Equable heptatonic - Revision history

ArrowHead294 at 13:47, 5 March 2025

2025-03-05T13:47:41Z

CompactStar at 08:47, 22 July 2023

2023-07-22T08:47:09Z

← Older revision		Revision as of 08:47, 22 July 2023
Line 1:		Line 1:
	In the theory of [[Margo Schulter]], '''equable heptatonic''' is a category of intervals which occupy regions intermediate between [[11/10]] and [[10/9]], or [[9/5]] and [[20/11]]. There are two heartland regions given below, with approximate cents ranges from Schulter's article [http://www.bestii.com/%7Emschulter/IntervalSpectrumRegions.txt Regions of the Interval Spectrum]:		In the theory of [[Margo Schulter]], '''equable heptatonic''' is a category of intervals which occupy regions intermediate between [[11/10]] and [[10/9]], or [[9/5]] and [[20/11]]. There are two heartland regions given below, with approximate cents ranges from Schulter's article [http://www.bestii.com/%7Emschulter/IntervalSpectrumRegions.txt Regions of the Interval Spectrum]:

	* Neut2–Maj2 – intermediate between [[11/10]] and [[10/9]] – 160¢–182¢ (submajor second)		* Neut2–Maj2 – intermediate between [[11/10]] and [[10/9]] – 160¢–182¢ (~submajor second)
	* min7–Neut7 – intermediate between [[9/5]] and [[20/11]] – 1018¢–1040¢ (supraminor seventh)		* min7–Neut7 – intermediate between [[9/5]] and [[20/11]] – 1018¢–1040¢ (~supraminor seventh)

	Equable heptatonic intervals are well-represented in [[7edo]] at 171.429¢ (1＼7) and 1028.571¢ (6＼7). They also appear in [[27edo]], [[34edo]] and [[41edo]]. As they fall in ambiguous zones between simpler categories, they are inevitably xenharmonic.		Equable heptatonic intervals are well-represented in [[7edo]] at 171.429¢ (1＼7) and 1028.571¢ (6＼7). They also appear in [[27edo]], [[34edo]] and [[41edo]]. As they fall in ambiguous zones between simpler categories, they are inevitably xenharmonic.

CompactStar at 08:46, 22 July 2023

2023-07-22T08:46:56Z

← Older revision		Revision as of 08:46, 22 July 2023
Line 1:		Line 1:
	In the theory of [[Margo Schulter]], '''equable heptatonic''' is a category of intervals which occupy regions intermediate between [[11/10]] and [[10/9]], or [[9/5]] and [[20/11]]. There are two heartland regions given below, with approximate cents ranges from Schulter's article [http://www.bestii.com/%7Emschulter/IntervalSpectrumRegions.txt Regions of the Interval Spectrum]:		In the theory of [[Margo Schulter]], '''equable heptatonic''' is a category of intervals which occupy regions intermediate between [[11/10]] and [[10/9]], or [[9/5]] and [[20/11]]. There are two heartland regions given below, with approximate cents ranges from Schulter's article [http://www.bestii.com/%7Emschulter/IntervalSpectrumRegions.txt Regions of the Interval Spectrum]:

	* Neut2–Maj2 – intermediate between [[11/10]] and [[10/9]] – 160¢–182¢		* Neut2–Maj2 – intermediate between [[11/10]] and [[10/9]] – 160¢–182¢ (submajor second)
	* min7–Neut7 – intermediate between [[9/5]] and [[20/11]] – 1018¢–1040¢		* min7–Neut7 – intermediate between [[9/5]] and [[20/11]] – 1018¢–1040¢ (supraminor seventh)

	Equable heptatonic intervals are well-represented in [[7edo]] at 171.429¢ (1＼7) and 1028.571¢ (6＼7). They also appear in [[27edo]], [[34edo]] and [[41edo]]. As they fall in ambiguous zones between simpler categories, they are inevitably xenharmonic.		Equable heptatonic intervals are well-represented in [[7edo]] at 171.429¢ (1＼7) and 1028.571¢ (6＼7). They also appear in [[27edo]], [[34edo]] and [[41edo]]. As they fall in ambiguous zones between simpler categories, they are inevitably xenharmonic.

