Yup. Another example: in most of the world (where the television system is PAL or SECAM) movies are played on TV or released on DVD at 25 frame per second. But to achieve this frame rate, they take the theatrical film release at 24 fps and speed the video and audio up by 25/24th (4.17%). Of course almost nobody knows this because nobody notices it. https://en.wikipedia.org/wiki/576i#PAL_speed-up
For NTSC, the film release is sped down by a much smaller amount (0.1%) during the 3:2 pulldown to adjust from 30 to the exact 29.97 fps that NTSC needs.
https://www.youtube.com/watch?v=z6i1VVikRu0
This video claims that TBS is currently increasing the speed of Seinfeld episodes a whopping 9%, reducing a 25 minute episode to some 22.5 minutes.
Technology can work in your favor too!
Speed up: ] key Speed down: [ key Normal speed: = key
Also, some youtubers speak way too fast. Slowing them down helps comprehension a lot, I find.
http://www.cinemablend.com/new/Message-From-Stanley-Kubrick-...
Though, I can now instantly tell if I'm watching a PAL or NTSC version of Star Trek TNG based on the the first few bars of the opening song.
Which is weird, because I don't even have pitch perfect hearing and I'm not even that musically inclined.
I was actually thinking about a similar but less subtle example: I use a transit system that involves tagging on and off with an RFID card (Clipper on Caltrain). When you tag your card, it makes one of three different noises depending on what happen—and I couldn't possibly tell you which one corresponds to what. But if I'm actually using it and I make a mistake, I notice immediately because I'm so acclimated to the pattern it normally makes!
If I hadn't realized this, the UI for the system would have looked absolutely terrible. The different beeps are the auditory equivalent of "mystery meat navigation" but even worse because they don't carry any semantic meaning at all. But because I always use the system in the same way and the noises were consistent, it actually works really well even if I never consciously learned what noise corresponds to what.
(The fact that there are wrong ways to use the system is bad design, but it's a function of how the whole train system is set up, not the fault of Clipper's designers.)
I'd be really interested to read anything more concrete about audio affordances though, if anyone knows of links to further research, etc!
A fantastic book on how these are all related is "metaphors we live by". I'd expand on this but I'm typing on mobile and on a hurry. But seriously: read the book. It takes a long afternoon. It's great, short, illuminating, and not excessively dense or padded.
* One beep - successfully paid fare
* Two beeps (different) - successfully paid fare, and you're about to run out of money on your card
* Two beeps (equal) - tagged off (e.g. on Caltrain or San Francisco Bay Ferry)
* Three beeps - read error or insufficient value
There might be others. Indeed, they've introduced a quieter "here is a Clipper reader" beep to help visually impaired people locate them: https://vimeo.com/183916243
[1] e.g. http://www.sciencedirect.com/science/article/pii/S0010027715...
And in cinema they were better (I seem to remember Geoffrey Rush 'playing' Rachmaninov 3rd Piano Concerto in that film, at excellent pitch in the cinema), so I knew they were sometimes right. But i think the tape, TV and DVD formats I'll have rewound most often in perplexity.
Another confounding: living in California a lot and not having incorrect pitch on local copies. And nowadays, when sources are digital, bit may have originated from analogue recordings, it's now very unclear what to expect.
No. For NTSC they just drop (throw away) 1 frame from every 1000 frames, so there's no speed-up or speed-down in audio track.
https://www.lynda.com/Pro-Tools-tutorials/Understanding-vide...
Let's say you have 100 seconds of film material with corresponding audio duration. That would be exactly 2400 frames, because film is 24 fps. When you do 2:3 pulldown (that's one of the methods used to do telecine, i.e. film conversion to television format) you'll get back exactly 3000 video frames. But in NTSC format, (if you'll leave audio untouched, i.e. it's duration didn't change, it's still is 100 seconds) for 100 seconds of video duration you must display 2997 video frames, not 3000. So you just throw away 1 frame from every 1000 frames to get the exact 29.97 fps.
Doing this, at worst case you'll get audio/video desynchronization of 33 ms, which I don't think is noticeable (I tend to visually notice desynchronization when it's at about 100 ms or more). But if you'll drop that 1 excessive frame in the middle (not at the end) of the sequence of 1000 frames, you'll get audio/video desynchronization which only varies from -16 ms to +16 ms. Which is not worth the trouble of fixing this by going the other way around it: leaving video untouched and slowing down the audio by 0.1%.
