The other day I noticed that the E/A sound table for A440 implied a SLIGHTLY out of tune A110.
The "Textbook" values for the sound chip are 3F9 and 0FE producing 109.99 and 440.3968 Hz.
If tuning the low A to match, you choose 3F8 to produce 110.1 instead.
What's the difference?
Well, when two notes are played together, and one is out of tune, you hear a beat sensation.
The "beat" is the two frequencies interfering constructively and destructively.
Try this: (in TI BASIC for everyone following at home)
10 CALL SOUND(4000, 109.99, 0, 110.4, 0)
20 GOTO 10
30 CALL SOUND(4000, 440.3968, 0, 438.67, 0)
40 GOTO 30
It's actually a cool sound effect that you will recognize from Munch Man.
You can hear the beat take place at f1-f2, which is 0.4 Hz in the first example, more like 2 Hz in the second.
A square wave (the kind the 76489 sound chip can generate) is composed of a fundamental frequency plus the odd harmonics at 1/n.
That is, a square wave at 110 contains f=110 plus f=440 at 1/3 or -10dB. (EDIT: no it doesn't, it's at f=330. My article falls apart here.)
Given f=109.99, the third harmonic is at 439.96 (EDIT: no, it's 330), but when playing A440, the closest the sound chip can get is either 438.67 or 440.3968. The chord A110+A440.3968 should give us a chance to hear a beat at 0.4 Hz. It should go away when the low A is tuned to 110.1.
I wonder if you can hear this beat in the 3rd harmonic:
10 CALL SOUND(2000, 109.99, 0, 440.3867, 10)
20 PRINT "BEAT"
30 CALL SOUND(2000, 110.1, 0, 440.3867, 10)
40 PRINT "NO BEAT"
50 GOTO 10
I think I can hear one? I can tell that the low A is moving a tiny bit, but the beat should have a quality like the first example of a 0.4 Hz beat. I think that I hear a beat at about 3 Hz on both of them. Not sure what's up with that.
Caveat: I did these tests on Classic99. I got out a 4A console to test real hardware, but a 4116 memory chip failed spectacularly. I'll write elsewhere of the joy of TDX@R HNRTRTLDNTR and playing B@R W@RR and TH HNV@DDRR.
Edited by FarmerPotato, Wed Jun 13, 2018 2:23 AM.