Every earlier MRI encoding row fixed the gyromagnetic ratio and scanned base field or gradient; this scan holds those fixed and scans the ratio itself. Exact arithmetic here means exact results for the stated model inputs; measured inputs still carry uncertainty and significant-figure limits.

highlighted = computed this step

Every earlier MRI row fixed the gyromagnetic ratio at four

Chapters one and six both kept the gyromagnetic ratio at 4 hertz per tesla and only ever varied base field or gradient. Here base field stays 1 tesla and gradient stays 1 tesla per metre, but the ratio itself drops to 2, giving frequencies 2, 4, 6 hertz at positions 0, 1, 2 metres.

f=2(Bbase+Gx)=2,4,6f=2(B_{\mathrm{base}}+Gx)=2,4,6
Low gyromagnetic ratioThe same field row now reads a lower frequency ladder.gamma=2 Hz/Tbase_field=1 Tgradient=1 T/mfreqs=2,4,6 Hz

The gyromagnetic ratio rescales the whole frequency ladder

Base field and gradient never change across these rows. The gyromagnetic ratio alone stretches or compresses the three checked frequencies together.

f0=γ1,f1=γ2,f2=γ3f_{0}=\gamma\cdot1,\quad f_{1}=\gamma\cdot2,\quad f_{2}=\gamma\cdot3
Baseline gyromagnetic ratioThis middle row is chapter one's own checked example.gamma=4 Hz/Tbase_field=1 Tgradient=1 T/mfreqs=4,8,12 Hz

A higher gyromagnetic ratio spreads the addresses further

At ratio 6 hertz per tesla, the same three fields 1, 2, 3 tesla give frequencies 6, 12, 18 hertz.

f=6(Bbase+Gx)=6,12,18f=6(B_{\mathrm{base}}+Gx)=6,12,18
High gyromagnetic ratioThe final row is rendered as the checked high-ratio case.gamma=6 Hz/Tbase_field=1 Tgradient=1 T/mfreqs=6,12,18 Hz