In part one I discussed frequency content of the standard chromatic and C Major diatonic scales. I’d like to move forward by discussing the frequency content of the C class of chords on piano.
Chords With Root Note C
If we take a look at the various C Chords in terms of frequency content, and format our plots such that each tick on the vertical axis coincides with the frequency content in semitone intervals, we obtain the following plot:
I’ll probably come back and re-organize this plot as the ordering of chords is a bit crazy since the python script I wrote just iterated through keys in a dictionary… but that’s a whole other story; for now it’s good enough.
From the above plot we can see that we are using A440 concert pitch, as A4 appears as 440 hz, and A5 appears as 880 hz, which is one octave higher.
Let’s take this same plot and change the vertical scale from frequency to number of semitone intervals.
From this plot it’s very easy to see that all of the C chords consist of a root note (in this case middle C), most have a major third as a second note, which is 4 semitones above the root, all the minor notes have a minor third as a second note, which is 3 semitones above the root, and nearly all have a perfect fifth as the third root, which is 7 semitones above the root. All of the numbered chords 7, 9, 11, and 13 have a minor seventh as the fourth note, which is 10 semitones above the root. All chords numbered 9, 11, and 13 have a major ninth as the fifth note, which is 14 semitones above the root, or a perfect octave plus a major second. All chords numbered 11 and 13 have an eleventh as the 6th note, or a perfect octave plus a perfect fourth, which is 17 semitones above the root, and finally both 13 chord have a thirteenth as the 7th note, or a perfect octave plus a major sixth, which is 21 semitones above the root.
Now, there’s one last easy thing we can do, and that’s to show the same plots in terms of the note contents of the chords, again, assuming we are in the fourth octave.
Since I’m using Linux For Tegra 28.1, checkout their vL4T28.1 release tag.
git checkout vL4T28.1
Run the get kernel sources script (note: this will take a while):
sudo ./getKernelSources.sh
Make sure that loadable kernel modules are enabled, and go ahead and write the kernel configuration file to .config, then let’s try to build the vanilla kernel to see if we have any issues to begin with.
sudo ./makeKernel.sh
Everything builds fine for me, so let’s get to patching the kernel with the PREEMPT_RT patch.
Kernel builds are typically located in the /usr/src directory, so let’s cd to where this kernel build is occurring: cd /usr/src/kernel/kernel-4.4
Get the rt preempt patch that EXACTLY matches our linux kernel version:
Make sure we have the xz-utils package to unpack .xz files: sudo apt install xz-utils unxz patch-4.4.38-rt49.patch.xz
Dry Run The Patch
Now, let’s do a patch dry run to see what we’re getting ourselves into: patch -p1 --dry-run <patch-4.4.38-rt49.patch | grep FAIL
Ok, so we get some hunks that fail, but it doesn’t look like it will be anything intractable. Let’s just go ahead and patch it, redirect the output to a log file and see what we have to manually fix.
So, it looks like we have three files that have been rejected, with rejection details being saved to the corresponding .rej files. Let’s take a look at the first, cpu.c.rej.
cd kernel ls
We see four files that we are interested in: cpu.c, which is the patched file, cpu.c.orig, which is the original, unpatched file, cpu.c.rej, which shows the rejected patch attempt, and cpu.o, which is the created object file.
Let’s open up cpu.c.rej and see what the issue is:
The exact line numbering that’s indicated by the reject file for kernel patches on this system has yet to make sense to me. It appears to be indicating that the issue in the original file starts at line 740 and persists for 9 lines, whereas the issue in the new file starts at line 1056 and goes for 14 lines. However, if we search for where the changes are we get to line 429… I’m assuming that it’s just a calling function that is somehow being caught at line 740, but in any case, let’s continue.
Begin The Manual Patching…
So, if we open up all three files, cpu.c, cpu.c.rej and cpu.c.orig, we can pretty easily see what the issue is: there is a trace_sched_cpu_hotplug()function call in there that the patch file wasn’t expecting.
