34edo - Revision history

Vector at 03:03, 7 April 2026

2026-04-07T03:03:15Z

← Older revision		Revision as of 03:03, 7 April 2026
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	* [[Tetracot]] (splitting 3/2 into four 10/9s), shared with [[Equiheptatonic\|7edo]] and [[27edo]])		* [[Tetracot]] (splitting 3/2 into four 10/9s), shared with [[Equiheptatonic\|7edo]] and [[27edo]])
	* [[Gammic]] (setting 25/24 to a tenth of 3/2), shared with 103edo		* [[Gammic]] (setting 25/24 to a tenth of 3/2), shared with 103edo

			== Notation ==

			=== Notation ===
			34edo may use ups and downs notation. It may also use the diaschismic notation detailed on 22edo's page.

	== Multiples ==		== Multiples ==

Hotcrystal0: fix in 306edo

2026-03-02T18:58:12Z

fix in 306edo

← Older revision		Revision as of 18:58, 2 March 2026
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	=== 306edo ===		=== 306edo ===
	~~306edo~~ is a convergent to 3/2, and as such has a nearly perfectly accurate 3/2 representation. Its step is the difference between 34edo's 3/2 and the near-just one. It also has a 7/4 accurate to within 0.2 cents.		306 is the decominator of a continued fraction convergent to log<sub>2</sub>(3/2), and as such 306edo has a nearly perfectly accurate 3/2 representation. Its step is the difference between 34edo's 3/2 and the near-just one. It also has a 7/4 accurate to within 0.2 cents.

	{{Harmonics in ED\|306\|31\|0}}		{{Harmonics in ED\|306\|31\|0}}

Hotcrystal0 at 13:54, 2 March 2026

2026-03-02T13:54:31Z

← Older revision		Revision as of 13:54, 2 March 2026
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	The new 7/4 supports [[Sensamagic]], doubling 9/7 to reach 5/3, and 2.5.7 [[Didacus]], splitting 5/4 into two wholetones that stack 5 times to reach 7/4. Additionally, the new 11/8 makes 14/11 equal to 81/64, supporting [[Pentacircle]] (and various gentle/neogothic temperaments).		The new 7/4 supports [[Sensamagic]], doubling 9/7 to reach 5/3, and 2.5.7 [[Didacus]], splitting 5/4 into two wholetones that stack 5 times to reach 7/4. Additionally, the new 11/8 makes 14/11 equal to 81/64, supporting [[Pentacircle]] (and various gentle/neogothic temperaments).

			{{Harmonics in ED\|68\|31\|0}}

	=== 306edo ===		=== 306edo ===
	306edo is a convergent to 3/2, and as such has a nearly perfectly accurate 3/2 representation. Its step is the difference between 34edo's 3/2 and the near-just one. It also has a 7/4 accurate to within 0.2 cents.		306edo is a convergent to 3/2, and as such has a nearly perfectly accurate 3/2 representation. Its step is the difference between 34edo's 3/2 and the near-just one. It also has a 7/4 accurate to within 0.2 cents.

			{{Harmonics in ED\|306\|31\|0}}

	=== 612edo ===		=== 612edo ===
	612edo doubles 306edo, adding the perfect fifth from [[12edo]] and a nearly perfect [[5/4]]. Its main utility is as a fine-grained interval size measurement system for the 11-limit, wherein 3/2 is 358 steps and 5/4 is 197 steps, as its step size is almost exactly a (consistently represented) [[schisma]]. The 12edo perfect fifth is 357 steps, 34edo's is 360 steps. Thus, 34edo is about twice as inaccurate as 12edo in its tuning of 3/2.		612edo doubles 306edo, adding the perfect fifth from [[12edo]] and a nearly perfect [[5/4]]. Its main utility is as a fine-grained interval size measurement system for the 11-limit, wherein 3/2 is 358 steps and 5/4 is 197 steps, as its step size is almost exactly a (consistently represented) [[schisma]]. The 12edo perfect fifth is 357 steps, 34edo's is 360 steps. Thus, 34edo is about twice as inaccurate as 12edo in its tuning of 3/2.

