1 tplarson 1.1 The Sound of the Sun:
2 An Introduction to the Sonification of Solar Harmonics (SoSH) Project
3
4 a more extensive discussion of helioseismology with added graphics can
5 be found at http://solar-center.stanford.edu/SoSH/ . short instructions
6 can be found in quickstart_audio.txt .
7
8 Section 1: Background
9 motivation for the project
10
11 Section 2: Helioseismology and Sonificiation
12 an introduction for beginners
13
14 Section 3: Instruments and Data
15 the data you will need and how to get it
16
17 Section 4: Software (Pure Data)
18 a detailed description of the software
19
20 Section 5: Building Your Own Patches
21 examples of applications
22 tplarson 1.1
23 Section 6: Extensions
24 combining timeseries
25
26 Section 7: Conclusion
27 prospects for the future and contact info
28
29
30 Section 1: Background
31
32 the sun is a resonant cavity for very low frequency acoustic waves, and
33 just like a musical instrument, it supports a number of oscillation
34 modes, also commonly known has harmonics. we are able to measure the
35 frequencies of these various harmonics by looking at how the sun's
36 surface oscillates in response to them. then, just as the frequency of
37 a plucked guitar string gets higher with more tension and lower with
38 greater thickness, we are able to infer properties of the solar interior
39 such as its pressure and density.
40
41 this study of acoustic waves inside the sun is called helioseismology;
42 an overview can be found at http://soi.stanford.edu/results/heliowhat.html .
43 tplarson 1.1 although it has allowed us to make measurements of unprecedented
44 precision, it remains largely unknown to the general public. of course,
45 when one learns of it for the first time, a natural question arises:
46 "what does the sun sound like?". and unfortunately even
47 helioseismologists rarely have much experiential knowledge of it. that
48 is, we analyze solar data scientifically, but we never listen to it. it
49 is the goal of this project to make such listening widely available.
50
51 the first widely recognized effort toward the sonification of
52 helioseismic data was undertaken by Alexander Kosovichev, based on
53 earlier work by Douglas Gough (see http://soi.stanford.edu/results/
54 sounds.html). although only a small amount of data was sonified,
55 physical effects such as scattering off the solar core were still
56 audible. with the sonification of a vastly larger dataset, one would
57 also be able to hear solar rotation, or perhaps even the effect of the
58 solar cycle. not only does this bring helioseismology and solar physics
59 into the realm of everyday experience for the nonscientist, but it might
60 even allow for new scientific discoveries. the fact is that we simply
61 don't know what might be audible in the data because we have never
62 listened to it.
63
64 tplarson 1.1 finally, we said above that the sun is like a musical instrument, but
65 one could also say that the sun *is* a musical instrument, in that it
66 has its own distinct set of harmonics. of course we can't play the sun
67 in the sense of sounding individual notes; rather all of the solar notes
68 are playing all the time simultaneously. with a little analysis,
69 however, the various solar tones can be separated from each other and
70 then used in musical composition.
71
72
73 Section 2: Helioseismology and Sonification
74
75 the strongest of the sun's harmonics have periods of about 5 minutes,
76 corresponding to frequencies of only about 0.003 hertz. unfortunately,
77 this is far below the range of human hearing, which is typically taken
78 to be 20 - 20,000 hertz, although most people are only sensitive to a
79 smaller range. hence, if we would like to experience the sound of the
80 sun with our ears, these very low sounds must be scaled to the range we
81 can hear.
82
83 but first, we need some exposition of what a mode on the sun looks like.
84 to begin with, it is a mathematical theorem that any arbitrary shape of
85 tplarson 1.1 the sun's surface can be expressed as a sum over its harmonics (this is
86 also true for a guitar string). in the case of the sun, we call them
87 spherical harmonics, and each of them are labelled by two integers: the
88 spherical harmonic degree l (ell) and the azimuthal order m. The degree
89 l is equal to or greater than zero, and for each l, there are 2*l+1 values
90 of m, ranging from -l to l.
91
92 the different spherical harmonics also sample different regions of the
93 sun. low values of the degree l penetrate almost all the way to the
94 core, whereas higher values are trapped closer to the surface.
95 similarly, modes with high values of m have their maximum amplitude at
96 low latitudes, whereas lower values sample higher latitudes. it is
97 because the different modes sample different regions that we are able to
98 use their frequencies to determine solar properties as a function of
99 both depth and latitude.
100
101 to determine the frequencies of the sun's harmonics, we might take an
102 image once a minute for 72 days. for each image, we decompose it into
103 its various spherical harmonic components. for each of these
104 components, we form a timeseries of its amplitude. from the timeseries
105 we are able to construct the power spectrum (acoustic power as a
106 tplarson 1.1 function of frequency). the location of peaks in the power spectrum
107 correspond to the frequencies of the modes (harmonics). the height of
108 the peak tells us the mode amplitude, and the width of the peak tells us
109 how much the oscillation is damped.
