Buzzardsmic clan: Difference between revisions

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The [[2.3.7 subgroup|2.3.7-subgroup]] [[comma]] for the '''buzzardsmic clan''' is the buzzardsma, [[65536/64827]], with [[monzo]] {{monzo| 16 -3 0 -4 }}, which implies that the tritave, [[3/1]], is divided into four intervals each representing a [[21/16]] subfourth. Tempering out this comma implies a sharpened 7th harmonic, and especially a sharpened [[~]]21/16 generator, which approaches the 480{{c}} fourth of [[5edo]].

The [[2.3.7 subgroup|2.3.7-subgroup]] [[comma]] for the '''buzzardsmic clan''' is the buzzardsma, [[65536/64827]], with [[monzo]] {{monzo| 16 -3 0 -4 }}, which implies that the tritave, [[3/1]], is divided into four intervals each representing a [[21/16]] subfourth. [[Tempering out]] this comma implies a sharpened [[7/1|7th]] [[harmonic]], and especially a sharpened [[~]]21/16 generator, which approaches the 480{{c}} fourth of [[5edo]].

Extensions of buzzard to incorporate prime 5 along its chain of generators (and therefore the full [[7-limit]]) include septimal buzzard (53 & 58), which tempers out [[1728/1715]] (and [[5120/5103]]); subfourth (58 & 63), which tempers out [[10976/10935]]; and lemongrass (63 & 68), which tempers out [[245/243]]. All are considered below.

Extensions of buzzard to incorporate [[prime interval|prime]] [[5/1|5]] along its chain of generators (and therefore the full [[7-limit]]) include septimal buzzard ({{nowrap| 53 & 58 }}), which tempers out [[1728/1715]] (and [[5120/5103]]); subfourth ({{nowrap| 58 & 63 }}), which tempers out [[10976/10935]]; and lemongrass ({{nowrap| 63 & 68 }}), which tempers out [[245/243]]. All are considered below.

Weak extensions include submajor (10 & 43), which tempers out [[225/224]] and splits [[32/21]] (the superfifth) in two; and thuja (15 & 43), which tempers out [[126/125]] and splits [[21/8]] into three.

Weak extensions include submajor ({{nowrap| 10 & 43 }}), which tempers out [[225/224]] and splits [[32/21]] (the superfifth) in two; and thuja ({{nowrap| 15 & 43 }}), which tempers out [[126/125]] and splits [[21/8]] into three.

Full 7-limit temperaments discussed elsewhere are:

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= 2.3.7 subgroup =

== Buzzard ==

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[[Optimal tuning]]s:

* [[CTE]]: ~2 = 1200.000, ~21/16 = 475.727

* [[CTE]]: ~2 = 1200.000{{c}}, ~21/16 = 475.727{{c}}

* [[CWE]]: ~2 = 1200.000, ~21/16 = 475.833

* [[CWE]]: ~2 = 1200.000{{c}}, ~21/16 = 475.833{{c}}

[[Badness]]:

[[Badness]] (Sintel): 0.824

* Smith: 0.0240

* Dirichlet: 0.824

= Strong extensions =

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Septimal buzzard is not only a naturally motivated extension to 2.3.7 buzzard, but the main extension to [[vulture]] of practical interest, finding prime 7 at only 3 generators down so that the generator is interpreted as a sharp ~[[21/16]], though buzzard is powerful as a full 13-limit system in its own right. It is most naturally described as 53 & 58 (though [[48edo]] is an interesting higher-damage tuning of it for some purposes). As one might expect, [[111edo]] (111 = 53 + 58) is a great tuning for it. [[~~MOS~~ scale]]s of 3, 5, 8, 13, 18, 23, 28, 33, 38, 43, 48 or 53 notes are available.

Septimal buzzard is not only a naturally motivated extension to 2.3.7 buzzard, but the main extension to [[vulture]] of practical interest, finding prime 7 at only 3 generators down so that the generator is interpreted as a sharp ~[[21/16]], though buzzard is powerful as a full 13-limit system in its own right. It is most naturally described as {{nowrap| 53 & 58 }} (though [[48edo]] is an interesting higher-damage tuning of it for some purposes). As one might expect, [[111edo]] (111 = 53 + 58) is a great tuning for it. [[Mos scale]]s of 5, 8, 13, 18, 23, 28, 33, 38, 43, 48 or 53 notes are available.

Its 13-limit [[S-expression]]-based comma list is {[[1728/1715|S6/S7]], [[5120/5103|S8/S9]], [[847/845|S11/S13]], [[676/675|S13/S15]]}, with the structure of its 7-limit implied by the first two equivalences combined with the nontrivial [[JI]] equivalence [[36/35|S6]] = [[64/63|S8]] × [[81/80|S9]]. [[Hemifamity]] leverages it by splitting [[36/35]] into two syntonic~septimal commas, so buzzard naturally finds an interval between [[6/5]] and [[7/6]] which in the 7-limit is [[32/27]] and in the 13-limit is [[13/11]]. Then the vanishing of the orwellisma implies [[49/48]], the large septimal diesis, is equated with 36/35, so 49/48 is also split into two so that the system also finds an interval between 7/6 and 8/7 which in the 7-limit is 7/6 inflected down by a comma or 8/7 inflected up by a comma, and in the 13-limit is [[15/13]], so that it is clear this system naturally wants to be extended to and interpreted in the full 13-limit.

