I begin my search for the royal psalms with a simple query - where does MLK occur as a root in the psalms? Here is the distribution by psalm and by book.
Several psalms stand out: 2, 24, 45, 47, 68, 72 - but I know there are others and they don't stand out, and there are some that stand out like 105 that are not royal - they mention kings in other contexts. So I added throne KS) to my search and also govern M$L. The graphs are too hard to see so here is a tabular summary.
The questions are many - among which is have I missed things (yes - see the next post where I find some of them) or selected false positives? (For example rule and proverb have the same three-letter root. Similarly throne and full moon! )
| Psalm | מלך | משׁל | כסא | |
| Psalm --2 | 3 | |||
| Psalm --5 | 1 | |||
| Psalm --9 | 2 | |||
| Psalm -10 | 1 | |||
| Psalm -11 | 1 | |||
| Psalm -18 | 1 | |||
| Psalm -19 | 1 | |||
| Psalm -21 | 1 | |||
| Psalm -22 | 1 | 1 | ||
| Psalm -24 | 5 | |||
| Psalm -28 | 1 | |||
| Psalm -29 | 1 | |||
| Psalm -44 | 1 | 1 | ||
| Psalm -45 | 6 | 1 | ||
| Psalm -46 | 1 | |||
| Psalm -47 | 4 | 1 | ||
| Psalm -48 | 1 | |||
| Psalm -49 | 1 | |||
| Psalm -59 | 1 | |||
| Psalm -61 | 1 | |||
| Psalm -66 | 1 | |||
| Psalm -68 | 5 | |||
| Psalm -69 | 1 | |||
| Psalm -72 | 5 | |||
| Psalm -74 | 1 | |||
| Psalm -76 | 1 | |||
| Psalm -78 | 1 | |||
| Psalm -79 | 1 | |||
| Psalm -84 | 1 | |||
| Psalm -89 | 2 | 1 | 5 | |
| Psalm -93 | 1 | 1 | ||
| Psalm -94 | 1 | |||
| Psalm -96 | 1 | |||
| Psalm -97 | 1 | 1 | ||
| Psalm -99 | 2 | |||
| Psalm 102 | 2 | |||
| Psalm 103 | 1 | 2 | 1 | |
| Psalm 105 | 4 | 2 | ||
| Psalm 110 | 2 | |||
| Psalm 114 | 1 | |||
| Psalm 119-V-Y | 1 | |||
| Psalm 122 | 2 | |||
| Psalm 132 | 2 | |||
| Psalm 135 | 4 | |||
| Psalm 136 | 4 | 2 | ||
| Psalm 138 | 1 | |||
| Psalm 143 | 1 | |||
| Psalm 144 | 1 | |||
| Psalm 145 | 4 | 1 | ||
| Psalm 146 | 1 | |||
| Psalm 147 | 1 | |||
| Psalm 148 | 1 | |||
| Psalm 149 | 1 | |||
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