Nine different entries in the OED for high. Goodness. But as far as I can tell, it is all the same word high which JRRT uses, meaning both far from bottom to top and elevated in social stature — even “5.002 for he could feel inside that it was high time for some meal or other”. High is a Germanic word and its earlier origins are debated and if you want to wander down a rabbit hole of Tocharian A and Tocharian B and their friends, do spend a pleasant hour with this word’s etymology!

• 1.004 about half our height,
• 1.079 The pines were roaring on the height,
• 1.109 “Five feet high the door
• 2.028 rising higher
• 2.028 and higher,
• 3.035 very old swords of the High Elves of the West,
• 3.040 beside the plain runes which say ‘five feet high the door
• 4.003 in the high hope of a midsummer morning,
• 4.005 They were high up
• 5.002 for he could feel inside that it was high time for some meal or other;
• 5.035 “But in low place/ Not in high place.'”
• 5.055 And beats high mountain down.
• 6.003 out of the little high valley,
• 6.034 And we are still pretty high up.
• 6.052 and up they went as high as ever they could trust the branches.
• 6.070 It was high summer,
• 6.080 as he got ready to spring down from on high
• 6.084 above the highest branches.
• 6.085 and they were high up
• 7.002 and saw that the birds were already high up
• 7.005 even from their great height,
• 7.009 except high
• 7.029 and beyond these to a high thorn-hedge
• 7.031 high
• 7.055 We were crossing by the High Pass
• 7.106 a splash of white on the floor came from the high moon,
• 7.130 As soon as they left his high hedges
• 7.151 high in the East,
• 8.028 and as high as he could throw it.
• 8.029 High it sprang
• 8.041 and so he must be light enough for the highest
• 8.088 in a row from a high branch.
• 8.131 They differed from the High Elves of the West,
• 8.132 at the feet of the high wooded lands.
• 9.015 a very high opinion indeed)
• 10.006 over high waterfalls
• 10.009 and towed away round the high shoulder of rock
• 10.034 and high over the lake.
• 10.036 Even Bilbo was given a seat at the high table,
• 11.005 and ever higher above them.
• 11.005 in a height called Ravenhill.
• 11.013 somewhere high above the cliff at the valley’s head
• 11.017 while Bofur was hauled up to the higher camp.
• 11.019 that led higher
• 11.019 and higher on to the mountain;
• 11.032 who had been watching from a high perch
• 11.038 A door five feet high
• 12.007 at the height of their wealth
• 13.044 when suddenly the roof sprang high
• 13.064 and climbed the high bank.
• 14.002 Only its high peak could they see
• 14.013 the dragon’s wrath blazed to its height,
• 14.014 He circled for a while high
• 14.015 Flames unquenchable sprang high into the night.
• 14.023 and crashed down from on high
• 14.025 The waxing moon rose higher
• 14.025 and higher
• 14.043 higher up the shore;
• 15.010 This very height was once named Ravenhill,
• 15.028 But now their hopes were higher;
• 15.028 and high,
• 17.031 The dwarves are exceedingly strong for their height,
• 17.048 climbed to the height of the Eastern shoulder
• 17.056 Rocks were hurled down from on high
• 18.052 in high summer.
• 18.053 But they came to that high point at morning,
• 18.053 On its highest peak

A common word, but so very much loved by Tolkien who bemoaned the encroachment of grey-brown smokestacks into the green countryside. Green is from roots which denote the growing and life of plants. Thank you, plants, for our oxygen.

