10ed7/4: Difference between revisions

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{| class="wikitable"
{| class="wikitable"
|-
|-
! | degree
! | Degree
! | cents value
! | Cents value
! | ratio
! | Ratio
|-
|-
| | 0
| | 0
Line 172: Line 172:


{| class="wikitable sortable"
{| class="wikitable sortable"
|-
|+ Direct mapping (even if inconsistent)
|+ Direct mapping (even if inconsistent)
|-
! Interval(s)
! Interval(s)
! Error (abs, [[cent|¢]])
! Error (abs, [[cent|¢]])
Line 180: Line 178:
|-
|-
| [[7/4]]
| [[7/4]]
|0.0
| 0.0
|-
|-
| [[2/1]]
| [[2/1]]
Line 186: Line 184:
|-
|-
| [[3/2]]
| [[3/2]]
|23.777
| 23.777
|-
|-
| [[5/4]]
| [[5/4]]
|1.217
| 1.217
|-
|-
| [[9/8]]
| [[9/8]]
|10.145
| 10.145
|-
|-
| [[11/8]]
| [[11/8]]
|29.978
| 29.978
|-
|-
| [[13/8]]
| [[13/8]]
|31.416
| 31.416
|-
|-
| [[15/8]]
| [[15/8]]
|22.56
| 22.56
|-
|-
| [[14/9]]
| [[14/9]]
|10.145
| 10.145
|-
|-
| [[28/15]]
| [[28/15]]
|14.849
| 14.849
|-
|-
| [[10/7]]
| [[10/7]]
|36.192
| 36.192
|-
|-
| [[16/11]]
| [[16/11]]
|29.496
| 29.496
|-
|-
| [[13/10]]
| [[13/10]]
|30.199
| 30.199
|-
|-
| [[9/5]]
| [[9/5]]
|48.112
| 48.112
|-
|-
| [[10/9]]
| [[10/9]]
|11.361
| 11.361
|-
|-
| [[26/15]]
| [[26/15]]
|16.567
| 16.567
|-
|-
| [[13/11]]
| [[13/11]]
|1.438
| 1.438
|-
|-
| [[13/7]]
| [[13/7]]
|5.993
| 5.993
|-
|-
| [[16/13]]
| [[16/13]]
|28.058
| 28.058
|-
|-
| [[7/6]]
| [[7/6]]
|23.777
| 23.777
|-
|-
| [[5/3]]
| [[5/3]]
|12.415
| 12.415
|-
|-
| [[20/13]]
| [[20/13]]
|29.275
| 29.275
|-
|-
| [[11/10]]
| [[11/10]]
|28.761
| 28.761
|-
|-
| [[8/5]]
| [[8/5]]
|38.626
| 38.626
|-
|-
| [[9/7]]
| [[9/7]]
|47.554
| 47.554
|-
|-
| [[11/9]]
| [[11/9]]
|40.122
| 40.122
|-
|-
| [[18/11]]
| [[18/11]]
|19.351
| 19.351
|-
|-
| [[24/13]]
| [[24/13]]
|4.281
| 4.281
|-
|-
| [[22/15]]
| [[22/15]]
|15.129
| 15.129
|-
|-
| [[15/13]]
| [[15/13]]
|42.907
| 42.907
|-
|-
| [[15/11]]
| [[15/11]]
|44.345
| 44.345
|-
|-
| [[16/9]]
| [[16/9]]
|27.264
| 27.264
|-
|-
| [[12/7]]
| [[12/7]]
|35.697
| 35.697
|-
|-
| [[7/5]]
| [[7/5]]
|1.217
| 1.217
|-
|-
| [[12/11]]
| [[12/11]]
|43.128
| 43.128
|-
|-
| [[4/3]]
| [[4/3]]
|13.632
| 13.632
|-
|-
| [[11/6]]
| [[11/6]]
|16.346
| 16.346
|-
|-
| [[13/12]]
| [[13/12]]
|41.69
| 41.69
|-
|-
| [[8/7]]
| [[8/7]]
|37.409
| 37.409
|-
|-
| [[20/11]]
| [[20/11]]
|30.713
| 30.713
|-
|-
| [[14/13]]
| [[14/13]]
|31.416
| 31.416
|-
|-
| [[6/5]]
| [[6/5]]
|24.994
| 24.994
|-
|-
| [[18/13]]
| [[18/13]]
|17.913
| 17.913
|-
|-
| [[15/14]]
| [[15/14]]
|22.56
| 22.56
|-
|-
| [[11/7]]
| [[11/7]]
|7.431
| 7.431
|-
|-
| [[13/9]]
| [[13/9]]
|41.56
| 41.56
|-
|-
| [[14/11]]
| [[14/11]]
|29.978
| 29.978
|-
|-
| [[22/13]]
| [[22/13]]
|38.847
| 38.847
|-
|-
| [[16/15]]
| [[16/15]]
|14.849
| 14.849
|}
|}


[[Category:Subminor seventh]]
[[Category:Subminor seventh]]
[[Category:Equal-step tuning]]
[[Category:Equal-step tuning]]
[[Category:Edonoi]]
[[Category:Edonoi]]

Revision as of 04:27, 24 May 2024

← 9ed7/4 10ed7/4 11ed7/4 →
Prime factorization 2 × 5
Step size 96.8826 ¢ 
Octave 12\10ed7/4 (1162.59 ¢) (→ 6\5ed7/4)
Twelfth 20\10ed7/4 (1937.65 ¢) (→ 2\1ed7/4)
Consistency limit 2
Distinct consistency limit 2

10ED7/4 is the equal division of the harmonic seventh into ten parts of 96.8826 cents each, corresponding to 12.3861 EDO.

Intervals

Degree Cents value Ratio
0 0.0000 1/1
1 96.8826 (7/4)1/10
2 193.7652 (7/4)1/5
3 290.6478 (7/4)3/10
4 387.5304 (7/4)2/5
5 484.4130 (7/4)1/2
6 581.2955 (7/4)3/5
7 678.1781 (7/4)7/10
8 775.0607 (7/4)4/5
9 871.9433 (7/4)9/10
10 968.8259 7/4
11 1065.7085 (7/4)11/10
12 1162.5911 (7/4)6/5
13 1259.4737 (7/4)13/10
14 1356.3563 (7/4)7/2
15 1453.2389 (7/4)3/2
16 1550.1215 (7/4)8/5
17 1647.0040 (7/4)17/10
18 1743.8866 (7/4)9/5
19 1840.7692 (7/4)19/10
20 1937.6518 (7/4)2 = 49/16
21 2034.5344 (7/4)21/10
22 2131.4170 (7/4)11/5
23 2228.2996 (7/4)23/10
24 2325.1822 (7/4)12/5
25 2422.0648 (7/4)5/2
26 2518.9474 (7/4)13/5
27 2615.8299 (7/4)27/10
28 2712.7125 (7/4)14/5
29 2809.5951 (7/4)29/10
30 2906.4777 (7/4)3 = 343/64
31 3003.3603 (7/4)31/10
32 3100.2429 (7/4)16/5
33 3197.1255 (7/4)33/10
34 3294.0081 (7/4)17/10
35 3390.8907 (7/4)7/2
36 3487.7733 (7/4)18/5
37 3584.6559 (7/4)37/10
38 3681.5384 (7/4)19/5

Just approximation

Only very few intervals like the just major third and the Huygens' tritone are well approximated by 10ed7/4.

15-odd-limit mappings

The following table shows how 15-odd-limit intervals are represented in 10ed7/4 (can be ordered by absolute error).

Direct mapping (even if inconsistent)
Interval(s) Error (abs, ¢)
7/4 0.0
2/1 37.409
3/2 23.777
5/4 1.217
9/8 10.145
11/8 29.978
13/8 31.416
15/8 22.56
14/9 10.145
28/15 14.849
10/7 36.192
16/11 29.496
13/10 30.199
9/5 48.112
10/9 11.361
26/15 16.567
13/11 1.438
13/7 5.993
16/13 28.058
7/6 23.777
5/3 12.415
20/13 29.275
11/10 28.761
8/5 38.626
9/7 47.554
11/9 40.122
18/11 19.351
24/13 4.281
22/15 15.129
15/13 42.907
15/11 44.345
16/9 27.264
12/7 35.697
7/5 1.217
12/11 43.128
4/3 13.632
11/6 16.346
13/12 41.69
8/7 37.409
20/11 30.713
14/13 31.416
6/5 24.994
18/13 17.913
15/14 22.56
11/7 7.431
13/9 41.56
14/11 29.978
22/13 38.847
16/15 14.849
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