Relative Mode

This package contains Python code for calculating relative mode from an audio signal. Relative mode refers to the degree between how major or minor does the segment of music sound at a given time. It is based on a classic key-finding algorithm (Krumhansl-Schmuckler, 1990) and extracts the pitch-class information using chromagrams. The relative mode is calculated as the difference between the strongest major key and the strongest minor key. Relative mode can vary from -1.0 (clearly in minor) to + 1.0 (clearly in major) and gives a value between these extremes for the whole excerpt. Alternatively the algorithm can provide the output for each window of analysis (segments of 3 seconds as a default).

The algorithm and how it is evaluated is fully documented in a manuscript titled “Major-minorness in Tonal music – Evaluation of Relative Mode Estimation using Expert Ratings and Audio-Based Key-finding Principles” by Tuomas Eerola and Michael Schutz (Psychology of Music, in press). Key-finding Principles” by Tuomas Eerola and Michael Schutz (Psychology of Music, 2025).

Libraries

import librosa
import librosa.display
import matplotlib
import numpy as np
from matplotlib import pyplot as plt
import pandas as pd

Load package using pip

pip install relative_mode

Make function calls explicit for the subsequent analyses.

from src.relative_mode import Tonal_Fragment
from src.relative_mode import relative_mode
from src.relative_mode import RME_across_time

Load a music example

Recording of J.S. Bach’s C Major Prelude (WTC Book I) (an extract).

filename = 'data/Bach_1_Gould_0_Major_bachGould1971.wav'
y, sr = librosa.load(filename)
plt.figure(figsize=(9,2.5))
librosa.display.waveshow(y, sr = sr)
plt.show()

Estimate relative mode

Here we don’t specify any parameters but just run relative_mode using the default parameters.

RM, RM_segments = relative_mode(y = y, sr = sr)
print(round(RM['tondeltamax'][0],3))

0.258

The value of 0.258 could be called “moderately in major”. Value closer to 0 would indicate no clear tendency for major or minor and any value below -0.30 would suggest clearly in minor key.

The relative mode can be computed with a different options. You can alter key profile (e.g. krumhansl, albrecht (default), aarden, or bellman), similarity metrics (pearson, cosine (default), or euclidean), chromatype from CENS to CQT. There are also some alternative outputs of the measure.

Here’s a variant analysis using a different distance measure and chroma type:

RM2, RM2_segments = relative_mode(y = y, sr = sr, profile = 'simple', distance = 'pearson', chromatype = 'CQT')
print(RM2)

   tonmaxmaj  tonmaxmin  tondeltamax
0   0.688322   0.640134     0.144563

This outputs the tondeltamax value of 0.145, which is the relative mode with these parameters. The extra outputs refer to the highest correlation coefficient with the major (tonmaxmaj) and minor (tonmaxmin). Note that the distance metrics have different scales so the outputs have been rescaled to be more easily comparable.

Estimate relative mode across the excerpt

The second output provides a relative mode value for each window of the analysis. The segment timing reflects the hoplen argument. Here we also remove the percussive sounds with an extra parameter (remove_percussive=True):

RM, RM_segments = relative_mode(y = y, sr = sr, winlen = 3.5, hoplen = 1.5, remove_percussive=True)
print(RM_segments)

    onset  tonmaxmaj  tonmaxmin   tonkey  tondeltamax
0     0.0   0.895319   0.730949  C major     1.068404
1     1.5   0.944695   0.805112  C major     0.907290
2     3.0   0.921238   0.838886  C major     0.535289
3     4.5   0.766527   0.850092  D minor    -0.543171
4     6.0   0.876043   0.834032  G major     0.273075
5     7.5   0.855947   0.757587  G major     0.639340
6     9.0   0.927221   0.858836  G major     0.444506
7    10.5   0.977284   0.850480  C major     0.824227
8    12.0   0.878142   0.710265  C major     1.091195
9    13.5   0.876234   0.803292  C major     0.474120
10   15.0   0.807938   0.873190  A minor    -0.424143
11   16.5   0.784958   0.905604  A minor    -0.784197
12   18.0   0.774552   0.893590  A minor    -0.773744
13   19.5   0.786032   0.799719  D minor    -0.088968
14   21.0   0.907874   0.857099  D major     0.330038
15   22.5   0.901390   0.771279  G major     0.845724
16   24.0   0.913086   0.787238  G major     0.818011
17   25.5   0.907057   0.806591  G major     0.653024
18   27.0   0.819221   0.881004  E minor    -0.401589
19   28.5   0.887434   0.874749  C major     0.082456

