Rodan: Difference between revisions
m partial undo; removed most 81-odds but most of the other intervals were here before. intervals are sorted by complexity anyhow |
m moved notation first and added comment on super/sub |
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See [[Gamelismic clan #Rodan]] for more information. | See [[Gamelismic clan #Rodan]] for more information. | ||
== Notation == | |||
A notation for rodan is listed in the notation guide for rank-2 pergens under [[pergen]] #8, {{nowrap|(P8, P5/3)}}. The generator is an upmajor second. The [[enharmonic unisons in ups and downs notation|enharmonic unison]] is a triple-down minor second. Thus three ups equals a diatonic semitone, and three generators equals a perfect fifth. 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" | |||
|+ style="font-size: 105%;" | Rodan nomenclature<br>for selected intervals | |||
|- | |||
! Ratio | |||
! Nominal | |||
! Example | |||
|- | |||
| 3/2 | |||
| Perfect fifth | |||
| C−G | |||
|- | |||
| 5/4 | |||
| Down major third | |||
| C−vE | |||
|- | |||
| 7/4 | |||
| Down minor seventh | |||
| C−vB♭ | |||
|- | |||
| 11/8 | |||
| Double-up fourth | |||
| C−^^F | |||
|- | |||
| 13/8 | |||
| Double-up minor sixth | |||
| C−^^A♭ | |||
|} | |||
Rodan's notation has much in common with that for 41edo and 46edo, since both edos map a minor second to three edosteps. It also resembles the notation for [[cassandra]]. All four notations notate the slendric tetrad (1–8/7–21/16–3/2) on C as C–^D–vF–G, 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. | |||
It is also possible, specifically when speaking of interval categories, to use the "super" and "sub" prefixes in lieu of "up" and "down", as in the interval chain below and in the context of larger rodan edos that map this comma to multiple edosteps. | |||
== Interval chain == | == Interval chain == | ||
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| 937.84 | | 937.84 | ||
| 12/7, 55/32 | | 12/7, 55/32 | ||
| | | | ||
|- | |- | ||
| 5 | | 5 | ||
| Line 131: | Line 166: | ||
| 151.35 | | 151.35 | ||
| 12/11, 35/32 | | 12/11, 35/32 | ||
| | | | ||
|- | |- | ||
| 17 | | 17 | ||
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Notice also the little interval between the largest of a category and the smallest of the next, which represents the differences between 16/15 and 14/13, between 11/9 and 16/13, between 7/5 and 45/32, between 13/8 and 18/11, and between 13/7 and 15/8. It spans 41 generator steps, so it vanishes in 41edo, but is tuned to the same size as the quark/syntonic comma in 46edo. 87edo tunes it to one half the size of the syntonic comma, which may be seen as a good compromise. | Notice also the little interval between the largest of a category and the smallest of the next, which represents the differences between 16/15 and 14/13, between 11/9 and 16/13, between 7/5 and 45/32, between 13/8 and 18/11, and between 13/7 and 15/8. It spans 41 generator steps, so it vanishes in 41edo, but is tuned to the same size as the quark/syntonic comma in 46edo. 87edo tunes it to one half the size of the syntonic comma, which may be seen as a good compromise. | ||
== Chords == | == Chords == | ||