Cycle through pair of spaces for two screens with one keyboard shortcut

I have two displays and created for each display with Mission Control several desktops (also known as Spaces):

Display 1: Desktops 1-5
Display 2: Desktops 6-10

I have following related settings adjusted

1. Disabled: Automatically rearrange Spaces based on most recent use
2. Enabled: Displays have separate Spaces

I want to treat the desktops of each display as 5 pairs:

1. Desktops 1,6
2. Desktops 2,7
3. Desktops 3,8
4. Desktops 4,9
5. Desktops 5,10

I have already changed the keyboard shortcuts as following (from here):

This works fine after I have deleted ~/Library/Preferences/com.apple.symbolichotkeys.plist.

How can I cycle through the pairs of desktops with one keyboard shortcut, e.g. ctrl-left/right?

I am actually testing Amethyst and want to use mod1+n/p (mod1=ctrl+shift). I am hoping that I could use AppleScript to increase/decrease the desktop number 'modulo 5'. I am on macOS 10.14.5.

Yabai: tiling window manager with support for spaces

https://github.com/koekeishiya/yabai/wiki#comparison-with-other-window-managers

Requirements of Yabai

• "System Integrity Protection (SIP)" must be disabled
• "Displays have separate spaces" must be enabled

Note

• Yabai allows you to switch to a different space without animation (great)

Disable the Mission Control Mappings and use this ~/.skhdrc file with mappings as the OP wants (uses jq, e.g. install with $ brew install jq)

ctrl - left : index=`yabai -m query --spaces --space | jq '.index'` &&\
                        if (($index != 1 && $index != 6 )) then\
                            new=$((index-1)); \
                            other=$(((new+4)%10+1));\
                            yabai -m space --focus "${other}"; yabai -m space --focus "${new}";\
                        fi
ctrl - right : index=`yabai -m query --spaces --space | jq '.index'` &&\
                        if (($index != 5 && $index != 10 )) then\
                            new=$((index+1)); \
                            other=$(((index+4)%10+1));\
                            yabai -m space --focus "${other}"; yabai -m space --focus "${new}";\
                        fi
# ctrl+1-5:

ctrl - 1 : index=`yabai -m query --displays --display | jq '.index'` &&\
                if (($index == 1)) then\
                    yabai -m space --focus 6; yabai -m space --focus 1;\
                else \
                    yabai -m space --focus 1; yabai -m space --focus 6;\
                fi
ctrl - 2 : index=`yabai -m query --displays --display | jq '.index'` &&\
                if (($index == 1)) then\
                    yabai -m space --focus 7; yabai -m space --focus 2;\
                else \
                    yabai -m space --focus 2; yabai -m space --focus 7;\
                fi
ctrl - 3 : index=`yabai -m query --displays --display | jq '.index'` &&\
                if (($index == 1)) then\
                    yabai -m space --focus 8; yabai -m space --focus 3;\
                else \
                    yabai -m space --focus 3; yabai -m space --focus 8;\
                fi
ctrl - 4 : index=`yabai -m query --displays --display | jq '.index'` &&\
                if (($index == 1)) then\
                    yabai -m space --focus 9; yabai -m space --focus 4;\
                else \
                    yabai -m space --focus 4; yabai -m space --focus 9;\
                fi
ctrl - 5 : index=`yabai -m query --displays --display | jq '.index'` &&\
                if (($index == 1)) then\
                    yabai -m space --focus 10; yabai -m space --focus 5;\
                else \
                    yabai -m space --focus 5; yabai -m space --focus 10;\
                fi

Addition: Yabai signal space_changed

When you click in the dock on a non-visible application, only the display changes which has the space with the desired application. You can use Yabai signal space_changed to react to any space change to change the space of the other display as well:

# file ~/.config/yabai/yabairc

yabai -m signal --add event=space_changed action="~/.config/yabai/maintain_paired_spaces.sh"

#!/usr/bin/env sh
# file: ~/.config/yabai/maintain_paired_spaces.sh

# Keep two displays with spaces [1-5] and [6-12] in sync
#
# yabai signal 'space_changed'
# Passes two arguments $YABAI_SPACE_ID and $YABAI_RECENT_SPACE_ID

# Note $YABAI_SPACE_ID is not the same as the mission control index.
# Translate YABAI_SPACE_ID to mission control index as following
new=$(yabai -m query --spaces | jq ".[] | select(.id == $YABAI_SPACE_ID) | .index")

# modulo arithmetic
other=$(((new+4)%10+1))

# Check if already visible
visible=$(yabai -m query --spaces | jq ".[] | select(.visible == 1 and .index == $other)")
if [ -z "$visible" ]; then
    yabai -m space --focus "${other}"
    display=$(yabai -m query --spaces --space $other | jq ".display")
fi

Note there is a small time delay.

Disable tiling

If you are not interested in a tiling window manager but want to use these mappings, you can choose the layout mode 'float' in ~/.config/yabai/yabairc:

yabai -m config layout                       float