Properties and Signatures of the <i>Mazhor Qatan</i>

Properties and Signatures of the <i>Mazhor Qatan</i>
Properties and Signatures of the Mazhor Qatan

by Remy Landau

The 19 Year Span Day Counts

The fixed Hebrew calendar arithmetic is premised on the notion of a constant lunar period lasting exactly 29d 12h 793p. The calendar then assumes that 235 complete lunar cycles add up to exactly 19 integral solar years.

Within these relationships, Hebrew months can be either 29 or 30 days long, and Hebrew years may contain either 12 months (common years) or 13 months (leap years).

An additionally implied constraint is that all lunar years begin within less than one month after the start of their corresponding solar years. The constraint may be expressed algebraically as

0 <= NumberOfYears * (LunarYearInMonths - SolarYearInMonths) <= 29d 12h 793p

Given the above information, the 19th century mathematician Carl Friedich Gauss determined that the number of months contained by any Hebrew year span can be algebraically expressed as

Yearspan.months = (235 * Yearspan + 12 * Yearspan MOD 19 ) / 19

Moreover, Gauss also noted that if Yearspan began from some Baseyear, then any Targetyear = Baseyear + Yearspan satisfying the relationship

12 * Targetyear MOD 19 < 7

is a 13-month year for any calendar system as defined above.

The fixed Hebrew calendar's Year count is such that

3 = Baseyear MOD 19

Consequently, for the fixed Hebrew calendar, the 13-month years correspond to the Hebrew year counts in accordance with

(12 * HebrewYear + 17) MOD 19 < 7

Consequently, in the fixed Hebrew calendar, 13-month years begin whenever the Hebrew year count, after division by 19, leaves a remainder that is either 0 , 3, 6, 8, 11, 14, or 17. Since the calendar was constructed at a time when no symbol existed for the value 0, this particular remainder was replaced by the value 19.

The positions of the 13-month years over every 19-year period that begins at 1 = HebrewYear MOD 19 is given the Hebrew acronym GUChADZT. The acronym is formed by the Hebrew letters Gimel, Vov, Het (Chet), Alef, Daled, Zayin, and Tet. Each letter respectively represents in Hebrew denumeration the numbers 3, 6, 8, 1, 4, 7, and 9. The number 10 is left out of the acronym.

In the Hebrew calendar, a period of 19 consecutive years is referred to as a Mahzor Qatan, that is, a small cycle.

Historically, there have been several documented Mahzorim Qatanim. However, these all followed the assumptions of the calendar, and really reflected a cycle count starting at a Hebrew year different than 1 = HebrewYear MOD 19.

The only part of the Hebrew calendar that repeats itself in every 19 years, once the year count start has been set, is the position of the 13-month years in the corresponding Mahzor Qatan. The Hebrew calendar does not repeat itself over 19 year periods. This simple idea can easily be determined from the fact that periods of 19 Hebrew years can have either 6938, 6939, 6940, 6941, or 6942 days. The distribution of the day counts is as follows...

19 YEAR SPANS
235 months = 6,939d 16h 595p
M'+/-	DAYS	MOD 7d	OCCURS
-2	0d	0	0
-1	6,938d	1	11,263
0	6,939d	2	311,544
1	6,940d	3	250,123
2	6,941d	4	113,011
3	6,942d	5	3,531
The *maximum* variance is 4 days

Since the 6939 and 6940 day spans dominate about 81.5% of the years in the full Hebrew calendar cycle of 689,472 years and the Gregorian calendar also can have 19 year spans of both 6939 and 6940 days, it is highly probable that a given Hebrew date and its corresponding Gregorian date will once again coincide in 19 years... but not necessarily every 19 years.

The correspondence between the Hebrew and Gregorian calendars repeats itself in a cycle of
14,389,970,112 Hebrew years which is also 14,390,140,400 Gregorian years!

In days, 14,389,970,112 Hebrew years = 5,255,890,855,047 days = 14,390,140,400 Gregorian years!

It is interesting to note that, in the Hebrew calendar, all 19 year spans which begin with 12-month years have the following day counts...

19 Year Spans Starting at Common Years
235 months = 6,939d 16h 595p
M'+/-	DAYS	MOD 7d	OCCURS
-2	0d	0	0
-1	0d	0	0
0	6,939d	2	17,099
1	6,940d	3	13,648
2	6,941d	4	5,246
3	6,942d	5	295
The *maximum* variance is 3 days

On the other hand, all 19 year spans which begin with 13-month years have the following day counts...

19 Year Spans Starting at Leap Years
235 months = 6,939d 16h 595p
M'+/-	DAYS	MOD 7d	OCCURS
-2	0d	0	0
-1	6,938d	1	1,609
0	6,939d	2	15,195
1	6,940d	3	12,334
2	6,941d	4	7,150
3	0d	0	0
The *maximum* variance is 3 days

See Weekly Question Archive for additional details on the day counts of 19 year spans.

Since there are 19 possible cycles of 19 years, and each may not have the same arithmetical properties as the other, a distinction must be made between each Mahzor Qatan. Therefore, for purposes of the following, it will be convenient to identify a Mahzor Qatan by the remainder when its first Hebrew year is divided by 19.

For example, the first year of the 304th Mahzor Qatan, counting from year 1H, is 5758H. The value 5758 when divided by 19 leaves a remainder of 1. Hence, that Mahzor Qatan is identified as being of the type 1 = HebrewYear MOD 19.

The year 5757H, was the last year of the 303rd Mahzor Qatan. The value 5757 when divided by 19 leaves the remainder 0. Hence, a 19 year span counted from the start year 5757H is is identified as being of the type 0 = HebrewYear MOD 19.

Similarly, a 19 year span counted from the start year 5750H is identified as being of the type 12 = HebrewYear MOD 19, since the value 5750 when divided by 19 leaves the remainder 12 and not 1.

When Rosh Hashana advances to a new day in the Gregorian calendar, it always does so in the 9th year of a Mahzor Qatan of the type 1 = HebrewYear MOD 19.

(See the Additional Notes on The Rosh HaShana Drift for more information on the latest possible occurrences of Rosh Hashana).

The following table shows, over the full and complete Hebrew calendar repetition cycle of 689,472 years, the number of times that any year begins on either Monday, Tuesday, Thursday or Shabbat in the Mahzor Qatan type 1 = HebrewYear MOD 19.

