
	Where results make sense

Topic: Twelfth root of two

Related Topics

square root

roots revival

root of unity

roots reggae

root mathematics

root mean square

root computing

root finding algorithm

root beer

American roots music

roots rock reggae

Kellogg, Brown and Root

In the News (Fri 17 Feb 12)

EXECUTIVE POWER

Iran

ANALYSIS

Pakistan

Family compact

	Shaku 2.2 Shakuhachi
		It's the inverse of 6% or the 1.6817 flute.
		(the twelfth root of two) and the length in shakus with the same factor.
		This is closer to reality (the builder's experience) than the twelfth root of two used in the progression of the notes.
	www.navaching.com /shaku/shaktwo.html (1435 words)

	Twelve-Tone Musical Scale
		The distance between two notes, measured as the ratio of their pitches, is called an interval.
		Larger intervals are multiples of the twelfth root of two, as shown in the table below.
		For example, the fifth, obtained by multiplying the twelfth root of two by itself seven times, is 1.498, which is very nearly a perfect 1.500.
	thinkzone.wlonk.com /Music/12Tone.htm (790 words)

	Tuning Systems (Site not responding. Last check: 2007-10-17)
		When one note has a frequency that is exactly two times the frequency of a second note, then the first note is one octave higher than the second note.
		Two notes that are exactly one octave apart sound good together because their frequencies are related in such a simple way.
		Figure 4: In equal temperament, the ratio of frequencies in a semitone is the twelfth root of two.
	cnx.org /content/m11639/latest (4071 words)

	Frequency
		The reason for the "twelfth root" is there are twelve notes per musical octave.
		The reason for the "two" is that a musical octave is generally defined as a doubling of frequency (x2).
		For "equal temperament" the frequency of the next note is derived by multiplying the frequency of the previous note, by 1.05946309435929526456182529494634 (which is approximately the twelfth root of 2).
	www.radio-flier.com /frequency1.htm (93 words)

	Music & Noise (Site not responding. Last check: 2007-10-17)
		octave -- an interval of two to one
		Especially harsh is the dissonance between notes whose frequencies are incommensurable; such a case occurs when one has two strings in unison and sounds one of them open, together with a part of the other which bears the same ratio as the side of a square bears to the diagonal ….
		Six semitones is equal to the twelfth root of two to the sixth power, which is equal to the square root of two.
	hypertextbook.com /physics/waves/music (1639 words)

	Twelfth root of two - Wikipedia, the free encyclopedia
		Systems of unequal temperament lacked the ability for free tonal modulation, as intervals in some keys were intolerably bad (which were referred to as "wolf fifths", as an allusion to howling).
		Since a musical interval is a ratio of frequencies, and the equal tempered chromatic scale is a way of dividing the octave (which has a ratio of 2:1) into twelve equal parts, the semitone must be that ratio which when multiplied by itself twelve times will be equal to two.
		The twelfth root of two was first calculated accurately by the Chinese mathematician Prince Chu Tsai-Yu of the Ming Dynasty.
	en.wikipedia.org /wiki/Twelfth_root_of_two (332 words)

	Search Results for root*
		Fibonacci proves that the root of the equation is neither an integer nor a fraction, nor the square root of a fraction.
		This fact having attracted notice, two months later he was challenged to extract the square root of a number of 53 digits; this he performed mentally, and a month later he dictated the answer which he had not meantime committed to writing.
		The root of the difficulty is that the proper medium for the accurate expression of physical principles, methods, and conclusions is mathematics: and that physical mathematics, regarded as a language, has an almost untranslatable vocabulary.
	www-groups.dcs.st-and.ac.uk /~history/Search/historysearch.cgi?SUGGESTION=root*&CONTEXT=1 (13217 words)

	CJOnline.com \| The Topeka Capital-Journal \| The Bard gets a break at TCT 05/24/02
		In this early scene from "Twelfth Night," Viola (Angela Peckham) finds herself shipwrecked in Illyria, where warnings by The Captain (Chuck Hughes) compel her to disguise herself as a boy and assume the name Cesario for protection.
		Not only that, but because Reilly was directing two other shows, the cast had to rehearse at odd hours.
		Reilly agreed, adding not only is the word "audience" derived from a root that means "to hear," people in Shakespeare's time would say they were going to hear a play rather than see one.
	www.cjonline.com /stories/052402/wee_twelfthnight.shtml (945 words)

	ChordWizard How Music Works (Site not responding. Last check: 2007-10-17)
		There is a magic number in western music, known as the twelfth root of two, and it has a value of approximately 1.0595.
		The frequency of a note, when multiplied by the twelfth root of two, gives the frequency of the next note up.
		This method of dividing the octave using the twelfth root of two is known as equal temperament tuning, pioneered several centuries ago in the time of JS Bach.
	www.chordwizard.com /hmw109.asp (369 words)

