View source for User:FilterNashi/Temperaments and tuning methods

{{DISPLAYTITLE:User:recentlymaterialized/zpi reference}}{{Editable user page}}

== [[Semitonismic]] & [[Rastmic]] ==
{| class="wikitable"
![[rank]]
| colspan="2" |2
|-
![[subgroup]]
| colspan="2" |2.3.11.17
|-
![[comma basis]]
| colspan="2" |[ -1  5 -2 0]  [[243/242]]
[ -5 -2  0 2]  [[289/288]]
|-
![[edo]]s
| colspan="2" |24, 10, 14, 34, 58, 38, 82, 62, 106, 6[+11], 130, 86[-11, -17], 44[+11], 154
|-
![[edo join]]
| colspan="2" |24 & 10
|-
![[mapping]]
| colspan="2" |[⟨2 0 -1 5], ⟨0 2 5 2]]
|-
![[preimage]]
|[[17/12]]
|153/88
|-
![[WE tuning]]
|600.224
|950.678
|-
![[CWE tuning]]
|600.000
|950.476
|-
!WE errors
| colspan="2" |0.447, -0.600, 1.847, -2.482
|-
!CWE errors
| colspan="2" |0.000, -1.003, 1.061, -4.004
|-
![[badness]]
| colspan="2" |0.204
|}
[https://sintel.pythonanywhere.com/result?subgroup=2.3.11.17&reduce=on&weights=weil&target=&edos=&commas=289%2F288%0D%0A243%2F242&submit_comma=submit see]

all the [[patent val]]: 10 14 24 34 38 48 58 62 72 82 96 106 120 130 154

==ed16.67074¢==
This segment is about the [[equal temperament]] of [[EPD]]16.67074[[cents]].

This is about 71.9824[[EDO]], so it's simply an alternative tuning of [[72edo]]. The [[comma basis]], [[mappings]], etc. show up as same as 72edo.

I use this for 2.3.5.7.11.17.19 [[subgroup]].

72edo didn't work well with 2.3.7.11.13 subgroup because it can't deal with the [[Harmonisma]], and map it to 1 [[step]].

see[https://sintel.pythonanywhere.com/result?subgroup=2%2C3%2C5%2C7%2C11%2C17%2C19&reduce=on&weights=weil&target=&edos=72&submit_edo=submit&commas=%5B-569+359%3E]{{Harmonics in equal|71.9824}}
==ed38.80714¢==
This segment is about the equal temperament of EPD38.80714cents.

This is about 30.922EDO, so it's simply an alternative tuning of [[31edo]]. The comma basis, mappings, etc. show up as same as 31edo.

I use this for 2.3.5.7.11 subgroup.

see[https://sintel.pythonanywhere.com/result?subgroup=2%2C3%2C5%2C7%2C11&reduce=on&weights=weil&target=&edos=31&submit_edo=submit&commas=%5B-569+359%3E]{{Harmonics in equal|30.922}}
==ed20.71628¢==
This segment is about the equal temperament of EPD20.71628cents.

This is about 57.925EDO, so it's simply an alternative tuning of [[58edo]]. The comma basis, mappings, etc. show up as same as 58edo.

I use this for 2.3.5.7.11.13 subgroup.

This is a [[parahemif]].

see[https://sintel.pythonanywhere.com/result?subgroup=2%2C3%2C5%2C7%2C11%2C13&reduce=on&weights=weil&target=&edos=58&submit_edo=submit&commas=]{{Harmonics in equal|57.925}}
==ed63.77698¢==
This segment is about the equal temperament of EPD63.77698cents.

This is about 18.8EDO, so it's simply an alternative tuning of [[19edo]]. The comma basis, mappings, etc. show up as same as 19edo.

I use this for 2.3.5.7 subgroup.

see[https://sintel.pythonanywhere.com/result?subgroup=2%2C3%2C5%2C7&reduce=on&weights=weil&target=&edos=19&submit_edo=submit&commas=10648%2F10647]{{Harmonics in equal|18.8}}
==ed44.21793¢==
This segment is about the equal temperament of EPD44.21793cents.

This is about 27.1383EDO, so it's simply an alternative tuning of [[27edo]]. The comma basis, mappings, etc. show up as same as 27edo.

I use this for 2.3.5.7 subgroup.

see[https://sintel.pythonanywhere.com/result?subgroup=2%2C3%2C5%2C7&reduce=on&weights=weil&target=&edos=27&submit_edo=submit&commas=]{{Harmonics in equal|27.14}}
==56edo==
I use this for 2.3.5.7.17.19 subgroup.

see[https://sintel.pythonanywhere.com/result?subgroup=2%2C3%2C5%2C7%2C11%2C19&reduce=on&weights=weil&target=&edos=56&submit_edo=submit&commas=] and the page of [[56edo]].

This is a [[meantone]] and it map [[513/512]] to -1 step.

==Equal temperaments for 19-horizon==
ed24.04706c~49.9021edo [[50edo]] see[https://sintel.pythonanywhere.com/result?subgroup=2%2C3%2C5%2C7%2C11%2C13%2C17%2C19&reduce=on&weights=weil&target=&edos=50&submit_edo=submit&commas=] this one can't deal with harmonisma but i'm okay with it

ed14.93521c~80.347edo [[80edo]] see[https://sintel.pythonanywhere.com/result?subgroup=2%2C3%2C5%2C7%2C11%2C13%2C17%2C19&reduce=on&weights=weil&target=&edos=80&submit_edo=submit&commas=] this is a [[gentle]].

==Equal temperaments for 5-horizon==
[[12edo]] see[https://sintel.pythonanywhere.com/result?subgroup=2%2C3%2C5&reduce=on&weights=weil&target=&edos=12&submit_edo=submit&commas=]

ed63.16848c~18.9968edo 19edo see[https://sintel.pythonanywhere.com/result?subgroup=2%2C3%2C5&reduce=on&weights=weil&target=&edos=19&submit_edo=submit&commas=]

[[34edo]] see[https://sintel.pythonanywhere.com/result?subgroup=2%2C3%2C5&reduce=on&weights=weil&target=&edos=34&submit_edo=submit&commas=]

ed22.64371c~52.9948edo [[53edo]] see[https://sintel.pythonanywhere.com/result?subgroup=2%2C3%2C5&reduce=on&weights=weil&target=&edos=53&submit_edo=submit&commas=]

==Tuning methods==
For 2.3.5.19 subgroup, i need a meantone while also separate the [[19/16]] and [[6/5]] in the right position. This requires a [[96/95]] on positive size, so 513/512 is on negative size.

50edo and 56edo can handle this.


For 13-horizon, i need a gentle or parahemif while also mapping [[91/90]], [[78/77]], [[66/65]], [[55/54]], [[65/64]], [[56/55]], [[99/98]] on positive sizes.

[[41edo]], 58edo are parahemifs would handle this.
80edo, [[87edo]] are gentles would handle this.