Fifths

Some articles on fifths, fifth:

Archicembalo - Tuning
... which given such a wide gamut of fifths becomes almost exactly a system of 31 equal divisions of the octave (see 31 equal temperament) ... This arises because after a cycle of 31 quarter-comma-tempered fifths, the 32nd pitch will be remarkably close to a pitch already existing in the system thus five of Vicentino's 36 possibilities became practically ... which the upper keyboard was tuned a quarter-comma higher than the lower, allowing pure fifths by playing chords across the manuals, giving a limited system of triadic just ...
Jing Fang - Music Theory
... Jing Fang was the first to notice how closely a succession of 53 just fifths approximates 31 octaves ... observation after learning to calculate the pythagorean comma between 12 fifths and 7 octaves (this had been published ca ... written for the prince of Huainan), and extended this method fivefold to a scale composed of 60 fifths, finding that after 53 new values became incredibly close to tones already calculated ...
Consecutive Fifths
... In music, consecutive fifths, or parallel fifths, are progressions in which the interval of a perfect fifth is followed by a different perfect fifth between the same two musical parts (or voices) for example ... as created by successive intervals of an octave plus a fifth) are equivalent to parallel fifths ... (1725–present) and during the common practice period, consecutive fifths were strongly discouraged ...
Temperament Ordinaire - 18th Century
... the middle C of the keyboard, and narrow the first four fifths going up, until the fourth, E, makes a very true major third with the first note C this is called 'the. 2nd, Continuing to tune by fifths, as soon as one has arrived at the sharp notes, one then widens the fifths - even though the thirds suffer by it - and one. 3rd, Return to C and tune the fifths going down, that is, F, B flat, and so on, widening them all the time, until one has arrived at D flat, which - when taken as C# - ought to be in harmony as a fifth with ...
Musical Temperament - Well Temperament and Equal Temperament
... Unlike meantone temperament, which alters the fifth to temper out the Syntonic comma, 12-TET tempers out the Pythagorean comma, thus creating a cycle of fifths that repeats itself exactly after 12 steps ... the intervals of Tertian harmony, thirds and fifths, to be fairly close to their just counterparts (the fifths almost imperceptibly beating, the thirds a little milder than the syntonic beating of ...