Tachanun is supplemented on Mondays and Thursdays by extended tachanunim starting "V'hu rachum". On those days, after tachanun is half-kadish (kadish l'ela, as some call it), a short paragraph that starts "Kel erech apayim", and the removal of the Torah scroll from where it's stored for reading.

I'm trying to determine whether "Kel erech apayim" is said on a Monday or Thursday on which tachanun is recited but the Torah isn't read from (because there's no Torah scroll, let's say, or because there's no one around who knows how to read it, or because there's no minyan, or some other reason). That, in fact, is my question, and you can stop reading now if you wish. The rest of this post illustrates whence my confusion has arisen.

Various sources seem to connect "Kel erech apayim" to tachanun, not to the Torah reading. The sidur of Bes Yaakov (Emden) clearly puts the paragraph in the section devoted to tachanun and not in the following section, devoted to the Torah reading. Shaare Efrayim, a book on the laws of the Torah reading, mentions (in chapter 10) various prayers said when the Torah scroll is taken out and put away, but does not mention "Kel erech apayim". And Taame Haminhagim mentions "Kel erech apayim" in paragraph 138, when discussing the late parts of shacharis, including tachanun, and not later, in the section about the Torah reading.

However, the ArtScroll sidurim and many other modern sidurim clearly put "Kel erech apayim" in the section devoted to the Torah reading. Not only that — the instructions in ArtScroll's English editions indicate that it's recited before the Torah is read, implying that it's not recited if the Torah isn't going to be read.

Is ArtScroll correct: do we recite "Kel erech apayim" only if the Torah is to be read? Does anyone (other than ArtScroll) say so?

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    kel erech apayim is recited on many days when Tachanun is not, e.g. during Nisan. It is equivalent to Lamnatzeyach, said the same days at that when they are Monday or Thursday. – CashCow Jan 15 '15 at 17:49

Your question is an interesting one. I researched this article on The Be'urei Hatefilah site (I highly recommend it, as it's one for the best resources on the web for Tefillah-related articles and insights.) My understanding is that there is some controversy. I recommend you read the whole article, but I will excerpt

Sefer Avudraham - Dinei Kri'at Hatorah-After completing the recital of V’Hu Rachum, it is customary to fall on one’s face as we discussed above.... Then they say the supplication: Hashem Elokei Yisroel Shuv Mai’Charon Apecha etc. Then they say: Kail Erech Aapyim V’Rav Chesed V’Emes.

So Avudraham seems to include it as part of Kri'at Hatorah (based on the title of where he mentions this.

Perushei Siddur Hatefillah L'Roke'ach The prayer: Kail Erech Apayim begins with G-d’s name (Kail) and ends with G-d’s name to teach that G-d is with us from the beginning to the end.

Since the prayer is recited just before taking out the Sefer Torah, it was composed with 24 words. We are saying the following: G-d, if we transgressed any part of Your Torah which is found in 24 books, please forgive us, G-d, with Your utmost compassion.

So, his explanation seems even stronger to relate this to Torah reading!

However, Machzor Vitri, 93: (the article is a PDF, and I have trouble copying Hebrew from there to here. See page 2 in that article) starts by just mentioning that this is said "on Monday's and Thursday's" without mentioning any connection of Kri'at Hatorah. Of course, the Torah is read each Monday and Thursday, anyway, but, perhaps, since he does not state any connection to it, we MIGHT infer that it should be said even if you can't read.

My own thinking:

It's connected to Torah reading, not Tachanun. The reason is that Half Kaddish is said before Kel Erech Apa'im, not after it. (See Rite and Reason, p. 68 for an explanation of why Half Kaddish is said between Tachanun and Ashrei.)

In conclusion - "tzarich iyun". B"N, we'll both keep hunting. Not that I'm lazy, but, I hope that you discover the answer before me, as I'd rather learn from you!

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