singsurf.org - Geometry and the imagination

# Variation in number of days between full moons

So how long is it between one full moon and the next?

The typical answer is 29 and a half days. However it can range between 29.8 days and 29.3 days.

More intrestingly the variation between the max and min number of days varies from year to year. In some years the variation can be more than half a day, in other years the diferance might be only a quater of a day.

For the real maths heads amongst you a spectral analysis gives two dominant frequencies of 1/413 days and 1/362 days. I.E. with dominant frequency of once every 413 days and beat frequency once every 7.92 years.

abs of Fourier coeff Frequency, cycles per 5787.87 days Wave Length (years:days)
17.2752 14 1 y 48 days
8.3210 16 361 days
2.9044 15
1.8641 13
1.1522 28

The above graph has been based on data from U.S. Naval Observatory Astronomical Applications Department

```NEW MOON	    FIRST QUARTER	FULL MOON   	LAST QUARTER	Days between full moons
04/01/90 10:40	11/01/90 04:57	18/01/90 21:17
26/01/90 19:20	02/02/90 18:32	09/02/90 19:16	17/02/90 18:48	29.60
25/02/90 08:54	04/03/90 02:05	11/03/90 10:58	19/03/90 14:30	29.65
26/03/90 19:48	02/04/90 10:24	10/04/90 03:18	18/04/90 07:02	29.68
25/04/90 04:27	01/05/90 20:18	09/05/90 19:31	17/05/90 19:45	29.68
24/05/90 11:47	31/05/90 08:11	08/06/90 11:01	16/06/90 04:48	29.65
22/06/90 18:55	29/06/90 22:07	08/07/90 01:23	15/07/90 11:04	29.60
22/07/90 02:54	29/07/90 14:01	06/08/90 14:19	13/08/90 15:54	29.54
20/08/90 12:39	28/08/90 07:34	05/09/90 01:46	11/09/90 20:53	29.48
19/09/90 00:46	27/09/90 02:06	04/10/90 12:02	11/10/90 03:31	29.43
18/10/90 15:37	26/10/90 20:26	02/11/90 21:48	09/11/90 13:02	29.41
17/11/90 09:05	25/11/90 13:11	02/12/90 07:50	09/12/90 02:04	29.42
17/12/90 04:22	25/12/90 03:16	31/12/90 18:35	07/01/91 18:35	29.45
15/01/91 23:50	23/01/91 14:21	30/01/91 06:10	06/02/91 13:52	29.48
14/02/91 17:32	21/02/91 22:58	28/02/91 18:25	08/03/91 10:32	29.51
16/03/91 08:10	23/03/91 06:03	30/03/91 07:17	07/04/91 06:45	29.54
14/04/91 19:38	21/04/91 12:39	28/04/91 20:58	07/05/91 00:46	29.57
14/05/91 04:36	20/05/91 19:46	28/05/91 11:37	05/06/03 15:30	29.61
12/06/91 12:06	19/06/91 04:19	27/06/91 02:58	05/07/91 02:50	29.64
11/07/91 19:06	18/07/91 15:11	26/07/91 18:24	03/08/91 11:25	29.64
10/08/91 02:28	17/08/91 05:01	25/08/91 09:07	01/09/91 18:16	29.61
