User:Overthink/The 7-limit in 53edo - Revision history

Overthink: deprecate page

2025-12-25T09:27:35Z

deprecate page

← Older revision		Revision as of 09:27, 25 December 2025
Line 1:		Line 1:
			; Development of this page is paused indefinitely. 171edo is much more interesting.
	In 53edo, the [[7-limit]] is well-approximated, and especially the 5- and 3-limits. On this page, we will analyze the approximations and structures of 53edo in the 7-limit.		In 53edo, the [[7-limit]] is well-approximated, and especially the 5- and 3-limits. On this page, we will analyze the approximations and structures of 53edo in the 7-limit.
	{\| class="mw-collapsible wikitable"		{\| class="mw-collapsible wikitable"

Overthink: cleaned up and expanded hemifamity table

2025-10-29T21:49:06Z

cleaned up and expanded hemifamity table

← Older revision		Revision as of 21:49, 29 October 2025
Line 242:		Line 242:
	\|}		\|}
	{\| class="wikitable"		{\| class="wikitable"
	\|+~~Interval~~ table (middle)		\|+Hemifamity interval table (middle)
	\|		\|
			\|256/175
	\|		\|
	\|		\|
Line 249:		Line 250:
	\|		\|
	\|		\|
	\|		\|256/245,
	\|256/245, 729/700		729/700
	\|384/245		\|384/245
	\|		\|
Line 256:		Line 257:
	\|		\|
	\|		\|
	\|		\|512/343
	\|		\|
	\|-		\|-
Line 263:		Line 264:
	\|27/25		\|27/25
	\|81/50		\|81/50
	\|128/105, 243/200		\|128/105,
			243/200
	\|64/35		\|64/35
	\|48/35		\|48/35
	\|36/35		\|36/35
	\|54/35		\|54/35
	\|81/70		\|81/70,
	\|243/140, 256/147		\|243/140,
			256/147
	\|64/49		\|64/49
	\|96/49		\|96/49
Line 282:		Line 285:
	\|9/5		\|9/5
	\|27/20		\|27/20
	\|64/63, 81/80		\|64/63,
			81/80
	\|32/21		\|32/21
	\|8/7		\|8/7
Line 291:		Line 295:
	\|243/224		\|243/224
	\|-		\|-
	\|28/15		\|28/15,
	\|7/5		4096/2187
	\|21/20		\|7/5,
	\|63/40, 128/81		1024/729
			\|21/20,
			256/243
			\|63/40,
			128/81
	\|32/27		\|32/27
	\|16/9		\|16/9
Line 302:		Line 310:
	\|9/8		\|9/8
	\|27/16		\|27/16
	\|81/64~~, 80/63~~		\|80/63,
	\|40/21		81/64
	\|10/7		\|40/21,
	\|15/14		243/128
			\|10/7,
			729/512
			\|15/14,
			2187/2048
	\|-		\|-
	\|448/243		\|448/243
Line 314:		Line 326:
	\|7/4		\|7/4
	\|21/16		\|21/16
	\|63/32, 160/81		\|63/32,
			160/81
	\|40/27		\|40/27
	\|10/9		\|10/9
Line 327:		Line 340:
	\|49/48		\|49/48
	\|49/32		\|49/32
	\|147/128, 280/243		\|147/128,
			280/243
	\|140/81		\|140/81
	\|35/27		\|35/27
Line 333:		Line 347:
	\|35/24		\|35/24
	\|35/32		\|35/32
	\|105/64, 400/243		\|105/64,
	\|315/256, 100/81		400/243
			\|315/256,
			100/81
	\|50/27		\|50/27
	\|25/18		\|25/18
	\|25/24		\|25/24
	\|-		\|-
	\|		\|343/192
	\|		\|343/256,
	\|		980/729
	\|		\|1029/1024,
	\|		245/243
	\|		\|245/162
	\|		\|245/216
	\|245/128, 1400/729		\|245/144
	\|		\|245/192
	\|		\|245/128,
	\|		1400/729
	\|		\|735/512,
	\|		350/243
	\|		\|175/162
	\|		\|175/108
			\|175/144
			\|175/96
			\|175/128
			\|250/243,
			525/512
	\|}		\|}
	{\| class="wikitable"		{\| class="wikitable"

Overthink: expanded hemifamity table a bit

2025-10-29T05:11:15Z

expanded hemifamity table a bit

← Older revision		Revision as of 05:11, 29 October 2025
Line 269:		Line 269:
	\|54/35		\|54/35
	\|81/70		\|81/70
	\|		\|243/140, 256/147
	\|		\|64/49
	\|		\|96/49
	\|		\|72/49
	\|		\|54/49
	\|-		\|-
	\|135/128		\|135/128

