• ### Does rotating a chromatic circle (constellation) 90 degrees create the Minor scale in ALL modes?

As mentioned here:

https://en.m.wikipedia.org/wiki/Chromatic_circle

In other words, not just the classical modes, but also all the ones listed here:

https://en.m.wikipedia.org/wiki/File:PitchConstellations.svg

I am pretty sure: Yes.
But just need a confirmation.

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• A ninety degree rotation is a shift of 3 semitones up or down. I am assuming you mean shifting the index back three semitones (90 degrees counter clockwise) which would bring 0 to the position of 9 (the major 6th). This would indeed shift the previous root note to the new position of a minor third. This only works for scales/modes with a major 6th though, as you would otherwise end up with a scale with no root note, i.e. the zero will be 'unmarked'.

• @svanya no, the rotation only works when the scale is otherwise the same except having a different starting note.
So all of the "classical modes" (Ionian, dorian, etc) are the same scale, but just have different starting notes, because if you're basing it on C Ionian you can play each of them just by starting on a different white key on the piano, otherwise they are the same.
One specific example is the Ionian and Aeolian modes, which are also what we call the "major" and "natural minor" scales, But this rotation would work for dorian, phrygian, lydian, mixolydian, and "locrian" also.

The minor and major pentatonic scales are also rotations of each other.

and as @bocanegra mentions, the only time when it would be exactly 90 degrees is if the new root note is a minor 3rd away (and for natural minor that can only be from the Ionian mode since the "raised" 4 isn't in the equivalent ionian mode)

• Thank you, both (@bocanegra and @seb-harmonik.ar) for your help on this matter.

Taking a different approach, might we do the following (given what the article says about dropping the 3rd, 6th, and 7th by one pitch to dervie the Minor scales for the other modes? See the pd file for demonstration.

The zip includes a text file of the "Other Modes" (with each constellation as a line) to experiment with/test against.

attempting-to-derive-Minors.zip

Or is the drop 3rd, 6th, 7th just another manifestation of the same principle y'all mention? Currently, y'all's explanations are pretty far over my head.

If this will not work,...do either of you know where or can point me to the chromatic constellations for the Minors of the Other Modes? The data will work fine for what I am doing. Just thought it better if it were more elegant/formulaic.

• The constellations for those following along (and to which I have been refering)

• @svanya

what the article says about dropping the 3rd, 6th, and 7th

The only thing that makes a scale/mode minor or major is the 3rd. The one we call natural minor or aeolian has minor 6th and 7th as well. There are other minor modes with less or more minor intervals

An easy way to think of the classic modes for me is the white keys on the keyboard, like @seb-harmonik.ar is hinting at. These are the start tones, modes and intervals (minor intervals denoted by lower case except 4rth and 5th on the account of musical convention)

C -> Ionian: I II III IV V VI VII (major)
D -> Dorian: I II iii IV V VI vii (minor)
E -> Phrygian: I ii iii IV V vi vii (minor)
F -> Lydian: I II III IV# V VI VII (major)
G -> Mixolydian: I II III IV V VI vii (major)
A -> Aeolian: I II iii IV V vi vii (minor)
B -> Locrian: I ii ii IV Vb vi vii (minor)

For each of the majors, they have a "parallel" minor which you could think of as a "90 degree shift" in the "no blacks allowed" chromatic circle - i.e.: 3 semitones down. Ionian becomes Aolian. Lydian becomes Dorian. Mixolydian becomes Phrygian.

HOWEVER, there are tons of modes/scales not accounted for here, a lot of which you can't play on white keys only. And there is no single major-to-minor transformative rule besides these:

1: Flattening the 3rd will effectively turn a major scale/mode into minor
2: A major scale will have a parallel minor scale 3 semitones below it IF AND ONLY IF the major scale has a major 6th in it

• Thank you, @bocanegra, for the info and insight. I really appreciate it.

Just to confirm, before I pursue a different avenue (ex. raw data): The below is or is not correct?

• @svanya the "hungarian gypsy scale" has a minor 3rd so it is minor per definition. The blue derivative you get from lowering the minor third is "asexual" or "genderfluid"- it is neither minor nor major as there is no third left to define it.

Also: the discussion quickly becomes confusing as we are using the same numbers to describe different things at the same time. A handy table (semitones | interval):

0 | I - 1rst (root)
1 | ii - Minor 2nd
2 | II - Major 2nd
3 | iii - Minor 3rd
4 | III - Major 3rd
5 | IV - 4th
6 | IV# or Vb - Sharp 4th or Flat 5th
7 | V - 5th
8 | vi Minor 6th
9 | VI Major 6th
10 | vii - Minor 7th
11 | VII - Major 7th

This is all based on western (read classic German) tradition and notation where a mode or a scale can not have more than 7 steps, 1rst, 4th and 5th can't be minor or major (but they can be flat or sharp), etc

• yes, if you look at modes from an arbitrary math perspective, you will find more modes than the ones listed in most books about music.

but "gypsy" & co dont follow the same rules as the others, i would not call it modes, i would call them scales.

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