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Tony Deff
Joined: May 25, 2008 Posts: 51 Location: Suffolk, UK
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Posted: Mon Oct 29, 2012 8:46 am Post subject:
Tone-Differential Chorus Subject description: Equal-Temperament's latent built-in chorus |
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The Pythagorean or Just (meaning true) major tone is the frequency ratio of 9:8, which is 204 cents.
This is easily calculated by subtracting the Harmonic Logarithm of 8 from that of 9 (see page 4 of PDF, centre table).
If we take the outputs of two tone-generators, nominally a whole-tone (200 cents) apart, divide the higher by 9 and the lower by 8, then the result will be two voices separated by a nominal 4 cents. We will have extracted the difference between the Just and the Equal-Temperament whole-tone.
The beauty of this is that digital instruments are already awash with real or implied divide-by-8s; we don't need to add any more. We just need to add the modulo-9 divider.
(Don't fret, that's just a fanciful name for divide-by-9, and is dead easy to implement using a single CD4017 or HC163 )
Another plus is that the output from a modulo-9 divider is not naturally a square-wave and will therefore contain even harmonics.
The harmonic structure does not conform to that of the boring old staircase/ramp and so, even though it has joined the chorus, it will stand out from the crowd.
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Fig.1: Simple implementation with duty-cycle of 55.5% |
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Last edited by Tony Deff on Fri Feb 08, 2013 9:39 am; edited 1 time in total |
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Tony Deff
Joined: May 25, 2008 Posts: 51 Location: Suffolk, UK
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Posted: Thu Feb 07, 2013 4:13 pm Post subject:
Waveform select Subject description: Choosing the tone colour |
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If the link from pin 11 (Y9) to pin 15 (reset) is made with a resistor, then grounding pin 15 with a switch will revert the 4017 to its native divide-by-10 mode (because the reset is active-high).
By cascading two such ICs and selecting one of the two reset pins by a two-way switch to ground [Fig. (a)],
then the final output will switch between 50% (divide-by-10 mode) and 55.5% (divide-by-9 mode)†.
This will allow a rapid audio comparison of the tonal difference, the constant divide-by-90 avoiding any confusion caused by a change of pitch.
Furthermore, if the clock input is taken from pin 6 of a 74HC4060 running at 5.0688MHz, you will have a handy A4 = 440Hz reference ...
5.0688 MHz. = 440.0 Hz.
9 × 10 × 128
For a 110Hz reference (guitar 5th string), use 'HC4060 output pin 13 instead, and generate a 33.3% duty-cycle.
You can also tune 220Hz and 440Hz to this because of the 2nd and 4th harmonics. The absence of 3rd, 6th and 9th harmonics reduces confusion (see tables below).
† Pin 12 ("Out") is active-high for the sum of time-slots Y0+Y1+Y2+Y3+Y4.
If the count is aborted at time-slot Y9 (via the reset link) then the active-high width of Out is unaffected, but the duty-cycle is changed.
In [Fig. (b)], the pulse width can be extended by adding one or two further time-slots to the 5 already summed by pin 12.
Q1 is a chopper/mixer for the analogue envelope, which will invert the pulse, so that the rectangular pulse width is
44.4% (S1 & S2 open)
33.3% (S1 closed)
22.2% (S1 & S2 closed)
There is nothing to stop you setting S1 and S2 in when pin 12 is putting-out a square-wave:
50.0% (S1 & S2 open)
40.0% (S1 closed)
30.0% (S1 & S2 closed)
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(a) Rapid comparison of 50% and 55% waveforms (b) Further modifying pulse width and output driver |
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Last edited by Tony Deff on Fri Feb 08, 2013 10:11 am; edited 4 times in total |
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Tony Deff
Joined: May 25, 2008 Posts: 51 Location: Suffolk, UK
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Tony Deff
Joined: May 25, 2008 Posts: 51 Location: Suffolk, UK
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Paradigm X
Joined: Feb 15, 2011 Posts: 363 Location: Null and void
Audio files: 2
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Posted: Fri Feb 08, 2013 2:03 pm Post subject:
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i wish i had the vaguest idea what was going in here. sounds great though |
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Tony Deff
Joined: May 25, 2008 Posts: 51 Location: Suffolk, UK
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Posted: Wed Feb 13, 2013 3:59 pm Post subject:
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Paradigm X wrote: | ... wish I had the vaguest idea what was going on here... |
It's best understood if you've wasted endless late nights of your life trying to understand implausible TV thrillers.
My presentation is based on the standard modus operandii of several episodes linked by flash-backs and confusing
sub-plots, based on an intial implausible premise of hot air cloaked by smoke and mirrors and further obfuscated
and lent undue gravitas by quasi-scientific mumbo-jumbo tech-speak (given mystic importance here by hyperlinks).
Having invested so much time trying to understand it, you are forced to view to the end in case you miss the vital bit
that makes sense of it all. I don't want to give the plot away so that you then stop viewing, but since you are the only
one to admit to giving-up in confusion, I will admit to being an ivory-tower-based virtual constructor, frustrated in the
real (surreal?) world by long-term illness. As with the TV programs on mind control, where the subject later carries-out
unconscious actions, I will be content if (even if many years from now) someone has an inventive stroke of genius kick-
started by something filtered subconsciously from the sticky goo of data posted here.
If you understood that, then either the smoke canister's empty or my mirror's broke. |
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