Ultrasonic theremin on an Arduino Nano

// Ultrasonic theremin: wave your hand over an HC-SR04 and a piezo plays a
// note for how far away it is. Closer is higher. On an Arduino Nano.
//
//   HC-SR04   TRIG -> D11, ECHO -> D10, VCC -> 5V, GND -> GND
//   piezo     D5 and GND
//   button    D2 and GND (INPUT_PULLUP): switches between the two modes
//
// Two ways to play:
//
//   scale   the hand picks one of eleven notes of the C major pentatonic
//           scale (C D E G A), two octaves from C5 to C7. Any notes from
//           this scale sound good together, so anything you play is a tune.
//   glide   the pitch slides smoothly with the hand, like a real theremin,
//           from 523 Hz at 50 cm to 2093 Hz at 5 cm.
//
// Farther than 50 cm (or nothing there at all) is silence, so take your hand
// away to stop.
//
// # Smoothing the readings
//
// An ultrasonic reading jumps around a little, and a hand is never quite
// still. The sketch keeps the last three readings and plays their median,
// the middle one, which throws away a single bad reading without lagging
// behind a hand that really moved.

const uint8_t TRIG = 11;
const uint8_t ECHO = 10;
const uint8_t PIEZO = 5;
const uint8_t BUTTON = 2;

const int NEAR_CM = 5;
const int FAR_CM = 50;

// C major pentatonic, C5 to C7.
const unsigned int SCALE[11] = {523, 587, 659, 784, 880, 1047, 1175, 1319, 1568, 1760, 2093};
const char *const NOTE_NAME[11] = {"C5", "D5", "E5", "G5", "A5", "C6", "D6", "E6", "G6", "A6", "C7"};

bool glide = false;
bool lastButton = HIGH;
int readings[3] = {999, 999, 999};
uint8_t next = 0;
int lastNote = -1;

int measureCm() {
  digitalWrite(TRIG, LOW);
  delayMicroseconds(2);
  digitalWrite(TRIG, HIGH);
  delayMicroseconds(10);
  digitalWrite(TRIG, LOW);
  // Give up after 6 ms: past about a meter, nobody is playing.
  unsigned long us = pulseIn(ECHO, HIGH, 6000UL);
  if (us == 0) return 999;
  return us / 58;
}

int median3(int a, int b, int c) {
  if ((a <= b && b <= c) || (c <= b && b <= a)) return b;
  if ((b <= a && a <= c) || (c <= a && a <= b)) return a;
  return c;
}

void setup() {
  Serial.begin(115200);
  pinMode(TRIG, OUTPUT);
  pinMode(ECHO, INPUT);
  pinMode(PIEZO, OUTPUT);
  pinMode(BUTTON, INPUT_PULLUP);
  Serial.println("Ultrasonic theremin: scale mode. Hand 5 to 50 cm above the sensor.");
}

void loop() {
  bool button = digitalRead(BUTTON);
  if (button == LOW && lastButton == HIGH) {
    glide = !glide;
    lastNote = -1;
    Serial.println(glide ? "glide mode" : "scale mode");
    delay(30);  // ride out the contact bounce
  }
  lastButton = button;

  readings[next] = measureCm();
  next = (next + 1) % 3;
  int cm = median3(readings[0], readings[1], readings[2]);

  if (cm > FAR_CM) {
    noTone(PIEZO);
    if (lastNote != -2) Serial.println("silence");
    lastNote = -2;
  } else {
    if (cm < NEAR_CM) cm = NEAR_CM;
    if (glide) {
      // Two octaves over the range: each 22.5 cm closer doubles the pitch.
      float octaves = 2.0 * (FAR_CM - cm) / (FAR_CM - NEAR_CM);
      unsigned int hz = 523.25 * pow(2.0, octaves);
      tone(PIEZO, hz);
      lastNote = -1;
    } else {
      int note = map(cm, FAR_CM, NEAR_CM, 0, 10);
      tone(PIEZO, SCALE[note]);
      if (note != lastNote) {
        Serial.print(NOTE_NAME[note]);
        Serial.print(" (");
        Serial.print(SCALE[note]);
        Serial.print(" Hz) at ");
        Serial.print(cm);
        Serial.println(" cm");
        lastNote = note;
      }
    }
  }
  delay(30);  // let the last ping's echoes die away before the next one
}