Overthink: Expanded page

2025-10-29T05:06:50Z

Expanded page

Show changes

Overthink: Cleaned up collapsible wikitable

2025-10-29T04:27:35Z

Cleaned up collapsible wikitable

← Older revision		Revision as of 04:27, 29 October 2025
Line 1:		Line 1:
	In 53edo, the [[7-limit]] is well-approximated, and especially the 5- and 3-limits. On this page, we will analyze the approximations and structures of 53edo in the 7-limit.		In 53edo, the [[7-limit]] is well-approximated, and especially the 5- and 3-limits. On this page, we will analyze the approximations and structures of 53edo in the 7-limit.
	{\| class="~~wikitable~~ mw-collapsible"		{\| class="mw-collapsible wikitable"
	\|+ Intervals of 53edo		\|+ style="font-size: 105%; white-space: nowrap;" \| Intervals of 53edo
			\|-
	! Steps		! Steps
	! Cents		! Cents

Overthink: added more to table

2025-10-29T04:06:02Z

added more to table

← Older revision		Revision as of 04:06, 29 October 2025
Line 12:		Line 12:
	\| 1		\| 1
	\| 22.642		\| 22.642
	\| 81/80, 64/63, 50/49~~, 531441/524288~~		\| 531441/524288, 81/80, 64/63, 50/49
	\|-		\|-
	\| 2		\| 2
	\| 45.283		\| 45.283
	\| 49/48, 128/125~~, ...~~		\| 36/35, 49/48, 128/125
	\|-		\|-
	\| 3		\| 3
Line 24:		Line 24:
	\| 4		\| 4
	\| 90.566		\| 90.566
	\| 256/243, 21/20		\| 256/243, 135/128, 21/20
	\|-		\|-
	\| 5		\| 5
Line 32:		Line 32:
	\| 6		\| 6
	\| 135.849		\| 135.849
	\| 27/25,		\| 27/25
	\|-		\|-
	\| 7		\| 7
	\| 158.491		\| 158.491
	\|		\| 35/32,
	\|-		\|-
	\| 8		\| 8
Line 52:		Line 52:
	\| 11		\| 11
	\| 249.057		\| 249.057
	\|		\| 81/70
	\|-		\|-
	\| 12		\| 12
Line 68:		Line 68:
	\| 15		\| 15
	\| 339.623		\| 339.623
	\|		\| 105/64, 243/200
	\|-		\|-
	\| 16		\| 16
	\| 362.264		\| 362.264
	\|		\| 100/81, 315/256
	\|-		\|-
	\| 17		\| 17
Line 80:		Line 80:
	\| 18		\| 18
	\| 407.547		\| 407.547
	\| 81/64		\| 81/64,
	\|-		\|-
	\| 19		\| 19
Line 88:		Line 88:
	\| 20		\| 20
	\| 452.830		\| 452.830
	\| 1/1		\| 64/49, 35/27
	\|-		\|-
	\| 21		\| 21
	\| 475.472		\| 475.472
	\| 1/1		\| 21/16
	\|-		\|-
	\| 22		\| 22
Line 100:		Line 100:
	\| 23		\| 23
	\| 520.755		\| 520.755
	\| 1/1		\| 27/20
	\|-		\|-
	\| 24		\| 24
	\| 543.396		\| 543.396
	\| 1/1		\| 2187/1600, 48/35
	\|-		\|-
	\| 25		\| 25
Line 112:		Line 112:
	\| 26		\| 26
	\| 588.679		\| 588.679
	\| 1/1		\| 729/512, 7/5, 45/32
	\|-		\|-
	\| 27		\| 27
	\| 611.321		\| 611.321
	\| 1/1		\| 1024/729, 10/7, 64/45
	\|-		\|-
	\| 28		\| 28
Line 221:		Line 221:
	\| 1200.000		\| 1200.000
	\| 2/1		\| 2/1
			\|}