Weekday Starts for All Years in the Mahzor Qatan
Year	Mon	Tue	Thu	Shbt	TOTAL
1	9837	3811	12272	10368	36288
2	10368	3281	12271	10368	36288
3	10368	5184	10368	10368	36288
4	9838	3811	12271	10368	36288
5	10368	3281	12271	10368	36288
6	10368	5184	10368	10368	36288
7	9838	3811	12271	10368	36288
8	10368	5184	10368	10368	36288
9	9838	3811	12271	10368	36288
10	10368	3281	12271	10368	36288
11	10368	5184	10368	10368	36288
12	9838	3811	12271	10368	36288
13	10368	3281	12271	10368	36288
14	10368	5184	10368	10368	36288
15	9838	3811	12271	10368	36288
16	10368	3280	12272	10368	36288
17	10368	5184	10368	10368	36288
18	9837	3811	12272	10368	36288
19	10368	5184	10368	10368	36288
TOTAL	193280	79369	219831	196992	689472

For the Mahzor Qatan type 1 = HebrewYear MOD 19, the table shows that over the 689,472 Hebrew year calendar cycle:-

Each year of the Mahzor Qatan begins the same number of times on Shabbat. The number 10,368 is exactly 2/(7*19) of the full calendar cycle.
The number of times that a leap year begins on either Monday, or Thursday is the same as the number of times that these years begin on Shabbat.
Leap years begin on Tuesdays exactly half as many times as they do on any other day of the week.
The weekday distribution of Rosh Hashana starts is identical for each of the leap years in the 19 year cycle, which are the 1st, 3rd, 8th, 11th, 14th, 17th and 19th years of the Mahzor Qatan.
The 16th year has an absolutely unique weekday distribution of Rosh Hashana starts.
The 1st and 18th years have the same weekday distribution of Rosh Hashana starts.
The 2nd, 5th, 10th, and 13th years have the same weekday distribution of Rosh Hashana starts.
The 4th, 7th, 9th, 12th, and 15th years have the same weekday distribution, of Rosh Hashana starts.

Over the full Hebrew calendar repetition cycle, the number of times that any year in the Mahzor Qatan does not begin on Shabbat is 36,288 - 10,368 = 25,920. This number is also equal to the number of halaqim (i.e., parts) in one day which is 24 * 1080 = 25,920.

Signatures of the Mazhor Qatan

Regardless of its type, the qeviyot for any Mahzor Qatan can only be combined and arranged in exactly 61 different ways for that type. See also The Qeviyot.

The signature of any Mahzor Qatan is the particular combination and arrangement of the qeviyot in that 19 year cycle.

For the type 1 Mahzor Qatan, the existence of its 61 signatures was demonstrated by The Rev. Sherrard Beaumont Burnaby beginning in Chapter 6, at page 146 of his book Elements of the Jewish and Muhammadan Calendars published by George Bell and Sons, London (1901). Burnaby noted that his thinking on this phenomenon was based on a paper published in 1843 by Professor Nesselmann. The paper, Beitrage zur Chronologie, was published in Crelle Journal fur die Mathematik, Band 26, page 59, Berlin 1843.

Yaaqov Loewinger noted that at around 1200j, a table containing the 61 signatures, apparently was conceived by the medieval Tosafist Isaac ben Abraham. Loewinger notes that by using this table, all of the qeviyot for any particular mahzor qatan can then be found by entering only the Tishrei molad of the first year in that cycle. He is presently preparing an article outlining this particular Hebrew calendar phenomenon as documented in the classical literature. Once that paper is published, it will be very interesting to see his report of the various classical methologies used to relate the Tishrei moladot to their signatures.

The non-analytical view of the signatures that follows is only a very small and specific part of the much larger problem related to the occurrence of the qeviyot found embedded, not only in any 19 year span, but also in any size of Hebrew year spans. Insights into the far larger problem are provided in questions 229 through 238 found in the Weekly Question Archive beginning with Weekly Questions 231-240.

The Signature Tables

The Signature Tables shown below are constructed relative to the Mahzor Qatan type 1 = HebrewYear MOD 19.

In the Signature Tables, the qeviyot are expressed as an alphabetic, representing the Tishrei 1 weekday, followed by the last two digits of the corresponding Hebrew year length.

The weekdays Shabbat, Monday, Tuesday, and Thursday are coded into the single Roman capitalized letter Z, B, G, H. These letters are the transliteration of the Hebrew symbols Zayin, Bet, Gimel, Heh which are traditionally used to represent these weekdays.

Since all of the possible single Hebrew year lengths the same leading hundreds digit 3, the numeral has been dropped for all of the year length notations. The desired qeviyah is then coded by abutting the two-digit year length code to the right of the weekday letter code. For example, Z85 represents the qeviyah of the 385 day Hebrew year beginning on Shabbat and H54 indicates a 354 day year starting on Thursday.

Explanation of the Columns in the Signature Tables
Column Title	Column Content
Signature	a sequence number from 1 to 61 reflecting the order in which the *signature* is first detected in the full Hebrew calendar cycle when viewed starting from year 1H.
Frequency	the number of times that the signature is found in the full Hebrew calendar cycle.
First Time	the Hebrew year at which the *signature* is first detected in the full Hebrew calendar cycle when viewed from year 1H.
Tishrei Molad	the *Tishrei Molad* corresponding to the year in the *First Time* column.
Earliest Molad	the lowest value of the *Tishrei Molad* found for the first year among all of the occurrences of the corresponding *signature*.
Latest Molad	the highest value of the *Tishrei Molad* found for the first year among all of the occurrences of the corresponding *signature*.
Signature Arrangement of the Qeviyot	the actual sequence of the 19 qeviyot in the *signature*.
The Qeviyot	the list of the qeviyot in the *signature*.
The Missing Qeviyot	the list of the qeviyot not in the *signature*.

The Signatures Ordered by First Occurrence

The first 13 signatures occur exactly 19 years apart. Then incremental gaps in the year counts appear between each of the subsequent entries in the signatures ordered by first occurrence. The 20th and 21st entries form the last pair of entries to be 19 years apart.

