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== Interval chains ==
== Interval chains ==
In the following table, odd harmonics 1–11 and their inverses are in '''bold'''.  
There are two different mappings of the 11-limit. One is just called ''pajara'' and is slightly more complex but suffers almost no loss of accuracy compared to the 7-limit. It is best tuned flat of 22edo. The other, called ''pajarous'' to avoid confusion, loses some accuracy for 3 and 5. It is best tuned sharp of 22edo. However, it equates [[12/11]] with [[10/9]], and the only tuning equating [[11/10]] with both is 22edo.
 
In the following tables, odd harmonics 1–11 and their inverses are in '''bold'''.  


{| class="wikitable center-1 right-2 right-4"
{| class="wikitable center-1 right-2 right-4"
|+ Pajara (12 & 22)
|-
|-
! rowspan="2" | #
! rowspan="2" | #
Line 81: Line 84:
| '''16/11'''
| '''16/11'''
| 43.1
| 43.1
| 45/44, 81/80
| 45/44, 56/55, 81/80
|}
|}
<nowiki/>* In 11-limit CWE tuning, octave-reduced
{| class="wikitable center-1 right-2 right-4"
 
|+ Pajarous (10 & 22)
There are two different mappings of the 11-limit. One is just called ''pajara'' and is slightly more complex but suffers almost no loss of accuracy compared to the 7-limit. It is best tuned flat of 22edo. The other, called ''pajarous'' to avoid confusion, loses some accuracy for 3 and 5. It is best tuned sharp of 22edo. However, it equates [[12/11]] with [[10/9]], and the only tuning equating [[11/10]] with both is 22edo.
 
{| class="wikitable mw-collapsible mw-collapsed"
|+ style="font-size: 105%; white-space: nowrap;" | Intervals of pajara (12 &amp; 22)
|-
|-
! Generator
! rowspan="2" | #
! −11
! colspan="2" | Period 0
! −10
! colspan="2" | Period 1
! −9
! −8
! −7
! −6
|-
|-
! Cents*
! Cents*
| 24.26
! Approximate ratios
| 131.15
| 238.03
| 344.92
| 451.80
| 558.69
|-
! Ratios
|
|
|
| 11/9
|
| 11/8
|-
! Generator
! −5
! −4
! −3
! −2
! −1
! 0
|-
! Cents*
! Cents*
| 65.57
! Approximate ratios
| 172.46
| 279.34
| 386.23
| 493.11
| 600.00
|-
|-
! Ratios
| 0
|  
| 0.0
| 11/10, 10/9
| '''1/1'''
| 7/6
| 600.0
| 5/4
| 4/3
| 7/5, 10/7
| 7/5, 10/7
|-
|-
! Generator
| 1
! 0
| 709.6
! 1
| '''3/2'''
! 2
| 109.6
! 3
| 15/14, 16/15, 21/20
! 4
! 5
|-
|-
! Cents*
| 2
| 0.00
| 219.1
| 106.89
| '''8/7''', '''9/8'''
| 213.77
| 819.1
| 320.66
| '''8/5'''
| 427.54
| 534.43
|-
|-
! Ratios
| 3
| 1/1
| 928.7
| 16/15, 15/14
| 12/7
| 9/8, 8/7
| 328.7
| 6/5
| 6/5, 11/9
| 14/11, 9/7
| 15/11
|-
|-
! Generator
| 4
! 6
| 438.2
! 7
! 8
! 9
! 10
! 11
|-
! Cents*
| 41.31
| 148.20
| 255.08
| 361.97
| 468.85
| 575.74
|-
! Ratios
|
| 12/11
|
|
|
|
|}
<nowiki />* In 11-limit POTE tuning
 
{| class="wikitable mw-collapsible mw-collapsed"
|+ style="font-size: 105%; white-space: nowrap;" | Intervals of pajarous (10 &amp; 22)
|-
! Generator
!
! −10
! −9
! −8
! −7
! −6
|-
! Cents*
|
| 109.09
| 218.18
| 327.27
| 436.36
| 545.45
|-
! Ratios
|
|
|
|
| 14/11
| 15/11
|-
! Generator
! −5
! −4
! −3
! −2
! −1
! 0
|-
! Cents*
| 54.55
| 163.64
| 272.73
| 381.82
| 490.91
| 600.00
|-
! Ratios
|
| 12/11, 10/9
| 7/6
| 5/4
| 4/3
| 7/5, 10/7
|-
! Generator
! 0
! 1
! 2
! 3
! 4
! 5
|-
! Cents*
| 0.00
| 109.09
| 218.18
| 327.27
| 436.36
| 545.45
|-
! Ratios
| 1/1
| 16/15, 15/14
| 9/8, 8/7
| 6/5, 11/9
| 9/7
| 9/7
| 11/8
| 1038.2
| 9/5, 11/6
|-
|-
! Generator
| 5
! 6
| 1147.8
! 7
| 27/14, 48/25, 55/28, <br>88/45, 96/49
! 8
| 535.9
! 9
| '''11/8''', 27/20
! 10
!
|-
|-
! Cents*
| 6
| 54.55
| 657.3
| 163.64
| 22/15
| 272.73
| 57.3
| 381.82
| 22/21, 33/32, 81/80
| 491.91
|
|-
! Ratios
|
| 11/10
|
|
|
|
|}
|}
<nowiki>*</nowiki> In 22edo tuning
<nowiki/>* In 11-limit CWE tuning, octave-reduced


== Scales ==
== Scales ==
Retrieved from "https://en.xen.wiki/w/Pajara"