Also as a sibling to your comment points out it's a blend of major and minor, so also in jazz you'll often see something like E7b9#9b13 written, but that really makes no sense in terms of a scale. The 9th is either flattened or sharpened, can't be both. So the next degree of the scale is the b10, which also makes sense when you think about something like a "diminished" scale which people play over this chord often.
He also used not to like the name diminished for the scale btw, but would refer to it as one of Messiaen's modes of limited transposition. I can't remember Messiaen's nomenclature exactly but the scales which people call the wholetone/semitone diminished and semitone/wholetone diminished are one of his symmetrical system of scales. IIRC there are 3 distinct "diminished" scales and all the other ones are just modes of these three. So you can see that the st/wt diminished starting on D is just a mode of the wt/st diminished starting on C for example.[1]
Also as a sibling to your comment points out it's a blend of major and minor, so also in jazz you'll often see something like E7b9#9b13 written, but that really makes no sense in terms of a scale. The 9th is either flattened or sharpened, can't be both. So the next degree of the scale is the b10, which also makes sense when you think about something like a "diminished" scale which people play over this chord often.
He also used not to like the name diminished for the scale btw, but would refer to it as one of Messiaen's modes of limited transposition. I can't remember Messiaen's nomenclature exactly but the scales which people call the wholetone/semitone diminished and semitone/wholetone diminished are one of his symmetrical system of scales. IIRC there are 3 distinct "diminished" scales and all the other ones are just modes of these three. So you can see that the st/wt diminished starting on D is just a mode of the wt/st diminished starting on C for example.[1]
[1] This is him https://williamkinghorn.org/Biography he was an awesome guy and I learned a lot from him