The Mahzor Qatan Type 1 Signatures
Initial Signature Occurrences In Ascending Hebrew Year Order
Statistics						Signature Arrangement of the Qeviyot
Signature	Frequency	First Time	Tishrei Molad	Earliest Molad	Latest Molad	1	2	3	4	5	6	7	8	9	10	11	12	13	14	15	16	17	18	19
1	539	1H	2d 5h 204p	2d 2h 924p	2d 5h 374p	B55	Z55	H83	G54	Z55	H85	H54	B83	Z55	H54	B83	Z55	H54	B85	B53	H54	B85	B55	Z83
2	1,605	20H	4d 21h 799p	4d 18h 24p	5d 1h 484p	H54	B55	Z83	H55	G54	Z85	Z53	G84	B55	Z55	H83	G54	Z55	H85	H54	B53	H85	H54	B83
3	539	39H	0d 14h 314p	0d 14h 154p	0d 16h 684p	Z55	H54	B85	B53	H55	G84	B55	Z83	H54	B55	Z85	Z53	G54	Z85	Z55	H54	B83	Z55	H83
4	829	58H	3d 6h 909p	3d 5h 379p	3d 9h 199p	G54	Z55	H85	H54	B53	H85	H54	B85	B53	H54	B85	B55	Z53	G84	B55	Z55	H83	G54	Z85
5	299	77H	5d 23h 424p	5d 22h 1,074p	6d 0h 404p	Z53	G54	Z85	Z55	H54	B83	Z55	H85	H54	B53	H85	H54	B55	Z83	H54	B55	Z83	H55	G84
6	2,438	96H	1d 15h 1,019p	1d 11h 744p	1d 22h 1,049p	B55	Z53	G84	B55	Z55	H83	G54	Z85	Z55	H54	B83	Z55	H54	B83	Z55	H54	B85	B53	H85
7	1,903	115H	4d 8h 534p	4d 2h 924p	4d 11h 714p	H54	B55	Z83	H54	B55	Z83	H55	G84	B55	Z53	G84	B55	Z55	H83	G54	Z55	H85	H54	B83
8	829	134H	0d 1h 49p	6d 22h 1,074p	0d 2h 894p	Z55	H54	B83	Z55	H54	B85	B53	H85	H54	B55	Z83	H54	B55	Z85	Z53	G54	Z85	Z55	H83
9	535	153H	2d 17h 644p	2d 15h 589p	2d 18h 19p	G54	Z55	H83	G54	Z55	H85	H54	B83	Z55	H54	B85	B53	H54	B85	B55	Z53	G84	B55	Z83
10	1,899	172H	5d 10h 159p	5d 9h 229p	5d 17h 1,079p	H55	G54	Z85	Z55	H54	B83	Z55	H83	G54	Z55	H85	H54	B53	H85	H54	B55	Z83	H54	B85
11	1,065	191H	1d 2h 754p	1d 0h 409p	1d 5h 329p	B53	H55	G84	B55	Z53	G84	B55	Z83	H55	G54	Z85	Z55	H54	B83	Z55	H54	B83	Z55	H85
12	1,903	210H	3d 19h 269p	3d 11h 744p	3d 20h 534p	H54	B53	H85	H54	B55	Z83	H54	B85	B53	H55	G84	B55	Z53	G84	B55	Z55	H83	G54	Z85
13	535	229H	6d 11h 864p	6d 11h 744p	6d 14h 174p	Z55	H54	B83	Z55	H54	B85	B53	H85	H54	B55	Z83	H54	B55	Z83	H54	B55	Z85	Z53	G84
14	1,065	286H	0d 13h 489p	0d 9h 229p	0d 14h 149p	Z55	H54	B85	B53	H55	G84	B55	Z83	H54	B55	Z83	H55	G54	Z85	Z55	H54	B83	Z55	H83
15	534	324H	5d 22h 599p	5d 20h 564p	5d 22h 1,069p	Z53	G54	Z85	Z55	H54	B83	Z55	H85	H54	B53	H85	H54	B55	Z83	H54	B55	Z83	H54	B85
16	833	476H	6d 10h 1,039p	6d 7h 874p	6d 11h 714p	Z55	H54	B83	Z55	H54	B83	Z55	H85	H54	B53	H85	H54	B55	Z83	H54	B55	Z85	Z53	G84
17	833	552H	3d 5h 179p	3d 1h 489p	3d 5h 329p	G54	Z55	H85	H54	B53	H85	H54	B83	Z55	H54	B85	B53	H55	G84	B55	Z53	G84	B55	Z85
18	829	666H	5d 8h 509p	5d 5h 379p	5d 9h 199p	H54	B55	Z85	Z53	G54	Z85	Z55	H83	G54	Z55	H85	H54	B53	H85	H54	B55	Z83	H54	B85
19	535	742H	2d 2h 729p	2d 0h 409p	2d 2h 919p	B55	Z55	H83	G54	Z55	H83	G54	Z85	Z55	H54	B83	Z55	H54	B85	B53	H54	B85	B55	Z83
20	1,903	875H	6d 22h 574p	6d 14h 179p	6d 22h 1,049p	Z55	H54	B83	Z55	H54	B85	B53	H85	H54	B55	Z83	H54	B55	Z83	H55	G54	Z85	Z53	G84
21	298	894H	2d 15h 89p	2d 14h 179p	2d 15h 584p	B55	Z55	H83	G54	Z55	H85	H54	B83	Z55	H54	B85	B53	H54	B85	B55	Z53	G84	B55	Z83
22	833	932H	1d 0h 199p	0d 20h 564p	1d 0h 404p	B53	H54	B85	B55	Z53	G84	B55	Z83	H55	G54	Z85	Z55	H54	B83	Z55	H54	B83	Z55	H85
23	539	1,065H	5d 20h 44p	5d 18h 4p	5d 20h 534p	Z53	G54	Z85	Z55	H54	B83	Z55	H83	G54	Z55	H85	H54	B53	H85	H54	B55	Z83	H54	B85
24	833	1,255H	4d 17h 594p	4d 14h 179p	4d 18h 19p	H54	B55	Z83	H54	B55	Z85	Z53	G84	B55	Z55	H83	G54	Z55	H85	H54	B53	H85	H54	B83
25	1,899	1,388H	2d 13h 439p	2d 5h 379p	2d 14h 149p	B55	Z55	H83	G54	Z55	H85	H54	B83	Z55	H54	B83	Z55	H54	B85	B53	H55	G84	B55	Z83
26	1,605	1,464H	6d 7h 659p	6d 0h 409p	6d 7h 869p	Z55	H54	B83	Z55	H54	B83	Z55	H85	H54	B53	H85	H54	B55	Z83	H54	B55	Z83	H55	G84
27	299	1,483H	2d 0h 174p	1d 22h 1,074p	2d 0h 404p	B55	Z53	G84	B55	Z55	H83	G54	Z85	Z55	H54	B83	Z55	H54	B85	B53	H54	B85	B55	Z83
28	535	1,578H	1d 10h 989p	1d 9h 229p	1d 11h 739p	B55	Z53	G84	B55	Z55	H83	G54	Z85	Z53	G54	Z85	Z55	H54	B83	Z55	H54	B85	B53	H85
29	535	1,654H	5d 5h 129p	5d 2h 924p	5d 5h 354p	H54	B55	Z85	Z53	G54	Z85	Z55	H83	G54	Z55	H83	G54	Z55	H85	H54	B53	H85	H54	B85
30	834	1,768H	0d 8h 459p	0d 5h 379p	0d 9h 224p	Z55	H54	B85	B53	H54	B85	B55	Z83	H54	B55	Z83	H55	G54	Z85	Z55	H54	B83	Z55	H83
