@inari said:

However what's not clear is how these different sample rates get into the filter blocks, which use x_sr for calculating their coefficients.

But they also use c_coef and c_x which take current sample rate into account because they are type _samplerate. From d_ugen.c:

/* ------------------------ samplerate~~ -------------------------- */

static t_class *samplerate_tilde_class;

typedef struct _samplerate
{
    t_object x_obj;
    t_float x_sr;
    t_canvas *x_canvas;
} t_samplerate;

static void samplerate_tilde_bang(t_samplerate *x)
{
    outlet_float(x->x_obj.ob_outlet, canvas_getsr(x->x_canvas));
}

static void *samplerate_tilde_new(void)
{
    t_samplerate *x = (t_samplerate *)pd_new(samplerate_tilde_class);
    outlet_new(&x->x_obj, &s_float);
    x->x_canvas = canvas_getcurrent();
    return (x);
}

static void samplerate_tilde_setup(void)
{
    samplerate_tilde_class = class_new(gensym("samplerate~"),
        (t_newmethod)samplerate_tilde_new, 0, sizeof(t_samplerate), 0, 0);
    class_addbang(samplerate_tilde_class, samplerate_tilde_bang);
}

/* -------------------- setup routine -------------------------- */

void d_ugen_setup(void)
{
    block_tilde_setup();
    samplerate_tilde_setup();
}

I think if you do the math it will work out but I could be missing something, OOP in C plus heavy pointer use plus math symbols thrown about with pointer symbols always leaves me a but unsure of what is going on if not completely lost.

@Luizagimenez said:

I have a work assigned to translate some Graphs from UV lightning on molecules to an array in Pure Data. Im trying to find a way to get the Quadratic Equations that have complex numbers to show on a somewhat precise array or graph, so i can use these numbers for frequencies, to create a movable bar to select a pixel of the graphic.

Pd can express any math formula, but it's more cumbersome for complicated math expressions than a text-based language. [expr] helps somewhat, though. A real-number (no complex) quadratic would look like this:

If a quadratic is ax2 + bx + c, and you need complex numbers, is it that a, b and c can be complex, or only x? Your graph suggests a real-number domain, in which case complex a, b, c would be the sum of 2 quadratics, one multiplied by i. So, the above patch, but duplicated, to give you a real and an imaginary result.

If x can be complex too, then it's more involved than that.

hjh

you could make a simple abstraction that just outputs a certain number when banged:
multi-math.zip

The ultrasonic distance sensors are usually digital, not analog. If this is the case, you're trying to read a digital signal as analog, which doesn't make much sense. This sensor has two pins, a trigger and an echo. You have to send a high voltage to the trigger pin, then pull it low, and read the echo pin which will help you compute the distance based on the time it took for this trigger pulse to arrive back at the echo pin.
The code below (copied from Arduino'g Project Hub), uses Arduino's pulseIn() function, to compute the distance:

// Define Trig and Echo pin:
#define trigPin 2
#define echoPin 3
//  Define variables:
long duration;
int distance;
void setup() {
  // Define  inputs and outputs:
  pinMode(trigPin, OUTPUT);
  pinMode(echoPin, INPUT);
  //Begin Serial communication at a baudrate of 9600:
  Serial.begin(9600);
}
void  loop() {
  digitalWrite(trigPin, LOW);
  delayMicroseconds(5);
  digitalWrite(trigPin,  HIGH);
  delayMicroseconds(10);
  digitalWrite(trigPin, LOW);
  // Read  the echoPin, pulseIn() returns the duration (length of the pulse) in microseconds:
  duration = pulseIn(echoPin, HIGH);
  // Calculate the distance:
  distance=  duration*0.034/2;
  // Print the distance on the Serial Monitor
  Serial.print("Distance  = ");
  Serial.print(distance);
  Serial.println(" cm");
  delay(1000);
}

I searched online and found the source of this pulseIn() function in Arduino's forum, which is this:

/*
  wiring_pulse.c - pulseIn() function
  Part of Arduino - http://www.arduino.cc/

  Copyright (c) 2005-2006 David A. Mellis

  This library is free software; you can redistribute it and/or
  modify it under the terms of the GNU Lesser General Public
  License as published by the Free Software Foundation; either
  version 2.1 of the License, or (at your option) any later version.