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[[Optimal tuning]]s:

* [[CTE]]: ~2 = 1200.000, ~21/16 = 475.555

* [[CTE]]: ~2 = 1200.000{{c}}, ~21/16 = 475.555{{c}}

: [[error map]]: {{val| 0.000 +0.263 +0.333 +4.510 }}

* [[POTE]]: ~2 = 1200.000, ~21/16 = 475.636

* [[POTE]]: ~2 = 1200.000{{c}}, ~21/16 = 475.636{{c}}

: error map: {{val| 0.000 +0.589 +2.045 +4.266 }}

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Optimal tunings:

* CTE: ~2 = 1200.000, ~21/16 = 475.625

* CTE: ~2 = 1200.000{{c}}, ~21/16 = 475.625{{c}}

* POTE: ~2 = 1200.000, ~21/16 = 475.700

* POTE: ~2 = 1200.000{{c}}, ~21/16 = 475.700{{c}}

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Optimal tunings:

* CTE: ~2 = 1200.000, ~21/16 = 475.615

* CTE: ~2 = 1200.000{{c}}, ~21/16 = 475.615{{c}}

* POTE: ~2 = 1200.000, ~21/16 = 475.697

* POTE: ~2 = 1200.000{{c}}, ~21/16 = 475.697{{c}}

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Optimal tunings:

* CTE: ~2 = 1200.000, ~21/16 = 475.638

* CTE: ~2 = 1200.000{{c}}, ~21/16 = 475.638{{c}}

* POTE: ~2 = 1200.000, ~21/16 = 475.692

* POTE: ~2 = 1200.000{{c}}, ~21/16 = 475.692{{c}}

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Optimal tunings:

* CTE: ~2 = 1200.000, ~21/16 = 475.617

* CTE: ~2 = 1200.000{{c}}, ~21/16 = 475.617{{c}}

* POTE: ~2 = 1200.000, ~21/16 = 475.679

* POTE: ~2 = 1200.000{{c}}, ~21/16 = 475.679{{c}}

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Optimal tunings:

* CTE: ~2 = 1200.000, ~21/16 = 475.454

* CTE: ~2 = 1200.000{{c}}, ~21/16 = 475.454{{c}}

* POTE: ~2 = 1200.000, ~21/16 = 475.436

* POTE: ~2 = 1200.000{{c}}, ~21/16 = 475.436{{c}}

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Optimal tunings:

* CTE: ~2 = 1200.000, ~21/16 = 475.495

* CTE: ~2 = 1200.000{{c}}, ~21/16 = 475.495{{c}}

* POTE: ~2 = 1200.000, ~21/16 = 475.464

* POTE: ~2 = 1200.000{{c}}, ~21/16 = 475.464{{c}}

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~~: mapping generators: ~2, ~21/16~~

[[Optimal tuning]] ([[POTE]]): ~2 = 1200.000{{c}}, ~21/16 = 475.991{{c}}

[[Optimal tuning]] ([[POTE]]): ~2 = ~~1\1~~, ~21/16 = 475.991

[[Badness]]: 0.140722

[[Badness]] (Smith): 0.140722

=== 11-limit ===

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Mapping: {{mapping| 1 0 17 4 11 | 0 4 -37 -3 -19 }}

Optimal tuning (POTE): ~2 = ~~1\1~~, ~21/16 = 475.995

Optimal tuning (POTE): ~2 = 1200.000{{c}}, ~21/16 = 475.995{{c}}

Badness: 0.045323

Badness (Smith): 0.045323

=== 13-limit ===

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Mapping: {{mapping| 1 0 17 4 11 16 | 0 4 -37 -3 -19 -31 }}

Optimal tuning (POTE): ~2 = ~~1\1~~, ~21/16 = 475.996

Optimal tuning (POTE): ~2 = 1200.000{{c}}, ~21/16 = 475.996{{c}}

Badness: 0.023800

Badness (Smith): 0.023800

== Lemongrass ==

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~~: mapping generators~~: ~2, ~21/16

[[Optimal tuning]] ([[POTE]]): ~2 = 1200.0000{{c}}, ~21/16 = 476.4448{{c}}

~~[[Optimal tuning]] ([[POTE]]): ~2 = 1\1, ~21/16 = 476.4448~~

[[Badness]] (Sintel): 2.902

= Weak extensions =

== Submajor ==

=== 7-limit ===

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: mapping generators: ~2, ~49/40