110
111 an easy way to understand spherical harmonics is in terms of their node
112 lines, which are the places on the sphere where the spherical harmonics
113 are zero. the degree l tells how many of these node lines there are in
114 total, and the order m gives the number in longitude, so the number of
115 node lines in latitude is l-m. so a spherical harmonic with m=0 has
116 only latitudinal bands, while one with m=l has only sections like an
117 orange. a third integer, the radial order n, tells how many nodes the
118 oscillation has along the sun's radius. since only the surface of the
119 sun is visible to us, all the values of n are present in each spherical
120 harmonic labelled by l and m, although only some of them will be excited
121 to any appreciable amplitude. The total mode, then, is represented as a
122 product of a spherical harmonic, which is a function of latitude and
123 longitude, and another function of radius. each n will have its own peak
124 in the power spectrum.
125
126 now, in a spherically symmetric sun, all values of m for a given l and n
127 tplarson 1.1 would have the same frequency. a break in spherical symmetry causes the
128 frequency to vary with m. the most significant deviation from spherical
129 symmetry in the sun is rotation about its axis. the spherical harmonic
130 decomposition, however, is only sensitive to the absolute value of m.
131 therefore the positive and negative values of m must be separated in the
132 power spectrum. we say that the positive frequency part of the spectrum
133 corresponds to negative m, and that the negative frequency part
134 corresponds to positive m. note that this particular convention for the
135 sign of m is completely arbitrary. if you want to understand what is
136 meant by "the negative frequency part of the power spectrum", you will
137 need to study the fourier transform, but such understanding is not
138 strictly necessary.
139
140 let us now return to the issue of sonification, the conversion of data
141 into audible sound. the most straightforward way to do so would be to
142 use the spherical harmonic timeseries we already have in hand and speed
143 them up. but by how much? the answer of course is arbitrary and will
144 depend on your preference, but as long as this choice is applied
145 consistently you will still be able to hear the real relationship
146 between different solar tones.
147
148 tplarson 1.1 let us suppose that we want to transpose a mode in the peak power range
149 at about 0.003 hertz up to 300 hertz; this amounts to speeding up the
150 timeseries by a factor of 100,000. if we have 72 days of data taken
151 once a minute, this amounts to 103,680 data points, or samples. it's
152 easy to see that the sped-up timeseries would now play in just over a
153 minute. one must also consider the sample rate, however, or the rate at
154 which audio is played back. speeding up the original sample rate of
155 (1/60) hertz by a factor of 100,000 yields a new sample rate of 1666.67
156 hertz, and one unfortunately finds very few audio players that will play
157 any sample rate less than 8000 hertz. assuming this sample rate, our
158 0.003 hertz mode on the sun will now be transposed up to 1440 hertz and
159 the timeseries will play in about 13 seconds.
160
161 but suppose you want to play it in a shorter time; 13 seconds is a long
162 time to sound a single note, although you might want to do so in some
163 circumstances. you could increase the sample rate further still, but at
164 some point the mode will be transposed to an uncomfortably high
165 frequency. to understand the solution to this problem, we must explore
166 the process by which we shall isolate the modes.
167
168 at this point in our processing, playing an unfiltered timeseries would
169 tplarson 1.1 sound just like static, or noise. this is because very many modes are
170 sounding simultaneously in any given timeseries, not to mention the
171 background noise involved in our observation of the modes. therefore,
172 if we want to isolate a single mode, we have to do some filtering.
173 luckily, as mentioned above, we have already measured the frequency,
174 amplitude, and width of many modes. we can use these fitted mode
175 parameters to pick out the particular part of the power spectrum
176 corresponding to a single mode, and set the rest of the power spectrum
177 artificially to zero. we then transform back into a function of time so
178 that we can play the filtered data back as a timeseries.
179
180 since we are selecting only a narrow range of frequencies, we have the
181 freedom to shift the entire power spectrum down in frequency before we
182 transform back to timeseries. this timeseries will play in the same
183 amount of time as before, but the frequencies in it will be transposed
184 down by the same factor that we shifted the power spectrum. for every
185 power of 2 shifted down, the tone will drop by one octave.
186
187 one approach might be to decide how long you want to sound each tone
188 (keeping in mind that looping is also an option). this will determine
189 the sample rate at which you will play the timeseries. then you can
190 tplarson 1.1 choose a downshift factor to suite yourself. as long as you use the
191 same sample rate and downshift factor when you sonify every mode, the
192 frequency relationships between them will be preserved.
193
194
195 Section 3: Data
196
197 in order to use the Sonification of Solar Harmonics (SoSH) tool, you
198 will first need to download some data. two types of data are required:
199 text files containing ascii tables of fitted mode parameters and wav
200 files containing the raw acoustic data. furthermore, these data can
201 originate from two different instruments: the Michelson Dopper Imager
202 (MDI) and the Helioseismic and Magnetic Imager (HMI). MDI is the older
203 instrument, and took data from may 1996 to april 2011. it was
204 superceded by HMI, which began taking data in april 2010 and remains in
205 operation today. the two instruments are quite similar; the most
206 important difference between them for our purpose is that MDI produced
207 an image once a minute, while HMI produces an image every 45 seconds.
208 for both instruments, however, we analyze the data using 72 day long
209 timeseries.
210
211 tplarson 1.1 if you have also downloaded the SoshPy Visualization Package, then you
212 may use its included python module to interactively retrieve whatever
213 data you need. instructions for this module are included in the
214 package. however, these data may also be downloaded from the web, and
215 instructions for doing so follow.
