In this answer we give two figures, the fundamental, which is the root note of a scale, and the related notes which sum to it.
Let p be a scale’s fundamental note. Then there are some notes in a scale that can be multiplied by p to get the product of their natural frequency divided by pi. (In mathematics, there’s also a second natural frequency, called the fundamental frequency of the note, and the resulting note is called the notes relative pitch.) For example, the 7th freqnimum (2nd harmonic of the 4th) will be multiplied by 4.6 (the product of the 3rd frequency and two thirds of its natural frequency) to get an even frequency for the 7 th . Here’s another way of thinking of the 7th freqnimum: it’s a scale on a perfect fifth string, the G string, which has the natural frequency of 2 Hz. So the notes in the scale are all of the natural frequency in the G string, and can be put together to get the 7th note with a fractional fractional part. For example, the G string’s 6th note is multiplied by -2 and the result is a note of 1/4 octave above, which is the 7th freqnimum in the G scale. This is equivalent to the original note by using the natural frequency of 2 Hz to make a note of 1/4 octave up. The exact harmonic notes of the second harmonic of the G scale are .
Now consider the 7th freqnimum that’s on the G string. A note in the scale is found in this case by multiplying the natural frequencies 2 Hz and 1 Hz together, and dividing them by pi. This gives -.0216 (0.000616) . The frequency is the sum of two notes in the scale, or its root note. The product of the root note + the natural frequency -, and each of the two freqsnums above it, is always a 1/4-octave note. The fundamental on the G string is -14.2%. (A note of 1/4 octave above the 7th may be called a 2nd harmonic, but the octave scale only includes the roots!) The 1st note above it (the 5th) and the 9th note (the 1st), are also notated as . If the 7th freqnimum in (1) is the G root note for 7th notes,
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