[[Optimal tuning]] ([[POTE]]): ~2 = ~~1\1~~, ~49/40 = 362.255

[[Optimal tuning]] ([[POTE]]): ~2 = 1200.000{{c}}, ~49/40 = 362.255{{c}}

[[Badness]]: 0.060533

[[Badness]] (Smith): 0.060533

==== 2.3.5.7.13 subgroup ====

This temperament naturally comes about from a structure in ~~EDOs~~ like [[43edo|43]] and [[53edo|53]] where two flattened ~[[13/8]] intervals reach the ~~[[No-fives subgroup temperaments#Buzzard|~~buzzard]] generator of ~[[21/16]], two of which produce a semitritave (that can here be equated to [[26/15]], providing a mapping of 5 significantly less complex than the [[vulture]] mapping), and two of those finally reach [[3/1]].

This temperament naturally comes about from a structure in edos like [[43edo|43]] and [[53edo|53]] where two flattened ~[[13/8]] intervals reach the buzzard generator of ~[[21/16]], two of which produce a semitritave (that can here be equated to [[26/15]], providing a mapping of 5 significantly less complex than the [[vulture]] mapping), and two of those finally reach [[3/1]].

Subgroup: 2.3.5.7.13

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Mapping: {{mapping| 1 4 -1 1 4 | 0 -8 11 6 -1 }}

Optimal tuning (CTE): ~2 = ~~1\1~~, ~16/13 = 362.242

Optimal tuning (CTE): ~2 = 1200.000{{c}}, ~16/13 = 362.242{{c}}

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Mapping: {{mapping| 1 4 -1 1 11 | 0 -8 11 6 -25 }}

Optimal tuning (POTE): ~2 = ~~1\1~~, ~27/22 = 362.101

Optimal tuning (POTE): ~2 = 1200.000{{c}}, ~27/22 = 362.101{{c}}

{{Optimal ET sequence|legend=1| 10, 43e, 53, 116, 169de, 285cde }}

Badness: 0.050582

Badness (Smith): 0.050582

==== 13-limit ====

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Mapping: {{mapping| 1 4 -1 1 11 4 | 0 -8 11 6 -25 -1 }}

Optimal tuning (POTE): ~2 = ~~1\1~~, ~16/13 = 362.105

Optimal tuning (POTE): ~2 = 1200.000{{c}}, ~16/13 = 362.105{{c}}

{{Optimal ET sequence|legend=1| 10, 43e, 53, 116, 169de, 285cdef }}

Badness: 0.027689

Badness (Smith): 0.027689

=== Interpental ===

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Mapping: {{mapping| 1 4 -1 1 -5 | 0 -8 11 6 28 }}

Optimal tuning (POTE): ~2 = ~~1\1~~, ~49/40 = 362.418

Optimal tuning (POTE): ~2 = 1200.000{{c}}, ~49/40 = 362.418{{c}}

Badness: 0.051806

Badness (Smith): 0.051806

==== 13-limit ====

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Mapping: {{mapping| 1 4 -1 1 -5 4 | 0 -8 11 6 28 -1 }}

Optimal tuning (POTE): ~2 = ~~1\1~~, ~16/13 = 362.402

Optimal tuning (POTE): ~2 = 1200.000{{c}}, ~16/13 = 362.402{{c}}

Badness: 0.029680

Badness (Smith): 0.029680

== Thuja ==

: ''For the 5-limit version ~~of this temperament~~, see [[Miscellaneous 5-limit temperaments #Thuja]].''

: ''For the 5-limit version, see [[Miscellaneous 5-limit temperaments #Thuja]].''

[[Subgroup]]: 2.3.5.7

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: mapping generators: ~2, ~175/128

[[Optimal tuning]] ([[POTE]]): ~2 = ~~1\1~~, ~175/128 = 558.605

[[Optimal tuning]] ([[POTE]]): ~2 = 1200.000{{c}}, ~175/128 = 558.605{{c}}

[[Badness]]: 0.088441

[[Badness]] (Smith): 0.088441

=== 11-limit ===

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Mapping: {{mapping| 1 -4 0 7 3 | 0 12 5 -9 1 }}

Optimal tuning (POTE): ~2 = ~~1\1~~, ~11/8 = 558.620

Optimal tuning (POTE): ~2 = 1200.000{{c}}, ~11/8 = 558.620{{c}}

Badness: 0.033078

Badness (Smith): 0.033078

=== 13-limit ===

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Mapping: {{mapping| 1 -4 0 7 3 -7 | 0 12 5 -9 1 23 }}

Optimal tuning (POTE): ~2 = ~~1\1~~, ~11/8 = 558.589

Optimal tuning (POTE): ~2 = 1200.000{{c}}, ~11/8 = 558.589{{c}}

Badness: 0.022838

Badness (Smith): 0.022838

=== 17-limit ===

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Mapping: {{mapping| 1 -4 0 7 3 -7 12 | 0 12 5 -9 1 23 -17 }}