	Physics behind music
		Two frequncies have pitches an octave apart if one frequency is double the other.
		Each corresponding frequency is multiplied by the twelfth root of two, so that by the end of the octave you will have multiplied by the twelfth root of two twelve times - for a factor of two, which is correct for the two ends of an octave.
		The keyboardist's twelfth roots do not exactly represent true thirds fifths and sevenths as played on a stringed instrument.
	www.physicsforums.com /showthread.php?p=45245 (916 words)

	Folk File: T
		Two musicologists, Austin and Alta Fife, elaborated greatly on "Songs of the Cowboys" in 1966, adding much annotation; their version includes a reprint of the original 1908 edition.
		For example, the G in the octave above C is the twelfth in the key of C. The compound interval formed by playing two notes a twelfth apart.
		twelfth root of two the mysterious multiplier for getting from one semitone to the next that always turns up in discussions of the equal-tempered scale.
	www.folklib.net /folkfile/t.shtml (6646 words)

	Learn more about Pitch (music) in the online encyclopedia. (Site not responding. Last check: 2007-10-17)
		In the west, the twelve-note chromatic scale is the most common method of organisation, with equal temperament now the most widely used method of tuning that scale.
		In it, the pitch ratio between any two successive notes of the scale is exactly the twelfth root of two.
		In well-tempered systems (as used in the time of Johann Sebastian Bach, for example), different methods of musical tuning were used.
	www.onlineencyclopedia.org /p/pi/pitch__music_.html (1559 words)

	Tuning The Guitar
		The number 1.0594631, the twelfth root of two, is the key to dividing a fingerboard into equal semitones.
		Conversely, if the twelfth fret note is sharp to the open note, the string is "too short", and the saddle must be moved away from the neck.
		Two cents isn't much but when you tune the D to the A the same way, the D ends up four cents flat.
	www.guyguitars.com /eng/handbook/Tuning/tuning.html (5192 words)

	LucyTuningLucyScaleDevelopmentsLucyTuned LullabiesPi tuningJohn Longitude Harrison (Site not responding. Last check: 2007-10-17)
		I had read how the position of the frets was calculated from the twelfth root of two, so that each of the twelve semitones in an octave had equal intervals of 100 cents.
		1) The Larger note as he calls it; This is a ratio of 2 to the 2pi root* of 2, or in BASIC computer terms 2^(1/(2*pi)), which equals a ratio of 1.116633 or 190.9858 cents, approximately 1.91 frets on a conventional guitar.
		It was difficult at first to remember that sharp and flat notes must conform to the key of the piece, but with a little practice everything became playable except for the frets between the ninth and the octave, where something was definitely wrong.
	www.lucytune.com /new_to_lt/pitch_01.html (1810 words)

	Lutherie Info - Calculating Fret Positions
		From this it should be apparent that fret position offset will be a function of the twelfth root of two.
		The twelfth root of two is the number which, if multiplied by itself twelve times, would equal two.
		Note that the root is expressed by exponentiation in the formula above – the twelfth root of 2 is the same as 2 raised to the 1/12
	www.liutaiomottola.com /formulae/fret.htm (1855 words)

	Swaras and Swarasthanas
		The name Madhyamam appears to be related to the central or madhya location in the seven notes and Panchamam is most probably derived from the number five, denoting the position of the note.
		An octave is a factor of two and there are twelve intervals in it.
		Then, we have x to be the twelfth root of two or a factor of approximately 1.06.
	www.carnaticmusic.esmartmusic.com /primer/swara.htm (1525 words)

	Graphical comparison of musical scales and mathematical progressions - Wikipedia, the free encyclopedia
		The geometric progression (fl) is based on the twelfth root of two (equal temperament) and is an exponential growth equation of this value over the octave interval.
		The arithmetic mean between any two notes is part of the linear progression.
		The arithmetic (red) progression is shown in comparison and progresses geometrically from octave to octave by a factor of two but progresses linearly within the octave for the interval of the octave.
	en.wikipedia.org /wiki/Graphical_comparison_of_musical_scales_and_mathematical_progressions (1040 words)

	Halfbakery: Chromatic spoons
		A set of twelve spoons, seven white and five fl, increasing in length by the twelfth root of two from the smallest to the largest.
		Thumbwax: the twelfth root of 2 is 1.059463, not, um, 2.
		The 12th root of 2 (or 1.059463) is exactly right for equal temperament tuning; if the first spoon is 10 cm long, the next one would be 10.594 cm (a half-step lower in pitch), then 11.225 cm, and so on, until the 13th spoon*, which is 20 cm (or one octave lower than the first.)
	www.halfbakery.com /lr/idea/Chromatic_20spoons (462 words)

	Music Theory - Chords (Site not responding. Last check: 2007-10-17)
		We have already found out that there are different types of scales identified by the root note of the scale and the rule governing the sequence of notes that form the scale.
		It is also a known fact in physics that when two waves are superimposed on each other, the resulting effect is most pronounced if the two waves are of equal frequency, and less pronounced if the frequencies vary.
		In the section about notes and their frequencies, I have stated that the fundamental frequency of a note is "twelfth root of two" times the that of its immediate lower note.
	mywebpage.netscape.com /manuevarghese/music/theorychords.html (1412 words)

