10ed7/4: Difference between revisions
Created |
m Removing from Category:Edonoi using Cat-a-lot |
||
| (9 intermediate revisions by 6 users not shown) | |||
| Line 1: | Line 1: | ||
'''10ED7/4''' is the [[Equal-step tuning|equal division]] of the [[7/4|harmonic seventh]] into ten parts of 96.8826 [[cent|cents]] each, corresponding to 12.3861 [[EDO]]. | {{Infobox ET}}{{todo|expand}} | ||
'''10ED7/4''' is the [[Equal-step tuning|equal division]] of the [[7/4|harmonic seventh]] into ten parts of 96.8826 [[cent|cents]] each, corresponding to 12.3861 [[EDO]]. | |||
== Theory == | |||
This tuning tempers out 36/35 and 50/49 in the 7-limit; 55/54 in the 11-limit; 34/33 and 56/51 in the 17-limit; 31/30 in the 31-limit; and 38/37 in the 37-limit. | |||
== Intervals == | == Intervals == | ||
{| class="wikitable" | {| class="wikitable mw-collapsible" | ||
|+ Intervals of 10ed7/4 | |||
|- | |- | ||
! | | ! | Degree | ||
! | | ! | Cents value | ||
! | | ! | Ratio | ||
|- | |- | ||
| | 0 | | | 0 | ||
| Line 164: | Line 169: | ||
| | (7/4)<sup>19/5</sup> | | | (7/4)<sup>19/5</sup> | ||
|} | |} | ||
== Just approximation == | |||
Only very few intervals like the [[5/4|just major third]] and the [[7/5|Huygens' tritone]] are well approximated by 10ed7/4. | |||
=== 15-odd-limit approximations === | |||
The following table shows how [[15-odd-limit intervals]] are represented in 10ed7/4 (can be ordered by absolute error). | |||
{| class="wikitable sortable mw-collapsible" | |||
|+ [[Direct approximation]] (even if [[inconsistent]]) | |||
! Interval(s) | |||
! Error (abs, [[cent|¢]]) | |||
|- | |||
|- | |||
| [[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 | |||
|} | |||
== Harmonics == | |||
{{Harmonics in equal | |||
| steps = 10 | |||
| num = 7 | |||
| denom = 4 | |||
}} | |||
{{Harmonics in equal | |||
| steps = 10 | |||
| num = 7 | |||
| denom = 4 | |||
| start = 12 | |||
| collapsed = 1 | |||
}} | |||
[[Category:Subminor seventh]] | |||
[[Category:Equal-step tuning]] | |||