Triangle Numbers Table

Using Triangle Numbers to create accelerating weeks, months, etc.

Triangle numbers are used to create Accelerating Weeks, Months, etc. Using 7 for example:

1 + 2 + 3 + 4 + 5 + 6 + 7 = 28

No.	Total days
2	3			363	360
3	6				360
4	10				360	260
5	15				360
7	28		364
8	36				360
9	45				360
10	55			363
11	66			363
12	78		364			260
13	91		364			260
14	105	365				260
15	120				360

Table of pyramid numbers, the total number of days, and the calendars in which they figure.

the 363-day calendar follows multi-year patterns.

Calendar Glyph Table

comparing glyphs from 260-day calendars

	theAbysmal 260-day calendar	Maya tzolkin	Nahua tōnalpōhualli	New Age dreamspell
I	turtle	waterlily	caiman	dragon
II	wind	wind	wind	wind
III	night	night	house	night
IV	web	net	lizard	seed
V	serpent	serpent	serpent	serpent
VI	death	death	death	worldbridger
VII	deer	deer	deer	hand
VIII	rabbit	Venus	rabbit	star
IX	moon	water	water	moon
X	coyote	dog	dog	dog
XI	raccoon	monkey	monkey	monkey
XII	mushroom	rain	grass	human
XIII	tobacco	young maize	reed	skywalker
XIV	bear	jaguar	jaguar	wizard
XV	goshawk	eagle	eagle	eagle
XVI	fisher	wax	vulture	warrior
XVII	earthquake	earth	earthquake	earth
XVIII	mirror	flint	knife	mirror
XIX	storm	rainstorm	rain	storm
XX	sun	sun	flower	sun

comparison of meaning assigned to 20 glyphs in four different calendar systems: theAbysmal, tzolkin, tōnalpōhualli, and dreamspell.

Table of Calendar Epochs

Comparing the dates when Calendars began framing their respective histories.

source:
Reingold, Edward M and Nachum Dershowitz. Calendrical Calculations – the Ultimate Edition. Cambridge University Press. New York, 2018.

Calendar	Epoch RD	Equivalents
Julian Day Number	-1721424.5	Nov 24, -4713 (GC) Jan 1, 4713 BCE (JC)
Hebrew	-1373427	Sep 7, -3760 (GC) Oct 7, 3761 BCE (JC)
Mayan	-1137142	Aug 11, -3113 (GC) Sep 6, 3114 BCE (JC)
Hindu Kali Yuga	-1132959	Jan 23, -3101 (GC) Feb 18, 3102 BCE (JC)
Chinese	-963099	Feb 15, -2636 (GC) Mar 8, 2637 BCE (JC)
Samaritan	-598573	Mar 3, -1638 (GC) Mar 15, 1639 BCE (JC)
Egyptian	-272787	Feb 18, -746 (GC) Feb 26, 747 BCE (JC)
Babylonian	-113502	Mar 29, -310 (GC) Apr 3, 311 BCE (JC)
Tibetan	-46410	Dec 7, -127 (GC) Dec 10, 128 BCE (JC)
Julian	-1	Dec 30, 0 (GC) Jan 1, 1 CE (JC)
Gregorian	1	Jan 1, 1 (GC) Jan 3, 1 CE (JC)
ISO	1	Jan 1, 1 (GC) Jan 3, 1 CE (JC)
Akan	37	Feb 6, 1 (GC) Feb 8, 1 CE (JC)
Ethiopic	2796	Aug 27, 8 (GC) Aug 29, 8 CE (JC)
Coptic	103605	Aug 29, 284 (GC) Aug 29, 284 CE (JC)
Armenian	201443	Jul 13, 552 (GC) Jul 11, 552 CE (JC)
Persian	226896	Mar 22, 622 (GC) Mar 19, 622 (JC)
Islamic	227015	Jul 19, 622 (GC) Jul 16, 622 CE (JC)
Zoroastrian	230638	Jun 19, 632 (GC) Jun 16, 632 CE (JC)
French Revolutionary	654415	Sep 22, 1792 (GC) Sep 11, 1792 CE (JC)
Bahá’í	673222	Mar 21, 1844 (GC) Mar9, 1844 CE (JC)
Modified Julian Day	678576	Nov 17, 1858 (GC) Nov 5, 1858 CE (JC)
Unix	719163	Jan 1, 1970 (GC) Dec 19, 1969 CE (JC)

GC = Gregorian Calendar
JC = Julian Calendar

Table of Mean Calendar Years

Comparing how Calendars approximate the Tropical Year and Lunar Month

source:
Reingold, Edward M and Nachum Dershowitz. Calendrical Calculations – the Ultimate Edition. Cambridge University Press. New York, 2018.

Calendar Year	Mean Year	Mean Month
Egyptian	365
Mayan Haab	365
Mayan (implicit)	365.24204	29.530864
Julian/Coptic/Ethiopic	365.25
Hebrew	365.24382	29.530594
Easter (Orthodox)	365.25	29.530851
Islamic (Arithmetic)		29.530556
Hindu Arya	365.25868	29.530582
Hindu Sũrya	365.25876	29.530588
Tibetan Phugpa	365.27065	29.530587
Gregorian	365.2425
Easter (Gregorian)	365.2425	29.53587
French (Arithmetic)	365.24225
Persian (Arithmetic)	365.24220
Astronomical Year
Year -1000	365.24257	29.530598
Year 0	365.24244	29.530595
Year 1000	365.24231	29.530591
Year 2000	365.24218	29.530588
Year 3000	365.24204	29.530584

Table – Divisions of theAbysmal Year

Of all the ways to reinvent the wheel…

No. of Days	Name	Measures per Year	Calendar
2	–	182	364
2	–	181	362
2	–	180	360
3	week	121	363
3	week	120	360
4	week	91	364
4	week	90	360
5	week	73	365
5	week	72	360
6	week	60	360
7	Week	52	364
8	week	45	360
9	week	40	360
10	week	36	360
11	Elevensie	33	363
12	week	30	360
13	week	28	364
14	Fortnight	26	364
15	Hōra	24	360
18	month	20	360
19	month	19	361
20	month	18	360
24	month	15	360
26	month	14	360
28	Month	13	364
30	month	12	360
33	Elevonth	11	363
36	month	10	360
40	month	9	360
45	eighth	8	360
52	House	7	364
60	sixth	6	360
72	fifth	5	360
73	fifth	5	365
90	quarter	4	360
91	quarter	4	364
120	Term	3	360
121	Term	3	363
180	Semester	2	360
181	Semester	2	362
182	Semester	2	364

Table of Weekdays and theAbysmal Year

theAbysmal Year, first and middle Weekdays, Number and Glyph of the Year

theAbysmal Year covers Dec 21 to Dec 20. The weekday that begins theAbysmal Year (Dec 22) changes by increments of 1 in a normal year and by 2 in a leap year. The Leap Day falls on Jun 21. In a Leap Year, the first Weekday falls on Dec 22, and then skips ahead by 1 on Jun 22. The cycle of weekdays repeats every 28 years.

The Year glyph repeats every 52 years in what is called a calendar round. This is created in how the 260-day calendar synchronizes with the 365-day year. Five calendar rounds make a Historical Era of 260 years. The current Era began 2012.

The glyphs are: XIII Tobacco, XVIII Mirror, III Night, VIII Rabbit.