Overthink: Added some intervals to table

2025-10-29T01:51:08Z

Added some intervals to table

← Older revision		Revision as of 01:51, 29 October 2025
Line 1:		Line 1:
	In 53edo, the [[7-limit]] is well-approximated, and especially the 5- and 3-limits. On this page, we will analyze the approximations and structures of 53edo in the 7-limit.		In 53edo, the [[7-limit]] is well-approximated, and especially the 5- and 3-limits. On this page, we will analyze the approximations and structures of 53edo in the 7-limit.
	{\| class="wikitable mw-collapsible ~~mw-collapsed~~"		{\| class="wikitable mw-collapsible"
	\|+ Intervals of 53edo		\|+ Intervals of 53edo
	! Steps		! Steps
Line 12:		Line 12:
	\| 1		\| 1
	\| 22.642		\| 22.642
	\| 1/1		\| 81/80, 64/63, 50/49, 531441/524288
	\|-		\|-
	\| 2		\| 2
	\| 45.283		\| 45.283
	\| 1/1		\| 49/48, 128/125, ...
	\|-		\|-
	\| 3		\| 3
	\| 67.925		\| 67.925
	\| 1/1		\| 28/27, 25/24
	\|-		\|-
	\| 4		\| 4
	\| 90.566		\| 90.566
	\| 1/1		\| 256/243, 21/20
	\|-		\|-
	\| 5		\| 5
	\| 113.208		\| 113.208
	\| 1/1		\| 16/15, 15/14, 2187/2048
	\|-		\|-
	\| 6		\| 6
	\| 135.849		\| 135.849
	\| 1/1		\| 27/25,
	\|-		\|-
	\| 7		\| 7
	\| 158.491		\| 158.491
	\| ~~1/1~~		\|
	\|-		\|-
	\| 8		\| 8
	\| 181.132		\| 181.132
	\| 1/1		\| 10/9
	\|-		\|-
	\| 9		\| 9
	\| 203.774		\| 203.774
	\| 1/1		\| 9/8
	\|-		\|-
	\| 10		\| 10
	\| 226.415		\| 226.415
	\| 1/1		\| 8/7
	\|-		\|-
	\| 11		\| 11
	\| 249.057		\| 249.057
	\| ~~1/1~~		\|
	\|-		\|-
	\| 12		\| 12
	\| 271.698		\| 271.698
	\| 1/1		\| 7/6, 75/64
	\|-		\|-
	\| 13		\| 13
	\| 294.340		\| 294.340
	\| 1/1		\| 32/27
	\|-		\|-
	\| 14		\| 14
	\| 316.981		\| 316.981
	\| 1/1		\| 6/5
	\|-		\|-
	\| 15		\| 15
	\| 339.623		\| 339.623
	\| ~~1/1~~		\|
	\|-		\|-
	\| 16		\| 16
	\| 362.264		\| 362.264
	\| ~~1/1~~		\|
	\|-		\|-
	\| 17		\| 17
	\| 384.906		\| 384.906
	\| 1/1		\| 5/4
	\|-		\|-
	\| 18		\| 18
	\| 407.547		\| 407.547
	\| 1/1		\| 81/64
	\|-		\|-
	\| 19		\| 19
	\| 430.189		\| 430.189
	\| 1/1		\| 9/7, 32/25
	\|-		\|-
	\| 20		\| 20

Overthink: Created page with incomplete table

2025-10-29T01:45:06Z

Created page with incomplete table

New page

In 53edo, the [[7-limit]] is well-approximated, and especially the 5- and 3-limits. On this page, we will analyze the approximations and structures of 53edo in the 7-limit.
{| class="wikitable mw-collapsible mw-collapsed"
|+ Intervals of 53edo
! Steps
! Cents
! Approximate ratios
|-
| 0
| 0.000
| 1/1
|-
| 1
| 22.642
| 1/1
|-
| 2
| 45.283
| 1/1
|-
| 3
| 67.925
| 1/1
|-
| 4
| 90.566
| 1/1
|-
| 5
| 113.208
| 1/1
|-
| 6
| 135.849
| 1/1
|-
| 7
| 158.491
| 1/1
|-
| 8
| 181.132
| 1/1
|-
| 9
| 203.774
| 1/1
|-
| 10
| 226.415
| 1/1
|-
| 11
| 249.057
| 1/1
|-
| 12
| 271.698
| 1/1
|-
| 13
| 294.340
| 1/1
|-
| 14
| 316.981
| 1/1
|-
| 15
| 339.623
| 1/1
|-
| 16
| 362.264
| 1/1
|-
| 17
| 384.906
| 1/1
|-
| 18
| 407.547
| 1/1
|-
| 19
| 430.189
| 1/1
|-
| 20
| 452.830
| 1/1
|-
| 21
| 475.472
| 1/1
|-
| 22
| 498.113
| 4/3
|-
| 23
| 520.755
| 1/1
|-
| 24
| 543.396
| 1/1
|-
| 25
| 566.038
| 1/1
|-
| 26
| 588.679
| 1/1
|-
| 27
| 611.321
| 1/1
|-
| 28
| 633.962
| 1/1
|-
| 29
| 656.604
| 1/1
|-
| 30
| 679.245
| 1/1
|-
| 31
| 701.887
| 3/2
|-
| 32
| 724.528
| 1/1
|-
| 33
| 747.170
| 1/1
|-
| 34
| 769.811
| 1/1
|-
| 35
| 792.453
| 1/1
|-
| 36
| 815.094
| 1/1
|-
| 37
| 837.736
| 1/1
|-
| 38
| 860.377
| 1/1
|-
| 39
| 883.019
| 1/1
|-
| 40
| 905.660
| 1/1
|-
| 41
| 928.302
| 1/1
|-
| 42
| 950.943
| 1/1
|-
| 43
| 973.585
| 1/1
|-
| 44
| 996.226
| 1/1
|-
| 45
| 1018.868
| 1/1
|-
| 46
| 1041.509
| 1/1
|-
| 47
| 1064.151
| 1/1
|-
| 48
| 1086.792
| 1/1
|-
| 49
| 1109.434
| 1/1
|-
| 50
| 1132.075
| 1/1
|-
| 51
| 1154.717
| 1/1
|-
| 52
| 1177.358
| 1/1
|-
| 53
| 1200.000
| 2/1