08/09/91 11:01	15/09/91 22:01	23/09/91 22:40	01/10/91 00:30	29.56
07/10/91 21:39	15/10/91 17:33	23/10/91 11:08	30/10/91 07:10	29.52
06/11/91 11:11	14/11/91 14:02	21/11/91 22:56	28/11/91 15:21	29.49
06/12/91 03:56	14/12/91 09:32	21/12/91 10:23	28/12/91 01:55	29.48
04/01/92 23:10	13/01/92 02:32	19/01/92 21:28	26/01/92 15:27	29.46
03/02/92 19:00	11/02/92 16:15	18/02/92 08:04	25/02/92 07:56	29.44
04/03/92 13:22	12/03/92 02:36	18/03/92 18:18	26/03/92 02:30	29.43
03/04/92 05:01	10/04/92 10:06	17/04/92 04:42	24/04/92 21:40	29.43
02/05/92 17:44	09/05/92 15:43	16/05/92 16:03	24/05/92 15:53	29.47
01/06/92 03:57	07/06/92 20:47	15/06/92 04:50	23/06/92 08:11	29.53
30/06/92 12:18	07/07/92 02:43	14/07/92 19:06	22/07/92 22:12	29.59
29/07/92 19:35	05/08/92 10:58	13/08/92 10:27	21/08/92 10:01	29.64
28/08/92 02:42	03/09/92 22:39	12/09/92 02:17	19/09/92 19:53	29.66
26/09/92 10:40	03/10/92 14:12	11/10/92 18:03	19/10/92 04:12	29.66
25/10/92 20:34	02/11/92 09:11	10/11/92 09:20	17/11/92 11:39	29.64
24/11/92 09:11	02/12/92 06:17	09/12/92 23:41	16/12/92 19:13	29.60
24/12/92 00:43	01/01/93 03:38	08/01/93 12:37	15/01/93 04:01	29.54
22/01/93 18:27	30/01/93 23:20	06/02/93 23:55	13/02/93 14:57	29.47
21/02/93 13:05	01/03/93 15:46	08/03/93 09:46	15/03/93 04:16	29.41
23/03/93 07:14	31/03/93 04:10	06/04/93 18:43	13/04/93 19:39	29.37
21/04/93 23:49	29/04/93 12:40	06/05/93 03:34	13/05/93 12:20	29.37
21/05/93 14:06	28/05/93 18:21	04/06/93 13:02	12/06/93 05:36	29.39
20/06/93 01:52	26/06/93 22:43	03/07/93 23:45	11/07/93 22:49	29.45
19/07/93 11:24	26/07/93 03:25	02/08/93 12:10	10/08/93 15:19	29.52
17/08/93 19:28	24/08/93 09:57	01/09/93 02:33	09/09/93 06:26	29.60
16/09/93 03:10	22/09/93 19:32	30/09/93 18:54	08/10/93 19:35	29.68
15/10/93 11:36	22/10/93 08:52	30/10/93 12:38	07/11/93 06:36	29.74
13/11/93 21:34	21/11/93 02:03	29/11/93 06:31	06/12/93 15:49	29.75
13/12/93 09:27	20/12/93 22:26	28/12/93 23:05	05/01/94 00:00	29.69
11/01/94 23:10	19/01/94 20:27	27/01/94 13:23	03/02/94 08:06	29.60
10/02/94 14:30	18/02/94 17:47	26/02/94 01:15	04/03/94 16:53	29.49
12/03/94 07:05	20/03/94 12:14	27/03/94 11:09	03/04/94 02:55	29.41
11/04/94 00:17	19/04/94 02:34	25/04/94 19:45	02/05/94 14:32	29.36
10/05/94 17:07	18/05/94 12:50	25/05/94 03:39	01/06/94 04:02	29.33
09/06/94 08:26	16/06/94 19:56	23/06/94 11:33	30/06/94 19:31	29.33
08/07/94 21:37	16/07/94 01:12	22/07/94 20:16	30/07/94 12:40	29.36
07/08/94 08:45	14/08/94 05:57	21/08/94 06:47	29/08/94 06:41	29.44