Xenllium at 04:30, 22 July 2023

2023-07-22T04:30:32Z

← Older revision		Revision as of 04:30, 22 July 2023
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	\| [[67/37]]		\| [[67/37]]
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	\| [[29/16]]		\| [[29/16]]
	\| 1029.577		\| 1029.577
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	\|-		\|-
	\| [[78/43]]		\| [[78/43]]
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	\| [[91/50]]		\| [[91/50]]
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	\| [[51/28]]		\| [[51/28]]
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	\|-		\|-
	\| 45＼[[52edo\|52]]		\| 45＼[[52edo\|52]]

Xenllium at 04:23, 22 July 2023

2023-07-22T04:23:33Z

← Older revision		Revision as of 04:23, 22 July 2023
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	Some equable heptatonic intervals in all two ranges, both just and tempered, are listed below.		Some equable heptatonic intervals in all two ranges, both just and tempered, are listed below.

	=== Neut2–Maj2 ===		=== Neut2–Maj2 (submajor second) ===
	{\| class="wikitable center-1 right-2"		{\| class="wikitable center-1 right-2"
	! Interval		! Interval
Line 244:		Line 244:
	\|}		\|}

	=== min7–Neut7 ===		=== min7–Neut7 (supraminor seventh) ===
	{\| class="wikitable center-1 right-2"		{\| class="wikitable center-1 right-2"
	! Interval		! Interval
Line 416:		Line 416:
	* [[Gallery of just intervals]]		* [[Gallery of just intervals]]

	[[Category:Equable heptatonic]]		[[Category:Equable heptatonic\| ]]
	[[Category:Intervals]]		[[Category:Intervals]]
	[[Category:Interval naming]]		[[Category:Interval naming]]

Xenllium: Created page with "In the theory of Margo Schulter, '''equable heptatonic''' is a category of intervals which occupy regions intermediate between 11/10 and 10/9, or 9/5 and 20/..."

2023-07-22T04:12:05Z

Created page with "In the theory of Margo Schulter, '''equable heptatonic''' is a category of intervals which occupy regions intermediate between 11/10 and 10/9, or 9/5 and 20/..."

New page

In the theory of [[Margo Schulter]], '''equable heptatonic''' is a category of intervals which occupy regions intermediate between [[11/10]] and [[10/9]], or [[9/5]] and [[20/11]]. There are two heartland regions given below, with approximate cents ranges from Schulter's article [http://www.bestii.com/%7Emschulter/IntervalSpectrumRegions.txt Regions of the Interval Spectrum]:

* Neut2–Maj2 – intermediate between [[11/10]] and [[10/9]] – 160¢–182¢
* min7–Neut7 – intermediate between [[9/5]] and [[20/11]] – 1018¢–1040¢

Equable heptatonic intervals are well-represented in [[7edo]] at 171.429¢ (1＼7) and 1028.571¢ (6＼7). They also appear in [[27edo]], [[34edo]] and [[41edo]]. As they fall in ambiguous zones between simpler categories, they are inevitably xenharmonic.

== Examples ==
Some equable heptatonic intervals in all two ranges, both just and tempered, are listed below.

=== Neut2–Maj2 ===
{| class="wikitable center-1 right-2"
! Interval
! Cents Value
! Prime Limit (if applicable)
|-
| [[34/31]]
| 159.920
| 31
|-
| 2＼[[15edo|15]]
| 160.000
| -
|-
| [[79/72]]
| 160.627
| 79
|-
| [[45/41]]
| 161.161
| 41
|-
| 7＼[[52edo|52]]
| 161.538
| -
|-
| [[101/92]]
| 161.579
| 101
|-
| [[56/51]]
| 161.915
| 17
|-
| 5＼[[37edo|37]]
| 162.162
| -
|-
| [[67/61]]
| 162.422
| 67
|-
| [[78/71]]
| 162.786
| 71
|-
| [[89/81]]
| 163.060
| 89
|-
| [[100/91]]
| 163.274
| 13
|-
| 3＼[[22edo|22]]
| 163.636
| -
|-
| 7＼[[51edo|51]]
| 164.706
| -
|-
| [[11/10]]
| 165.004
| 11
|-
| 4＼[[29edo|29]]
| 165.517
| -
|-
| 5＼[[36edo|36]]
| 166.667
| -
|-
| [[98/89]]
| 166.772
| 89
|-
| [[87/79]]
| 166.995
| 79
|-
| [[76/69]]
| 167.284
| 23
|-
| 6＼[[43edo|43]]
| 167.442
| -
|-
| [[65/59]]
| 167.670
| 59
|-
| 7＼[[50edo|50]]
| 168.000
| -
|-
| [[54/49]]
| 168.213
| 7
|-
| [[97/88]]
| 168.577
| 97
|-
| [[43/39]]
| 169.035
| 43
|-
| [[75/68]]
| 169.627
| 17
|-
| [[32/29]]
| 170.423
| 29
|-
| [[85/77]]
| 171.125
| 17
|-
| 1＼[[7edo|7]]
| 171.429
| -
|-
| [[53/48]]
| 171.550
| 53
|-
| [[74/67]]
| 172.037
| 67
|-
| [[95/86]]
| 172.309
| 43
|-
| [[21/19]]
| 173.268
| 19
|-
| [[94/85]]
| 174.237
| 47
|-
| [[73/66]]
| 174.517
| 77
|-
| 7＼[[48edo|48]]
| 175.000
| -
|-
| [[52/47]]
| 175.021
| 47
|-
| [[83/75]]
| 175.465
| 83
|-
| 6＼[[41edo|41]]
| 175.610
| -
|-
| [[31/28]]
| 176.210
| 31
|-
| 5＼[[34edo|34]]
| 176.471
| -
|-
| [[72/65]]
| 177.069
| 13
|-
| [[41/37]]
| 177.718
| 41
|-
| 4＼[[27edo|27]]
| 177.778
| -
|-
| [[92/83]]
| 178.227
| 83
|-
| [[51/46]]
| 178.636
| 23
|-
| 7＼[[47edo|47]]
| 178.723
| -
|-
| [[61/55]]
| 179.253
| 61
|-
| [[71/64]]
| 179.697
| 71
|-
| 3＼[[20edo|20]]
| 180.000
| -
|-
| [[81/73]]
| 180.031
| 73
|-
| [[91/82]]
| 180.291
| 41
|-
| 5＼[[33edo|33]]
| 181.818
| -
|-
| [[10/9]]
| 182.404
| 5
|-
| 7＼[[46edo|46]]
| 182.609
| -
|-
| 2＼[[13edo|13]]
| 184.615
| -
|}