A friend of mine bought the DVD of 'Rent' when it first came out in our region. A month or two after it came out, the DVD got re-issued because it's a musical, and people had been complaining that the conversion had been messed up. I think she got the re-release for free.
I could see making a case that Planck time is special enough for 440 vs 432 to matter, but it is so far off the scale of human hearing that its even integer points would form an effectively continuous scale when it comes to audio.
Hate to be a stickler, but: "...conductors of negligible cross-section and of infinite length." It's still one of my least favorite SI definitions.
- 1 Liter of pure water at 4 Celsius is 1 Kg.
- 1 Liter is a cube with 10 cm on each side.
All our music would sound wrong.
[0] of 4 measurements (761, 767, 771, 780) — the exact mean being 769.75
60 Hz is everywhere, often at a subliminal level, sometimes at an obvious/conscious level like when you walk underneath powerlines or use a garage-door opener. In any case I suspect it's a lot more obvious and perceptible to most people than any cosmic vibrations. I bet fixing your music to resonate with THAT, would (perhaps sadly) feel a lot more "cosmically in-tune" than what they're proposing with 432 Hz.
Then again, maybe it's just a number and our brains couldn't care less either way.
Meaningless in practice, but it makes it convenient to describe the tuning of, for example, a stringed instrument.
[(1,1),(9,8),(5,4),(4,3),(3,2),(5,3),(15,8),(2,1)]
Main> map (\(x,y) -> (432.0 * (fromIntegral x)) / (fromIntegral y)) majscale
[432.0,486.0,540.0,576.0,648.0,720.0,810.0,864.0]
That's pretty cool. The whole major scale comes out as whole numbers in just intonation. (In 12-tone equal temperament it doesn't, because 12TET uses the 12th root of 2 as a uniform division of the octave.) This looks like your explanation isn't just a neat trick, it's likely to be the reason why 432hz was proposed as a standard in the first place.
Main> let scale = [(1,1),(16,15),(10,9),(9,8),(6,5),(5,4),(4,3),(45,32),(3,2),(8,5),(5,3),(15,8),(9,5),(15,8),(2,1)]
Main> map (\(x,y) -> (432.0 * (fromIntegral x)) / (fromIntegral y)) scale
[432.0,460.8,480.0,486.0,518.4,540.0,576.0,607.5,648.0,691.2,720.0,810.0,777.6,810.0,864.0]
..and if we construct a more chromatic scale, not all of them come out quite as whole numbers, but we don't have any repeating decimals or anything like that (though we would if we included weirder intervals like 8/7). Nice.
edit: This works for a just major scale constructed starting from A. If you construct a scale from a different root note, it might not work out quite as cleanly.
But really, the moment you decide thirds and fifths both matter, and you want to build them on more than one note, you have to either continuously re-tune or give up on JI and worry about temperament instead. The numbers work great in a Pythagorean tuning, where only fifths matter: that tuning gets you both A=432 and C=512 (middle C = 256).
Just to pick two:
45360/100 is not that far away either
55440 (a superior highly composite number, 2ˆ4 ⋅ 3ˆ2 ⋅ 5 ⋅ 7 ⋅ 11 ) would have a built in Base-10 mnemonic
https://en.wikipedia.org/wiki/Highly_composite_number
https://en.wikipedia.org/wiki/Superior_highly_composite_numb...
Even introducing the factors of 5 creates centuries of complications (temperament) that caused us to finally give up and throw out all the integer factors, replacing them with the twelfth root of 2.
(Anyone who wants to reply saying that factors of 7 explain "blue notes", please be specific about how this works. I think this is a fictitious idea in music theory that propagates itself because it would be really cool if it were true, but the usual explanations produce false predictions.)