05/09/94 18:33	12/09/94 11:34	19/09/94 20:00	28/09/94 00:23	29.55
05/10/94 03:55	11/10/94 19:17	19/10/94 12:18	27/10/94 16:44	29.68
03/11/94 13:35	10/11/94 06:14	18/11/94 06:57	26/11/94 07:04	29.78
02/12/94 23:54	09/12/94 21:06	18/12/94 02:17	25/12/94 19:06	29.81
01/01/95 01:56	08/01/95 15:46	16/01/95 20:26	24/01/95 04:58	29.76
30/01/95 22:48	07/02/95 12:54	15/02/95 12:15	22/02/95 13:04	29.66
01/03/95 11:48	09/03/95 10:14	17/03/95 01:26	23/03/95 20:10	29.55
31/03/95 02:09	08/04/95 05:35	15/04/95 12:08	22/04/95 03:18	29.45
29/04/95 17:36	07/05/95 21:44	14/05/95 20:48	21/05/95 11:36	29.36
29/05/95 09:27	06/06/95 10:26	13/06/95 04:03	19/06/95 22:01	29.30
28/06/95 00:50	05/07/95 20:02	12/07/95 10:49	19/07/95 11:10	29.28
27/07/95 15:13	04/08/95 03:16	10/08/95 18:15	18/08/95 03:04	29.31
26/08/95 04:31	02/09/95 09:03	09/09/95 03:37	16/09/95 21:09	29.39
24/09/95 16:55	01/10/95 14:36	08/10/95 15:52	16/10/95 16:26	29.51
24/10/95 04:36	30/10/95 21:17	07/11/95 07:20	15/11/95 11:40	29.64
22/11/95 15:43	29/11/95 06:28	07/12/95 01:27	15/12/95 05:31	29.75
22/12/95 02:22	28/12/95 19:06	05/01/96 20:51	13/01/96 20:45	29.81
20/01/96 12:50	27/01/96 11:14	04/02/96 15:58	12/02/96 08:37	29.80
18/02/96 23:30	26/02/96 05:52	05/03/96 09:23	12/03/96 17:15	29.73
19/03/96 10:45	27/03/96 01:31	04/04/96 00:07	10/04/96 23:36	29.61
17/04/96 22:49	25/04/96 20:40	03/05/96 11:48	10/05/96 05:04	29.49
17/05/96 11:46	25/05/96 14:13	01/06/96 20:47	08/06/96 11:05	29.37
16/06/96 01:36	24/06/96 05:23	01/07/96 03:58	07/07/96 18:55	29.30
15/07/96 16:15	23/07/96 17:49	30/07/96 10:35	06/08/96 05:25	29.28
14/08/96 07:34	22/08/96 03:36	28/08/96 17:52	04/09/96 19:06	29.30
12/09/96 23:07	20/09/96 11:23	27/09/96 02:51	04/10/96 12:04	29.37
12/10/96 14:14	19/10/96 18:09	26/10/96 14:11	03/11/96 07:50	29.47
11/11/96 04:16	18/11/96 01:09	25/11/96 04:10	03/12/96 05:06	29.58
10/12/96 16:56	17/12/96 09:31	24/12/96 20:41	02/01/97 01:45	29.69
09/01/97 04:26	15/01/97 20:02	23/01/97 15:11	31/01/97 19:40	29.77
07/02/97 15:06	14/02/97 08:57	22/02/97 10:27	02/03/97 09:37	29.80
09/03/97 01:15	16/03/97 00:06	24/03/97 04:45	31/03/97 19:38	29.76
07/04/97 11:02	14/04/97 17:00	22/04/97 20:33	30/04/97 02:37	29.66
06/05/97 20:46	14/05/97 10:55	22/05/97 09:13	29/05/97 07:51	29.53
05/06/97 07:03	13/06/97 04:51	20/06/97 19:09	27/06/97 12:42	29.41
04/07/97 18:40	12/07/97 21:44	20/07/97 03:20	26/07/97 18:28	29.34
03/08/97 08:14	11/08/97 12:42	18/08/97 10:55	25/08/97 02:23	29.32