			{{Harmonics in ED\|612\|31\|0}}

	{{Navbox EDO}}		{{Navbox EDO}}

	{{Cat\|Edos}}		{{Cat\|Edos}}

Overthink: /* Edostep interpretations */ add two

2026-03-02T02:30:56Z

Edostep interpretations: add two

← Older revision		Revision as of 02:30, 2 March 2026
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	34edo's edostep, the ''sextula'', has the following interpretations in the 2.3.5.13.17 subgroup:		34edo's edostep, the ''sextula'', has the following interpretations in the 2.3.5.13.17 subgroup:

	* 81/80, the difference between the fifth-generated major third and the classical major third		* [[81/80]], the difference between the fifth-generated major third and the classical major third
	* 128/125, the difference between the 5-limit enharmonic intervals		* [[128/125]], the difference between the 5-limit enharmonic intervals
			* [[40/39]], the difference between [[13/10]] and [[4/3]] and between [[15/13]] and [[9/8]]; also between [[6/5]] and [[16/13]], among others
			* [[65/64]], the difference between [[8/5]] and [[13/8]]

	''TODO: add to list''		''TODO: add to list''

Inthar: /* Additional regular temperaments */

2026-02-26T01:35:44Z

Additional regular temperaments

← Older revision		Revision as of 01:35, 26 February 2026
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	=== Additional regular temperaments ===		=== Additional regular temperaments ===
	Alongside Kleismic (shared with [[15edo]] and [[19edo]]), and Diaschismic (shared with [[12edo]]), 34edo supports the following temperaments:		Alongside [[Kleismic]] (shared with [[15edo]] and [[19edo]]), and [[Diaschismic]] (shared with [[12edo]]), 34edo supports the following temperaments:

	* Tetracot (splitting 3/2 into four 10/9s), shared with [[Equiheptatonic\|7edo]] and [[27edo]])		* [[Tetracot]] (splitting 3/2 into four 10/9s), shared with [[Equiheptatonic\|7edo]] and [[27edo]])
	* Gammic (setting 25/24 to a tenth of 3/2), shared with 103edo		* [[Gammic]] (setting 25/24 to a tenth of 3/2), shared with 103edo

	== Multiples ==		== Multiples ==

Vector at 03:44, 22 February 2026

2026-02-22T03:44:18Z

← Older revision		Revision as of 03:44, 22 February 2026
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	=== 612edo ===		=== 612edo ===
	612edo doubles 306edo, adding the perfect fifth from [[12edo]] and a nearly perfect [[5/4]]. Its main utility is as a fine-grained interval size measurement system for the 11-limit, wherein 3/2 is 358 steps and 5/4 is 197 steps, as its step size is almost exactly a (consistently represented) [[schisma]]. The 12edo perfect fifth is 357 steps, 34edo's is 360 steps. Thus, 34edo is about twice as inaccurate as 12edo in its tuning of 3/2.{{Cat\|Edos}}		612edo doubles 306edo, adding the perfect fifth from [[12edo]] and a nearly perfect [[5/4]]. Its main utility is as a fine-grained interval size measurement system for the 11-limit, wherein 3/2 is 358 steps and 5/4 is 197 steps, as its step size is almost exactly a (consistently represented) [[schisma]]. The 12edo perfect fifth is 357 steps, 34edo's is 360 steps. Thus, 34edo is about twice as inaccurate as 12edo in its tuning of 3/2.

			{{Navbox EDO}}

			{{Cat\|Edos}}

Vector at 03:42, 22 February 2026

2026-02-22T03:42:40Z

← Older revision		Revision as of 03:42, 22 February 2026
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	The new 7/4 supports [[Sensamagic]], doubling 9/7 to reach 5/3, and 2.5.7 [[Didacus]], splitting 5/4 into two wholetones that stack 5 times to reach 7/4. Additionally, the new 11/8 makes 14/11 equal to 81/64, supporting [[Pentacircle]] (and various gentle/neogothic temperaments).		The new 7/4 supports [[Sensamagic]], doubling 9/7 to reach 5/3, and 2.5.7 [[Didacus]], splitting 5/4 into two wholetones that stack 5 times to reach 7/4. Additionally, the new 11/8 makes 14/11 equal to 81/64, supporting [[Pentacircle]] (and various gentle/neogothic temperaments).