216
217 first, pick a single directory for storing data on your computer; for
218 your convenience we have included a data directory in the zip archive
219 you have unpacked. if you elect to use a different directory (such as
220 your browser's download directory), you will simply need to enter it the
221 first time you run the SoSH tool. if you have downloaded the version of
222 the SoSH tool that includes demo data files, these will already be found
223 in the unpacked data directory. the quickstart guide includes
224 instructions for using those specific files.
225
226 in any case, the data are available at
227 http://sun.stanford.edu/~tplarson/audio/ , where you will find separate
228 directories for MDI and HMI. within each, you will find a series of
229 subdirectories that are day numbers suffixed with 'd'. the day number
230 corresponds to the first day of the 72 day timeseries and is actually
231 the number of days since 1 january 1993. day number 1216 was 1 may
232 tplarson 1.1 1996. a full table converting day numbers to dates can be found at the
233 above url as well.
234
235 clicking on a directory will show two ascii files containing the mode
236 parameters; download both of these to your data directory. the file
237 without "msplit" at the end contains one line for every degree l and
238 (radial) order n for which the fitting succeeded. the first five
239 numbers of each line are all that we will use here; they are degree l,
240 order n, mean frequency, amplitude, and width. these numbers are the
241 same for all m, the mean frequency being the average over m. the file
242 with "mpslit" at the end tells us only how the frequency varies with m.
243 make sure that however you download them, the file names stay intact;
244 some browsers like to add or delete filename extensions. this is good
245 to check if you get "file not found" errors later.
246
|
249 tplarson 1.1 you need not view these files, but keep in mind that in general the
250 fitting does not succeed for every value of n. put another way, every
251 file will have l values ranging exactly from 0 to 300, the upper limit
252 being a somewhat arbitrary choice. for every value of l, exactly 2*l+1
253 values of m will appear in the msplit file. what may vary widely,
254 however, is which values of n appear for different values of l. we
255 typically only find modes with n=0 in timeseries with l>100. modes with
256 n=28 (higher values are rare) are only likely to be found for l=5-15.
257 looked at from the other direction, for l=0 we typically find modes with
258 n=10-25. for l=100, n=10 is the highest value we might find. above
259 l=200, we have only n=0. in all cases, one may expect to find holes in
260 the coverage of n for values of l close to the edge of the range.
261
262 one way to get much higher mode coverage, at the cost of time
263 resolution, is to perform an average. an example of such an average can
264 be found in the files "mdi.average.modes" and "hmi.average.modes" in the
265 corresponding directories at http://sun.stanford.edu/~tplarson/audio/,
266 along with the corresponding msplit files. the stand alone patch
267 described in the next section is set to use these averaged mode
268 parameters by default, which means those averages will be used for all
269 day numbers. in this case, no further mode parameter files would need
270 tplarson 1.1 to be downloaded.
271
272 next you will need to download some actual audio files. to do so click
273 on the wavfiles subdirectory, where you will find a selection of modes,
274 labelled by l and m. except for m=0, each mode has both a real and an
275 imaginary part, labelled by "datar" and "datai" respectively; make sure
276 you always get both. these files contain exactly the same data as we
277 use for scientific analysis. the file formats have simply been changed
278 from fits (flexible image transport system) to wav. pick an assortment
279 of modes and download them to your data directory. of course you may
280 play these sounds files just as they are if you want to hear the
281 unfiltered data.
282
283
284 Section 4: Software (Pure Data)
285
286 now we are ready to dive into a description of the software by which the
287 scheme laid out in section 2 can be accomplished. one freely available
288 option is pure data, available from http://puredata.info . pure data
289 provides a graphical interface for audio processing. programs in pure
290 data are called "patches". once you have it installed, run the program
291 tplarson 1.1 and the main Pd console will open. first you will want to test that it
292 is communicating with your soundcard. to do so, click on "Media" and
293 then "Test Audio and MIDI". this will open a patch called testtone.pd .
294 if you see changing numbers under audio input, you are connected to your
295 computer's microphone, although that is unneeded for this project. more
296 important is the audio out, which you can test by clicking in the boxes
297 under "test tones".
298
299 once this is working, you are ready to use the SoSH tool. unzip the
300 archive and open the patch modefilter_standalone.pd . if you've never
301 looked at a pure data patch before, this will probably look rather
302 confusing, so i will provide an extremely brief introduction. there are
303 three types of boxes in pure data: messages, numbers, and objects.
304 messages are the boxes with an indentation along the right side, perhaps
305 to make the box look like a flag. messages are basically the equivalent
306 of strings, but they can also be automatically converted to numbers.
307 number boxes have a little notch out of the upper right corner. the
308 internal storage for numbers is floating point, but you can also cast to
309 int. an important difference between number boxes and message boxes is
310 that the contents of the latter can be saved. for instance, if one
311 wants to initialize a number, a common way is with a message. also,
312 tplarson 1.1 numbers may be entered while the patch is running, whereas messages
313 cannot. the remaining rectangular boxes are objects, which are like
314 functions. the first element in an object box is the name of the
315 object, which often corresponds to a patch file (extension .pd) of the
316 same name. this is optionally followed by the object's creation
317 arguments. all three types of boxes have inlets on the top and outlets
318 on the bottom.