01/09/97 23:52	10/09/97 01:31	16/09/97 18:50	23/09/97 13:35	29.33
01/10/97 16:51	09/10/97 12:22	16/10/97 03:46	23/10/97 04:48	29.37
31/10/97 10:01	07/11/97 21:43	14/11/97 14:12	21/11/97 23:58	29.43
30/11/97 02:14	07/12/97 06:09	14/12/97 02:37	21/12/97 21:43	29.52
29/12/97 16:56	05/01/98 14:18	12/01/98 17:24	20/01/98 19:40	29.62
28/01/98 06:01	03/02/98 22:53	11/02/98 10:23	19/02/98 15:27	29.71
26/02/98 17:26	05/03/98 08:41	13/03/98 04:34	21/03/98 07:38	29.76
28/03/98 03:14	03/04/98 20:18	11/04/98 22:23	19/04/98 19:53	29.74
26/04/98 11:41	03/05/98 10:04	11/05/98 14:29	19/05/98 04:35	29.67
25/05/98 19:32	02/06/98 01:45	10/06/98 04:18	17/06/98 10:38	29.58
24/06/98 03:50	01/07/98 18:43	09/07/98 16:01	16/07/98 15:13	29.49
23/07/98 13:44	31/07/98 12:05	08/08/98 02:10	14/08/98 19:48	29.42
22/08/98 02:03	30/08/98 05:06	06/09/98 11:21	13/09/98 01:58	29.38
20/09/98 17:01	28/09/98 21:11	05/10/98 20:12	12/10/98 11:11	29.37
20/10/98 10:09	28/10/98 11:46	04/11/98 05:18	11/11/98 00:28	29.38
19/11/98 04:27	27/11/98 00:23	03/12/98 15:19	10/12/98 17:53	29.42
18/12/98 22:42	26/12/98 10:46	02/01/99 02:49	09/01/99 14:22	29.48
17/01/99 15:46	24/01/99 19:15	31/01/99 16:06	08/02/99 11:58	29.55
16/02/99 06:39	23/02/99 02:43	02/03/99 06:58	10/03/99 08:40	29.62
17/03/99 18:48	24/03/99 10:18	31/03/99 22:49	09/04/99 02:51	29.66
16/04/99 04:22	22/04/99 19:01	30/04/99 14:55	08/05/99 17:28	29.67
15/05/99 12:05	22/05/99 05:34	30/05/99 06:40	07/06/99 04:20	29.66
13/06/99 19:03	20/06/99 18:13	28/06/99 21:37	06/07/99 11:57	29.62
13/07/99 02:24	20/07/99 09:00	28/07/99 11:25	04/08/99 17:27	29.58
11/08/99 11:08	19/08/99 01:47	26/08/99 23:48	02/09/99 22:17	29.52
09/09/99 22:02	17/09/99 20:06	25/09/99 10:51	02/10/99 04:02	29.46
09/10/99 11:34	17/10/99 15:00	24/10/99 21:02	31/10/99 12:04	29.42
08/11/99 03:53	16/11/99 09:03	23/11/99 07:04	29/11/99 23:18	29.42
07/12/99 22:32	16/12/99 00:50	22/12/99 17:31	29/12/99 14:04	29.44
06/01/00 01:14	14/01/00 13:34	21/01/00 04:40	28/01/00 07:57	29.46
05/02/00 13:03	12/02/00 23:21	19/02/00 16:27	27/02/00 03:53	29.49
06/03/00 05:17	13/03/00 06:59	20/03/00 04:44	28/03/00 00:21	29.51
04/04/00 18:12	11/04/00 13:30	18/04/00 17:41	26/04/00 19:30	29.54
04/05/00 04:12	10/05/00 20:00	18/05/00 07:34	26/05/00 11:55	29.58
02/06/00 12:14	09/06/00 03:29	16/06/00 22:27	25/06/00 01:00	29.62
01/07/00 19:20	08/07/00 12:53	16/07/00 13:55	24/07/00 11:02	29.64