Gregorian Year	theAbysmal Year	First Weekday (Dec 22)	Leap Year Weekday (Jun 22)	Year Glyph (Dec 21)
2012-13	0	Sat		1~XIII
2013-14	1	Sun		2~XVIII
2014-15	2	Mon		3~III
2015-16	3	Tue	Wed	4~VIII
2016-17	4	Thu		5~XIII
2017-18	5	Fri		6~XVIII
2018-19	6	Sat		7~III
2019-20	7	Sun	Mon	8~VIII
2020-21	8	Tue		9~XIII
2021-22	9	Wed		10~XVIII
2022-23	10	Thu		11~III
2023-24	11	Fri	Sat	12~VIII
2024-25	12	Sun		13~XIII
2025-26	13	Mon		1~XVIII
2026-27	14	Tue		2~III
2027-28	15	Wed	Thu	3~VIII
2028-29	16	Fri		4~XIII
2029-30	17	Sat		5~XVIII
2030-31	18	Sun		6~III
2031-32	19	Mon	Tue	7~VIII
2032-33	20	Wed		8~XIII
2033-34	21	Thu		9~XVIII
2034-35	22	Fri		10~III
2035-36	23	Sat	Sun	11~VIII
2036-37	24	Mon		12~XIII
2037-38	25	Tue		13~XVIII
2038-39	26	Wed		1~III
2039-40	27	Thu	Fri	2~VIII
2040-41	28			3~XIII
2041-42	29			4~XVIII
2042-43	30			5~III
2043-44	31			6~VIII
2044-45	32			7~XIII
2045-46	33			8~XVIII
2046-47	34			9~III
2047-48	35			10~VIII
2048-49	36			11~XIII
2049-50	37			12~XVIII
2050-51	38			13~III
2051-52	39			1~VIII
2052-53	40			2~XIII
2053-54	41			3~XVIII
2054-55	42			4~III
2055-56	43			5~VIII
2056-57	44			6~XIII
2057-58	45			7~XVIII
2058-59	46			8~III
2060-61	47			9~VIII
2061-62	48			10~XIII
2062-63	49			11~XVIII
2063-64	50			12~III
2064-65	51			13~VIII

Table of theAbysmal Weeks & Months

the weeks and months and other things of theAbysmal Annual Calendar

A reference for the even measures within theAbysmal Calendar Year

days per year	market week	weeks per year	weeks per month	days per month	months per year
365	5-day	73	–	–	–
364	4-day	91	7	28	13
364	4-day	91	13	52	7
364	7-day	52	4	28	13
364	13-day	28	4	52	7
363	3-day	121	11	33	11
363	11-day	11	3	33	11
361	19-day	19	–	19	19
360	5-day	72	3	15	24
360	5-day	72	4	20	18
360	6-day	60	3	18	20
360	6-day	60	4	24	15
360	6-day	60	5	30	12
360	8-day	45	3	24	15
360	8-day	45	5	40	9
360	9-day	40	4	36	10
360	9-day	40	5	45	8
360	10-day	36	3	30	12
360	10-day	36	4	40	9
360	12-day	30	3	36	10
360	12-day	30	5	60	6

Table of the days, weeks, and months of
theAbysmal Calendar Year

Equalnights Table

The word Equinox means “equal night”, however, the date when day and night are equal varies depending on where you live relative to the Equator. For Cornwall, the Equinox falls on Sep 22, 2020, whereas the equalnight falls on Sep 25.

Source: Freeman, Gordon R. Canada’s Stonehenge: Astounding Archaeological Discoveries in Canada, England, and Wales. Calgary: Kingsley Pub., 2009.

When Day = Night
Date	Latitude
from Equator to N Pole
Feb 3 – 9	3° N
Feb 25 – 26	5° N
Mar 7-8	10° N
Mar 13-14	20° N
Mar 15-16	30°N
Mar 16-17	40° N
Mar 17-18	50-80° N
Mar 18 the Sun rises	90° N
from S Pole to Equator
Mar 22 the Sun sets	90° S
Mar 22-23	50-80° S
Mar 23-24	30-40° S
Mar 26-27	20° S
Mar 31-Apr 1	10° S
Apr 14-15	5° S
Apr 3-May 6	3° S
from Equator to S Pole
Aug 9-12	3° S
Aug 28-29	5° S
Sep 10-11	10° S
Sep 16-17	20° S
Sep 18-19	30° S
Sep 19-20	40-60° S
Sep 20-21	80° S
Sep 20 the Sun rises	90° S
from N Pole to Equator
Sep 24	90° N
Sep 24-25	60-80° N
Sep 25-26	40-50° N
Sep 26-27	30° N
Sep 29-30	20° N
Oct 5-6	10° N
Oct 17-18	5° N
Nov 4-10	3°N

Musical Day Table 432 Hz

Musical Scales from Pitch to Beat to Day

seconds/day – the number of Modified Seconds that fit into a full day of 86400 SI seconds

new:SI second – how long each Modified Second is in terms of SI seconds.
NB: A4 is the note where the Modified and SI seconds (at 432 Hz) are the same.

