Paragraphs in this page are:
Combining theoretical issues
Finding intervals in a scale
Finding scales for an interval
Combining theoretical issues
Now that we know intervals and mode-scales, the next logical step is to find the relation between them. This page is in a way relevant to the next (chord to scale) page and the present paragraph is valid for that page too.
The relation between intervals and scales though, has to be in such a way not to mess with music system issues. That's why modes like the Harmonic minor and Melodic minor are not going to be presented here, since they are alterations of the Natural minor (or Aeolian) for Tonal (think harmonic) reasons.
Only the Major (Ionian) and the Dorian Mode will be discussed here as ones that represent various issues and the work method can easily be transferred to other mode research, altering the results accordingly.
Keep in mind a definition prequisite for understanding the page: The Degree.
| The Degree is the position of a tone according to the interval distance from the base of a scale, measured primarily as a number and secondary as the interval quality. |
As you will soon find out, when the scale is known the degree is named only as quantity (number) because the scale notes are already known since a Scale is a Mode applied from a certain tone.
But when we seek the scales, the degrees have to present themselves as interval quantity as well as quality, because otherwise we won't be able to find the scale base.
Finding intervals in a scale
Let's now look at two very well known Modes: The Major (Ionian) and the Dorian.
The Major is the Mode that fully represents the Major tonal harmony.
The Dorian is legendary for various music genres that favor inprovization.
One score is worth thousants of words.
Let's see the C Major (Ionian) Scale intervals.
 |
Scale results for Ionian according to degrees:
| Interval |
Degrees |
Interval |
Degrees |
| 2nd Majors: | 1
2 4 5 6 |
2nd minors: | 3 7 |
| 3rd
Majors: |
1
4 5 |
3rd minors: | 2
3 6 7 |
| 4th
Perfects: |
1
2 3 5 6 7 |
4th
Augmented: |
4 |
| 5th
Perfects: |
1
2 3 4 5 6 |
5th
diminished: |
7 |
| 6th
Majors: |
1
2 4 5 |
6th
minors: |
3
6 7 |
| 7th Majors: | 1 4 |
7th minors: | 2
3 5 6 7 |
Vertical interval relation according to scale base:
If we search which intervals start from the base, therefore have the degree of 1, we find out the vertical relation of all notes to the base one.
So, the Major (Ionian) Mode in general has: 1P 2M 3M 4P 5P 6M 7M.
P stands for Perfect, M stands for Major.
So, All note degrees in the Major Mode are either Perfect or Major.
Let's now see the C Dorian Scale intervals.
 |
Scale results for Dorian according to degrees:
| Interval | Degrees | Interval | Degrees |
| 2nd Majors: | 1
3 4 5 7 |
2nd minors: | 2 6 |
| 3rd Majors: | 3
4 7 |
3rd minors: | 1
2 5 6 |
| 4th Perfects: | 1
2 4 5 6 7 |
4th Augmented: | 3 |
| 5th Perfects: | 1
2 3 4 5 7 |
5th diminished: | 6 |
| 6th Majors: | 1
3 4 7 |
6th minors: | 2
5 6 |
| 7th Majors: | 3 7 |
7th minors: | 1
2 4 5 6 |
What we see in first sight is that certain intervals are located elsewhere and certain degrees produce different intervals than the Major (Ionian) Mode.
Vertical interval relation according to scale base:
The intervals from the base are also different than the ones from the Major Mode.
Now, the Dorian Mode in general has: 1P 2M 3m 4P 5P 6M 7m.
P stands for Perfect, M stands for Major, m stands for minor.
So, the Dorian Mode has 2nd and 6th Major, 3rd and 7th minor plus Perfects.
Finding scales for an interval
Since the reversed question is more complicated, we will focus on one Mode, the Major one.
The good part is that the relation is one to one:
If a certain scale has x specific intervals, the specific interval can belong to no more no less than x scales.
The bad part is this:
To find the specific scales, we have to count in the opposite direction considering quality as well as quantity in order to find the scale bases.
Let's work on a specific question:
In which Major scales does the C-E interval belong to?
1) C-E is 3rd Major.
2) Looking back to the previous paragraph, we see that C Major Scale, therefore the C Major Mode, so ALL SCALES have the 3rd Major positioned in the 1 4 5 degrees.
3) The degrees are 1stPerfect, 4thPerfect and 5thPerfect.
4) We count down these degrees as intervals from the in-question interval's base which is C.
5) We find C,G,F Major Scales.
 |
There is also another method: To test all scales according to accidentals and/or key signature and find out which scales comply to the interval notes, but it is more time consuming and less harmony oriented.
This question can adopt to different intervals and different modes. Keep in mind that different intervals belong to different numbers of scales and different modes produce different intervals as well as notes in their degree numbers.