37edo: Difference between revisions
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== Theory == | == Theory == | ||
37edo | 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]]). | 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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=== No-3 approach === | === No-3 approach === | ||
If prime 3 is ignored, 37edo represents the no-3 23-odd-limit consistently. | If prime 3 is ignored, 37edo represents the no-3 23-odd-limit consistently, and is distinctly consistent within the no-3 16-integer-limit. | ||
== Intervals == | == Intervals == | ||
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! Degrees | ! Degrees | ||
! Cents | ! Cents | ||
! colspan="3" | [[Ups and | ! colspan="3" | [[Ups and downs notation]] | ||
|- | |- | ||
| 0 | | 0 | ||
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default [[File:37-EDO_Evo-SZ_Sagittal.svg]] | default [[File:37-EDO_Evo-SZ_Sagittal.svg]] | ||
</imagemap> | </imagemap> | ||
== Regular temperament properties == | == Regular temperament properties == | ||
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|} | |} | ||
== | == Instruments == | ||
* [[ | |||
; Lumatone | |||
* [[Lumatone mapping for 37edo]] | |||
; Fretted instruments | |||
* [[Skip fretting system 37 2 7]] | |||
== Music == | == Music == | ||
; [[Beheld]] | ; [[Beheld]] | ||
* [https://www.youtube.com/watch?v=IULi2zSdatA ''Mindless vibe''] (2023) | * [https://www.youtube.com/watch?v=IULi2zSdatA ''Mindless vibe''] (2023) | ||
; [[Bryan Deister]] | |||
* [https://www.youtube.com/shorts/e7dLJTsS3PQ ''37edo''] (2025) | |||
* [https://www.youtube.com/shorts/m9hmiH8zong ''37edo jam''] (2025) | |||
; [[Francium]] | ; [[Francium]] | ||
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* ''[https://www.youtube.com/watch?v=_m5u4VviMXw Galantean Drift]'' (2025) | * ''[https://www.youtube.com/watch?v=_m5u4VviMXw Galantean Drift]'' (2025) | ||
== | == See also == | ||
* [[User:Unque/37edo Composition Theory|Unque's approach]] | |||
* [[ | |||
== External links == | == External links == | ||