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Topic: Perfect fifth

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	Perfect fifth - Wikipedia, the free encyclopedia
		The perfect fifth or diapente is one of three musical intervals that span five diatonic scale degrees; the others being the diminished fifth, which is one semitone smaller, and the augmented fifth, which is one semitone larger.
		The 'perfect fifth is abbreviated as P5 and its inversion is the perfect fourth.
		The circle of fifths is a model of pitch space for the chromatic scale (chromatic circle) which considers nearness not as adjacency but as the number of perfect fifths required to get from one note to another.
	en.wikipedia.org /wiki/Perfect_fifth (415 words)

	Fifth - Wikipedia, the free encyclopedia
		In the United States, the Fifth Amendment to the United States Constitution
		Fifth (Stargate), a robotic character in the television series Stargate SG-1
		This is a disambiguation page: a list of articles associated with the same title.
	en.wikipedia.org /wiki/Fifth (114 words)

	Perfect numbers
		It is not known when perfect numbers were first studied and indeed the first studies may go back to the earliest times when numbers first aroused curiosity.
		Perfect numbers were studied by Pythagoras and his followers, more for their mystical properties than for their number theoretic properties.
		Today the usual definition of a perfect number is in terms of its divisors, but early definitions were in terms of the 'aliquot parts' of a number.
	www-gap.dcs.st-and.ac.uk /~history/HistTopics/Perfect_numbers.html (4360 words)

	Sonic Glossary: Fifth
		The fifth is crucial to all tonal harmony.
		By taking the triads that lie a perfect fifth apart from one another - that is, the triads built on the tonic, the dominant, and the subdominant - we have the three most important chords in tonal harmony: chords I, V, and IV, familiar to all players of the guitar.
		The triads and keys of the tonic, dominant and subdominant, which are separated by perfect fifths, are the most important components of tonal harmony, and the most frequent goals of modulation.
	www.columbia.edu /ccnmtl/draft/paul/sonic/fifth.html (996 words)

	Stability of Intervals
		For example pitch classes C and G when combined harmonically could be considered a perfect fifth C up to G or a perfect fourth G up to C. The classification of an interval class is based on the half step distance between the two pitch classes in their smallest combination.
		A perfect fourth and a perfect fifth are considered as Interval Class (IC) 5.
		Perfect Unisons and perfect octaves are considered to be duplicate pitch classes, so their IC number is zero.
	learn.southsuburbancollege.edu /fhanzelin/stability_of_intervals.htm (798 words)

	LilyTears: Music
		Between the perfect fourth and the perfect fifth is an interval sometimes called a tritone, because its size is that of three consecutive "tones".
		After the perfect fifth is the minor sixth, then the major sixth, minor seventh, major seventh and the perfect eighth or octave.
		Perfect Pitch is very rare, very difficult (though possible) to develop and enables a very different perspective of music than usual, akin to suddenly seeing color where everyone else is seeing only a grayscale.
	lilytears.com /arts/music/eartraining.htm (1560 words)

	FAQTs - Knowledge Base - Edit Entry
		The perfect 5th is (in theory) !/ 2 the distane from the root.
		This means that the distance from root note to "perfect" fifth, may be (very close to) !/ 2 the distance to the octave.
		The perfect fifth should be be 6 semi-tones sharp of the root, The distance from that fifth, to the octave, should also be 6 semi-tones, not 5.
	www.faqts.com /knowledge_base/entry/edit/index.phtml?aid=13476&fid=740&return_url=/knowledge_base/view.phtml/aid/13476/fid/740 (443 words)

	TonalityGUIDE: circle of fifths (Site not responding. Last check: 2007-11-07)
		The perfect fifth - the first interval in the harmonic series - is crucial in tonal music.
		As explained in chords and scales, the perfect fifth is also the only interval by which you can cycle all the way through the whole major scale.
		All major scales a perfect fifth apart are related in this way, and if you imagine the notes above as part of a longer series of fifths, D and A represent two of many overlapping groups of seven notes.
	www.tonalityguide.com /thkeyscircle.php (398 words)

	(excerpted from another context) (Site not responding. Last check: 2007-11-07)
		The syntonic comma is 22 cents, the denominator of the fraction, and the number of cents flat from the perfect fifth is the numerator of the fraction.
		For example, the fifth interval in 1/4 comma meantone temperament is 5.5 cents flat relative to the perfect, Pythagorean fifth interval.
		The perfect fifth is 702 cents and equal temperament is 700 cents, a difference of 2 cents.
	www.autoharpworks.com /pages/Post/doc/tune/temperament_names.htm (625 words)

