Xenharmonic Wiki

375edo: Difference between revisions

VisualWikitext
Francium (talk | contribs)
4,840 edits
Created page with "{{Infobox ET}} {{EDO intro|375}} == Theory == 375et is only consistent to the 3-odd-limit and the harmonic 3 is about halfway between its steps. It can be used in the 2.9..."
 
ArrowHead294 (talk | contribs)
15,220 edits
mNo edit summary
 
(3 intermediate revisions by 2 users not shown)
Line 1: Line 1:
{{Infobox ET}}
{{Infobox ET}}
{{EDO intro|375}}
{{ED intro}}


== Theory ==
== Theory ==
375et is only consistent to the [[3-odd-limit]] and the harmonic 3 is about halfway between its steps. It can be used in the 2.9.5.7.13.17.19 [[subgroup]]. Using the patent val, it tempers out 40500000/40353607, 52734375/52706752 and [[6144/6125]] in the 7-limit; 100663296/100656875, 10333575/10307264, 166698/166375, 759375/758912, 151263/151250, [[540/539]], 4302592/4296875, 825000/823543, [[5632/5625]], 16808715/16777216, 1362944/1361367, 4108797/4096000, 67110351/67108864, 805255/802816 and [[1771561/1769472]] in the 11-limit. It [[support]]s [[aufic]] and [[persephone]].
375edo is in[[consistent]] to the [[5-odd-limit]] and [[harmonic]] [[3/1|3]] is about halfway between its steps. It can be used as a temperament in the 2.9.5.7.13.17.19 [[subgroup]], in which it [[tempering out|tempers out]] [[250047/250000]], 589824/588245, and {{monzo| 8 7 -13 }} ([[parakleisma]]).
 
For the full 7-limit, the 375cd [[val]] is the best, where it tempers out [[1029/1024]] and [[15625/15552]], [[support]]ing [[tritikleismic]]. In the 11-limit it tempers out [[385/384]] and [[441/440]], supporting undecimal tritikleismic.
 
Using the [[patent val]], it tempers out [[6144/6125]] and 177147/175616, supporting [[aufo]]. In the 11-limit it tempers out [[540/539]] and [[5632/5625]], supporting [[aufic]] and [[persephone]].  


=== Odd harmonics ===
=== Odd harmonics ===
Line 9: Line 13:


=== Subsets and supersets ===
=== Subsets and supersets ===
375 factors into 3 × 5<sup>3<sup> with subset edos {{EDOs|3, 5, 15, 25, 75, and 125}}. [[1175edo]], which triples it, gives a good correction to the harmonic 3 and is consistent to the [[15-odd-limit]].
Since 375 factors into 3 × 5<sup>3</sup>, 375edo has subset edos {{EDOs| 3, 5, 15, 25, 75, and 125 }}. [[1175edo]], which triples it, gives a good correction to the harmonic 3 and is consistent to the [[15-odd-limit]].


== Regular temperament properties ==
== Regular temperament properties ==
{| class="wikitable center-4 center-5 center-6"
{| class="wikitable center-4 center-5 center-6"
! rowspan="2" |[[Subgroup]]
|-
! rowspan="2" |[[Comma list|Comma List]]
! rowspan="2" | [[Subgroup]]
! rowspan="2" |[[Mapping]]
! rowspan="2" | [[Comma list|Comma List]]
! rowspan="2" |Optimal<br>8ve Stretch (¢)
! rowspan="2" | [[Mapping]]
! colspan="2" |Tuning Error
! rowspan="2" | Optimal<br>8ve Stretch (¢)
! colspan="2" | Tuning Error
|-
|-
![[TE error|Absolute]] (¢)
! [[TE error|Absolute]] (¢)
![[TE simple badness|Relative]] (%)
! [[TE simple badness|Relative]] (%)
|-
|-
|2.9
| 2.9
|{{monzo|1189 -375}}
| {{monzo| 1189 -375 }}
|{{mapping|375 1189}}
| {{mapping| 375 1189 }}
| -0.1404
| −0.1404
| 0.1404
| 0.1404
| 4.39
| 4.39
|-
|-
|2.9.5
| 2.9.5
|{{monzo|8 7 -13}}, {{monzo|97 -24 -9}}
| {{monzo| 8 7 -13 }}, {{monzo| 97 -24 -9 }}
|{{mapping|375 1189 871}}
| {{mapping| 375 1189 871 }}
| -0.2208
| −0.2208
| 0.1615
| 0.1615
| 5.05
| 5.05
|-
|-
|2.9.5.7
| 2.9.5.7
|250047/250000, 26873856/26796875, 26985857024/26904200625
| 250047/250000, 589824/588245, {{monzo| 8 7 -13 }}
|{{mapping|375 1189 871 1053}}
| {{mapping| 375 1189 871 1053 }}
| -0.2345
| −0.2345
| 0.1418
| 0.1418
| 4.43
| 4.43
|}
|}
Retrieved from "https://en.xen.wiki/w/375edo"