User:Moremajorthanmajor/7L 3s (perfect eleventh-equivalent): Difference between revisions

The generator range reflects two extremes: one where L = s (3\10), and another where s = 0 (2\7). Between these extremes, there is an infinite continuum of possible generator sizes. By taking freshman sums of the two edges (adding the numerators, then adding the denominators), we can fill in this continuum with compatible ~ed8/3s, increasing in number of tones as we continue filling in the in-betweens. Thus, the smallest in-between ~ed8/3 would be (3+2)\(10+7) = 5\17 – five degrees of [[17edXI]]:

{| class="wikitable center-all"

!Cents

!L

!Comments

|-

|514.286||1||1||1.000||

|-

|510.000||6||5||1.200||

|-

|509.{{Overline|09}}||5||4||1.250||

|-

|508.475||9||7||1.286||

|-

|507.692||4||3||1.333||

|-

|506.{{Overline|6}}||7||5||1.400||

|-

|505.263||3||2||1.500||L/s = 3/2

|-

|504.000||8||5||1.600||

|-

|503.226||5||3||1.667||

|-

|502.326||7||4||1.750||

|-

|501.{{Overline|81}}||9||5||1.800||

|-

|500.000||2||1||2.000||Basic Bolivar

(Generators smaller than this are proper)

|-

|101\143

|499.{{Overline|0099}}

|

|-

|89\126

|498.876

|15

|

|-

|77\109

|498.701

|13

|

|-

|65\92

|498.452

|11

|

|-

|498.113||9||4||2.250||

|-

|497.561||7||3||2.333||

|-

|496.552||5||2||2.500||

|-

|495.652||8||3||2.667||

|-

|494.118||3||1||3.000||L/s = 3/1

|-

|73\103

|493.151

|13

|

|-

|492.857||10||3||3.333||

|-

|492.308||7||2||3.500||

|-

|491.803||11||3||3.667||

|-

|490.{{Overline|90}}||4||1||4.000||

|-

|489.796||9||2||4.500||

|-

|488.{{Overline|8}}||5||1||5.000||

|-

|487.500||6||1||6.000||

|-

|480.000||1||0||→ inf||

|}The scale produced by stacks of 5\17 is the 12edo diatonic scale.