You get better at HR with no mod by playing higher AR/CS/OD.
WTB reasonable amount of AR10, OD9.8, HP10, CS5.2 maps NOMOD.
"Hard Rock (named after the hardest difficulty of the DS game Elite Beat Agents) decreases hit circle size by 1 tick while increasing the overall difficulty, approach rate, and the HP drain by 2 or 3 ticks of their original value up to a maximum of 10. The difference in AR is often hard to notice except when used on maps with an original AR of 7 or greater, as it will push the AR to the maximum value of 10. Hard Rock can be a very difficult mod (especially on insane maps) as it not only demands higher cursor accuracy, it also requires the ability to read lightning-fast approach circles. " - Osu!Wiki
You get better with DT by playing faster maps and higher BPM no mod.
"Double Time increases the overall beatmap's speed to 150% of the original, reducing the length of the song by 33%. This might be considered deceptive because the BPM is not actually doubled, despite being called "Double Time". The method used to increase the speed doesn't increase the pitch of the song, but can make it sound "muddy".
Because the song is sped up, the approach rate also increases, which often makes it quite difficult when paired with Hard Rock. " - Osu!Wiki
Additionaly:
AR: " Double Time: The AR value doesn't change, but the 1.5x play speed causes circles to stay on screen 33% shorter. " (Osu!Wiki),
https://osu.ppy.sh/wiki/File:ARTable.pngOD: "Double Time: The OD value doesn't change, but the 1.5x play speed causes hit windows to be 33% shorter. " (Osu!Wiki)
https://osu.ppy.sh/wiki/File:ODTable.pngThat's all what i say about pure facts and diffrence betwin nomod and this 2 mods. In a way where you do not deny this.