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==Intervals==
==Intervals==


{| class="wikitable"
{| class="wikitable center-1 right-2 right-3"
|-
|-
! | Steps
! Steps
! | Cents
! [[Cent]]s
!Hekts
! [[Hekt]]s
! | BP nonatonic degree
! BP nonatonic degree
! | Corresponding JI intervals
! Corresponding JI intervals
! | Comments
! Comments
! | Generator for...
! Generator for...
|-
|-
| | 1
| 1
| | 146.3
| 146.3
|100
| 100
| | A1/m2
| A1/m2
| | 27/25~49/45
| 27/25~49/45
| |  
|
| |  
|
|-
|-
| | 2
| 2
| | 292.6
| 292.6
|200
| 200
| | M2/d3
| M2/d3
| | 25/21
| 25/21
| |  
|
| | [[Sirius]]
| [[Sirius]]
|-
|-
| | 3
| 3
| | 438.9
| 438.9
|300
| 300
| | A2/P3/d4
| A2/P3/d4
| | 9/7
| 9/7
| |  
|
| | [[Bohlen-Pierce|Linear BP]]
| [[Bohlen-Pierce|Linear BP]]
|-
|-
| | 4
| 4
| | 585.2
| 585.2
|400
| 400
| | A3/m4/d5
| A3/m4/d5
| | 7/5
| 7/5
| |  
|
| | [[Canopus]]
| [[Canopus]]
|-
|-
| | 5
| 5
| | 731.5
| 731.5
|500
| 500
| | M4/m5
| M4/m5
| | 75/49
| 75/49
| | False 3/2
| False 3/2
| | false Father
| false Father
|-
|-
| | 6
| 6
| | 877.8
| 877.8
|600
| 600
| | A4/M5
| A4/M5
| | 5/3
| 5/3
| |  
|
| | [[Arcturus]]
| [[Arcturus]]
|-
|-
| | 7
| 7
| | 1024.1
| 1024.1
|700
| 700
| | A5/m6/d7
| A5/m6/d7
| | 9/5
| 9/5
| |  
|
| | Arcturus
| Arcturus
|-
|-
| | 8
| 8
| | 1170.4
| 1170.4
|800
| 800
| | M6/m7
| M6/m7
| | 49/25
| 49/25
| | False 2/1
| False 2/1
| | false Father
| false Father
|-
|-
| | 9
| 9
| | 1316.7
| 1316.7
|900
| 900
| | A6/M7/d8
| A6/M7/d8
| | 15/7
| 15/7
| |  
|
| | Canopus
| Canopus
|-
|-
| | 10
| 10
| | 1463
| 1463.0
|1000
| 1000
| | P8/d9
| P8/d9
| | 7/3
| 7/3
| |  
|
| | Linear BP
| Linear BP
|-
|-
| | 11
| 11
| | 1609.3
| 1609.3
|1100
| 1100
| | A8/m9
| A8/m9
| | 63/25
| 63/25
| |  
|
| | Sirius
| Sirius
|-
|-
| | 12
| 12
| | 1755.7
| 1755.7
|1200
| 1200
| | M9/d10
| M9/d10
| | 25/9~135/49
| 25/9~135/49
| |  
|
| |  
|
|-
|-
| | 13
| 13
| | 1902.0
| 1902.0
|1300
| 1300
| | A9/P10
| A9/P10
| | 3/1
| 3/1
| | Tritave
| Tritave
| |  
|
|}
|}


Revision as of 13:58, 25 May 2021

13edt divides the tritave (3/1) into 13 equal parts of 146.304 cents each, corresponding to 8.202edo. It is the equal-tempered version of the well-known Bohlen-Pierce scale. In the 7-limit, it tempers out 245/243 and 3125/3087, the same commas as bohpier temperament. It is less impressive in higher p-limits, but makes for excellent no-twos 7-limit harmony. For higher limits, the multiples of 13 (26edt, 39edt and 52edt) come to the fore.

Below is a plot of the no-twos Z-function, in terms of which 13edt is the fourth no-twos zeta peak edt.

13edt.png

Intervals

Steps Cents Hekts BP nonatonic degree Corresponding JI intervals Comments Generator for...
1 146.3 100 A1/m2 27/25~49/45
2 292.6 200 M2/d3 25/21 Sirius
3 438.9 300 A2/P3/d4 9/7 Linear BP
4 585.2 400 A3/m4/d5 7/5 Canopus
5 731.5 500 M4/m5 75/49 False 3/2 false Father
6 877.8 600 A4/M5 5/3 Arcturus
7 1024.1 700 A5/m6/d7 9/5 Arcturus
8 1170.4 800 M6/m7 49/25 False 2/1 false Father
9 1316.7 900 A6/M7/d8 15/7 Canopus
10 1463.0 1000 P8/d9 7/3 Linear BP
11 1609.3 1100 A8/m9 63/25 Sirius
12 1755.7 1200 M9/d10 25/9~135/49
13 1902.0 1300 A9/P10 3/1 Tritave

See also

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