User:VectorGraphics/Interesting scales
16edo scales and temperaments
16edo contains several MOS patterns, with RTT interpretations.
Slendric
In 16edo slendric, the generator is 3\16, an arto third or supermajor second 8/7. Three generators make a 3/2, represented by 16edo's flat fifth 9\16, and in 16edo, two generators make 13/10. The slendric MOS #1 appears as the "slendric chord" in my mavila theory.
| Note | MOS #1 | MOS #2 | MOS #3 |
|---|---|---|---|
| 0 | # | # | # |
| 1 | |||
| 2 | # | ||
| 3 | # | # | # |
| 4 | |||
| 5 | # | ||
| 6 | # | # | # |
| 7 | |||
| 8 | # | ||
| 9 | # | # | # |
| 10 | |||
| 11 | # | ||
| 12 | # | # | # |
| 13 | |||
| 14 | # | ||
| 15 | # | # | |
| 16/0 | # | # | # |
Magic
In 16edo magic, the generator is 5\16, a classical major third of 5/4, and five generators make 3/2, represented by 9\16.
| Note | MOS #1 | MOS #2 | MOS #3 |
|---|---|---|---|
| 0 | # | # | # |
| 1 | |||
| 2 | # | ||
| 3 | # | # | |
| 4 | # | # | # |
| 5 | # | # | # |
| 6 | |||
| 7 | # | ||
| 8 | # | # | |
| 9 | # | # | # |
| 10 | # | # | # |
| 11 | |||
| 12 | # | ||
| 13 | # | # | |
| 14 | # | # | # |
| 15 | # | # | # |
| 16/0 | # | # | # |
The series of MOSes made by magic is huge in 16edo, these are just the three most "interesting" examples. Magic MOS #1 is used in 16edo Ollatiu music in Quaternity.
Fendo
16edo is at the bottom of the fendo tuning range, with the generator, 6\16, essentially being exactly 13/10. Additionally, this is the only 16edo tuning to use the sharp fifth of 750c instead of the flat fifth of 675c.
| Note | MOS #1 | MOS #2 |
|---|---|---|
| 0 | # | # |
| 1 | ||
| 2 | # | # |
| 3 | ||
| 4 | # | |
| 5 | ||
| 6 | # | # |
| 7 | ||
| 8 | # | # |
| 9 | ||
| 10 | # | |
| 11 | ||
| 12 | # | # |
| 13 | ||
| 14 | # | |
| 15 | ||
| 16/0 | # | # |
The second "MOS" is actually 8edo, an equalized 5L3s.
Mavila
Main article: User:VectorGraphics/16edo theory
16edo mavila is probably the most notable 16edo temperament and set of MOSes. In mavila temperament, four 3/2s (represented by 16edo's flat 9\16 fifth) make 6/5, making it somewhat of an "evil twin" to meantone, in which they make 5/4. In terms of mediants, mavila fifths produce diatonic mediants in the "third" range whose relative size is swapped from diatonic, and thus range from 655 to 686 cents.
| Note | MOS #1 | MOS #2 | MOS #3 |
|---|---|---|---|
| 0 | # | # | # |
| 1 | |||
| 2 | # | # | # |
| 3 | |||
| 4 | # | # | # |
| 5 | |||
| 6 | # | # | |
| 7 | |||
| 8 | # | ||
| 9 | # | # | # |
| 10 | |||
| 11 | # | # | # |
| 12 | |||
| 13 | # | # | |
| 14 | |||
| 15 | # | ||
| 16/0 | # | # | # |
Fendo
There are several "fendo" scales (in which the fourth is used as a tendo third, represented in RTT by tempering out 40/39) available.
5edo
| Note | MOS #1 | MOS #2 |
|---|---|---|
| 0 | # | # |
| 1 | # | |
| 2 | # | # |
| 3 | # | |
| 4 | # | # |
| 5/0 | # | # |
The second MOS is the entire scale, equivalent to an equalized antipentic.
13edo
WIP