47edo: Difference between revisions

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== Theory ==

47edo has a fifth which is 12.593-cent flat, unless you use the alternative fifth which is 12.939-cent sharp, similar to [[35edo]]. The soft [[5L 2s|diatonic]] scale generated from its flat fifth is so soft, with L/s = 7/6, that it stops sounding like [[meantone]] or even a [[flattone]] system like [[26edo]] or [[40edo]], but just sounds like a [[circulating temperament]] of [[7edo]]. It has therefore not aroused much interest, but its best approximation to [[9/8]] is actually quite good, one-third-of-a-cent sharp.

47edo has a fifth which is 12.593-cent flat, unless you use the alternative fifth which is 12.939-cent sharp, similar to [[35edo]]. The soft [[5L 2s|diatonic]] scale generated from its flat fifth is so soft, with {{nowrap|L/s {{=}} 7/6}}, that it stops sounding like [[meantone]] or even a [[flattone]] system like [[26edo]] or [[40edo]], but just sounds like a [[circulating temperament]] of [[7edo]]. It has therefore not aroused much interest, but its best approximation to [[9/8]] is actually quite good, one-third-of-a-cent sharp.

47edo is a diatonic edo because its 5th falls between 4\7 = 686{{~~cent~~}} and 3\5 = 720{{~~cent~~}}, as does its alternate 5th as well. 47edo is one of the most difficult diatonic edos to notate, because no other diatonic edos 5th is as flat (see [[42edo]] for the opposite extreme).

47edo is a diatonic edo because its 5th falls between {{nowrap|4\7 {{=}} 686{{c}}}} and {{nowrap|3\5 {{=}} 720{{c}}}}, as does its alternate 5th as well. 47edo is one of the most difficult diatonic edos to notate, because no other diatonic edos 5th is as flat (see [[42edo]] for the opposite extreme).

=== Odd harmonics ===

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D# is next to E. This notation requires quadruple, quintuple, and even sextuple ups and downs, as well as single sharps and flats.

===Sagittal notation===

=== Ups and downs notation ===

====Best fifth notation====

Using [[Helmholtz–Ellis]] accidentals and the sharp fifth, 47edo can be notated using [[ups and downs notation|ups and downs]]:

With the flat fifth, notation is identical to standard notation:

=== Sagittal notation ===

==== Best fifth notation ====

This notation uses the same sagittal sequence as [[42edo#Second-best fifth notation|42b]].

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</imagemap>

====Second-best fifth notation====

==== Second-best fifth notation ====

=====Evo and Revo flavors=====

===== Evo and Revo flavors =====

File:47b_Sagittal.svg

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</imagemap>

=====Alternative Evo flavor=====

===== Alternative Evo flavor =====

File:47b_Alternative_Evo_Sagittal.svg

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</imagemap>

=====Evo-SZ flavor=====

===== Evo-SZ flavor =====

File:47b_Evo-SZ_Sagittal.svg

@@ Line 1: / Line 1: @@
 {{Infobox ET}}
-{{EDO intro|47}}
+{{ED intro}}
 == Theory ==
-edo has a fifth which is 12.593-cent flat, unless you use the alternative fifth which is 12.939-cent sharp, similar to [[35edo]]. The soft [[5L 2s|diatonic]] scale generated from its flat fifth is so soft, with L/s = 7/6, that it stops sounding like [[meantone]] or even a [[flattone]] system like [[26edo]] or [[40edo]], but just sounds like a [[circulating temperament]] of [[7edo]]. It has therefore not aroused much interest, but its best approximation to [[9/8]] is actually quite good, one-third-of-a-cent sharp.
+edo has a fifth which is 12.593-cent flat, unless you use the alternative fifth which is 12.939-cent sharp, similar to [[35edo]]. The soft [[5L 2s|diatonic]] scale generated from its flat fifth is so soft, with {{nowrap|L/s {{=}} 7/6}}, that it stops sounding like [[meantone]] or even a [[flattone]] system like [[26edo]] or [[40edo]], but just sounds like a [[circulating temperament]] of [[7edo]]. It has therefore not aroused much interest, but its best approximation to [[9/8]] is actually quite good, one-third-of-a-cent sharp.
-edo is a diatonic edo because its 5th falls between 4\7 = 686{{cent}} and 3\5 = 720{{cent}}, as does its alternate 5th as well. 47edo is one of the most difficult diatonic edos to notate, because no other diatonic edos 5th is as flat (see [[42edo]] for the opposite extreme).
+edo is a diatonic edo because its 5th falls between {{nowrap|4\7 {{=}} 686{{c}}}} and {{nowrap|3\5 {{=}} 720{{c}}}}, as does its alternate 5th as well. 47edo is one of the most difficult diatonic edos to notate, because no other diatonic edos 5th is as flat (see [[42edo]] for the opposite extreme).
 === Odd harmonics ===
@@ Line 326: / Line 326: @@
 D# is next to E. This notation requires quadruple, quintuple, and even sextuple ups and downs, as well as single sharps and flats.
-===Sagittal notation===
+=== Ups and downs notation ===
-====Best fifth notation====
+Using [[Helmholtz–Ellis]] accidentals and the sharp fifth, 47edo can be notated using [[ups and downs notation|ups and downs]]:
+{{Sharpness-sharp8}}
+With the flat fifth, notation is identical to standard notation:
+{{Sharpness-sharp1}}
+=== Sagittal notation ===
+==== Best fifth notation ====
 This notation uses the same sagittal sequence as [[42edo#Second-best fifth notation|42b]].
@@ Line 339: / Line 346: @@
 </imagemap>
-====Second-best fifth notation====
+==== Second-best fifth notation ====
-=====Evo and Revo flavors=====
+===== Evo and Revo flavors =====
 <imagemap>
 File:47b_Sagittal.svg
@@ Line 351: / Line 357: @@
 </imagemap>
-=====Alternative Evo flavor=====
+===== Alternative Evo flavor =====
 <imagemap>
 File:47b_Alternative_Evo_Sagittal.svg
@@ Line 362: / Line 367: @@
 </imagemap>
-=====Evo-SZ flavor=====
+===== Evo-SZ flavor =====
 <imagemap>
 File:47b_Evo-SZ_Sagittal.svg