Optimal tuning (POTE): ~2 = ~~1\1~~, ~11/8 = 558.509

Optimal tuning (POTE): ~2 = 1200.000{{c}}, ~11/8 = 558.509{{c}}

Badness: 0.022293

Badness (Smith): 0.022293

=== 19-limit ===

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Mapping: {{mapping| 1 -4 0 7 3 -7 12 1 | 0 12 5 -9 1 23 -17 7 }}

Optimal tuning (POTE): ~2 = ~~1\1~~, ~11/8 = 558.504

Optimal tuning (POTE): ~2 = 1200.000{{c}}, ~11/8 = 558.504{{c}}

Badness: 0.018938

Badness (Smith): 0.018938

=== 23-limit ===

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Mapping: {{mapping| 1 -4 0 7 3 -7 12 1 5 | 0 12 5 -9 1 23 -17 7 -1 }}

Optimal tuning (POTE): ~2 = ~~1\1~~, ~11/8 = 558.522

Optimal tuning (POTE): ~2 = 1200.000{{c}}, ~11/8 = 558.522{{c}}

Badness: 0.016581

Badness (Smith): 0.016581

=== 29-limit ===

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Mapping: {{mapping| 1 -4 0 7 3 -7 12 1 5 3 | 0 12 5 -9 1 23 -17 7 -1 4 }}

Optimal tuning (POTE): ~2 = ~~1\1~~, ~11/8 = 558.520

Optimal tuning (POTE): ~2 = 1200.000{{c}}, ~11/8 = 558.520{{c}}

Badness: 0.013762

Badness (Smith): 0.013762

== Anthoine ==

Anthoine is generated by [[5/4]] and tempers out [[3125/3087]] in addition to the buzzardsma, so that 32/21 is found at 5 generators up. It is most notable as the 25 & 28 temperament and as the chain of 5/4s present in 53edo.

Anthoine is generated by [[5/4]] and tempers out [[3125/3087]] in addition to the buzzardsma, so that 32/21 is found at 5 generators up. It is most notable as the {{nowrap| 25 & 28 }} temperament and as the chain of 5/4's present in 53edo.

~~=== 7-limit ===~~

Subgroup: 2.3.5.7

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Mapping: {{mapping| 1 8 2 -2 | 0 -20 1 15 }}

: mapping generators: ~2, ~5/4

Optimal tuning (CTE): ~2 = ~~1\1~~, ~5/4 = 384.856

Optimal tuning (CTE): ~2 = 1200.000{{c}}, ~5/4 = 384.856{{c}}

{{Optimal ET sequence|legend=1| 25, 53, 184, 237d, 290d, 343dd }}

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[[Category:Temperament clans]]

[[Category:Pages with mostly numerical content]]

~~[[Category:Buzzard]]~~

[[Category:Buzzardsmic clan| ]]

[[Category:Rank 2]]

[[Category:Listen]]

