Notes that are one octave apart have the same name and are related in frequency values. Given the frequency of any note, the frequency of same note one octave higher is doubled and this pattern continues as you move up and down the notes on a keyboard or any other musical instrument. Song writers and singers use this knowledge to change the pitch of a note up or down to align with a person\u2019s vocal range. Regardless of which [latex]C[\/latex] is played or sung, the pitch is the same and the frequency is related by a power or two.<\/p>\r\n Notes that are one octave apart share the same name and have a frequency relationship where the higher note's frequency is double that of the lower note. When moving to a lower octave, the frequency of the note is halved.<\/p>\r\n<\/div>\r\n<\/section>\r\n Labeled keys on a keyboard are numbered for ease in identification. For example, middle [latex]C[\/latex] is labeled as [latex]C_4[\/latex] on a full keyboard as it is the fourth C from the left in a set of eight notes. The frequency of [latex]C_4[\/latex] is [latex]262[\/latex] Hz, rounded to the nearest whole number.<\/p>\r\n Let's look at an example of finding the approximate frequency of a given note.<\/p>\r\n Given that the frequency of [latex]C_4[\/latex] is [latex]262[\/latex] Hz, find the approximate frequency of [latex]C_6[\/latex].<\/p>\r\n The frequency of each consecutive higher octave doubles. Given that the frequency of [latex]C_4[\/latex] is [latex]262[\/latex] Hz, the frequency of [latex]C_5[\/latex] is found by doubling the frequency of [latex]C_4[\/latex], which is [latex]524[\/latex] Hz. In similar fashion, the frequency of [latex]C_6[\/latex] is found by doubling the frequency of [latex]C_5[\/latex], which yields [latex]1,048[\/latex] Hz.<\/p>\r\n The approximate frequency of [latex]C_6[\/latex] is [latex]1,048[\/latex] Hz.<\/p>\r\n<\/section>\r\n Try it yourself.<\/p>\r\n Given that the frequency of [latex]E_4[\/latex] is [latex]330[\/latex] Hz, find the approximate frequency of [latex]E_2[\/latex] rounded to the nearest whole number.<\/p>\r\n\r\n[reveal-answer q=\"4333\"]Show Solution[\/reveal-answer] The frequency of each consecutive lower octave halves. Given that the frequency of [latex]E_4[\/latex] is [latex]330[\/latex] Hz, the frequency of [latex]E_3[\/latex] is found by halving the frequency of [latex]E_4[\/latex], which is [latex]165[\/latex] Hz. In similar fashion, the frequency of [latex]E_2[\/latex] is found by halving the frequency of [latex]E_3[\/latex], which yields [latex]82.5[\/latex] Hz.<\/p>\r\n We were asked to round this up to the nearest whole number, so the approximate frequency of [latex]E_2[\/latex] is [latex]83[\/latex] Hz.<\/p>\r\n\r\n[\/hidden-answer]<\/section>\r\n [ohm2_question hide_question_numbers=1]13362[\/ohm2_question]<\/p>\r\n<\/section>\r\n We have explored some basics components of frequency, pitch, note relationships, and octaves, which are building blocks of music. It may be exciting to learn that the mathematical relationships found in music are vast and grow in complexity beyond the math commonly studied in high school.<\/p>\r\n Streaming services have grown exponentially in popularity thanks in large part to customized music listening through phone use and devices such as Google as well as Amazon Echo and Alexa devices for home and vehicles, adding to ways that artists are paid royalties. Spotify, which was launched in 2008, typically plays artists [latex]$0.06[\/latex] per time a song is streamed, with some artists receiving up to [latex]$0.84[\/latex] per play amounting to over [latex]$9[\/latex] billion in revenue for Spotify in 2020. Since 2014, Spotify\u2019s revenue has grown over a billion dollars a year, with roughly half of their revenue being paid out in royalties, which was good news for artists during the Covid-19 pandemic when in-person concerts and shopping were hindered.<\/p>\r\n<\/section>","rendered":" Notes that are one octave apart have the same name and are related in frequency values. Given the frequency of any note, the frequency of same note one octave higher is doubled and this pattern continues as you move up and down the notes on a keyboard or any other musical instrument. Song writers and singers use this knowledge to change the pitch of a note up or down to align with a person\u2019s vocal range. Regardless of which [latex]C[\/latex] is played or sung, the pitch is the same and the frequency is related by a power or two.<\/p>\n Notes that are one octave apart share the same name and have a frequency relationship where the higher note’s frequency is double that of the lower note. When moving to a lower octave, the frequency of the note is halved.<\/p>\n<\/div>\n<\/section>\n Labeled keys on a keyboard are numbered for ease in identification. For example, middle [latex]C[\/latex] is labeled as [latex]C_4[\/latex] on a full keyboard as it is the fourth C from the left in a set of eight notes. The frequency of [latex]C_4[\/latex] is [latex]262[\/latex] Hz, rounded to the nearest whole number.<\/p>\n Let’s look at an example of finding the approximate frequency of a given note.<\/p>\n Given that the frequency of [latex]C_4[\/latex] is [latex]262[\/latex] Hz, find the approximate frequency of [latex]C_6[\/latex].<\/p>\n The frequency of each consecutive higher octave doubles. Given that the frequency of [latex]C_4[\/latex] is [latex]262[\/latex] Hz, the frequency of [latex]C_5[\/latex] is found by doubling the frequency of [latex]C_4[\/latex], which is [latex]524[\/latex] Hz. In similar fashion, the frequency of [latex]C_6[\/latex] is found by doubling the frequency of [latex]C_5[\/latex], which yields [latex]1,048[\/latex] Hz.<\/p>\n The approximate frequency of [latex]C_6[\/latex] is [latex]1,048[\/latex] Hz.<\/p>\n<\/section>\n Try it yourself.<\/p>\n Given that the frequency of [latex]E_4[\/latex] is [latex]330[\/latex] Hz, find the approximate frequency of [latex]E_2[\/latex] rounded to the nearest whole number.<\/p>\nfrequencies of octaves<\/h3>\r\n
\r\n[hidden-answer a=\"4333\"]\r\n\r\nSpotify Royalty Payments<\/h4>\r\n
Frequencies of Octaves<\/h2>\n
frequencies of octaves<\/h3>\n