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A good little tune that was composed around the year 1515, " The Battle of Otterburn ": http://www.contemplator.com/child/otterbrn.html
Hey 2020, that video on your last post isn't available again?
lolAh well 2020, so easy, then I did take 1.5 hours to find my way out of a maze when visiting London, I think it was at Earls Court, no Hampton Court. Probably designed by King Henry V111 just to confuse people from distant lands and muddle them up.
"Octaves" of a note are just multiples of the original frequency. Let's say that a length of hollow tube has a frequency of 264 Hz and we'll call it "C".
If the length is half of the original length, the frequency will be double. This creates another "C" but one octave higher than the first (264 x 2 = 528 Hz).
If the length is quarter of the original, the frequency will be quadruple. This creates yet another "C" but two octaves higher than the original (264 x 4 = 1,056 Hz).
If the length is double, the frequency is halved. This creates "C" again but one octave lower than the original (264 / 2 = 132 Hz).
We can summarise the relationship between octaves and frequency as follows:
Tube Length Note Octave Frequency
Original C Original 264 Hz = 264 Hz
Half C Up 1 264 x 2 = 528 Hz
Quarter C Up 2 264 x 4 = 1,056 Hz
Double C Down 1 264 / 2 = 132 Hz
For simplicity, let's call 132 Hz = "C1", 264 Hz = "C2", 528 Hz = "C3" and 1,056 Hz = "C4". By convention, the first note in a numbered octave is "A" (ie G#3 is followed by A4).
Tuning Notes
Let's look at the hollow tube length again. Halving it gives us an octave higher. What happens for lengths in between? Well, for lengths in between, we get the notes in between.
If we use fractions where the numerator and denominator are whole numbers, we are creating the "just intonation" sysem of tuning. The fractions are listed in the table below and are referenced to "C".
Tube Length Frequency Note
Original ... 264 x 1 = 264 Hz ... C3
3 / 4 ... 264 x 4 / 3 = 352 Hz ... F3
2 / 3 ... 264 x 3 / 2 = 396 Hz ... G3
3 / 5 ... 264 x 5 / 3 = 440 Hz ... A4
4 / 5 ... 264 x 5 / 4 = 330 Hz ... E3
For most cultures, the "just intonation" tuning has been in use for thousands of years. This makes sense because we are using multiples of the original length (and then normalising them to the octave) to create notes.
The just-intonation tuning system works fine and sounds beautiful. However, it has only one drawback... you cannot transpose a song (ie you can only play songs in any key but "C"). When you play in another key (eg "D"), the tuning sounds wrong.
The "equal-tempered" tuning was developed to overcome this problem.
Equal-Tempered Tuning
How does it work? Well, if you think about it, tuning is not linear. You can double the frequency to get the next octave up but you have to quadruple it to get the next octave after that. Consequently, the notes within a scale are not equally distributed in frequency (nor in length).
This is how it's worked out! "A4" (the note "A" at the fourth octave) is deemed to be at 440 Hz and, therefore, "A5" will be at 880 Hz. We then take logarithms of A4 and A5 frequencies. Next, we mark in 11 equally spaced points between log(A4) and log(A5). On the logarithmic scale, this is the same as having 12 equally spaced notes per octave. We then apply arc-logarithms to those points and arrive the equal-tempered tuning.
Calculation for Equal-Tempered tuning [A4 = 440Hz]
Hertz Octave=1 Octave=2 Octave=3 Octave=4 Octave=5 Octave=6
0 A 55.000 110.000 220.000 440.000 880.000 1,760.000
1 A#/Bb 58.270 116.541 233.082 466.164 932.328 1,864.655
2 B 61.735 123.471 246.942 493.883 987.767 1,975.533
3 C 65.406 130.813 261.626 523.251 1,046.502 2,093.005
4 C#/Db 69.296 138.591 277.183 554.365 1,108.731 2,217.461
5 D 73.416 146.832 293.665 587.330 1,174.659 2,349.318
6 D#/Eb 77.782 155.563 311.127 622.254 1,244.508 2,489.016
7 E 82.407 164.814 329.628 659.255 1,318.510 2,637.020
8 F 87.307 174.614 349.228 698.456 1,396.913 2,793.826
9 F#/Gb 92.499 184.997 369.994 739.989 1,479.978 2,959.955
10 G 97.999 195.998 391.995 783.991 1,567.982 3,135.963
11 G#/Ab 103.826 207.652 415.305 830.609 1,661.219 3,322.438
12 A 110.000 220.000 440.000 880.000 1,760.000 3,520.000
Since this tuning is mathematically derived, a song will sound "correct" when played in a different key.