@@ Line 1: / Line 1: @@
 {{Technical data page}}
-The [[2.3.7 subgroup|2.3.7-subgroup]] [[comma]] for the '''buzzardsmic clan''' is the buzzardsma, [[65536/64827]], with [[monzo]] {{monzo| 16 -3 0 -4 }}, which implies that the tritave, [[3/1]], is divided into four intervals each representing a [[21/16]] subfourth. Tempering out this comma implies a sharpened 7th harmonic, and especially a sharpened [[~]]21/16 generator, which approaches the 480{{c}} fourth of [[5edo]].
+The [[2.3.7 subgroup|2.3.7-subgroup]] [[comma]] for the '''buzzardsmic clan''' is the buzzardsma, [[65536/64827]], with [[monzo]] {{monzo| 16 -3 0 -4 }}, which implies that the tritave, [[3/1]], is divided into four intervals each representing a [[21/16]] subfourth. [[Tempering out]] this comma implies a sharpened [[7/1|7th]] [[harmonic]], and especially a sharpened [[~]]21/16 generator, which approaches the 480{{c}} fourth of [[5edo]].
-Extensions of buzzard to incorporate prime 5 along its chain of generators (and therefore the full [[7-limit]]) include septimal buzzard (53 & 58), which tempers out [[1728/1715]] (and [[5120/5103]]); subfourth (58 & 63), which tempers out [[10976/10935]]; and lemongrass (63 & 68), which tempers out [[245/243]]. All are considered below.
+Extensions of buzzard to incorporate [[prime interval|prime]] [[5/1|5]] along its chain of generators (and therefore the full [[7-limit]]) include septimal buzzard ({{nowrap| 53 & 58 }}), which tempers out [[1728/1715]] (and [[5120/5103]]); subfourth ({{nowrap| 58 & 63 }}), which tempers out [[10976/10935]]; and lemongrass ({{nowrap| 63 & 68 }}), which tempers out [[245/243]]. All are considered below.
-Weak extensions include submajor (10 & 43), which tempers out [[225/224]] and splits [[32/21]] (the superfifth) in two; and thuja (15 & 43), which tempers out [[126/125]] and splits [[21/8]] into three.
+Weak extensions include submajor ({{nowrap| 10 & 43 }}), which tempers out [[225/224]] and splits [[32/21]] (the superfifth) in two; and thuja ({{nowrap| 15 & 43 }}), which tempers out [[126/125]] and splits [[21/8]] into three.
 Full 7-limit temperaments discussed elsewhere are:
@@ Line 15: / Line 15: @@
 = 2.3.7 subgroup =
 == Buzzard ==
 {{Main| Buzzard }}
@@ Line 26: / Line 25: @@
 [[Optimal tuning]]s:
-* [[CTE]]: ~2 = 1200.000, ~21/16 = 475.727
+* [[CTE]]: ~2 = 1200.000{{c}}, ~21/16 = 475.727{{c}}
-* [[CWE]]: ~2 = 1200.000, ~21/16 = 475.833
+* [[CWE]]: ~2 = 1200.000{{c}}, ~21/16 = 475.833{{c}}
 {{Optimal ET sequence|legend=1| 5, 33, 38, 43, 48, 53, 58 }}
-[[Badness]]:
+[[Badness]] (Sintel): 0.824
-* Smith: 0.0240
-* Dirichlet: 0.824
 = Strong extensions =
@@ Line 41: / Line 38: @@
 {{See also| Vulture family }}
-Septimal buzzard is not only a naturally motivated extension to 2.3.7 buzzard, but the main extension to [[vulture]] of practical interest, finding prime 7 at only 3 generators down so that the generator is interpreted as a sharp ~[[21/16]], though buzzard is powerful as a full 13-limit system in its own right. It is most naturally described as 53 & 58 (though [[48edo]] is an interesting higher-damage tuning of it for some purposes). As one might expect, [[111edo]] (111 = 53 + 58) is a great tuning for it. [[MOS scale]]s of 3, 5, 8, 13, 18, 23, 28, 33, 38, 43, 48 or 53 notes are available.
+Septimal buzzard is not only a naturally motivated extension to 2.3.7 buzzard, but the main extension to [[vulture]] of practical interest, finding prime 7 at only 3 generators down so that the generator is interpreted as a sharp ~[[21/16]], though buzzard is powerful as a full 13-limit system in its own right. It is most naturally described as {{nowrap| 53 & 58 }} (though [[48edo]] is an interesting higher-damage tuning of it for some purposes). As one might expect, [[111edo]] (111 = 53 + 58) is a great tuning for it. [[Mos scale]]s of 5, 8, 13, 18, 23, 28, 33, 38, 43, 48 or 53 notes are available.