31/07/00 02:25	07/08/00 01:02	15/08/00 05:13	22/08/00 18:51	29.64
29/08/00 10:19	05/09/00 16:27	13/09/00 19:37	21/09/00 01:28	29.60
27/09/00 19:53	05/10/00 10:59	13/10/00 08:53	20/10/00 07:59	29.55
27/10/00 07:58	04/11/00 07:27	11/11/00 21:15	18/11/00 15:24	29.52
25/11/00 23:11	04/12/00 03:55	11/12/00 09:03	18/12/00 00:41	29.49
25/12/00 17:22	02/01/01 22:31	09/01/01 20:24	16/01/01 12:35	29.47
24/01/01 13:07	01/02/01 14:02	08/02/01 07:12	15/02/01 03:23	29.45
23/02/01 08:21	03/03/01 02:03	09/03/01 17:23	16/03/01 20:45	29.42
25/03/01 01:21	01/04/01 10:49	08/04/01 03:22	15/04/01 15:31	29.42
23/04/01 15:26	30/04/01 17:08	07/05/01 13:52	15/05/01 10:11	29.44
23/05/01 02:46	29/05/01 22:09	06/06/01 01:39	14/06/01 03:28	29.49
21/06/01 11:58	28/06/01 03:19	05/07/01 15:04	13/07/01 18:45	29.56
20/07/01 19:44	27/07/01 10:08	04/08/01 05:56	12/08/01 07:53	29.62
19/08/01 02:55	25/08/01 19:55	02/09/01 21:43	10/09/01 18:59	29.66
17/09/01 10:27	24/09/01 09:31	02/10/01 13:49	10/10/01 04:20	29.67
16/10/01 19:23	24/10/01 02:58	01/11/01 05:41	08/11/01 12:21	29.66
15/11/01 06:40	22/11/01 23:21	30/11/01 20:49	07/12/01 19:52	29.63
14/12/01 20:47	22/12/01 20:56	30/12/01 10:40	06/01/02 03:55	29.58
13/01/02 13:29	21/01/02 17:46	28/01/02 22:50	04/02/02 13:33	29.51
12/02/02 07:41	20/02/02 12:02	27/02/02 09:17	06/03/02 01:24	29.44
14/03/02 02:02	22/03/02 02:28	28/03/02 18:25	04/04/02 15:29	29.38
12/04/02 19:21	20/04/02 12:48	27/04/02 03:00	04/05/02 07:16	29.36
12/05/02 10:45	19/05/02 19:42	26/05/02 11:51	03/06/02 00:05	29.37
10/06/02 23:46	18/06/02 00:29	24/06/02 21:42	02/07/02 17:19	29.41
10/07/02 10:26	17/07/02 04:47	24/07/02 09:07	01/08/02 10:22	29.48
08/08/02 19:15	15/08/02 10:12	22/08/02 22:29	31/08/02 02:31	29.56
07/09/02 03:10	13/09/02 18:08	21/09/02 13:59	29/09/02 17:03	29.65
06/10/02 11:18	13/10/02 05:33	21/10/02 07:20	29/10/02 05:28	29.72
04/11/02 20:34	11/11/02 20:52	20/11/02 01:34	27/11/02 15:46	29.76
04/12/02 07:34	11/12/02 15:49	19/12/02 19:10	27/12/02 00:31	29.73
02/01/03 20:23	10/01/03 13:15	18/01/03 10:48	25/01/03 08:33	29.65
01/02/03 10:48	09/02/03 11:11	16/02/03 23:51	23/02/03 16:46	29.54
03/03/03 02:35	11/03/03 07:15	18/03/03 10:34	25/03/03 01:51	29.45
01/04/03 19:19	09/04/03 23:40	16/04/03 19:36	23/04/03 12:18	29.38
01/05/03 12:15	09/05/03 11:53	16/05/03 03:36	23/05/03 00:31	29.33
31/05/03 04:20	07/06/03 20:28	14/06/03 11:16	21/06/03 14:45	29.32
29/06/03 18:39	07/07/03 02:32	13/07/03 19:21	21/07/03 07:01	29.34
