Equal Loudness

Published: July 27, 2017, 12:26 am

Updated: July 27, 2017, 1:00 am

Been working on this one for a long while.

The following is the Equal Loudness Curves for a Base Line Frequency of 1000 Hz at a given dB.

The Equation is after the graph.

C_a0 = [

+584918276 / 6720025

-103831586233635427 / 2856403612062000

+794378430029096923 / 44344167963480000

-38790811232122019033 / 6917690202302880000

+37290541565009947 / 37059054655194000

-738665642886403 / 6829476135552000

+1647218534123999 / 232527401758080000

-17127252623983 / 62603531242560000

+870630168487 / 162769181230656000

-56221133 / 4340511499484160

-905135371 / 697582205274240000

+288653 / 18245186754795000

]

C_a1 = [

-3148422351 / 73920275

+350719588425816859 / 3618111241945200

-2749900318774382348879 / 32859028460938680000

+184187318986680779843 / 4868004216435360000

-304469880071493491323 / 29573125614844812000

+4039288331398095383 / 2226682399235374080

-2846249053261467499 / 13254061900210560000

+21072389935899833 / 1220768859229920000

-453528524769713 / 488307543691968000

+1247486431379 / 39064603495357440

-9246037442197 / 14649226310759040000

+1459285789 / 269467373609280000

]

C_a2 = [

+13775563019696468657 / 286514985900

-11370687841337045781409 / 447293972218500

+2623964381772455081232641 / 432355637643930000

-26195228365460186517092369 / 30331410887020320000

+19257428086889614312685471 / 236585004918758496000

-42429730168597174960451 / 7952437140126336000

+3289631551439307860611 / 13254061900210560000

-2858105252150952217 / 348791102637120000

+91886157892771247 / 488307543691968000

-186376057166539 / 65107672492262400

+380358058025653 / 14649226310759040000

-26618573567 / 250219704065760000

]

C_b0 = [

+2440054313 / 66528247500

+15281212647019205947 / 23779560070416150000

-27090847859486093 / 72300273853500000

+183705368522726020559 / 1556480295518148000000

-13411492411525987063 / 622592118207259200000

+53014340147053 / 21587424566400000

-583193465228323 / 3170828205792000000

+43588562278253 / 4695264843192000000

-699757893089 / 2219579744054400000

+20335583869 / 2929845262151808000

-65705659541 / 732461315537952000000

+7542863 / 14596149403836000000

]

C_b1 = [

-76491486421 / 133056495000

+30320926993346633617 / 19643984405995950000

-174734326454194660313 / 107149005850887000000

+1917876348523432946867 / 2112366115346058000000

-241931045702670842107 / 806539789495767600000

+1125460855949461513 / 17995816804165200000

-8442094840824031589 / 994054642515792000000

+555391994065074779 / 732461315537952000000

-1609256576101003 / 36623065776897600000

+14712087679 / 9301096070323200

-35046960646427 / 1098691973306928000000

+22035038441 / 80840212082784000000

]

C_b2 = [

+3203642632288579763 / 1868575995000

-28134398538370546066702831 / 34754741641377450000

+35462675141771432481607843 / 205368927880866750000

-24985925347641185318078257 / 1137427908263262000000

+10953119633866074692074357 / 5914625122968962400000

-59241454935478259413 / 545327781944400000

+1499446630060632052277 / 331351547505264000000

-10894249571301009259 / 81384590615328000000

+33642484958483449 / 12207688592299200000

-550915346016881 / 14649226310759040000

+112128401223491 / 366230657768976000000

-394653897679 / 350307585692064000000

]

C_c0 = [

+825637271 / 133056495000

-43616754460623251 / 5595190604803800000

+67105762471947743 / 13303250389044000000

-5242324777357478887 / 3112960591036296000000

+410491040596403969 / 1245184236414518400000

-50951052122581 / 1252070624851200000

+14407967694649 / 4359888782964000000

-6744609743791 / 37562118745536000000

+158004029551 / 24415377184598400000

-1087708261 / 7324613155379520000

+359545181 / 183115328884488000000

-71831 / 6311848390848000000

]

