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Gordon Charlton
Joined: Oct 07, 2006
Posts: 75
Location: UK
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 Posted: Mon Sep 03, 2007 5:05 am Post subject:
computing microtonal intervals with rational numbers
Subject description: an ANS Forth rational arithmetic word-set |
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I noticed there is at least one Forth programmer around here (Hi Blue Hell!) and I remembered a word-set I wrote ages ago when I was programming that might be useful if you want to do maths beyond */ with microtonal frequencies or generate rational approximations to equal temperament intervals.
It's a rational number word-set (i.e. two thirds is represented as 2 3 rather than a floating point approximation) with a full range of basic arithmetic functions. To avoid overflow it implements a mediant rounding scheme as described in The Art of Computer Programming by D E Knuth. (Volume 2, Seminumerical Algorithms 2nd Edition (1981, Addison Wesley), 4.5.3 Analysis of Euclids Algorithm, page 363, exercise 40) which has been shown to generate best possible approximations.
http://ftp.aarnet.edu.au/pub/forth/Scientific/vulgar.fth
It appears to work fine on gforth.
 WTF's Forth? - Here's a little intro to a weird language, showing how it corresponds directly to data flow diagrams like in Max/MSP.
http://www.forth.org/forth_intro/stackflo.htm
Last edited by Gordon Charlton on Mon Sep 03, 2007 5:29 am; edited 3 times in total |
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seraph
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Joined: Jun 21, 2003
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Location: Firenze, Italy
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| Posted: Mon Sep 03, 2007 5:11 am Post subject:
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| Gordon Charlton wrote: | | Gordon has been using Forth since 1985 when he bought a Jupiter Ace, which was styled after the Sinclair ZX80 but had Forth in ROM. These days he uses an Apple Macintosh with 4Meg of RAM, or 4096 times as much as the Jupiter Ace. Both machines are similar, however, in that the operating system uses roughly half the available RAM! |
 http://www.forth.org/forth_intro/credits.htm
how old is this page 
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| Quote: | | Don't die with your music still in you - Wayne Dyer |
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Gordon Charlton
Joined: Oct 07, 2006
Posts: 75
Location: UK
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| Posted: Mon Sep 03, 2007 5:23 am Post subject:
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I wrote it about 14 years and five macs ago. 
The dodgy html (") worked just fine at the time. |
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blue hell
Site Admin
Joined: Apr 03, 2004
Posts: 24085
Location: The Netherlands, Enschede
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Posted: Mon Sep 03, 2007 5:38 am Post subject:
Re: computing microtonal intervals with rational numbers
Subject description: an ANS Forth rational arithmetic word-set |
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| Gordon Charlton wrote: | | ages ago |
| Code: | | .( Vulgar Maths Words. Version FSL1.1 23rd April 1996) CR |
Hope your code calculates more accurate 
Serious though, this looks like a very well documented and useful package to me.
Good also to see triple numbers being used, I thought I was the only person in the world to have a need for that (for address calculations on the larger PIC processors).
BTW, by the time I was done with my Sinclair ZX81 it did have 4th in ROM (and basic still).
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also .. could someone please turn down the thermostat a bit.
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seraph
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| Posted: Mon Sep 03, 2007 5:44 am Post subject:
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| Gordon Charlton wrote: |
I wrote it about 14 years and five macs ago.
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...maybe an update, once in awhile...
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dewdrop_world
Joined: Aug 28, 2006
Posts: 858
Location: Guangzhou, China
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blue hell
Site Admin
Joined: Apr 03, 2004
Posts: 24085
Location: The Netherlands, Enschede
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Posted: Mon Sep 03, 2007 5:52 am Post subject:
Re: computing microtonal intervals with rational numbers
Subject description: an ANS Forth rational arithmetic word-set |
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| dewdrop_world wrote: | The site isn't responding for me...
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Hmm, it still works here.
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Jan
also .. could someone please turn down the thermostat a bit.
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seraph
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Joined: Jun 21, 2003
Posts: 12398
Location: Firenze, Italy
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Posted: Mon Sep 03, 2007 6:05 am Post subject:
Re: computing microtonal intervals with rational numbers
Subject description: an ANS Forth rational arithmetic word-set |
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| Blue Hell wrote: | | dewdrop_world wrote: | The site isn't responding for me...
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Hmm, it still works here. |
here too
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| Quote: | | Don't die with your music still in you - Wayne Dyer |
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