User:Zhenlige/12neji: Difference between revisions

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This is a list of 12-tone [[NEJI]]s designed by me.

This is a list of 12-tone [[NEJI]]s designed by me. The goal is to make a scale that satisfy the restrictions below:

*The [[octave]] is just, and all [[3/2|fifths]] are acceptable (≤8 [[cent]]s off from just).

*The least common denominator is small enough (≤256).

*Most notes are in a manageable [[prime limit]].

*It contains some simple just intervals.

== 1 ==

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Assuming G centered:

*One fifth flatten by [[243/242]] (~7.139 cents) at B-F♯

*Two fifths flatten by approximately half of [[153/152]] (~5.7 cents ~~each~~) at G♯-D♯~~-A♯~~

*Two fifths flatten by approximately half of [[153/152]] at G♯-D♯-A♯

*One fifth flatten by [[513/512]] (~3.3 cents) at F-C

**One fifth flatten by 305/304 (~5.686 cents) at D♯-A♯

*One fifth flatten by [[1089/1088]] (~1.6 cents) at F♯-C♯

**One fifth flatten by 306/305 (~5.667 cents) at G♯-D♯

*Seven ~~pure~~ fifths at C-G-D-A-E-B, C♯-G♯ and A♯-F

*One fifth flatten by [[513/512]] (~3.378 cents) at F-C

*One fifth flatten by [[1089/1088]] (~1.590 cents) at F♯-C♯

*Seven just fifths at C-G-D-A-E-B, C♯-G♯ and A♯-F

== 2 ==

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2/1

</pre>

=== Fifths ===

Assuming G centered:

*Two fifths flatten by approximately half of [[153/152]] at G♯-D♯-A♯

**One fifth flatten by 305/304 (~5.686 cents) at D♯-A♯

**One fifth flatten by 306/305 (~5.667 cents) at G♯-D♯

*One fifth flatten by [[324/323]] (~5.352 cents) at A-E

*One fifth flatten by [[513/512]] (~3.378 cents) at F-C

*One fifth flatten by [[969/968]] (~1.788 cents) at E-B

*One fifth flatten by [[1089/1088]] (~1.590 cents) at F♯-C♯

*Six just fifths at C-G-D-A, B-F♯, C♯-G♯ and A♯-F

[[Category:Pages with Scala files]]

[[Category:12-tone scales]]

[[Category:Tempered scales]]

@@ Line 1: / Line 1: @@
-This is a list of 12-tone [[NEJI]]s designed by me.
+This is a list of 12-tone [[NEJI]]s designed by me. The goal is to make a scale that satisfy the restrictions below:
+*The [[octave]] is just, and all [[3/2|fifths]] are acceptable (≤8 [[cent]]s off from just).
+*The least common denominator is small enough (≤256).
+*Most notes are in a manageable [[prime limit]].
+*It contains some simple just intervals.
 == 1 ==
@@ Line 25: / Line 29: @@
 Assuming G centered:
 *One fifth flatten by [[243/242]] (~7.139 cents) at B-F♯
-*Two fifths flatten by approximately half of [[153/152]] (~5.7 cents each) at G♯-D♯-A♯
+*Two fifths flatten by approximately half of [[153/152]]  at G♯-D♯-A♯
-*One fifth flatten by [[513/512]] (~3.3 cents) at F-C
+**One fifth flatten by 305/304 (~5.686 cents) at D♯-A♯
-*One fifth flatten by [[1089/1088]] (~1.6 cents) at F♯-C♯
+**One fifth flatten by 306/305 (~5.667 cents) at G♯-D♯
-*Seven pure fifths at C-G-D-A-E-B, C♯-G♯ and A♯-F
+*One fifth flatten by [[513/512]] (~3.378 cents) at F-C
+*One fifth flatten by [[1089/1088]] (~1.590 cents) at F♯-C♯
+*Seven just fifths at C-G-D-A-E-B, C♯-G♯ and A♯-F
 == 2 ==
@@ Line 50: / Line 56: @@
 /1
 </pre>
+=== Fifths ===
+Assuming G centered:
+*Two fifths flatten by approximately half of [[153/152]]  at G♯-D♯-A♯
+**One fifth flatten by 305/304 (~5.686 cents) at D♯-A♯
+**One fifth flatten by 306/305 (~5.667 cents) at G♯-D♯
+*One fifth flatten by [[324/323]] (~5.352 cents) at A-E
+*One fifth flatten by [[513/512]] (~3.378 cents) at F-C
+*One fifth flatten by [[969/968]] (~1.788 cents) at E-B
+*One fifth flatten by [[1089/1088]] (~1.590 cents) at F♯-C♯
+*Six just fifths at C-G-D-A, B-F♯, C♯-G♯ and A♯-F
 [[Category:Pages with Scala files]]
 [[Category:12-tone scales]]
 [[Category:Tempered scales]]