Question: The holiday celbrated halfway betwee summer and Autumn Equinox, falls under the umbrella term naming days such at it, Candlemas, and what other two names "Quarter Days"?

Context paragraphs:
Lammas: Lammas Day (Anglo-Saxon "hlaf-mas", "loaf-mass"), is a holiday celebrated in some English-speaking countries in the Northern Hemisphere, usually between 1 August and 1 September.  It is a festival to mark the annual wheat harvest, and is the first harvest festival of the year.  On this day it was customary to bring to church a loaf made from the new crop, which began to be harvested at Lammastide, which falls at the halfway point between the summer Solstice and Autumn September Equinox.

Term and Quarter Days (Scotland) Act 1990: The Term and Quarter Days (Scotland) Act 1990 is an Act of the Parliament of the United Kingdom which defined the dates of the Scottish Term and Quarter Days.  These are customary divisions of the legal year when contracts traditionally begin and end and payments are due.  It received Royal Assent on 13 July 1990 and immediate commencement, with the dates of the days changing twelve months later.  The changes arose from a Scottish Law Commission "Report on the Scottish Term and Quarter Days".

Samhain: Samhain (pronounced or , ] ) is a Gaelic festival marking the end of the harvest season and the beginning of winter or the "darker half" of the year.  Traditionally, it is celebrated from 31 October to 1 November, as the Celtic day began and ended at sunset.  This is about halfway between the autumn equinox and the winter solstice.  It is one of the four Gaelic seasonal festivals, along with Imbolc, Bealtaine and Lughnasadh.  Historically, it was widely observed throughout Ireland, Scotland and the Isle of Man.  Similar festivals are held at the same time of year in other Celtic lands; for example the Brythonic Calan Gaeaf (in Wales), Kalan Gwav (in Cornwall), and Kalan Goañv (in Brittany).

Chuseok: Chuseok (추석 ; 秋夕 ; ] ), literally "Autumn eve", once known as hangawi (한가위 ; ] ; from archaic Korean for "the great middle (of autumn)"), is a major harvest festival and a ten-day holiday in North Korea and South Korea celebrated on the 15th day of the 8th month of the lunar calendar on the full moon.  Like many other harvest festivals around the world, it is held around the autumn equinox, i.e. at the very end of summer or in early autumn.

Lughnasadh: Lughnasadh or Lughnasa (pronounced , ) is a Gaelic festival marking the beginning of the harvest season.  Historically, it was widely observed throughout Ireland, Scotland and the Isle of Man.  In Modern Irish it is called "Lúnasa ", in Scottish Gaelic: "Lùnastal" , and in Manx: "Luanistyn" .  Originally it was held on 1 August, or about halfway between the summer solstice and autumn equinox.  However, over time the celebrations shifted to the Sundays nearest this date.  Lughnasadh is one of the four Gaelic seasonal festivals, along with Samhain, Imbolc and Beltane.  It corresponds to other European harvest festivals such as the Welsh "Gŵyl Awst " and the English Lammas.

Scottish term days: Scottish term and quarter days are the four divisions of the legal year, historically used as the days when contracts and leases would begin and end, servants would be hired or dismissed, and rent, interest on loans, and ministers' stipends would become due.  The Term Days are Whitsunday and Martinmas, and together with Candlemas and Lammas they constitute the Quarter Days.  Although they were fixed by the Term and Quarter Days (Scotland) Act 1990 as falling on the 28th day every three months, they originally occurred on holy days, corresponding roughly to old quarter days used in both Scotland and Ireland, thus:

Out of the Ordinary Festival: Out of the Ordinary Festival was an annual family- and eco-friendly festival near Hailsham (grid reference TQ 569 088) in the Sussex countryside.  It celebrated the autumn equinox in England with a variety of live music, talks and workshops, performances, activities for children with green and ethical businesses, many powered by solar panels and wind generators.  It started as a development of The Antiquarian Society in Brighton.  The festival took place for three days in the autumn and had a capacity of 5,000 people.  The festival was held at Knockhatch Park, a setting which comprises an ex-landfill site (Arlington Landfill Site, near Hailsham - grid reference TQ 569 088).  The festival was renamed Over the Moon in 2012 and ran until 2013.

Wheel of the Year: The Wheel of the Year is an annual cycle of seasonal festivals, observed by many modern Pagans.  It consists of either four or eight festivals: either the solstices and equinoxes, known as the "quarter days", or the four midpoints between, known as the "cross quarter days"; syncretic traditions like Wicca often celebrate all eight festivals.

Miķeļi: Miķeļi (] ) or Miķeļdiena is a Latvian autumn equinox and annual harvest festival and market.  Latvian Miķeļi dainas referred to good and rich husbands as bread fathers, who are associated with the autumn harvest ripening.  In different regions, the Miķeļi celebration was also called Mīkaļiem or Mīklāli, but it is also known to other households as Sila Miķelis, Miega Miķelis, and Miega Mača.  According to an old calendar, this holiday is celebrated around autumn solstice time (around 21–23 September), when the duration of night is same as the duration of day.

Dożynki: Dożynki ("Dozhinki", 'Obzhynky', Polish: "Dożynki" , Russian: "Обжинки" 'Obzhynki'; Belarusian: "Прачыстая" 'Prachystaya'; Czech: "Dožínky, Obžinky" ; Kashubian: "Òżniwinë" ; "Dormition") is a Slavic harvest festival.  In pre-Christian times the feast usually fell on the autumn equinox , in modern times it is usually celebrated on one of the Sundays following the end of the harvest season, which fall on different days in different regions of Europe.

Supporting paragraphs: Scottish term days Lammas
Answer: Whitsunday and Martinmas