electro-music.com   Dedicated to experimental electro-acoustic
and electronic music
 
    Front Page  |  Articles  |  Radio
 |  Media  |  Forum  |  Wiki  |  Links  |  Store
Forum with support of Syndicator RSS
 FAQFAQ   CalendarCalendar   SearchSearch   MemberlistMemberlist   UsergroupsUsergroups   LinksLinks
 RegisterRegister   ProfileProfile   Log in to check your private messagesLog in to check your private messages   Log inLog in  Chat RoomChat Room 
 Forum index » DIY Hardware and Software » Developers' Corner
Tone-Differential Chorus
Post new topic   Reply to topic Moderators: DrJustice
Page 1 of 1 [6 Posts]
View unread posts
View new posts in the last week
Mark the topic unread :: View previous topic :: View next topic
Author Message
Tony Deff



Joined: May 25, 2008
Posts: 42
Location: Suffolk, UK

PostPosted: Mon Oct 29, 2012 8:46 am    Post subject:  Tone-Differential Chorus
Subject description: Equal-Temperament's latent built-in chorus
Reply with quote  Mark this post and the followings unread

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).

Idea 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. Razz

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. Laughing


Four cent singers.jpg
 Description:
Fig.1: Simple implementation with duty-cycle of 55.5%
 Filesize:  55.96 KB
 Viewed:  1587 Time(s)

Four cent singers.jpg



Last edited by Tony Deff on Fri Feb 08, 2013 9:39 am; edited 1 time in total
Back to top
View user's profile Send private message
Tony Deff



Joined: May 25, 2008
Posts: 42
Location: Suffolk, UK

PostPosted: Thu Feb 07, 2013 4:13 pm    Post subject:  Waveform select
Subject description: Choosing the tone colour
Reply with quote  Mark this post and the followings unread

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)


Chorus Pulse Width select.png
 Description:
(a) Rapid comparison of 50% and 55% waveforms
(b) Further modifying pulse width and output driver
 Filesize:  31.88 KB
 Viewed:  55 Time(s)
This image has been reduced to fit the page. Click on it to enlarge.

Chorus Pulse Width select.png



Last edited by Tony Deff on Fri Feb 08, 2013 10:11 am; edited 4 times in total
Back to top
View user's profile Send private message
Tony Deff



Joined: May 25, 2008
Posts: 42
Location: Suffolk, UK

PostPosted: Fri Feb 08, 2013 8:45 am    Post subject: Reply with quote  Mark this post and the followings unread

There are 4 theoretical tone-colours to choose from when using a divided-by-9 rectangular wave.
In practice, the 11% (1/9) ratio is too harsh to be of much conventional use (too many intense harmonics).

The first table calculates absolute voltage levels for a 1V amplitude pulse, disregarding that the more a pulse deviates from square, the weaker its fundamental — its power is taken by the up-coming new harmonics. Because of this, you are liable to whack-up the volume to compensate, which will also boost the harmonics. Consequently, the second table computes the harmonic levels as relative to the fundamental, which suddenly feel a lot more significant. This approach also throws-up the strange fact that the relative powers of the 8th and 10th harmonics are constant, regardless of duty-cycle.


Modulo-9 harmonics.png
 Description:
 Filesize:  11.38 KB
 Viewed:  1289 Time(s)

Modulo-9 harmonics.png


Back to top
View user's profile Send private message
Tony Deff



Joined: May 25, 2008
Posts: 42
Location: Suffolk, UK

PostPosted: Fri Feb 08, 2013 10:40 am    Post subject: Reply with quote  Mark this post and the followings unread

Of course, you could always build your own waveform, using 8 variable resistors (Fig C), summing from any 8 of outputs Y0 - Y8 . The unused output serves a a zero reference. The harmonic structure would be anybody's guess!

It would be wise to avoid deep chasms in the pyramids (Fig D), as the screeching high harmonics — produced when the workers fall in — produces much the same result as the 11% pulse.

In (a), 2/9 and 3/9 rectangular pulse waveforms produce different results when applied together.


9-slot Lego.gif
 Description:
 Filesize:  33.03 KB
 Viewed:  50 Time(s)
This image has been reduced to fit the page. Click on it to enlarge.

9-slot Lego.gif


Back to top
View user's profile Send private message
Paradigm X



Joined: Feb 15, 2011
Posts: 280
Location: Null and void

PostPosted: Fri Feb 08, 2013 2:03 pm    Post subject: Reply with quote  Mark this post and the followings unread

i wish i had the vaguest idea what was going in here. sounds great though Cool
Back to top
View user's profile Send private message
Tony Deff



Joined: May 25, 2008
Posts: 42
Location: Suffolk, UK

PostPosted: Wed Feb 13, 2013 3:59 pm    Post subject: Reply with quote  Mark this post and the followings unread

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.
Back to top
View user's profile Send private message
Display posts from previous:   
Post new topic   Reply to topic Moderators: DrJustice
Page 1 of 1 [6 Posts]
View unread posts
View new posts in the last week
Mark the topic unread :: View previous topic :: View next topic
 Forum index » DIY Hardware and Software » Developers' Corner
Jump to:  

You cannot post new topics in this forum
You cannot reply to topics in this forum
You cannot edit your posts in this forum
You cannot delete your posts in this forum
You cannot vote in polls in this forum
You cannot attach files in this forum
You can download files in this forum
e-m mkii

Please support our site. If you click through and buy from
our affiliate partners, we earn a small commission.


Forum with support of Syndicator RSS
Powered by phpBB © 2001, 2005 phpBB Group
Copyright © 2003 through 2009 by electro-music.com - Conditions Of Use