TromboneBoi9
Joined 2 May 2023
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I don't know about you, but I love the seventh harmonic. These scales are named after the [[cloudy comma]]. | I don't know about you, but I love the seventh harmonic. These scales are named after the [[cloudy comma]]. | ||
'''''Cumulus Alpha''''' is a 5L6s [[MOS]] with [[7/4]] as the generator and [[2/1]] as the period. | '''''Cumulus Alpha''''' is a 5L6s [[MOS]] with [[7/4]] as the generator and [[2/1]] as the period. This appears to approximate a subset of [[26edo|26-EDO]]; it approximates the whole of 26-EDO when extended to a 5L21s MOS, which I dub '''''Cumulus Holo-Alpha'''''. | ||
{| class="wikitable mw-collapsible" | {| class="wikitable mw-collapsible" | ||
!Steps | !Steps | ||
!Ratio | !Ratio | ||
!Cents | !Cents | ||
!Approx. 26-EDO Degree | |||
|- | |- | ||
|0 | |0 | ||
|1/1 | |1/1 | ||
|0.000 | |0.000 | ||
|0 | |||
|- | |- | ||
|1 | |1 | ||
|16807/16384 | |16807/16384 | ||
|43.130 | |43.130 | ||
|1 | |||
|- | |- | ||
|2 | |2 | ||
|8/7 | |8/7 | ||
|231.174 | |231.174 | ||
|5 | |||
|- | |- | ||
|3 | |3 | ||
|2401/2048 | |2401/2048 | ||
|275.304 | |275.304 | ||
|6 | |||
|- | |- | ||
|4 | |4 | ||
|64/49 | |64/49 | ||
|462.348 | |462.348 | ||
|10 | |||
|- | |- | ||
|5 | |5 | ||
|343/256 | |343/256 | ||
|506.478 | |506.478 | ||
|11 | |||
|- | |- | ||
|6 | |6 | ||
|512/343 | |512/343 | ||
|693.522 | |693.522 | ||
|15 | |||
|- | |- | ||
|7 | |7 | ||
|49/32 | |49/32 | ||
|737.652 | |737.652 | ||
|16 | |||
|- | |- | ||
|8 | |8 | ||
|4096/2401 | |4096/2401 | ||
|924.696 | |924.696 | ||
|20 | |||
|- | |- | ||
|9 | |9 | ||
|7/4 | |7/4 | ||
|968.826 | |968.826 | ||
|21 | |||
|- | |- | ||
|10 | |10 | ||
|32768/16807 | |32768/16807 | ||
|1155.870 | |1155.870 | ||
|25 | |||
|- | |- | ||
|11 | |11 | ||
|2/1 | |2/1 | ||
|1200.000 | |1200.000 | ||
|26 | |||
|} | |} | ||
'''''Cumulus Beta''''' is an 4L5s MOS with [[7/6]] as the generator and [[2/1]] as the period. Amazingly, it approximates all intervals of [[9edo|9-EDO]] within a cent! | '''''Cumulus Beta''''' is an 4L5s MOS with [[7/6]] as the generator and [[2/1]] as the period. Amazingly, it approximates all intervals of [[9edo|9-EDO]] within a cent! | ||
| Line 403: | Line 416: | ||
|0.000 | |0.000 | ||
|} | |} | ||
'''''Cumulus Gamma''''' is an | '''''Cumulus Gamma''''' is an 3L8s MOS with [[9/7]] as the generator and [[2/1]] as the period. It approximates all intervals of [[11edo|11-EDO]] within 10 cents. | ||
{| class="wikitable mw-collapsible" | {| class="wikitable mw-collapsible" | ||
!Steps | !Steps | ||
!Ratio | !Ratio | ||
!Cents | !Cents | ||
! | !11-EDO Difference | ||
|- | |- | ||
|0 | |0 | ||
|1/1 | |1/1 | ||
|0.000 | |0.000 | ||
|0 | |0.000 | ||
|- | |- | ||
|1 | |1 | ||
|729/686 | |729/686 | ||
|105.252 | |105.252 | ||
| | |3.839 | ||
|- | |- | ||
|2 | |2 | ||
|67228/59049 | |||
|224.580 | |||
| -6.398 | |||
|- | |||
|3 | |||
|98/81 | |98/81 | ||
|329.832 | |329.832 | ||
| | | -2.559 | ||
|- | |- | ||
| | |4 | ||
|9/7 | |9/7 | ||
|435.084 | |435.084 | ||
| | |1.280 | ||
|- | |- | ||
| | |5 | ||
|6561/4802 | |6561/4802 | ||
|540.336 | |540.336 | ||
|5 | |5.119 | ||
|- | |||
|6 | |||
|9604/6561 | |||
|659.664 | |||
| -5.119 | |||
|- | |- | ||
| | |7 | ||
|14/9 | |14/9 | ||
|764.916 | |764.916 | ||
| | | -1.280 | ||
|- | |- | ||
| | |8 | ||
|81/49 | |81/49 | ||
|870.168 | |870.168 | ||
| | |2.559 | ||
|- | |||
|9 | |||
|59049/33614 | |||
|975.420 | |||
|6.398 | |||
|- | |- | ||
| | |10 | ||
|1372/729 | |1372/729 | ||
|1094.748 | |1094.748 | ||
| | | -3.839 | ||
|- | |- | ||
| | |11 | ||
|2/1 | |2/1 | ||
|1200.000 | |1200.000 | ||
| | |0.000 | ||
|} | |} | ||