319
320 another important concept in pure data is its own unique data type
321 called bang, which can be thought of like a mouse click. the message
322 "bang" will also automatically convert to a bang. bangs are used
323 throughout pure data as triggers for various events, or they can be used
324 to signal event detection as well. in the graphical interface, bangs
325 are represented by clickable circles, which we have enlarged and colored
326 green or light blue in our patch. you have probably noticed an object
327 called [loadbang]; its sole purpose is to output a single bang when the
328 patch loads. this is typically used for initialization: sending a bang
329 to a number or message box causes its contents to be output. you may
330 also notice a toggle, represented as an empty green square in our patch,
331 also clickable. this functions like a normal boolean, but it is not a
332 separate data type; it is simply 0 or 1. finally, arrays in pure data,
333 tplarson 1.1 also called tables, come with their own graphical representation.
334 examples visible on the front of our patch are gain, input-r, input-i,
335 and output. (the $0 preceding these names resolves to a unique integer
336 when the patch loads; this becomes necessary when this patch is used as
337 a subpatch to avoid conflicting names. other dollar sign substitutions
338 are more like one would expect: they resolve to some element of the
339 input, depending on the context.)
340
341 now, to use the patch, the first thing you have to do is make sure the
342 data directory is set properly. if you are using the data directory
343 that was unpacked along with the zip archive, you don't have to do
344 anything, since the patch is already to set to look in "../data".
345 otherwise, set the data directory by clicking the light blue bang at
346 lower left. a dialog box will open; just select any file in your data
347 directory and the object [set-directory] will strip the file name and
348 output the path. you should now see your path show up in the message
349 box at right. if you now save the patch file, this will be saved as
350 your default data directory and you won't need to set it any more.
351
352 by default, the patch is set to use MDI data. in particular, this means
353 that it assumes the data was taken at a sample rate of (1/60) hertz,
354 tplarson 1.1 which in turn means that 72 days of data contain 103680 data points.
355 the patch will also use the string "mdi" as the stem for input file
356 names. if you are using HMI data, you may click the message box with
357 "hmi" at the lower left of the patch, and this will be used as the stem
358 for file names. the HMI sample rate of (1/45) hertz will also be used,
359 which means that 72 days of data would contain 138240 data points.
360
361 the next step is to click on the message box with "pd dsp 1", which will
362 turn on digital signal processing. this doesn't need to be on to load
363 files or access arrays, but it does to do any fourier transforms or
364 playback. finally, the inputs you must provide are the day number
365 corresponding to the 72 day timeseries, the spherical harmonic degree l,
366 the radial order n, and the azimuthal order m. note that even if you
367 want to leave one of these at its default value of zero, you must still
368 click on the number box and enter "0". now, to search for this mode,
369 click the green bang at the upper left. the object [triggerlogic] will
370 then decide what to do. typically, the object [loadaudio] is triggered,
371 as you will see when the bang connected to it flashes. we have left
372 these large bangs throughout the patch to make the triggering visible,
373 but you may also use them to manually run the different parts
374 separately.
375 tplarson 1.1
376 by default, the patch will look for an averaged mode parameter file. if
377 you have downloaded the mode parameters for a particular day number and
378 wish to use them, you must click on the message box with "%dd.modes" at
379 the bottom left of the patch before clicking the bang to start
380 processing. the "%d" will be replaced with the day number you have
381 entered.
382
383 the object [loadaudio] searches for audio files such as the ones you
384 have just downloaded. note that the needed input files will depend only
385 on l and the absolute value of m, and that the modes have a real and an
386 imaginary part. the exception is m=0, which has a real part only. if
387 [loadaudio] is successfully able to load the necessary audio files into
388 the arrays input-r and input-i, it will automatically trigger the object
389 [fft-analyze]. this object will perform a fast fourier transform (fft)
390 of the input arrays, storing the result in two arrays called fft-r1 and
391 fft-i1. if you want to see these arrays, simply click on the object [pd
392 fft-arrays]. if you do so you will see an option to write them out to
393 wav files, in case you want to compare pure data's fft output to your
394 expectations. you will also see two unused arrays; these could be used
395 to store amplitude or phase information if such were desired.
396 tplarson 1.1
397 by this time, if you are inquisitive enough, you might have noticed that
398 (for MDI) all of the arrays so far have a length of 131072, which is
399 2^17, rather than the actual number of samples, which is 103680. this
400 is because pure data requires the block size to be a power of 2 for its
401 fft algorithm. the result is effectively to zero pad the end of the
402 timeseries. this has no effect on the frequency content of the sound,
403 and we truncate the output array at the original number of samples, so
404 it will play in the same amount of time as the original. (if you to set
405 block size to less than the number of samples, only this many are
406 output.) if using HMI data, the number of samples is 138240, and so a
407 block size of 2^18=262144 will be used.
408
409 (note: pure data in windows doesn't work with block sizes above 65536.
410 if you are running windows, you may have already seen pure data crash.