 Its 13-limit [[S-expression]]-based comma list is {[[1728/1715|S6/S7]], [[5120/5103|S8/S9]], [[847/845|S11/S13]], [[676/675|S13/S15]]}, with the structure of its 7-limit implied by the first two equivalences combined with the nontrivial [[JI]] equivalence [[36/35|S6]] = [[64/63|S8]] × [[81/80|S9]]. [[Hemifamity]] leverages it by splitting [[36/35]] into two syntonic~septimal commas, so buzzard naturally finds an interval between [[6/5]] and [[7/6]] which in the 7-limit is [[32/27]] and in the 13-limit is [[13/11]]. Then the vanishing of the orwellisma implies [[49/48]], the large septimal diesis, is equated with 36/35, so 49/48 is also split into two so that the system also finds an interval between 7/6 and 8/7 which in the 7-limit is 7/6 inflected down by a comma or 8/7 inflected up by a comma, and in the 13-limit is [[15/13]], so that it is clear this system naturally wants to be extended to and interpreted in the full 13-limit.
@@ Line 52: / Line 49: @@
 [[Optimal tuning]]s:
-* [[CTE]]: ~2 = 1200.000, ~21/16 = 475.555
+* [[CTE]]: ~2 = 1200.000{{c}}, ~21/16 = 475.555{{c}}
 : [[error map]]: {{val| 0.000 +0.263 +0.333 +4.510 }}
-* [[POTE]]: ~2 = 1200.000, ~21/16 = 475.636
+* [[POTE]]: ~2 = 1200.000{{c}}, ~21/16 = 475.636{{c}}
 : error map: {{val| 0.000 +0.589 +2.045 +4.266 }}
@@ Line 69: / Line 66: @@
 Optimal tunings:
-* CTE: ~2 = 1200.000, ~21/16 = 475.625
+* CTE: ~2 = 1200.000{{c}}, ~21/16 = 475.625{{c}}
-* POTE: ~2 = 1200.000, ~21/16 = 475.700
+* POTE: ~2 = 1200.000{{c}}, ~21/16 = 475.700{{c}}
 {{Optimal ET sequence|legend=0| 53, 58, 111, 280cd }}
@@ Line 84: / Line 81: @@
 Optimal tunings:
-* CTE: ~2 = 1200.000, ~21/16 = 475.615
+* CTE: ~2 = 1200.000{{c}}, ~21/16 = 475.615{{c}}
-* POTE: ~2 = 1200.000, ~21/16 = 475.697
+* POTE: ~2 = 1200.000{{c}}, ~21/16 = 475.697{{c}}
 {{Optimal ET sequence|legend=0| 53, 58, 111, 280cdf }}
@@ Line 99: / Line 96: @@
 Optimal tunings:
-* CTE: ~2 = 1200.000, ~21/16 = 475.638
+* CTE: ~2 = 1200.000{{c}}, ~21/16 = 475.638{{c}}
-* POTE: ~2 = 1200.000, ~21/16 = 475.692
+* POTE: ~2 = 1200.000{{c}}, ~21/16 = 475.692{{c}}
 {{Optimal ET sequence|legend=0| 53, 58, 111 }}
@@ Line 114: / Line 111: @@
 Optimal tunings:
-* CTE: ~2 = 1200.000, ~21/16 = 475.617
+* CTE: ~2 = 1200.000{{c}}, ~21/16 = 475.617{{c}}
-* POTE: ~2 = 1200.000, ~21/16 = 475.679
+* POTE: ~2 = 1200.000{{c}}, ~21/16 = 475.679{{c}}
 {{Optimal ET sequence|legend=0| 53, 58h, 111 }}
@@ Line 129: / Line 126: @@
 Optimal tunings:
-* CTE: ~2 = 1200.000, ~21/16 = 475.454
+* CTE: ~2 = 1200.000{{c}}, ~21/16 = 475.454{{c}}
-* POTE: ~2 = 1200.000, ~21/16 = 475.436
+* POTE: ~2 = 1200.000{{c}}, ~21/16 = 475.436{{c}}
 {{Optimal ET sequence|legend=0| 5, 48, 53 }}
@@ Line 144: / Line 141: @@
 Optimal tunings:
-* CTE: ~2 = 1200.000, ~21/16 = 475.495
+* CTE: ~2 = 1200.000{{c}}, ~21/16 = 475.495{{c}}
-* POTE: ~2 = 1200.000, ~21/16 = 475.464
+* POTE: ~2 = 1200.000{{c}}, ~21/16 = 475.464{{c}}
 {{Optimal ET sequence|legend=0| 5, 48f, 53 }}
@@ Line 158: / Line 155: @@
 {{Mapping|legend=1| 1 0 17 4 | 0 4 -37 -3 }}
-: mapping generators: ~2, ~21/16
+[[Optimal tuning]] ([[POTE]]): ~2 = 1200.000{{c}}, ~21/16 = 475.991{{c}}
-[[Optimal tuning]] ([[POTE]]): ~2 = 1\1, ~21/16 = 475.991
 {{Optimal ET sequence|legend=1| 58, 121, 179, 300bd, 479bcd }}
-[[Badness]]: 0.140722
+[[Badness]] (Smith): 0.140722
 === 11-limit ===
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 Mapping: {{mapping| 1 0 17 4 11 | 0 4 -37 -3 -19 }}