29/07/03 06:53	05/08/03 07:28	12/08/03 04:48	20/08/03 00:48	29.39
27/08/03 17:26	03/09/03 12:34	10/09/03 16:36	18/09/03 19:03	29.49
26/09/03 03:09	02/10/03 19:09	10/10/03 07:27	18/10/03 12:31	29.62
25/10/03 12:50	01/11/03 04:25	09/11/03 01:13	17/11/03 04:15	29.74
23/11/03 22:59	30/11/03 17:16	08/12/03 20:37	16/12/03 17:42	29.81
23/12/03 09:43	30/12/03 10:03	07/01/04 15:40	15/01/04 04:46	29.79
21/01/04 21:05	29/01/04 06:03	06/02/04 08:47	13/02/04 13:40	29.71
20/02/04 09:18	28/02/04 03:24	06/03/04 23:14	13/03/04 21:01	29.60
20/03/04 22:41	28/03/04 23:48	05/04/04 11:03	12/04/04 03:46	29.49
19/04/04 13:21	27/04/04 17:32	04/05/04 20:33	11/05/04 11:04	29.40
19/05/04 04:52	27/05/04 07:57	03/06/04 04:20	09/06/04 20:02	29.32
17/06/04 20:27	25/06/04 19:08	02/07/04 11:09	09/07/04 07:34	29.28
17/07/04 11:24	25/07/04 03:37	31/07/04 18:05	07/08/04 22:01	29.29
16/08/04 01:24	23/08/04 10:12	30/08/04 02:22	06/09/04 15:11	29.35
14/09/04 14:29	21/09/04 15:54	28/09/04 13:09	06/10/04 10:12	29.45
14/10/04 02:48	20/10/04 21:59	28/10/04 03:07	05/11/04 05:53	29.58
12/11/04 14:27	19/11/04 05:50	26/11/04 20:07	05/12/04 00:53	29.71
12/12/04 01:29	18/12/04 16:40	26/12/04 15:06	03/01/05 17:46	29.79
10/01/05 12:03	17/01/05 06:57	25/01/05 10:32	02/02/05 07:27	29.81
08/02/05 22:28	16/02/05 00:16	24/02/05 04:54	03/03/05 17:36	29.77
10/03/05 09:10	17/03/05 19:19	25/03/05 20:58	02/04/05 00:50	29.67
08/04/05 20:32	16/04/05 14:37	24/04/05 10:06	01/05/05 06:24	29.55
08/05/05 08:45	16/05/05 08:56	23/05/05 20:18	30/05/05 11:47	29.43
06/06/05 21:55	15/06/05 01:22	22/06/05 04:14	28/06/05 18:23	29.33
06/07/05 12:02	14/07/05 15:20	21/07/05 11:00	28/07/05 03:19	29.28
05/08/05 03:05	13/08/05 02:38	19/08/05 17:53	26/08/05 15:18	29.29
03/09/05 18:45	11/09/05 11:37	18/09/05 02:01	25/09/05 06:41	29.34
03/10/05 10:28	10/10/05 19:01	17/10/05 12:14	25/10/05 01:17	29.43
02/11/05 01:24	09/11/05 01:57	16/11/05 00:57	23/11/05 22:11	29.53
01/12/05 15:01	08/12/05 09:36	15/12/05 16:15	23/12/05 19:36	29.64
31/12/05 03:12
```

### judyfogarty1@comcast.net

judy fogarty Sun Oct 22 2017

I'm really confused, and need to get this right. I'm writing a novel called MOON, which begins on a full moon and ends on one. A full moon is "Day 1" in the novel and the next full moon is "Day 31." Is that because the 29 days are literally between the full moons, with the actual full moon days added to equal 31?

Subject: