Buzzard - Revision history

Unque at 21:19, 28 July 2026

2026-07-28T21:19:42Z

← Older revision		Revision as of 21:19, 28 July 2026
Line 135:		Line 135:

	==== Valinorsmic Buzzard ====		==== Valinorsmic Buzzard ====
	The "canonical" mapping of prime 11 is to equate the inflection comma with 100/99; this equally spaces the ~~sequence~~ 21/16 - 4/3 - 27/20 - 15/11~~, and maps 13/11 to the diatonic minor third, right in the middle of 6/5 and 7/6~~.		The "canonical" mapping of prime 11 is to equate the inflection comma with 100/99; this equally spaces the sequences 7/6 - 13/11 - 6/5 - 40/33, as well as 21/16 - 4/3 - 27/20 - 15/11.

	==== Telepathic Buzzard ("Buteo") ====		==== Telepathic Buzzard ("Buteo") ====

FloraC: /* Extensions */ math error? Described here was an undocumented low-accuracy 11-limit extension

2026-07-23T10:21:35Z

Extensions: math error? Described here was an undocumented low-accuracy 11-limit extension

← Older revision		Revision as of 10:21, 23 July 2026
Line 135:		Line 135:

	==== Valinorsmic Buzzard ====		==== Valinorsmic Buzzard ====
	The "canonical" mapping of prime 11 is to equate the inflection comma with 100/99; this equally spaces the sequence ~~11/9 - 5/4 - 81/64 - 9/7, as well as~~ 21/16 - 4/3 - 27/20 - 15/11~~. One detriment of this extension is that the tunings of 11/8~~ and 13/~~8 are rather close together, with their difference in most tunings being closer~~ to ~~250c rather than~~ the ~~290c that we get in just intonation;~~ in ~~fact, this difference is~~ the ~~semifourth at -2 generators, which makes 11~~/~~8 equivalent to 169~~/~~120~~.		The "canonical" mapping of prime 11 is to equate the inflection comma with 100/99; this equally spaces the sequence 21/16 - 4/3 - 27/20 - 15/11, and maps 13/11 to the diatonic minor third, right in the middle of 6/5 and 7/6.

	==== Telepathic Buzzard ("Buteo") ====		==== Telepathic Buzzard ("Buteo") ====

Unque at 19:06, 21 July 2026

2026-07-21T19:06:55Z

@@ Line 15: / Line 15: @@
 | Odd limit 2 = 15 | Mistuning 2 = 4.09 | Complexity 2 = 43
 }}
-'''Buzzard''', 2.3.7[{{e|48}} & {{e|53}}], is a 2.3.7 temperament that splits 3/1 into four sharpened 21/16 subfourths. It can be considered the "simplest 2.3.7 temperament after [[Slendric]]" since it equates two (not one) 64/63's with one 49/48, exaggerating the difference between 21/16 and 64/49. Since Buzzard sharpens 147/128, equating it to an exact semifourth at -2 generators, it can be extended to 2.3.7.13/5 by equating 147/128 to 15/13, thus tempering out the huntsma, 640/637.
+'''Buzzard''', 2.3.7[{{e|48}} & {{e|53}}], is a 2.3.7 temperament that splits 3/1 into four sharpened 21/16 subfourths. It can be considered the "simplest 2.3.7 temperament after [[Slendric]]" since it equates two (not one) 64/63's with one 49/48, exaggerating the difference between 21/16 and 64/49.  This 64/63 interval is primarily used as an inflection comma, as it separates the simple 3-limit intervals from 7-limit consonances; as a result of this "spine and comma" arrangement of the consonances, the MOS scales generated by Buzzard are not always the primary type of scale considered in the temperament.
 == List of patent vals ==
@@ Line 126: / Line 128: @@
 |}
-{{Navbox regtemp}}
+== Extensions ==
 {{Cat| temperaments}}

Inthar at 06:22, 1 July 2026

2026-07-01T06:22:15Z

← Older revision		Revision as of 06:22, 1 July 2026
Line 15:		Line 15:
	\| Odd limit 2 = 15 \| Mistuning 2 = 4.09 \| Complexity 2 = 43		\| Odd limit 2 = 15 \| Mistuning 2 = 4.09 \| Complexity 2 = 43
	}}		}}
	'''Buzzard''', {{e\|48}} & {{e\|53}}, is a 2.3.7 temperament that splits 3/1 into four sharpened 21/16 subfourths. It can be considered the "simplest 2.3.7 temperament after [[Slendric]]" since it equates two (not one) 64/63's with one 49/48, exaggerating the difference between 21/16 and 64/49. Since Buzzard sharpens 147/128, equating it to an exact semifourth at -2 generators, it can be extended to 2.3.7.13/5 by equating 147/128 to 15/13, thus tempering out the huntsma, 640/637.		'''Buzzard''', 2.3.7[{{e\|48}} & {{e\|53}}], is a 2.3.7 temperament that splits 3/1 into four sharpened 21/16 subfourths. It can be considered the "simplest 2.3.7 temperament after [[Slendric]]" since it equates two (not one) 64/63's with one 49/48, exaggerating the difference between 21/16 and 64/49. Since Buzzard sharpens 147/128, equating it to an exact semifourth at -2 generators, it can be extended to 2.3.7.13/5 by equating 147/128 to 15/13, thus tempering out the huntsma, 640/637.