-Optimal tuning (POTE): ~2 = 1\1, ~21/16 = 475.995
+Optimal tuning (POTE): ~2 = 1200.000{{c}}, ~21/16 = 475.995{{c}}
 {{Optimal ET sequence|legend=1| 58, 121, 179e, 300bde }}
-Badness: 0.045323
+Badness (Smith): 0.045323
 === 13-limit ===
@@ Line 186: / Line 181: @@
 Mapping: {{mapping| 1 0 17 4 11 16 | 0 4 -37 -3 -19 -31 }}
-Optimal tuning (POTE): ~2 = 1\1, ~21/16 = 475.996
+Optimal tuning (POTE): ~2 = 1200.000{{c}}, ~21/16 = 475.996{{c}}
 {{Optimal ET sequence|legend=1| 58, 121, 179ef, 300bdef }}
-Badness: 0.023800
+Badness (Smith): 0.023800
 == Lemongrass ==
@@ Line 199: / Line 194: @@
 {{Mapping|legend=1| 1 0 17 4 | 0 4 26 -3 }}
-: mapping generators: ~2, ~21/16
+[[Optimal tuning]] ([[POTE]]): ~2 = 1200.0000{{c}}, ~21/16 = 476.4448{{c}}
-[[Optimal tuning]] ([[POTE]]): ~2 = 1\1, ~21/16 = 476.4448
+{{Optimal ET sequence|legend=1| 5, …, 63, 68 }}
-{{Optimal ET sequence|legend=1| 5, ..., 63, 68 }}
 [[Badness]] (Sintel): 2.902
 = Weak extensions =
 == Submajor ==
 === 7-limit ===
@@ Line 216: / Line 208: @@
 {{Mapping|legend=1| 1 4 -1 1 | 0 -8 11 6 }}
+: mapping generators: ~2, ~49/40
-[[Optimal tuning]] ([[POTE]]): ~2 = 1\1, ~49/40 = 362.255
+[[Optimal tuning]] ([[POTE]]): ~2 = 1200.000{{c}}, ~49/40 = 362.255{{c}}
 {{Optimal ET sequence|legend=1| 10, 33, 43, 53 }}
-[[Badness]]: 0.060533
+[[Badness]] (Smith): 0.060533
 ==== 2.3.5.7.13 subgroup ====
-{{ See also | Greater tendoneutralic }}
+{{See also| Greater tendoneutralic }}
-This temperament naturally comes about from a structure in EDOs like [[43edo|43]] and [[53edo|53]] where two flattened ~[[13/8]] intervals reach the [[No-fives subgroup temperaments#Buzzard|buzzard]] generator of ~[[21/16]], two of which produce a semitritave (that can here be equated to [[26/15]], providing a mapping of 5 significantly less complex than the [[vulture]] mapping), and two of those finally reach [[3/1]].
+This temperament naturally comes about from a structure in edos like [[43edo|43]] and [[53edo|53]] where two flattened ~[[13/8]] intervals reach the buzzard generator of ~[[21/16]], two of which produce a semitritave (that can here be equated to [[26/15]], providing a mapping of 5 significantly less complex than the [[vulture]] mapping), and two of those finally reach [[3/1]].
 Subgroup: 2.3.5.7.13
@@ Line 234: / Line 227: @@
 Mapping: {{mapping| 1 4 -1 1 4 | 0 -8 11 6 -1 }}
-Optimal tuning (CTE): ~2 = 1\1, ~16/13 = 362.242
+Optimal tuning (CTE): ~2 = 1200.000{{c}}, ~16/13 = 362.242{{c}}
 {{Optimal ET sequence|legend=1| 10, 33, 43, 53 }}
@@ Line 249: / Line 242: @@
 Mapping: {{mapping| 1 4 -1 1 11 | 0 -8 11 6 -25 }}
-Optimal tuning (POTE): ~2 = 1\1, ~27/22 = 362.101
+Optimal tuning (POTE): ~2 = 1200.000{{c}}, ~27/22 = 362.101{{c}}
 {{Optimal ET sequence|legend=1| 10, 43e, 53, 116, 169de, 285cde }}
-Badness: 0.050582
+Badness (Smith): 0.050582
 ==== 13-limit ====
@@ Line 262: / Line 255: @@
 Mapping: {{mapping| 1 4 -1 1 11 4 | 0 -8 11 6 -25 -1 }}
-Optimal tuning (POTE): ~2 = 1\1, ~16/13 = 362.105
+Optimal tuning (POTE): ~2 = 1200.000{{c}}, ~16/13 = 362.105{{c}}
 {{Optimal ET sequence|legend=1| 10, 43e, 53, 116, 169de, 285cdef }}
-Badness: 0.027689
+Badness (Smith): 0.027689
 === Interpental ===
@@ Line 275: / Line 268: @@
 Mapping: {{mapping| 1 4 -1 1 -5 | 0 -8 11 6 28 }}
-Optimal tuning (POTE): ~2 = 1\1, ~49/40 = 362.418
+Optimal tuning (POTE): ~2 = 1200.000{{c}}, ~49/40 = 362.418{{c}}
 {{Optimal ET sequence|legend=1| 43, 53, 96, 149d }}
-Badness: 0.051806
+Badness (Smith): 0.051806
 ==== 13-limit ====
@@ Line 288: / Line 281: @@
 Mapping: {{mapping| 1 4 -1 1 -5 4 | 0 -8 11 6 28 -1 }}
-Optimal tuning (POTE): ~2 = 1\1, ~16/13 = 362.402