411 to avoid this, click on the message box containing "65536" before
412 turning on the dsp. the patch will function normally, but only the
413 first 65536 samples of each file will be used. you may also avoid the
414 crash by altering the source code and recompiling. a discussion of this
415 topic can be found at https://github.com/pure-data/pure-data/issues/68 .)
416
417 tplarson 1.1 at this point, if the fft has been performed successfully, the object
418 [text-filer-reader] is triggered. this searches the text files you
419 downloaded earlier to find the mode parameters corresponding to the
420 numbers you entered. if it finds the mode, it ouputs, after its status
421 code, the mode's amplitude, width, and a measure of background noise.
422 if no mode is found, the status code triggers the message "no data
423 found", and you should try another value of n. (also check the Pd
424 console for error messages.) the amplitude is wired to a number box for
425 your information. the width will be converted into units of bins and
426 then used as input to the object [makegain]. the noise parameter is
427 unused here. these three parameters will depend on l and n, but not m.
428 finally, the last outlet from [text-file-reader] gives the mode's
429 frequency, which does vary with m. the frequency is also converted to
430 bin number, and the [makegain] object is triggered. this function
431 creates the gain array, which is 1.0 in a frequency interval centered on
432 the mode frequency and of length 2 times the width, and 0.0 elsewhere.
433 if so desired, you may enter the parameter "width factor" to
434 multiplicatively increase the width of this interval. notice how a
435 message was used to initialize this number to one.
436
437 once the gain array is generated, then one of the [fft-resynth-???m]
438 tplarson 1.1 objects will be triggered, depending on the sign of m. as mentioned
439 above, the two signs of m are extracted differently from the fourier
440 transform, but in both cases the fft is multiplied by the gain array and
441 then inverse transformed, the result being written into the output array
442 ($0-output). if you have entered a value for the downshift factor, the
443 fft will be shifted down by this amount before the inverse transform.
444 note that we treat a value of zero as meaning no shift.
445
446 next, the output array is played back in a loop. the default sample
447 rate is 8000 hertz, but you may go up to 44100 hertz for the 103680
448 samples to play in only 2.4 seconds (in that case, if you haven't
449 applied any downshift factor, the mode will probably sound quite high).
450 you can change the sample rate by clicking on one of the nearby message
451 boxes, or by entering one manually. to hear the output, you will need
452 to enter the output level (volume). note that each loop is multiplied
453 by a window function, which consists of a 50 ms fade in/out at the
454 beginning/end of the loop. the length of the fade ramp may be adjusted
455 on the front of the patch in the lower left corner. the object
456 [window-gen] then calculates the window array. in section 6 we discuss
457 how and when you might turn windowing off.
458
459 tplarson 1.1 at this point you may adjust the downshift factor, which will retrigger
460 the resynthesis, and the result should play immediately. you can turn
461 off playback by clicking the toggle. you may also elect to save the
462 output as a wav file file by clicking the light blue bang at lower
463 right. the instrument, day number, l, m, and n will be encoded in the
464 output file name.
465
466 now, should you like to listen to another mode, you may enter its
467 "quantum" numbers l, n, and m, and then click on the green bang again.
468 if only n or the sign of m has changed, no new audio needs to be loaded,
469 and the object [text-file-reader] is triggered directly. the rest of
470 the processing chain follows as before. note that the names of output
471 wav files do not encode the sample rate, downshift factor, or width
472 factor. hence, if you want to save the same mode with different values
473 for these parameters, you will have to rename the output file or
474 manually edit the patch.
475
476
477 Section 5: Building Your Own Patches
478
479 once you have played with the patch for a while, you may become
480 tplarson 1.1 interested in creating a pure data patch yourself. in what follows we
481 describe a short sequence of patches that we have created to illustrate
482 how this is done. the first of these is example1.pd . open this file
483 and click on the object [modefilter0] to see how we have converted the
484 modefilter_standalone.pd patch from above for use as a preliminary
485 subpatch in example1.pd . first, you will see that all of the
486 initialization that we had in modefilter_standalone.pd has been moved to
487 the outer patch, including the object [window-gen]. don't forget to
488 reset the data directory if needed. second, you will see that we have
489 added inlets and outlets. the order in which these objects appear from
490 left to right in the patch determine the order the inlets and outlets
491 have in the outer patch. this is the reason you see [inlet] and
492 [outlet] objects sometimes placed far away from what they are connected
493 to. for inlets, we have chosen, from left to right, the following: a
494 bang to start the processing, the day number, degree l, radial order n,
495 azimuthal order m, width multiplication factor, and a toggle to turn
496 playback on and off. for outlets, we have chosen, from left to right,
497 the following: the output audio stream, the amplitude of the mode
498 determined by the fit, and the name of the output array for this
499 particular instance of [modefilter0]. by this time you have probably
500 noticed that some of the connections between objects are drawn as thin
501 tplarson 1.1 lines while others are drawn bold. the difference is that thin lines
502 carry control information, while the thick lines carry signal data,
503 which is always processed at 44100 samples per second. furthermore, it
504 is conventional for objects that handle signal data to have names ending
505 in '~'.
506
507 note here a distinction in how pure data uses subpatches. often, as you
508 have seen here, the subpatch is loaded from a file of the same name with
509 the .pd suffix. this type of subpatch is also called an abstraction.
