37edo: Difference between revisions

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== Theory ==

37edo ~~is the 10th [[no-threes subgroup temperaments|no-3]] [[zeta peak edo]], containing~~ very accurate approximations of harmonics [[5/1|5]], [[7/1|7]], [[11/1|11]] and [[13/1|13]]. ~~It has an extremely~~ accurate ~~harmonic 11~~, being only 0.03 cents sharp.

37edo has very accurate approximations of harmonics [[5/1|5]], [[7/1|7]], [[11/1|11]] and [[13/1|13]], making it a good choice for a [[no-threes subgroup temperaments|no-threes]] approach. Harmonic 11 is particularly accurate, being only 0.03 cents sharp.

Using its best (and sharp) fifth, 37edo tempers out 250/243, making it a variant of [[porcupine]] temperament. It is the [[optimal patent val]] for [[Porcupine family #Porcupinefish|porcupinefish]], which is about as accurate as 13-limit porcupine extensions will be. Using its alternative flat fifth, it tempers out [[16875/16384]], making it a [[negri]] tuning. It also tempers out 2187/2000, resulting in a temperament where three minor whole tones make up a fifth ([[gorgo]]/[[laconic]]).

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! Degrees

! Cents

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

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

|-

| 0

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default [[File:37-EDO_Evo-SZ_Sagittal.svg]]

</imagemap>

~~== Approximation to JI ==~~

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

~~{{ZPI~~

~~| zpi = 161~~

~~| steps = 37.0275229191254~~

~~| step size = 32.4083250889078~~

~~| tempered height = 5.287327~~

~~| pure height = 4.97538~~

~~| integral = 0.891828~~

~~| gap = 15.095854~~

~~| octave = 1199.10802828959~~

~~| consistent = 8~~

~~| distinct = 8~~

}}

== Regular temperament properties ==

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; [[Bryan Deister]]

* [https://www.youtube.com/shorts/e7dLJTsS3PQ ''37edo''] (2025)

* [https://www.youtube.com/shorts/m9hmiH8zong ''37edo jam''] (2025)

; [[Francium]]

@@ Line 9: / Line 9: @@
 == Theory ==
-edo is the 10th [[no-threes subgroup temperaments|no-3]] [[zeta peak edo]], containing very accurate approximations of harmonics [[5/1|5]], [[7/1|7]], [[11/1|11]] and [[13/1|13]]. It has an extremely accurate harmonic 11, being only 0.03 cents sharp.
+edo has very accurate approximations of harmonics [[5/1|5]], [[7/1|7]], [[11/1|11]] and [[13/1|13]], making it a good choice for a [[no-threes subgroup temperaments|no-threes]] approach. Harmonic 11 is particularly accurate, being only 0.03 cents sharp.
 Using its best (and sharp) fifth, 37edo tempers out 250/243, making it a variant of [[porcupine]] temperament. It is the [[optimal patent val]] for [[Porcupine family #Porcupinefish|porcupinefish]], which is about as accurate as 13-limit porcupine extensions will be. Using its alternative flat fifth, it tempers out [[16875/16384]], making it a [[negri]] tuning. It also tempers out 2187/2000, resulting in a temperament where three minor whole tones make up a fifth ([[gorgo]]/[[laconic]]).
@@ Line 350: / Line 350: @@
 ! Degrees
 ! Cents
-! colspan="3" | [[Ups and Downs Notation]]
+! colspan="3" | [[Ups and downs notation]]
 |-
 | 0
@@ Line 630: / Line 630: @@
 default [[File:37-EDO_Evo-SZ_Sagittal.svg]]
 </imagemap>
-== Approximation to JI ==
-=== Zeta peak index ===
-{{ZPI
-| zpi = 161
-| steps = 37.0275229191254
-| step size = 32.4083250889078
-| tempered height = 5.287327
-| pure height = 4.97538
-| integral = 0.891828
-| gap = 15.095854
-| octave = 1199.10802828959
-| consistent = 8
-| distinct = 8
-}}
 == Regular temperament properties ==
@@ Line 913: / Line 898: @@
 ; [[Bryan Deister]]
 * [https://www.youtube.com/shorts/e7dLJTsS3PQ ''37edo''] (2025)
+* [https://www.youtube.com/shorts/m9hmiH8zong ''37edo jam''] (2025)
 ; [[Francium]]