4L 3s: Difference between revisions
m comment out part mentioning temperaments |
m comment out according to temp restriction policy |
||
| Line 27: | Line 27: | ||
'''J/Q&''' J&/K@ '''K/L@''' '''L/K&''' L&/M@ '''M/N@''' '''N/M&''' N&/O@ '''O/P@''' '''P/O@''' P&/J@ '''J''' | '''J/Q&''' J&/K@ '''K/L@''' '''L/K&''' L&/M@ '''M/N@''' '''N/M&''' N&/O@ '''O/P@''' '''P/O@''' P&/J@ '''J''' | ||
== Scale tree == | == Scale tree == | ||
The spectrum looks like this: | The spectrum looks like this: | ||
| Line 84: | Line 83: | ||
| | 929.023 | | | 929.023 | ||
| | 38.71 | | | 38.71 | ||
| style="text-align:center;" | | | style="text-align:center;" | | ||
|- | |- | ||
| | | | | | ||
| Line 129: | Line 128: | ||
| | 947.368 | | | 947.368 | ||
| | 63.158 | | | 63.158 | ||
| style="text-align:center;" | | | style="text-align:center;" | | ||
|- | |- | ||
| | | | | | ||
| Line 144: | Line 143: | ||
| | 951.941 | | | 951.941 | ||
| | 70.588 | | | 70.588 | ||
| style="text-align:center;" | | | style="text-align:center;" | | ||
|- | |- | ||
| | | | | | ||
| Line 159: | Line 158: | ||
| | 960 | | | 960 | ||
| | 80 | | | 80 | ||
| style="text-align:center;" | L/s = 3. | | style="text-align:center;" | L/s = 3. | ||
|- | |- | ||
| | | | | | ||
| Line 249: | Line 248: | ||
| | 970.003 | | | 970.003 | ||
| | 94.004 | | | 94.004 | ||
| style="text-align:center;" | | | style="text-align:center;" | | ||
|- | |- | ||
| | | | | | ||
| Line 309: | Line 308: | ||
| | 981.818 | | | 981.818 | ||
| | 109.091 | | | 109.091 | ||
| style="text-align:center;" | Boundary of propriety (generators <br>larger than this are proper) | | style="text-align:center;" | Boundary of propriety (generators <br>larger than this are proper) | ||
|- | |- | ||
| | | | | | ||
| Line 384: | Line 383: | ||
| | 1000 | | | 1000 | ||
| | 133.333 | | | 133.333 | ||
| style="text-align:center;" | Optimum rank range (L/s=3/2) | | style="text-align:center;" | Optimum rank range (L/s=3/2) | ||
|- | |- | ||
| | | | | | ||
| Line 399: | Line 398: | ||
| | 1008 | | | 1008 | ||
| | 144 | | | 144 | ||
| style="text-align:center;" | | | style="text-align:center;" | | ||
|- | |- | ||
| | | | | | ||
| Line 414: | Line 413: | ||
| | 1012.5 | | | 1012.5 | ||
| | 150 | | | 150 | ||
| style="text-align:center;" | | | style="text-align:center;" | | ||
|- | |- | ||
| | | | | | ||
| Line 444: | Line 443: | ||
| | 1017.391 | | | 1017.391 | ||
| | 156.522 | | | 156.522 | ||
| style="text-align:center;" | | | style="text-align:center;" | | ||
|- | |- | ||
| | | | | | ||
| Line 459: | Line 458: | ||
| | 1018.868 | | | 1018.868 | ||
| | 158.491 | | | 158.491 | ||
| style="text-align:center;" | | | style="text-align:center;" | | ||
|- | |- | ||
| | 2\7 | | | 2\7 | ||
| Line 476: | Line 475: | ||
| style="text-align:center;" | | | style="text-align:center;" | | ||
|} | |} | ||
<!-- | |||
There are two notable harmonic entropy minima: [[Kleismic_family|kleismic]], in which the generator is 6/5 and 6 of them make a 3/1, and [[Starling_temperaments|myna]], in which the generator is also 6/5 but now '''10''' of them make a 6/1 (so no 4/3's or 3/2's appear in this scale). | There are two notable harmonic entropy minima: [[Kleismic_family|kleismic]], in which the generator is 6/5 and 6 of them make a 3/1, and [[Starling_temperaments|myna]], in which the generator is also 6/5 but now '''10''' of them make a 6/1 (so no 4/3's or 3/2's appear in this scale). | ||
== Tuning ranges == | == Tuning ranges == | ||
=== Sixix === | === Sixix === | ||
| Line 724: | Line 723: | ||
* The chroma of sixix[7] is the difference between the sharp fifth and the flat fifth, and functions much like a(n untempered) comma in sixix harmony, giving two slightly different flavors of fifths, minor thirds, major thirds, etc, much like in [[porcupine]] harmony. Tempering out this comma leads to [[7edo]]. | * The chroma of sixix[7] is the difference between the sharp fifth and the flat fifth, and functions much like a(n untempered) comma in sixix harmony, giving two slightly different flavors of fifths, minor thirds, major thirds, etc, much like in [[porcupine]] harmony. Tempering out this comma leads to [[7edo]]. | ||
--> | |||
== Samples == | == Samples == | ||
[[File:Sixix Fugue.mp3]] | [[File:Sixix Fugue.mp3]] A fugue in [[18edo]] (WIP) | ||
[[Category:Scales]] | [[Category:Scales]] | ||
[[Category:MOS scales]] | [[Category:MOS scales]] | ||
[[Category:Abstract MOS patterns]] | [[Category:Abstract MOS patterns]] | ||