510 however, subpatches may also be defined as part of the parent patch,
511 using the [pd ] object. here we have used this type of subpatch to hold
512 arrays that needn't be visible on the front of the patch, or to make a
513 patch more readable.
514
515 the inputs to [modefilter0] which must be given are the first five. in
516 examle1.pd we have left the width factor to take on its default value.
517 we have connected a toggle to the final inlet, and we have connected the
518 starting bang to this toggle so that everything will run with a single
519 click. you may want to delete this last connection if you will be
520 sonifying multiple modes, since the next time you click the bang it will
521 turn off the toggle. the right two outlets are now connected for
522 tplarson 1.1 information only, but one might imagine using the amplitude to set the
523 volume the mode is played at, for example. the amplitude units are
524 arbitrary, but the values do accurately reflect the amplitude ratios
525 between the modes as measured on the sun. there are two parameters that
526 should be the same for all instances of [modefilter0]: the playback
527 sample rate and the frequency downshift factor. these two parameters
528 are therefore set in the outer patch and broadcast using a [send] object
529 (abbreviated to [s ] in practice). inside [modefilter0] the broadcast
530 is received by the [receive] object (abbreviated [r ]). to hear the
531 output coming out of the left outlet, we must connect to the
532 digital-to-analog converter, represented by the object [dac~], just as
533 we previously did in modefilter_standalone.pd . (the object
534 [audio_safety~] is one provided with this project; its purpose is to
535 filter out corrupted data.)
536
537 you will also see that we have also connected the output audio stream to
538 the inlet of a [fiddle~] object. the documentation for this built-in
539 object can be viewed by right clicking on it and selecting "Help". in
540 short, it measures the pitch and amplitude of the stream on its inlet.
541 here, it tells us what tone we are actually generating at a particular
542 playback sample rate and after shifting down in frequency.
543 tplarson 1.1
544 finally, the next step is to make a copy of the [modefilter0] object and
545 everything connected to it, which you can do in Edit mode by
546 highlighting the relevant boxes and selecting "Duplicate" from the edit
547 menu. move the new copy to wherever you would like to put it, and now
548 you can listen to two modes at once, turning them on and off with the
549 toggles connected to the right inlets. it works to have two copies of
550 [audio-safety~] and [dac~], but common practice would be to have only
551 one, and connect all the left outlets of the [modefilter0] objects to
552 the same inlet of [audio-safety~]. it is one of the features of pure
553 data that it automatically sums audio signals at inlets. of course, one
554 should also adjust the respective volumes of the modes to avoid
555 clipping. you should end up with something like example2.pd, which has
556 two [modefilter0] objects, but you may add as many as you like.
557
558 aside from the second copy of [modefilter0], in example2.pd we have also
559 added a calculation of the total transposition factor. this illustrates
560 another important consideration to bear in mind, which is that a visual
561 programming language does not explicitly specify the order in which
562 operations are carried out. furthermore, the default behavior for
563 objects in pure data is for only their leftmost inlet to trigger the
564 tplarson 1.1 output. we call this the hot inlet and the other inlets cold. the
565 canonical way to deal with this situation is with the [trigger] object
566 (abbreviated [t ]). as before, you can view its documentation by right
567 clicking on it and selecting "Help". basically this object distributes
568 its inlet to its outlets in right to left order, converting as specified
569 by its creations arguments. in the example shown in example2.pd, the
570 downshift factor is sent first as a float to the cold inlet of the [/ ]
571 (division) object, and then a bang is sent to the hot inlet of the
572 [float] object (abbreviated [f ]). here, the built-in object [select]
573 (abbreviated [sel ]) is used to replace 0 with 1 and pass all other
574 numbers unchanged. the [float] object serves to store numbers and
575 output them when it receives a bang on its left inlet. the result is
576 that the division will be performed regardless of the order in which the
577 sample rate and downshift factor are specified. for more examples of
578 using the [trigger] object, see modefilter0.pd . note that the [float]
579 object is often not needed because most of pure data's mathematical
580 objects store the value of their left inlet automatically and reuse it
581 when a bang is received. on the other hand, if space allows, explicitly
582 using the [float] object can make code more readable.
583
584 (note: if you open example1.pd and example2.pd at the same time, you
585 tplarson 1.1 will get error messages in the pure data console about the array window
586 being multiply defined. also, the first time you run any of the
587 example*.pd patches, you will have to set the data directory and save,
588 unless you are using the default data directory.)
589
590 keep in mind that if you want to see what is happening inside the
591 [modefilter0] subpatch, you can click on it and interact with it
592 directly. you can view all the arrays involved, for instance, or change
593 the value of the width factor. you can also still save the output array
594 to a wav file as before. each copy of [modefilter0] in your patch
595 corresponds to a separate instance, and you can interact with each
596 instance separately, although this can be confusing if you have many
597 instances open at once.
598
599 if we want to have greater control over the synchronization of playback
600 between various modes, we will need to use the output arrays generated
601 by the various instances of [modefilter0]. as an example, we have
602 created example3.pd, wherein we use the array names with the [tabread]
603 object, which simply reads elements of an array. the other new object
604 here is [until], which outputs a given number of bangs, here equal to
605 the block size. (see the help for both these objects.)
