{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "
" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "\n", "\n", "\n", "Following Section 1.1.1 of [Müller, FMP, Springer 2015], we introduce in this notebook the notions of musical notes, pitches, and the twelve-tone equal-tempered scale. \n", "
" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Notes and Pitches\n", "\n", "In music, the term **note** is often used in a rather loose way and may refer to both a musical symbol (when talking about score representations) as well as a pitched sound (when talking about audio representations). When thought of a musical symbol, each note has several attributes that determine the relative duration and the pitch of a sound to \n", "be performed by a musician. The notion of **pitch** is not strict and refers to a perceptual property that allows a listener to order a sound on a frequency-related scale. As discussed in Section 1.3 of [Müller, FMP, Springer 2015], playing a note on an instrument results in a (more or less) periodic sound of a certain **fundamental frequency**. This fundamental frequency is closely related to what is meant by the pitch of a note. The term \"pitch\" allows us to order pitched sounds from \"lower\" to \"higher\"—similarly to the keys of a piano keyboard ordered from left to right." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Pitch Class and Octaves\n", "\n", "Two notes with fundamental frequencies in a ratio equal to any power of two (e.g., half, twice, or four times) are perceived as very similar. Because of that, all notes with this kind of relation can be grouped under the \n", "same **pitch class**. This observation also leads to the fundamental notion of an **octave**, which is defined to be the interval between one musical note and another one with half or double its fundamental frequency. Using this definition, a pitch class is a set of all pitches or notes that are an integer number of octaves apart. The following figure and sound example illustrates these concepts for the pitch class $\\mathrm{C}$:\n", "\n", "" ] }, { "cell_type": "code", "execution_count": 1, "metadata": { "execution": { "iopub.execute_input": "2024-02-15T08:44:54.118770Z", "iopub.status.busy": "2024-02-15T08:44:54.118456Z", "iopub.status.idle": "2024-02-15T08:44:55.052324Z", "shell.execute_reply": "2024-02-15T08:44:55.051665Z" } }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Pitch class C = {..., C1, C2, C3, C4, C5, C6, C7, ...}\n" ] }, { "data": { "text/html": [ "\n", " \n", " " ], "text/plain": [ "\n", " | \n", " | \n", " | \n", " | \n", " | \n", " | \n", " | \n", " | \n", " |