Those that teach the "noon to noon" day cycle cite historical references to show that our modern day did not always begin at midnight. True, but this is not applicable to the matter at hand.  Quoting historical records showing that noonday was indeed sometimes used as the start of a day, the claim then becomes that this "proves" that noon is the proper time to begin the solar Israelite day.   Man historically has used many divisions and parts of the day and night to keep time.  Sunrise, sunset, midnight, noon, plus any division thereof can be used, and has been used, to begin the "fancy of an era" when it comes to beginning a "day".  Simply because history shows that noon has been used at times in the past to start a day, it has no bearing on the Biblical start of Yahweh's solar calendar day.

  Those that teach the "noon to noon" day cycle, do so upon the misconception that the words "even" or "evening" in the Bible means "noon" because, they reason, at noon the daylight hours are divided evenly into precisely equal (even) halves.  [ Note: Yet that point itself isn't exactly correct either when checking noon, sunset, sunrise times throughout the year ]

      The word for "evening" in the Old Testament is the Hebrew word "er-reb" (Strong's # 6153, 6150) and it means  "dusk, sunset, dark, night".  In the New Testament we see that "even" (Greek 'op-see-os' Strong's #3798) was when the sun was down. (Mark 1:32) 

         The belief that Yahweh set lights in the firmament of heaven to "divide the day" is the basic foundation of the "noon to noon" Sabbath theory.  Such a teaching is grounded in a careless misquote of a single Bible verse.  Let's read the pertinent part of that verse. 

    Genesis 1:14 tells us, "And God said 'Let there be lights in the firmament of the heaven to divide the day from the night..."; not to divide the day from the day as the noon Sabbath proponents claim.  Genesis 1:18 tells us the same thing.  The Sun and the stars divide the light from darkness.  The Sun is always out in the day and the stars are always out at night. (clouds notwithstanding)

    It is further suggested that the term "even, at the going down of the Sun" (I Ki. 22:35,36; Deut.16:6) actually means that the Sun begins to "go down" one minute after high noon, and so spends the rest of the afternoon "going down" until it sets over the horizon.     Once again, this interpretation supposes that the word "even" here somehow means "noon" in the original Hebrew text.  It does not.  "Noon" is the Hebrew 'tso-har' (Strong's #6672); while "Even"  is  "ereb"  which means "dusk/darkish".  Thus, "Tso-har" (noon), the brightest part of day, is never used in the Bible to describe when the Sun begins to go down. The phrase "going down of the Sun" means to make the Earth dark, dusky (Ereb)  as night arrives at EVENING, sunset.

 An interesting verse is Amos 8:9 where we see a reference to a solar eclipse:  "And it shall come to pass in that day, saith Yahweh God, that I will cause the Sun to go down at noon (tso-har), and I will darken the Earth in the clear day."

 This verse makes a point of contrasting the "going down of the Sun" as oppositely compared to "noon".  This emphasizes the fact that normally the sun does not go down (darken the Earth) at noon; but as a specific sign Yahweh would darken the Earth in the clear day (at noon).  It follows that if the term "going down of the Sun" means "to darken the Earth", and since the "going down of the Sun" is "even" (I Ki.22:35,36 etc. above) , then "even" is when the Earth is darkened each day ...... at Sunset!

  Also, King David declares in Psalm 55:17, "Evening (ereb), and morning, and at noon (tsohar) will I pray, and cry aloud: and Yahweh shall hear my voice."  If evening (ereb) was indeed noon, King David would be saying here, "Noon, morning, and noon will I pray".  This would make no sense at all and would be a needless redundant phrase.  The Bible teaches that evening is sundown  (the going down of the Sun when it's on the horizon), when the Earth begins to become dark.