31	1,065	1,787H	3d 0h 1,054p	2d 20h 564p	3d 1h 484p	G54	Z55	H85	H54	B53	H85	H54	B83	Z55	H54	B85	B53	H55	G84	B55	Z53	G84	B55	Z83
32	535	1,844H	4d 2h 679p	4d 0h 409p	4d 2h 919p	H54	B55	Z83	H54	B55	Z83	H54	B85	B55	Z53	G84	B55	Z55	H83	G54	Z55	H85	H54	B83
33	535	2,167H	0d 19h 1,074p	0d 18h 24p	0d 20h 534p	B53	H54	B85	B55	Z53	G84	B55	Z83	H54	B55	Z85	Z53	G54	Z85	Z55	H54	B83	Z55	H85
34	298	2,319H	1d 8h 434p	1d 7h 874p	1d 9h 199p	B53	H55	G84	B55	Z53	G84	B55	Z85	Z53	G54	Z85	Z55	H54	B83	Z55	H54	B85	B53	H85
35	298	2,395H	5d 2h 654p	5d 1h 489p	5d 2h 894p	H54	B55	Z83	H55	G54	Z85	Z53	G84	B55	Z55	H83	G54	Z55	H85	H54	B53	H85	H54	B85
36	535	2,490H	4d 13h 389p	4d 11h 744p	4d 14h 174p	H54	B55	Z83	H54	B55	Z85	Z53	G84	B55	Z55	H83	G54	Z55	H83	G54	Z55	H85	H54	B83
37	540	2,566H	1d 7h 609p	1d 5h 334p	1d 7h 869p	B53	H55	G84	B55	Z53	G84	B55	Z85	Z53	G54	Z85	Z55	H54	B83	Z55	H54	B83	Z55	H85
38	299	2,585H	4d 0h 124p	3d 22h 1,074p	4d 0h 404p	H54	B53	H85	H54	B55	Z83	H54	B85	B55	Z53	G84	B55	Z55	H83	G54	Z55	H85	H54	B83
39	535	2,680H	3d 10h 939p	3d 9h 229p	3d 11h 739p	H54	B53	H85	H54	B55	Z83	H54	B85	B53	H54	B85	B55	Z53	G84	B55	Z55	H83	G54	Z85
40	535	2,756H	0d 5h 79p	0d 2h 924p	0d 5h 354p	Z55	H54	B85	B53	H54	B85	B55	Z83	H54	B55	Z83	H54	B55	Z85	Z53	G54	Z85	Z55	H83
41	295	2,908H	0d 17h 519p	0d 16h 689p	0d 17h 1,079p	Z55	H54	B85	B53	H55	G84	B55	Z83	H54	B55	Z85	Z53	G54	Z85	Z55	H54	B83	Z55	H85
42	5	2,984H	4d 11h 739p	4d 11h 719p	4d 11h 739p	H54	B55	Z83	H54	B55	Z85	Z53	G84	B55	Z53	G84	B55	Z55	H83	G54	Z55	H85	H54	B83
43	534	3,079H	3d 22h 474p	3d 20h 564p	3d 22h 1,069p	H54	B53	H85	H54	B55	Z83	H54	B85	B55	Z53	G84	B55	Z55	H83	G54	Z55	H83	G54	Z85
44	5	3,174H	3d 9h 209p	3d 9h 204p	3d 9h 224p	H54	B53	H85	H54	B53	H85	H54	B85	B53	H54	B85	B55	Z53	G84	B55	Z55	H83	G54	Z85
45	540	3,269H	2d 19h 1,024p	2d 18h 24p	2d 20h 559p	G54	Z55	H85	H54	B53	H85	H54	B83	Z55	H54	B85	B53	H54	B85	B55	Z53	G84	B55	Z83
46	5	9,634H	0d 20h 549p	0d 20h 539p	0d 20h 559p	B53	H54	B85	B55	Z53	G84	B55	Z83	H55	G54	Z85	Z53	G54	Z85	Z55	H54	B83	Z55	H85
47	5	23,124H	6d 11h 719p	6d 11h 719p	6d 11h 739p	Z55	H54	B83	Z55	H54	B85	B53	H85	H54	B53	H85	H54	B55	Z83	H54	B55	Z85	Z53	G84
48	4	35,873H	5d 5h 364p	5d 5h 359p	5d 5h 374p	H54	B55	Z85	Z53	G54	Z85	Z55	H83	G54	Z55	H85	H54	B53	H85	H54	B53	H85	H54	B85
49	5	42,352H	5d 9h 219p	5d 9h 204p	5d 9h 224p	H55	G54	Z85	Z53	G54	Z85	Z55	H83	G54	Z55	H85	H54	B53	H85	H54	B55	Z83	H54	B85
50	5	55,652H	5d 2h 919p	5d 2h 899p	5d 2h 919p	H54	B55	Z85	Z53	G54	Z85	Z53	G84	B55	Z55	H83	G54	Z55	H85	H54	B53	H85	H54	B85
51	4	75,051H	0d 5h 374p	0d 5h 359p	0d 5h 374p	Z55	H54	B85	B53	H54	B85	B55	Z83	H54	B55	Z83	H55	G54	Z85	Z53	G54	Z85	Z55	H83
52	5	75,792H	0d 2h 899p	0d 2h 899p	0d 2h 919p	Z55	H54	B85	B53	H54	B85	B53	H85	H54	B55	Z83	H54	B55	Z85	Z53	G54	Z85	Z55	H83
53	5	82,081H	1d 9h 204p	1d 9h 204p	1d 9h 224p	B55	Z53	G84	B55	Z53	G84	B55	Z85	Z53	G54	Z85	Z55	H54	B83	Z55	H54	B85	B53	H85
54	5	88,541H	5d 20h 544p	5d 20h 539p	5d 20h 559p	Z53	G54	Z85	Z55	H54	B83	Z55	H85	H54	B53	H85	H54	B53	H85	H54	B55	Z83	H54	B85
55	4	108,491H	1d 22h 1,054p	1d 22h 1,054p	1d 22h 1,069p	B55	Z53	G84	B55	Z55	H83	G54	Z85	Z55	H54	B83	Z55	H54	B85	B53	H54	B85	B53	H85
56	4	114,780H	3d 5h 359p	3d 5h 359p	3d 5h 374p	G54	Z55	H85	H54	B53	H85	H54	B85	B53	H54	B85	B55	Z53	G84	B55	Z53	G84	B55	Z85
57	5	161,159H	2d 14h 154p	2d 14h 154p	2d 14h 174p	B55	Z55	H83	G54	Z55	H85	H54	B83	Z55	H54	B85	B53	H54	B85	B53	H55	G84	B55	Z83
58	5	167,448H	3d 20h 539p	3d 20h 539p	3d 20h 559p	H54	B53	H85	H54	B55	Z83	H54	B85	B55	Z53	G84	B55	Z53	G84	B55	Z55	H83	G54	Z85
59	5	213,827H	3d 5h 334p	3d 5h 334p	3d 5h 354p	G54	Z55	H85	H54	B53	H85	H54	B85	B53	H54	B85	B53	H55	G84	B55	Z53	G84	B55	Z85
60	4	246,545H	0d 18h 4p	0d 18h 4p	0d 18h 19p	B53	H54	B85	B53	H55	G84	B55	Z83	H54	B55	Z85	Z53	G54	Z85	Z55	H54	B83	Z55	H85
61	4	305,483H	6d 22h 1,054p	6d 22h 1,054p	6d 22h 1,069p	Z55	H54	B83	Z55	H54	B85	B53	H85	H54	B55	Z83	H54	B55	Z85	Z53	G54	Z85	Z53	G84

