Cycles of 13 (and 26)

B"H

The cycles of 52 weeks (364 days) can also be divided into 28 cycles of 13 days. With each day dedicated to two halachot, it may also be considered 28 cycles of 26 halachot (728). (This is connected to the gematria of Shabat (702), which is 27 x 26). 27 are the letters of the Hebrew Alphabet including the final letters, and 26 is the gematria of the name of Hashem (See Bnei Issaschar)

The thirteenth cycle of 13 days (or 26 halachot) falls from the 3rd of Adar until the 17th of Adar. Within that cycle, the time that would represent the same proportion, 13/28, would be the second half of the 9th of Adar, a day known for a violent outbreak in the usually peaceful arguments between Beit Hillel and Beit Shamai, reminiscent of the lack of respect/baseless hatred associated with the Counting of the Omer and the Three Weeks of Mourning. See The-Story-of-9Adar-A-Day-of-Disagreement.

Also, by using this same proportion yet counting from the 1st Adar until Purim, the 14th of Adar, time 13/28 would fall in the middle of the 7th of Adar, Moshe Rabbeinu's birthday and yahrzeit.

Purim is essentially about the 13 attributes of mercy - G-d's mercy for us, which is above nature is truly infinite (interestingly, the Torah reading usually falls on Ki Tissah, about the sin of the golden calf, and how Hashem forgave us even then, and revealed an even greater closeness to Moshe)

Cycles of thirteen are also connected to Nassi reading starting on Rosh Chodesh Nissan all the way to right before Pessach. Each of the the thirteen attributes appears connected to a Tribe (including Levi) - each attribute appears distinctively related to one of the tribes. There is also a very deep connection between the Thirteen Attributes and Nissan in general, and of course with Elul.

There are two main definitions of the 13 attributes. One given to Moshe and one given to Micah. Those given to Moshe represent the outer vessels, and those given to Micah represent the inner ones. The first thirteen appear to be connected to those given to Micah (inner revelation), and the second 13 those given to Moshe (outer revelation). That would bring us to 26. The last 2 cycles, in Elul and the beginning of Tishrei, would be a combination of both inner and outer dimensions (the inner vessels as revealed within the outer ones, and the outer vessels as revealed within the inner ones), and would also serve as a microcosm for the whole year.

Another idea that appears to contain 13 elements are the levels/steps mentioned by Rabbi Pinchas Ben Yair (see below), which also serves as the basis for the Ramchal's Mesilat Yesharim.

The 13 Attributes of Mercy according to Kabbalah:

1. א-ל / G‑d — mighty in compassion to give all creatures according to their need;
2. רַחוּם / rachum — merciful, that humankind may not be distressed;
3. וְחַנּוּן / ve’chanun — and gracious if humankind is already in distress;
4. אֶרֶךְ אַפַּיִם / erech apayim — slow to anger; (once, to the righteous)
5. אֶרֶךְ אַפַּיִם / erech apayim — slow to anger; (repeated again for the wicked)
6. וְרַב-חֶסֶד / ve’rav chesed — and plenteous in kindness;
7. וֶאֱמֶת / ve’emet — and truth;
8. נֹצֵר חֶסֶד / notzer chesed — keeping kindness 
9. לָאֲלָפִים / laalafim — unto thousands;
10. נֹשֵׂא עָוֹן / noseh avon — forgiving iniquity;
11. וָפֶשַׁע / vafeshah — and transgression;
12. וְחַטָּאָה / vechata'ah — and sin;
13. וְנַקֵּה / venakeh — and pardoning.

The Mystical 13:

1. מִי אֵ-ל כָּמוֹךָ / mee E-l kamocha — Who is a G‑d like you (in compassion);
2. נֹשֵׂא עָו‍ֹן / noseh avon — who bears iniquity;
3. וְעֹבֵר עַל פֶּשַׁע / ve’over al pesha — and overlooks sin;
4. לִשְׁאֵרִית נַחֲלָתוֹ / lishi’eirit nachalato — For the remnant of his heritage;
5. לֹא הֶחֱזִיק לָעַד אַפּוֹ / lo hechzik le’ad apoh — He does not retain his anger forever;
6. כִּי חָפֵץ חֶסֶד הוּא/ ki chafetz chesed hu — for He desires kindness;
7. יָשׁוּב יְרַחֲמֵנוּ/ yashuv yerachamanu — He shall again have mercy on us;
8. יִכְבֹּשׁ עֲו‍ֹנֹתֵינוּ / yichbosh avonoteinu — and suppresses our iniquities;
9. וְתַשְׁלִיךְ בִּמְצֻלוֹת יָם כָּל חַטֹּאתָם / vetashlich bimtzolet yam kol chatotam — casts our sins into the depths of the sea;
10. תִּתֵּן אֱמֶת לְיַעֲקֹב / titein emet le’Yaakov — You grant truth to Jacob;
11. חֶסֶד לְאַבְרָהָם / chesed le’Avraham — kindness to Abraham;
12. אֲשֶׁר נִשְׁבַּעְתָּ לַאֲבֹתֵינוּ / asher nishba’ata le’avotaynu — which You previously swore to our forefathers;
13. מִימֵי קֶדֶם / mimei kedem — from the earliest days.

