14ed5 - Revision history

BudjarnLambeth: Intervals harmonics

2024-10-06T01:14:53Z

Intervals harmonics

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 {{Infobox ET}}
 '''The 14 equal divisions of [[5/1]]''' system divides the 5th harmoinc or pentave into 14 equal steps of 199.022 cents each.  It is essentially a compressed [[6edo]] whole tone scale with a tempered octave of 1194.13 cents.
 == Theory ==
 ed5 is the first ED5 which can reasonably be described as a 5.7.11 subgroup temperament, excluding harmonics 2 and 3 as implied by pentaves, with the mapping {{val|14 17 21}}. 7/5 is mapped to near 2edo's tritone at 597 cents, while 11/5 mapped to the square root of five, a major ninth of 1393 cents. The mapping of 11/5 to the square root of five means 14ed5 supports [[juggernaut]] temperament, one of the lowest-badness 5.7.11 temperaments, much lower than even 5-limit meantone, where the period is the square root of five (~11/5) and the generator is ~7/5. As such 14ed5 can be considered a no-twos-or-threes analog of [[12edo]] and [[13edt]].
-{{Stub}}
+== Intervals ==

CompactStar at 07:37, 22 August 2023

2023-08-22T07:37:19Z

← Older revision		Revision as of 07:37, 22 August 2023
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	'''The 14 equal divisions of [[5/1]]''' system divides the 5th harmoinc or pentave into 14 equal steps of 199.022 cents each. It is essentially a compressed [[6edo]] whole tone scale with a tempered octave of 1194.13 cents.		'''The 14 equal divisions of [[5/1]]''' system divides the 5th harmoinc or pentave into 14 equal steps of 199.022 cents each. It is essentially a compressed [[6edo]] whole tone scale with a tempered octave of 1194.13 cents.
	== Theory ==		== Theory ==
	14ed5 is the first ED5 which can reasonably be described as a 5.7.11 subgroup temperament, excluding harmonics 2 and 3 as implied by pentaves, with the mapping {{val\|14 17 21}}. 7/5 is mapped to near 2edo's tritone at 597 cents, while 11/5 mapped to the square root of five, a major ninth of 1393 cents. The mapping of 11/5 means 14ed5 supports [[juggernaut]] temperament, one of the lowest-badness 5.7.11 temperaments, much lower than even 5-limit meantone, where the period is the square root of five (11/5) and the generator is 7/5. As such 14ed5 can be considered a no-twos-or-threes analog of [[12edo]] and [[13edt]].		14ed5 is the first ED5 which can reasonably be described as a 5.7.11 subgroup temperament, excluding harmonics 2 and 3 as implied by pentaves, with the mapping {{val\|14 17 21}}. 7/5 is mapped to near 2edo's tritone at 597 cents, while 11/5 mapped to the square root of five, a major ninth of 1393 cents. The mapping of 11/5 to the square root of five means 14ed5 supports [[juggernaut]] temperament, one of the lowest-badness 5.7.11 temperaments, much lower than even 5-limit meantone, where the period is the square root of five (~11/5) and the generator is ~7/5. As such 14ed5 can be considered a no-twos-or-threes analog of [[12edo]] and [[13edt]].

	{{Stub}}		{{Stub}}

CompactStar at 07:36, 22 August 2023

2023-08-22T07:36:51Z

← Older revision		Revision as of 07:36, 22 August 2023
Line 2:		Line 2:
	'''The 14 equal divisions of [[5/1]]''' system divides the 5th harmoinc or pentave into 14 equal steps of 199.022 cents each. It is essentially a compressed [[6edo]] whole tone scale with a tempered octave of 1194.13 cents.		'''The 14 equal divisions of [[5/1]]''' system divides the 5th harmoinc or pentave into 14 equal steps of 199.022 cents each. It is essentially a compressed [[6edo]] whole tone scale with a tempered octave of 1194.13 cents.
	== Theory ==		== Theory ==
	14ed5 is the first ED5 which can reasonably be described as a 5.7.11 subgroup temperament, excluding harmonics 2 and 3 as implied by pentaves, with the mapping {{val\|14 17 21}}. 7/5 is mapped to near 2edo's tritone at 597 cents, while 11/5 mapped to the square root of five, a major ninth of 1393 cents. The mapping of 11/5 means 14ed5 supports [[juggernaut]] temperament, one of the lowest-badness 5.7.11 temperaments, much lower than even 5-limit meantone, where the period is the square root of five (11/5) and the generator is 7/5. As such 14ed5 can be considered a no-twos-or-threes analog of 12edo.		14ed5 is the first ED5 which can reasonably be described as a 5.7.11 subgroup temperament, excluding harmonics 2 and 3 as implied by pentaves, with the mapping {{val\|14 17 21}}. 7/5 is mapped to near 2edo's tritone at 597 cents, while 11/5 mapped to the square root of five, a major ninth of 1393 cents. The mapping of 11/5 means 14ed5 supports [[juggernaut]] temperament, one of the lowest-badness 5.7.11 temperaments, much lower than even 5-limit meantone, where the period is the square root of five (11/5) and the generator is 7/5. As such 14ed5 can be considered a no-twos-or-threes analog of [[12edo]] and [[13edt]].

