Please help to fill out the spreadsheet below using the instruction
Here is the instruction:
B D E circle tonal frequency in Ha, based tonal frequency based on of on multiples/sub-multiples of multiplication/division by rational values of multiples fifths A440 the twelth root of 2 and submultiples of A440 F 440 1 466.16 880.00 2 D count by 12 count by 7 start at note F 1 1 F 2 2 F 3 3 G 4 4 GM 5 5 A 6 6 AM 7 7 B 8 10 9 2 CM 10 3D 11 4 DM 12 5 E 1 6 F 2 7 FM 3 1 G 4 2 GM 5 3 A 6 4 AM 7 5 B 8 6 9 7 CM 10 1 D 11 2 DM 12 3 E 1 4 F 2 5 FM 3 6 G 4 7 GN 5 1 A 6 2 AM 7 3 B 8 4C 9 5 CM 10 6 D 11 7 D 12 1 E 1 2 F 2 3 FW 4 G 4 5 GM 5 6 A 6 7 AM 7 1 B 8 2C 9 3 CM 10 4 D 11 5 DM 12 6 E 3 A 4 E 6 B The Rubric The entry in cell E6 is the note A440, with its frequency denoted as 440 Hz To begin, add 12 to get E18, and set the value in cell E18 equal to twice 440, equal to 880 Continue, by populating cells with the appropriate factors of two in frequency to get 1760 and 3520 Hz Next, continue by populating the appropriate cell with the value 3 * 440 = 1320; then populate the appropriate cell with 2 * 1320 to get 2640 Hz Populate the appropriate cell with the value 1320 * 12 to get 660 Continue this decimation process until frequencies are assigned to each of the 48 notes The First Steps Since notes on a piano, including the black keys, represent a multiplicative increase in frequency, it is possible to approximate the rubric defined in the previous slides by assuming each "half-step" in frequency (A to A# or E to F, where there is no E# in the scale) by a factor of the twelfth root of 2, which is equal to 1.059463 Populate column F by multiplying/dividing the value of A440 by factors of 1.059463 to get values for the remaining cells in column F Next, using the rubric, populate column E. Inspect and compare the values, row by row, in columns E and F. Compare these values graphically Note in particular the harmonic relationships. . Rational Numbers Treating A440 as starting point, try and find rational numbers (e.g., fractions) that relate the frequencies in column E to the reference frequency A440. Provide these fractions as text entries in column G. Note that formatting column G as fractions, as opposed to floating point numbers, will do this quickly. For example, A880 would be represented in column G by the number 2. A1630 would be identified in column G by the number 3, etc. Note that fractions less than 1 would also be used in column G. Values such as 1 % and 1 /4 will appear, and are easily converted to 3/2 and 5/4. Some example entries are provided. B D E circle tonal frequency in Ha, based tonal frequency based on of on multiples/sub-multiples of multiplication/division by rational values of multiples fifths A440 the twelth root of 2 and submultiples of A440 F 440 1 466.16 880.00 2 D count by 12 count by 7 start at note F 1 1 F 2 2 F 3 3 G 4 4 GM 5 5 A 6 6 AM 7 7 B 8 10 9 2 CM 10 3D 11 4 DM 12 5 E 1 6 F 2 7 FM 3 1 G 4 2 GM 5 3 A 6 4 AM 7 5 B 8 6 9 7 CM 10 1 D 11 2 DM 12 3 E 1 4 F 2 5 FM 3 6 G 4 7 GN 5 1 A 6 2 AM 7 3 B 8 4C 9 5 CM 10 6 D 11 7 D 12 1 E 1 2 F 2 3 FW 4 G 4 5 GM 5 6 A 6 7 AM 7 1 B 8 2C 9 3 CM 10 4 D 11 5 DM 12 6 E 3 A 4 E 6 B The Rubric The entry in cell E6 is the note A440, with its frequency denoted as 440 Hz To begin, add 12 to get E18, and set the value in cell E18 equal to twice 440, equal to 880 Continue, by populating cells with the appropriate factors of two in frequency to get 1760 and 3520 Hz Next, continue by populating the appropriate cell with the value 3 * 440 = 1320; then populate the appropriate cell with 2 * 1320 to get 2640 Hz Populate the appropriate cell with the value 1320 * 12 to get 660 Continue this decimation process until frequencies are assigned to each of the 48 notes The First Steps Since notes on a piano, including the black keys, represent a multiplicative increase in frequency, it is possible to approximate the rubric defined in the previous slides by assuming each "half-step" in frequency (A to A# or E to F, where there is no E# in the scale) by a factor of the twelfth root of 2, which is equal to 1.059463 Populate column F by multiplying/dividing the value of A440 by factors of 1.059463 to get values for the remaining cells in column F Next, using the rubric, populate column E. Inspect and compare the values, row by row, in columns E and F. Compare these values graphically Note in particular the harmonic relationships. . Rational Numbers Treating A440 as starting point, try and find rational numbers (e.g., fractions) that relate the frequencies in column E to the reference frequency A440. Provide these fractions as text entries in column G. Note that formatting column G as fractions, as opposed to floating point numbers, will do this quickly. For example, A880 would be represented in column G by the number 2. A1630 would be identified in column G by the number 3, etc. Note that fractions less than 1 would also be used in column G. Values such as 1 % and 1 /4 will appear, and are easily converted to 3/2 and 5/4. Some example entries are provided