Indeed, if we check the patch file and search for out_release, we find:
This entry in the patch file indicates that it wants to add cpu_unplug_done(cpu);and out_cancel:after out_release and before cpu_hotplug_done(), but there is an extra trace_sched_cpu_hotplug()in there messing things up. Since the patch file didn’t expect this, it fails because it doesn’t quite know what to do. Let’s manually patch it by placing this inside of out cancel:
Let’s save cpu.c and consider this file patched!
Yeah!
Moving on to the next rejected file, suspend.c.rej, we see that this patch failed in two places:
Let’s search for this area in the patched file to see what the issue is.
So, here we see the first issue, thre is a pm_suspend_marker()call in between return -EINVAL;and error =. Let’s manually patch this part and find the second issue.
Finding the second issue, it looks like the line pm_suspend_marker("exit")is unexpected, so let’s manually patch this like we did the first issue.
Save it and consider it patched!
Now, on to the third one: /net/ipv4/tcp_ipv4.c.rej
And proceeding like we did before to find these same spots in the output patched file:
We again see that there is an unexpected line (the .uid method). Manually add the lock and unlock function calls:
Finding the second section that was rejected, we also see it’s an issue involving locks:
Save it, and we should (hopefully) be done patching!
Building After The Manual Patch
Now, let’s pick up where the jetson hacks scripts have left off:
cd kernel/kernel-4.4 make xconfig
Before changing any of the configuration parameters, let’s verify that things compile without tweaking the preemption model. Just go ahead and save the default values as .config. Continuing on with the jetson hacks stuff, lets go back to the git directory and source the makeKernel.shscript and see if it compiles.
Ok, shit blows up, not what we were hoping to see. It looks like this may be an issue in the way nvidia prefers you build kernels, going back and seeing how good our GoogleFu skills are we find this discussion:
It looks like we need to set some environment variables and select the make output directory. Let’s make these changes in the jetson hacks makeKernel.sh shell script.
Ok, let’s try making again.
We get a bunch of garbage, so let’s start from a clean slate using make mrproperlike it suggests.
we need sudo…
Ok, then let’s manually call the commands:
mkdir $TEGRA_KERNEL_OUT make O=$TEGRA_KERNEL_OUT tegra18_defconfig make O=$TEGRA_KERNEL_OUT prepare make O=$TEGRA_KERNEL_OUT zImage
It looks like we are seeing an issue with compiler warning flags. From a little more GoogleFu it appears that if we are using gcc5.x or higher we can suppress these warnings for incompatible pointer type. Let’s see if we need to chance which version of gcc we are using:
Since we’re using gcc 5.4.0 we can go into the main kernel Makefile and set -Wno-incompatible-pointer-types.
nano /usr/src/kernel/kernel-4.4/Makefile and then search for the kbuild flag corresponding to incompatible pointer types.
Let’s change this line that enforces correct pointer usage to: KBUILD_CFLAGS += $(call cc-option,-Wnoerror=incompatible-pointer-types) Note: I’m not very concerned about doing this since the only places that this occurs is in the cryptography library. Let’s save this change and manually try building the kernel image.
nvidia@tegra-ubuntu:/usr/src/kernel/kernel-4.4$ sudo make -j4 O=$TEGRA_KERNEL_OUT zImage
HO. LEE. SHIT. It built.
Selecting The Preemption Model
Phew, ok, let’s go back and make the config file and select the fully preemptive preemption model.
sudo rm -rf out/ mkdir $TEGRA_KERNEL_OUT make O=$TEGRA_KERNEL_OUT tegra18_defconfig make O=$TEGRA_KERNEL_OUT xconfig
In the configuration menu let’s go to Kernel Features -> Preemption Model -> Fully Preemptible Kernel (RT) Note: if you are using a different system this will probably appear under a different tab.
If you want, you can also select to append a string to the local version. I was uncertain if it would automatically append -rt49, so I manually added this to the local version name. It does indeed add -rt49, so this was redundant.
