Pandas: sorting by integer notation value - pandas

Question

In this dataframe, column key values correspond to integer notation of each song key.
df
track key
0 Last Resort 4
1 Casimir Pulaski Day 8
2 Glass Eyes 8
3 Ohio - Live At Massey Hall 1971 7
4 Ballad of a Thin Man 11
5 Can You Forgive Her? 11
6 The Only Thing 3
7 Goodbye Baby (Baby Goodbye) 4
8 Heart Of Stone 0
9 Ohio 0
10 the gate 2
11 Clampdown 2
12 Cry, Cry, Cry 4
13 What's Happening Brother 8
14 Stupid Girl 11
15 I Don't Wanna Play House 7
16 Inner City Blues (Make Me Wanna Holler) 11
17 The Lonesome Death of Hattie Carroll 4
18 Paint It, Black - (Original Single Mono Version) 5
19 Let Him Run Wild 11
20 Undercover (Of The Night) - Remastered 5
21 Between the Bars 7
22 Like a Rolling Stone 0
23 Once 2
24 Pale Blue Eyes 5
25 The Way You Make Me Feel - 2012 Remaster 1
26 Jeremy 2
27 The Entertainer 7
28 Pressure 9
29 Play With Fire - Mono Version / Remastered 2002 2
30 D-I-V-O-R-C-E 9
31 Big Shot 0
32 What's Going On 1
33 Folsom Prison Blues - Live 0
34 American Woman 1
35 Cocaine Blues - Live 8
36 Jesus, etc. 5
the notation is as follows:
'C' --> 0
'C#'--> 1
'D' --> 2
'Eb'--> 3
'E' --> 4
'F' --> 5
'F#'--> 6
'G' --> 7
'Ab'--> 8
'A' --> 9
'Bb'--> 10
'B' --> 11
what is specific about this notation is that 11 is closer to 0 than 2, for instance.
GOAL:
given an input_notation = 0, I would like to sort according to closeness to key 0, or 'C'.
you can get closest value by doing:
closest_key = (input_notation -1) % 12
so I would like to sort according to this logic, having on top input_notation values and then closest matches, like so:
8 Heart Of Stone 0
9 Ohio 0
22 Like a Rolling Stone 0
31 Big Shot 0
33 Folsom Prison Blues - Live 0
(...)
I have tried:
v = df[['key']].values
df = df.iloc[np.lexsort(np.abs(v - (input_notation - 1) %12 ).T)]
but this does not work..
any clues?

Answer 1

You can define the closeness firstly and then use argsort with iloc to sort the data frame:
input_notation = 0
# define the closeness or distance
diff = (df.key - input_notation).abs()
closeness = np.minimum(diff, 12 - diff)
# use argsort to calculate the sorting index, and iloc to reorder the data frame
closest_to_input = df.iloc[closeness.argsort(kind='mergesort')]
closest_to_input.head()
# track key
#8 Heart Of Stone 0
#9 Ohio 0
#22 Like a Rolling Stone 0
#31 Big Shot 0
#33 Folsom Prison Blues - Live 0