	John Greschak - Tempo Scales in Polytempo Music: A Survey
		The ratio between any two successive tempi of this scale is equal to the sixteenth root of two.
		In this tempo scale, there are twelve tempi per octave and the ratio between any two successive tempi is equal to the twelfth root of two.
		Rounded to two decimal places, the tempi in a 12-step equal-tempered scale from 60 to 120 would be: 60.00, 63.57, 67.35, 71.35, 75.60, 80.09, 84.85, 89.90, 95.24, 100.91, 106.91, 113.26 and 120.00.
	www.greschak.com /polytempo/ptts.htm (3001 words)

	New Page 1 (Site not responding. Last check: 2007-10-17)
		The smallest interval in Western music is the semitone, which is the twelfth root of two, as mentioned before.
		The two basic accidentals are the flat and the sharp.
		Thus there are two versions, A and B, with A starting on a semitone and B starting on a whole tone.
	library.thinkquest.org /05aug/01262/lessonscales.html (1779 words)

	dale.emery.name - Twelfth Root of Two - Coincidence
		dale.emery.name - Twelfth Root of Two - Coincidence
		One tweak is that, I think, the two of us play different chords in a few places—and not just different forms of the same chord.
		Another tweak is the switch to 3/4 time during the chorus and the two measure "turnaround" that bumps us back into the 4/4 feel of the verses.
	www.dale.emery.name /trot/2003/04/coincidence.html (251 words)

	LucyTuningLucyScaleDevelopmentsLucyTuned LullabiesPi tuningJohn Longitude Harrison (Site not responding. Last check: 2007-10-17)
		I learned to find middle C by its position near the piano lock, and the fact that it was the sharpest of the two adjacent white notes, with two fl notes to the right and three fl to the left before another pair of white notes.
		I found that an octave was the doubling of frequency and that the frequency of each adjacent ascending note could be found by multiplying the lower frequency by the twelfth root of two.
		I was introduced to the Jacob's ladder, a high voltage spark, which repeatedly climbed between two tall electrodes on his desk giving off loud crackles, radio interference, and the ionic charge which my nostrils recognised as the feel of the air after a thunderstorm.
	www.lucytune.com /bio/music_pi_01.html (1911 words)

	MTA2000html
		The fundamental unit is the octave, which has the unique property that its two notes are felt in some indefinable way to be the same, though in pitch level they are recognizably different.
		The twelfth root of two is approximately 1.059463094.
		The higher of the two tones (f2) is placed over the lower (f1) because we are considering an upward interval.
	www.aeroinvest.com /broadcast/mta2000pr/intervalScales2.htm (815 words)

	Calculating Fret Distances
		It happens to be the case that to calculate frequencies of succeeding half-tones using equal temperament, one takes the frequency of the previous note and multiplies it by the twelfth root of two.
		This is because we want to construct a sequence of twelve frequencies such that the twelfth frequency is exactly double the first frequency.
		The distance between these two nodes is the wavelength associated with the frequency at which this standing wave vibrates.
	www.ugrad.cs.jhu.edu /~ihsahn/FretScale.html (558 words)

	[No title] (Site not responding. Last check: 2007-10-17)
		If one tail releases its grip so that the string is divided into two parts, one twice as long as the other, the longer part oscillates with frequency 3/2 of the entire string's frequency.
		Higher harmonics are constructed in a similar manner, sequentially holding the string at a point 1/n its length and plucking the longer piece.
		The point of all of this is that the first time you plucked the string (holding only the two ends), the other harmonics you constructed, (n+1)/n, also occurred, even though you didn't explicitly pluck them.
	www.stanford.edu /~ambrad/12.html (774 words)

	Tantrum (Site not responding. Last check: 2007-10-17)
		For equal temperament, the 360 degrees of a circle are divided equally into twelve 30° sections; each section represents the twelfth root of two (two to the one-twelfth power) -- the equal-tempered semitone.
		In this program, the position of the endpoints of the spokes are shown in a magnified view, and the spokes corresponding to a root and the just-tuned intervals as measured from that root can be moved as a set, keeping the angles (intervals) constant.
		In the example above, the mouse has been clicked on the minor 3rd of the B triad, which is the pitch class D. As a result, this tuning element, as well as the root of the D triad, the fifth of the G triad and the major 3rd of the B-flat triad, have become highlighted.
	www.well.com /user/smalin/tantrum.html (528 words)

	[No title] (Site not responding. Last check: 2007-10-17)
		The relationship between any two adjacent notes is a factor of the twelfth root of two.
		This routine 'normalizes' the frequency by forcing it into an octave between two C's (ch and cl for Chigh and Clow).
		The frequency for a C is 440 times (the twelfth root of two, cubed).
	www.webcom.com /jawknee/Mirage/C64/source.explanation (585 words)

Try your search on: Qwika (all wikis)