  This library is distributed in the hope that it will be useful,
  but WITHOUT ANY WARRANTY; without even the implied warranty of
  MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU
  Lesser General Public License for more details.

  You should have received a copy of the GNU Lesser General
  Public License along with this library; if not, write to the
  Free Software Foundation, Inc., 59 Temple Place, Suite 330,
  Boston, MA  02111-1307  USA

  $Id: wiring.c 248 2007-02-03 15:36:30Z mellis $
*/

#include "wiring_private.h"
#include "pins_arduino.h"

/* Measures the length (in microseconds) of a pulse on the pin; state is HIGH
 * or LOW, the type of pulse to measure.  Works on pulses from 2-3 microseconds
 * to 3 minutes in length, but must be called at least a few dozen microseconds
 * before the start of the pulse. */
unsigned long pulseIn(uint8_t pin, uint8_t state, unsigned long timeout)
{
    // cache the port and bit of the pin in order to speed up the
    // pulse width measuring loop and achieve finer resolution.  calling
    // digitalRead() instead yields much coarser resolution.
    uint8_t bit = digitalPinToBitMask(pin);
    uint8_t port = digitalPinToPort(pin);
    uint8_t stateMask = (state ? bit : 0);
    unsigned long width = 0; // keep initialization out of time critical area
    
    // convert the timeout from microseconds to a number of times through
    // the initial loop; it takes 16 clock cycles per iteration.
    unsigned long numloops = 0;
    unsigned long maxloops = microsecondsToClockCycles(timeout) / 16;
    
    // wait for any previous pulse to end
    while ((*portInputRegister(port) & bit) == stateMask)
        if (numloops++ == maxloops)
            return 0;
    
    // wait for the pulse to start
    while ((*portInputRegister(port) & bit) != stateMask)
        if (numloops++ == maxloops)
            return 0;
    
    // wait for the pulse to stop
    while ((*portInputRegister(port) & bit) == stateMask) {
        if (numloops++ == maxloops)
            return 0;
        width++;
    }

    // convert the reading to microseconds. The loop has been determined
    // to be 20 clock cycles long and have about 16 clocks between the edge
    // and the start of the loop. There will be some error introduced by
    // the interrupt handlers.
    return clockCyclesToMicroseconds(width * 21 + 16); 
}

This is already getting complicated, as pulseIn() uses other functions which should be found and translated to Pd. I guess the best thing you can do is try to translate the first code chuck in this reply to Pd, and when you read a high voltage in the echo pin, do some math to calculate the distance.
In essence, set a digital input and a digital output pin on the Bela, trigger the output pin with a high and low signal, and keep reading the input pin (you should probably use a pull-down resistor there), until you get a high. Calculate the time it took with the [timer] object and do some simple math to get the distance. Do that with distances you know first, and then use the rule of three based on the known distance and the time you get. At least, that's how I would try to get this to work.

Another solution is to use an infrared proximity sensor, which is analog, and it's probably much easier to use. But this gets the proximity of obstacles right in front of it only, while the ultrasonic range finder has a wider field where it can detect obstacles.

@alexandros

thanks for the suggestion! I"ve never compiled anything before, but I gave it a shot...

I'm getting this error in PD after loading the 3 compiled objects (6 files: grambidec.pd_darwin, grambidec.pd_darwin.o, grambiman.pd_darwin, grambiman.pd_darwin.o, grambipan.pd_darwin, grambipan.pd_darwin.o):

 load_object: Symbol "grambiman_setup" not found in "/Users/brianlindgren/Documents/Pd/externals/grambiman.pd_darwin"

Also make is generating a bunch of warnings:

