Lecture: Music Representations

After working through the material of this lecture, you should be able to answer the following questions:

• How can music be represented? What are the differences between sheet music, symbolic, and audio representations?
• What is the twelve-tone equal-tempered scale refer to? How are notes specified using the scientific pitch notation? What is an octave number? What are pitch classes and chroma values?
• What is a piano-roll representation? What does it encode? How can it be visualized?
• What is a MIDI representation? What are the main parameters?
• What does an audio representation encode? What is a waveform?
• What is a sinusoid? What are the three parameters that specify a sinusoid? What does the unit "Hertz" (Hz) refer to?
• What is the relation between a MIDI note number and its center frequency? (See Eq. 1.1.)
• What does the unit "cent" measure? How is it defined? (See Eq. 1.4.)
• What is the difference between intensity and loudness? What are equal-loudness contours?
• What does the unit "decibel" (dB) measure? How is it defined? (See Eq. 1.6.)
• To which musical properties does timbre refer to?
• What is tremolo? What is vibrato?

Reading Assignments

Müller, FMP, Springer 2021
Chapter 1: Music Representations

• Introduction of Chapter 1
• Section 1.1: Sheet Music Representations
  • Section 1.1.1: Musical Notes and Pitches
• Section 1.2: Symbolic Representations:
  • Section 1.2.1: Piano Roll Representation
  • Section 1.2.2: MIDI Representations
• Section 1.3: Audio Representations
  • Section 1.3.1: Waves and Waveforms
  • Section 1.3.2: Frequency and Pitch
  • Section 1.3.3: Dynamics, Intensity, and Loudness
  • Section 1.3.4: Timbre

FMP Notebooks

• Part 1: Music Representations
• Musical Notes and Pitches
• Piano Roll Representations
• Waves and Waveforms
• Frequency and Pitch
• Dynamics, Intensity, and Loudness
• Timbre

Slides

• Music Representations: Slides (PDF), Handouts (6 slides per page) (PDF)

Videos

There are a numerous videos at YouTube on sound, waveforms, and their properties. Some of the videos may be too basic for you, others may give you additional explanations. Explore YouTube videos by yourself. Here are some pointers to start with.

• What is Sound? The Fundamental Science Behind Sound (9:40)
  Air pressure; pressure wave; waveform; compression; rarefaction; frequency; Hertz; amplitude; vinyl record
• Sound: Wavelength, Frequency and Amplitude (5:48)
  Vibrations; waves; loudspeaker; longitudinal wave; transverse wave; human hearing range; frequency; amplitude
• What is the difference between a Noise and a Note? (7:48)
  Sound waves; pitch; standing wave; interference; resonance; nodes
• Frequency, Wave Shape and Pitch (7:05)
  Piano keyboard; frequency; wavelength; speed; human hearing range
• MIDI Tutorial: What is MIDI and how is it used? (2:41)
  MIDI event data; pitch; velocity; MIDI controller; MIDI sequencer
• Multi-Sensor Cello Recordings for Instantaneous Frequency Estimation (2:01)
  Cello note; string movement; finger movement; F0; vibrato

Music Acoustics and Sound Production

In the lecture, we had some further discussions on the physics of music and how sounds are generated by musical instruments. In the following, you find some materials, links, and videos connected to the field known as Music Acoustics:

• Alexander Luce: How sound is created by instruments:
  Slides (PPTX), Slides (PDF), Handouts (6 slides per page) (PDF)
• Wikipedia page on Musical acoustics
• Joe Wolfe: Music Acoustics, UNSW Sydney
  Extensive source on the science of music (including the physics of waves and sounds, strings, woodwind, brass, percussion, voices, and many more links)
• What Does Sound Look Like? (2:31)
  Shows sound waves as they travel through the air thanks to a clever photographic trick.
• Motion of Plucked String (1:33)
  What happens to a string when it is plucked?
• Modes on a String (7:55)
  A basic explanation and demonstration of normal modes on a string.
• Standing Waves Introduction (11:31)
  Reflection with and without inversion caused by fixed and free ends are demonstrated.
• Stringed Instrument Frequencies (7:19)
  Harmonic numbers, fundamental frequency, guitar used to demonstrate harmonic numbers

Question & Answer Session