	== List of patent vals ==		== List of patent vals ==

Inthar at 14:20, 14 April 2026

2026-04-14T14:20:53Z

← Older revision		Revision as of 14:20, 14 April 2026
Line 15:		Line 15:
	\| Odd limit 2 = 15 \| Mistuning 2 = 4.09 \| Complexity 2 = 43		\| Odd limit 2 = 15 \| Mistuning 2 = 4.09 \| Complexity 2 = 43
	}}		}}
	'''Buzzard''' is a 2.3.7 temperament that splits 3/1 into four sharpened 21/16 subfourths. It can be considered the "simplest 2.3.7 temperament after [[Slendric]]" since it equates two (not one) 64/63's with one 49/48, exaggerating the difference between 21/16 and 64/49. Since Buzzard sharpens 147/128, equating it to an exact semifourth at -2 generators, it can be extended to 2.3.7.13/5 by equating 147/128 to 15/13, thus tempering out the huntsma, 640/637.		'''Buzzard''', {{e\|48}} & {{e\|53}}, is a 2.3.7 temperament that splits 3/1 into four sharpened 21/16 subfourths. It can be considered the "simplest 2.3.7 temperament after [[Slendric]]" since it equates two (not one) 64/63's with one 49/48, exaggerating the difference between 21/16 and 64/49. Since Buzzard sharpens 147/128, equating it to an exact semifourth at -2 generators, it can be extended to 2.3.7.13/5 by equating 147/128 to 15/13, thus tempering out the huntsma, 640/637.

	== List of patent vals ==		== List of patent vals ==

Inthar at 14:20, 14 April 2026

2026-04-14T14:20:33Z

← Older revision		Revision as of 14:20, 14 April 2026
Line 15:		Line 15:
	\| Odd limit 2 = 15 \| Mistuning 2 = 4.09 \| Complexity 2 = 43		\| Odd limit 2 = 15 \| Mistuning 2 = 4.09 \| Complexity 2 = 43
	}}		}}
	'''Buzzard''' is a 2.3.7 temperament that splits 3/1 into four sharpened 21/16 subfourths. It can be considered the "simplest 2.3.7 temperament after [[Slendric]]" since it equates two (not one) 64/63's with one 49/48. Since Buzzard sharpens 147/128, equating it to an exact semifourth at -2 generators, it can be extended to 2.3.7.13/5 by equating 147/128 to 15/13, thus tempering out the huntsma, 640/637.		'''Buzzard''' is a 2.3.7 temperament that splits 3/1 into four sharpened 21/16 subfourths. It can be considered the "simplest 2.3.7 temperament after [[Slendric]]" since it equates two (not one) 64/63's with one 49/48, exaggerating the difference between 21/16 and 64/49. Since Buzzard sharpens 147/128, equating it to an exact semifourth at -2 generators, it can be extended to 2.3.7.13/5 by equating 147/128 to 15/13, thus tempering out the huntsma, 640/637.

	== List of patent vals ==		== List of patent vals ==

Inthar at 14:19, 14 April 2026

2026-04-14T14:19:15Z

← Older revision		Revision as of 14:19, 14 April 2026
Line 16:		Line 16:
	}}		}}
	'''Buzzard''' is a 2.3.7 temperament that splits 3/1 into four sharpened 21/16 subfourths. It can be considered the "simplest 2.3.7 temperament after [[Slendric]]" since it equates two (not one) 64/63's with one 49/48. Since Buzzard sharpens 147/128, equating it to an exact semifourth at -2 generators, it can be extended to 2.3.7.13/5 by equating 147/128 to 15/13, thus tempering out the huntsma, 640/637.		'''Buzzard''' is a 2.3.7 temperament that splits 3/1 into four sharpened 21/16 subfourths. It can be considered the "simplest 2.3.7 temperament after [[Slendric]]" since it equates two (not one) 64/63's with one 49/48. Since Buzzard sharpens 147/128, equating it to an exact semifourth at -2 generators, it can be extended to 2.3.7.13/5 by equating 147/128 to 15/13, thus tempering out the huntsma, 640/637.
	~~{{Navbox regtemp}}~~
	~~{{Cat\| temperaments}}~~

	== List of patent vals ==		== List of patent vals ==
Line 127:		Line 125:
	\|480.00		\|480.00
	\|}		\|}

