User:MissMagenta/EDKL: Difference between revisions

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Equal divisions of the Komornik–Loreti Seventh, which is the Komornik–Loreti constant used as a musical interval.
Equal divisions of the Komornik–Loreti Seventh, or the Kleventh which has a size of ~1005.2719677332628 cents. The Kleventh is the [[wikipedia:Komornik–Loreti_constant|Komornik–Loreti constant]] used as a musical interval. Using the Komornik–Loreti constant as an interval is a completely arbitrary choice.


 
==Correspondence of EDKL to EDO==
== Correspondence of EDN to EDO ==
{| class="wikitable"
{| class="wikitable"
|+
|+
!Tuning
!Tuning
!Equivalent edo
!Equivalent EDO
!Comment
!Comment
|-
|-
|2edn
|1edkl
|
|[[1edo]]
|A stack of two major sixths
|Warning: Inaccurate to 1edo by ~194.8 cents in step size
|-
|-
|3edn
|2edkl
|[[2edo]]
|[[2edo]]
|Warning: Inaccurate to 2edo by ~98 cents in step size
|-
|3edkl
|[[3edo]]
|Warning: Inaccurate to 3edo by ~65 cents in step size
|-
|4edkl
|[[5edo]]
|
|
|-
|-
|4edn
|5edkl
|[[6edo]]
|
|
| rowspan="2" |Neither are equivalent with [[3edo]]
|-
|-
|5edn
|6edkl
|[[7edo]]
|
|
|-
|-
|6edn
|7edkl
|[[4edo]]
|[[8edo]]
|With a stretch
|
|-
|-
|7edn
|8edkl
|[[5edo]]
|[[10edo]]
|
|
|-
|-
|8edn
|9edkl
|[[11edo]]
|
|
|Entirely misses 2/1, falling halfway between 5edo and 6edo
|-
|-
|9edn
|10edkl
|[[6edo]]
|[[12edo]]
|With a considerable stretch
|Has a good fifth (~0.1% off a just fifth)
|-
|-
|10edn
|11edkl
|[[7edo]]
|[[13edo]]
|
|
|-
|-
|11edn
|12edkl
|[[14edo]]
|
|
| rowspan="2" |Neither are equivalent to 8edo
|-
|-
|12edn
|13edkl
|[[16edo]]
|Has a phenomenal major third (~0.01% off a just major third)
|-
|14edkl
|[[17edo]]
|
|
|-
|-
|13edn
|15edkl
|[[9edo]]
|[[18edo]]
|
|
|-
|-
|14edn
|16edkl
|[[19edo]]
|
|
| rowspan="2" |Neither are equivalent to 10edo
|-
|-
|15edn
|17edkl
|[[20edo]]
|
|
|-
|-
|16edn
|18edkl
|[[11edo]]
|[[21edo]]
|Has a great fourth (~4 cents off a just fourth)
|-
|19edkl
|[[23edo]]
|Similarly to 23edo, completely misses the fifth and fourth.
|-
|20edkl
|[[24edo]]
|Has the 10edkl fifth, with a good approximation of the 11-limit
|-
|21edkl
|[[25edo]]
|
|
|-
|-
|17edn
|22edkl
|[[12edo]]
|[[26edo]]
|With a noticeable stretch, given the dominance of 12edo this is more likely to sound like out of tune 12edo than it's own tuning
|Good fourth, bad fifth
|-
|-
|18edn
|26edkl
|[[31edo]]
|
|
|Entirely misses 2/1, falling halfway between 12 and 13edo
|-
|-
|19edn
|31edkl
|[[13edo]]
|[[37edo]]
|Noticeably compressed
|
|-
|-
|20edn
|36edkl
|[[14edo]]
|[[43edo]]
|Noticeably stretched
|
|-
|-
|21edn
|62edkl
|[[74edo]]
|
|
|Entirely misses 2/1, falling halfway between 14edo and 15edo
|-
|-
|22edn
|88edkl
|[[105edo]]
|
|
|Cannot be considered equivalent to [[15edo]]
|-
|-
|23edn
|1000edkl
|[[16edo]]
|[[1194edo]]
|
|
|-
|-
|24edn
|2396edkl
|[[17edo]]
|[[2857edo]]
|Some equivalences can be spotted due to 17edo's fame but it's a heavy stretch amounting to 40%
|
|}
|}
To see correspondences of EDKLs to other [[Equal-step tuning|equal tunings]] go [[User:MissMagenta/Correspondence of EDKL to Equal Tunings|here]].

Latest revision as of 02:43, 29 January 2025

Equal divisions of the Komornik–Loreti Seventh, or the Kleventh which has a size of ~1005.2719677332628 cents. The Kleventh is the Komornik–Loreti constant used as a musical interval. Using the Komornik–Loreti constant as an interval is a completely arbitrary choice.

Correspondence of EDKL to EDO

Tuning Equivalent EDO Comment
1edkl 1edo Warning: Inaccurate to 1edo by ~194.8 cents in step size
2edkl 2edo Warning: Inaccurate to 2edo by ~98 cents in step size
3edkl 3edo Warning: Inaccurate to 3edo by ~65 cents in step size
4edkl 5edo
5edkl 6edo
6edkl 7edo
7edkl 8edo
8edkl 10edo
9edkl 11edo
10edkl 12edo Has a good fifth (~0.1% off a just fifth)
11edkl 13edo
12edkl 14edo
13edkl 16edo Has a phenomenal major third (~0.01% off a just major third)
14edkl 17edo
15edkl 18edo
16edkl 19edo
17edkl 20edo
18edkl 21edo Has a great fourth (~4 cents off a just fourth)
19edkl 23edo Similarly to 23edo, completely misses the fifth and fourth.
20edkl 24edo Has the 10edkl fifth, with a good approximation of the 11-limit
21edkl 25edo
22edkl 26edo Good fourth, bad fifth
26edkl 31edo
31edkl 37edo
36edkl 43edo
62edkl 74edo
88edkl 105edo
1000edkl 1194edo
2396edkl 2857edo

To see correspondences of EDKLs to other equal tunings go here.

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