++++ info: using Makefile.pdlibbuilder version 0.7.0
++++ info: using Pd API /Applications/Pd-0.54-1.app/Contents/Resources/src/m_pd.h
++++ info: making target all in lib grambidec~
++++ info: making grambidec.pd_darwin.o in lib grambidec~
cc -DPD -I "/Applications/Pd-0.54-1.app/Contents/Resources/src"  -DUNIX -DMACOSX -I /sw/include    -Wall -Wextra -Wshadow -Winline -Wstrict-aliasing -O3 -ffast-math -funroll-loops -fomit-frame-pointer -arch arm64 -mmacosx-version-min=10.6 -o grambidec.pd_darwin.o -c grambidec.c
grambidec.c:41:24: warning: unused variable 'x' [-Wunused-variable]
    t_grambidec_tilde *x = (t_grambidec_tilde *)(w[1]);
                       ^
grambidec.c:43:16: warning: unused variable 'APin2' [-Wunused-variable]
    t_sample  *APin2 =    (t_sample *)(w[3]);
               ^
grambidec.c:44:16: warning: unused variable 'APin3' [-Wunused-variable]
    t_sample  *APin3 =    (t_sample *)(w[4]);
               ^
grambidec.c:45:16: warning: unused variable 'APin4' [-Wunused-variable]
    t_sample  *APin4 =    (t_sample *)(w[5]);
               ^
grambidec.c:69:24: warning: unused variable 'x' [-Wunused-variable]
    t_grambidec_tilde *x = (t_grambidec_tilde *)(w[1]);
                       ^
grambidec.c:78:23: warning: variable 'sample2' set but not used [-Wunused-but-set-variable]
    t_sample sample1, sample2, sample3, sample4;
                      ^
grambidec.c:78:41: warning: variable 'sample4' set but not used [-Wunused-but-set-variable]
    t_sample sample1, sample2, sample3, sample4;
                                        ^
grambidec.c:102:24: warning: unused variable 'x' [-Wunused-variable]
    t_grambidec_tilde *x = (t_grambidec_tilde *)(w[1]);
                       ^
grambidec.c:113:41: warning: variable 'sample4' set but not used [-Wunused-but-set-variable]
    t_sample sample1, sample2, sample3, sample4;
                                        ^
grambidec.c:143:24: warning: unused variable 'x' [-Wunused-variable]
    t_grambidec_tilde *x = (t_grambidec_tilde *)(w[1]);
                       ^
grambidec.c:185:24: warning: unused variable 'x' [-Wunused-variable]
    t_grambidec_tilde *x = (t_grambidec_tilde *)(w[1]);
                       ^
grambidec.c:228:24: warning: unused variable 'x' [-Wunused-variable]
    t_grambidec_tilde *x = (t_grambidec_tilde *)(w[1]);
                       ^
grambidec.c:282:24: warning: unused variable 'x' [-Wunused-variable]
    t_grambidec_tilde *x = (t_grambidec_tilde *)(w[1]);
                       ^
grambidec.c:351:37: warning: unused parameter 's' [-Wunused-parameter]
void *grambidec_tilde_new(t_symbol *s, int argc, t_atom *argv) //, t_floatarg test
                                    ^
grambidec.c:473:5: warning: performing pointer subtraction with a null pointer has undefined behavior [-Wnull-pointer-subtraction]
    CLASS_MAINSIGNALIN(grambidec_tilde_class, t_grambidec_tilde, APf);
    ^~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
/Applications/Pd-0.54-1.app/Contents/Resources/src/m_pd.h:529:59: note: expanded from macro 'CLASS_MAINSIGNALIN'
    class_domainsignalin(c, (char *)(&((type *)0)->field) - (char *)0)
                                                          ^ ~~~~~~~~~
15 warnings generated.
++++ info: linking objects in grambidec.pd_darwin for lib grambidec~
cc -undefined suppress -flat_namespace -bundle  -arch arm64 -mmacosx-version-min=10.6  -o grambidec.pd_darwin grambidec.pd_darwin.o  -lc   