The Signatures Ordered by Tishrei Molad of First Occurrence

The most surprising observation in the ordered arrangement is that all of the Tishrei moladot are in precise ascending order.

The next observation to be made is that all of the entries in the Earliest Molad column are exactly 5 halaqim more than the entries in their immediately preceding Latest Molad column.

Since the moladot cycle from 6d 23h 1079p to 0d 0h 0p, the very first Earliest Molad shown, namely, 6d 22h 1,074p, does indeed precede the very first Latest Molad, namely, 0d 2h 894p.

The Mahzor Qatan Type 1 Signatures
Initial Signature Occurrences Ordered by Their First Year Tishrei Molad
Statistics						Signature Arrangement of the Qeviyot
Signature	Frequency	First Time	Tishrei Molad	Earliest Molad	Latest Molad	1	2	3	4	5	6	7	8	9	10	11	12	13	14	15	16	17	18	19
8	829	134H	0d 1h 49p	6d 22h 1,074p	0d 2h 894p	Z55	H54	B83	Z55	H54	B85	B53	H85	H54	B55	Z83	H54	B55	Z85	Z53	G54	Z85	Z55	H83
52	5	75,792H	0d 2h 899p	0d 2h 899p	0d 2h 919p	Z55	H54	B85	B53	H54	B85	B53	H85	H54	B55	Z83	H54	B55	Z85	Z53	G54	Z85	Z55	H83
40	535	2,756H	0d 5h 79p	0d 2h 924p	0d 5h 354p	Z55	H54	B85	B53	H54	B85	B55	Z83	H54	B55	Z83	H54	B55	Z85	Z53	G54	Z85	Z55	H83
51	4	75,051H	0d 5h 374p	0d 5h 359p	0d 5h 374p	Z55	H54	B85	B53	H54	B85	B55	Z83	H54	B55	Z83	H55	G54	Z85	Z53	G54	Z85	Z55	H83
30	834	1,768H	0d 8h 459p	0d 5h 379p	0d 9h 224p	Z55	H54	B85	B53	H54	B85	B55	Z83	H54	B55	Z83	H55	G54	Z85	Z55	H54	B83	Z55	H83
14	1,065	286H	0d 13h 489p	0d 9h 229p	0d 14h 149p	Z55	H54	B85	B53	H55	G84	B55	Z83	H54	B55	Z83	H55	G54	Z85	Z55	H54	B83	Z55	H83
3	539	39H	0d 14h 314p	0d 14h 154p	0d 16h 684p	Z55	H54	B85	B53	H55	G84	B55	Z83	H54	B55	Z85	Z53	G54	Z85	Z55	H54	B83	Z55	H83
41	295	2,908H	0d 17h 519p	0d 16h 689p	0d 17h 1,079p	Z55	H54	B85	B53	H55	G84	B55	Z83	H54	B55	Z85	Z53	G54	Z85	Z55	H54	B83	Z55	H85
60	4	246,545H	0d 18h 4p	0d 18h 4p	0d 18h 19p	B53	H54	B85	B53	H55	G84	B55	Z83	H54	B55	Z85	Z53	G54	Z85	Z55	H54	B83	Z55	H85
33	535	2,167H	0d 19h 1,074p	0d 18h 24p	0d 20h 534p	B53	H54	B85	B55	Z53	G84	B55	Z83	H54	B55	Z85	Z53	G54	Z85	Z55	H54	B83	Z55	H85
46	5	9,634H	0d 20h 549p	0d 20h 539p	0d 20h 559p	B53	H54	B85	B55	Z53	G84	B55	Z83	H55	G54	Z85	Z53	G54	Z85	Z55	H54	B83	Z55	H85
22	833	932H	1d 0h 199p	0d 20h 564p	1d 0h 404p	B53	H54	B85	B55	Z53	G84	B55	Z83	H55	G54	Z85	Z55	H54	B83	Z55	H54	B83	Z55	H85
11	1,065	191H	1d 2h 754p	1d 0h 409p	1d 5h 329p	B53	H55	G84	B55	Z53	G84	B55	Z83	H55	G54	Z85	Z55	H54	B83	Z55	H54	B83	Z55	H85
37	540	2,566H	1d 7h 609p	1d 5h 334p	1d 7h 869p	B53	H55	G84	B55	Z53	G84	B55	Z85	Z53	G54	Z85	Z55	H54	B83	Z55	H54	B83	Z55	H85
34	298	2,319H	1d 8h 434p	1d 7h 874p	1d 9h 199p	B53	H55	G84	B55	Z53	G84	B55	Z85	Z53	G54	Z85	Z55	H54	B83	Z55	H54	B85	B53	H85
53	5	82,081H	1d 9h 204p	1d 9h 204p	1d 9h 224p	B55	Z53	G84	B55	Z53	G84	B55	Z85	Z53	G54	Z85	Z55	H54	B83	Z55	H54	B85	B53	H85
28	535	1,578H	1d 10h 989p	1d 9h 229p	1d 11h 739p	B55	Z53	G84	B55	Z55	H83	G54	Z85	Z53	G54	Z85	Z55	H54	B83	Z55	H54	B85	B53	H85
6	2,438	96H	1d 15h 1,019p	1d 11h 744p	1d 22h 1,049p	B55	Z53	G84	B55	Z55	H83	G54	Z85	Z55	H54	B83	Z55	H54	B83	Z55	H54	B85	B53	H85
55	4	108,491H	1d 22h 1,054p	1d 22h 1,054p	1d 22h 1,069p	B55	Z53	G84	B55	Z55	H83	G54	Z85	Z55	H54	B83	Z55	H54	B85	B53	H54	B85	B53	H85
27	299	1,483H	2d 0h 174p	1d 22h 1,074p	2d 0h 404p	B55	Z53	G84	B55	Z55	H83	G54	Z85	Z55	H54	B83	Z55	H54	B85	B53	H54	B85	B55	Z83
19	535	742H	2d 2h 729p	2d 0h 409p	2d 2h 919p	B55	Z55	H83	G54	Z55	H83	G54	Z85	Z55	H54	B83	Z55	H54	B85	B53	H54	B85	B55	Z83
1	539	1H	2d 5h 204p	2d 2h 924p	2d 5h 374p	B55	Z55	H83	G54	Z55	H85	H54	B83	Z55	H54	B83	Z55	H54	B85	B53	H54	B85	B55	Z83
25	1,899	1,388H	2d 13h 439p	2d 5h 379p	2d 14h 149p	B55	Z55	H83	G54	Z55	H85	H54	B83	Z55	H54	B83	Z55	H54	B85	B53	H55	G84	B55	Z83
57	5	161,159H	2d 14h 154p	2d 14h 154p	2d 14h 174p	B55	Z55	H83	G54	Z55	H85	H54	B83	Z55	H54	B85	B53	H54	B85	B53	H55	G84	B55	Z83
21	298	894H	2d 15h 89p	2d 14h 179p	2d 15h 584p	B55	Z55	H83	G54	Z55	H85	H54	B83	Z55	H54	B85	B53	H54	B85	B55	Z53	G84	B55	Z83
9	535	153H	2d 17h 644p	2d 15h 589p	2d 18h 19p	G54	Z55	H83	G54	Z55	H85	H54	B83	Z55	H54	B85	B53	H54	B85	B55	Z53	G84	B55	Z83
45	540	3,269H	2d 19h 1,024p	2d 18h 24p	2d 20h 559p	G54	Z55	H85	H54	B53	H85	H54	B83	Z55	H54	B85	B53	H54	B85	B55	Z53	G84	B55	Z83
