How to fine tune text colors for black background?

Question

In a current project, I want to display formulas with different colours on black background. My idea is that they are easy to distinguish, have good contrast to the black background and fit together nicely.

Here is a first draft:

Currently, I chose these 5 colors: #09B0EC, #ED3EFA, #f3ae99, #20BF55, #F7F858, which I created with a contrast tool and a palette generator.

Question: How can I make sure that my colours fit together nicely? At the moment, I chose them only by eye. And further: When I want to add two more colours, how would I choose them wisely?

The colours are only labels for equations. Their only technical function is to simplify their recognition in mathematical derivations. I don't know much about colour harmony, but I am open to any suggestions to enhance and expand my palette so that math people can also enjoy the beauty of harmonic colours.

Edit: This is how the colors are positioned in a HSV Wheel:

Answer 1

• There are 2 factors your should think about when choosing colors:
  
  1. contrast
  2. complimentary colors

1. contrast
   there are 2 official guidelines to look into when it comes to contrast
   WCAG 2.1 (A/AA/AAA) and section508 which basically boils down to a minimum contrast ratio of 4.5:1 and a recommended contrast ratio of 7:1 you can go here to download a free program to measure the contrast ratio of the colors you want to use in respect to the background color.

2. complimentary colors
   when it comes to complementary colors (when you want to pick 5 colors that not only are light enough for the recommended contrast ratios but also look good together) it is helpful to think of colors as on a 360deg circle.
   colors on a screen consist of hue, saturation, and lightness and to find complementary colors the important value is the hue (as opposed to lightness when it comes to contrast) which goes from
   

   • 0/360 = red
     
   • 90 = light green
     
   • 180 = cyan
     
   • 270 = purple
     
   • etc.
     

   So if your starting color is blue (hue 240):
   

   • to find 1 more complementary colors you would divide the 360-colorwheel in 2 and get the color 180deg away or 60 = yellow (blue + yellow)
     
   • if 2 more... divide into 3 (blue + cyan + green)
     
   • ...
     
   • but you need 4 more (5 in total) giving us
     (hue => 240 - 312 - 24 - 96 - 168) or (blue - magenta - orange - light green - light cyan)
     
     

   Your starting color is #09b0ec or hsl(196, 93%, 48%) contrast ratio of 8.45:1
   keeping saturation and contrast ratio (roughly) the same, your next 4 colors should then be
   
   

   • hsl(268, 93%, 77%) or
     #c18efb (contrast ratio - 8.52:1)
     
   • hsl(340, 93%, 73%) or
     #fa7aa5 (contrast ratio - 8.39:1)
     
   • hsl(52, 93%, 38%) or
     #bba307 (contrast ratio - 8.35:1)
     
   • hsl(124, 93%, 39%) or
     #07c013 (contrast ratio - 8.55:1)
     
     
     
     

   and to keep adding colors just keep dividing the color-wheel keeping saturation and contrast ratio (roughly) the same
   
   the basic idea is colors used should be as far from each other on the color-wheel as possible as to be as distinctive as possible
   
   go here to play with different hue, saturation and lightness settings to find your five colors