We present a detailed timing study of the brightest persistent X-ray source Sco X-1 using the data collected by the Hard X-ray Modulation Telescope ($Insight$-HXMT) from July 2017 to August 2018. A complete $Z$-track hardness-intensity diagram (HID) is obtained. The normal branch oscillations (NBOs) at $sim$ 6 Hz in the lower part of the normal branch (NB) and the flare branch oscillations (FBOs) at $sim$ 16 Hz in the beginning part of the flaring branch (FB) are found in observations with the Low Energy X-ray Telescope (LE) and the Medium Energy X-ray Telescope (ME) of $Insight$-HXMT, while the horizontal branch oscillations (HBOs) at $sim$ 40 Hz and the kilohertz quasi-periodic oscillations (kHz QPOs) at $sim$ 800 Hz are found simultaneously up to 60 keV for the first time on the horizontal branch (HB) by the High Energy X-ray Telescope (HE) and ME. We find that for all types of the observed QPOs, the centroid frequencies are independent of energy, while the root mean square (rms) increases with energy; the centroid frequencies of both the HBOs and kHz QPOs increase along the $Z$-track from the top to the bottom of the HB; and the NBOs show soft phase lags increasing with energy. A continuous QPO transition from the FB to NB in $sim$ 200 s are also detected. Our results indicate that the non-thermal emission is the origin of all types of QPOs, the innermost region of the accretion disk is non-thermal in nature, and the corona is nonhomogeneous geometrically.
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