Save and quit xconfig.
Continuing on, prepare the kernel and make it. make -j4 O=$TEGRA_KERNEL_OUT prepare sudo make -j4 O=$TEGRA_KERNEL_OUT zImage
This builds fine, so let’s make and install the kernel modules and device tree blobs.
sudo make O=$TEGRA_KERNEL_OUT dtb sudo make O=$TEGRA_KERNEL_OUT modules sudo make O=$TEGRA_KERNEL_OUT modules_install
This by default installs modules in /lib/modules/ I’m unsure if we need the compressed zImage or the regular binary Image file, so let’s just copy both over from the output directory:
sudo cp arch/arm64/boot/zImage /boot/zImage
sudo cp arch/arm64/boot/Image /boot/Image
Let’s verify that the compressed and binary files have been copied to the boot directory.
Looks good! Now, for the new kernel to take effect, reboot the machine and verify that the new kernel is being used. Let’s note the original system information using uname -rand uname -a.
Verify The Kernel Is Loaded
After rebooting, let’s verify that the kernel name has changed to reflect our patched image:
Cool! It looks like the new kernel has taken effect. Now, the last check to be performed is to start a thread with priority level 99 and verify that it in fact shows this priority level in htop.
Verifying The Kernel Is Fully Preemptible
We can create a simple little function to do this: make sure to include the pthread.h and sched files
Alright, let’s compile this and run and see how it looks in htop.
Awesome, htop shows this thread has a priority level of RT, which is the highest allowed by the system. Looks like we are finished!
Thanks to all these posts for helping me through this:
One thing about music theory that’s always bothered me is the disconnect between pitch interval and pitch frequency content. Hopefully this will become a little series where I attempt to easily bridge this gap with frequency domain plots.
Chromatic Scale
First things first, let’s take a look at the chromatic scale ranging from middle c (c’) to tenor c (c”), using scientific pitch notation ISO 16, with A 440hz concert pitch (A above middle C having a pitch of 440 hz):
Chromatic Scale Frequencies
It’s easy to see a few things from this plot:
The notes of the chromatic scale are A, A#, B, C, C#, D, D#, E, F, F#, G, G#.
Some people refer to the chromatic scale as the dodecatonic scale as it consists of 12 notes per octave. In this case tonic refers to tones, not the presence of a tonic. In 12-tone equal temperament each tone is separated by a 100 cent wide semitone interval, thereby making the chromatic scale nondiatonic with no tonic note.
Each interval of the chromatic scale consists of one semitone, or half step, indicated by the letter S.
Each of the intervals are made up of 100 logarithmic units of measure named cents. Aside: Like the decibel’s relation to intensity, a cent is a ratio between two close frequencies, therefore, the frequency range encompassed by a cent must be proportional to the two frequencies. The number of cents between two pitches, a and b, can be calculated by:
Mathematically, the pitch frequency increases exponentially as a function of number of intervals, as dictated by the following equation:
where is the output frequency, is the starting input frequency, and is the number of intervals from the input pitch.
Due to the fact that the chromatic scale is exponential, and doubles every 12 intervals, it results in a monotonically increasing linear plot when viewed with semi-log axes.
Intervals
Visualizing the chromatic scale on a semi-log plot makes understanding intervals very straight forward.
minor seconds: 1 semitone wide (100 cents, or 1 interval) major seconds: 2 semitones wide minor thirds: 3 semitones wide major thirds: 4 semitones wide perfect fourths: 5 semitones wide diminished fifths: 6 semitones wide (also called an augmented fourth) perfect fifths: 7 semitones wide minor sixths: 8 semitones wide (also called an augmented fifth) major sixths: 9 semitones wide minor sevenths: 10 semitones wide major sevenths: 11 semitones wide perfect octaves: 12 semitones wide
Diatonic Scale
Moving on from the chromatic scale, let’s look at the diatonic major scale (Ionian mode) in C.
