Negri: Difference between revisions

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Negri is a temperament generated by a generator of approximately 125.7549 cents, which can be identified with a tempered 16/15, such that:

Negri is a temperament generated by a generator of approximately 125.7549 cents, which can be identified with a tempered [[16/15]], such that:

* Two of them make a tempered 7/6~8/7~15/13

* Two of them make a tempered [[7/6]]~[[8/7]]~[[15/13]]

* Three of them make a tempered 5/4~16/13

* Three of them make a tempered [[5/4]]~[[16/13]]

* Four of them make a tempered 4/3.

* Four of them make a tempered [[4/3]].

It is most naturally viewed as a 2.3.5.7.13 subgroup temperament (tempering out [[49/48]], [[65/64]] and [[225/224]]).

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It is an important temperament which is most notable for being in [[19edo]], where it is generated by the "diatonic half step" of 2\19, but can also be found (albeit not very accurately) in [[9edo]] and [[10edo]].

It forms 9-note MOS's at ~~1L8s~~, with the mode ssssLssss being particularly useful as it has 4:5:6's on the 1/1 and 3/2, as well as 10-note MOS's at ~~9L1s~~, which is also useful in that it makes 4:5:6 and 10:12:15 share the same "shape" of generic intervals in the scale (as in other rank-2 decatonic scales such as [[Pajara]] and [[Blackwood]] scales; this is because 5/4 and 6/5 get tempered to the same thing in [[10edo]]).

It forms 9-note MOS's at [[1L 8s]], with the mode ssssLssss being particularly useful as it has 4:5:6's on the 1/1 and 3/2, as well as 10-note MOS's at [[9L 1s]], which is also useful in that it makes 4:5:6 and 10:12:15 share the same "shape" of generic intervals in the scale (as in other rank-2 decatonic scales such as [[Pajara]] and [[Blackwood]] scales; this is because 5/4 and 6/5 get tempered to the same thing in [[10edo]]).

The 7-limit extensions can also be viewed as joining with the [[~~Marvel_temperaments~~#Negri|Marvel temperament family]]; the tuning information below is also located there.

The 7-limit extensions can also be viewed as joining with the [[Marvel temperaments #Negri|Marvel temperament family]]; the tuning information below is also located there.

==5-limit==

== Temperament data ==

=== 5-limit ===

[[Comma|Comma]]s: 16875/16384

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EDOs: [[9edo|9]], [[10edo|10]], [[19edo|19]], [[86edo|86]]

==7-limit==

=== 7-limit ===

[[Comma|Comma]]s: 49/48, 225/224

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EDOs: [[9edo|9]], [[10edo|10]], [[19edo|19]], [[86edo|86]]

==11-limit==

=== 11-limit ===

Commas: 45/44, 49/48, 56/55

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[[Badness|Badness]]: 0.0262

==13-limit==

=== 13-limit ===

Commas: 45/44, 49/48, 56/55, 78/77

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EDOs: 9, 10, 19

== Examples ==

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[https://youtu.be/bCLZChG6U6c Negri Comma Pump] played by [[Mike Battaglia]]

[[Category:Temperament]]

[[Category:Negri| ]]

@@ Line 5: / Line 5: @@
 | ja =
 }}
-Negri is a temperament generated by a generator of approximately 125.7549 cents, which can be identified with a tempered 16/15, such that:
+Negri is a temperament generated by a generator of approximately 125.7549 cents, which can be identified with a tempered [[16/15]], such that:
-* Two of them make a tempered 7/6~8/7~15/13
+* Two of them make a tempered [[7/6]]~[[8/7]]~[[15/13]]
-* Three of them make a tempered 5/4~16/13
+* Three of them make a tempered [[5/4]]~[[16/13]]
-* Four of them make a tempered 4/3.
+* Four of them make a tempered [[4/3]].
 It is most naturally viewed as a 2.3.5.7.13 subgroup temperament (tempering out [[49/48]], [[65/64]] and [[225/224]]).
@@ Line 15: / Line 15: @@
 It is an important temperament which is most notable for being in [[19edo]], where it is generated by the "diatonic half step" of 2\19, but can also be found (albeit not very accurately) in [[9edo]] and [[10edo]].
-It forms 9-note MOS's at 1L8s, with the mode ssssLssss being particularly useful as it has 4:5:6's on the 1/1 and 3/2, as well as 10-note MOS's at 9L1s, which is also useful in that it makes 4:5:6 and 10:12:15 share the same "shape" of generic intervals in the scale (as in other rank-2 decatonic scales such as [[Pajara]] and [[Blackwood]] scales; this is because 5/4 and 6/5 get tempered to the same thing in [[10edo]]).
+It forms 9-note MOS's at [[1L 8s]], with the mode ssssLssss being particularly useful as it has 4:5:6's on the 1/1 and 3/2, as well as 10-note MOS's at [[9L 1s]], which is also useful in that it makes 4:5:6 and 10:12:15 share the same "shape" of generic intervals in the scale (as in other rank-2 decatonic scales such as [[Pajara]] and [[Blackwood]] scales; this is because 5/4 and 6/5 get tempered to the same thing in [[10edo]]).
-The 7-limit extensions can also be viewed as joining with the [[Marvel_temperaments#Negri|Marvel temperament family]]; the tuning information below is also located there.
+The 7-limit extensions can also be viewed as joining with the [[Marvel temperaments #Negri|Marvel temperament family]]; the tuning information below is also located there.
-==5-limit==
+== Temperament data ==
+=== 5-limit ===
 [[Comma|Comma]]s: 16875/16384
@@ Line 31: / Line 32: @@
 EDOs: [[9edo|9]], [[10edo|10]], [[19edo|19]], [[86edo|86]]
-==7-limit==
+=== 7-limit ===
 [[Comma|Comma]]s: 49/48, 225/224
@@ Line 42: / Line 43: @@
 EDOs: [[9edo|9]], [[10edo|10]], [[19edo|19]], [[86edo|86]]
-==11-limit==
+=== 11-limit ===
 Commas: 45/44, 49/48, 56/55
@@ Line 53: / Line 54: @@
 [[Badness|Badness]]: 0.0262
-==13-limit==
+=== 13-limit ===
 Commas: 45/44, 49/48, 56/55, 78/77
@@ Line 61: / Line 62: @@
 EDOs: 9, 10, 19
 == Examples ==
@@ Line 71: / Line 71: @@
 [https://youtu.be/bCLZChG6U6c Negri Comma Pump] played by [[Mike Battaglia]]
+[[Category:Temperament]]
+[[Category:Negri| ]] <!-- main article -->