# From Ratios to Scales – Diatonic Minor Scale

### 5 Limit C Minor Diatonic Scale

Let's now create a tuning system for a combined scale using the 5 limit minor scale for the 1, 4, and 5 chords to create the ratio's for all the intervals we will need. Below is the 5 limit diatonic minor scale below:

Musical Ratio Musical Interval Note Hz Value
1/1 Root C 130.81
9/8 Major 2nd D 147.16
6/5 Minor 3rd Eb 156.97
4/3 Perfect 4th F 174.42
3/2 Perfect 5th G 196.22
8/5 Minor 6th Ab 209.30
9/5 Minor 7th Bb 235.46
2/1 Octave C 261.76

### 5 Limit F Minor Diatonic Scale - C Minor Ratio's

Next let's take this same scale and build it for the key of F, the 4th scale degree of the diatonic scale in the key of c.  Since our objective is to create a "combined" scale of these respective diatonic scales we need to multiply the ratio that is the root of the new scale by the ratio we want to generate for the scale, the result is the ratio in relation to the root of the parent scale (in this case the key of c).

Musical Ratio
for Diatonic Scale
Musical Interval
in Relation to Root
Interval Note Hz Value
4/3 * 1/1 4/3 Root F 174.42
4/3 * 9/8 3/2 Major 2nd G 196.22
4/3 * 6/5 8/5 Minor 3rd Ab 209.30
4/3 * 4/3 16/9 Perfect 4th Bb 232.56
4/3 * 3/2 2/1 Perfect 5th C 290.69
4/3 * 8/5 16/15 Minor 6th Db 279.07
4/3 * 9/5 6/5 Minor 7th Eb 313.96
2/1 4/3 Octave F 348.83

### 5 Limit G Minor Diatonic Scale - C Minor Ratio's

Now let's do calculate the ratio's for the major diatonic scale for G and the ratio's in relationship to the root.

Musical Ratio
for Diatonic Scale
Musical Interval
in Relation to Root
Interval Note Hz Value
3/2 * 1/1 3/2 Root F 196.22
3/2 * 9/8 27/16 Major 2nd G 220.75
3/2 * 6/5 9/5 Minor 3rd A 235.46
3/2 * 4/3 2/1 Perfect 4th Bb 261.62
3/2 * 3/2 9/8 Perfect 5th C 294.33
3/2 * 8/5 6/5 Major 6th D 313.95
3/2 * 9/5 27/20 Major 7th E 353.20
2/1 3/2 Octave F 392.44

### C Minor Combined Scale with F & G Major

Let's finish up this scale by adding the notes that aren't present in C Major from the F and G major diatonic scales, like we did in lesson 2, to create a "combined major scale".  Notice this is an 11 note scale and isn't a full chromatic scale.  This scale doesn't have any note/ratio's for a major 3rd, tritone, major 6th, or major 7th. Also note how there are 2 different minor 7ths, 16/9 and 9/5, we will come back to this in feature writings.

Ratio Interval Note Hz Value
1/1 Root C 130.81
16/15 Minor 2nd Db 139.53
9/8 Major 2nd D 147.16
6/5 Minor 3rd Eb 156.97
4/3 Perfect 4th F 174.42
27/20 4th F 176.6
3/2 Perfect 5th G 196.22
8/5 Minor 6th A 209.30
27/16 Major 6th A 220.75
16/9 Minor 7th Bb 232.56
9/5 Minor 7th Bb 235.46
2/1 Octave C 261.76
Scroll to Top