217edo: Difference between revisions

| rowspan="2" | <big>{{Sagittal| |( }}</big>

| rowspan="2" | <big>{{Sagittal| )|( }}</big>

| rowspan="2" | <big>{{Sagittal| ~|( }}</big>

| rowspan="2" | <big>{{Sagittal| /| }}</big>

| rowspan="2" | <big>{{Sagittal| |) }}</big>

| rowspan="2" | <big>{{Sagittal| (| }}</big>

| rowspan="2" | <big>{{Sagittal| (|( }}</big>

| rowspan="2" | <big>{{Sagittal| //| }}</big>

| rowspan="2" | <big>{{Sagittal| /|) }}</big>

| rowspan="2" | <big>{{Sagittal| /|\ }}</big>

| <big>{{Sagittal|#}}{{sagittal| \!/ }}</big>

| <big>{{Sagittal|#}}{{sagittal| \!) }}</big>

| <big>{{Sagittal|#}}{{sagittal| \\! }}</big>

| <big>{{Sagittal|#}}{{sagittal| (!( }}</big>

| <big>{{Sagittal|#}}{{sagittal| (! }}</big>

| <big>{{Sagittal|#}}{{sagittal| !) }}</big>

| <big>{{Sagittal|#}}{{sagittal| \! }}</big>

| <big>{{Sagittal|#}}{{sagittal| ~!( }}</big>

| <big>{{Sagittal|#}}{{sagittal| )!( }}</big>

| <big>{{Sagittal|#}}{{sagittal| !( }}</big>

| <big>{{Sagittal|#}}</big>

| <big>{{Sagittal| (|) }}</big>

| <big>{{Sagittal| (|\ }}</big>

| <big>{{Sagittal| )||( }}</big>

| <big>{{Sagittal| ~||( }}</big>

| <big>{{Sagittal| )||~ }}</big>

| <big>{{Sagittal| ||) }}</big>

| <big>{{Sagittal| ||\ }}</big>

| <big>{{Sagittal| (||( }}</big>

| <big>{{Sagittal| //|| }}</big>

| <big>{{Sagittal| /||) }}</big>

| <big>{{Sagittal| /||\ }}</big>

The 5-up (quup) alteration neatly maps to the pythagorean-septimal comma.{{Ups and downs sharpness|217|false}}

 

 

This could be useful when [[31edo]] is used as a base tuning, where the whole palette of 217edo is only used to provide subtle inflections of the 31edo pitches, similar to how one might use [[159edo]] to provide subtle corrections of [[53edo]] pitches. It also can be written with SZ half-sharps and up/down. The main drawback of this notation is that the best fifth is '''^P5''', so that ~4:5:6 is from C written as C-E-^G, compared to C-^<E-G to the usual chain-of-fifths ups-and-downs notation.

|+Alternative 31edo-based notation

|-

| rowspan="2" | ^

| rowspan="2" | ^^

| rowspan="2" | ^^^

=== '''7edo-based whitewood notation''' ===

Since {{nowrap| 217 {{=}} 7 × 31}}, one '''''could''''' use the inherited [[Whitewood family|whitewood]] fifth, ditch sharps and flats, and instead use ups and downs to represent pitch deviations from the perfect nominals. Since 31=15*2+1, all pitches can be notated with ups, downs, quips and quids. ~4:5:6 becomes C-^^^>E-^^^G.

! Sharp

Symbol

| rowspan="2" |h

| ^

|^^

|^^^

vv>

| vv>>>

^^^>>