Piano: Rewrite application

Goals:
- Switch to a more typical LibGUI arrangement
- Separate GUI (MainWidget) and audio (AudioEngine)
- Improve on existing features while retaining the same feature set

Improvements:
- Each GUI element is a separate widget
- The wave (WaveWidget) scales with the window
- The piano roll (RollWidget) scales horizontally and scrolls vertically
- The piano (KeysWidget) fits as many notes as possible
- The knobs (KnobsWidget) are now sliders
- All mouse and key events are handled in constant time
- The octave can be changed while playing notes
- The same note can be played with the mouse, keyboard and roll at the
  same time, and the volume of the resulting note is scaled accordingly
- Note frequency constants use the maximum precision available in a
  double

Applications/Piano/KeysWidget.h

@@ -0,0 +1,61 @@
+/*
+ * Copyright (c) 2018-2020, Andreas Kling <kling@serenityos.org>
+ * Copyright (c) 2019-2020, William McPherson <willmcpherson2@gmail.com>
+ * All rights reserved.
+ *
+ * Redistribution and use in source and binary forms, with or without
+ * modification, are permitted provided that the following conditions are met:
+ *
+ * 1. Redistributions of source code must retain the above copyright notice, this
+ *    list of conditions and the following disclaimer.
+ *
+ * 2. Redistributions in binary form must reproduce the above copyright notice,
+ *    this list of conditions and the following disclaimer in the documentation
+ *    and/or other materials provided with the distribution.
+ *
+ * THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS IS"
+ * AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
+ * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE
+ * DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT HOLDER OR CONTRIBUTORS BE LIABLE
+ * FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL
+ * DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR
+ * SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER
+ * CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY,
+ * OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE
+ * OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
+ */
+
+#pragma once
+
+#include "Music.h"
+#include <LibGUI/GFrame.h>
+
+class AudioEngine;
+
+class KeysWidget final : public GFrame {
+    C_OBJECT(KeysWidget)
+public:
+    virtual ~KeysWidget() override;
+
+    int key_code_to_key(int key_code) const;
+    int mouse_note() const;
+
+    void set_key(int key, Switch);
+
+private:
+    KeysWidget(GWidget* parent, AudioEngine&);
+
+    virtual void paint_event(GPaintEvent&) override;
+    virtual void mousedown_event(GMouseEvent&) override;
+    virtual void mouseup_event(GMouseEvent&) override;
+    virtual void mousemove_event(GMouseEvent&) override;
+
+    int note_for_event_position(Point) const;
+
+    AudioEngine& m_audio_engine;
+
+    u8 m_key_on[note_count] { 0 };
+
+    bool m_mouse_down { false };
+    int m_mouse_note { -1 };
+};