Buzzard: Difference between revisions

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'''Buzzard''' is the [[regular temperament]] tempering out [[1728/1715]] and [[5120/5103]] in the 7-limit, and extends to the 13-limit.  
'''Buzzard''' is a [[regular temperament|temperament]] that splits a tempered [[3/1|perfect twelfth (3/1)]] into four [[generator]]s 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<ref>[https://yahootuninggroupsultimatebackup.github.io/tuning-math/topicId_10541.html#10551 Yahoo! Tuning Group (Archive) | ''Names for important high-complexity temperaments'']</ref>.  
Buzzard was named by [[Herman Miller]] in 2004<ref>[https://yahootuninggroupsultimatebackup.github.io/tuning-math/topicId_10541.html#10551 Yahoo! Tuning Group (Archive) | ''Names for important high-complexity temperaments'']</ref>.  


See [[Vulture family #Buzzard]] for more technical data.
See [[Buzzardsmic clan #Buzzard]] and [[Buzzardsmic clan #Septimal buzzard]] for technical data.
 
== Interval chain ==
In the following table, odd harmonics and subharmonics 1–21 are in '''bold'''.
 
{| class="wikitable center-1 right-2"
|-
! rowspan="2" | #
! rowspan="2" | Cents*
! colspan="2" | 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
|
|}
<nowiki/>* In 13-limit CWE tuning


== Chords ==
== Chords ==
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[[Category:Buzzard| ]] <!-- main article -->
[[Category:Buzzard| ]] <!-- main article -->
[[Category:Temperaments]]
[[Category:Rank-2 temperaments]]
[[Category:Vulture family]]
[[Category:Vulture family]]
[[Category:Orwellismic temperaments]]
[[Category:Orwellismic temperaments]]
[[Category:Hemifamity temperaments]]
[[Category:Hemifamity temperaments]]

Latest revision as of 13:53, 28 April 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 and Buzzardsmic clan #Septimal 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

Main article: Chords of buzzard

Notes

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