76edo: Difference between revisions

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== Theory ==

76edo's [[patent val]] is [[contorted]] in the 5-limit, reflecting the fact that 76 = 4 × 19. In the 7-limit it [[tempering out|tempers out]] [[2401/2400]] in addition to [[81/80]], and so [[support]]s the [[squares]] temperament. In the 11-limit, it tempers out [[245/242]] and [[385/384]], and supports [[pombe]], the 24 & 26 temperament. In the 13-limit, it tempers out 105/104, 144/143, 351/350 and 364/363. While the 44\76 = 11\19 fifth is already flat, the 43\76 fifth, even flatter, is an almost perfect approximation to the [[hornbostel]] temperament's [[POTE]] fifth, whereas its sharp fifth, 45\76, makes for an excellent [[superpyth]] fifth. Hence you can do hornbostel/mavila, squares/meantone, and superpyth all with the same equal division.

76edo's [[patent val]] is [[contorted]] in the 5-limit, reflecting the fact that 76 = 4 × 19. In the 7-limit it [[tempering out|tempers out]] [[2401/2400]] in addition to [[81/80]], and so [[support]]s the [[squares]] temperament. In the 11-limit, it tempers out [[245/242]] and [[385/384]], and supports [[pombe]], the {{nowrap|24 & 26}} temperament. In the 13-limit, it tempers out 105/104, 144/143, 351/350 and 364/363. While the 44\76 = 11\19 fifth is already flat, the 43\76 fifth, even flatter, is an almost perfect approximation to the [[hornbostel]] temperament's [[POTE]] fifth, whereas its sharp fifth, 45\76, makes for an excellent [[superpyth]] fifth. Hence you can do hornbostel/mavila, squares/meantone, and superpyth all with the same equal division.

Using the 76dgh val, 76edo provides an excellent tuning for [[teff]] temperament, a low-complexity, medium-accuracy, and high-limit (17- or 19-limit) temperament.

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== Notation ==

===Sagittal notation===

=== Ups and downs notation ===

Using [[Helmholtz–Ellis]] accidentals, 76edo can also be notated using [[ups and downs notation]] along with Stein–Zimmerman [[24edo#Notation|quarter-tone]] accidentals:

Here, a sharp raises by four steps, and a flat lowers by four steps, so arrows can be used to fill in the gap.

=== Sagittal notation ===

This notation uses the same sagittal sequence as EDOs [[62edo#Sagittal notation|62]] and [[69edo#Sagittal notation|69]], and is a superset of the notations for EDOs [[38edo#Sagittal notation|38]] and [[19edo#Sagittal notation|19]].

~~====Evo flavor====~~

==== Evo flavor ====

File:76-EDO_Evo_Sagittal.svg

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</imagemap>

====Revo flavor====

==== Revo flavor ====

File:76-EDO_Revo_Sagittal.svg

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</imagemap>

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

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

File:76-EDO_Evo-SZ_Sagittal.svg

@@ Line 1: / Line 1: @@
 {{Infobox ET}}
-{{EDO intro|76}}
+{{ED intro}}
 == Theory ==
-edo's [[patent val]] is [[contorted]] in the 5-limit, reflecting the fact that 76 = 4 × 19. In the 7-limit it [[tempering out|tempers out]] [[2401/2400]] in addition to [[81/80]], and so [[support]]s the [[squares]] temperament. In the 11-limit, it tempers out [[245/242]] and [[385/384]], and supports [[pombe]], the 24 &amp; 26 temperament. In the 13-limit, it tempers out 105/104, 144/143, 351/350 and 364/363. While the 44\76 = 11\19 fifth is already flat, the 43\76 fifth, even flatter, is an almost perfect approximation to the [[hornbostel]] temperament's [[POTE]] fifth, whereas its sharp fifth, 45\76, makes for an excellent [[superpyth]] fifth. Hence you can do hornbostel/mavila, squares/meantone, and superpyth all with the same equal division.
+edo's [[patent val]] is [[contorted]] in the 5-limit, reflecting the fact that 76 = 4 × 19. In the 7-limit it [[tempering out|tempers out]] [[2401/2400]] in addition to [[81/80]], and so [[support]]s the [[squares]] temperament. In the 11-limit, it tempers out [[245/242]] and [[385/384]], and supports [[pombe]], the {{nowrap|24 &amp; 26}} temperament. In the 13-limit, it tempers out 105/104, 144/143, 351/350 and 364/363. While the 44\76 = 11\19 fifth is already flat, the 43\76 fifth, even flatter, is an almost perfect approximation to the [[hornbostel]] temperament's [[POTE]] fifth, whereas its sharp fifth, 45\76, makes for an excellent [[superpyth]] fifth. Hence you can do hornbostel/mavila, squares/meantone, and superpyth all with the same equal division.
 Using the 76dgh val, 76edo provides an excellent tuning for [[teff]] temperament, a low-complexity, medium-accuracy, and high-limit (17- or 19-limit) temperament.
@@ Line 17: / Line 17: @@
 == Notation ==
-===Sagittal notation===
+=== Ups and downs notation ===
+Using [[Helmholtz–Ellis]] accidentals, 76edo can also be notated using [[ups and downs notation]] along with Stein–Zimmerman [[24edo#Notation|quarter-tone]] accidentals:
+{{Sharpness-sharp4}}
+Here, a sharp raises by four steps, and a flat lowers by four steps, so arrows can be used to fill in the gap.
+=== Sagittal notation ===
 This notation uses the same sagittal sequence as EDOs [[62edo#Sagittal notation|62]] and [[69edo#Sagittal notation|69]], and is a superset of the notations for EDOs [[38edo#Sagittal notation|38]] and [[19edo#Sagittal notation|19]].
-====Evo flavor====
+==== Evo flavor ====
 <imagemap>
 File:76-EDO_Evo_Sagittal.svg
@@ Line 31: / Line 36: @@
 </imagemap>
-====Revo flavor====
+==== Revo flavor ====
 <imagemap>
 File:76-EDO_Revo_Sagittal.svg
@@ Line 43: / Line 47: @@
 </imagemap>
-====Evo-SZ flavor====
+==== Evo-SZ flavor ====
 <imagemap>
 File:76-EDO_Evo-SZ_Sagittal.svg