M_SQRT2=1.41421
ASPECT=1.77777 #set as desired
UHD_X=3840
PIX_PER_CM=28.34
xCMs=UHD_X/PIX_PER_CM #set numerator to desired pixel width

set terminal pngcairo size (xCMs)cm,(xCMs/ASPECT)cm

# Set so that desired ASPECT line is in the middle
set yrange [0:UHD_X/ASPECT]

# Align graph to boundary
set bmargin .05
set rmargin .05
set tmargin .01
set lmargin .01

# Align tic labels inside graph
set ytics offset 4,-.4
set xtics offset -1.5,1.3

set key font "sans,10" at 200,460

# Setup the grid
set tics scale 0 font "sans,8"
set grid lt 1 lw .5 lc rgb "gray"

set ytics (240,320,480,640,720,768,800,1080,1200,1440,1536,1600,1800,2160)
set xtics (320,480,640,800,854,960,1024,1280,1366,1920,2048,2560,3200,3840)

# set output "stdout.png"
plot [0:UHD_X] \
x/1.29411 title "letter", \
x/1.33333 title "4:3", \
x/M_SQRT2 title "A4", \
x/1.50000 title "3:2", \
x/1.60000 title "8:5", \
x/1.66666 title "5:3", \
x/1.77777 title "16:9"