Krumhansl-Schmuckler key estimation

ks_key.py

import numpy as np
import scipy.linalg
import scipy.stats

def ks_key(X):
    '''Estimate the key from a pitch class distribution
    
    Parameters
    ----------
    X : np.ndarray, shape=(12,)
        Pitch-class energy distribution.  Need not be normalized
        
    Returns
    -------
    major : np.ndarray, shape=(12,)
    minor : np.ndarray, shape=(12,)
    
        For each key (C:maj, ..., B:maj) and (C:min, ..., B:min),
        the correlation score for `X` against that key.
    '''
    X = scipy.stats.zscore(X)
    
    # Coefficients from Kumhansl and Schmuckler
    # as reported here: http://rnhart.net/articles/key-finding/
    major = np.asarray([6.35, 2.23, 3.48, 2.33, 4.38, 4.09, 2.52, 5.19, 2.39, 3.66, 2.29, 2.88])
    major = scipy.stats.zscore(major)
    
    minor = np.asarray([6.33, 2.68, 3.52, 5.38, 2.60, 3.53, 2.54, 4.75, 3.98, 2.69, 3.34, 3.17])
    minor = scipy.stats.zscore(minor)
    
    # Generate all rotations of major
    major = scipy.linalg.circulant(major)
    minor = scipy.linalg.circulant(minor)
    
    return major.T.dot(X), minor.T.dot(X)

how is the correlation score greater than 1?

I've slightly adapted this code and fixed "greater than 1" issue mentioned by @devanshugupta.

import numpy as np
import scipy.linalg
from scipy.stats import zscore

from typing import List


@dataclass
class KeyEstimator:

    # adapted from:
    # https://gist.github.com/bmcfee/1f66825cef2eb34c839b42dddbad49fd

    major = np.asarray(
        [6.35, 2.23, 3.48, 2.33, 4.38, 4.09, 2.52, 5.19, 2.39, 3.66, 2.29, 2.88]
    )
    minor = np.asarray(
        [6.33, 2.68, 3.52, 5.38, 2.60, 3.53, 2.54, 4.75, 3.98, 2.69, 3.34, 3.17]
    )

    def __post_init__(self):
        self.major = zscore(self.major)
        self.major_norm = scipy.linalg.norm(self.major)
        self.major = scipy.linalg.circulant(self.major)

        self.minor = zscore(self.minor)
        self.minor_norm = scipy.linalg.norm(self.minor)
        self.minor = scipy.linalg.circulant(self.minor)

    def __call__(self, x: np.array) -> List[np.array]:

        x = zscore(x)
        x_norm = scipy.linalg.norm(x)

        coeffs_major = self.major.T.dot(x) / self.major_norm / x_norm
        coeffs_minor = self.minor.T.dot(x) / self.minor_norm / x_norm

        return coeffs_major, coeffs_minor