	{{Stub}}		{{Stub}}

CompactStar at 07:36, 22 August 2023

2023-08-22T07:36:30Z

← Older revision		Revision as of 07:36, 22 August 2023
Line 2:		Line 2:
	'''The 14 equal divisions of [[5/1]]''' system divides the 5th harmoinc or pentave into 14 equal steps of 199.022 cents each. It is essentially a compressed [[6edo]] whole tone scale with a tempered octave of 1194.13 cents.		'''The 14 equal divisions of [[5/1]]''' system divides the 5th harmoinc or pentave into 14 equal steps of 199.022 cents each. It is essentially a compressed [[6edo]] whole tone scale with a tempered octave of 1194.13 cents.
	== Theory ==		== Theory ==
	14ed5 is the first ED5 which can reasonably be described as a 5.7.11 subgroup temperament, excluding harmonics 2 and 3 as implied by pentaves, with the mapping {{val\|14 17 21}}. 7/5 is mapped to near 2edo's tritone at 597 cents, while 11/5 mapped to the square root of five, a major ninth of 1393 cents. The mapping of 11/5 means 14ed5 supports [[juggernaut]] temperament, one of the lowest-badness 5.7.11 temperaments, much lower than even 5-limit meantone. As such 14ed5 can be considered a no-twos-or-threes analog of 12edo.		14ed5 is the first ED5 which can reasonably be described as a 5.7.11 subgroup temperament, excluding harmonics 2 and 3 as implied by pentaves, with the mapping {{val\|14 17 21}}. 7/5 is mapped to near 2edo's tritone at 597 cents, while 11/5 mapped to the square root of five, a major ninth of 1393 cents. The mapping of 11/5 means 14ed5 supports [[juggernaut]] temperament, one of the lowest-badness 5.7.11 temperaments, much lower than even 5-limit meantone, where the period is the square root of five (11/5) and the generator is 7/5. As such 14ed5 can be considered a no-twos-or-threes analog of 12edo.

	{{Stub}}		{{Stub}}

CompactStar at 07:35, 22 August 2023

2023-08-22T07:35:58Z

← Older revision		Revision as of 07:35, 22 August 2023
Line 2:		Line 2:
	'''The 14 equal divisions of [[5/1]]''' system divides the 5th harmoinc or pentave into 14 equal steps of 199.022 cents each. It is essentially a compressed [[6edo]] whole tone scale with a tempered octave of 1194.13 cents.		'''The 14 equal divisions of [[5/1]]''' system divides the 5th harmoinc or pentave into 14 equal steps of 199.022 cents each. It is essentially a compressed [[6edo]] whole tone scale with a tempered octave of 1194.13 cents.
	== Theory ==		== Theory ==
	14ed5 is the first ED5 which can reasonably be described as a 5.7.11 subgroup temperament, excluding harmonics 2 and 3 as implied by pentaves, with the mapping {{val\|14 17 21}}. 7/5 is mapped to near 2edo's tritone at 597 cents, while 11/5 mapped to the square root of five, a major ninth of 1393 cents. The mapping of 11/5 means 14ed5 supports [[juggernaut]] temperament, one of the lowest-badness 5.7.11 temperaments, ~~comparable to octave~~-~~repeating~~ meantone~~, and as~~ such 14ed5 can be considered a no-twos-or-threes analog of 12edo.		14ed5 is the first ED5 which can reasonably be described as a 5.7.11 subgroup temperament, excluding harmonics 2 and 3 as implied by pentaves, with the mapping {{val\|14 17 21}}. 7/5 is mapped to near 2edo's tritone at 597 cents, while 11/5 mapped to the square root of five, a major ninth of 1393 cents. The mapping of 11/5 means 14ed5 supports [[juggernaut]] temperament, one of the lowest-badness 5.7.11 temperaments, much lower than even 5-limit meantone. As such 14ed5 can be considered a no-twos-or-threes analog of 12edo.

