## 4 Educational Guide
### Music Representations (Part 1)  
Musical information can be represented in many different ways. In ([1], Chapter 1), three widely used music representations are introduced: sheet music, symbolic, and audio representations. The term **sheet music** is used to refer to visual representations of a musical score either given in printed form or encoded digitally in some image format. The term **symbolic** stands for any kind of symbolic representation where the entities have an explicit musical meaning. Finally, the term **audio** is used to denote music recordings given in the form of acoustic waveforms. The boundaries between these classes are not clear. In particular, as illustrated by Figure 4, symbolic representations may be close to both sheet music as well as audio representations [24]. In Part 1 of the FMP notebooks, which is closely associated with the textbook's first chapter, we introduce basic terminology used throughout the following FMP notebooks. Furthermore, we offer visual and acoustic material as well as Python code examples to study musical and acoustic properties of music, including frequency, pitch, dynamics, and timbre. We now go through the FMP notebooks of Part 1 one by one while indicating how these notebooks can be used for possible experiments and exercises. We start with the FMP Notebook Sheet Music Representations, where we take up the example of [PERSON]'s Fifth Symphony. Besides the piano reduced version and a full orchestral score, we also show a computer-generated sheet music representation. The comparison of these versions is instructive, since it demonstrates the huge differences one may have between different layouts, also indicating that the generation of visually pleasing sheet music representations from score representations is an art in itself. Besides the visual data, the notebook also provides different recordings of this passage, including a synthesized orchestral version created from a full score and a recording by the Vienna Philharmonic orchestra conducted by [PERSON] (1946). The comparison between the mechanical and performed versions shows that one requires additional knowledge not directly specified in the sheet music to make the music come alive. In the data folder of Part 1 (data/C1), one finds additional representations of our [PERSON] example including a piano, orchestral, and string quartet version. The files with the extension.sib, which were generated by the Sibelius music notation software application, have been exported in other symbolic formats (.mid,.sib,.xml), image formats (.png), and audio formats (.wav,.mp3). Such systematically generated data is well suited for hands-on exercises that allow teachers and students to experiment within a controlled setting. This is also one reason why we will take up the [PERSON] (and other) examples again and again throughout the FMP notebooks. In the FMP Notebook Musical Notes and Pitches, we deepen the concepts as introduced in ([1], Section 1.1.1). We show how to generate musical sounds using a simple sinusoidal model, which can then be used to obtain acoustic representations of concepts such as octaves, pitch classes, and musical scales. In the FMP Notebook Chroma and Shepard Tones, we generate Shepard tones, which are weighted superpositions of sine waves separated by octaves. These tones can be used to sonify the chromatic circle and [PERSON]'s helix of pitch as shown in the notebook's figures. Extending the notion of the twelve-tone discrete chromatic circle, one can generate a pitch-continuous version, where the Shepard tones ascend (or descend) continuously. Originally created by the French composer [PERSON], this continuous version is also known as the Shepard-Risset glissando. To implement such a glissando, one requires a chirp function with an exponential (rather than a linear) frequency increase.