Respectively speaking; when is wheat harvest time and barley harvest time per scriptures?

A bit long but maybe this will help

Agriculture - Tilling the ground (Gen. 2:15; 4:2, 3, 12) and rearing cattle were the chief employments in ancient times. The Egyptians excelled in agriculture. And after the Israelites entered into the possession of the Promised Land, their circumstances favoured in the highest degree a remarkable development of this art. Agriculture became indeed the basis of the Mosaic commonwealth.

The year in Palestine was divided into six agricultural periods:-

I. SOWING TIME. Tisri, latter half (beginning about the autumnal equinox.) Marchesvan. Kisleu, former half. Early rain due = first showers of autumn.

II. UNRIPE TIME. Kisleu, latter half. Tebet. Sebat, former half.

III. COLD SEASON. Sebat, latter half. Adar. [Veadar.] Nisan, former half. Latter rain due (Deut. 11:14; Jer. 5:24; Hos. 6:3; Zech. 10:1; James 5:7; Job 29:23).

IV. HARVEST TIME. Nisan, latter half. (Beginning about vernal equinox. Barley green. Passover.) Ijar. Sivan, former half., Wheat ripe. Pentecost.

V. SUMMER (total absence of rain) Sivan, latter half. Tammuz. Ab, former half.

VI. SULTRY SEASON Ab, latter half. Elul. Tisri, former half., Ingathering of fruits.

The six months from the middle of Tisri to the middle of Nisan were occupied with the work of cultivation, and the rest of the year mainly with the gathering in of the fruits. The extensive and easily-arranged system of irrigation from the rills and streams from the mountains made the soil in every part of Palestine richly productive (Ps. 1:3; 65:10; Prov. 21:1; Isa. 30:25; 32:2, 20; Hos. 12:11), and the appliances of careful cultivation and of manure increased its fertility to such an extent that in the days of Solomon, when there was an abundant population, "20,000 measures of wheat year by year" were sent to Hiram in exchange for timber (1 Kings 5:11), and in large quantities also wheat was sent to the Tyrians for the merchandise in which they traded (Ezek. 27:17). The wheat sometimes produced an hundredfold (Gen. 26:12; Matt. 13:23). Figs and pomegranates were very plentiful (Num. 13:23), and the vine and the olive grew luxuriantly and produced abundant fruit (Deut. 33:24).

Lest the productiveness of the soil should be exhausted, it was enjoined that the whole land should rest every seventh year, when all agricultural labour would entirely cease (Lev. 25:1-7; Deut. 15:1-10).

It was forbidden to sow a field with divers seeds (Deut. 22:9). A passer-by was at liberty to eat any quantity of corn or grapes, but he was not permitted to carry away any (Deut. 23:24, 25; Matt. 12:1). The poor were permitted to claim the corners of the fields and the gleanings. A forgotten sheaf in the field was to be left also for the poor. (See Lev. 19:9, 10; Deut. 24:19.)

Agricultural implements and operations.

The sculptured monuments and painted tombs of Egypt and Assyria throw much light on this subject, and on the general operations of agriculture. Ploughs of a simple construction were known in the time of Moses (Deut. 22:10; comp. Job 1:14). They were very light, and required great attention to keep them in the ground (Luke 9:62). They were drawn by oxen (Job 1:14), cows (1 Sam. 6:7), and asses (Isa. 30:24); but an ox and an ass must not be yoked together in the same plough (Deut. 22:10). Men sometimes followed the plough with a hoe to break the clods (Isa. 28:24). The oxen were urged on by a "goad," or long staff pointed at the end, so that if occasion arose it could be used as a spear also (Judg. 3:31; 1 Sam. 13:21).

When the soil was prepared, the seed was sown broadcast over the field (Matt. 13:3-8). The "harrow" mentioned in Job 39:10 was not used to cover the seeds, but to break the clods, being little more than a thick block of wood. In highly irrigated spots the seed was trampled in by cattle (Isa. 32:20); but doubtless there was some kind of harrow also for covering in the seed scattered in the furrows of the field.

The reaping of the corn was performed either by pulling it up by the roots, or cutting it with a species of sickle, according to circumstances. The corn when cut was generally put up in sheaves (Gen. 37:7; Lev. 23:10-15; Ruth 2:7, 15; Job 24:10; Jer. 9:22; Micah 4:12), which were afterwards gathered to the threshing-floor or stored in barns (Matt. 6:26).

The process of threshing was performed generally by spreading the sheaves on the threshing-floor and causing oxen and cattle to tread repeatedly over them (Deut. 25:4; Isa. 28:28). On occasions flails or sticks were used for this purpose (Ruth 2:17; Isa. 28:27). There was also a "threshing instrument" (Isa. 41:15; Amos 1:3) which was drawn over the corn. It was called by the Hebrews a moreg, a threshing roller or sledge (2 Sam. 24:22; 1 Chr. 21:23; Isa. 3:15). It was somewhat like the Roman tribulum, or threshing instrument.

When the grain was threshed, it was winnowed by being thrown up against the wind (Jer. 4:11), and afterwards tos