We learn in The Complete Story of Tishrei:
Thus, the sounding of the Shofar during the month of Elul is a call for repentance and preparation for the New Year. Being the last month of the year, it is the time for self-searching and spiritual stock-taking. The Shofar is therefore heard every morning on weekdays throughout the month of Elul, except on the day before Rosh-Hashanah. This interruption is made in order to distinguish between the sounding of the Shofar during Elul, which is a matter of custom and tradition, but not an express command in the Torah (hence no blessing is recited before sounding the Shofar during Elul), and the sounding of the Shofar on Rosh-Hashanah, which is the special precept of that festival, as expressly ordained in the Torah.
From the article: Teshuvah, a Time for Opening the Gates of Heaven we learn:
Blowing of shofar during each day
Opening of Heaven’s Gates
Favourable for prayers to be Answered
Time of Repentance and Judgement
Next year’s outcome determined during Elul
During Ramadan "heaven's gates" are also opened. It is a time for repentance and seeking God's favour.
Arfajah said "We were with `Utbah ibn Farqad while he was discussing Ramadan. A companion of the Prophet entered upon the scene. When `Utbah saw him, he became shy and stopped talking. The man [the companion] spoke about Ramadan, saying "I heard the Messenger of Allah say during Ramadan: "The gates of Hell are closed, the gates of Paradise are opened, and the devils are in chains. An angel calls out : 'O you who intend to do good deeds, have glad tidings. O you who intend to do evil, refrain, until Ramadan is completed. [Ahmad and an-Nasa'i]
Ramadan is the month of ELUL in the Hebrew calendar. Islam has their calendar wrong.
Elul begins dawn 27 August 2014