what model did you ask? here's the exact reply I received from Claude Sonnet, which appears to be exactly the answer you were expecting:
"Among the seven modes of C major, only Dorian is its own reflection.
Understanding Mode Reflections
When we reflect a mode, we reverse its interval pattern. The modes of C major and their interval patterns are:
Ionian: W-W-H-W-W-W-H
Dorian: W-H-W-W-W-H-W
Phrygian: H-W-W-W-H-W-W
Lydian: W-W-W-H-W-W-H
Mixolydian: W-W-H-W-W-H-W
Aeolian: W-H-W-W-H-W-W
Locrian: H-W-W-H-W-W-W
The Palindromic Nature of Dorian
Dorian mode is palindromic, meaning it produces the same scale whether you read its interval pattern forwards or backwards. When you reverse the Dorian interval pattern W-H-W-W-W-H-W, you get exactly the same sequence: W-H-W-W-W-H-W.
Mirror Pairs Among the Other Modes
The remaining modes form mirror pairs with each other:
Ionian-Phrygian: Mirror pair
Lydian-Locrian: Mirror pair
Mixolydian-Aeolian: Mirror pair
For example, when you reflect the C major scale (Ionian), which has the interval pattern W-W-H-W-W-W-H, you get H-W-W-W-H-W-W, which corresponds to the Phrygian mode.
This symmetrical relationship exists because the whole diatonic scale system can be symmetrically inverted, creating these natural mirror relationships between the modes"
"Among the seven modes of C major, only Dorian is its own reflection.
Understanding Mode Reflections When we reflect a mode, we reverse its interval pattern. The modes of C major and their interval patterns are:
Ionian: W-W-H-W-W-W-H
Dorian: W-H-W-W-W-H-W
Phrygian: H-W-W-W-H-W-W
Lydian: W-W-W-H-W-W-H
Mixolydian: W-W-H-W-W-H-W
Aeolian: W-H-W-W-H-W-W
Locrian: H-W-W-H-W-W-W
The Palindromic Nature of Dorian Dorian mode is palindromic, meaning it produces the same scale whether you read its interval pattern forwards or backwards. When you reverse the Dorian interval pattern W-H-W-W-W-H-W, you get exactly the same sequence: W-H-W-W-W-H-W.
Mirror Pairs Among the Other Modes The remaining modes form mirror pairs with each other:
Ionian-Phrygian: Mirror pair
Lydian-Locrian: Mirror pair
Mixolydian-Aeolian: Mirror pair
For example, when you reflect the C major scale (Ionian), which has the interval pattern W-W-H-W-W-W-H, you get H-W-W-W-H-W-W, which corresponds to the Phrygian mode.
This symmetrical relationship exists because the whole diatonic scale system can be symmetrically inverted, creating these natural mirror relationships between the modes"