	{{Stub}}		{{Stub}}

CompactStar at 07:35, 22 August 2023

2023-08-22T07:35:11Z

← Older revision		Revision as of 07:35, 22 August 2023
Line 2:		Line 2:
	'''The 14 equal divisions of [[5/1]]''' system divides the 5th harmoinc or pentave into 14 equal steps of 199.022 cents each. It is essentially a compressed [[6edo]] whole tone scale with a tempered octave of 1194.13 cents.		'''The 14 equal divisions of [[5/1]]''' system divides the 5th harmoinc or pentave into 14 equal steps of 199.022 cents each. It is essentially a compressed [[6edo]] whole tone scale with a tempered octave of 1194.13 cents.
	== Theory ==		== Theory ==
	14ed5 is the first ED5 which can reasonably be described as a 5.7.11 subgroup temperament, excluding harmonics 2 and 3 as implied by pentaves, with the mapping {{val\|14 17 21}}. ~~The best approximation of~~ 7/5 is near 2edo's tritone at 597 cents, while 11/5 mapped to the square root of five, a major ninth of 1393 cents. The mapping of 11/5 means 14ed5 supports [[juggernaut]] temperament, one of the lowest-badness 5.7.11 temperaments, comparable to octave-repeating meantone, and as such 14ed5 can be considered a no-twos-or-threes analog of 12edo.		14ed5 is the first ED5 which can reasonably be described as a 5.7.11 subgroup temperament, excluding harmonics 2 and 3 as implied by pentaves, with the mapping {{val\|14 17 21}}. 7/5 is mapped to near 2edo's tritone at 597 cents, while 11/5 mapped to the square root of five, a major ninth of 1393 cents. The mapping of 11/5 means 14ed5 supports [[juggernaut]] temperament, one of the lowest-badness 5.7.11 temperaments, comparable to octave-repeating meantone, and as such 14ed5 can be considered a no-twos-or-threes analog of 12edo.

	{{Stub}}		{{Stub}}

CompactStar at 07:34, 22 August 2023

2023-08-22T07:34:55Z

← Older revision		Revision as of 07:34, 22 August 2023
Line 3:		Line 3:
	== Theory ==		== Theory ==
	14ed5 is the first ED5 which can reasonably be described as a 5.7.11 subgroup temperament, excluding harmonics 2 and 3 as implied by pentaves, with the mapping {{val\|14 17 21}}. The best approximation of 7/5 is near 2edo's tritone at 597 cents, while 11/5 mapped to the square root of five, a major ninth of 1393 cents. The mapping of 11/5 means 14ed5 supports [[juggernaut]] temperament, one of the lowest-badness 5.7.11 temperaments, comparable to octave-repeating meantone, and as such 14ed5 can be considered a no-twos-or-threes analog of 12edo.		14ed5 is the first ED5 which can reasonably be described as a 5.7.11 subgroup temperament, excluding harmonics 2 and 3 as implied by pentaves, with the mapping {{val\|14 17 21}}. The best approximation of 7/5 is near 2edo's tritone at 597 cents, while 11/5 mapped to the square root of five, a major ninth of 1393 cents. The mapping of 11/5 means 14ed5 supports [[juggernaut]] temperament, one of the lowest-badness 5.7.11 temperaments, comparable to octave-repeating meantone, and as such 14ed5 can be considered a no-twos-or-threes analog of 12edo.