ld: warning: -undefined suppress is deprecated
ld: warning: -undefined suppress is deprecated
++++ info: making grambiman.pd_darwin.o in lib grambidec~
cc -DPD -I "/Applications/Pd-0.54-1.app/Contents/Resources/src"  -DUNIX -DMACOSX -I /sw/include    -Wall -Wextra -Wshadow -Winline -Wstrict-aliasing -O3 -ffast-math -funroll-loops -fomit-frame-pointer -arch arm64 -mmacosx-version-min=10.6 -o grambiman.pd_darwin.o -c grambiman.c
grambiman.c:64:24: warning: unused variable 'x' [-Wunused-variable]
    t_grambiman_tilde *x = (t_grambiman_tilde *)(w[1]);
                       ^
grambiman.c:139:24: warning: unused variable 'x' [-Wunused-variable]
    t_grambiman_tilde *x = (t_grambiman_tilde *)(w[1]);
                       ^
grambiman.c:226:24: warning: unused variable 'x' [-Wunused-variable]
    t_grambiman_tilde *x = (t_grambiman_tilde *)(w[1]);
                       ^
grambiman.c:252:32: warning: variable 'sample3' set but not used [-Wunused-but-set-variable]
    t_sample sample1, sample2, sample3, sample4, sample10;
                               ^
grambiman.c:306:24: warning: unused variable 'x' [-Wunused-variable]
    t_grambiman_tilde *x = (t_grambiman_tilde *)(w[1]);
                       ^
grambiman.c:370:37: warning: unused parameter 's' [-Wunused-parameter]
void *grambiman_tilde_new(t_symbol *s, int argc, t_atom *argv)
                                    ^
grambiman.c:436:5: warning: performing pointer subtraction with a null pointer has undefined behavior [-Wnull-pointer-subtraction]
    CLASS_MAINSIGNALIN(grambiman_tilde_class, t_grambiman_tilde, APf);
    ^~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
/Applications/Pd-0.54-1.app/Contents/Resources/src/m_pd.h:529:59: note: expanded from macro 'CLASS_MAINSIGNALIN'
    class_domainsignalin(c, (char *)(&((type *)0)->field) - (char *)0)
                                                          ^ ~~~~~~~~~
7 warnings generated.
++++ info: linking objects in grambiman.pd_darwin for lib grambidec~
cc -undefined suppress -flat_namespace -bundle  -arch arm64 -mmacosx-version-min=10.6  -o grambiman.pd_darwin grambiman.pd_darwin.o  -lc   
ld: warning: -undefined suppress is deprecated
ld: warning: -undefined suppress is deprecated
++++ info: making grambipan.pd_darwin.o in lib grambidec~
cc -DPD -I "/Applications/Pd-0.54-1.app/Contents/Resources/src"  -DUNIX -DMACOSX -I /sw/include    -Wall -Wextra -Wshadow -Winline -Wstrict-aliasing -O3 -ffast-math -funroll-loops -fomit-frame-pointer -arch arm64 -mmacosx-version-min=10.6 -o grambipan.pd_darwin.o -c grambipan.c
grambipan.c:423:5: warning: performing pointer subtraction with a null pointer has undefined behavior [-Wnull-pointer-subtraction]
    CLASS_MAINSIGNALIN(grambipan_tilde_class, t_grambipan_tilde, APf);
    ^~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
/Applications/Pd-0.54-1.app/Contents/Resources/src/m_pd.h:529:59: note: expanded from macro 'CLASS_MAINSIGNALIN'
    class_domainsignalin(c, (char *)(&((type *)0)->field) - (char *)0)
                                                          ^ ~~~~~~~~~
1 warning generated.
++++ info: linking objects in grambipan.pd_darwin for lib grambidec~
cc -undefined suppress -flat_namespace -bundle  -arch arm64 -mmacosx-version-min=10.6  -o grambipan.pd_darwin grambipan.pd_darwin.o  -lc   
ld: warning: -undefined suppress is deprecated
ld: warning: -undefined suppress is deprecated
++++info: target all in lib grambidec~ completed

