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Full 7-limit temperaments discussed elsewhere are:
Full 7-limit temperaments discussed elsewhere are:
* [[Blackwood]] (+28/27) → [[Limmic temperaments #Blackwood|Limmic temperaments]]
* [[Blackwood]] (+28/27) → [[Blackwood family #Blackwood|Blackwood family]]
* ''[[Quadrasruta]]'' (+2048/2025) → [[Diaschismic family #Quadrasruta|Diaschismic family]]
* ''[[Quadrasruta]]'' (+2048/2025) → [[Diaschismic family #Quadrasruta|Diaschismic family]]
* ''[[Hemikleismic]] (+4000/3969) → [[Kleismic family #Hemikleismic|Kleismic family]]
* ''[[Hemikleismic]] (+4000/3969) → [[Kleismic family #Hemikleismic|Kleismic family]]
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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 {{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.
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.
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]]. [[Aberschismic]] 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.


[[Subgroup]]: 2.3.5.7
[[Subgroup]]: 2.3.5.7
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Comma list: 176/175, 540/539, 5120/5103
Comma list: 176/175, 540/539, 5120/5103


Mapping: {{mapping| 1 0 -6 4 -12 | 0 4 21 -3 39 }}
{{Mapping|legend=0| 1 0 -6 4 -12 | 0 4 21 -3 39 }}


Optimal tunings:  
Optimal tunings:  
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Comma list: 176/175, 351/350, 540/539, 676/675
Comma list: 176/175, 351/350, 540/539, 676/675


Mapping: {{mapping| 1 0 -6 4 -12 -7 | 0 4 21 -3 39 27 }}
{{Mapping|legend=0| 1 0 -6 4 -12 -7 | 0 4 21 -3 39 27 }}


Optimal tunings:  
Optimal tunings:  
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Comma list: 176/175, 256/255, 351/350, 442/441, 540/539
Comma list: 176/175, 256/255, 351/350, 442/441, 540/539


Mapping: {{mapping| 1 0 -6 4 -12 -7 14 | 0 4 21 -3 39 27 -25 }}
{{Mapping|legend=0| 1 0 -6 4 -12 -7 14 | 0 4 21 -3 39 27 -25 }}


Optimal tunings:  
Optimal tunings:  
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Comma list: 176/175, 256/255, 286/285, 324/323, 351/350, 540/539
Comma list: 176/175, 256/255, 286/285, 324/323, 351/350, 540/539


Mapping: {{mapping| 1 0 -6 4 -12 -7 14 -12 | 0 4 21 -3 39 27 -25 41 }}
{{Mapping|legend=0| 1 0 -6 4 -12 -7 14 -12 | 0 4 21 -3 39 27 -25 41 }}


Optimal tunings:  
Optimal tunings:  
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Comma list: 99/98, 385/384, 2200/2187
Comma list: 99/98, 385/384, 2200/2187


Mapping: {{mapping| 1 0 -6 4 9 | 0 4 21 -3 -14 }}
{{Mapping|legend=0| 1 0 -6 4 9 | 0 4 21 -3 -14 }}


Optimal tunings:  
Optimal tunings:  
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Comma list: 99/98, 275/273, 385/384, 572/567
Comma list: 99/98, 275/273, 385/384, 572/567


Mapping: {{mapping| 1 0 -6 4 9 -7 | 0 4 21 -3 -14 27 }}
{{Mapping|legend=0| 1 0 -6 4 9 -7 | 0 4 21 -3 -14 27 }}


Optimal tunings:  
Optimal tunings:  
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Comma list: 540/539, 896/891, 12005/11979
Comma list: 540/539, 896/891, 12005/11979


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


Optimal tunings:  
Optimal tunings:  
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Comma list: 352/351, 364/363, 540/539, 676/675
Comma list: 352/351, 364/363, 540/539, 676/675