31	1,065	1,787H	3d 0h 1,054p	2d 20h 564p	3d 1h 484p	G54	Z55	H85	H54	B53	H85	H54	B83	Z55	H54	B85	B53	H55	G84	B55	Z53	G84	B55	Z83
17	833	552H	3d 5h 179p	3d 1h 489p	3d 5h 329p	G54	Z55	H85	H54	B53	H85	H54	B83	Z55	H54	B85	B53	H55	G84	B55	Z53	G84	B55	Z85
59	5	213,827H	3d 5h 334p	3d 5h 334p	3d 5h 354p	G54	Z55	H85	H54	B53	H85	H54	B85	B53	H54	B85	B53	H55	G84	B55	Z53	G84	B55	Z85
56	4	114,780H	3d 5h 359p	3d 5h 359p	3d 5h 374p	G54	Z55	H85	H54	B53	H85	H54	B85	B53	H54	B85	B55	Z53	G84	B55	Z53	G84	B55	Z85
4	829	58H	3d 6h 909p	3d 5h 379p	3d 9h 199p	G54	Z55	H85	H54	B53	H85	H54	B85	B53	H54	B85	B55	Z53	G84	B55	Z55	H83	G54	Z85
44	5	3,174H	3d 9h 209p	3d 9h 204p	3d 9h 224p	H54	B53	H85	H54	B53	H85	H54	B85	B53	H54	B85	B55	Z53	G84	B55	Z55	H83	G54	Z85
39	535	2,680H	3d 10h 939p	3d 9h 229p	3d 11h 739p	H54	B53	H85	H54	B55	Z83	H54	B85	B53	H54	B85	B55	Z53	G84	B55	Z55	H83	G54	Z85
12	1,903	210H	3d 19h 269p	3d 11h 744p	3d 20h 534p	H54	B53	H85	H54	B55	Z83	H54	B85	B53	H55	G84	B55	Z53	G84	B55	Z55	H83	G54	Z85
58	5	167,448H	3d 20h 539p	3d 20h 539p	3d 20h 559p	H54	B53	H85	H54	B55	Z83	H54	B85	B55	Z53	G84	B55	Z53	G84	B55	Z55	H83	G54	Z85
43	534	3,079H	3d 22h 474p	3d 20h 564p	3d 22h 1,069p	H54	B53	H85	H54	B55	Z83	H54	B85	B55	Z53	G84	B55	Z55	H83	G54	Z55	H83	G54	Z85
38	299	2,585H	4d 0h 124p	3d 22h 1,074p	4d 0h 404p	H54	B53	H85	H54	B55	Z83	H54	B85	B55	Z53	G84	B55	Z55	H83	G54	Z55	H85	H54	B83
32	535	1,844H	4d 2h 679p	4d 0h 409p	4d 2h 919p	H54	B55	Z83	H54	B55	Z83	H54	B85	B55	Z53	G84	B55	Z55	H83	G54	Z55	H85	H54	B83
7	1,903	115H	4d 8h 534p	4d 2h 924p	4d 11h 714p	H54	B55	Z83	H54	B55	Z83	H55	G84	B55	Z53	G84	B55	Z55	H83	G54	Z55	H85	H54	B83
42	5	2,984H	4d 11h 739p	4d 11h 719p	4d 11h 739p	H54	B55	Z83	H54	B55	Z85	Z53	G84	B55	Z53	G84	B55	Z55	H83	G54	Z55	H85	H54	B83
36	535	2,490H	4d 13h 389p	4d 11h 744p	4d 14h 174p	H54	B55	Z83	H54	B55	Z85	Z53	G84	B55	Z55	H83	G54	Z55	H83	G54	Z55	H85	H54	B83
24	833	1,255H	4d 17h 594p	4d 14h 179p	4d 18h 19p	H54	B55	Z83	H54	B55	Z85	Z53	G84	B55	Z55	H83	G54	Z55	H85	H54	B53	H85	H54	B83
2	1,605	20H	4d 21h 799p	4d 18h 24p	5d 1h 484p	H54	B55	Z83	H55	G54	Z85	Z53	G84	B55	Z55	H83	G54	Z55	H85	H54	B53	H85	H54	B83
35	298	2,395H	5d 2h 654p	5d 1h 489p	5d 2h 894p	H54	B55	Z83	H55	G54	Z85	Z53	G84	B55	Z55	H83	G54	Z55	H85	H54	B53	H85	H54	B85
50	5	55,652H	5d 2h 919p	5d 2h 899p	5d 2h 919p	H54	B55	Z85	Z53	G54	Z85	Z53	G84	B55	Z55	H83	G54	Z55	H85	H54	B53	H85	H54	B85
29	535	1,654H	5d 5h 129p	5d 2h 924p	5d 5h 354p	H54	B55	Z85	Z53	G54	Z85	Z55	H83	G54	Z55	H83	G54	Z55	H85	H54	B53	H85	H54	B85
48	4	35,873H	5d 5h 364p	5d 5h 359p	5d 5h 374p	H54	B55	Z85	Z53	G54	Z85	Z55	H83	G54	Z55	H85	H54	B53	H85	H54	B53	H85	H54	B85
18	829	666H	5d 8h 509p	5d 5h 379p	5d 9h 199p	H54	B55	Z85	Z53	G54	Z85	Z55	H83	G54	Z55	H85	H54	B53	H85	H54	B55	Z83	H54	B85
49	5	42,352H	5d 9h 219p	5d 9h 204p	5d 9h 224p	H55	G54	Z85	Z53	G54	Z85	Z55	H83	G54	Z55	H85	H54	B53	H85	H54	B55	Z83	H54	B85
10	1,899	172H	5d 10h 159p	5d 9h 229p	5d 17h 1,079p	H55	G54	Z85	Z55	H54	B83	Z55	H83	G54	Z55	H85	H54	B53	H85	H54	B55	Z83	H54	B85
23	539	1,065H	5d 20h 44p	5d 18h 4p	5d 20h 534p	Z53	G54	Z85	Z55	H54	B83	Z55	H83	G54	Z55	H85	H54	B53	H85	H54	B55	Z83	H54	B85
54	5	88,541H	5d 20h 544p	5d 20h 539p	5d 20h 559p	Z53	G54	Z85	Z55	H54	B83	Z55	H85	H54	B53	H85	H54	B53	H85	H54	B55	Z83	H54	B85
15	534	324H	5d 22h 599p	5d 20h 564p	5d 22h 1,069p	Z53	G54	Z85	Z55	H54	B83	Z55	H85	H54	B53	H85	H54	B55	Z83	H54	B55	Z83	H54	B85
5	299	77H	5d 23h 424p	5d 22h 1,074p	6d 0h 404p	Z53	G54	Z85	Z55	H54	B83	Z55	H85	H54	B53	H85	H54	B55	Z83	H54	B55	Z83	H55	G84
26	1,605	1,464H	6d 7h 659p	6d 0h 409p	6d 7h 869p	Z55	H54	B83	Z55	H54	B83	Z55	H85	H54	B53	H85	H54	B55	Z83	H54	B55	Z83	H55	G84
16	833	476H	6d 10h 1,039p	6d 7h 874p	6d 11h 714p	Z55	H54	B83	Z55	H54	B83	Z55	H85	H54	B53	H85	H54	B55	Z83	H54	B55	Z85	Z53	G84
47	5	23,124H	6d 11h 719p	6d 11h 719p	6d 11h 739p	Z55	H54	B83	Z55	H54	B85	B53	H85	H54	B53	H85	H54	B55	Z83	H54	B55	Z85	Z53	G84
13	535	229H	6d 11h 864p	6d 11h 744p	6d 14h 174p	Z55	H54	B83	Z55	H54	B85	B53	H85	H54	B55	Z83	H54	B55	Z83	H54	B55	Z85	Z53	G84
20	1,903	875H	6d 22h 574p	6d 14h 179p	6d 22h 1,049p	Z55	H54	B83	Z55	H54	B85	B53	H85	H54	B55	Z83	H54	B55	Z83	H55	G54	Z85	Z53	G84
61	4	305,483H	6d 22h 1,054p	6d 22h 1,054p	6d 22h 1,069p	Z55	H54	B83	Z55	H54	B85	B53	H85	H54	B55	Z83	H54	B55	Z85	Z53	G54	Z85	Z53	G84

