列表理解的频率数据帧？

Question

I'm trying to build a pandas DataFrame of chromatic frequencies between A1 (55Hz) and A8 (7040Hz). Essentially, I want it to look like this...

df = pd.DataFrame(columns=['A', 'A#', 'B', 'C', 'C#', 'D', 'D#', 'E', 'F', 'F#', 'G', 'G#'])
df.loc[0] = (55, 58.27, 61.74, 32.7, 34.65, 36.71, 38.89, 41.2, 43.65, 49, 51.91)

But without having to manually assign all the frequencies to their respective notes and with an octave per row (octave 1 to 8).

Based on the site http://pages.mtu.edu/~suits/notefreqs.html , the space between each note (or a 'half-step') given a single note is...

def hz_stepper(fixed_note, steps):
    a = 2 ** (1/12)
    return fixed_note * a ** steps

Using that function 'hz_stepper', I can chromatically increase or decrease a given note n times by assigning 1 or -1 to steps variable.

My question is, how do I create a DataFrame where all the rows look like how I did it manually, but using a list comprehension to form the rows?

Answer 1

just iterate over the pitches and reshape the result afterwards:

import numpy as np
import pandas as pd

base = 55.
n_octave = 8
columns = ['A', 'A#', 'B', 'C', 'C#', 'D', 'D#', 'E', 'F', 'F#', 'G', 'G#']

factors = 2**(np.arange(12 * n_octave) / 12.)
pd.DataFrame(data=base * factors.reshape((n_octave, 12)), columns=columns)

Explanation

factors are the desired frequencies as 1d numpy array, but they are not in the tabular form required for the DataFrame. reshape creates a view of the array content, that has shape (n_octave, 12) such that rows are contiguous. Eg

>>> np.arange(6).reshape((2, 3))
array([[0, 1, 2],
       [3, 4, 5]])

This is just the format needed for the DataFrame.

Answer 2

from your begining :

df = pd.DataFrame(columns=['A', 'A#', 'B', 'C', 'C#', 'D', 'D#', 'E', 'F', 'F#', 'G', 'G#'])
df.loc[0] = 55*2**(np.arange(12)/12)
for i in range(8): df.loc[i+1]=2*df.loc[i]