The Earth and Beyond
The Planets.
A planet is a natural satellite of a star.
Click on a planet for more information.
Meaning of the name
Kamal - [ ... ]Or simply want to know the meaning of a particular name, then look no further. ... Kamal. Meaning:. Lotus flower. Gender: ... Find the meaning of your name. ...
utopianvision.co.uk/services/indian-names/?name=Kamal - 19k
The mathematical theory of the ET scale was first published by Chu Tsai-Yu in China during the days of the Ming Dynasty in 1584. In those days, there used to be a lot of trade between Europe and China. In 1636, i.e, barely 52 years later, Simon Stevin and Marin Mersenne wrote about ET scale in Europe. The Ming Dynasty ended in 1592, however, Chu's publication was to change the world's music forever. ET scale was used first in Germany in 1690 and the Organ in Newcastle-upon-Tyne at the St.Nicholas Church was the first to be tuned to ET scale in 1842.
Each note in the ET scale is at a distance of a multiple of 1.0594631 from the previous note. The tuning of the keyboards of Pianos, Organs, Accordions, and Harmoniums is done in this manner. This magic number is the "12th root of 2". This means that when any number is multiplied by this magic number 12 times, the original number will be doubled. (Refer to following table)
Table shows % distances of every note in Octave (Saptak) as per 12-Tone-Equitempered (ET) Scale (as tuned in Pianos, Synthesizers, Keyboards, Organs, Harmoniums, Accordions)
Remember : Multiply Hz frequency of any key by 1.0594631 to get the frequency of next key; and divide to get the frequency of the previous key.
From Sa
Take any starting key as S = say 100 Hz
Note : All the 12 notes in the Equitempered Scale are "Unnatural".
Practical Example : Komal Dhaivat of 'A' or Saphet 6 is 'F'. 'A' is 440 Hz. F will be at a distance of Komal Dhaivat i.e., at 58.74%. 440 x 58.74% + = 698.456 Hz.
In ET scale, if we listen to the Shadja and Gandhar (played together) in any key taken as the Shadja, we find that there is no consonance. This is because, the S-G distance in the tempered scale is almost 26% whereas the Natural S-G distance as heard on a Tanpura is a pure 25%. S-P distance in tempered scale is 49.83% whereas the Natural S-P distance as heard on a Tanpura is a pure 50%. Similarly, there are differences in all other notes between the ET scale and the Natural scale.
Pythagorean comma@Everything2.com - [ .... ]9 Mar 2 006 ... The frequencies,
in Hertz, of the two notes in an octave constitute a ... of
an octave into twelve equal intervals (
the 12th root of 2).
Quote:
Pythagorean comma
(thing) by JerboaKolinowski (4.7 y) Mon Mar 12 2001 at 3:54:56
A fraction, specifically 531441/524288, which is the interval (or: ratio of frequencies) between a note generated by 12 successive multiplications of a frequency by 3/2 (going 12 turns around the 'cycle of fifths') and one generated by seven doublings of the original frequency (by "going up 7 octaves")
You can arrive at this ratio as follows: starting with 1, get the next term by multiplying the previous term by 3/2 and then again by 1/2 if the result is greater than 1 (except at the very end.) This gives you:
c 1
g 3/2
'g 3/4
d 9/8
'd 9/16
a 27/32
e 81/64
'e 81/128
b 243/256
f# 729/512
'f# 729/1024
c# 2187/2048
'c# 2187/4096
g# 6561/8192
d# 19683/16384
'd# 19683/32768
a# 59049/65536
f 177147/131072
'f 177147/262144
c 531441/524288
Once you have done this little sum, you can enter the pythagorean comma (531441/524288) into a search engine like google and find out all kinds of wonderful things about music theory!
Essentially, the value represents the amount of disharmony to be distributed around the 12-tone musical scale. It amounts to about 1/55 of an octave, or, in the modern nomenclature, about 23 cents (0.23 of a semitone in equal temperament).
Different tuning systems or intonations may be characterised by where they put this extra 23 cents: the pythagorean tuning (or temperament) hides it all in one fifth (the so-called "wolf fifth" or "wolf tone"), which has the effect of making keys harmonically distant from that particular fifth sound very concordant and harmonically close ones discordant.
Other systems, like just intonation and mean temperament distribute the disharmony using an uneven sequence of rational intervals (ie ratios composed of two integers) between successive semitones, while the modern equal temperament distributes it evenly over all 12 notes, so that each successive note (going up in semitones) has the same ratio to its successor as its predecessor has to it, namely 1::2^1/12, making all keys equally discordant.
|
