Pythagorean tuning - Revision history

User 144: category formation

2006-05-22T12:26:51Z

category formation

← Older revision		Revision as of 22:26, 22 May 2006
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	==External Link==		==External Link==
	http://www.medieval.org/emfaq/harmony/pyth.html		http://www.medieval.org/emfaq/harmony/pyth.html
			[[category:music]]

Morgant: adding external link

2005-08-09T05:42:47Z

adding external link

← Older revision		Revision as of 15:42, 9 August 2005
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	'''Pythagorean tuning''' is a method of tuning the 12-note chromatic musical scale based on a series of perfect fifth intervals. The method is named for the 6th centrury BC mathematician and philosopher [[Pythagoras]]. Pythagoras defined harmonics as being mathematical relationships between the vibrational frequencies of various notes. A perfect fifth is defined as a frequency ratio of 3:2, whereas an octave is 2:1. Consequently, a problem of the Pythagorean tuning method is that no series of perfect fifths can be made equal to an octave. This resulted in higher octave notes being out of tune with respect to their lower octave counterparts. The problem was corrected by Bach with his well-tempered clavier (known today as equal temperament) by slightly flattening each fifth to make up for the discrepancy - in effect, distributing the problem throughout the entire scale so that is it not noticeable.		'''Pythagorean tuning''' is a method of tuning the 12-note chromatic musical scale based on a series of perfect fifth intervals. The method is named for the 6th centrury BC mathematician and philosopher [[Pythagoras]]. Pythagoras defined harmonics as being mathematical relationships between the vibrational frequencies of various notes. A perfect fifth is defined as a frequency ratio of 3:2, whereas an octave is 2:1. Consequently, a problem of the Pythagorean tuning method is that no series of perfect fifths can be made equal to an octave. This resulted in higher octave notes being out of tune with respect to their lower octave counterparts. The problem was corrected by Bach with his well-tempered clavier (known today as equal temperament) by slightly flattening each fifth to make up for the discrepancy - in effect, distributing the problem throughout the entire scale so that is it not noticeable.

			==External Link==
			http://www.medieval.org/emfaq/harmony/pyth.html

Elyas at 15:24, 8 June 2005

2005-06-08T15:24:24Z

← Older revision		Revision as of 01:24, 9 June 2005
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	'''Pythagorean tuning''' is a method of tuning the 12-note chromatic musical scale based on a series of perfect fifth intervals. The method is named for the 6th centrury BC mathematician and philosopher [[Pythagoras]]. Pythagoras ~~and his students, notably Nicomachus,~~ defined harmonics as being mathematical relationships between the vibrational frequencies of various notes. A perfect fifth is defined as a frequency ratio of 3:2, whereas an octave is 2:1. Consequently, a problem of the Pythagorean tuning method is that no series of perfect fifths can be made equal to an octave. This resulted in higher octave notes being out of tune with respect to their lower octave counterparts. The problem was corrected by Bach with his well-tempered clavier (known today as equal temperament) by slightly flattening each fifth to make up for the discrepancy - in effect, distributing the problem throughout the entire scale so that is it not noticeable.		'''Pythagorean tuning''' is a method of tuning the 12-note chromatic musical scale based on a series of perfect fifth intervals. The method is named for the 6th centrury BC mathematician and philosopher [[Pythagoras]]. Pythagoras defined harmonics as being mathematical relationships between the vibrational frequencies of various notes. A perfect fifth is defined as a frequency ratio of 3:2, whereas an octave is 2:1. Consequently, a problem of the Pythagorean tuning method is that no series of perfect fifths can be made equal to an octave. This resulted in higher octave notes being out of tune with respect to their lower octave counterparts. The problem was corrected by Bach with his well-tempered clavier (known today as equal temperament) by slightly flattening each fifth to make up for the discrepancy - in effect, distributing the problem throughout the entire scale so that is it not noticeable.

Elyas at 15:22, 8 June 2005

2005-06-08T15:22:33Z

← Older revision		Revision as of 01:22, 9 June 2005
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	'''Pythagorean tuning''' is a method of tuning the 12-note chromatic musical scale based on a series of perfect fifth intervals. The method is named for the 6th centrury BC mathematician and philosopher [[Pythagoras]]. Pythagoras and his students, notably Nicomachus, defined harmonics as being mathematical relationships between the vibrational frequencies of various notes. A perfect fifth is defined as a frequency ratio of 3:2, whereas an octave is 2:1. Consequently, a problem of the Pythagorean tuning method is that no series of perfect fifths can be made equal to an octave. This resulted in higher octave notes being out of tune with respect to their lower octave counterparts. ~~This~~ problem was corrected by Bach with his well-tempered clavier, known today as equal temperament, by slightly flattening each fifth to make up for the discrepancy - in effect, distributing the problem throughout the entire scale so that is it not noticeable.		'''Pythagorean tuning''' is a method of tuning the 12-note chromatic musical scale based on a series of perfect fifth intervals. The method is named for the 6th centrury BC mathematician and philosopher [[Pythagoras]]. Pythagoras and his students, notably Nicomachus, defined harmonics as being mathematical relationships between the vibrational frequencies of various notes. A perfect fifth is defined as a frequency ratio of 3:2, whereas an octave is 2:1. Consequently, a problem of the Pythagorean tuning method is that no series of perfect fifths can be made equal to an octave. This resulted in higher octave notes being out of tune with respect to their lower octave counterparts. The problem was corrected by Bach with his well-tempered clavier (known today as equal temperament) by slightly flattening each fifth to make up for the discrepancy - in effect, distributing the problem throughout the entire scale so that is it not noticeable.

Elyas: created stub for Pythagorean tuning

2005-06-08T15:21:25Z

created stub for Pythagorean tuning

New page

'''Pythagorean tuning''' is a method of tuning the 12-note chromatic musical scale based on a series of perfect fifth intervals. The method is named for the 6th centrury BC mathematician and philosopher [[Pythagoras]]. Pythagoras and his students, notably Nicomachus, defined harmonics as being mathematical relationships between the vibrational frequencies of various notes. A perfect fifth is defined as a frequency ratio of 3:2, whereas an octave is 2:1. Consequently, a problem of the Pythagorean tuning method is that no series of perfect fifths can be made equal to an octave. This resulted in higher octave notes being out of tune with respect to their lower octave counterparts. This problem was corrected by Bach with his well-tempered clavier, known today as equal temperament, by slightly flattening each fifth to make up for the discrepancy - in effect, distributing the problem throughout the entire scale so that is it not noticeable.