C_c1 = [

+41556109 / 133056495000

-1078949069560794073 / 903623282675813700000

+126983827110067897 / 88015254806085750000

-2901994967663087941 / 4224732230692116000000

+7024221150843994039 / 70975501475627548800000

+113120648593443731 / 4175029498566326400000

-53386943636210971 / 3976218570063168000000

+886614309148877 / 366230657768976000000

-4967137318061 / 20927466158227200000

+9301008757 / 697582205274240000

-1774350301453 / 4394767893227712000000

+5591609 / 1092435298416000000

]

C_c2 = [

-1579116737978502889 / 42977247885000

+113157235346395245101563 / 6319043934795900000

-1060494490076383381193 / 268543874313000000

+1183363080962496121637519 / 2274855816526524000000

-1076007134249986807202713 / 23658500491875849600000

+3856888720151962529819 / 1391676499522108800000

-8378559335141774357 / 69758220527424000000

+25109372899822447 / 6782049217944000000

-554936413978513 / 6975822052742400000

+302255378387 / 266349569286528000

-14170081917209 / 1464922631075904000000

+2007857 / 53794162422000000

]

x is the Linear Frequency with a nominal range of 1 to 31, however it can be extended.

f is the Frequency in Hz.

d is the Decibel level at 1000 Hz.

f₀(x) - f₅(x) are special Low and High pass filters and operate with the -2/π².

