34edo: Difference between revisions

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! Ratios of 7<br />Using the 34 Val

! Ratios of 7<br />Using the 34d Val

! colspan="3" | [[Ups and ~~Downs Notation~~]]

! colspan="3" | [[Ups and downs notation]]

([[Enharmonic unisons in ups and downs notation|EUs]]: v<sup>4</sup>A1 and ^^d2)

! colspan="2" | [[Solfege|Solfeges]]

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|}

Chords can be named using ups and downs as C upminor, D downmajor seven, etc. See [[Ups and ~~Downs Notation~~ #Chord names in other EDOs]].

Chords can be named using ups and downs as C upminor, D downmajor seven, etc. See [[Ups and downs notation #Chord names in other EDOs]].

== Notation ==

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{{Q-odd-limit intervals|34.1|apx=val|header=none|tag=none|title=15-odd-limit intervals by 34d val mapping}}

Of particular interest is the fact that the 34d val allows all 15-odd-limit intervals to be mapped consistently except for 7/4 ~~itself~~.

Of particular interest is the fact that the 34d val allows all 15-odd-limit intervals to be mapped consistently except for 7/4 and 8/7.

~~=== Zeta peak index ===~~

~~{{ZPI~~

~~| zpi = 144~~

~~| steps = 34.0448410043159~~

~~| step size = 35.2476312005063~~

~~| tempered height = 6.685147~~

~~| pure height = 5.810937~~

~~| integral = 1.241437~~

~~| gap = 16.236989~~

~~| octave = 1198.41946081721~~

~~| consistent = 6~~

~~| distinct = 6~~

}}

== Tuning by ear ==

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* "Locksmiths" from ''The Decatonic Album'' (2024) – [https://open.spotify.com/track/2Hzun107B8bxcZaMOClN6T Spotify] | [https://francium223.bandcamp.com/track/locksmiths Bandcamp] | [https://www.youtube.com/watch?v=pQLbtF0Obhc YouTube]

* [https://www.youtube.com/watch?v=HG0kJBHjuZ4 ''Plane Sonatina No. 2''] (2025)

* [https://www.youtube.com/watch?v=ZrjbxQbdVw4 ''cucumber service''] (2025)

; [[Adam Freese]]

@@ Line 27: / Line 27: @@
 ! Ratios of 7<br />Using the 34 Val
 ! Ratios of 7<br />Using the 34d Val
-! colspan="3" | [[Ups and Downs Notation]]
+! colspan="3" | [[Ups and downs notation]]
 ([[Enharmonic unisons in ups and downs notation|EUs]]: v<sup>4</sup>A1 and ^^d2)
 ! colspan="2" | [[Solfege|Solfeges]]
@@ Line 417: / Line 417: @@
 |}
-Chords can be named using ups and downs as C upminor, D downmajor seven, etc. See [[Ups and Downs Notation #Chord names in other EDOs]].
+Chords can be named using ups and downs as C upminor, D downmajor seven, etc. See [[Ups and downs notation #Chord names in other EDOs]].
 == Notation ==
@@ Line 478: / Line 478: @@
 {{Q-odd-limit intervals|34.1|apx=val|header=none|tag=none|title=15-odd-limit intervals by 34d val mapping}}
-Of particular interest is the fact that the 34d val allows all 15-odd-limit intervals to be mapped consistently except for 7/4 itself.
+Of particular interest is the fact that the 34d val allows all 15-odd-limit intervals to be mapped consistently except for 7/4 and 8/7.
-=== Zeta peak index ===
-{{ZPI
-| zpi = 144
-| steps = 34.0448410043159
-| step size = 35.2476312005063
-| tempered height = 6.685147
-| pure height = 5.810937
-| integral = 1.241437
-| gap = 16.236989
-| octave = 1198.41946081721
-| consistent = 6
-| distinct = 6
-}}
 == Tuning by ear ==
@@ Line 800: / Line 786: @@
 * "Locksmiths" from ''The Decatonic Album'' (2024) – [https://open.spotify.com/track/2Hzun107B8bxcZaMOClN6T Spotify] | [https://francium223.bandcamp.com/track/locksmiths Bandcamp] | [https://www.youtube.com/watch?v=pQLbtF0Obhc YouTube]
 * [https://www.youtube.com/watch?v=HG0kJBHjuZ4 ''Plane Sonatina No. 2''] (2025)
+* [https://www.youtube.com/watch?v=ZrjbxQbdVw4 ''cucumber service''] (2025)
 ; [[Adam Freese]]