Rabbi Avraham ben David of Luneil, the author of "Sefer HaManhig," writes, "From Parshat Bereshit through the 17th of Tammuz, the Haftarah is chosen to correspond to the Parshah topic by topic; but from there on - the choice of Haftarah is determined entirely by the time of year and the corresponding historical events" (Hilchot Taanit, Din 16).
There is a sequence of ten, really twelve Haftarot (the two of "Teshuvah," Repentance, are usually not counted): Three of Punishment, Seven of Consolation, and Two of Repentance.
The "Shulchan Aruch" identifies the Haftarot:
Three of Punishment
"Divrei Yirmiyahu," "The Words of Yirmiyahu," from the beginning of Sefer Yirmiyahu through the Second Chapter, Verse 3
"Hear the Words of HaShem," beginning with Yirmiyahu, Chapter 2,
"The Vision of Yeshayahu ben Amotz," on the Shabbat preceding Tisha B'Av, from the First Chapter of Yeshayahu, Chanted to the melody of Megilat Eichah, the Scroll of Lamentations
Seven of Consolation
"Be comforted, Be comforted, My People…," Yeshayahu 40:1)
"But Zion said, 'HaShem has left me, and the L-rd has forgotten me…' " (Yeshayahu 49:14)
"Impoverished one, one who has endured storms…" (Yeshayahu 54:11)
"I, even I, am the One Who comforts you…" (Yeshayahu 51:12)
"Sing out, you who were barren,…" (Yeshayahu 54:1)
"Arise, Shine forth …" (Yeshayahu 60:1)
"I will surely delight in the L-rd,…" (Yeshayahu 61:10)
Two of "Teshuvah," Repentance
"Seek the L-rd when He is near,…" (Yeshayahu 55:6), read on "Tzom Gedaliah," during Afternoon Prayer
"Return, O Israel," read on "Shabbat Shuvah," the Sabbath of Repentance, the Shabbat between Rosh HaShanah and Yom Kippur (Hoshea 14:2)
The Ratio Rationale
The reason for the ratio of three to seven of "punishment" to "comfort" is that it takes a long time to be comforted when one has sustained a major loss, as we see in the Torah, in connection with Yaakov Avinu, when his children sought to comfort him with the happy news that Yosef was still alive, that at first he refused to believe them (45:26). It was only Serach bat Asher, with her sweet and gentle manner, who could convince him that indeed, his long-lost son was still alive.
"Here too, after such destruction, it would be impossible to accept consolation delivered with such rapidity. It would be like saying to one who has been begging in the streets, 'tomorrow you will be king!' which could not be believed, as it says in (Shemot 6:9), 'And they didn't (couldn't) listen to Moshe, from shortness of breath and from hard labor.' " (Machzor Vitry)
The Avudraham makes the leading verses of the Seven Haftarot of Consolation into a conversation between the Holy One, Blessed be He, the People of Israel and the Prophets, as cited by Rabbi Shlomo Yosef Zevin, ZT"L.
"On the first Shabbat, the Holy One says through the Prophets, 'Be comforted, Be comforted, My People.' But the People refuse to accept the words of the Prophets. So that we hear on the second Shabbat, 'And Zion answered, "HaShem has left me, and the L-rd has forgotten me!" ' On the third Shabbat, the Prophets report to HaShem 'The impoverished, the storm-tossed one has not been comforted' - 'She refuses to accept comfort from us; she wants to hear it from You alone!' "
"Therefore, on the fourth Shabbat, the Holy One, Blessed be He, assures the People, 'It is I, even I Who is comforting you.' And on the fifth Shabbat, He continues to raise their spirits, 'Sing out, you who were barren, who had not yet given birth.' And even on the sixth, 'Arise, give forth light, for your light has come.'
"Then and only then, on the seventh Shabbat does the People of Israel believe that her time of suffering is over, 'I will rejoice in HaShem, my soul will delight in my G-d…' "
Thus, by allocating three Haftarot to "Mussar," reproof and warning of dire punishment, and seven to consolation and promises of future redemption, did the Rabbis take note of human nature, and of the principle that "HaShem's reward is greater than His punishment." (RASHI on Shemot 20:6, based on Tosefta to Masechet Sotah, Chapter 4)
The Repentance Exception
Although the historical and psychological sequence would normally be: Warning of Punishment, then Repentance, and only then Redemption, that order could not be maintained here, because it was necessary to put the Haftarot whose content relates to Repentance at the Time of Repentance, between Rosh HaShanah and Yom Kippur.