Some Values Table

·	Decibels
Linear - Frequency	0	10	20	30	40	50	60	70	80	90	100	110	120
-1.0 - 12.40	134.32	122.54	115.03	111.80	112.85	118.16	127.75	141.61	159.74	182.15	208.83	239.78	275.01
-0.5 - 13.92	102.66	98.48	96.65	97.17	100.04	105.27	112.85	122.78	135.07	149.71	166.70	186.04	207.74
0.0 - 15.63	82.88	83.15	84.69	87.49	91.56	96.88	103.47	111.32	120.43	130.81	142.45	155.35	169.51
0.5 - 17.54	70.75	73.51	76.96	81.10	85.93	91.45	97.66	104.57	112.16	120.45	129.42	139.09	149.44
1.0 - 19.69	63.82	67.92	72.43	77.38	82.75	88.55	94.77	101.42	108.50	116.01	123.94	132.30	141.08
1.5 - 22.10	59.65	64.35	69.39	74.76	80.47	86.52	92.90	99.62	106.68	114.07	121.80	129.86	138.26
2.0 - 24.80	54.92	59.80	65.01	70.53	76.38	82.54	89.03	95.83	102.96	110.41	118.17	126.26	134.67
2.5 - 27.84	50.54	55.55	60.89	66.55	72.54	78.85	85.49	92.45	99.73	107.34	115.28	123.54	132.13
3.0 - 31.25	46.87	52.05	57.55	63.38	69.55	76.05	82.87	90.03	97.52	105.35	113.50	121.98	130.80
3.5 - 35.08	43.73	49.08	54.76	60.78	67.14	73.82	80.85	88.21	95.90	103.93	112.29	120.99	130.02
4.0 - 39.37	40.81	46.33	52.19	58.38	64.91	71.78	78.98	86.52	94.40	102.61	111.16	120.05	129.28
4.5 - 44.19	37.90	43.58	49.60	55.96	62.65	69.68	77.05	84.76	92.81	101.19	109.92	118.98	128.38
5.0 - 49.61	34.93	40.77	46.94	53.46	60.32	67.51	75.05	82.92	91.13	99.69	108.58	117.80	127.37
5.5 - 55.68	31.90	37.91	44.27	50.96	57.99	65.35	73.06	81.09	89.47	98.18	107.23	116.62	126.34
6.0 - 62.50	28.90	35.11	41.66	48.54	55.75	63.29	71.16	79.37	87.90	96.77	105.97	115.50	125.37
6.5 - 70.15	26.04	32.45	39.19	46.26	53.65	61.36	69.40	77.77	86.46	95.48	104.82	114.49	124.48
7.0 - 78.75	23.39	29.99	36.90	44.14	51.70	59.58	67.77	76.29	85.13	94.28	103.76	113.55	123.67
7.5 - 88.39	21.00	27.73	34.79	42.17	49.87	57.88	66.22	74.88	83.86	93.15	102.77	112.71	122.96
8.0 - 99.21	18.88	25.69	32.83	40.30	48.11	56.24	64.70	73.50	82.62	92.07	101.86	111.97	122.42
8.5 - 111.36	17.02	23.83	31.00	38.52	46.40	54.62	63.20	72.14	81.42	91.07	101.06	111.41	122.11
9.0 - 125.00	15.37	22.13	29.28	36.82	44.74	53.05	61.75	70.83	80.30	90.17	100.41	111.05	122.07
9.5 - 140.31	13.90	20.57	27.68	35.21	43.17	51.56	60.38	69.63	79.30	89.41	99.94	110.90	122.29
10.0 - 157.49	12.54	19.14	26.21	33.74	41.75	50.22	59.16	68.57	78.45	88.79	99.61	110.89	122.64
10.5 - 176.78	11.25	17.82	24.88	32.44	40.50	49.06	58.12	67.67	77.73	88.28	99.33	110.88	122.93
11.0 - 198.43	9.99	16.59	23.70	31.32	39.45	48.10	57.25	66.92	77.09	87.78	98.98	110.70	122.92
11.5 - 222.72	8.74	15.44	22.64	30.35	38.57	47.29	56.52	66.25	76.49	87.23	98.47	110.23	122.48
12.0 - 250.00	7.46	14.32	21.66	29.49	37.80	46.60	55.87	65.63	75.87	86.59	97.80	109.49	121.66
12.5 - 280.62	6.16	13.21	20.72	28.68	37.09	45.95	55.27	65.04	75.27	85.95	97.08	108.66	120.70
13.0 - 314.98	4.90	12.12	19.78	27.87	36.39	45.34	54.72	64.53	74.77	85.45	96.55	108.08	120.05
13.5 - 353.55	3.73	11.10	18.89	27.11	35.74	44.80	54.29	64.19	74.52	85.27	96.45	108.05	120.07
14.0 - 396.85	2.77	10.25	18.15	26.48	35.25	44.44	54.06	64.10	74.58	85.49	96.82	108.59	120.78
14.5 - 445.45	2.12	9.70	17.71	26.15	35.02	44.33	54.07	64.24	74.84	85.88	97.34	109.24	121.58
15.0 - 500.00	1.75	9.47	17.60	26.13	35.06	44.39	54.13	64.27	74.81	85.75	97.10	108.84	120.99
15.5 - 561.23	1.15	9.11	17.40	26.05	35.03	44.35	54.02	64.03	74.39	85.08	96.12	107.50	119.23
