After thinking yesterday about octaveless notes I decided to write something to generate the tones I had in mind. Here they are as two-second mp3s:

Bb	B	C	Db
A			D
Ab			Eb
G	Gb	F	E

The code is on github. It uses portaudio so it should work cross platform if you want to compile it. The important parts of the code are:

#define sine(i,F) ((float) sin( (((double)(i)*(double)(F))/SAMPLE_RATE) * M_PI * 2. ))

float freq(float note)
{
  return 440*(pow(2, (note-69.0)/12));
}

float intensity(float note, int octave)
{
  float bass_n = fmod(note, 12);

  switch(octave) {
  case 0:
    return 0.00 + 0.01*bass_n;
  case 1:
    return 0.12 + 0.01*bass_n;
  case 2:
    return 0.24 + 0.01*bass_n;
  case 3:
    return 0.32 - 0.01*bass_n;
  case 4:
    return 0.22 - 0.01*bass_n;
  case 5:
    return 0.10 - 0.01*bass_n;
  }
  return 0; // never reached
}

float synth(float phase, float note) {
  return pow(2,(sine(phase, note)));
}

# A440 = 69, as in midi
# phase is constantly increasing, once per sample
#
float sample_val(float note, unsigned int phase)
{
  note = fmod(note, 12);

  return log2(synth(phase, freq(note + 12*0)) * intensity(note, 0) +
              synth(phase, freq(note + 12*1)) * intensity(note, 1) +
              synth(phase, freq(note + 12*2)) * intensity(note, 2) +
              synth(phase, freq(note + 12*3)) * intensity(note, 3) +
              synth(phase, freq(note + 12*4)) * intensity(note, 4) +
              synth(phase, freq(note + 12*5)) * intensity(note, 5));
}

# call sample_val as:
# for (int i = 0 ; i < 1000000 ; i++)
#   send_to_speaker(sample_val(69, i));