on high

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adj. high·er, high·est
a. Having a relatively great elevation; extending far upward: a high mountain; a high tower.
b. Extending a specified distance upward: a cabinet ten feet high.
2. Far or farther from a reference point: was too high in the offensive zone to take a shot.
a. Being at or near the peak or culminating stage: the high tourist season; high summer.
b. Advanced in development or complexity: high forms of animal life; higher mathematics.
c. Far removed in time; remote: high antiquity.
a. Slightly spoiled or tainted; gamy. Used of meat.
b. Having a bad smell; malodorous.
a. Having a pitch corresponding to a relatively large number of sound-wave cycles per second: the high tones of a flute.
b. Raised in pitch; not soft or hushed: a high voice.
6. Situated relatively far from the equator: a high latitude.
a. Of great importance: set a high priority on funding the housing program.
b. Eminent in rank or status: a high official.
c. Serious; grave: high crimes and misdemeanors.
d. Constituting a climax; crucial: The chase scene is the high point of the film.
e. Characterized by lofty or stirring events or themes: high adventure; high drama.
8. Lofty or exalted in quality or character: a person of high morals.
a. Greater than usual or expected, as in quantity, magnitude, cost, or degree: "A high price has to be paid for the happy marriage with the four healthy children" (Doris Lessing).
b. Favorable: He has a high opinion of himself.
10. Of great force or violence: high winds.
a. Informal Excited or euphoric: high spirits.
b. Slang Intoxicated by alcohol or a drug, such as cocaine or marijuana.
12. Luxurious; extravagant: high living.
13. Linguistics Of or relating to vowels produced with part of the tongue close to the palate, as in the vowel of tree.
14. Of, relating to, or being the gear configuration or setting, as in an automotive transmission, that produces the greatest vehicular speed with respect to engine speed.
adv. higher, highest
1. At, in, or to a lofty position, level, or degree: saw a plane high in the sky; prices that had gone too high.
2. In an extravagant or luxurious way: made a fortune and lived high.
1. A lofty place or region.
2. A high level or degree: Summer temperatures reached an all-time high.
3. The high gear configuration of a transmission.
4. A center of high atmospheric pressure; an anticyclone.
a. Informal An excited or euphoric condition: The team was on a high after winning in overtime.
b. Slang An intoxicated or euphoric condition induced by alcohol or a drug.
high and dry
1. In a position of helplessness; stranded: went off and left me high and dry.
2. Nautical Out of water. Used of a ship, for example.
high and low
Here and there; everywhere: searched high and low for the keys.
on high
1. High in the sky.
2. In heaven.
3. In a position of authority.

[Middle English, from Old English hēah.]

high′ly adv.
American Heritage® Dictionary of the English Language, Fifth Edition. Copyright © 2016 by Houghton Mifflin Harcourt Publishing Company. Published by Houghton Mifflin Harcourt Publishing Company. All rights reserved.
References in classic literature ?
297: Hesiod also says that those with Zetes (34) turned and prayed to Zeus: `There they prayed to the lord of Aenos who reigns on high.'