Looking into the musical notes and color correspondence

the_color_of_notes.py

"""
 I've often seen that “color of musical notes” thing, 
 and I always wondered about it (especially because I’d like to use it as educational support when I teach my (reluctant) 
 daughter music). 
 The mappings I see are not always consistent, but one comes up most often; 
 the one where the red-to-violet range is mapped to the C-to-B range. 
 Now this could just so happen to be correct, but the choice that C as the canonical root note of a scale seems 
 to be arbitrary, whereas red as the first color is a physical reality, leading me to think that:
- The choice of C as the root note was purposely based on the red-to-violet correspondence
- It’s a crock of s**t 
 
Here's look into the numbers…

The conclusion is:

It’s a lie. At least the C -> red, D -> Orange, ..., B -> Violet is.

But… It does seem to correspond to an A-based scale! 
That is A -> Red (on the orange side), B -> Yellow, C -> Green, D -> Blue, E -> Blue-Violet, F -> Red-Violet, G -> Red

Which now makes me think that it’s the reason why we call it “A” in the first place...

The following script prints:

abs_note  log2_base_freq   Color  color_freq_THz
       C            0.03   Green           566.0
      C#            0.11    Cyan           600.0
       D            0.20    Blue           638.0
      D#            0.28    Blue           638.0
       E            0.36  Violet           714.0
       F            0.45  Violet           714.0
      F#            0.53  Violet           714.0
       G            0.61     Red           428.0
      G#            0.70     Red           428.0
       A            0.78     Red           428.0
      A#            0.86  Orange           484.0
       B            0.95  Yellow           517.0
       
"""
import requests
import pandas as pd
import numpy as np
import re
from collections import Counter

note_to_abs_note = lambda note: re.compile('[#A-G]+').match(note).group(0)

def get_notes_base_freq():
    url = 'https://pages.mtu.edu/~suits/notefreqs.html'
    r = requests.get(url)
    html = r.content
    _, df = pd.read_html(html)
    df.columns = ['Note', 'Frequency', 'Wavelength']
    df['abs_note'] = list(map(note_to_abs_note, df['Note']))
    df['log2_freq'] = np.log2(df['Frequency'])
    df['log2_base_freq'] = np.mod(df['log2_freq'], 1)  # to get a representative frequency number for a note
    
    # the decimals=2 is what leads to a consistent note->log2_base_freq mapping:
    df['log2_base_freq'] = np.round(df['log2_base_freq'], decimals=2)  
    assert len(Counter(df['log2_base_freq'])) == len(Counter(df['abs_note']))  # assert that we're good!
    
    t = df[['abs_note', 'log2_base_freq']].groupby('abs_note').mean()
    return t.reset_index()

def get_color_base_freq():
    url = 'https://en.wikipedia.org/wiki/Color'
    r = requests.get(url)
    html = r.content
    tables = pd.read_html(html)
    d = tables[2]  # chose number 2 manually (see "the way I got the color data" section)
    d = d[['Color', '(THz)']]
    d = d.iloc[1:8]
    d['(THz)'] = d['(THz)'].astype(float)
    d['Color'] = d['Color'].replace('Violet (visible)', 'Violet')
    t = d['(THz)'] * 1e12  # Tera means 10^12 (10 ** 12 == 1e12)
    d['log2_base_freq'] = np.mod(np.log2(t), 1)
    d['color_freq_THz'] = d['(THz)']
    del d['(THz)']
    return d

notes = get_notes_base_freq()
color = get_color_base_freq()

the_truth_about_it = pd.merge_asof(notes.sort_values('log2_base_freq'), 
                                   color.sort_values('log2_base_freq'), 
                                   on='log2_base_freq')

print(the_truth_about_it.to_string(index=False))

"""
Prints:

abs_note  log2_base_freq   Color  color_freq_THz
       C            0.03   Green           566.0
      C#            0.11    Cyan           600.0
       D            0.20    Blue           638.0
      D#            0.28    Blue           638.0
       E            0.36  Violet           714.0
       F            0.45  Violet           714.0
      F#            0.53  Violet           714.0
       G            0.61     Red           428.0
      G#            0.70     Red           428.0
       A            0.78     Red           428.0
      A#            0.86  Orange           484.0
       B            0.95  Yellow           517.0
"""

A jupyter notebook with the code, and other stuff, here: https://github.com/thorwhalen/my_notebooks/blob/master/Sound%20and%20light%20--%20the%20color%20of%20musical%20notes.ipynb