Note	Frequency (Hz)	Wavelength (cm)	seconds/day	Modified:SI second
C0	16.05	2,148.96	3,210	26.92
C#0/Db0	17.01	2,028.35	3,402	25.40
D0	18.02	1,914.50	3,604	23.97
D#0/Eb0	19.09	1,807.05	3,818	22.63
E0	20.23	1,705.63	4,046	21.35
F0	21.43	1,609.90	4,286	20.16
F#0/Gb0	22.70	1,519.54	4,540	19.03
G0	24.05	1,434.26	4,810	17.96
G#0/Ab0	25.48	1,353.76	5,096	16.95
A0	27.00	1,277.78	5,400	16.00
A#0/Bb0	28.61	1,206.06	5,722	15.10
B0	30.31	1,138.37	6,062	14.25
C1	32.11	1,074.48	6,422	13.45
C#1/Db1	34.02	1,014.17	6,804	12.70
D1	36.04	957.25	7,208	11.99
D#1/Eb1	38.18	903.53	7,636	11.31
E1	40.45	852.81	8,090	10.68
F1	42.86	804.95	8,572	10.08
F#1/Gb1	45.41	759.77	9,082	9.51
G1	48.11	717.13	9,622	8.98
G#1/Ab1	50.97	676.88	10,194	8.48
A1	54.00	638.89	10,800	8.00
A#1/Bb1	57.21	603.03	11,442	7.55
B1	60.61	569.19	12,122	7.13
C2	64.22	537.24	12,844	6.73
C#2/Db2	68.04	507.09	13,608	6.35
D2	72.08	478.63	14,416	5.99
D#2/Eb2	76.37	451.76	15,274	5.66
E2	80.91	426.41	16,182	5.34
F2	85.72	402.47	17,144	5.04
F#2/Gb2	90.82	379.89	18,164	4.76
G2	96.22	358.56	19,244	4.49
G#2/Ab2	101.94	338.44	20,388	4.24
A2	108.00	319.44	21,600	4.00
A#2/Bb2	114.42	301.52	22,884	3.78
B2	121.23	284.59	24,246	3.56
C3	128.43	268.62	25,686	3.36
C#3/Db3	136.07	253.54	27,214	3.17
D3	144.16	239.31	28,832	3.00
D#3/Eb3	152.74	225.88	30,548	2.83
E3	161.82	213.20	32,364	2.67
F3	171.44	201.24	34,288	2.52
F#3/Gb3	181.63	189.94	36,326	2.38
G3	192.43	179.28	38,486	2.24
G#3/Ab3	203.88	169.22	40,776	2.12
A3	216.00	159.72	43,200	2.00
A#3/Bb3	228.84	150.76	45,768	1.89
B3	242.45	142.30	48,490	1.78
C4	256.87	134.31	51,374	1.68
C#4/Db4	272.14	126.77	54,428	1.59
D4	288.33	119.66	57,666	1.50
D#4/Eb4	305.47	112.94	61,094	1.41
E4	323.63	106.60	64,726	1.33
F4	342.88	100.62	68,576	1.26
F#4/Gb4	363.27	94.97	72,654	1.19
G4	384.87	89.64	76,974	1.12
G#4/Ab4	407.75	84.61	81,550	1.06
A4	432.00	79.86	86,400	1.00
A#4/Bb4	457.69	75.38	91,538	0.94
B4	484.90	71.15	96,980	0.89
C5	513.74	67.15	102,748	0.84
C#5/Db5	544.29	63.39	108,858	0.79
D5	576.65	59.83	115,330	0.75
D#5/Eb5	610.94	56.47	122,188	0.71
E5	647.27	53.30	129,454	0.67
F5	685.76	50.31	137,152	0.63
F#5/Gb5	726.53	47.49	145,306	0.59
G5	769.74	44.82	153,948	0.56
G#5/Ab5	815.51	42.30	163,102	0.53
A5	864.00	39.93	172,800	0.50
A#5/Bb5	915.38	37.69	183,076	0.47
B5	969.81	35.57	193,962	0.45
C6	1,027.47	33.58	205,494	0.42
C#6/Db6	1,088.57	31.69	217,714	0.40
D6	1,153.30	29.91	230,660	0.37
D#6/Eb6	1,221.88	28.24	244,376	0.35
E6	1,294.54	26.65	258,908	0.33
F6	1,371.51	25.15	274,302	0.31
F#6/Gb6	1,453.07	23.74	290,614	0.30