+Optimal tuning (POTE): ~2 = 1200.000{{c}}, ~16/13 = 362.402{{c}}
 {{Optimal ET sequence|legend=1| 43, 53, 96, 149d }}
-Badness: 0.029680
+Badness (Smith): 0.029680
 == Thuja ==
-: ''For the 5-limit version of this temperament, see [[Miscellaneous 5-limit temperaments #Thuja]].''
+: ''For the 5-limit version, see [[Miscellaneous 5-limit temperaments #Thuja]].''
 [[Subgroup]]: 2.3.5.7
@@ Line 302: / Line 295: @@
 {{Mapping|legend=1| 1 -4 0 7 | 0 12 5 -9 }}
+: mapping generators: ~2, ~175/128
-[[Optimal tuning]] ([[POTE]]): ~2 = 1\1, ~175/128 = 558.605
+[[Optimal tuning]] ([[POTE]]): ~2 = 1200.000{{c}}, ~175/128 = 558.605{{c}}
 {{Optimal ET sequence|legend=1| 15, 43, 58 }}
-[[Badness]]: 0.088441
+[[Badness]] (Smith): 0.088441
 === 11-limit ===
@@ Line 316: / Line 310: @@
 Mapping: {{mapping| 1 -4 0 7 3 | 0 12 5 -9 1 }}
-Optimal tuning (POTE): ~2 = 1\1, ~11/8 = 558.620
+Optimal tuning (POTE): ~2 = 1200.000{{c}}, ~11/8 = 558.620{{c}}
 {{Optimal ET sequence|legend=1| 15, 43, 58 }}
-Badness: 0.033078
+Badness (Smith): 0.033078
 === 13-limit ===
@@ Line 329: / Line 323: @@
 Mapping: {{mapping| 1 -4 0 7 3 -7 | 0 12 5 -9 1 23 }}
-Optimal tuning (POTE): ~2 = 1\1, ~11/8 = 558.589
+Optimal tuning (POTE): ~2 = 1200.000{{c}}, ~11/8 = 558.589{{c}}
 {{Optimal ET sequence|legend=1| 15, 43, 58 }}
-Badness: 0.022838
+Badness (Smith): 0.022838
 === 17-limit ===
@@ Line 342: / Line 336: @@
 Mapping: {{mapping| 1 -4 0 7 3 -7 12 | 0 12 5 -9 1 23 -17 }}
-Optimal tuning (POTE): ~2 = 1\1, ~11/8 = 558.509
+Optimal tuning (POTE): ~2 = 1200.000{{c}}, ~11/8 = 558.509{{c}}
 {{Optimal ET sequence|legend=1| 15, 43, 58 }}
-Badness: 0.022293
+Badness (Smith): 0.022293
 === 19-limit ===
@@ Line 355: / Line 349: @@
 Mapping: {{mapping| 1 -4 0 7 3 -7 12 1 | 0 12 5 -9 1 23 -17 7 }}
-Optimal tuning (POTE): ~2 = 1\1, ~11/8 = 558.504
+Optimal tuning (POTE): ~2 = 1200.000{{c}}, ~11/8 = 558.504{{c}}
 {{Optimal ET sequence|legend=1| 15, 43, 58h }}
-Badness: 0.018938
+Badness (Smith): 0.018938
 === 23-limit ===
@@ Line 368: / Line 362: @@
 Mapping: {{mapping| 1 -4 0 7 3 -7 12 1 5 | 0 12 5 -9 1 23 -17 7 -1 }}
-Optimal tuning (POTE): ~2 = 1\1, ~11/8 = 558.522
+Optimal tuning (POTE): ~2 = 1200.000{{c}}, ~11/8 = 558.522{{c}}
 {{Optimal ET sequence|legend=1| 15, 43, 58hi }}
-Badness: 0.016581
+Badness (Smith): 0.016581
 === 29-limit ===
@@ Line 383: / Line 377: @@
 Mapping: {{mapping| 1 -4 0 7 3 -7 12 1 5 3 | 0 12 5 -9 1 23 -17 7 -1 4 }}
-Optimal tuning (POTE): ~2 = 1\1, ~11/8 = 558.520
+Optimal tuning (POTE): ~2 = 1200.000{{c}}, ~11/8 = 558.520{{c}}
 {{Optimal ET sequence|legend=1| 15, 43, 58hi }}
-Badness: 0.013762
+Badness (Smith): 0.013762
 == Anthoine ==
-Anthoine is generated by [[5/4]] and tempers out [[3125/3087]] in addition to the buzzardsma, so that 32/21 is found at 5 generators up. It is most notable as the 25 & 28 temperament and as the chain of 5/4s present in 53edo.
+Anthoine is generated by [[5/4]] and tempers out [[3125/3087]] in addition to the buzzardsma, so that 32/21 is found at 5 generators up. It is most notable as the {{nowrap| 25 & 28 }} temperament and as the chain of 5/4's present in 53edo.
-=== 7-limit ===
 Subgroup: 2.3.5.7
@@ Line 398: / Line 391: @@
 Mapping: {{mapping| 1 8 2 -2 | 0 -20 1 15 }}
+: mapping generators: ~2, ~5/4
-Optimal tuning (CTE): ~2 = 1\1, ~5/4 = 384.856
+Optimal tuning (CTE): ~2 = 1200.000{{c}}, ~5/4 = 384.856{{c}}
 {{Optimal ET sequence|legend=1| 25, 53, 184, 237d, 290d, 343dd }}
@@ Line 407: / Line 401: @@
 [[Category:Temperament clans]]
 [[Category:Pages with mostly numerical content]]
-[[Category:Buzzard]]
 [[Category:Buzzardsmic clan| ]] <!-- main article -->
 [[Category:Rank 2]]
 [[Category:Listen]]