• 1.002 like a porthole, painted green,
• 1.004 (chiefly green and yellow);
• 1.006 and more green,
• 1.008 and the grass was very green.
• 1.021 and scuttled inside his round green door,
• 1.023 on the hobbit’s beautiful green front-door.
• 1.032 he said when he caught sight of Dwalin’s green hood hanging up.
• 1.047 but a hard rat-tat on the hobbit’s beautiful green door.
• 1.050 and a pale green one;
• 1.068 Then Gandalf’s smoke-ring would go green
• 1.070 in a green cloth.
• 1.094 in the Battle of the Green Fields,
• 2.010 and shall await your respected person at the Green Dragon Inn,
• 3.008 some of them green pleasant places to look at,
• 3.012 The last green had almost faded out of the grass,
• 5.035 Saw an eye in a green face.
• 5.103 in Gollum’s eyes had become a green fire,
• 5.106 and saw Gollum’s eyes like small green lamps
• 5.127 and his eyes went green.
• 6.064 another in green.
• 7.014 and then began to march through the long green grass
• 7.116 green, blue, red, silver-grey, yellow, white;
• 8.002 in a sort of darkened green glimmer.
• 8.005 and sometimes pairs of yellow or red or green eyes
• 8.041 he was greened
• 8.042 he saw all round him a sea of dark green,
• 8.058 in green
• 8.071 green and white gems
• 8.124 At any rate here the light was greener,
• 11.004 it had been green
• 11.007 The mountain’s sides were green with woods
• 12.022 in a spout of green
• 12.091 The dragon has withered all the pleasant green,
• 12.096 green as grass,
• 14.031 to the green shores of the lake.
• 15.044 They bore with them the green banner of the Elvenking
• 18.053 and darkly green at the nearer edge
• 19.027 But the land was green
• 19.032 Look at last on meadows green

I am gobsmacked by how rare this word is in our story! Etymonline.com says:

from PIE *bhle-was “light-colored, blue, blond, yellow,” from root *bhel- (1) “to shine, flash, burn,” also “shining white” and forming words for bright colors.

Definitely sky colors, and definitely slippery to modern English speakers — but I’ve seen the sky be salmon, gold, white, so very blue that it makes me weep. Now I’m fascinated to look at all the color words. After the poetry words.

• 1.007 He had a tall pointed blue hat,
• 1.017 and lasses going off into the Blue for mad adventures?
• 1.026 with a blue beard
• 1.038 both with blue hoods,
• 1.040 and they both swept off their blue hoods
• 1.092 Gandalf struck a blue light on the end of his magic staff,
• 3.013 and blue.
• 3.050 blue sky
• 4.002 where things were blue
• 4.035 into a tower of blue glowing smoke,
• 4.041 now it was bright as blue flame
• 5.035 in a blue face
• 6.064 Then he set one alight with bright blue fire,
• 6.064 one in blue flames,
• 7.116 green, blue, red, silver-grey, yellow, white;
• 8.106 by the tip of a blue hood sticking out at the top.
• 11.022 but of what lay beyond the blue distance,
• 15.044 and the blue banner of the Lake,
• 18.053 blue

More muttering going on than I had imagined! Apparently this one is nearly the four thousandth most common word in the Project Gutenberg corpus.

• 2.031 and Thorin muttered something about supper,
• 2.036 and muttering,
• 5.033 Mouthless mutters.
• 7.083 and muttered:
• 8.068 he muttered,
• 8.126 he kept on muttering
• 9.033 they muttered.
• 10.012 where they sat or lay muttering
• 15.034 and they muttered
• 17.035 muttering

We do already have mouthful, since we broadly didn’t lemmatize in the first go-round, but now that I’m adding common words, here it is again in context of other mouths!

• 1.090 who was wagging his mouth
• 1.100 and when Bilbo tried to open his mouth to ask a question,
• 1.100 till Bilbo shut his mouth tight with a snap.
• 1.110 so that he forgot to keep his mouth shut.
• 2.046 “Shut yer mouth!”
• 2.059 “He wouldn’t make above a mouthful,”
• 2.103 so shut yer mouth!” said Bert.
• 4.034 with his mouth open.
• 5.033 Mouthless mutters.
• 5.056 in his mouth;
• 5.130 The cry brought Bilbo’s heart to his mouth,
• 5.148 Bilbo’s heart jumped into his mouth.
• 7.092 in their mouths,
• 7.153 and put his hands to his mouth
• 8.142 At that Thorin shut his mouth
• 9.003 and at the far end were gates before the mouth of a huge cave
• 9.018 beyond the steep slope out of which the main mouth opened.
• 9.026 in his mouth,
• 10.006 There it had a wide mouth with stony clifflike gates at either side
• 10.007 Not far from the mouth of the Forest River
• 11.038 a yawning mouth leading

Poor Gollum has only six.

• 2.080 in his teeth for that,
• 4.033 and all his soldiers gnashed their teeth, clashed their shields,
• 5.032 Teeth!
• 5.032 teeth!
• 5.033 Toothless bites,
• 5.070 goblins’ teeth,
• 6.082 and gnashed their teeth;
• 12.072 my teeth are swords,
• 14.030 but the Master ground his chattering teeth.