Special note - The decision to use A4 = 440 Hz, 12 notes per octave and naming them A to G was due to historical circumstances. Any other combination would also be valid. However, the equal-tempered tuning is now the de facto system.
PS YOu can even take the test yourself at BBC news here :-
http://news.bbc.co.uk/2/hi/science/nature/7124156.stm
Chimps beat humans in memory test
By Helen Briggs
Science reporter, BBC News
Counting test
Number memory test Chimpanzees have an extraordinary photographic memory that is far superior to ours, research suggests.
Young chimps outperformed university students in memory tests devised by Japanese scientists.
The tasks involved remembering the location of numbers on a screen, and correctly recalling the sequence.
The findings, published in Current Biology, suggest we may have under-estimated the intelligence of our closest living relatives.
Until now, it had always been assumed that chimps could not match humans in memory and other mental skills.
"There are still many people, including many biologists, who believe that humans are superior to chimpanzees in all cognitive functions," said lead researcher Tetsuro Matsuzawa of Kyoto University.
We are still underestimating the intellectual capability of chimpanzees, our evolutionary neighbours
Dr Tetsuro Matsuzawa
"No one can imagine that chimpanzees - young chimpanzees at the age of five - have a better performance in a memory task than humans.
"Here we show for the first time that young chimpanzees have an extraordinary working memory capability for numerical recollection - better than that of human adults tested in the same apparatus, following the same procedure."
Memory tests
Dr Matsuzawa and colleagues tested three pairs of mother and baby chimpanzees against university students in a memory task involving numbers.
Human v Chimp
The mothers and their five-year-old offspring had already been taught to "count" from one to nine.
During the experiment, each subject was presented with various numerals from one to nine on a touch screen monitor.
The numbers were then replaced with blank squares and the test subject had to remember which number appeared in which location, then touch the appropriate square.
They found that, in general, the young chimps performed better than their mothers and the adult humans.
The university students were slower than all of the three young chimpanzees in their response.
The researchers then varied the amount of time that the numbers appeared on-screen to compare the working memory of humans and chimps.
HOW FAST CAN YOU COUNT?
Humans can instantly "see" about four or five dots at a glance - but research suggests chimps are sometimes better than humans at counting in this way.
Take the test
Chimps performed much better than university students in speed and accuracy when the numbers appeared only briefly on screen.
The shortest time duration, 210 milliseconds, did not leave enough time for the subjects to explore the screen by eye movement - something we do all the time when we read.
This is evidence, the researchers believe, that young chimps have a photographic memory which allows them to memorise a complex scene or pattern at a glance. This is sometimes present in human children but declines with age, they say.
"Young chimpanzees have a better memory than human adults," Dr Matsuzawa told BBC News.
"We are still underestimating the intellectual capability of chimpanzees, our evolutionary neighbours."
'Ground-breaking'
Dr Lisa Parr, who works with chimps at the Yerkes Primate Center at Emory University in Atlanta, US, described the research as "ground-breaking".
Dr Matsuzawa and chimps Ai and Ayuma
She said the importance of these primates for understanding the skills necessary for the evolution of modern humans was unparalleled.
"They are our closest living relatives and thus are in a unique position to inform us about our evolutionary heritage," said Dr Parr.
"These studies tell us that elaborate short-term memory skills may have had a much more salient function in early humans than is present in modern humans, perhaps due to our increasing reliance on language-based memory skills."
The research is published in Current Biology, a publication of Cell Press.
yesssactually I'm looking for a tune (Chopin or someone) that goes ...
probably a Mazurka / fast dance thing, 6/8 I guess
dah
DAH dah dah dah dah dah DAH - dah dah dah dah
DAH dah dah - dah dah DAH - - - dah -
DAH dah dah dah dah dah DAH - dah dah dah dah
DAH dah dah - dah dah DAH
anyone know the name ? (just jokin)
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