	A Brief History of Tunings and Temperaments (Site not responding. Last check: 2007-11-07)
		That means we have to raise the perfect fifth ratio 3/2 to the 12th power to get to the high B#, and the octave ratio 2/1 to the 7th power to get to the high C. Well, 2 to the 7th is 128, whereas 1.5 to the 12th is 129.746.
		And the beauty of those perfect 3rds and near perfect 6ths are heightened in all that Renaissance choral polyphony, and in the subsequent rise in the use of keyboard instruments in the early Baroque.
		Each fifth in the white-key intervals would then be narrowed by 1/6th of a comma, and all the associated 3rds would be squeezed closer to their perfect 5/4 (1.25) state.
	members.iquest.net /~taldr/temperaments.htm (4360 words)

	Keith Prater Online Music School
		The Perfect Fifth(P5), gets its' name because one note of the interval is the fifth note of a major scale (ascending or descending) beginning on the other note of the interval, and is exactly seven semitones higher or lower than the other note.
		The perfect fifth is used as the anchor to tonality.
		The perfect fifth is also used to finish a piece of music or phrase.
	www25.brinkster.com /musicschool/course2/lesson6.html (173 words)

	Tantrum (Site not responding. Last check: 2007-11-07)
		A just-tuned perfect fifth (a frequency ratio of 3:2) is not 210°, but about 210.58°.
		This discrepancy corresponds to the out-of-tuneness of the final perfect fifth in the Pythagorean temperament (equivalent to about 23 cents, known as the ditonic comma).
		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)

	Dolmetsch Online - Music Theory Online - Intervals
		All intervals that are not perfect (the perfect intervals are the unison, fourth, fifth and octave) are called 'major', i.e.
		The sequence for perfect intervals (unisons, octaves, fourths and fifths) is double diminished - diminished - perfect - augmented - double augmented as the interval to the key-note is increasingly widened.
		For example, the interval 'C to G' is a perfect fifth while the interval 'C to A double flat' is a diminished sixth, but to the listener, the two intervals played on a modern piano, sound identical.
	www.dolmetsch.com /musictheory12.htm (1894 words)

	The Circle of Fifths (Site not responding. Last check: 2007-11-07)
		It keeps the F sharp, and adds C sharp, which is a perfect fifth higher than F sharp (although written a perfect fourth lower, in order to stay on the staff).
		The circle of fifths works just as well for minor keys, but you would start counting at A minor, since that is the minor key with no sharps and flats.
		Using the circle of fifths, we find that the most closely related major keys (one in each direction) are G major, with only one sharp, and A major, with three sharps.
	cnx.rice.edu /content/m10865/2.2 (838 words)

	On Modes, by Jody Nagel
		It seems that the essence of the character of a specific seven-note "white-key" diatonic mode can be demonstrated completely by simply juxtaposing (1) the perfect fifth found between scale degrees 1 and 5 and (2) the tritone contained within that mode.
		Put simply, the perfect fifth between scale degrees 1 and 5 provides tonality, and the placement of the tritone provides a specific modality.
		Thus, relative to a C-G perfect fifth, the pitch classes B and F constitute the "Ionian Tritone." Again relative to a C-G perfect fifth, the pitch classes Eb and A constitute the "Dorian Tritone." The named tritones are each shown in Example 1.
	www.jomarpress.com /nagel/articles/OnModes.html (2227 words)

	Marc Sabatella's Jazz Improvisation Primer: Basic Theory
		Expanding by half steps, the remaining intervals are the minor third, major third, perfect fourth, tritone, perfect fifth, minor sixth, major sixth, minor seventh, major seventh, and finally, the octave.
		For example, the tritone interval from C to Gb, which is actually the same as the interval from C to F#, is called a diminished fifth, because the interval from C to G is a perfect fifth.
		The motion of roots in this progression is upwards by perfect fourth, or, equivalently, downward by perfect fifth.
	www.outsideshore.com /primer/primer/ms-primer-4-1.html (2093 words)

