User:Unque/37edo Composition Theory - Revision history

Lériendil: added category

2025-04-14T18:16:33Z

added category

← Older revision		Revision as of 18:16, 14 April 2025
Line 292:		Line 292:

	Additionally, [[Diamond MOS notation]] may be more useful than Circle of Fifths notation for describing structures that do not adhere closely to the Circle of Fifths, such as Orgone or Cubical.		Additionally, [[Diamond MOS notation]] may be more useful than Circle of Fifths notation for describing structures that do not adhere closely to the Circle of Fifths, such as Orgone or Cubical.

			[[Category:Approaches to tuning systems]]

Lériendil: added breadcrumb here

2025-04-03T20:37:55Z

added breadcrumb here

← Older revision		Revision as of 20:37, 3 April 2025
Line 1:		Line 1:
			{{breadcrumb\|37edo}}

	'''Note: This page is currently under construction, and will be subject to major expansion in the near future. Come back soon!'''		'''Note: This page is currently under construction, and will be subject to major expansion in the near future. Come back soon!'''

Unque at 23:17, 23 January 2025

2025-01-23T23:17:53Z

← Older revision		Revision as of 23:17, 23 January 2025
Line 26:		Line 26:
	\|1\37		\|1\37
	\|32.43		\|32.43
	\|[[55/54]], [[56/55]]		\|[[55/54]]+, [[56/55]]
	\|		\|
	\|D♭		\|D♭
Line 33:		Line 33:
	\|2\37		\|2\37
	\|64.86		\|64.86
	\|[[28/27]]		\|[[28/27]]+
	\|[[Sycamore~~]]/[[Unicorn~~]]		\|[[Sycamore]]
	\|Bｷ = E𝄫		\|Bｷ = E𝄫
	\|~~Sycamore uses diatonic fifth, Unicorn uses antidiatonic fifth~~		\|
	\|-		\|-
	\|3\37		\|3\37
Line 68:		Line 68:
	\|7\37		\|7\37
	\|227.03		\|227.03
	\|~~10/9-,~~ 9/8+, [[8/7]]		\|9/8+, [[8/7]]
	\|[[Gorgo]]/[[Shoe]]		\|[[Gorgo]]/[[Shoe]]
	\|D		\|D
	\|~~10/9 using antidiatonic fifth, or~~ 9/8 using diatonic fifth		\|9/8 using diatonic fifth
	\|-		\|-
	\|8\37		\|8\37
	\|259.46		\|259.46
	\|[[15/13]]		\|[[15/13]]+
	\|[[Barbados]]		\|[[Barbados]]
	\|E♭		\|E♭
Line 96:		Line 96:
	\|11\37		\|11\37
	\|356.76		\|356.76
	\|[[11/9]], [[16/13]]		\|[[11/9]]+, [[16/13]]
	\|[[Beatles]]		\|[[Beatles]]
	\|B𝄪 = Ed		\|B𝄪 = Ed
Line 117:		Line 117:
	\|14\37		\|14\37
	\|454.05		\|454.05
	\|[[9/7]], [[13/10]]		\|[[9/7]]+, [[13/10]]
	\|[[Ammonite]]		\|[[Ammonite]]
	\|E		\|E
Line 236:		Line 236:
	\| 31\37		\| 31\37
	\|1005.41		\|1005.41
	\|16/9		\|16/9, 10/9
	\|Didacus		\|Didacus
	\|C♭		\|C♭
Line 243:		Line 243:
	\|32\37		\|32\37
	\|1037.84		\|1037.84
	\|16/9-, [[20/11\|9/5]]		\|16/9-, [[20/11\|9/5]]+
	\|Porcupine		\|Porcupine
	\|Aｷ = D𝄫		\|Aｷ = D𝄫
Line 264:		Line 264:
	\|35\37		\|35\37
	\|1135.14		\|1135.14
	\|[[27/14]]		\|[[27/14]]+
	\|Sycamore~~/Unicorn~~		\|Sycamore
	\|A♯		\|A♯
	\|		\|
Line 271:		Line 271:
	\|36\37		\|36\37
	\|1167.57		\|1167.57
	\|[[55/28]], [[55/27]]		\|[[55/28]], [[55/27]]+
	\|		\|
	\|B		\|B

