Rodan: Difference between revisions
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== Notation == | == Notation == | ||
A notation for rodan | 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 interval 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" | ||
| Line 162: | Line 162: | ||
|- | |- | ||
| 5/4 | | 5/4 | ||
| | | Downmajor third | ||
| C-vE | | C-vE | ||
|- | |- | ||
| 7/4 | | 7/4 | ||
| | | Downminor seventh | ||
| C-vBb | | C-vBb | ||
|- | |- | ||
| 11/8 | | 11/8 | ||
| | | Dup fourth | ||
| C-^^F | | C-^^F | ||
|- | |- | ||
| 13/8 | | 13/8 | ||
| | | Dupminor sixth | ||
| C-^^Ab | | C-^^Ab | ||
|} | |} | ||
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 (1-8/7-21/16-3/2) 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, for example 11/10. | |||
== Chords == | == Chords == | ||
Revision as of 11:36, 23 December 2024
Rodan is a temperament of the gamelismic clan and one of the notable extensions to slendric. Like slendric, it is generated by an 8/7, three of which gives 3/2. In addition it finds harmonic 5 at +17 generator steps, and the second defining comma for it is 245/243.
A reasonable tuning would be between 41edo and 46edo. 87edo makes for a very recommendable option.
See Gamelismic clan #Rodan for more information.
Interval chain
Prime harmonics are in bold.
| # | Cents* | Approximate Ratios | |
|---|---|---|---|
| 13-limit | 17-limit Extension | ||
| 0 | 0.000 | 1/1 | |
| 1 | 234.482 | 8/7 | |
| 2 | 468.964 | 21/16 | 17/13 |
| 3 | 703.446 | 3/2 | |
| 4 | 937.929 | 12/7 | |
| 5 | 1172.411 | 63/32, 160/81 | |
| 6 | 206.893 | 9/8 | |
| 7 | 441.375 | 9/7 | 22/17 |
| 8 | 675.857 | 40/27 | |
| 9 | 910.339 | 22/13, 27/16, 33/28 | |
| 10 | 1144.821 | 27/14, 35/18, 64/33 | 33/17 |
| 11 | 179.304 | 10/9 | |
| 12 | 413.786 | 14/11, 33/26, 80/63 | |
| 13 | 648.268 | 16/11 | |
| 14 | 882.750 | 5/3 | |
| 15 | 1117.232 | 21/11, 40/21 | |
| 16 | 151.714 | 12/11 | |
| 17 | 386.196 | 5/4 | |
| 18 | 620.679 | 10/7 | |
| 19 | 855.161 | 18/11, 64/39 | 28/17 |
| 20 | 1089.643 | 15/8 | 32/17 |
| 21 | 124.125 | 14/13, 15/14 | |
| 22 | 358.607 | 16/13, 27/22 | 21/17 |
| 23 | 593.088 | 45/32 | 24/17 |
| 24 | 827.570 | 21/13 | |
| 25 | 1062.052 | 24/13 | |
* in 13-limit POTE tuning
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 interval 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.
| Ratio | Nominal | Example |
|---|---|---|
| 3/2 | Perfect fifth | C-G |
| 5/4 | Downmajor third | C-vE |
| 7/4 | Downminor seventh | C-vBb |
| 11/8 | Dup fourth | C-^^F |
| 13/8 | Dupminor sixth | C-^^Ab |
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 (1-8/7-21/16-3/2) 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, for example 11/10.
Chords
Scales
Tuning spectrum
Gencom: [2 8/7; 154/153 196/195 245/243 273/272 364/363]
Gencom mapping: [⟨1 1 -1 3 6 8 8], ⟨0 3 17 -1 -13 -22 -20]]
| Edo Generator |
Eigenmonzo (Unchanged-interval) |
Fifth (¢) |
Comments |
|---|---|---|---|
| 8/7 | 693.522 | ||
| 17/13 | 696.642 | ||
| 7/6 | 699.847 | ||
| 21\36 | 700.000 | Lower bound of 7- and 9-odd-limit diamond monotone | |
| 9/7 | 700.750 | ||
| 4/3 | 701.955 | ||
| 24\41 | 702.439 | Lower bound of 11- to 17-odd-limit diamond monotone | |
| 15/14 | 702.778 | ||
| 7/5 | 702.915 | 7- and 9-odd-limit minimax | |
| 11/9 | 703.041 | 11-odd-limit minimax | |
| 75\128 | 703.125 | ||
| 18/13 | 703.220 | 13- and 15-odd-limit minimax | |
| 16/15 | 703.240 | ||
| 12/11 | 703.244 | ||
| 15/11 | 703.359 | ||
| 13/12 | 703.371 | ||
| 15/13 | 703.410 | ||
| 51\87 | 703.448 | ||
| 5/4 | 703.467 | 5-odd-limit minimax | |
| 11/10 | 703.500 | ||
| 13/10 | 703.522 | ||
| 11/8 | 703.542 | ||
| 16/13 | 703.564 | ||
| 13/11 | 703.597 | ||
| 18/17 | 703.726 | 17-odd-limit minimax | |
| 17/15 | 703.748 | ||
| 78\133 | 703.759 | ||
| 6/5 | 703.791 | ||
| 20/17 | 703.894 | ||
| 24/17 | 703.956 | ||
| 17/16 | 704.257 | ||
| 10/9 | 704.292 | ||
| 27\46 | 704.348 | Upper bound of 11- to 17-odd-limit diamond monotone | |
| 14/11 | 704.377 | ||
| 3\5 | 720.000 | Upper bound of 7- and 9-odd-limit diamond monotone |
Music
- Pianodactyl (archived 2010) – SoundCloud | detail | play – rodan[26] in 87edo tuning