Looking at the diatonic major scale in C we observe some readily apparent things:
The diatonic scale consists of 7 distinct notes per octave, A, B, C, D, E, F, G. Some people may refer to this as being heptatonic as it contains 7 tones.
The intervals between the pitches of the chromatic scale are structured in a manner to separate the semitone (half step) intervals as much as possible, being separated from each other by a series of two or three tones (full steps).
The notes of the diatonic scale are made up of 8 degrees with the following names: 1) Tonic (key note) 2) Supertonic 3) Mediant 4) Subdominant 5) Dominant 6) Submediant 7) Subtonic (leading tone) 8) Tonic (Octave)
The tonic note is the first scale degree of a diatonic scale. Similar to how a root is the reference note of a chord, a tonic is the reference note of a scale. As the name implies, the diatonic scale consists of two tonic notes, with the second being one octave higher than the first.
Another characteristic of the diatonic scale is the presence of a subtonic note, which is the seventh scale degree. This is a note that resolves to a note one semitone higher or lower, meaning that it moves from dissonance, or an unstable sound, to consonance, a stable sound. The seventh scale degree has a strong affinity for, and leads melodically to, the tonic.
Moving On
Further on in this series I will plot other scales and modes, as well as common chords, chord progressions and songs in terms of frequency vs time.
Alright, this is one that people have asked me to explain to them at the gym using actual numbers on more than one equation. It’s easy to understand that a barbell with weights only loaded on one side is able to balance, but people have asked some variant of “how stable is a bar that has weights on one side?” Well, let’s get into it!
Quick Physics Primer
In order to answer this one, we’ll take advantage of a branch of classical mechanics that people typically call statics; that is, analysis of forces on a body that result in no motion. Two concepts that you will have to understand are the notions of balance of forces, and balance of moments. A balance of forces is easy enough to imagine, a simple example is if you were to push horizontally on a wall, the wall pushes back on you with the exact same amount of force in the opposite direction, thereby causing the forces acting on the person-wall system to balance to 0. Balance of moments is exactly the same, but using moments, that is, forces that cause rotational motion.; most people will call this a torque, but physics uses the term moment. Think of two kids on a seesaw, one weighs 90 pounds and the other 80 pounds, each 4 feet from the center pivot point. The moment created by the 90 pound child we will call M1, and has magnitude 90 lbs x 4 feet = 360 lb-ft. Similarly, the moment created by the second child is 80 lbs x 4 feet = 320 lb-ft. So, if they are at rest and the smaller child is up in the air and the larger child is sitting on the ground, how much force is the ground exerting against the larger child? Easy! We know our forces and moments have to balance because there is no motion, so by looking at our moments we can construct the equation 360 = 320 + ground. Solving for the ground force we are left with 40 lb-ft, which upon dividing by the distance the force is from the center pivot, we obtain 10 pounds, as one would expect. Alright, now on to answering the question we actually care about.
Solution
Since we are dealing with moments, we need to know the actual dimensions of the barbell and weights we are asking about. Let’s assume we are using a Rogue Ohio Bar, and it’s being loaded with Rogue HG 2.0 bumper plates. I’ve chosen these plates because they are rather thick and will create a worst case scenario since they will force the loaded weight to hang further to one side. Now, with this bar and plates the dimensions we are about are as follows:
Unbalanced 45 lb Barbell
With all of this in mind, let’s create a free body diagram to visualize all of the forces and moments.
Unbalanced Barbell FBD
Alright, let’s talk about this picture. There are five main things that I’ve added that we care about: Forces acting on the system from the weight plates F1, and F2, forces acting on the system from the weight of the barbell, F3, forces acting on the system from the reactionary (balancing) forces caused by the squat rack R1, R2, the coordinate system that I’ve chosen to use, describing the X, Y, Z directions and coordinate system origin, O, from which all of my measurements will be relative to, and the distances these forces are from the origin. Since the barbell is axisymmetric we can apply the 45 pound force resulting from the mass of the barbell as a point force acting at its center of mass. Similarly, we can do this with the two plates. You may notice that I chose to place my coordinate system origin through the line of action of the first reactionary force, this is on purpose. This allows me to neglect the moment created by R1 since it passes through the origin, resulting in a moment of .
