52edo: Difference between revisions

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Using the sharp fifth rather than the flat fifth (that is, using the 52b val), it contains a version of [[porcupine]] temperament, and combining 30\52 with 31\52 leads to a whole tone of 9\52, or 208 cents, which can be used inconsistently.

The 5\52 ~~interval approximates~~ [[~~31/29~~]] ~~well, and when used as~~ a ~~generator produces~~ [[~~tricesimoprimal miracloid~~]] ~~temperament~~. ~~The relationship is also preserved exactly in the period-52 [[french deck]] temperament~~.

The 11\52 (253.846{{c}}) [[semifourth]] is a very accurate [[22/19]], with an error of only +0.041{{c}} and a closing error of only 9.3%.

~~The~~ 11~~\52 (253.846{{c}})~~ [[~~semifourth~~]] ~~is a very~~ accurate [[22/19]]~~, with an error~~ of ~~only +0~~.~~041{{c}} and a closing error of only~~ 9.3%.

52edo has an accurate [[11/9]], but unfortunately, in the [[2.3.11 subgroup]], neither the patent val nor the 52b val map it consistently. The 52e val does, but that would be requiring you to give up 26edo's accurate [[11/8]]. Perhaps the best way of getting 11/9 to map correctly would be to use the 2.9.11 subgroup.

=== Odd harmonics ===

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! Degrees

! [[Cents]]s

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

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

|-

| 0

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=== Ups and downs notation ===

Using [[Helmholtz–Ellis]] accidentals, 52edo can also be notated using [[ups and downs notation]] or Stein–Zimmerman [[24edo#Notation|quarter tone]] accidentals:

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* [https://www.youtube.com/shorts/lNJCZz7EjL0 ''microtonal improvisation in 52edo''] (2025)

* [https://www.youtube.com/watch?v=3uo24YpEN0E ''Waltz in 52edo''] (2025)

* [https://www.youtube.com/shorts/PgSsSM5pJcM ''52edo improv''] (2025)

* [https://www.youtube.com/watch?v=ejpqSEwfSZg ''March in 52edo''] (2025)

* [https://www.youtube.com/shorts/ovA5-YkjxWk ''52edo groove''] (2026)

* [https://www.youtube.com/shorts/YMjz4thpjxQ ''52edo jam''] (2026)

; [[Claudi Meneghin]]

@@ Line 7: / Line 7: @@
 Using the sharp fifth rather than the flat fifth (that is, using the 52b val), it contains a version of [[porcupine]] temperament, and combining 30\52 with 31\52 leads to a whole tone of 9\52, or 208 cents, which can be used inconsistently.
-The 5\52 interval approximates [[31/29]] well, and when used as a generator produces [[tricesimoprimal miracloid]] temperament. The relationship is also preserved exactly in the period-52 [[french deck]] temperament.
+The 11\52 (253.846{{c}}) [[semifourth]] is a very accurate [[22/19]], with an error of only +0.041{{c}} and a closing error of only 9.3%.
-The 11\52 (253.846{{c}}) [[semifourth]] is a very accurate [[22/19]], with an error of only +0.041{{c}} and a closing error of only 9.3%.
+edo has an accurate [[11/9]], but unfortunately, in the [[2.3.11 subgroup]], neither the patent val nor the 52b val map it consistently. The 52e val does, but that would be requiring you to give up 26edo's accurate [[11/8]]. Perhaps the best way of getting 11/9 to map correctly would be to use the 2.9.11 subgroup.
 === Odd harmonics ===
@@ Line 22: / Line 22: @@
 ! Degrees
 ! [[Cents]]s
-! colspan="3" | [[Ups and Downs Notation]]
+! colspan="3" | [[Ups and downs notation]]
 |-
 | 0
@@ Line 348: / Line 348: @@
 === Ups and downs notation ===
 Using [[Helmholtz–Ellis]] accidentals, 52edo can also be notated using [[ups and downs notation]] or Stein–Zimmerman [[24edo#Notation|quarter tone]] accidentals:
-{{Sharpness-sharp2a}}
+{{Ups and downs sharpness}}
 {{sharpness-sharp2}}
@@ Line 396: / Line 396: @@
 * [https://www.youtube.com/shorts/lNJCZz7EjL0 ''microtonal improvisation in 52edo''] (2025)
 * [https://www.youtube.com/watch?v=3uo24YpEN0E ''Waltz in 52edo''] (2025)
+* [https://www.youtube.com/shorts/PgSsSM5pJcM ''52edo improv''] (2025)
+* [https://www.youtube.com/watch?v=ejpqSEwfSZg ''March in 52edo''] (2025)
+* [https://www.youtube.com/shorts/ovA5-YkjxWk ''52edo groove''] (2026)
+* [https://www.youtube.com/shorts/YMjz4thpjxQ ''52edo jam''] (2026)
 ; [[Claudi Meneghin]]

52edo: Difference between revisions

Lucius Chiaraviglio (talk | contribs)