76edo: Difference between revisions

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== Theory ==

~~''It is recommended to read the page [[regular temperament]] first to understand this section.''~~

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.

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== Instruments ==

~~; Fretted instruments~~

* [[Skip fretting system 76 2 17]]

=== 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 3: / Line 3: @@
 == Theory ==
-''It is recommended to read the page [[regular temperament]] first to understand this section.''
 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.
@@ Line 65: / Line 63: @@
 == Instruments ==
-; Fretted instruments
-* [[Skip fretting system 76 2 17]]
+=== 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)