Working Out The Math
With all of this illustrated, let’s go ahead and construct our force and moment balance equations.
Sum of Forces:
Sum of Moments:
If we rearrange these equations we obtain:
We also know that forces F1, F2, and F3 are all 45 pounds. We can plug these values into equations 1 and 2 and solve for the second reactionary force. Doing this allows us to find out how much force the far side squat rack support arm is pushing back against the bar with. When this value drops to 0 or lower, the bar will lose contact with the rack since the support arm would then have to be pulling that side of the bar down in the negative y direction for forces to balance.
Simplifying further yields:
Finally solving for the second reactionary moment:
And dividing by the lever arm distance to obtain the reactionary force:
Now that we know R2, we can plug this in to equation 1 to find the first reactionary force.
Solving for R1 we obtain:
Cool! So we can see that with this setup the barbell is still stable on the squat rack as the second support arm is exerting more than 8.5 lbs upwards to keep the barbell from falling.
Moving On
In a second part to this I will address the worst case scenario of when the bar is pulled all the way to one side, thereby creating longer lever arms for the plates, and a shorter lever arm for the mass of the barbell. We can even go as far as to solve for what kind of force would be required to start the bar tipping off the rack if someone were to bump in to it from the far side. Until then, happy lifting!
My First Summer in the Sierra is based upon John Muir’s personal diary, beginning June 3rd, 1869 and ending September 22nd of the same year. During this time he was employed by a sheep owner named Mr. Delaney to assist in herding his flock to the headwaters of the Merced and Tuolumne rivers. Although he was employed to assist in the sheep herding, he was left mostly to his own devices to explore, investigate the flora, bask in the religious grandeur of the alpine scenery, and document it, all while being accompanied by a St. Bernard named Carlo.
Personal Relation To The Book
After moving from California back home to Minnesota, I found myself soon lamenting the lack of natural beauty and respect commanded by the high sierras. Among other outdoors type books, I was hoping this would assist in scratching my itch for alpine adventure, though, not so surprisingly, it only exacerbated that itch.
One of the things to which I could easily relate was Muir’s interpretation of these vistas as being religious; seemingly literally bringing him closer to god. One thing I have always had a difficult time elucidating to others is the bond one feels with a mountain when they are on it by themselves, in the back country, with no one around. In doing such a thing by oneself, everything is amplified; the emotions of every little noise you hear are heightened, the feeling of accomplishment when summitting is enhanced, the work involved even seems to be greater when one realizes they are the only one that can safely bring themselves out alive. This appeared to be something Muir realized, and in feeling so connected to the landscape, in it’s immense beauty, he was positive that there could not possibly be any more manifest evidence of the existence of God than in the Yosemite valley.
One thing is also evident when reading My First Summer: Muir was a damned crazy man. He longed to climb trees during storms just to experience the storm the way a tree would. To charge at bears to see what they would look like while running; it is somewhat surprising that his natural curiosity didn’t result in his demise. I do find it difficult to believe that this “interview”, as he calls it, actually happened, along with the story of him “feeling” like his old professor friend was in the valley, so he rushed head long down a mountain to realize he was indeed there.
His eloquence in documenting this vastly emotional and religious summer has surely helped advanced his fame; I am curious though, how much time he spent post-processing his manuscripts to achieve the literary beauty we are left with today. One more thing is obvious from this work, and that is Muir loved to be overly didactic when it comes to flora. The book is seemingly bubbling with Muir’s excitement and enthusiasm for the Yosemite valley; appearing to be one of the first of many zealots worshiping the spiritual power of the region.
