h"
 
+#include "audio_io/juce_SampleRateHelpers.cpp"
+
 //==============================================================================
 #if JUCE_MAC || JUCE_IOS
  #include <juce_audio_basics/midi/ump/juce_UMP.h>
diff --git a/modules/juce_audio_devices/native/juce_linux_ALSA.cpp b/modules/juce_audio_devices/native/juce_linux_ALSA.cpp
index 1b010c3e86..644a54db31 100644
--- a/modules/juce_audio_devices/native/juce_linux_ALSA.cpp
+++ b/modules/juce_audio_devices/native/juce_linux_ALSA.cpp
@@ -50,17 +50,15 @@ namespace
 
 static void getDeviceSampleRates (snd_pcm_t* handle, Array<double>& rates)
 {
-    const int ratesToTry[] = { 22050, 24000, 32000, 44100, 48000, 88200, 96000, 176400, 192000, 0 };
-
     snd_pcm_hw_params_t* hwParams;
     snd_pcm_hw_params_alloca (&hwParams);
 
-    for (int i = 0; ratesToTry[i] != 0; ++i)
+    for (const auto rateToTry : SampleRateHelpers::getAllSampleRates())
     {
         if (snd_pcm_hw_params_any (handle, hwParams) >= 0
-             && snd_pcm_hw_params_test_rate (handle, hwParams, (unsigned int) ratesToTry[i], 0) == 0)
+             && snd_pcm_hw_params_test_rate (handle, hwParams, (unsigned int) rateToTry, 0) == 0)
         {
-            rates.addIfNotAlreadyThere ((double) ratesToTry[i]);
+            rates.addIfNotAlreadyThere (rateToTry);
         }
     }
 }
diff --git a/modules/juce_audio_devices/native/juce_mac_CoreAudio.cpp b/modules/juce_audio_devices/native/juce_mac_CoreAudio.cpp
index 232d713136..70c3ee483e 100644
--- a/modules/juce_audio_devices/native/juce_mac_CoreAudio.cpp
+++ b/modules/juce_audio_devices/native/juce_mac_CoreAudio.cpp
@@ -294,15 +294,11 @@ public:
 
             if (OK (AudioObjectGetPropertyData (deviceID, &pa, 0, nullptr, &size, ranges)))
             {
-                for (auto r : { 8000, 11025, 16000, 22050, 24000, 32000,
-                                44100, 48000, 88200, 96000, 176400,
-                                192000, 352800, 384000, 705600, 768000 })
+                for (const auto rate : SampleRateHelpers::getAllSampleRates())
                 {
-                    auto rate = (double) r;
-
                     for (int j = size / (int) sizeof (AudioValueRange); --j >= 0;)
                     {
-                        if (rate >= ranges[j].mMinimum - 2 && rate <= ranges[j].mMaximum + 2)
+                        if (ranges[j].mMinimum - 2 <= rate && rate <= ranges[j].mMaximum + 2)
                         {
                             newSampleRates.add (rate);
                             break;
@@ -315,6 +311,11 @@ public:
         if (newSampleRates.isEmpty() && sampleRate > 0)
             newSampleRates.add (sampleRate);
 
+        auto nominalRate = getNominalSampleRate();
+
+        if ((nominalRate > 0) && ! newSampleRates.contains (nominalRate))
+            newSampleRates.addUsingDefaultSort (nominalRate);
+
         return newSampleRates;
     }
 
diff --git a/modules/juce_audio_devices/native/juce_win32_ASIO.cpp b/modules/juce_audio_devices/native/juce_win32_ASIO.cpp
index 904c7f4baf..20385a084a 100644
--- a/modules/juce_audio_devices/native/juce_win32_ASIO.cpp
+++ b/modules/juce_audio_devices/native/juce_win32_ASIO.cpp
@@ -349,13 +349,9 @@ public:
         Array<double> newRates;
 
         if (asioObject != nullptr)
-        {
-            for (auto rate : { 8000, 11025, 16000, 22050, 24000, 32000,
-                               44100, 48000, 88200, 96000, 176400,
-                               192000, 352800, 384000, 705600, 768000 })
-                if (asioObject->canSampleRate ((double) rate) == 0)
-                    newRates.add ((double) rate);
-        }
+            for (const auto rate : SampleRateHelpers::getAllSampleRates())
+                if (asioObject->canSampleRate (rate) == 0)
+                    newRates.add (rate);
 
         if (newRates.isEmpty())
         {
diff --git a/modules/juce_audio_devices/native/juce_win32_WASAPI.cpp b/modules/juce_audio_devices/native/juce_win32_WASAPI.cpp
index ae927e08c6..07afc84890 100644
--- a/modules/juce_audio_devices/native/juce_win32_WASAPI.cpp
+++ b/modules/juce_audio_devices/native/juce_win32_WASAPI.cpp
@@ -676,9 +676,7 @@ private:
 
     void querySupportedSampleRates (WAVEFORMATEXTENSIBLE format, ComSmartPtr<IAudioClient>& audioClient)
     {
-        for (auto rate : { 8000, 11025, 16000, 22050, 24000, 32000,
-                           44100, 48000, 88200, 96000, 176400,
-                           192000, 352800, 384000, 705600, 768000 })
+        for (auto rate : SampleRateHelpers::getAllSampleRates())
         {
             if (rates.contains (rate))
                 continue;
@@ -695,7 +693,7 @@ private:
                                                                                         : &nearestFormat)))
             {
                 if (nearestFormat != nullptr)
-                    rate = (int) nearestFormat->nSamplesPerSec;
+                    rate = (double) nearestFormat->nSamplesPerSec;
 
                 if (! rates.contains (rate))
                     rates.addUsingDefaultSort (rate);