606 tplarson 1.1
607 once the two output arrays have been created by the two instances of
608 [modefilter0], you can simply click the new bang to create the sum of
609 each multiplied by its amplitude, which will be displayed in the array
610 sumtest. click the message box with "sumtest normalize" to scale the
611 new array so that its absolute value never exceeds one (necessary to
612 avoid clipping). you may click the message box with "sumtest const 0"
613 to reset this array to zero.
614
615 perhaps you have noticed the absence of [trigger] objects in the new
616 code. this was done to make the code more readable, but this practice
617 should be avoided. pure data actually sends data along the connections
618 in the same order that you made them in time, although this is
619 invisible. as it happens, we made the connections in the correct order
620 for the code to work, but there is no way for one to tell the order by
621 looking at the patch.
622
623 we now move from "teaching" patches to real finalized patches. in
624 example_addition.pd we have moved the mode addition logic into a new
625 object [modeaddition] and correctly implemented the triggering. this
626 new object takes as a creation argument the name of the array for the
627 tplarson 1.1 result. this array must be created on the parent patch first. we also
628 added the ability to write the result out as wav file. to listen to the
629 new array (be sure to normalize first!) we have put an [arbitrarySR]
630 object on the parent patch, previously used only inside [modefilter0].
631
632 you will also notice that we have replaced [modefilter0] with a new
633 finalized version of the base patch, [modefilter], which has subsumed
634 the [fiddle~] object. we added two new outlets: one for the frequency
635 resulting from the mode parameter file (in units of microhertz) and one
636 for the frequency measured by the [fiddle~] object (in hertz). this
637 allows us to use the calculated transposition factor to compare the
638 input frequency (measured by fitting) to the output frequency (generated
639 by the patch). [modefilter] also sends a bang to outdone once the
640 resynthesis completes; this will be used in the next section.
641
642 now let us suppose that we would like to add an arbitrary number of
643 modes. one way to do so would be to modify [modeaddition] so that
644 rather than take two arrays and two amplitudes as input, it would take
645 only one of each and add the corresponding array to a running sum. we
646 could execute this object once for each array we want to add and then
647 normalize the result at the end. this is implemented in the object
648 tplarson 1.1 [modesum], illustrated in example_sum.pd . because we are reading and
649 writing from the same array, we need an additional [trigger] object to
650 make sure this is done in the proper order. further, we need to
651 condition the array name somewhat, due to subtleties in the way pure
652 data handles symbols (essentially repeating what is done inside
653 [modefilter]).
654
655 although there are too many overlapping connections to follow by eye, in
656 example_sum.pd we now have five instances of the [modefilter] subpatch,
657 and we have arranged them so that most of the inputs fall along the
658 right edge of the screen (the toggles are especially enlarged for ease
659 of use with a touchscreen). once you have the modes you want loaded,
660 you may add them up by clicking the corresponding bangs. the result is
661 placed in the array sumhold, which is now placed in the subpatch [pd
662 sumarray]. to listen to it, first normalize the array by clicking the
663 corresponding message (top middle of the patch) and then play it with
664 [arbitrarySR]. to create a new sum, first reset sumhold to zero. you
665 may also save to file in either the [modesum] or [pd sumarray]
666 subpatches, but notice the file name is a constant "modesum.wav", so
667 this file must be renamed if you want to save multiple sums.
668
669 tplarson 1.1
670 Section 6: Extensions
671
672 various properties of the sun are known to change with an 11 year
673 period; this variation is known as the solar cycle. since we have 15
674 years of MDI data and 9 years of HMI data so far, we now have the
675 opportunity to discover whether or not the effects of the solar cycle
676 might be audible. in order to do so, we would like to concatenate our
677 various output arrays together. for MDI, the available data span 76
678 72-day time intervals with 74 72-day timeseries (144 days of data are
679 missing). as of this writing, HMI has been operating for almost 9
680 years, or 44 contiguous 72-day timeseries so far. this is a significant
681 extension of our coverage of the solar cycle. further, one might
682 inquire as to whether there might be systematic differences between the
683 two instruments during the time of their overlap.
684
685 an example of how one might concatenate timeseries is shown in
686 example_concat.pd. here you will also notice two new objects: [modecat]
687 and [arbitrarySRmulti]. the first of these is quite simple: it takes
688 the array named on its right inlet and copies it into the array named as
689 a creation argument for the object, starting at the index given on its
690 tplarson 1.1 middle inlet. for this index to be calculated properly, you must first
691 enter the day number of the first timeseries you will process. inside
692 [modecat] it is assumed that the target array is large enough, but we
693 have already ensured this in the outer patch. as usual, you may write
694 the resulting array to a file. to listen to it, the new object
695 [arbitrarySRmulti] takes as a middle inlet the total number of
696 timeseries that have been concatenated. the same window array will be
697 applied to each segment. more complicated crossfading may be desired,
698 especially in the case of MDI, which has one of its timeseries offset
699 from the others. this is dealt with in the next example below.