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


Optimal tunings:  
Optimal tunings:  
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== Lemongrass ==
== Lemongrass ==
Lemongrass tempers out [[245/243]] and may be described as the {{nowrap| 63 & 68 }} temperament. Characterized by a sharper generator than septimal buzzard, lemongrass compresses the septimal comma so much that the syntonic comma is no longer equated with it but with twice of it, or the large septimal diesis. [[68edo]] itself is a great tuning for this, though [[63edo]] and [[73edo]] are also possible.  
Named by [[Lériendil]] in 2025, lemongrass tempers out [[245/243]] and may be described as the {{nowrap| 63 & 68 }} temperament. Characterized by a sharper generator than septimal buzzard, lemongrass compresses the septimal comma so much that the syntonic comma is no longer equated with it but with twice of it, or the large septimal diesis. [[68edo]] itself is a great tuning for this, though [[63edo]] and [[73edo]] are also possible.  


[[Subgroup]]: 2.3.5.7
[[Subgroup]]: 2.3.5.7
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Comma list: 169/168, 225/224, 640/637
Comma list: 169/168, 225/224, 640/637


Mapping: {{mapping| 1 -4 10 7 3 | 0 8 -11 -6 1 }}
{{Mapping|legend=0| 1 -4 10 7 3 | 0 8 -11 -6 1 }}


Optimal tunings:  
Optimal tunings:  
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Comma list: 225/224, 385/384, 6655/6561
Comma list: 225/224, 385/384, 6655/6561


Mapping: {{mapping| 1 -4 10 7 -14 | 0 8 -11 -6 25 }}
{{Mapping|legend=0| 1 -4 10 7 -14 | 0 8 -11 -6 25 }}


Optimal tunings:  
Optimal tunings:  
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Comma list: 169/168, 225/224, 275/273, 385/384
Comma list: 169/168, 225/224, 275/273, 385/384


Mapping: {{mapping| 1 -4 10 7 -14 3 | 0 8 -11 -6 25 1 }}
{{Mapping|legend=0| 1 -4 10 7 -14 3 | 0 8 -11 -6 25 1 }}


Optimal tunings:  
Optimal tunings:  
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Comma list: 99/98, 176/175, 51200/50421
Comma list: 99/98, 176/175, 51200/50421


Mapping: {{mapping| 1 -4 10 7 23 | 0 8 -11 -6 -28 }}
{{Mapping|legend=0| 1 -4 10 7 23 | 0 8 -11 -6 -28 }}


Optimal tunings:  
Optimal tunings:  
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Comma list: 99/98, 169/168, 176/175, 640/637
Comma list: 99/98, 169/168, 176/175, 640/637


Mapping: {{mapping| 1 -4 10 7 23 3 | 0 8 -11 -6 -28 1 }}
{{Mapping|legend=0| 1 -4 10 7 23 3 | 0 8 -11 -6 -28 1 }}


Optimal tunings:  
Optimal tunings:  
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Comma list: 126/125, 176/175, 1344/1331
Comma list: 126/125, 176/175, 1344/1331


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


Optimal tunings:  
Optimal tunings:  
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Comma list: 126/125, 144/143, 176/175, 364/363
Comma list: 126/125, 144/143, 176/175, 364/363


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


Optimal tunings:  
Optimal tunings:  
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Comma list: 126/125, 144/143, 176/175, 221/220, 256/255
Comma list: 126/125, 144/143, 176/175, 221/220, 256/255


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


Optimal tunings:  
Optimal tunings:  
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Comma list: 96/95, 126/125, 144/143, 153/152, 176/175, 221/220
Comma list: 96/95, 126/125, 144/143, 153/152, 176/175, 221/220


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


Optimal tunings:  
Optimal tunings:  
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Comma list: 96/95, 126/125, 144/143, 153/152, 176/175, 221/220, 231/230
Comma list: 96/95, 126/125, 144/143, 153/152, 176/175, 221/220, 231/230