Unque at 15:07, 23 January 2025

2025-01-23T15:07:44Z

← Older revision		Revision as of 15:07, 23 January 2025
Line 34:		Line 34:
	\|64.86		\|64.86
	\|[[28/27]]		\|[[28/27]]
	\|[[Sycamore]]/[[~~Octaphore#2.3.7 Unicorn\|~~Unicorn]]		\|[[Sycamore]]/[[Unicorn]]
	\|Bｷ = E𝄫		\|Bｷ = E𝄫
	\|Sycamore uses diatonic fifth, Unicorn uses antidiatonic fifth		\|Sycamore uses diatonic fifth, Unicorn uses antidiatonic fifth
Line 54:		Line 54:
	\|5\37		\|5\37
	\|162.16		\|162.16
	\|[[11/10\|10/9]], [[9/8]]-		\|[[11/10\|10/9]]+, [[9/8]]-
	\|[[Porcupine]]		\|[[Porcupine]]
	\|B♯		\|B♯
	\|9/8 using antidiatonic fifth		\|10/9 using diatonic fifth, or 9/8 using antidiatonic fifth
	\|-		\|-
	\|6\37		\|6\37
	\|194.59		\|194.59
	\|[[19/17]], 9/8		\|10/9, [[19/17]], 9/8
	\|[[Didacus]]		\|[[Didacus]]
	\|C♯		\|C♯
	\|9/8 using dual fifths		\|10/9 = 9/8 using dual fifths
	\|-		\|-
	\|7\37		\|7\37
	\|227.03		\|227.03
	\|9/8+, [[8/7]]		\|10/9-, 9/8+, [[8/7]]
	\|[[Gorgo]]/[[Shoe]]		\|[[Gorgo]]/[[Shoe]]
	\|D		\|D
	\|9/8 using diatonic fifth		\|10/9 using antidiatonic fifth, or 9/8 using diatonic fifth
	\|-		\|-
	\|8\37		\|8\37
Line 78:		Line 78:
	\|[[Barbados]]		\|[[Barbados]]
	\|E♭		\|E♭
	\|		\|Barbados utilizes split-3 shenanigans
	\|-		\|-
	\|9\37		\|9\37
	\|291.89		\|291.89
	\|[[13/11]], [[19/16]]		\|[[13/11]], [[19/16]]
	\|		\|[[847/845\|Cuthbert]]
	\|F♭		\|F♭
	\|		\|
Line 216:		Line 216:
	\|908.11		\|908.11
	\|[[32/19]], [[22/13]]		\|[[32/19]], [[22/13]]
	\|		\|Cuthbert
	\|G♯		\|G♯
	\|		\|
Line 251:		Line 251:
	\|1070.27		\|1070.27
	\|[[13/7]]		\|[[13/7]]
	\|		\|Cubical
	\|Bd		\|Bd
	\|		\|
Line 271:		Line 271:
	\|36\37		\|36\37
	\|1167.57		\|1167.57
	\|[[55/28]]		\|[[55/28]], [[55/27]]
	\|		\|
	\|B		\|B

Unque at 00:00, 17 January 2025

2025-01-17T00:00:43Z

Show changes

Unque: Created page with "'''Note: This page is currently under construction, and will be subject to major expansion in the near future. Come back soon!''' If it wasn't clear before, I definitely have..."

2025-01-16T16:15:13Z

Created page with "'''Note: This page is currently under construction, and will be subject to major expansion in the near future. Come back soon!''' If it wasn't clear before, I definitely have..."

New page

'''Note: This page is currently under construction, and will be subject to major expansion in the near future. Come back soon!'''

If it wasn't clear before, I definitely have a "type" when it comes to selecting tuning systems. [[37edo|37 Equal Divisions of the Octave]] is another 11-limit system with a sharp diatonic fifth and supports Porcupine temperament. Being 15 + 22, fans of [[15edo]] and [[22edo]] will likely be drawn to 37edo as a structural extension of the two; additionally, fans of split-prime systems may also be drawn to 37 due to its slightly ambiguous harmonic nature (see ''Intervals'').

As always, this page will be full of personal touches that may not reflect an objective truth or even wide consensus about how to use 37edo; I encourage learning musicians to experiment with different ideas and develop styles that best suit their own needs, rather than to take my word (or anyone else's for that matter) at face value as a great truth of music.

