User:Moremajorthanmajor/Ed13: Difference between revisions

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'''Ed13''' means '''Division of the Thirteenth Harmonic (13/1) into n equal parts'''.
'''Ed13''' means '''Division of the Thirteenth Harmonic ([[13/1]]) into n equal parts'''.


= Division of the thirteenth harmonic into n equal parts =
= Division of the thirteenth harmonic into n equal parts =
The thirteenth harmonic is particularly wide as far as equivalences go. There are (at absolute most) ~3 triskaidecataves within the human hearing range; imagine if that were the case with octaves. If one does indeed deal with hendecatave equivalence, this fact shapes one's musical approach dramatically. The thirteenth harmonic causes the ideal chromatic scale to "break down" during the third octave:
The thirteenth harmonic is particularly wide as far as equivalences go. There are (at absolute most) ~3 triskaidecataves within the human hearing range; imagine if that were the case with octaves. If one does indeed deal with triskaidecatave equivalence, this fact shapes one's musical approach dramatically. The thirteenth harmonic causes the ideal chromatic scale to "break down" after the tritave:
{| class="wikitable"
{| class="wikitable"
|+
|+
Line 9: Line 9:
!M2
!M2
!m3
!m3
!M3
!P4
!P4
!A4
!A4
Line 25: Line 26:
!A11
!A11
d12
d12
|-
| 1/1
| 16/15 <br>15/14
| 10/9 <br>9/8 <br>8/7
| 7/6 <br>6/5
| 5/4
| 4/3
| 7/5
| 3/2
| 8/5
| 5/3
| 7/4 <br>9/5
| ''11/6'' <br>''13/7'' <br>15/8
| 2/1
| 15/7 <br>''13/6''
| ''11/5'' <br>9/4
| 7/3 <br>12/5
| 5/2 <br>''13/5''
| 8/3 <br>''11/4''
| 14/5 <br>17/6
|-
!P12
!P12
!m13
!m13
Line 39: Line 61:
d19
d19
!P19
!P19
!''m20''
!m20
!''M20''
!M20
!m21
!m21
!M21
!M21
!P22
! colspan="2" |P22
|-
|-
| rowspan="2" |1/1
| 3/1
| rowspan="2" |15/14
| 16/5 <br>''13/4''
| rowspan="2" |8/7
| 10/3 <br>17/5
| rowspan="2" |6/5
| 7/2 <br>18/5
| rowspan="2" |4/3
| ''11/3'' <br>15/4
| rowspan="2" |7/5
| 4/1
| rowspan="2" |3/2
| 17/4 <br>''13/3''
| rowspan="2" |8/5
| 9/2
| rowspan="2" |5/3
| 14/3
| rowspan="2" |7/2
| 5/1
| rowspan="2" |15/8
| 16/3 <br>''11/2''
| rowspan="2" |2/1
| 28/5 <br>''17/3''
| rowspan="2" |15/7
| 6/1
| rowspan="2" |9/4
| ''13/2''
| rowspan="2" |7/3
| 20/3
| rowspan="2" |5/2
| 7/1
| rowspan="2" |8/3
| 15/2
| rowspan="2" |11/4
| colspan="2" |8/1
| rowspan="2" |3/1
| rowspan="2" |''13/4''
| rowspan="2" |10/3
| rowspan="2" |7/2
| rowspan="2" |15/4
| rowspan="2" |4/1
| rowspan="2" |17/4
| rowspan="2" |9/2
| rowspan="2" |14/3
| rowspan="2" |5/1
| rowspan="2" |16/3
| rowspan="2" |11/2
| rowspan="2" |6/1
| colspan="2" |13/2
| rowspan="2" |7/1
| rowspan="2" |15/2
| rowspan="2" |8/1
|-
|''32/5''
|''20/3''
|}
|}
== Individual pages for ED13s ==
* [[7ed13]]
* [[10ed13]] - [[Sensi]] generator
* [[14ed13]] - [[Kleismic]] generator
* [[37ed13]] - compare [[10edo]]
* [[45ed13]]
[[Category:Edonoi]]

Latest revision as of 13:40, 19 May 2025

Ed13 means Division of the Thirteenth Harmonic (13/1) into n equal parts.

Division of the thirteenth harmonic into n equal parts

The thirteenth harmonic is particularly wide as far as equivalences go. There are (at absolute most) ~3 triskaidecataves within the human hearing range; imagine if that were the case with octaves. If one does indeed deal with triskaidecatave equivalence, this fact shapes one's musical approach dramatically. The thirteenth harmonic causes the ideal chromatic scale to "break down" after the tritave:

Unison m2 M2 m3 M3 P4 A4

d5

P5 m6 M6 m7 M7 P8 m9 M9 m10 M10 P11 A11

d12

1/1 16/15
15/14 		10/9
9/8
8/7 		7/6
6/5 		5/4 4/3 7/5 3/2 8/5 5/3 7/4
9/5 		11/6
13/7
15/8 		2/1 15/7
13/6 		11/5
9/4 		7/3
12/5 		5/2
13/5 		8/3
11/4 		14/5
17/6
P12 m13 M13 m14 M14 P15 m16 M16 m17 M17 P18 A18

d19

P19 m20 M20 m21 M21 P22
3/1 16/5
13/4 		10/3
17/5 		7/2
18/5 		11/3
15/4 		4/1 17/4
13/3 		9/2 14/3 5/1 16/3
11/2 		28/5
17/3 		6/1 13/2 20/3 7/1 15/2 8/1

Individual pages for ED13s

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