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


Optimal tunings:  
Optimal tunings:  
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Comma list: 96/95, 116/115, 126/125, 144/143, 153/152, 176/175, 221/220, 231/230
Comma list: 96/95, 116/115, 126/125, 144/143, 153/152, 176/175, 221/220, 231/230


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


Optimal tunings:  
Optimal tunings:  
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== Subsedia ==
== Subsedia ==
Subsedia tempers out the [[mirkwai comma]] and may be described as the {{nowrap| 111 & 121 }} temperament. The generator for subsedia is 0.5 cents flat of [[15/14]]-wide semitone. In this temperament, three generators make ~[[16/13]], five make ~[[24/17]], twelve make ~[[16/7]], sixteen make ~[[3/1]], and 45 make ~22/1.
Named by [[Xenllium]] in 2022, subsedia tempers out the [[canopic comma]] and may be described as the {{nowrap| 111 & 121 }} temperament. The generator for subsedia is 0.5 cents flat of [[15/14]]-wide semitone. In this temperament, three generators make ~[[16/13]], five make ~[[24/17]], twelve make ~[[16/7]], sixteen make ~[[3/1]], and 45 make ~22/1.  


[[Subgroup]]: 2.3.5.7
[[Subgroup]]: 2.3.5.7
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Comma list: 540/539, 1375/1372, 65536/64827
Comma list: 540/539, 1375/1372, 65536/64827


Mapping: {{mapping| 1 0 5 4 -1 | 0 16 -27 -12 45 }}
{{Mapping|legend=0| 1 0 5 4 -1 | 0 16 -27 -12 45 }}


Optimal tunings:  
Optimal tunings:  
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Comma list: 352/351, 540/539, 676/675, 1375/1372
Comma list: 352/351, 540/539, 676/675, 1375/1372


Mapping: {{mapping| 1 0 5 4 -1 4 | 0 16 -27 -12 45 -3 }}
{{Mapping|legend=0| 1 0 5 4 -1 4 | 0 16 -27 -12 45 -3 }}


Optimal tunings:  
Optimal tunings:  
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Comma list: 256/255, 352/351, 442/441, 540/539, 715/714
Comma list: 256/255, 352/351, 442/441, 540/539, 715/714


Mapping: {{mapping| 1 0 5 4 -1 4 3 | 0 16 -27 -12 45 -3 11 }}
{{Mapping|legend=0| 1 0 5 4 -1 4 3 | 0 16 -27 -12 45 -3 11 }}


Optimal tunings:  
Optimal tunings:  
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Comma list: 256/255, 352/351, 400/399, 442/441, 456/455, 715/714
Comma list: 256/255, 352/351, 400/399, 442/441, 456/455, 715/714


Mapping: {{mapping| 1 0 5 4 -1 4 3 10 | 0 16 -27 -12 45 -3 11 -58 }}
{{Mapping|legend=0| 1 0 5 4 -1 4 3 10 | 0 16 -27 -12 45 -3 11 -58 }}


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


Anthoine is generated by [[5/4]] and tempers out [[3125/3087]] in addition to the buzzardsma; note that the data below shows the octave complement generator, ~8/5, so that buzzard's generator 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. Its ploidacot is 13-sheared-20-cot.  
Named by [[Lériendil]] in 2025, anthoine is generated by [[5/4]] and tempers out [[3125/3087]] in addition to the buzzardsma; note that the data below shows the octave complement generator, ~8/5, so that buzzard's generator 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. Its ploidacot is 13-sheared-20-cot.  


[[Subgroup]]: 2.3.5.7
[[Subgroup]]: 2.3.5.7
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[[Badness]] (Sintel): 4.57
[[Badness]] (Sintel): 4.57


[[Category:Buzzardsmic clan| ]] <!-- main article -->
[[Category:Temperament clans]]
[[Category:Temperament clans]]
[[Category:Buzzardsmic clan| ]] <!-- main article -->
[[Category:Catalogs of rank-2 temperaments]]
[[Category:Rank 2]]
[[Category:Listen]]