== Intervals ==
37edo is a rather interesting 19-limit system, but it does have some amount of harmonic ambiguity in the 3-limit. The two mappings for 3/2 are respectively a [[5L 2s|diatonic]] and [[2L 5s|antidiatonic]] generator; I will here use + to indicate JI interpretations that use the diatonic 3-limit, and - to indicate those that use the antidiatonic 3-limit.
{| class="wikitable"
|+
!Intervals
!Cents
!JI Intervals
!As a generator
!Notation
!Notes
|-
|0\37
|0.00
|1/1
|
|C
|
|-
|1\37
|32.43
|[[55/54]], [[56/55]]
|
|D♭
|
|-
|2\37
|64.86
|[[28/27]]
|[[Sycamore]]/[[Octaphore#2.3.7 Unicorn|Unicorn]]
|
|Sycamore uses diatonic fifth, Unicorn uses antidiatonic fifth
|-
|3\37
|97.30
|[[17/16]]
|[[Passion]]
|Cｷ
|
|-
|4\37
|129.73
|[[14/13]], [[16/15]]
|[[Negri]]
|
|Patent val 7 technically doesn't count as Negri, but it's the same structure
|-
|5\37
|162.16
|[[11/10|10/9]], [[9/8]]-
|[[Porcupine]]
|B♯
|9/8 using antidiatonic fifth
|-
|6\37
|194.59
|[[19/17]], 9/8
|[[Didacus]]
|C♯
|9/8 using dual fifths
|-
|7\37
|227.03
|9/8+, [[8/7]]
|[[Gorgo]]/[[Shoe]]
|D
|9/8 using diatonic fifth
|-
|8\37
|259.46
|[[15/13]]
|[[Barbados]]
|E♭
|
|-
|9\37
|291.89
|[[13/11]], [[19/16]]
|
|
|
|-
|10\37
|324.32
|[[77/64]]
|[[Orgone]]
|Dｷ
|Not a good 6/5, but 77/64 is rather complex; I just think of it as half of 16/11
|-
|11\37
|356.76
|[[11/9]], [[16/13]]
|[[Beatles]]
|
|Bisects the diatonic fifth
|-
|12\37
|389.19
|[[5/4]]
|[[Würschmidt|Wuerschmidt]]
|
|
|-
|13\37
|421.62
|[[14/11]]
|[[1573/1568|Lambeth]]
|D♯
|
|-
|14\37
|454.05
|[[9/7]], [[13/10]]
|[[Ammonite]]
|E
|
|-
|15\37
|486.49
|[[4/3]]+
|[[Ultrapyth]]
|F
|Diatonic fourth
|-
|16\37
|518.92
|4/3-
|[[Undecimation]]
|
|Antidiatonic fourth
|-
|17\37
|551.35
|[[11/8]]
|[[Emka]]
|Eｷ
|
|-
|18\37
|583.78
|[[7/5]]
|
|Fｷ
|
|-
|19\37
|616.22
|[[10/7]]
|
|
|
|-
|20\37
|648.65
|[[16/11]]
|Emka
|E♯
|
|-
|21\37
|681.08
|[[3/2]]-
|Undecimation
|F♯
|Antidiatonic fifth
|-
|22\37
|713.51
|3/2+
|Ultrapyth
|G
|Diatonic fifth
|-
|23\37
|745.95
|[[20/13]], [[14/9]]
|Ammonite
|
|
|-
|24\37
|778.38
|[[11/7]]
|Lambeth
|
|
|-
|25\37
|810.81
|[[8/5]]
|Wuerschmidt
|Gｷ
|
|-
|26\37
|843.24
|[[13/8]], [[18/11]]
|Beatles
|
|
|-
|27\37
|875.68
|[[128/77]]
|Orgone
|
|
|-
|28\37
|908.11
|[[32/19]], [[22/13]]
|
|G♯
|
|-
|29\37
|940.54
|[[26/15]]
|Barbados
|
|
|-
|30\37
|972.97
|[[7/4]], [[16/9]]+
|Gorgo/Shoe
|B♭
|16/9 using diatonic fourths
|-
|31\37
|1005.41
|16/9
|Didacus
|C♭
|16/9 using dual fourths
|-
|32\37
|1037.84
|16/9-, [[20/11|9/5]]
|Porcupine
|
|16/9 using antidiatonic fourths
|-
|33\37
|1070.27
|[[15/8]], 13/7
|Negri
|Bd
|
|-
|34\37
|1102.70
|[[32/17]]
|Passion
|Cd
|
|-
|35\37
|1135.14
|[[27/14]]
|Sycamore/Unicorn
|
|
|-
|36\37
|1167.57
|[[55/28]], [[108/55]]
|
|B
|
|-
|37\37
|1200.00
|[[2/1]]
|
|C
|
|}