This is my Makefile:

# Makefile for mylib

lib.name = grambidec~

class.sources = grambidec.c grambiman.c grambipan.c

datafiles = grambilib-help.pd readme.md

include Makefile.pdlibbuilder

Any suggestion? Thanks again!

Hi all - I'm trying to compile PD for my M1 Mac and I have not been able to figure out how to get this to work. It keeps ending up with an Intel based app even though when I run configure it appears to be set up correctly. Configure gives this output:

pd 0.54.0 is now configured

Platform:             Mac OSX
Float size:           default
Debug build:          no
Universal build:      no
Localizations:        yes
Source directory:     .
Installation prefix:  /usr/local

Compiler:             gcc
CPPFLAGS:             -DNDEBUG  
CFLAGS:               -mmacosx-version-min=10.6 -ffast-math -fno-finite-math-only -funroll-loops -fomit-frame-pointer -O3  -g -O2
LDFLAGS:              -L/usr/local/lib  
INCLUDES:             -I/usr/local/include 
LIBS:                 

External extension:   d_fat
External CFLAGS:      -fPIC
External LDFLAGS:     -bundle -undefined dynamic_lookup
Deken identifier:     darwin-arm64

fftw:                 no
wish(tcl/tk):         default search paths
watchdog:             yes
audio APIs:           PortAudio 
midi APIs:            PortMidi 

However, when I subsequently run 'make' and then 'make app' the app it generates is an Intel app. I can tell by looking at the app with 'get info' in Finder, or by looking at it in Activity Monitor when it is running and seeing that it is an Intel process. Can somebody please help me make this natively for Mac architecture?

(FYI, I am doing a custom compile because I need to extend the MIDI FIFO size to avoid overflow for my specific use case)

Thanks!

@esaruoho Like this?
slowarray.pd

The time and frequency arrays output floats in the range of 0-1 which are shifted to the desired range, for time it is 1-60 minutes by the [*1000]->[*60] and for frequency it is 8.5hz-17hz, [*8.5] to shift the 0-1 output of line to span 8.5 hz and [+8.5] to get it to run from 8.5hz up to 17hz.

Edit, error in the math for the time, should be {* 1000]->[* 60]->[* 60], first converts 0-1 to ms, second converts to seconds, third does minutes. lost a [* 60] somehow. Or you can just [* 3e+06] instead but I like to keep the math easy to read. Fixed the file but not the image.

the image from fishcrystal contains an important, basic part of the answer in that plot: the math required for a multi-point-crossfader is identical to the math in a "equal-power" stereo panner.

using modulation -> list -> modulo -> cos function, as seen above, is a nice short data rate implementation.
if you want to use signals, where you dont have lists, you can optimize that principle further by using buffers and then only use +- offsets when reading out the function for the different inputs.

Hi,

I am trying to get ofelia to run on a couple of rpi. Right now I am trying a rpi 3B+ running https://blokas.io/patchbox-os/

I run ofeila with the ofelia-fast-prototyping abs on my mac successfully.

Following install instructions here https://github.com/cuinjune/Ofelia
after running
sudo ./install_dependencies.sh
it ends like this:

detected Raspberry Pi
installing gstreamer omx
Reading package lists... Done
Building dependency tree... Done
Reading state information... Done
gstreamer1.0-omx is already the newest version (1.0.0.1-0+rpi12+jessiepmg).
The following package was automatically installed and is no longer required:
  raspinfo
Use 'sudo apt autoremove' to remove it.
0 upgraded, 0 newly installed, 0 to remove and 0 not upgraded.
Updating ofxOpenCV to use openCV4
sed: can't read /home/patch/Documents/Pd/externals/addons/ofxOpenCv/addon_config.mk: No such file or directory
sed: can't read /home/patch/Documents/Pd/externals/addons/ofxOpenCv/addon_config.mk: No such file or directory

When running the example patches in Pd I get this in PD console:

opened alsa MIDI client 130 in:1 out:1
JACK: cannot connect input ports system:midi_capture_1 -> pure_data:input_2
/home/patch/Documents/Pd/externals/ofelia/ofelia.l_arm: libboost_filesystem.so.1.67.0: cannot open shared object file: No such file or directory
 ofelia d $0-of
... couldn't create
/home/patch/Documents/Pd/externals/ofelia/ofelia.l_arm: libboost_filesystem.so.1.67.0: cannot open shared object file: No such file or directory
 ofelia d $0-of
... couldn't create
/home/patch/Documents/Pd/externals/ofelia/ofelia.l_arm: libboost_filesystem.so.1.67.0: cannot open shared object file: No such file or directory
 ofelia d $0-of
... couldn't create
/home/patch/Documents/Pd/externals/ofelia/ofelia.l_arm: libboost_filesystem.so.1.67.0: cannot open shared object file: No such file or directory
 ofelia d $0-of
... couldn't create
/home/patch/Documents/Pd/externals/ofelia/ofelia.l_arm: libboost_filesystem.so.1.67.0: cannot open shared object file: No such file or directory
 ofelia d $0-of
... couldn't create
/home/patch/Documents/Pd/externals/ofelia/ofelia.l_arm: libboost_filesystem.so.1.67.0: cannot open shared object file: No such file or directory
 ofelia f ;
 ofBackground(20) ;
 ofSetSmoothLighting(true) ;
 ofSetSphereResolution(24) ;
 local width , height = ofGetWidth() * 0.12 , ofGetHeight() * 0.12 ;
 sphere = ofSpherePrimitive() ;
 sphere:setRadius(width) ;
 icoSphere = ofIcoSpherePrimitive() ;
 icoSphere:setRadius(width) ;
 plane = ofPlanePrimitive() ;
 plane:set(width * 1.5 , height * 1.5) ;
 cylinder = ofCylinderPrimitive() ;
 cylinder:set(width * 0.7 , height * 2.2) ;
 cone = ofConePrimitive() ;
 cone:set(width * 0.75 , height * 2.2) ;
 box = ofBoxPrimitive() ;
 box:set(width * 1.25) ;
 local screenWidth , screenHeight = ofGetWidth() , ofGetHeight() ;
 plane:setPosition(screenWidth * 0.2 , screenHeight * 0.25 , 0) ;
 box:setPosition(screenWidth * 0.5 , screenHeight * 0.25 , 0) ;
 sphere:setPosition(screenWidth * 0.8 , screenHeight * 0.25 , 0) ;
 icoSphere:setPosition(screenWidth * 0.2 , screenHeight * 0.75 , 0) ;
 cylinder:setPosition(screenWidth * 0.5 , screenHeight * 0.75 , 0) ;
 cone:setPosition(screenWidth * 0.8 , screenHeight * 0.75 , 0) ;
 pointLight = ofLight() ;
 pointLight:setPointLight() ;
 pointLight:setDiffuseColor(ofFloatColor(0.85 , 0.85 , 0.55)) ;
 pointLight:setSpecularColor(ofFloatColor(1 , 1 , 1)) ;
 pointLight2 = ofLight() ;
 pointLight2:setPointLight() ;
 pointLight2:setDiffuseColor(ofFloatColor(238 / 255 , 57 / 255 , 135 / 255)) ;
 pointLight2:setSpecularColor(ofFloatColor(0.8 , 0.8 , 0.9)) ;
 pointLight3 = ofLight() ;
 pointLight3:setPointLight() ;
 pointLight3:setDiffuseColor(ofFloatColor(19 / 255 , 94 / 255 , 77 / 255)) ;
 pointLight3:setSpecularColor(ofFloatColor(18 / 255 , 150 / 255 , 135 / 255)) ;
 material = ofMaterial() ;
 material:setShininess(120) ;
 material:setSpecularColor(ofFloatColor(1 , 1 , 1)) ;
... couldn't create
/home/patch/Documents/Pd/externals/ofelia/ofelia.l_arm: libboost_filesystem.so.1.67.0: cannot open shared object file: No such file or directory
 ofelia f ;
 pointLight = nil ;
 pointLight2 = nil ;
 pointLight3 = nil ;
 collectgarbage() ;
... couldn't create
/home/patch/Documents/Pd/externals/ofelia/ofelia.l_arm: libboost_filesystem.so.1.67.0: cannot open shared object file: No such file or directory
 ofelia f ;
 local width , height , time = ofGetWidth() , ofGetHeight() , ofGetElapsedTimef() ;
 pointLight:setPosition((width * 0.5) + math.cos(time * 0.5) * (width * 0.3) , height / 2 , 500) ;
 pointLight2:setPosition((width * 0.5) + math.cos(time * 0.15) * (width * 0.3) , height * 0.5 + math.sin(time * 0.7) * height , -300) ;
 pointLight3:setPosition(math.cos(time * 1.5) * width * 0.5 , math.sin(time * 1.5) * width * 0.5 , math.cos(time * 0.2) * width) ;
... couldn't create
/home/patch/Documents/Pd/externals/ofelia/ofelia.l_arm: libboost_filesystem.so.1.67.0: cannot open shared object file: No such file or directory
 ofelia f ;
 local spinX = math.sin(ofGetElapsedTimef() * 0.35) ;
 local spinY = math.cos(ofGetElapsedTimef() * 0.075) ;
 ofEnableDepthTest() ;
 ofEnableLighting() ;
 pointLight:enable() ;
 pointLight2:enable() ;
 pointLight3:enable() ;
 material:beginMaterial() ;
 plane:rotateDeg(spinX , 1 , 0 , 0) ;
 plane:rotateDeg(spinY , 0 , 1 , 0) ;
 plane:draw() ;
 box:rotateDeg(spinX , 1 , 0 , 0) ;
 box:rotateDeg(spinY , 0 , 1 , 0) ;
 box:draw() ;
 sphere:rotateDeg(spinX , 1 , 0 , 0) ;
 sphere:rotateDeg(spinY , 0 , 1 , 0) ;
 sphere:draw() ;
 icoSphere:rotateDeg(spinX , 1 , 0 , 0) ;
 icoSphere:rotateDeg(spinY , 0 , 1 , 0) ;
 icoSphere:draw() ;
 cylinder:rotateDeg(spinX , 1 , 0 , 0) ;
 cylinder:rotateDeg(spinY , 0 , 1 , 0) ;
 cylinder:draw() ;
 cone:rotateDeg(spinX , 1 , 0 , 0) ;
 cone:rotateDeg(spinY , 0 , 1 , 0) ;
 cone:draw() ;
 material:endMaterial() ;
 ofDisableLighting() ;
 ofDisableDepthTest() ;
... couldn't create