			{{Stub}}

CompactStar at 07:34, 22 August 2023

2023-08-22T07:34:51Z

← Older revision		Revision as of 07:34, 22 August 2023
Line 2:		Line 2:
	'''The 14 equal divisions of [[5/1]]''' system divides the 5th harmoinc or pentave into 14 equal steps of 199.022 cents each. It is essentially a compressed [[6edo]] whole tone scale with a tempered octave of 1194.13 cents.		'''The 14 equal divisions of [[5/1]]''' system divides the 5th harmoinc or pentave into 14 equal steps of 199.022 cents each. It is essentially a compressed [[6edo]] whole tone scale with a tempered octave of 1194.13 cents.
	== Theory ==		== Theory ==
	14ed5 is the first ED5 which can reasonably be described as a 5.7.11 subgroup temperament, excluding harmonics 2 and 3 as implied by pentaves, with the mapping {{val\|14 17 21}}. The best approximation of 7/5 is near 2edo's tritone at 597 cents, while 11/5 mapped to the square root of five, a major ninth of 1393 cents. The mapping of 11/5 means 14ed5 supports [[juggernaut]] temperament, one of the lowest-badness 5.7.11 temperaments, comparable to octave-repeating meantone, so as such 14ed5 can be considered a no-twos-or-threes analog of 12edo.		14ed5 is the first ED5 which can reasonably be described as a 5.7.11 subgroup temperament, excluding harmonics 2 and 3 as implied by pentaves, with the mapping {{val\|14 17 21}}. The best approximation of 7/5 is near 2edo's tritone at 597 cents, while 11/5 mapped to the square root of five, a major ninth of 1393 cents. The mapping of 11/5 means 14ed5 supports [[juggernaut]] temperament, one of the lowest-badness 5.7.11 temperaments, comparable to octave-repeating meantone, and as such 14ed5 can be considered a no-twos-or-threes analog of 12edo.

CompactStar at 07:34, 22 August 2023

2023-08-22T07:34:36Z

← Older revision		Revision as of 07:34, 22 August 2023
Line 2:		Line 2:
	'''The 14 equal divisions of [[5/1]]''' system divides the 5th harmoinc or pentave into 14 equal steps of 199.022 cents each. It is essentially a compressed [[6edo]] whole tone scale with a tempered octave of 1194.13 cents.		'''The 14 equal divisions of [[5/1]]''' system divides the 5th harmoinc or pentave into 14 equal steps of 199.022 cents each. It is essentially a compressed [[6edo]] whole tone scale with a tempered octave of 1194.13 cents.
	== Theory ==		== Theory ==
	14ed5 is the first ED5 which can reasonably be described as a 5.7.11 subgroup temperament, excluding harmonics 2 and 3 as implied by pentaves, with the mapping {{val\|14 17 21}}. The best approximation of 7/5 is near 2edo's tritone at 597 cents, while ~~the best approximation of~~ 11/5 is the square root of five, a major ninth of 1393 cents.		14ed5 is the first ED5 which can reasonably be described as a 5.7.11 subgroup temperament, excluding harmonics 2 and 3 as implied by pentaves, with the mapping {{val\|14 17 21}}. The best approximation of 7/5 is near 2edo's tritone at 597 cents, while 11/5 mapped to the square root of five, a major ninth of 1393 cents. The mapping of 11/5 means 14ed5 supports [[juggernaut]] temperament, one of the lowest-badness 5.7.11 temperaments, comparable to octave-repeating meantone, so as such 14ed5 can be considered a no-twos-or-threes analog of 12edo.

CompactStar at 07:33, 22 August 2023

2023-08-22T07:33:00Z

← Older revision		Revision as of 07:33, 22 August 2023
Line 2:		Line 2:
	'''The 14 equal divisions of [[5/1]]''' system divides the 5th harmoinc or pentave into 14 equal steps of 199.022 cents each. It is essentially a compressed [[6edo]] whole tone scale with a tempered octave of 1194.13 cents.		'''The 14 equal divisions of [[5/1]]''' system divides the 5th harmoinc or pentave into 14 equal steps of 199.022 cents each. It is essentially a compressed [[6edo]] whole tone scale with a tempered octave of 1194.13 cents.
	== Theory ==		== Theory ==
	14ed5 is the first ED5 which can reasonably be described as a 5.7.11 subgroup temperament, excluding harmonics 2 and 3 as implied by pentaves, with the mapping {{val\|14 17 21}}. The best approximation of 7/5 is near 2edo's tritone at 597 cents, while the best approximation of 11/5 is a major ninth of 1393 cents~~, also being the square root of five~~.		14ed5 is the first ED5 which can reasonably be described as a 5.7.11 subgroup temperament, excluding harmonics 2 and 3 as implied by pentaves, with the mapping {{val\|14 17 21}}. The best approximation of 7/5 is near 2edo's tritone at 597 cents, while the best approximation of 11/5 is the square root of five, a major ninth of 1393 cents.