Simple Chords Dataset

This dataset contains 3 subdatasets:

1. Triad Dataset

 This dataset contains 1.080 piano-roll examples of triads (3-note chords). Each example is a 45-d vector where each vector entry represents a single note and its value represents the volume of that note between 0 and 1. Table 1 shows the connection between a musical note and its corresponding entry on the piano-roll vector.

Table 1: Piano-roll vector to note

Vector Entry
Note
Vector Entry
Note
Vector Entry
Note
Vector Entry
Note

1
Cn1
13

Cn2

25
Cn3
37
Cn4

2
Db1
14
Db2
26
Db3
38
Db4

3
Dn1
15
Dn2
27
Dn3
39
Dn4

4
Eb1
16
Eb2
28
Eb3
40
Eb4

5
En1
17
En2
29
En3
41
En4

6
Fn1
18
Fn2
30
Fn3
42
Fn4

7
Gb1
19
Gb2
31
Gb3
43
Gb4

8
Gn1
20
Gn2
32
Gn3
44
Gn4

9
Ab1
21
Ab2
33
Ab3
45
Ab4

10
An1
22
An2
34
An3

11
Bb1
23
Bb2
35
Bb3

12
Bn1
24
Bn2
36
Bn3

Each example is a basic triad. There are 10 triad types in this dataset. Each triad musical structure and vector structure are shown on table 2. The vector structure shows the second and third note position relative to the first note of the triad. Augmented on first inversion and Augmented on second inversion have the same vector structure as Augmented so they are indistinguishable from one another, therefore, they are not added to the dataset to avoid repetition of examples.

Table 2: Musical and vector structure of dataset triads

Triad Name
Musical Structure
Vector Structure

Major (m)
(first, major third, fifth)
(0,4,7) 

Major first inversion (m1)
(major third, fifth, eight)
(0,3,8) 

Major second inversion (m2)
(fifth, eight, major tenth)
(0,5,9) 

Minor (n)
(first, minor third, fifth)
(0,3,7) 

Minor first inversion (n1)
(minor third, fifth, eight)
(0,4,9) 

Minor second inversion (n2)
(fifth, eight, minor tenth)
(0,5,8) 

Diminished (d) 
(first, minor third, diminished fifth)
(0,3,6) 

Diminished first inversion (d1)
(minor third, diminished fifth,  eight)
(0,3,9) 

Diminished second inversion (d2)
(diminished fifth, eight, minor tenth)
(0,6,7) 

Augmented (a)
(first, major third,  augmented fifth)
(0,4,8) 

There are examples of all the triad types with all the 12 available notes of the western musical system as base note: Cn, Db, Dn, Eb, En, Fn, Gb, Gn, Ab, An, Bb, and Bn. (n is natural, b is flat). Also, the chords were recorded across 3 octaves for a total of 36 base notes. The vector has 45 entries because when the base note is Bb3 (36th entry), on the worst case (major triad second inversion or diminished triad first inversion), the third note is an Ab4 (45th entry). Finally, each example was created with three different volumes: forte (f) with an amplitude of 1, metsoforte (m) with an amplitude of 2/3, and piano (p) with an amplitude of 1/3.

On resume, there are 10 triad types, 12 base notes, 3 octaves and 3 volumes for a total of 10*12*3*3 = 1,080 examples. The dataset is saved on a Numpy array.

2. Tetrad Dataset

The Tetrad Dataset contains 792 examples of tetrads (4-note chords). Just like the Triad Dataset, each example is a 45-d vector where each vector entry represents a single note and it value represents the volume of that note between 0 and 1.

Each example is a basic seventh-chord tetrad. There are 8 seventh chord types in this dataset. Each tetrad musical structure and vector structure are shown on table 3. The vector structure shows the second, third and fourth note position relative to the first note of the tetrad.

Table 3: Musical and vector structure of dataset tetrads

Tetrad Name
Musical Structure
Vector Structure

Augmented Major (augMaj7)
(first, major third,  augmented fifth, major seventh)
(0,4,8, 11)

Major Seventh (maj7) 
(first, major third, fifth, major seventh)
(0,4,7, 11)

Minor Major Seventh (minMaj7)
(first, minor third, augmented fifth, major seventh)
(0,3,7, 11)

Augmented Seventh (aug7)
(first, major third, augmented fifth, minor seventh)
(0,4,8, 10)

Dominant Seventh (7)
(first, major third, fifth, minor seventh)
(0,4,7, 10)

Minor Seventh (m7)
(first, minor third, fifth, minor seventh)
(0,3,7, 10)

Half Diminished (m7b5)
(first, minor third, diminished fifth, minor seventh)
(0,3,6, 10)

Diminished Seventh (dim7)
(first, minor third, diminished fifth, diminished seventh)
(0,3,6, 9)

Each of this tetrads were recorded with 33 base notes, ranging from Cn1 to An3 as shown in \ref{tab:vector_to_note} to make sure t0 use all the 45 notes available and avoiding overflow that will lead to less than 4 notes per chord. Finally, each example was created with three different volumes: forte (f) with an amplitude of 1, metsoforte (m) with an amplitude of 2/3, and piano (p) with an amplitude of 1/3.

On resume, there are 8 tetrad types, 33 base notes and 3 volumes for a total of 8*33*3 = 792 examples. The dataset is saved on a Numpy array.

3. Random Dataset

The Random Validation Dataset is a dataset that contains 3,000 examples 3 random notes distributed uniformly across the 45 possible different notes. 1,000 examples are generated by selecting 3 random notes out of the 45 possible notes. Then, each of the 1,000 examples is saved on the three possible different volumes: forte (f) with an amplitude of 1, metsoforte (m) with an amplitude of 2/3, and piano (p) with an amplitude of 1/3. This gives a total of 3,000 examples.