Favorite Quotes
Now, some of the quotes from the book that were saturated with highlighter:
“We are now in the mountains and they are in us, kindling enthusiasm, making every nerve quiver, filling every pore and cell of us. Our flesh-and-bone tabernacle seems transparent as glass to the beauty about us, as if truly an inseparable part of it, thrilling with the air and trees, streams and rocks, in the waves of the sun – a part of all nature, neither old nor young, sick nor well, but immortal.”
In speaking regarding the lowly life of a shephard: “Coming into his dingy hovel-cabin at night, stupidly weary, he finds nothing to balance and level his life with the universe. No, after his dull drag all day after the sheep, he must get his supper… and depends on the genial stupefaction of tobacco for the rest.”
“I have oftentimes found the curious twining lily… Like man, it has few friends, and the blind question, ‘Why was it made?’ goes on and on with never a guess that first of all it might have been made for itself.”
“Another glorious Sierra day in which one seems to be dissolved and absorbed and sent pulsing onward we know not where. Life seems neither long nor short, and we take no more heed to save time or make haste than do the trees and stars. This is true freedom, a good practical sort of immortality.”
“The daylight fades, the color spell is broken, and the forest breathes free in the night breeze beneath the stars.”
In speaking about escaped sheep: “Having escaped restraint, they were, like some people we know of, afraid of their freedom, did not know what to do with it, and seemed glad to get back into the old familiar bondage.”
“Oh, these vase, calm, measureless mountain days, inciting at once to work and rest! Days in whose light everything seems equally divine, opening a thousand windows to show us God. Nevermore, however weary, should one faint by the way who gains the blessings of one mountain day; whatever his fate, long life, short life, stormy or calm, he is rich forever.”
“Every morning, arising from the death of sleep, the happy plants and all our fellow animal creatures great and small, and even the rocks, seemed to be shouting, ‘Awake, awake, rejoice, rejoice, come love us and join in our song. Come! Come!’ Looking back through the stillness and romantic enchanting beauty and peace of the camp grove, this June seems the greatest of all the months of my life, the most truly, divinely free, boundless like eternity, immortal. Everything in it seems equally divine – one smooth, pure, wild glow of Heaven’s love, never to be blotted or blurred by anything past or to come.”
“So extravagant is Nature with her choicest treasures, spending plant beauty as she spends sunshine, pouring it forth into land and sea, garden and desert. And so the beauty of lilies falls on angles and men, bears and squirrels, wolves and sheep, birds and bees, but as far as I have seen, man alone, and the animals he tames, destroy these gardens.”
In regards to his encounter with a bear: “… I thought I should like to see his gait in running, so I made a sudden rush at him, shouting and swinging my hat to frighten him, expecting to see him make haste to get away, But to my dismay he did not run or show any sign of running. On the contrary, he stood his ground ready to fight and defend himself, lowered his head, thrust it forward, and looked sharply and fiercely at me… We stood staring at each other in solemn silence within a dozen yards or thereabouts… How long our awfully strenuous interview lasted, I don’t know; but at length in the slow fullness of time he pulled his huge paws down off the log, and with magnificent deliberation turned and walked leisurely up the meadow…”
“As to our own work, duty, influence, etc., concerning which so much fussy pother is made, it will not fail of its due effect, though, like a lichen on a stone, we keep silent.”
“No wonder the hills and groves were God’s first temples, and the more they are cut down and hewn into cathedrals and churches,the farther off and dimmer seems the Lord himself.”
“It seems strange that visitors to Yosemite should be so little influenced by its novel grandeur, as if their eyes were bandaged and their ears stopped. Most of those I saw yesterday were looking down as if wholly unconscious of anything going on about them, while the sublime rocks were trembling with the tones of the mighty chanting congregation of waters gathered from all the mountains round about, making music that might draw angels out of heaven.”
This Is Water: Some Thoughts, Delivered on a Significant Occasion, about Living a Compassionate Life by David Foster Wallace
Summary
This is Water is an essay written by writer and philosopher David Foster Wallace, delivered as a commencement address in 2005. It is a short essay, composed at times with only a few words per page, reading just as much like poetry as philosophical essay. At the heart of the essay the author asks, and in turn answers the questions: How do we keep from going through adult life unconsciously, comfortably entrenched in habit? How do we remove ourselves from the foreground of our thoughts and achieve compassion?
