Working on music program - improving note frequencies

CALCULATED FREQUENCIES OF NOTES USING ORIGINAL PROGRAM VALUES

When I looked at the table of note values and fitted them to the desired note pitches, I saw that these were not ideal. The ratio of the counts for notes in the two octaves should be powers of two, but differed. For example, the bottom note which I believe is E, has a count of 213 but the middle E was 105 and the top E was 51 according to the program. 

RECALCULATED TO GET CLOSE TO CORRECT PITCHES

I put together a spreadsheet to calculate the frequency of the counter values in the program as the divider into the frequency of the inner loop at 17.5 KHz. I compared it to the correct pitch values for the notes and then calculated the closest integer to achieve the proper frequency. 

Pgm count	frequency	note	desired	new count	Integer	Ifreq	deviation
213	82.16	E	82.41	212.35	212	82.55	100.17%
201	87.06	F	87.31	200.44	200	87.50	100.22%
189	92.59	F#	92.5	189.19	189	92.59	100.10%
179	97.77	G	98	178.57	178	98.31	100.32%
169	103.55	Ab	103.83	168.54	168	104.17	100.32%
159	110.06	A	110	159.09	159	110.06	100.06%
150	116.67	Bb	116.54	150.16	150	116.67	100.11%
142	123.24	B	123.47	141.73	141	124.11	100.52%
134	130.60	C	130.81	133.78	133	131.58	100.59%
124	141.13	C#	138.59	126.27	126	138.89	100.22%
118	148.31	D	146.83	119.19	119	147.06	100.16%
111	157.66	Eb	155.56	112.50	112	156.25	100.44%
105	166.67	E	164.81	106.18	106	165.09	100.17%
99	176.77	F	174.61	100.22	100	175.00	100.22%
93	188.17	F#	185	94.59	94	186.17	100.63%
88	198.86	G	196	89.29	89	196.63	100.32%
83	210.84	Ab	207.65	84.28	84	208.33	100.33%
78	224.36	A	220	79.55	79	221.52	100.69%
74	236.49	Bb	233.08	75.08	75	233.33	100.11%
69	253.62	B	246.94	70.87	70	250.00	101.24%
65	269.23	C	261.63	66.89	66	265.15	101.35%
61	286.89	C#	277.18	63.14	63	277.78	100.22%
57	307.02	D	293.66	59.59	59	296.61	101.00%
54	324.07	Eb	311.13	56.25	56	312.50	100.44%
51	343.14	E	329.63	53.09	53	330.19	100.17%

As you can see, the worst note is only 1.35% off pitch while many are fractions of a percent. Since the speed of the IBM 1130 depends on the actual numerical value for operations like addition and subtraction, the time in the inner loop will be a bit fuzzy, drifting around the 17.5KHz rate. 

The new ratios are much closer to the powers of two they should be, with my three E notes at 53, 106 and 212. I coded using these new values as part of the port over to assembler and the demo monitor system.