The Qeviyot In Each Signature

The most significant finding of this analysis is that the Mahzor Qatan of type 1 = HebrewYear MOD 19 can have no fewer than 9 and no more than 13 different qeviyot.

More generally, 19 year periods measured from first years corresponding to Hebrew Year MOD 19 = either 12, 13, or 14 will contain all of the 14 existing qeviyot.

The Mahzor Qatan Type 1 Signatures
The Qeviyot in Each of the Signatures
Statistics			The Qeviyot
Signature	Frequency	First Time	1	2	3	4	5	6	7	8	9	10	11	12	13	14
26	1,605	1,464H	Z55	B53	B55	H54	H55	Z83	B83	G84	H85
40	535	2,756H	Z53	Z55	B53	B55	G54	H54	Z83	Z85	B85	H83
56	4	114,780H	Z53	Z55	B53	B55	G54	H54	Z85	B85	G84	H85
48	4	35,873H	Z53	Z55	B53	B55	G54	H54	Z85	B85	H83	H85
29	535	1,654H	Z53	Z55	B53	B55	G54	H54	Z85	B85	H83	H85
16	833	476H	Z53	Z55	B53	B55	H54	Z83	Z85	B83	G84	H85
19	535	742H	Z55	B53	B55	G54	H54	Z83	Z85	B83	B85	H83
1	539	1H	Z55	B53	B55	G54	H54	Z83	B83	B85	H83	H85
51	4	75,051H	Z53	Z55	B53	B55	G54	H54	H55	Z83	Z85	B85	H83
37	540	2,566H	Z53	Z55	B53	B55	G54	H54	H55	Z85	B83	G84	H85
59	5	213,827H	Z53	Z55	B53	B55	G54	H54	H55	Z85	B85	G84	H85
15	534	324H	Z53	Z55	B53	B55	G54	H54	Z83	Z85	B83	B85	H85
54	5	88,541H	Z53	Z55	B53	B55	G54	H54	Z83	Z85	B83	B85	H85
52	5	75,792H	Z53	Z55	B53	B55	G54	H54	Z83	Z85	B85	H83	H85
18	829	666H	Z53	Z55	B53	B55	G54	H54	Z83	Z85	B85	H83	H85
45	540	3,269H	Z53	Z55	B53	B55	G54	H54	Z83	B83	B85	G84	H85
53	5	82,081H	Z53	Z55	B53	B55	G54	H54	Z85	B83	B85	G84	H85
4	829	58H	Z53	Z55	B53	B55	G54	H54	Z85	B85	G84	H83	H85
44	5	3,174H	Z53	Z55	B53	B55	G54	H54	Z85	B85	G84	H83	H85
50	5	55,652H	Z53	Z55	B53	B55	G54	H54	Z85	B85	G84	H83	H85
13	535	229H	Z53	Z55	B53	B55	H54	Z83	Z85	B83	B85	G84	H85
47	5	23,124H	Z53	Z55	B53	B55	H54	Z83	Z85	B83	B85	G84	H85
7	1,903	115H	Z53	Z55	B55	G54	H54	H55	Z83	B83	G84	H83	H85
42	5	2,984H	Z53	Z55	B55	G54	H54	Z83	Z85	B83	G84	H83	H85
36	535	2,490H	Z53	Z55	B55	G54	H54	Z83	Z85	B83	G84	H83	H85
32	535	1,844H	Z53	Z55	B55	G54	H54	Z83	B83	B85	G84	H83	H85
30	834	1,768H	Z55	B53	B55	G54	H54	H55	Z83	Z85	B83	B85	H83
5	299	77H	Z53	Z55	B53	B55	G54	H54	H55	Z83	Z85	B83	G84	H85
11	1,065	191H	Z53	Z55	B53	B55	G54	H54	H55	Z83	Z85	B83	G84	H85
49	5	42,352H	Z53	Z55	B53	B55	G54	H54	H55	Z83	Z85	B85	H83	H85
31	1,065	1,787H	Z53	Z55	B53	B55	G54	H54	H55	Z83	B83	B85	G84	H85
17	833	552H	Z53	Z55	B53	B55	G54	H54	H55	Z85	B83	B85	G84	H85
34	298	2,319H	Z53	Z55	B53	B55	G54	H54	H55	Z85	B83	B85	G84	H85
27	299	1,483H	Z53	Z55	B53	B55	G54	H54	Z83	Z85	B83	B85	G84	H83
33	535	2,167H	Z53	Z55	B53	B55	G54	H54	Z83	Z85	B83	B85	G84	H85
61	4	305,483H	Z53	Z55	B53	B55	G54	H54	Z83	Z85	B83	B85	G84	H85
23	539	1,065H	Z53	Z55	B53	B55	G54	H54	Z83	Z85	B83	B85	H83	H85
8	829	134H	Z53	Z55	B53	B55	G54	H54	Z83	Z85	B83	B85	H83	H85
24	833	1,255H	Z53	Z55	B53	B55	G54	H54	Z83	Z85	B83	G84	H83	H85
58	5	167,448H	Z53	Z55	B53	B55	G54	H54	Z83	Z85	B85	G84	H83	H85
43	534	3,079H	Z53	Z55	B53	B55	G54	H54	Z83	Z85	B85	G84	H83	H85
39	535	2,680H	Z53	Z55	B53	B55	G54	H54	Z83	Z85	B85	G84	H83	H85
9	535	153H	Z53	Z55	B53	B55	G54	H54	Z83	B83	B85	G84	H83	H85
21	298	894H	Z53	Z55	B53	B55	G54	H54	Z83	B83	B85	G84	H83	H85
38	299	2,585H	Z53	Z55	B53	B55	G54	H54	Z83	B83	B85	G84	H83	H85
6	2,438	96H	Z53	Z55	B53	B55	G54	H54	Z85	B83	B85	G84	H83	H85
55	4	108,491H	Z53	Z55	B53	B55	G54	H54	Z85	B83	B85	G84	H83	H85
28	535	1,578H	Z53	Z55	B53	B55	G54	H54	Z85	B83	B85	G84	H83	H85
14	1,065	286H	Z55	B53	B55	G54	H54	H55	Z83	Z85	B83	B85	G84	H83
10	1,899	172H	Z55	B53	B55	G54	H54	H55	Z83	Z85	B83	B85	H83	H85
57	5	161,159H	Z55	B53	B55	G54	H54	H55	Z83	B83	B85	G84	H83	H85
25	1,899	1,388H	Z55	B53	B55	G54	H54	H55	Z83	B83	B85	G84	H83	H85
3	539	39H	Z53	Z55	B53	B55	G54	H54	H55	Z83	Z85	B83	B85	G84	H83
22	833	932H	Z53	Z55	B53	B55	G54	H54	H55	Z83	Z85	B83	B85	G84	H85
46	5	9,634H	Z53	Z55	B53	B55	G54	H54	H55	Z83	Z85	B83	B85	G84	H85
20	1,903	875H	Z53	Z55	B53	B55	G54	H54	H55	Z83	Z85	B83	B85	G84	H85
60	4	246,545H	Z53	Z55	B53	B55	G54	H54	H55	Z83	Z85	B83	B85	G84	H85
41	295	2,908H	Z53	Z55	B53	B55	G54	H54	H55	Z83	Z85	B83	B85	G84	H85
2	1,605	20H	Z53	Z55	B53	B55	G54	H54	H55	Z83	Z85	B83	G84	H83	H85
12	1,903	210H	Z53	Z55	B53	B55	G54	H54	H55	Z83	Z85	B85	G84	H83	H85
35	298	2,395H	Z53	Z55	B53	B55	G54	H54	H55	Z83	Z85	B85	G84	H83	H85