700
701 we have also introduced the number of samples per day, sperday, which is
702 1440 for MDI and 1920 for HMI. in this connection, we also note that
703 for a given sample rate, HMI will require a different downshift factor
704 to achieve the same total transposition factor as we use for MDI, namely
705 only 3/4 as much. alternatively, if you want for the HMI timeseries to
706 play in the same amount of time as the MDI timeseries, use a different
707 sample rate and the same downshift factor.
708
709 another change that we have made is that by default this patch will look
710 for a different mode parameter file for each day number; this has both
711 tplarson 1.1 advantages and disadvantages. an advantage of using the averaged mode
712 parameters is that the filtering of each timeseries will use exactly the
713 same frequency interval. the peak frequency may shift within this
714 interval, but the output sound would not be contaminated by the loss or
715 addition of frequency bins at the edge of the interval. the
716 disadvantage of using the averaged mode parameters is that we lose all
717 information about how the amplitudes change with time. in any case, we
718 now give the width multiplication factor a default value of 1.2 to
719 somewhat mitigate the effect of varying widths.
720
721 of course if one is ambitious, then they could create new mode parameter
722 files where some parameters are averaged and some are not. or, by
723 interpolating mode parameters, one could attempt to use 36 day
724 timeseries.
725
726 finally, in example_concat.pd we have included an example of how to use
727 the built-in object [qlist]. its purpose is to act as a sequencer,
728 sending messages to specified [recieve] objects at certain times. it
729 reads this information from a text file. we have included two such
730 files, qlist.mdi and qlist.mdi, which list the available day numbers for
731 the two instruments. for testing, you may wish to use a subset of one
732 tplarson 1.1 of these. for example, suppose we take the first 5 lines of qlist.hmi
733 and place them in a new file, qlist.hmitest. to use it, we would then
734 click the bang to set it as the sequence file. then we would click the
735 "hmi" message box and enter "6328" for the day number of the first
736 timeseries. then we can enter the desired mode's l, n, and m as usual,
737 and click the bang to start the sequence. before listening to the
738 result, we would also enter "5" at the top of the patch for the number
739 of timeseries.
740
741 the text file read by [qlist] contains lines of the form "time
742 send_object message;". for exampe, the first line of qlist.hmi is "0
743 daynumber 6328;" which means at time zero send the message "6328" to
744 daynumber. the next line is "14000 daynumber 6400;" which means to wait
745 14 seconds and then send the message "6400" to daynumber. the 14
746 seconds is the time it takes for the fft's to run: 262144/44100 ~ 6
747 seconds to run through the block, which must happen twice, and we add an
748 additional 2 seconds for file loads and array processing. the remaining
749 lines of qlist.hmi are of this same form. as each new timeseries is
750 generated, the concatenation is triggered automatically when the
751 resynthesis completes, with the [s outdone] inside [modefilter]. once
752 the sequence is finished running, you may listen to the result using
753 tplarson 1.1 [arbitrarySRmulti].
754
755 you may also use this patch to do the same thing with MDI. the file
756 qlist.mdi contains the sequence for all 74 MDI timeseries, but for the
757 number of timeseries you should enter "76". this will leave 144 days
758 worth of the target array at zero, which is as it should be for missing
759 data. as before, make sure that the "mdi" message box has been clicked
760 and enter "1216" for the day number of the first timeseries. of course
761 you may edit qlist.mdi to make a shorter sequence; in that case adjust
762 the day number of the first timeseries and the total number
763 accordinglingly.
764
765 a close inspection of qlist.mdi will reveal the the timeseries beginning
766 on day number 2116 is offset from the others by 36 days. the 108 days
767 preceding and the 36 days following this timeseries are missing. hence,
768 if we use [arbitrarySRmulti] to listen to the full mission, the window
769 will not be applied properly to this one segment. often this is not a
770 problem, but it could be. further, we have as yet no mechanism to apply
771 any windowing to the files we write. if you listen to the concatenated
772 timeseries without windowing, you will hear clicks between some of them.
773
774 tplarson 1.1 these concerns are addressed in example_concat2.pd. we have added a new
775 object, [applywindow], which simply multiplies the array specified on
776 its right inlet with the window and puts the result in the array named
777 as a creation argument. we have also generalized the previous patch so
778 that now one may add two modes together before concatenating, and each
779 sum will be multiplied by the window beforehand. we now count the
780 number of bangs sent to outdone and trigger [modeaddition] every two of
781 them. [modeaddition] will trigger [applywindow] which will then trigger
782 [modecat]. at the end of the sequence the final array will be in
783 sumtest as before, which can be viewed by clicking [pd catarrary]. to
784 listen to the result, you will need to manually normalize sumtest.
785 also, make sure the toggle connected to [s window-on] is set to zero,
786 which it is when the patch loads. you may want to turn it on to listen
787 to individual modes.
788
789 a somewhat more sophisticated implementation of the same idea can be
790 found in example_sequencer.pd. as before, we have replaced
791 [modeaddition] with [modecat], but we now need only a single instance of
792 modefilter. another notable change from the previous example is that we
793 now use [qlist] in its other mode, where each line of the input file is
794 retrieved with a "next" message. the first "next" message will
795 tplarson 1.1 immediately send every line that is not preceded by a number.
796 subsequent "next" messages will step through the rest of the lines. in
797 our implementation the numbers at the beginning of these lines are
798 unused, so we simply use "0".
799
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