We know our bodies do follow circadian rhythms, so you have the initial link to length of day. Then everything else is split into sets of 12, a number with exceptional properties that natural selection may optimize towards:
"The number twelve, a superior highly composite number, is the smallest number with four non-trivial factors (2, 3, 4, 6), and the smallest to include as factors all four numbers (1 to 4) within the subitizing range. As a result of this increased factorability of the radix and its divisibility by a wide range of the most elemental numbers (whereas ten has only two non-trivial factors: 2 and 5, and not 3, 4, or 6), duodecimal representations fit more easily than decimal ones into many common patterns, as evidenced by the higher regularity observable in the duodecimal multiplication table. As a result, duodecimal has been described as the optimal number system.[4]"
https://en.wikipedia.org/wiki/Duodecimal http://dozenal.org/
Edit:
Another thing is that our current system of setting the duration of a second as a constant may be non-optimal for some purposes. Other systems let the length of time units vary with the seasons. It is interesting to think that under these systems, by maintaining the same base frequency, the tone of the note would change over the course of the year and with latitude. https://en.wikipedia.org/wiki/Roman_timekeeping
That's exactly why, actually. This is what the second was once defined as, but the problem is that the length of a day varies slightly - up to ~8s depending on the time of year and other seconds. As the article mentions, the amount of time that is defined as one second is now taken as an arbitrary fraction of the decay time for Cs-137 that is close the mean value of the length of the second defined relative to the time it takes the planet to rotate.
In terms of keeping time in our common lives it's not really a problem for there to be a little bit of ambiguity in how long a day/minute/second is, but this is important for things that rely on precision timing - like tuning in music. It'd also be crazy hard to keep track of how long a second is at any given moment, since some of the variation is random from tidal forces.
I think you could use something like this, which may be accurate enough:
https://en.wikipedia.org/wiki/Sunrise_equation
It may be more accurate to use something like the JPL ephemerides to convert between the two though:
https://naif.jpl.nasa.gov/pub/naif/toolkit_docs/FORTRAN/req/...
Finally, the current definition of a second is meant to approximate the previous definition of a second. I am saying the previous one may have some correlation with biological activity.
edit: Or perhaps you meant to tune variably, and not redefine the second. That sounds more sensible, but not as practical.
A day is defined as sunrise to sundown.
A night is defined as sundown to sunrise.
Every day consists of 12 hours.
Every night consists of 12 hours.
Each hour consists of 60 minutes.
Each minute consists of 60 seconds.
There are always 60*60*12 = 43,200 seconds each day and night.
Within a given day or night every second is of equal length.*
On the equinox (length of day = length of night) we will have a "base unit" s0.
At times/places when there is more daylight than that, the duration of a second
during the day s_d > s0 and during the night s_n < s0.
*It may be better to continuously vary the duration of a second so there
is not a sudden change at sundown/sunup. It can perhaps be linked to
https://en.wikipedia.org/wiki/Solar_zenith_angle. I think the Egyptians used
to use Sirius at night for this, but don't remember where I heard that.
Anyway now we can always be monitoring the position of the sun even when we
cannot see it at the moment.
Move to the equator? J/k, I would not think this system would be law, or used for all purposes. Despite the huge pain that dealing with timestamps from various locations can sometimes be today, I suspect my scheme would make it more difficult to synchronize long distance activities.
It would more be a chill, get back to nature, type of timekeeping. Used at resorts and rehab centers.
The only free parameters are:
F0 = the pitch of A4 on the when there are 12 hours of day/night
k = a scaling factor that determines how much to change the pitch based on duration of the variable second
I am saying the second was originally linked to length of day, so the calibrated clock should be used. Also, at some point the differences due to latitude changes, etc will be biologically indistinguishable from stuff like the effect of clouds.
How precisely is that 24.2 known I wonder..
By recording the daily rhythms of hormones and body temperatures in 24 healthy young and old men and women over a one-month period, the researchers conclude that our internal clocks run on a daily cycle of 24 hours, 11 minutes.
...
Researchers previously reported a range of 13 to 65 hours, with a median of 25 hours, 12 minutes. The variation between our subjects, with a 95 percent level of confidence, was no more than plus or minus 16 minutes, a remarkably small range.
http://news.harvard.edu/gazette/story/1999/07/human-biologic...
The second is the duration of 9 192 631 770 periods of the radiation corresponding to the transition between the two hyperfine levels of the ground state of the cesium 133 atom.
Not sure of the numerological significance of 9192631770.
It has none. It just happens to make the new cesium-based definition of a second roughly equal to the historical definition of a second as 1/86400 of a mean solar day.
