Why is Yom Tov Seven Days? Shavuot One?

Question

The Three regalim got me thinking.

Firstly, why is Sukkot and Pesach specifically 7 days - what is behind this number? Additionally, why is Sukkot and Pesach seven days long while Shavout only one?

Answer 1

Rambam discusses the different day lengths of the three holidays in Guide for the Perplexed 3:43. Quotes are from the Friedlander translation:

Sukkot

The Feast of Tabernacles, which is a feast of rejoicing and gladness, is kept seven days, in order that the idea of the festival may be more noticeable.

Passover

but if the eating of unleavened bread on Passover were only commanded for one day, we should not have noticed it, and its object would not have been manifest. For it frequently happens that we take the same kind of food for two or three days. But by our continuing for a whole period [of seven days] to eat unleavened bread, its object becomes clear and evident.

Shavuot

As that great revelation took place only on one day, so we keep its anniversary only one day:

As for the particular significance of seven (as opposed to, say, six or eight) Ralbag writes in his commentary to Exodus Chapter 20 that the number seven is significant because it represents God who is the seventh level of existence:

והנה ימצא עוד תועלת בו בדעות והוא שכבר למדנו מענין השבת שבכאן לצורות שבע מדרגות והמדרגה השביעית היא קדש והוא ה' יתעלה והם צורות היסודות והם האיכויות כאילו תאמר החום והקור והלחות והיובש וצורות המתדמי החלקים המורכבים מהיסודות וצורות הצמחים וצורות הבעלי חיים וצורת האדם והוא השכל ההיולאני וצורות השכלים הנבדלים והצורה השביעית אשר שפעו ממנה כל אלו הצורות היא ה' יתעלה והנה לשאר הצורות ימצא דבקות מה בחומר ומלאכות מיוחדות יסודרו מהם זולתי לה' יתעלה וזה כולו מבואר במעט עיון למי שעיין בדברינו בחלק השלישי מהמאמר החמישי מספר מלחמות ה

In his commentary to Judges Chapter 6 he references this as the explanation for why many things in Judaism are based on the number seven, and Sukkot is one of the example he gives:

והנה היה זה המספר לשביעיות ר"ל שהקיפו העיר שבעה ימים והיו שם שבעה כהנים ושבעה שופרות היובלים וביום השביעי הקיפו העיר שבע פעמים [לסיבה בעינה] שזכרנו במספר השבעה שזכרנו בתורה כמו השמיטה ושבעה שמטות ושבע שבתות שהם שבעה ימים שבע פעמים ושבעה ימי הפסח ושבעה ימי סוכה

Earlier in the aforecited chapter Rambam also touches on the significance of Passover being specifically seven days:

The reason for the Passover is well known. It is kept seven days, because the period of seven days is the unit of time intermediate between a day and a month. It is also known how great is the importance of this period in Nature, and in many religious duties. For the Law always follows Nature, and in some respects brings it to perfection; for Nature is not capable of designing and thinking, whilst the Law is the result of the wisdom and guidance of God, who is the author of the intellect of all rational beings.

(Alternatively, as per the sources in my answer here, once we establish that the holidays need to have multiple days to make the point noticeable it is invalid to ask why the precise number of days was chosen. Because no matter what number was chosen you could ask why a different number wasn't chosen; therefore, it is possible that a particular number is just arbitrary, because an arbitrary number is needed.)