			{{Navbox regtemp}}
			{{Cat\| temperaments}}

Inthar at 14:18, 14 April 2026

2026-04-14T14:18:42Z

← Older revision		Revision as of 14:18, 14 April 2026
Line 15:		Line 15:
	\| Odd limit 2 = 15 \| Mistuning 2 = 4.09 \| Complexity 2 = 43		\| Odd limit 2 = 15 \| Mistuning 2 = 4.09 \| Complexity 2 = 43
	}}		}}
	'''Buzzard''' is a 2.3.7 temperament that splits 3/1 into four sharpened 21/16 subfourths. It can be considered the "simplest 2.3.7 temperament after [[Slendric]]" since it equates two (not one) 64/63's with one 49/48. Since Buzzard sharpens 147/128, it can be extended to 2.3.7.13/5 by equating 147/128 to 15/13, thus tempering out the huntsma, 640/637.		'''Buzzard''' is a 2.3.7 temperament that splits 3/1 into four sharpened 21/16 subfourths. It can be considered the "simplest 2.3.7 temperament after [[Slendric]]" since it equates two (not one) 64/63's with one 49/48. Since Buzzard sharpens 147/128, equating it to an exact semifourth at -2 generators, it can be extended to 2.3.7.13/5 by equating 147/128 to 15/13, thus tempering out the huntsma, 640/637.
	{{Navbox regtemp}}		{{Navbox regtemp}}
	{{Cat\| temperaments}}		{{Cat\| temperaments}}

Vector at 22:09, 14 March 2026

2026-03-14T22:09:19Z

← Older revision		Revision as of 22:09, 14 March 2026
Line 18:		Line 18:
	{{Navbox regtemp}}		{{Navbox regtemp}}
	{{Cat\| temperaments}}		{{Cat\| temperaments}}

			== List of patent vals ==
			{\| class="wikitable"
			\|+
			!Edo
			!Fifth tuning
			!7/4 tuning
			!Generator tuning
			\|-
			\|23
			\|678.26
			\|991.30
			\|469.57
			\|-
			\|28
			\|685.71
			\|985.71
			\|471.43
			\|-
			\|33
			\|690.91
			\|981.82
			\|472.73
			\|-
			\|38
			\|694.74
			\|978.95
			\|473.68
			\|-
			\|43
			\|697.67
			\|976.74
			\|474.42
			\|-
			\|48
			\|700.00
			\|975.00
			\|475.00
			\|-
			\|101
			\|700.99
			\|974.26
			\|475.25
			\|-
			\|53
			\|701.89
			\|973.58
			\|475.47
			\|-
			\|111
			\|702.70
			\|972.97
			\|475.68
			\|-
			\|58
			\|703.45
			\|972.41
			\|475.86
			\|-
			\|179
			\|703.91
			\|972.07
			\|475.98
			\|-
			\|121
			\|704.13
			\|971.90
			\|476.03
			\|-
			\|184
			\|704.35
			\|971.74
			\|476.09
			\|-
			\|63
			\|704.76
			\|971.43
			\|476.19
			\|-
			\|131
			\|705.34
			\|970.99
			\|476.34
			\|-
			\|68
			\|705.88
			\|970.59
			\|476.47
			\|-
			\|73
			\|706.85
			\|969.86
			\|476.71
			\|-
			\|78
			\|707.69
			\|969.23
			\|476.92
			\|-
			\|83
			\|708.43
			\|968.67
			\|477.11
			\|-
			\|5
			\|720.00
			\|960.00
			\|480.00
			\|}

Inthar at 21:27, 24 February 2026

2026-02-24T21:27:19Z

← Older revision		Revision as of 21:27, 24 February 2026
Line 15:		Line 15:
	\| Odd limit 2 = 15 \| Mistuning 2 = 4.09 \| Complexity 2 = 43		\| Odd limit 2 = 15 \| Mistuning 2 = 4.09 \| Complexity 2 = 43
	}}		}}
	'''Buzzard''' is a 2.3.7 temperament that splits 3/1 into four sharpened 21/16 subfourths. It can be considered the "simplest 2.3.7 temperament after [[Slendric]]" since it equates two (not one) 64/63's with one 49/48. Since Buzzard sharpens 147/128, it can be extended to 2.3.7.13/5 by tempering out the huntsma, 640/637.		'''Buzzard''' is a 2.3.7 temperament that splits 3/1 into four sharpened 21/16 subfourths. It can be considered the "simplest 2.3.7 temperament after [[Slendric]]" since it equates two (not one) 64/63's with one 49/48. Since Buzzard sharpens 147/128, it can be extended to 2.3.7.13/5 by equating 147/128 to 15/13, thus tempering out the huntsma, 640/637.
	{{Navbox regtemp}}		{{Navbox regtemp}}
	{{Cat\| temperaments}}		{{Cat\| temperaments}}