time
month
At a glance
In short
Both words come out month in English, but they name different things. Malbim and Rav Hirsch explain that chodesh is properly the new moon, the month's beginning, from chadash, "new," and that "month" is only a secondary, borrowed sense. When a pasuk uses chodesh where one would expect Rosh Chodesh, it means the new moon, not the month. Rabbi Klein holds that yerach is kin to yareach, the moon, and on that basis suggests, though not as a ruling, that it names the month as a full span of days; Malbim reads it simply as a period of thirty days. The Levush records the custom that a kesubah names the month chodesh and a get names it yerach, so the two are not interchangeable even in a document.
Distinctions
Chodesh (חדש)
Malbim and Rav Hirsch: the primary sense is not "month" but "the beginning of the month." Hence the places where chodesh stands where one would expect Rosh Chodesh: Bamidbar 28:14, Shmuel I 20:18, Yeshayahu 1:13. The word carries chadash, "new," and chiddush, renewal, so what it names is the novelty of the month. For Rabbi Klein this is also why the first of the months is Nissan, whose very meaning is "miracles," because Yetzias Mitzrayim, one of the greatest miracles of all time, happened then.
Yerach (ירח) and yareach (ירח)
Rabbi Aharon Marcus ties yerach to oraiach, "path," and to the Aramaic itrachish, "it happened." Marcus does not explain the thematic link between these words; the reading that follows is Rabbi Klein's own ("to me it seems fairly clear"). Chodesh, being bound up with "new," alludes to Hashem's introducing new occurrences outside the normal system of nature, which is what we call miracles; that, he suggests, is why chodesh is the word we use colloquially, since we wish to focus on Hashem and His awesome miracles. Yerach, tied to "path," connotes nothing "happening" beyond the regular system of nature: time running its course naturally, as if the month just happened, seemingly without Hashem's miraculous intervention. That, on this reading, is why it is the less common word.
The practical custom
Rabbi Mordechai Jaffe, the Levush: the custom is that a get dates the month as a yerach and a kesubah as a chodesh. Yerach carries being sent away, from geresh yerachim (Devarim 33:14); chodesh carries newness, and taking a wife is ki yikach ish ishah chadashah (Devarim 24:5).
Where the authorities disagree
The simple view: some say that chodesh is Aramaic and yerach Hebrew. Others, Rabbi Klein says, offer a more sophisticated approach.
Malbim: chodesh is the month's beginning, and yerach is a period of thirty days as such, whether or not those thirty days answer to any lunar event. On this reading yerach is a unit of counting, not an astronomical term.
Against that, Rabbi Klein holds that in truth yerach is related to yareach, the moon, whose lunar movements help fix the month's length. On that basis, he says, we may posit the cleaner division: chodesh denotes the beginning of the month, yerach the entire month as a whole. He offers this as a suggestion, not as a ruling.
Rav Hirsch offers another way of dividing them, which, Rabbi Klein says, fits his own model: chodesh is the month as an abstract unit of time, measured by the moon's light vanishing and returning, while yerach is the month as a vehicle of maturation, the passage of time made tangible in the growth of produce. On this understanding, yerach is a month bound to the rules of nature.
Also discussed in
Radak on these roots
Sefer HaShorashim
ח-ד-ש
To renew, with חָדָשׁ, new. The חֹדֶשׁ, the month, is named for the renewal of the moon; the word means the whole thirty days, and also the first day alone.
Renewing
וְחִדְּשׁוּ עָרֵי חֹרֶב (Yeshayahu 61:4), they will renew the waste cities; תְּחַדֵּשׁ עֵדֶיךָ נֶגְדִּי (Iyov 10:17), You renew Your witnesses against me; and of itself, תִּתְחַדֵּשׁ כַּנֶּשֶׁר נְעוּרָֽיְכִי (Tehillim 103:5), your youth renews itself like the eagle. The whole sense of renewal is well known.