16.0 - 629.96	1.01	9.22	17.74	26.56	35.68	45.10	54.83	64.85	75.18	85.80	96.73	107.96	119.49
16.5 - 707.11	1.16	9.80	18.69	27.83	37.23	46.89	56.80	66.97	77.40	88.08	99.01	110.21	121.65
17.0 - 793.70	0.54	9.58	18.82	28.27	37.94	47.81	57.89	68.19	78.69	89.41	100.33	111.47	122.81
17.5 - 890.90	0.09	9.82	19.60	29.44	39.34	49.30	59.32	69.40	79.54	89.74	99.99	110.31	120.69
18.0 - 1000.00	0.00	10.00	20.00	30.00	40.00	50.00	60.00	70.00	80.00	90.00	100.00	110.00	120.00
18.5 - 1122.46	0.08	10.00	19.94	29.89	39.86	49.84	59.84	69.85	79.87	89.91	99.97	110.03	120.12
19.0 - 1259.92	0.09	9.89	19.73	29.59	39.49	49.42	59.37	69.36	79.37	89.42	99.49	109.60	119.73
19.5 - 1414.21	-0.14	9.63	19.42	29.24	39.07	48.93	58.80	68.70	78.61	88.55	98.51	108.49	118.49
20.0 - 1587.40	-0.63	9.22	19.05	28.87	38.67	48.46	58.24	68.00	77.75	87.48	97.20	106.91	116.60
20.5 - 1781.80	-1.33	8.66	18.59	28.46	38.26	48.00	57.68	67.29	76.84	86.33	95.76	105.12	114.42
21.0 - 2000.00	-2.16	7.98	18.02	27.94	37.75	47.44	57.03	66.50	75.85	85.10	94.23	103.24	112.15
21.5 - 2244.92	-3.10	7.16	17.27	27.22	37.02	46.67	56.16	65.49	74.67	83.70	92.57	101.28	109.84
22.0 - 2519.84	-4.15	6.17	16.30	26.25	36.02	45.60	55.00	64.21	73.24	82.09	90.75	99.23	107.53
22.5 - 2828.43	-5.31	5.01	15.12	25.04	34.75	44.27	53.58	62.70	71.61	80.33	88.84	97.16	105.27
23.0 - 3174.80	-6.52	3.75	13.83	23.70	33.37	42.83	52.10	61.16	70.02	78.68	87.13	95.38	103.43
23.5 - 3563.59	-7.61	2.61	12.65	22.48	32.13	41.58	50.85	59.92	68.79	77.48	85.97	94.28	102.39
24.0 - 4000.00	-8.25	1.92	11.91	21.74	31.41	40.90	50.23	59.39	68.38	77.21	85.86	94.35	102.68
24.5 - 4489.85	-8.02	2.08	12.04	21.88	31.59	41.17	50.62	59.94	69.13	78.19	87.12	95.92	104.59
25.0 - 5039.68	-6.57	3.44	13.36	23.20	32.96	42.63	52.22	61.73	71.15	80.49	89.75	98.93	108.02
25.5 - 5656.85	-3.71	6.15	15.98	25.78	35.54	45.28	54.98	64.65	74.30	83.91	93.48	103.03	112.55
26.0 - 6349.60	0.32	9.96	19.62	29.31	39.02	48.75	58.50	68.28	78.08	87.90	97.74	107.61	117.50
26.5 - 7127.19	4.83	14.17	23.58	33.07	42.64	52.28	62.00	71.80	81.67	91.62	101.65	111.75	121.93
27.0 - 8000.00	8.73	17.68	26.77	36.00	45.36	54.87	64.51	74.29	84.21	94.26	104.46	114.79	125.26
27.5 - 8979.70	10.85	19.35	28.07	37.01	46.18	55.58	65.19	75.03	85.10	95.39	105.91	116.65	127.61
28.0 - 10079.37	10.50	18.47	26.80	35.47	44.51	53.90	63.64	73.74	84.19	94.99	106.15	117.67	129.54
28.5 - 11313.71	8.08	15.44	23.34	31.78	40.76	50.27	60.33	70.92	82.05	93.71	105.92	118.66	131.94
29.0 - 12699.21	5.66	12.30	19.71	27.88	36.81	46.50	56.95	68.16	80.13	92.87	106.36	120.62	135.63
29.5 - 14254.38	6.61	12.43	19.21	26.97	35.69	45.38	56.04	67.67	80.26	93.82	108.36	123.86	140.32
30.0 - 16000.00	12.76	17.74	23.82	30.98	39.23	48.58	59.01	70.53	83.15	96.85	111.64	127.52	144.49
30.5 - 17959.39	17.59	22.17	27.90	34.77	42.78	51.93	62.23	73.67	86.25	99.97	114.84	130.85	148.00
31.0 - 20158.74	25.47	30.40	36.40	43.47	51.61	60.81	71.09	82.43	94.84	108.32	122.87	138.48	155.17
31.5 - 22627.42	42.83	49.34	56.57	64.52	73.19	82.59	92.70	103.54	115.09	127.37	140.37	154.09	168.53
32.0 - 25398.42	74.83	84.93	94.98	104.97	114.91	124.79	134.61	144.38	154.09	163.74	173.34	182.88	192.36

Entry #4,194

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Equal Loudness

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