	Guidelines for Part-Writing, Melodic Composition and Harmonic Progression (Site not responding. Last check: 2007-11-07)
		Hidden fifths are OK (i.e., a perfect fifth approached in similar motion in two voices) unless they are direct (outer voices approached by leap in the soprano).
		Each time a major scale is raised a perfect fifth, a sharp is added to correct the 7th scale step.
		Each time a major scale is lowered a perfect fifth, a flat is added to correct the 4th scale step.
	cctr.umkc.edu /user/bauera/Guide.html (591 words)

	Interval (Site not responding. Last check: 2007-11-07)
		A perfect octave is the "same" note an octave - 12 half-steps - higher or lower.
		Listen to the unison, octave, perfect fourth, and perfect fifth.
		This unique interval, which cannot be spelled as a major, minor, or perfect interval, is considered unusually dissonant and unstable (tending to want to resolve to another interval) in Western Music.
	cnx.rice.edu /content/m10867/latest (1065 words)

	The Family of Equal-interval Tunings (Site not responding. Last check: 2007-11-07)
		However, if the the perfect fifths are all just, the resulting major third will not be just -- it will be sharp (if you'd like to see the arithmetic behind this, click here).
		In the Pythagorean tuning, the perfect fifth is pure, the major 3rd is very sharp, and the minor 3rd is very flat.
		In equal temperament, the perfect fifth is a little flat, and the thirds are slightly better than in Pythagorean tuning.
	www.well.com /user/smalin/equal5th.htm (477 words)

	INTERNET CELLO SOCIETY
		A-B-C-D-E is five notes apart, or a perfect fifth.) The middle line in bass clef is a D; the middle line in tenor clef is an A. (Count the notes from D to A, ie.
		For example, the open D is on the third or middle line of the bass clef staff, and the A is on the fifth or top line of the staff.
		B on the A string, a perfect fifth higher, is one space above the top line or three staff spaces above the E. This is all leading the trick I used to use, believe it or not.
	www.cello.org /index.cfm?fuseaction=tips&tip=tip3 (502 words)

	and
		Since C to G is a perfect fifth (7 half steps), C to Gb would be a diminished fifth (6 half steps).
		B to F is also a diminished fifth (since B to F# is a perfect fifth).
		Since C to F is a perfect fourth (5 half steps), C to F# would be an augmented fourth (6 half steps).
	www.musictheory.net /lessons/xml/id31_en_uk.xml (422 words)

	Microtonal Music Composition Software, An Overview
		One must learn and memorize that C# is the perfect fifth for A and that D is the perfect fifth for Bb.
		The major triad (left) is identified by (a) the tonic, (b) the perfect fifth, which is one point to the right of the tonic, and (c) the major third, which is four points to the right of the tonic.
		The minor triad is identified by (a) the tonic, (b) the perfect fifth, and (c) the minor third, which is three points to the left of the tonic.
	tonalsoft.com /pub/update/update.2005-03-12.12-00.aspx (1052 words)

	New Page 1 (Site not responding. Last check: 2007-11-07)
		If you remain on the white keys (no accidentals) then all the fourths and fifths are perfect except for the fourth from f up to b which is augmented, and the fifth from b up to f, which is diminished.
		Notice that the fifth from b to f is the only fifth that contains both natural half steps (b-c and e-f), and the fourth from f to b is the only fourth that doesn't contain any natural half steps.
		Those fifths with one half step and three whole steps (total of 7 half steps) are perfect fifths.
	www.auburn.edu /~schafwr/4th5thhints.html (260 words)

	Tom Pankhurst's TonalityGUIDE (pilot project) (Site not responding. Last check: 2007-11-07)
		There is a close relationship between any two keys whose tonics are a perfect fifth apart (the page on fifth-related major keys looks at the example of D and A major).
		The easiest way to write all the flattened and sharpened notes of the chromatic scale in a series of perfect fifths is to start with the scale of C major organised as a series of perfect fifths.
		Be careful not to confuse the modulatory circle of fifths with the diatonic chains of fifths that stay in the same key.
	www.tonalityguide.com /thkeyscircle2.php (834 words)

	About the tuning of the Piano: Inharmonicity
		Similarly the frequency ratio for three octaves is 8:1, and for a twelfth (octave and a fifth) is 3:1.
		To demonstrate this for a known result, the frequency ratio for a perfect fourth (4:3) can be found from that for a perfect fifth (3:2) since together they make one octave (2:1): C to G (perfect fifth) and G to C (perfect fourth).
		The perfect fifth has a frequency ratio 3:2 and the octave a ratio of 2:1.
	www.postpiano.com /support/updates/tech/Tuning.htm (747 words)

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