New
וְאֵין כָּל־ חָדָשׁ תַּחַת הַשָּֽׁמֶשׁ (Koheles 1:9), there is nothing new under the sun; וְיָשָׁן מִפְּנֵי חָדָשׁ תּוֹצִֽיאוּ (Vayikra 26:10), you shall bring out the old before the new; and חֲדָשִׁים לַבְּקָרִים (Eichah 3:23), new every morning. וְהוּא חָגוּר חֲדָשָׁה (Shmuel II 21:16), and he was girded with a new one, means a new sword; so וּמַֽאֲכָלוֹ בְּרִאָֽה (Chavakuk 1:16), and his food is fat, means a fat sheep, and וַֽאֲנִי תְפִלָּֽה (Tehillim 109:4), and I am prayer, means a man of prayer.
אִשָּׁה חֲדָשָׁה
כִּֽי־יִקַּח אִישׁ אִשָּׁה חֲדָשָׁה (Devarim 24:5), when a man takes a new wife, means one new to him, which leaves out a man who takes back his own divorcee; a widow, or another man's divorcee, is included.
The month, and its first day
The חֹדֶשׁ is named for the renewal of the moon, which renews itself in it, and the whole thirty days together are called חדש. The first day alone, Rosh Chodesh, is also called חדש: מָחָר חֹדֶשׁ (Shmuel I 20:18), tomorrow is Rosh Chodesh; לֹֽא־ חֹדֶשׁ וְלֹא שַׁבָּת (Melachim II 4:23), it is neither Rosh Chodesh nor Shabbos; וְהָיָה מִֽדֵּי־ חֹדֶשׁ בְּחָדְשׁוֹ (Yeshayahu 66:23), and it shall be, each Rosh Chodesh in its time; בַּשַּׁבָּתוֹת וּבֶֽחֳדָשִׁים (Yechezkel 46:3), on the Shabbosos and on Roshei Chodashim. But in בְּיֽוֹם־ הַחֹדֶשׁ הַשֵּׁנִי (Shmuel I 20:34), on the second day of the month, it names the whole month. His father takes לֹֽא־חֹדֶשׁ וְלֹא שַׁבָּת of the whole thirty days, that is, not yet a month has passed, nor even a week, since you saw him. חֹדֶשׁ יָמִֽים (Bamidbar 11:20), a month of days, is a full month, thirty days.
A month decreed
עַתָּה יֹֽאכְלֵם חֹדֶשׁ אֶת־חֶלְקֵיהֶֽם (Hoshea 5:7), now a month shall devour them with their portions, is the month decreed upon them, the month of Av; and so בְּחָדְשָׁהּ יִמְצָאֽוּנְהָ (Yirmiyahu 2:24), in her month they will find her, is the month decreed upon her, when she cannot be saved from the hand of those who seek her. His father reads בְּחָדְשָׁהּ as an infinitive, in her renewing; that is, why do none who seek her weary? Because at every time they find her renewed, as though she were only now beginning to run before them.
[פִּעֵל] וְחִדְּשׁוּ עָרֵי חֹרֶב (ישעיה סא, ד), תְּחַדֵּשׁ עֵדֶיךָ נֶגְדִּי (איוב י, יז). וההתפעל תִּתְחַדֵּשׁ כַּנֶּשֶׁר נְעוּרָֽיְכִי (תהלים קג, ה). והתאר וְאֵין כָּל־חָדָשׁ תַּחַת הַשָּֽׁמֶשׁ (קהלת א, ט), וְיָשָׁן מִפְּנֵי חָדָשׁ תּוֹצִֽיאוּ (ויקרא כו, י), כִּֽי־יִקַּח אִישׁ אִשָּׁה חֲדָשָׁה (דברים כד, ה), וְהוּא חָגוּר חֲדָשָׁה (שמואל ב' כא, טז), פירוש חרב חדשה. וכן וּמַֽאֲכָלוֹ בְּרִאָֽה (חבקוק א, טז) שפירושו שה בריאה, וַֽאֲנִי תְפִלָּֽה (תהלים