Frequency choices even then were driven by cost/complexity to the extent that e.g. rather than trying to synchronise things in other ways or decoupling various clock rates, the CPU clock rate of many computer models were chosen based on how other things were clocked.
The Commodore 64's and Amiga's at least were both clocked slightly differently in the US and Europe because the CPU clock affected bus timings, and bus timings affected the custom chips for graphics and sound, and it was most convenient to time it all to match the video refresh rate of NTSC and PAL respectively.
Given that, I'm not at all surprised if the BBC decades earlier found it more complicated to handle 439Hz given whatever clock signals they had available to create it from and/or wanted to be able to match it against.
Pun intended?
(Technically nonsense, of course.)
I would take it a step further. I'd make up my own units based on seemingly natural things and then tune to numerically interesting values of those.
"This next song's beat is 432 times faster than a cricket chirping at 50 degrees C."
Edit: An exception would be trying to 'fatten' the sound of an acoustic guitar and using a 25-35ms delay, which puts it close enough that it's not perceivable as a delay, but will provide a noticeable effect on the tone of the guitar.
Presumably the music's timing is based on seconds, though, right? That might conceivably mean that primeness could potentially matter. I don't really think that it does, mind. But I'm not so quick to think that it doesn't, either.
I recognize that this bit is entirely personal, but I think that can make otherwise "simple" music more enjoyable. But my enjoyment of music is almost entirely dependent on the careful management of the "Wall of Sound" effect and by how much noise (in the form of timbre, attacks, number of different voices) is introduced or removed from the track. And I think that's the key difference between, say: a library piece, or a movie score; and pieces meant to be listened on their own.
Also, the expression "cargo cult numerology" pretty much made my day.
Tighter differences between each notes' frequencies??
Please explain this thought.
For instance, a half-tone from 432Hz is 457.69Hz, which gives out a difference of 25.69Hz; but a half-tone from 440Hz is 446.16Hz, which gives out a difference of 26.16Hz. Between 432Hz and 864Hz we can fit a whole scale, while in the same frequency range we'd be missing a note with 440Hz tuning.
Of course, this is a slight difference and it might not be noticeable at all. I personally don't hear much difference between the two tuning. Instead, I'm playing devil's advocate.
Then most songs would sound 'better' a half-step down, etc.
The boiling point of water in Celsius is 100 degrees, and the freezing point is 0 degrees; in Fahrenheit, 212 and 32, respectively. What's significant is the scale of each unit. 99C is colder than 211 Fahrenheit.
In the case of music, which is all about relative frequencies, establishing A determines the size of the steps. The above poster is proposing that A=432 yields more interesting frequency relationships than A=440. I have no idea.
Consider the beggining of Bach's "Little" Fugue in G Minor (BWV 578), where the subject of the fugue is first introduced by a soprano voice and then repeated by an alto voice, while the soprano voice does the coutersubject. I'd say that, played in isolation, the melody sounds better when sung by the alto voice. But lowering the whole Fugue by a half-step wouldn't make it much better.
But unless the music also contains some 1Hz modulation (or a power-of-two multiple thereof) then the 432 base frequency isn't related to anything fundamental in musical terms. Speaking as a DJ, if you take a track and play it a little bit faster or slower it still sounds great or awful as at the default speed in most cases. 432Hz vs 440Hz is a ~2% difference, while DJ equipment commonly allows for +/-10% pitch variation so you can match the pace of different tracks smoothly while people are dancing. Only the very tiny number of people with perfect pitch find this disorienting to listen to. If there were really something special about the duration of the second and the base pitch relative to that, you'd have expected it to emerge from dancefloors years ago. In reality 432Hz is basically cargo cult numerology, something fun to think about when you are not having any success coming up with a kickass tune. And kickass tunes derive their quality from the relative rations of the note pitches, not from some absolute Magic Frequency.
Trust me on this. I really love numerology, sacred geometry and so on, and I try to integrate this into my artistic work regardless of medium. I would love for there to be some special key that would unlock the gate to cosmic/ biological/ quantum harmony and allow my artistic work to automatically echo the heartbeat of the universe. I'm a mystic by temperament and have been looking for such things my whole life. I would go so far as to say I have some religious faith in the significance of such things. But this ain't it.