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"by a notch" is a correct and usable phrase in written English.
You can use it when referring to something being increased, decreased, or improved by a small amount. For example: "He's upped his game by a notch; he's definitely got what it takes to win this competition!".
Exact(55)
Fitch lowered its rating on Lucent by a notch and also said its outlook remained negative.
It downgraded China's local currency debt on April 9 by a notch.
In other countries too, second-quarter numbers have been raised by a notch.
Standard & Poor's cut its corporate credit rating for Lucent by a notch and said its outlook remained negative.
Go to North Korea and your faith in humanity is forever dialled down by a notch or two.
Moody's lowered its rating by a notch in December, to Aa3, roughly the same as the S.&P.'s AA-.
Mexico's Fiscal Woes Fitch's downgrade this week of Mexico's credit rating by a notch, to BBB, was a warning.
Similar(4)
The overexpression of Upd in ept mutant cells has also been shown to occur by a Notch-dependent mechanism [6].
The epidermis of the Xenopus embryo contains ciliated cells whose precursors are regularly spaced throughout the outer layer by a Notch-mediated lateral inhibition signal (Deblandre et al., 1999).
This is done by placing a notch in the closed-loop at a frequency corresponding to the rotational speed.
We filtered this noise by using a notch filter with 2048 coefficients.
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Since I tried Ludwig back in 2017, I have been constantly using it in both editing and translation. Ever since, I suggest it to my translators at ProSciEditing.

Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com