קט, ד), איש תפלה, והדומים להם. חֲדָשִׁים לַבְּקָרִים (איכה ג, כג). ורוצה לומר באשה חדשה שתהיה חדשה אצלו פרט למחזיר גרושתו, אבל אלמנה וגרושת אחר במשמע. וכל ענין החדוש ידוע. ונקרא הַחֹדֶשׁ כן על חדוש הירח שמתחדש בו. ונקראו כל השלשים יום בכלל חדש. ונקרא יום הראשון לבדו חדש, מָחָר חֹדֶשׁ (שמואל א' כ, יח), לֹֽא־חֹדֶשׁ וְלֹא שַׁבָּת (מלכים ב' ד, כג), וְהָיָה מִֽדֵּי־חֹדֶשׁ בְּחָדְשׁוֹ (ישעיה סו, כג), בַּשַּׁבָּתוֹת וּבֶֽחֳדָשִׁים (יחזקאל מו, ג). כל אלו והדומים להם על יום הראשון בלבד. אבל בְּיֽוֹם־הַחֹדֶשׁ הַשֵּׁנִי (שמואל א' כ, לד), הוא שם על כלו ופירושו יום שני מהחדש. ואדוני אבי ז"ל פירוש לֹֽא־חֹדֶשׁ וְלֹא שַׁבָּת כל השלשים יום כלומר לא עבר עדיין חדש ולא אפילו שבוע שראית אותו. חֹדֶשׁ יָמִֽים (במדבר יא, כ), חֹדֶשׁ יָמִֽים שלמים והוא שלשים יום. עַתָּה יֹֽאכְלֵם חֹדֶשׁ אֶת־חֶלְקֵיהֶֽם (הושע ה, ז), החדש שנגזר עליהם והוא חדש אב. וכן בְּחָדְשָׁהּ יִמְצָאֽוּנְהָ (ירמיה ב, כד), בחדש שנגזר עליה שלא תוכל להנצל מכף מבקשיה. ואדוני אבי ז"ל פירוש בְּחָדְשָׁהּ מקור, כלומר למה לא ייעפו כל מבקשיה? כי בכל עת ימצאו אותה בחדושה כאילו עתה מתחלת לרוץ לפניהם.
י-ר-ח
יָרֵחַ, the moon; and יֶרַח, a month, since the moon renews itself each month.
The moon
עָשָׂה יָרֵחַ לְמוֹעֲדִים (Tehillim 104:19), He made the moon for appointed times, and וְיָרֵחַ לֹא יַגִּיהַ אוֹרוֹ (Yeshayahu 13:10), which he glosses: the moon shall not give its light.
The month
Because the moon renews itself every month, the month is called יֶרַח: בְּיֶרַח הָאֵתָנִים (Melachim I 8:2), in the month of Eisanim, and מִי יִתְּנֵנִי כְיַרְחֵי קֶדֶם (Iyov 29:2), would that I were as in the months of old. And because the moon renews itself many times, it is spoken of in the plural although it is only one: גֶּרֶשׁ יְרָחִים (Devarim 33:14), the yield of the moons, meaning that the moon ripens the fruits.
עָשָׂה יָרֵחַ לְמֽוֹעֲדִים (תהלים קד, יט), וְיָרֵחַ לֹֽא־יַגִּיהַ אוֹרֽוֹ (ישעיה יג, י), וירח לא יאיר אורו. וִֽירֵחֵךְ לֹא יֵֽאָסֵף (ישעיה ס, כ), היא הלבנה. ולפי שהלבנה מתחדשת בכל חדש נקרא החדש יֶרַח. בְּיֶרַח הָאֵֽתָנִים (מלכים א' ח, ב), בסגול, מִֽי־יִתְּנֵנִי כְיַרְחֵי־קֶדֶם (איוב כט, ב). ולפי שהירח מתחדש פעמים רבות קראו בלשון רבים ואף על פי שאינו אלא אחד ואמר גֶּרֶשׁ יְרָחִֽים (דברים לג, יד), פירוש כי הירח יבשל הפירות.
Radak, Sefer HaShorashim, Berlin 1847. Public domain, digitised by Sefaria from the National Library of Israel.
Sources
Rabbi Reuven Chaim Klein, "Old Month versus New Month," What's in a Word?, Ohr Somayach, 17 March 2018.
Cited in the essay: Bamidbar 28:14; Shmuel I 20:18; Yeshayahu 1:13; Devarim 24:5, 33:14; Malbim and Rav Hirsch on chodesh and yerach; Rabbi Aharon Marcus, Barzilai (עמ' 130); Levush on the wording of a get and a kesubah.