One can also visualise the relative mode across time. In this case there is a cubic interpolation to make the lines between the windows appear smooth, but one can alter this interpolation parameter.

fig, RM3 = RME_across_time(filename = filename, winlen = 2, hoplen = 2, cropfirst = 0, croplast = 15, chromatype = 'CENS', profile = 'albrecht', distance = 'cosine', plot = True, interpolation='cubic')
fig
plt.show()

Extras

Weights to normalise the output across distance metrics

The tondeltamax output depends on the distance metric used. To normalise close to between -1 and +1 for an easier use of the algorithm, a weight is assigned to the raw delta value. These weights were empirically derived by creating all possible 3 to 5-note chords and calculating the relative mode with the available distance metrics. For cosine distance metric, the weight is 6.5, for pearson correlation, 10.0, and for euclidean distance, 3.0. The purpose is to keep the output more easily understandable (max major corr. - max minor corr.) * weigth.

Alternative analyses

In the article (Eerola & Schutz, 2025), we assess various parameters of the model (key profiles, distance measures, alternative formulations of the model) in Experiment 1. We also examine what could explain the variations in model success across recordings used in Experiment 3. Here we briefly report these alternative explorations.

Experiment 1: Alternative analyses

The model compares the difference between highest maximum major key strength and the maximum minor key strength. We also have two alternative formulations of the model, one that utilises comparison with the parallel minor and another one relying on the relative minor.

The parallel minor key of the major key received lower correlation with the expert ratings (r = 0.698) than the actual model (r = 0.840). The second alternative relies on the relative minor key of the major key. This alternative received a lower correlation (r = 0.766) with the expert ratings compared to the proposed model. For this reason, we did not pursue these two alternatives further.

We also run alternative formulations of window length (1 to 5 seconds) and overlap (0 to 75% overlap) which did not provide substantially better fit with the data. Finally, the way of summarizing the RME across the analysis windows with the mean values did not appear to be significantly different from the taking median of the predictions within the analysis windows (r = 0.785).

Experiment 3: Alternative analyses

To identify the consistent noise factors in the RME analysis from audio, we extracted dynamics, several timbral descriptors (brightness, spectral centroid, spectral flux, rms, roughness) and tempo descriptors for each excerpt using Essentia, and added these as additional predictors to the regression with RME model predicting the expert ratings. However, no single audio descriptor could contribute significantly (more than 2 % of the variance accounted) to the model that already had a highly successful predictor (RME) within it. A more extensive analysis of the potential additional considerations would benefit from a larger set of materials and from systematic alterations of the most plausible variations of these factors.

Improvements to the implementation

Version 0.0.4, 7 February 2026

• RME_across_time accepts interpolation parameter to control the way output is interpolated across the analysis windows. cubic is the default, but linear and none are possible as well.

• The output of the segments has now explicit time code (onset time in seconds).

• The parameters cropfirst and cropfirst now work for RME_across_time.

• The output of the RM_across_time has now tonmaxmaj and tonmaxmin output and the numeric output is unaffected by interpolation.

• A new option remove_percussive has been added to remove percussive noise (using Librosa’s median filtering solution, see librosa.decompose.hpss) from the signal. Filtering is set to False by default.

References

Eerola, T. & Schutz, M. (2025). Major-minorness in Tonal music – Evaluation of Relative Mode Estimation using Expert Ratings and Audio-Based Key-finding Principles. Psychology of Music, 0(0). https://doi.org/10.1177/03057356251326065