The 13 Attributes of Mercy ("halachic" opinion):

1. י-ה-ו-ה / Hashem — compassion before a person sins;
2. י-ה-ו-ה / Hashem — compassion after a person has sinned;
3. א-ל / G‑d — mighty in compassion, to give all creatures according to their need;
4. רַחוּם / rachum — merciful, that humankind may not be distressed;
5. וְחַנּוּן / ve’chanun — and gracious if humankind is already in distress;
6. אֶרֶךְ אַפַּיִם / erech apayim — slow to anger;
7. וְרַב-חֶסֶד / ve’rav chesed — and plenteous in kindness;
8. וֶאֱמֶת / ve’emet — and truth;
9. נֹצֵר חֶסֶד לָאֲלָפִים / notzer chesed laalafim — keeping kindness unto thousands;
10. נֹשֵׂא עָוֹן / noseh avon — forgiving iniquity;
11. וָפֶשַׁע / vafeshah — and transgression;
12. וְחַטָּאָה / VeChata'ah — and sin;
13. וְנַקֵּה / VeNakeh — and pardoning.

(http://www.chabad.org/parshah/article_cdo/aid/3609722/jewish/What-Are-the-13-Attributes-of-Mercy.htm)


Avodah Zarah 20b

From here Rabbi Pineḥas ben Ya’ir would say: Torah study leads to care in the performance
of mitzvot. Care in the performance of mitzvot leads to diligence in their observance. Diligence
leads to cleanliness of the soul. Cleanliness of the soul leads to abstention from all evil.
Abstention from evil leads to purity and the elimination of all base desires. Purity leads to
piety. Piety leads to humility. Humility leads to fear of sin. Fear of sin leads to holiness.
Holiness leads to the Divine Spirit. The Divine Spirit leads to the resurrection of the dead.
And piety is greater than all of them, as it is stated: “Then You did speak in a vision to
Your pious ones” (Psalms 89:20).

Sotah Chapter 9:15

Rabbi Pinchas Ben Yair said: Diligence leads to cleanliness, cleanliness leads to purity,
and purity leads to separateness, and separateness leads to holiness, and holiness
leads to humility, and humility leads to dread of sin, and dread of sin leads to piety, and
piety leads to the Holy Spirit, and the Holy Spirit leads to the resurrection of the dead,
and the resurrection of the dead will come with Elijah the Prophet, may he be
remembered for good, Amen

תורה מביאה לידי 1

2 זהירות זהירות מביאה לידי

3 זריזות זריזות מביאה לידי

4 נקיות  נקיות מביאה לידי

5 פרישות פרישות מביאה לידי

6 טהרה טהרה מביאה לידי

7 חסידות חסידות מביאה לידי

8 ענוה ענוה מביאה לידי

9 יראת חטא יראת חטא מביאה לידי

10 קדושה קדושה מביאה לידי

11 רוח הקודש רוח הקודש מביאה לידי

12 תחיית המתים

13 [וּתְחִיַּת הַמֵּתִים בָּא עַל יְדֵי אֵלִיָּהוּ זָכוּר לַטּוֹב, אָמֵן:]


Thirteen Stories of Rebbe Nachman:

• Tale 1: The Lost Princess
• Tale 2: The Emperor and the King
• Tale 3: The Son Who Could Not Walk
• Tale 4: The King Who Decreed Conversion
• Tale 5: The King's Son Who Was Made of Precious Stones
• Tale 6: The Humble King
• Tale 7: The Fly and the Spider
• Tale 8: The Rabbi and His Only Son
• Tale 9: The Clever Man and the Simple Man
• Tale 10: The Burgher and the Pauper
• Tale 11: The King's Son and the Maid's Son Who Were Exchanged
• Tale 12: The Prayer Leader
• Tale 13: The Seven Beggars

Books by Rav Shalom Arush:

1. The Garden of Emuna
2.  The Garden of Peace
3. Women's Wisdom
4. The Garden of Yearning; A New Light (In the Garden of Yearning and Will)
5. In Forest Fields
6. The Garden of Riches
7. The Garden of Gratitude
8. The Garden of Education
9. The Garden of Wisdom
10. The Garden of Purity
11. The Garden of Knowledge
12. The Garden of Healing
13. Say Thank You and See Miracles (The Garden of  Miracles)