Buzzard: Difference between revisions

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== Tunings ==
== Tunings ==
=== Norm-based tunings ===
{| class="wikitable mw-collapsible mw-collapsed"
{| class="wikitable mw-collapsible mw-collapsed"
|+ style="font-size: 105%; white-space: nowrap;" | 2.3.7-subgroup norm-based tunings
|+ style="font-size: 105%; white-space: nowrap;" | 2.3.7-subgroup norm-based tunings
Line 215: Line 216:
| POTE: ~21/16 = 475.6972{{c}}
| POTE: ~21/16 = 475.6972{{c}}
|}
|}
=== Tuning spectrum ===
{| class="wikitable center-all left-4"
|-
! Edo<br>generator
! [[Eigenmonzo|Unchanged interval<br>(eigenmonzo)]]
! Generator (¢)
! Comments
|-
|
| [[21/16]]
| 470.7809
|
|-
| [[48edo|19\48]]
|
| 475.0000
| 48eef val, lower bound of 7- and 9-odd-limit diamond monotone
|-
| [[53edo|21\53]]
|
| 475.4717
| Lower bound of 11- through 15-odd-limit diamond monotone
|-
|
| [[3/2]]
| 475.4888
|
|-
|
| [[15/8]]
| 475.5307
|
|-
|
| [[5/4]]
| 475.5387
|
|-
|
| [[5/3]]
| 475.5505
|
|-
|
| [[9/5]]
| 475.5695
|
|-
|
| [[13/8]]
| 475.5751
|
|-
|
| [[13/12]]
| 475.5901
|
|-
| [[164edo|65\164]]
|
| 475.6098
| 164d val
|-
|
| [[13/9]]
| 475.6115
|
|-
|
| [[11/8]]
| 475.6748
|
|-
| [[111edo|44\111]]
|
| 475.6757
|
|-
|
| [[15/14]]
| 475.6944
|
|-
|
| [[11/6]]
| 475.6961
|
|-
|
| [[15/13]]
| 475.7023
|
|-
|
| [[11/9]]
| 475.7228
|
|-
|
| [[13/7]]
| 475.7234
|
|-
|
| [[7/5]]
| 475.7287
|
|-
| [[169edo|67\169]]
|
| 475.7396
| 169cdf val
|-
|
| [[21/13]]
| 475.7595
|
|-
|
| [[11/7]]
| 475.7736
|
|-
|
| [[21/20]]
| 475.7766
|
|-
|
| [[21/11]]
| 475.8036
|
|-
|
| [[11/10]]
| 475.8336
|
|-
| [[58edo|23\58]]
|
| 475.8621
| Upper bound of 11- through 15-odd-limit diamond monotone
|-
|
| [[13/11]]
| 475.8992
|
|-
|
| [[9/7]]
| 475.9167
|
|-
|
| [[15/11]]
| 475.9321
|
|-
|
| [[15/13]]
| 476.1295
|
|-
|
| [[7/6]]
| 476.1613
|
|-
| [[63edo|25\63]]
|
| 476.1905
| 63ceef val
|-
|
| [[7/4]]
| 477.0580
|
|-
| [[5edo|2\5]]
|
| 480.0000
| 5e val, upper bound of 7- and 9-odd-limit diamond monotone
|}
<nowiki>*</nowiki> Besides the octave


== References ==
== References ==

Revision as of 17:28, 27 October 2025

Buzzard is a temperament that splits a tempered perfect twelfth (3/1) into four generators of 21/16 subfourths, tempering out 65536/64827. If harmonic 5 is desired, it is found by twenty-one generators octave-reduced, tempering out 1728/1715 and 5120/5103. It extends to the 13-limit by tempering out 176/175, 351/350, 540/539, and 676/675.

Buzzard was named by Herman Miller in 2004[1].

See Buzzardsmic clan #Buzzard for technical data.

Interval chain

In the following table, odd harmonics and subharmonics 1–21 are in bold.

# Cents* Approximate ratios
13-limit 19-limit extension
0 0.00 1/1
1 475.68 21/16
2 951.35 26/15 19/11
3 227.03 8/7
4 702.70 3/2
5 1178.38 63/32, 160/81
6 454.06 13/10
7 929.73 12/7
8 205.41 9/8
9 681.08 40/27
10 1156.76 35/18, 39/20, 96/49
11 432.44 9/7
12 908.11 22/13, 27/16
13 183.79 10/9
14 659.46 35/24 19/13
15 1135.14 27/14
16 410.82 33/26 19/15
17 886.49 5/3
18 162.17 11/10
19 637.84 13/9
20 1113.52 40/21 19/10
21 389.20 5/4
22 864.87 33/20 28/17
23 140.55 13/12
24 616.22 10/7
25 1091.90 15/8 32/17
26 367.58 26/21 21/17
27 843.25 13/8
28 118.93 15/14

* In 13-limit CWE tuning

Chords and harmony

See also: Chords of buzzard

Tunings

Norm-based tunings

2.3.7-subgroup norm-based tunings
Euclidean
Constrained Constrained & skewed Destretched
Tenney CTE: ~21/16 = 475.7273 ¢ CWE: ~21/16 = 475.8328 ¢ POTE: ~21/16 = 475.8717 ¢
7-limit norm-based tunings
Euclidean
Constrained Constrained & skewed Destretched
Tenney CTE: ~21/16 = 475.5546 ¢ CWE: ~21/16 = 475.6144 ¢ POTE: ~21/16 = 475.6361 ¢
13-limit norm-based tunings
Euclidean
Constrained Constrained & skewed Destretched
Tenney CTE: ~21/16 = 475.6153 ¢ CWE: ~21/16 = 475.6760 ¢ POTE: ~21/16 = 475.6972 ¢

Tuning spectrum

Edo
generator 		Unchanged interval
(eigenmonzo) 		Generator (¢) Comments
21/16 470.7809
19\48 475.0000 48eef val, lower bound of 7- and 9-odd-limit diamond monotone
21\53 475.4717 Lower bound of 11- through 15-odd-limit diamond monotone
3/2 475.4888
15/8 475.5307
5/4 475.5387
5/3 475.5505
9/5 475.5695
13/8 475.5751
13/12 475.5901
65\164 475.6098 164d val
13/9 475.6115
11/8 475.6748
44\111 475.6757
15/14 475.6944
11/6 475.6961
15/13 475.7023
11/9 475.7228
13/7 475.7234
7/5 475.7287
67\169 475.7396 169cdf val
21/13 475.7595
11/7 475.7736
21/20 475.7766
21/11 475.8036
11/10 475.8336
23\58 475.8621 Upper bound of 11- through 15-odd-limit diamond monotone
13/11 475.8992
9/7 475.9167
15/11 475.9321
15/13 476.1295
7/6 476.1613
25\63 476.1905 63ceef val
7/4 477.0580
2\5 480.0000 5e val, upper bound of 7- and 9-odd-limit diamond monotone

* Besides the octave

References

  1. ↑ Yahoo! Tuning Group (Archive) | Names for important high-complexity temperaments
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