Rodan: Difference between revisions
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'''Rodan''' is a [[temperament]] of the [[gamelismic clan]] and one of the notable [[extension]]s to [[slendric]]. Like slendric, it is generated by an [[8/7]], three of which gives [[3/2]]. In addition it finds [[5/1|harmonic 5]] at +17 generator steps, and the second defining comma for it is [[245/243]]. | '''Rodan''' is a [[temperament]] of the [[gamelismic clan]] and one of the notable [[extension]]s to [[slendric]]. Like slendric, it is generated by an [[8/7]], three of which gives [[3/2]]. In addition it finds [[5/1|harmonic 5]] at +17 generator steps, and the second defining comma for it is [[245/243]]. | ||
Reasonable tunings would be between [[41edo]] and [[46edo]]. [[87edo]] makes for a very recommendable option. | |||
See [[Gamelismic clan #Rodan]] for more information. | See [[Gamelismic clan #Rodan]] for more information. | ||
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{| class="wikitable center-1 right-2" | {| class="wikitable center-1 right-2" | ||
|- | |||
! rowspan="2" | # | ! rowspan="2" | # | ||
! rowspan="2" | Cents* | ! rowspan="2" | Cents* | ||
| Line 146: | Line 147: | ||
| | | | ||
|} | |} | ||
<nowiki>* | <nowiki />* In 13-limit POTE tuning | ||
== Notation == | == Notation == | ||
A notation for rodan is listed in the notation guide for rank-2 pergens under [[pergen]] #8, (P8, P5/3). The generator is an upmajor 2nd. The [[Enharmonic unisons in ups and downs notation|enharmonic unison]] is a trudminor 2nd, thus three ups equals a diatonic semitone, and three generators equals a perfect 5th. In rodan in particular, ^1 equals ~81/80 and ~64/63, and ^^1 equals ~33/32 and ~[[1053/1024]]. | A notation for rodan is listed in the notation guide for rank-2 pergens under [[pergen]] #8, (P8, P5/3). The generator is an upmajor 2nd. The [[Enharmonic unisons in ups and downs notation|enharmonic unison]] is a trudminor 2nd, thus three ups equals a diatonic semitone, and three generators equals a perfect 5th. In rodan in particular, ^1 equals ~81/80 and ~64/63, and ^^1 equals ~33/32 and ~[[1053/1024]]. | ||
{| class="wikitable center-1 center-3" | {| class="wikitable center-1 center-3" | ||
|+Rodan nomenclature<br>for selected intervals | |+ style="font-size: 105%;" | Rodan nomenclature<br />for selected intervals | ||
|- | |||
! Ratio | ! Ratio | ||
! Nominal | ! Nominal | ||
| Line 159: | Line 161: | ||
| 3/2 | | 3/2 | ||
| Perfect fifth | | Perfect fifth | ||
| | | C−G | ||
|- | |- | ||
| 5/4 | | 5/4 | ||
| Downmajor third | | Downmajor third | ||
| | | C−vE | ||
|- | |- | ||
| 7/4 | | 7/4 | ||
| Downminor seventh | | Downminor seventh | ||
| | | C−vB♭ | ||
|- | |- | ||
| 11/8 | | 11/8 | ||
| Dup fourth | | Dup fourth | ||
| | | C−^^F | ||
|- | |- | ||
| 13/8 | | 13/8 | ||
| Dupminor sixth | | Dupminor sixth | ||
| | | C−^^A♭ | ||
|} | |} | ||
Rodan's notation has much in common with that for 41edo and 46edo, since both edos map a minor 2nd to three edosteps. It also resembles the notation for [[cassandra]]. All four notations notate the slendric tetrad (1 | |||
Rodan's notation has much in common with that for 41edo and 46edo, since both edos map a minor 2nd to three edosteps. It also resembles the notation for [[cassandra]]. All four notations notate the slendric tetrad ({{dash|1, 8/7, 21/16, 3/2|med}}) on C as {{nowrap|C, ^D, vF, G|med}}, and all four notations notate 5/4, 7/4, 11/8, and 13/8 as in the table above. But the notations diverge for other intervals, such as 11/10. | |||
== Chords == | == Chords == | ||
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{| class="wikitable center-all left-4" | {| class="wikitable center-all left-4" | ||
|- | |- | ||
! Edo<br>Generator | ! Edo<br />Generator | ||
! [[Eigenmonzo|Eigenmonzo<br>(Unchanged-interval)]] | ! [[Eigenmonzo|Eigenmonzo<br />(Unchanged-interval)]] | ||
! Fifth<br>(¢) | ! Fifth<br />(¢) | ||
! Comments | ! Comments | ||
|- | |- | ||