	{{Cat\|Edos}}		=== 306edo ===
			306edo is a convergent to 3/2, and as such has a nearly perfectly accurate 3/2 representation. Its step is the difference between 34edo's 3/2 and the near-just one. It also has a 7/4 accurate to within 0.2 cents.

			=== 612edo ===
			612edo doubles 306edo, adding the perfect fifth from [[12edo]] and a nearly perfect [[5/4]]. Its main utility is as a fine-grained interval size measurement system for the 11-limit, wherein 3/2 is 358 steps and 5/4 is 197 steps, as its step size is almost exactly a (consistently represented) [[schisma]]. The 12edo perfect fifth is 357 steps, 34edo's is 360 steps. Thus, 34edo is about twice as inaccurate as 12edo in its tuning of 3/2.{{Cat\|Edos}}

Inthar: /* 68edo */

2026-02-19T02:39:01Z

68edo

← Older revision		Revision as of 02:39, 19 February 2026
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	* Gammic (setting 25/24 to a tenth of 3/2), shared with 103edo		* Gammic (setting 25/24 to a tenth of 3/2), shared with 103edo

	== 68edo ==		== Multiples ==
			=== 68edo ===
	68edo is the double of 34edo, and improves its mapping of 7 much as 34edo improves 17edo's mapping of 5. This improves the mappings of 11 and 19 as well, making 68edo function as a general 19-limit system.		68edo is the double of 34edo, and improves its mapping of 7 much as 34edo improves 17edo's mapping of 5. This improves the mappings of 11 and 19 as well, making 68edo function as a general 19-limit system.

Lériendil at 01:08, 10 February 2026

2026-02-10T01:08:18Z

← Older revision		Revision as of 01:08, 10 February 2026
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	The new 7/4 supports [[Sensamagic]], doubling 9/7 to reach 5/3, and 2.5.7 [[Didacus]], splitting 5/4 into two wholetones that stack 5 times to reach 7/4. Additionally, the new 11/8 makes 14/11 equal to 81/64, supporting [[Pentacircle]] (and various gentle/neogothic temperaments).		The new 7/4 supports [[Sensamagic]], doubling 9/7 to reach 5/3, and 2.5.7 [[Didacus]], splitting 5/4 into two wholetones that stack 5 times to reach 7/4. Additionally, the new 11/8 makes 14/11 equal to 81/64, supporting [[Pentacircle]] (and various gentle/neogothic temperaments).

			{{Cat\|Edos}}

Inthar: /* Scales */

2026-02-08T16:20:59Z

Scales

← Older revision		Revision as of 16:20, 8 February 2026
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	34edo contains 17edo's diatonic scale and alongside it a zarlino scale. Other scales it includes are:		34edo contains 17edo's diatonic scale and alongside it a zarlino scale. Other scales it includes are:

			* the blackdye scale, with steps 1-5-3-5-1-5-3-5-1-5 (sLmLsLmLsL)
	* Diaschismic[12], with steps 3-3-3-3-3-2-3-3-3-3-3-2 (LLLLLsLLLLLs)		* Diaschismic[12], with steps 3-3-3-3-3-2-3-3-3-3-3-2 (LLLLLsLLLLLs)
	** the Delkian scale, a MODMOS of diaschismic[12] with steps 3-3-3-2-3-3-3-3-3-3-2-3 (LLLsLLLLLLsL)		** the Delkian scale, a MODMOS of diaschismic[12] with steps 3-3-3-2-3-3-3-3-3-3-2-3 (LLLsLLLLLLsL)