I should also have mentioned Victor's help in the TimeWarp
conversation from that time, to which I am also indebted. Thanks!

On 9/7/07, Steven Yi <stevenyi@gmail.com> wrote:
> Hi Tim,
>
> Blue has a TempoMapper class that does beatsToSeconds and
> secondsToBeats with a given Csound style timewarp string
> (t-statement).  This is used by blue's TimeWarp noteProcessor,
> allowable on a per-soundObject basis, as well as used by blue when
> following a render if a t-statement is used globally so that
> accelerando's and such are followed correctly.
>
> The math and code for all of this was worked out on this list April
> 2006 and the Java code I have not is based on python code that Istvan
> Varga posted.  The Java class I use can be seen here:
>
> http://bluemusic.cvs.sourceforge.net/bluemusic/blue/src/main/java/blue/noteProcessor/TempoMapper.java?revision=1.7&view=markup
>
> The thread for that is availble here:
>
> http://www.nabble.com/Calculating-Seconds-to-Beats-in-TimeWarp-tf1435368.html#a3904918
>
> I'll reiterate at this point that I'm indebted to Istvan for his help
> on this.  The thread is also an interesting read I think about how
> this all works.
>
> Hope that helps!
> steven
>
>
> On 9/7/07, Tim Mortimer <timmortimer@d2.net.au> wrote:
> >
> > http://www.nabble.com/file/p12552632/integratethis.jpg integratethis.jpg
> >
> > greets,
> >
> > The attached jpeg attempts to illustrate how i intend to use integration to
> > calculate how much "absolute" time passes in a score when a tempo ramp of a
> > certain duration becomes active for that period of the score.
> >
> > in the case of this example, the tempo decreases from 120BPM to 30BPM over a
> > period of "4 beats"/ 4 "score seconds".
> >
> > My maths is pretty rusty (i did a year 12 bridging course a couple of years
> > ago - at the time because i had just started using Max, & was desparately
> > trying to find out what a Markov chain was, but anyway.. the Calculus & Trig
> > have proven pretty useful along the way......)
> >
> > But I'm having trouble trying to integrate the formula in the attached jpeg.
> >
> > Can anyone assist? Once I have seen it done once, I should be able to apply
> > the integrated function universally (more or less) to all my tempo ramping
> > requirements.
> >
> > i do know the basics of integration (eg integrate x^2 = x^3/3 for example..)
> >
> > but im stumped by the additional scalars & denominators in my formula, &
> > hence by what my desired "ramp time" formula looks like (but i'm pretty sure
> > it's along the lines of what i'm proposing - see the diagram)
> >
> > I suppose what makes my approach "a bit fancy" (beyond the method, which
> > some may feel excessive) is that i like to think that the perception of
> > tempo - like that of pitch, is an exponential / power of 2 type
> > relationship: i.e the perception of "speeding up" & "slowing down" is more
> > meaningful in terms of "twice as fast" / "half as fast", & hence i want to
> > use a power of 2 curve to impose this "perception" onto my tempo ramping -
> > rather than simply a linear increase / decrease in BPM value...
> >
> > Ok, so i realise this may not be the  "normal" way to go about
> > "accumulating" time vis a vis changes in score tempo, however doing it by
> > the way I am attempting has some benefits (for me at least, in this
> > instance) that i see...
> >
> > 1) it's ultimately more accurate
> >
> > 2) it will fit into my "python score paradigm" tempo system with a minimum
> > of fuss (trust me - it has no accumulated score time - just a timeline
> > "function" to which it makes reference to determine current absolute time
> > for the scored event..)
> >
> > 3) u then only need to apply any tempo based calculations to significant
> > score events, which is someways is surely computationally more efficient
> > than accumulating ammassed time on each & every control rate clock - when on
> > 99% of these "clock ticks" no event is actually taking place anyway
> >
> > so, err, any help from the maths brains out there on this one appreciated...
> >
> > kind regards
> >
> > Tim
> > --
> > View this message in context: http://www.nabble.com/tempo-ramp-by-integration---help-needed-tf4400537.html#a12552632
> > Sent from the Csound - General mailing list archive at Nabble.com.
> >
> > --
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> >
>