Thankful for help!

@lead said:

So, starting with the smallest number of decimal places and ending with the smallest number of decimal places is preferable, does that make sense?

Formally, it doesn't make sense.

The ratio for 2 semitones down is 2 ** (-2 / 12). 2 is a prime number. Raising any (positive) prime number to a fractional power results in an irrational number, with infinitely many decimal places (without ending up in a repeating sequence).

A rational number times an irrational number must be irrational. So your initial bpm value * the ratio is irrational and has infinitely many decimal places. To say "this one has 3 places" glosses over the real situation.

What you're really doing is rounding this irrational number to an arbitrary number of places. The denominator of the rounded number will be 10 ** num_places -- thus both the numerator and denominator are integers and the result is rational.

The difference (or quotient, depending how you want to measure it) between bpm * ratio and the rounded version is an error value.

And the math problem, then, is to minimize the error.

You can see it more clearly if you use a language with double precision floats, e.g., SuperCollider:

f = { |bpm, semitones = -2, places = 3|
    var r = 2 ** (semitones / 12);  // '.midiratio'
    var bpm2 = bpm * r;
    var rounded = bpm2.round(10 ** places.neg);
    // for easier comparison I'll "absolute-value" the error values
    var errorDiff = bpm2 absdif: rounded;
    var errorRatio = bpm2 / rounded;
    if(errorRatio < 1) { errorRatio = 1 / errorRatio };
    [bpm2, errorDiff, errorRatio]
};

f.value(69);  // [ 61.472011551683, 1.1551683407163e-05, 1.0000001879178 ]
f.value(59);  // [ 52.56302437028, 2.4370280016228e-05, 1.0000004636394 ]
f.value(77);  // [ 68.599201296806, 0.00020129680612513, 1.0000029343985 ]

... where, indeed, the error for 77 * r is about an order of magnitude worse.

@jameslo -- "It would be cool if you were asking https://math.stackexchange.com/questions/2438510/can-i-find-the-closest-rational-to-any-given-real-if-i-assume-that-the-denomina "

I think this is exactly what the problem reduces to -- what is the closest rational to x where the denominator = 1000. (However, the numerical methods in the thread will likely evaluate better with double precision floats. Pd prints 6 digits so it may not be clear what you're seeing.)

Actually something else... if x is the original bpm and y is the adjusted, find x and y where the error is minimized. So far the assumption is that x is an integer, but maybe the error could be even lower if they're both fractions.

hjh