The Qeviyot Missing From Each Signature

Since a type 1 Mahzor Qatan can have missing between 1 to 5 qeviyot it is interesting to note that the qeviyot Z55, B55, and H54 are always present in all the type 1 Mahzorim Qatanim.

The Mahzor Qatan Type 1 Signatures
The Qeviyot Missing in Each of the Signatures
Statistics			The MissingQeviyot
Signature	Frequency	First Time	1	2	3	4	5
26	1,605	1,464H	Z53	G54	Z85	B85	H83
40	535	2,756H	H55	B83	G84	H85
56	4	114,780H	H55	Z83	B83	H83
48	4	35,873H	H55	Z83	B83	G84
29	535	1,654H	H55	Z83	B83	G84
16	833	476H	G54	H55	B85	H83
19	535	742H	Z53	H55	G84	H85
1	539	1H	Z53	H55	Z85	G84
51	4	75,051H	B83	G84	H85
37	540	2,566H	Z83	B85	H83
59	5	213,827H	Z83	B83	H83
15	534	324H	H55	G84	H83
54	5	88,541H	H55	G84	H83
52	5	75,792H	H55	B83	G84
18	829	666H	H55	B83	G84
45	540	3,269H	H55	Z85	H83
53	5	82,081H	H55	Z83	H83
4	829	58H	H55	Z83	B83
44	5	3,174H	H55	Z83	B83
50	5	55,652H	H55	Z83	B83
13	535	229H	G54	H55	H83
47	5	23,124H	G54	H55	H83
7	1,903	115H	B53	Z85	B85
42	5	2,984H	B53	H55	B85
36	535	2,490H	B53	H55	B85
32	535	1,844H	B53	H55	Z85
30	834	1,768H	Z53	G84	H85
5	299	77H	B85	H83
11	1,065	191H	B85	H83
49	5	42,352H	B83	G84
31	1,065	1,787H	Z85	H83
17	833	552H	Z83	H83
34	298	2,319H	Z83	H83
27	299	1,483H	H55	H85
33	535	2,167H	H55	H83
61	4	305,483H	H55	H83
23	539	1,065H	H55	G84
8	829	134H	H55	G84
24	833	1,255H	H55	B85
58	5	167,448H	H55	B83
43	534	3,079H	H55	B83
39	535	2,680H	H55	B83
9	535	153H	H55	Z85
21	298	894H	H55	Z85
38	299	2,585H	H55	Z85
6	2,438	96H	H55	Z83
55	4	108,491H	H55	Z83
28	535	1,578H	H55	Z83
14	1,065	286H	Z53	H85
10	1,899	172H	Z53	G84
57	5	161,159H	Z53	Z85
25	1,899	1,388H	Z53	Z85
3	539	39H	H85
22	833	932H	H83
46	5	9,634H	H83
20	1,903	875H	H83
60	4	246,545H	H83
41	295	2,908H	H83
2	1,605	20H	B85
12	1,903	210H	B83
35	298	2,395H	B83

The Surviving Qeviyot

The above tables demonstrate that 19 year cycles contain neither the same number nor the same combinations of qeviyot. They also demonstrate that even though there are 14 qeviyot possible the type 1 Mahzor Qatan only can have from 9 to 13 different qeviyot.

An analysis over all of the 19 different types of Mahzorim Qatanim reveals the following statistics.

Number of Qeviyot By Mahzor Qatan Type
Mahzor Qatan Types	Minimum Number	Maximum Number
7, 8, 18, 19	9	12
1, 2, 3, 4, 5, 11, 15, 16, 17	9	13
12, 13, 14	9	14
6, 9, 10	10	13

Mahzor Qatan types 12, 13, and 14 are the only kinds of 19 year cycles that can possibly contain all of the 14 qeviyot within their 19 year spans. None of the type 1 cycles have all of the 14 qeviyot. This is the cycle on which we base the Hebrew year count and which leads to the leap year distribution known as GUChADZT.

Looking at the qeviyot occurring in all of the 19 year spans in the full Hebrew calendar cycle, it is possible to notice that between 1 and 3 will always appear within the signatures for any Mahzor Qatan type. These qeviyot may be described as the Surviving Qeviyot. They are Z55, B55, and H54. In particular, the qeviah H54 is found in any and all periods of 19 Hebrew years.

The Surviving Qeviyot By Mahzor Qatan Type
Mahzor Qatan Types	Surviving Qeviyot
3, 4, 11, 12, 14, 15			H54
13	Z55		H54
1, 2, 5, 6, 7, 8, 9, 10, 16, 17, 18, 19	Z55	B55	H54

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Remy Landau

First  Paged 19 Oct 1997
Next Revised 19 Feb 2008