Buzzard
| Buzzard |
1728/1715, 5120/5103 (7-limit);
176/175, 351/350, 540/539, 676/675
(13-limit)
15-odd-limit: 4.09¢
15-odd-limit: 43 notes
Buzzard, 2.3.7[48 & 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.
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
| 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 |
Extensions
While 13/5 has an obvious mapping via the 15/13 semifourth at -2 generators, 13 and 5 themselves are less obvious, as is 11.
Aberschismic Buzzard
The most common extension of Buzzard is Aberschismic -- that is, tempering out 5120/5103. This equates the 64/63 inflection comma with 81/80 and 105/104, allowing the 5-limit and 7-limit consonances to each be reached by one inflection away from a 3-limit consonance. This also provides a corresponding mapping of prime 13 as the difference between 15/8 and 15/13.
Valinorsmic Buzzard
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")
An alternative mapping of prime 11 is to conflate the inflection comma with 55/54 instead. This equally spaces the 7/6 - 32/27 - 6/5 - 11/9 sequence, as well as 21/16 - 4/3 - 27/20 - 11/8. This tuning is sometimes called Buteo, to distinguish from the Valinormic tuning that is considered the canonical extension of Buzzard.
Sensamagic Buzzard ("Lemongrass")
An alternative way to reach prime 5 is to equate 49/48 with 81/80, thus equating the sequence 5/4 - 80/63 - 81/64 - 9/7. Prime 13 is still the difference between 15/8 and 15/13, but in this case the tuning of 15/8 is much flatter than in Aberschismic Buzzard, thus providing a sharper tuning of 13/8. This extension is sometimes called Lemongrass, to distinguish from the Aberschismic tuning that is considered canonical.