In short, Wallace makes his case to the 2005 graduating class of Kenyon College, that the true value of a liberal arts education is “learning how to think”, as the platitude often goes, which he expands to mean having the ability to choose to live your life consciously and compassionately. The first few sentences explain the essay’s namesake: “There are these two young fish swimming along and they happen tot meet an older fish swimming the other way, who nods at them and says, ‘Morning, boys. How’s the water?’ And the two young fish swim on for a bit, and eventually one of them looks over at the other and goes, ‘What the hell is water?'” He ultimately resolves to explain his didactic parable as an example that many adults, who have not been taught how to think, live the majority of their life in an unconscious state, completely unaware of the ubiquitous things around them.
Favorite Quotes
What follows are some of the sentences that were highlighted by the time I finished reading the essay.
“True, there are plenty of religious people who seem arrogantly certain of their own interpretations, too. They’re probably even more repulsive than atheists, at least to most of us here, but the fact is that the religious dogmatists’ problem is exactly the same as the story’s atheists – arrogance, blind certainty, a closed-mindedness that’s like an imprisonment so complete that the prisoner doesn’t even know he’s locked up. The point here is that I think this is one part of what the liberal arts mantra of “teaching me how to think” is really supposed to mean: to be just a little less arrogant, to have some “critical awareness” about myself and my certainties… because a huge percentage of the stuff that I tend to be automatically certain of is, it turns out, totally wrong and deluded.”
“Probably the most dangerous thing about an academic education, at least in my own case, is that it enables my tendency to over-intellectualize stuff, to get lost in abstract thinking instead of simply paying attention to what’s going on in front of me. Instead of paying attention to what’s going on inside me. As I’m sure you guys know by now, it is extremely difficult to stay alert and attentive instead of getting hypnotized by the constant monologue inside your head.”
“‘Learning how to think’ really means learning how to exercise some control over how and what you think.”
“And I submit that this is what the real, no-shit value of your liberal arts education is supposed to be about: How to keep from going through your comfortable, prosperous, respectable adult life dead, unconscious, a slave to your head and to your natural default setting of being uniquely, completely, imperially alone, day in and day out.”
“If you’re automatically sure that you know what reality is and who and what is really important – if you want to operate on your default setting – then you, like me, probably will not consider possibilities that aren’t pointless and annoying. But if you’ve really learned how to think, how to pay attention, then you will know you have other options. It will actually be within your power to experience a crowded, hot, slow, consumer-hell-type situation as not only meaningful, but sacred, on fire with the same force that lit the stars – compassion, love, the subsurface unity of all things.”
“…Look, the insidious thing about these forms of worship is not that they’re evil or sinful; it is that they are unconscious. They are default settings. They’re the kind of worship you just gradually slip into, day after day, getting more and more selective about what you see and how you measure value without ever being fully aware that that’s what you’re doing.”
“The really important kind of freedom involves attention, and awareness, and discipline, and effort, and being able truly to care about other people and to sacrifice for them, over and over, in myriad petty little unsexy ways, every day. That is real freedom. That is being taught how to think. The alternative is unconsciousness, the default setting, the ‘rat race’ – the constant, gnawing sense of having had and lose some infinite thing.”
“The capital-T Truth is about life before death. It is about making it to thirty, or maybe even fifty, without wanting to shoot yourself in the head. It is about the real value of a real education, which has nothing to do with grades or degrees and everything to do with simple awareness – awareness of what is so real and essential, so hidden in plain sight all around us, that we have to keep reminding ourselves over and over: ‘This is water’. ‘This is water’. ‘These Eskimos might be much more than they seem.’ It is unimaginably hard to do this – to live consciously, adultly, day in and day out.”
is the output frequency, 
is the starting input frequency, and 
is the number of intervals from the input pitch.
.
