76edo: Difference between revisions

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~~[[Skip fretting system 76 2 17]]~~

== 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 {{nowrap|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 {{nowrap|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 ===

76edo can be notated with [[ups and downs]], spoken as up, dup, downsharp, sharp, upsharp etc. and down, dud, upflat etc. Note that dup is equivalent to dudsharp and dud is equivalent to dupflat.

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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Line 49:

</imagemap>

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

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

File:76-EDO_Evo-SZ_Sagittal.svg

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In the diagrams above, a sagittal symbol followed by an equals sign (=) means that the following comma is the symbol's [[Sagittal notation#Primary comma|primary comma]] (the comma it ''exactly'' represents in JI), while an approximately equals sign (≈) means it is a secondary comma (a comma it ''approximately'' represents in JI). In both cases the symbol exactly represents the tempered version of the comma in this EDO.

== Instruments ==

=== Skip fretting ===

'''[[Skip fretting]] system 76 2 17''' optimizes the subminor chord, 0-17-44 of 76edo.

7/6 can be found on adjacent strings, as each string is tuned 17\76 apart.

If you’re playing a 6-string with the lowest string at an arbitrary root within 76edo, the strings will be as follows, from thickest to thinnest:

0 17 34 51 68 9

Note that the thinnest string is in the next octave.

Each fret is 2\76, or 1\38. This puts the perfect 5th at the 3rd string (34\76), 5th fret (10\76). That gives us 44\76. If you want to add more notes to your chord, 59\76 (12/7) can be found on the 4th string, 4th fret. The 8ve is found on the 5th string, 4th fret. The subminor 10th is found on the 6th string, 4th fret.

A regular minor chord, with a 19\76 3rd, is also easily playable. 19\76 is found on the 2nd string, 1st fret; as well as on the 6th string, 5th fret.

=== Keyboards ===

[[Lumatone mapping for 76edo|Lumatone mappings for 76edo]] are available.

== Music ==

; [[Bryan Deister]]

* [https://www.youtube.com/shorts/IUqoN9YhTtQ ''microtonal improvisation in 76edo''] (2025)

@@ Line 1: / Line 1: @@
 {{Infobox ET}}
-{{EDO intro|76}}
+{{ED intro}}
-[[Skip fretting system 76 2 17]]
 == 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 {{nowrap|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 {{nowrap|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 20: / Line 17: @@
 == Notation ==
-===Sagittal notation===
+=== Ups and downs notation ===
+edo can be notated with [[ups and downs]], spoken as up, dup, downsharp, sharp, upsharp etc. and down, dud, upflat etc. Note that dup is equivalent to dudsharp and dud is equivalent to dupflat.
+{{Sharpness-sharp4a}}
+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 34: / Line 38: @@
 </imagemap>
-====Revo flavor====
+==== Revo flavor ====
 <imagemap>
 File:76-EDO_Revo_Sagittal.svg
@@ Line 46: / Line 49: @@
 </imagemap>
-====Evo-SZ flavor====
+==== Evo-SZ flavor ====
 <imagemap>
 File:76-EDO_Evo-SZ_Sagittal.svg
@@ Line 59: / Line 61: @@
 In the diagrams above, a sagittal symbol followed by an equals sign (=) means that the following comma is the symbol's [[Sagittal notation#Primary comma|primary comma]] (the comma it ''exactly'' represents in JI), while an approximately equals sign (≈) means it is a secondary comma (a comma it ''approximately'' represents in JI). In both cases the symbol exactly represents the tempered version of the comma in this EDO.
+== Instruments ==
+=== Skip fretting ===
+'''[[Skip fretting]] system 76 2 17''' optimizes the subminor chord, 0-17-44 of 76edo.
+/6 can be found on adjacent strings, as each string is tuned 17\76 apart.
+If you’re playing a 6-string with the lowest string at an arbitrary root within 76edo, the strings will be as follows, from thickest to thinnest:
+17 34 51 68 9
+Note that the thinnest string is in the next octave.
+Each fret is 2\76, or 1\38. This puts the perfect 5th at the 3rd string (34\76), 5th fret (10\76). That gives us 44\76. If you want to add more notes to your chord, 59\76 (12/7) can be found on the 4th string, 4th fret. The 8ve is found on the 5th string, 4th fret. The subminor 10th is found on the 6th string, 4th fret.
+A regular minor chord, with a 19\76 3rd, is also easily playable. 19\76 is found on the 2nd string, 1st fret; as well as on the 6th string, 5th fret.
+=== Keyboards ===
+[[Lumatone mapping for 76edo|Lumatone mappings for 76edo]] are available.
+== Music ==
+; [[Bryan Deister]]
+* [https://www.youtube.com/shorts/IUqoN9YhTtQ ''microtonal improvisation in 76edo''] (2025)