118edo: Difference between revisions
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! Cents | ! Cents | ||
! Marks | ! Marks | ||
! Approximate Ratios * | ! Approximate Ratios* | ||
! Eliora's Naming System<br />(+Shruti 22 correspondence) | ! Eliora's Naming System<br />(+Shruti 22 correspondence) | ||
! Chemical Notation<br />(see below, if base note = 0) | ! Chemical Notation<br />(see below, if {{nowrap|base note {{=}} 0}}) | ||
! [[Ups and downs notation]] | ! [[Ups and downs notation]] | ||
! [[SKULO interval names|SKULO]] notation | ! [[SKULO interval names|SKULO]] notation | ||
| Line 1,103: | Line 1,103: | ||
| D | | D | ||
|} | |} | ||
<nowiki />* | <nowiki />* {{sg|2.3.5.7.11.17.19 subgroup}} | ||
<nowiki />** Based on a dual-interval interpretation for the 13th harmonic | <nowiki />** Based on a dual-interval interpretation for the 13th harmonic | ||
| Line 1,115: | Line 1,115: | ||
The following are the correspondences of the periodic table structure with 118edo: | The following are the correspondences of the periodic table structure with 118edo: | ||
* 2\118 is the width of the s-block, and is also the size of the Pythagorean and syntonic commas in 118edo. | * 2\118 is the width of the s-block, and is also the size of the Pythagorean and syntonic commas in 118edo. | ||
* 87\118 (francium, start of period 7) and 89\118 (actinium, start of the 7f-block), form 5/3 and 27/16 respectively. | * 87\118 (francium, start of period 7) and 89\118 (actinium, start of the 7f-block), form 5/3 and 27/16 respectively. | ||
* Mercury, ending the 6d-block, corresponds to 8/5. | * Mercury, ending the 6d-block, corresponds to 8/5. | ||
| Line 1,122: | Line 1,122: | ||
== Regular temperament properties == | == Regular temperament properties == | ||
{ | {{comma basis begin}} | ||
|- | |- | ||
| 2.3 | | 2.3 | ||
| Line 1,160: | Line 1,151: | ||
| 0.370 | | 0.370 | ||
| 3.89 | | 3.89 | ||
|-style="border-top: double;" | |- style="border-top: double;" | ||
| 2.3.5.7.11.13 | | 2.3.5.7.11.13 | ||
| 196/195, 352/351, 384/384, 625/624, 729/728 | | 196/195, 352/351, 384/384, 625/624, 729/728 | ||
| Line 1,167: | Line 1,158: | ||
| 0.604 | | 0.604 | ||
| 5.93 | | 5.93 | ||
|-style="border-top: double;" | |- style="border-top: double;" | ||
| 2.3.5.7.11.13 | | 2.3.5.7.11.13 | ||
| 169/168, 325/324, 364/363, 385/384, 3136/3125 | | 169/168, 325/324, 364/363, 385/384, 3136/3125 | ||
| Line 1,174: | Line 1,165: | ||
| 0.650 | | 0.650 | ||
| 6.39 | | 6.39 | ||
|-style="border-top: double;" | |- style="border-top: double;" | ||
| 2.3.5.7.11.17 | | 2.3.5.7.11.17 | ||
| 289/288, 385/384, 441/440, 561/560, 3136/3125 | | 289/288, 385/384, 441/440, 561/560, 3136/3125 | ||
| Line 1,188: | Line 1,179: | ||
| 0.376 | | 0.376 | ||
| 3.69 | | 3.69 | ||
{{comma basis end}} | |||
* 118et is lower in relative error than any previous equal temperaments in the 5-limit. Not until [[171edo|171]] do we find a better one in terms of absolute error, and not until [[441edo|441]] do we find one in terms of relative error. | * 118et is lower in relative error than any previous equal temperaments in the 5-limit. Not until [[171edo|171]] do we find a better one in terms of absolute error, and not until [[441edo|441]] do we find one in terms of relative error. | ||
=== Rank-2 temperaments === | === Rank-2 temperaments === | ||
{ | {{rank-2 begin}} | ||
|- | |- | ||
| 1 | | 1 | ||
| Line 1,290: | Line 1,274: | ||
| 6/5<br />(33/28) | | 6/5<br />(33/28) | ||
| [[Semiparakleismic]] | | [[Semiparakleismic]] | ||
{{rank-2 end}} | |||
{{orf}} | |||
== Instruments == | == Instruments == | ||
| Line 1,302: | Line 1,286: | ||
[[Category:Gamelismic]] | [[Category:Gamelismic]] | ||
[[Category:Guiron]] | [[Category:Guiron]] | ||
[[Category:Listen]] | |||
[[Category:Parakleismic]] | [[Category:Parakleismic]] | ||
[[Category:Portent]] | [[Category:Portent]] | ||
[[Category:Schismic]] | [[Category:Schismic]] | ||