G6	1,539.47	22.41	307,894	0.28
G#6/Ab6	1,631.01	21.15	326,202	0.26
A6	1,728.00	19.97	345,600	0.25
A#6/Bb6	1,830.75	18.84	366,150	0.24
B6	1,939.61	17.79	387,922	0.22
C7	2,054.95	16.79	410,990	0.21
C#7/Db7	2,177.14	15.85	435,428	0.20
D7	2,306.60	14.96	461,320	0.19
D#7/Eb7	2,443.76	14.12	488,752	0.18
E7	2,589.07	13.33	517,814	0.17
F7	2,743.03	12.58	548,606	0.16
F#7/Gb7	2,906.14	11.87	581,228	0.15
G7	3,078.95	11.21	615,790	0.14
G#7/Ab7	3,262.03	10.58	652,406	0.13
A7	3,456.00	9.98	691,200	0.13
A#7/Bb7	3,661.50	9.42	732,300	0.12
B7	3,879.23	8.89	775,846	0.11
C8	4,109.90	8.39	821,980	0.11
C#8/Db8	4,354.29	7.92	870,858	0.10
D8	4,613.21	7.48	922,642	0.09
D#8/Eb8	4,887.52	7.06	977,504	0.09
E8	5,178.15	6.66	1,035,630	0.08
F8	5,486.06	6.29	1,097,212	0.08
F#8/Gb8	5,812.28	5.94	1,162,456	0.07
G8	6,157.89	5.60	1,231,578	0.07
G#8/Ab8	6,524.06	5.29	1,304,812	0.07
A8	6,912.00	4.99	1,382,400	0.06
A#8/Bb8	7,323.01	4.71	1,464,602	0.06
B8	7,758.46	4.45	1,551,692	0.06

the Ringing of the Atmosphere

Apparently, the atmosphere makes music.

Two articles for future reference:

An Array of Ringing Global Free Modes Discovered in Tropical Surface Pressure Data

“Abstract

“We used newly available ERA5 hourly global data to examine the variations of atmospheric circulation on global scales and high frequencies. The space–time spectrum of surface pressure displays a typical red background spectrum but also a striking number of isolated peaks. Some peaks represent astronomically forced tides, but we show that most peaks are manifestations of the ringing of randomly excited global-scale resonant modes, reminiscent of the tones in a spectrum of a vibrating musical instrument. A few such modes have been tentatively identified in earlier observational investigations, but we demonstrate the existence of a large array of normal mode oscillations with periods as short as 2 h. This is a powerful and uniquely detailed confirmation of the predictions of the theory of global oscillations that has its roots in the work of Laplace two centuries ago. The delineation of the properties of the modes provides valuable diagnostic information about the atmospheric circulation. Notably the amplitudes and widths of the normal mode spectral peaks contain information on the forcing mechanisms and energy dissipation for the modes, and the simulation of these properties for each of the many modes we have identified can serve as tests for global climate and weather prediction models.”

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