Fish, dwarves, eagles, houses, Smaug himself, things on the borders of the Desolation of the Dragon, the thrush, Roäc, ravens, and bats!

• 5.033 Wingless flutters,
• 6.074 But, funny little birds, they had no wings!
• 6.082 the dark rush of their beating wings smote them to the floor
• 7.002 and cling between his wings.
• 7.008 May the wind under your wings bear you
• 7.034 and its two long wings.
• 12.014 with wings folded like an immeasurable bat,
• 12.016 Smaug stirred a wing,
• 12.029 beating his great wings
• 12.072 my wings a hurricane,
• 12.090 it silently spread its wings
• 14.011 beneath the awful beating of his wings.
• 14.021 and silvered his great wings.
• 14.040 among all things with wings
• 15.004 Then he fluttered his wings
• 15.013 Before long there was a fluttering of wings,
• 15.013 slowly flapped his wings,
• 15.021 and strong of wing,
• 17.040 so dense that no light could be seen between their wings.

Around the 13th century the word came to also mean “to produce tears” as well as to make a loud noise.

Cry, etymonline.com

• 2.113 they cried.
• 3.027 father!” they cried to Thorin,
• 4.043 and horrible cries
• 4.044 so that do what they could the dwarves heard the cries
• 4.048 in full cry,
• 5.033 Voiceless it cries,
• 5.034 Half a moment!’ cried Bilbo,
• 5.051 Fish! fish!’ he cried.
• 5.077 cried Bilbo very much relieved;
• 5.091 Bilbo heard him crying.
• 5.094 cried Bilbo,
• 5.130 The cry brought Bilbo’s heart to his mouth,
• 5.139 they cried.
• 6.051 what shall we do!’ he cried.
• 6.052 Up the trees quick!’ cried Gandalf;
• 6.065 and they fled off down the slopes crying
• 6.082 Loud cried the Lord of the Eagles,
• 6.092 he cried
• 7.002 The dwarves were crying farewells
• 7.007 Farewell!’ they cried,
• 7.110 he cried.
• 7.114 they all cried.
• 7.118 he cried,
• 7.132 and the cries of goblins.
• 8.009 and peering forward cried:
• 8.030 he cried.
• 8.033 Before Thorin could cry out
• 8.043 but at length the cries of the dwarves,
• 8.045 they cried,
• 8.048 he cried.
• 8.072 and their cries.
• 8.073 But the cries of the others got steadily further
• 8.073 and cries for help
• 8.080 the cries for help had come
• 8.130 their cries as the spiders caught them
• 9.042 Ha, ha!’ came a cry.
• 9.046 cried some,
• 9.067 cried the raftman.
• 10.029 cried Thorin
• 10.030 Pressing forward before the Master’s table they cried:
• 11.034 cried Bilbo.
• 12.024 inside the tunnel when Bifur gave a cry:
• 12.086 cried the dwarves.
• 13.014 he cried.
• 13.025 Fili! Kili!’ he cried as loud as he could –
• 13.027 Faintly the dwarves heard his small cries,
• 13.033 and cried out to one another,
• 13.036 he cried.
• 13.040 Thorin!’ he cried aloud.
• 13.063 cried the others.
• 13.070 Hear, hear!’ cried Bilbo,
• 14.008 they cried,
• 14.009 he cried.
• 14.029 he cried.
• 14.032 and people further off took up the cry:
• 14.034 were now heard as loudly crying that the dwarves
• 14.040 crying and piping.
• 15.001 and crying unceasingly above.
• 15.003 he cried.
• 15.023 cried Thorin.
• 15.024 cried Bilbo,
• 15.025 cried the dwarves as if they had not heard him;
• 15.046 and he cried:
• 15.056 one cried,
• 17.014 cried Thorin,
• 17.015 he cried
• 17.023 cried Bard.
• 17.027 he cried to them.
• 17.031 when a cry was heard
• 17.041 Halt!’ cried Gandalf,
• 17.042 The elves cried out with many voices.
• 17.048 and already their cries
• 17.051 With cries of ‘Moria!’
• 17.052 when a cry rang out on the heights above.
• 17.057 he cried,
• 17.062 He gave a great cry:
• 17.065 The Eagles! the Eagles!’ Bilbo cried,
• 17.065 Soon they too took up the cry,
• 17.066 The Eagles!’ cried Bilbo once more,
• 18.009 he cried,
• 19.035 he cried.