=== min7–Neut7 ===
{| class="wikitable center-1 right-2"
! Interval
! Cents Value
! Prime Limit (if applicable)
|-
| 11＼[[13edo|13]]
| 1015.385
| -
|-
| 39＼[[46edo|46]]
| 1017.391
| -
|-
| [[9/5]]
| 1017.596
| 5
|-
| 28＼[[33edo|33]]
| 1018.182
| -
|-
| 17＼[[20edo|20]]
| 1020.000
| -
|-
| 40＼[[47edo|47]]
| 1021.277
| -
|-
| [[92/51]]
| 1021.364
| 23
|-
| [[83/46]]
| 1021.773
| 83
|-
| 23＼[[27edo|27]]
| 1022.222
| -
|-
| [[74/41]]
| 1022.282
| 41
|-
| [[65/36]]
| 1022.931
| 13
|-
| 29＼[[34edo|34]]
| 1023.529
| -
|-
| [[56/31]]
| 1023.790
| 31
|-
| 35＼[[41edo|41]]
| 1024.390
| -
|-
| [[47/26]]
| 1024.979
| 47
|-
| 41＼[[48edo|48]]
| 1025.000
| -
|-
| [[85/47]]
| 1025.763
| 47
|-
| [[38/21]]
| 1026.732
|
|-
| [[67/37]]
| 1027.963
| 67
|-
| 6＼[[7edo|7]]
| 1028.571
| -
|-
| [[29/16]]
| 1029.577
| 19
|-
| [[78/43]]
| 1030.965
| 43
|-
| [[49/27]]
| 1031.787
| 7
|-
| 43＼[[50edo|50]]
| 1032.000
| -
|-
| [[69/38]]
| 1032.716
| 23
|-
| 37＼[[43edo|43]]
| 1032.558
| -
|-
| [[89/49]]
| 1033.228
| 89
|-
| 31＼[[36edo|36]]
| 1033.333
| -
|-
| 25＼[[29edo|29]]
| 1034.483
| -
|-
| [[20/11]]
| 1034.996
| 11
|-
| 44＼[[51edo|51]]
| 1035.294
| -
|-
| 19＼[[22edo|22]]
| 1036.364
| -
|-
| [[91/50]]
| 1036.726
|
|-
| [[71/39]]
| 1037.214
| 71
|-
| 32＼[[37edo|37]]
| 1037.838
| -
|-
| [[51/28]]
| 1038.085
|
|-
| 45＼[[52edo|52]]
| 1038.462
| -
|-
| [[82/45]]
| 1038.839
| 41
|-
| 13＼[[15edo|15]]
| 1040.000
| -
|-
| [[31/17]]
| 1040.080
| 31
|}

== See also ==
* [[Interseptimal interval|Interseptimal regions]]
* [[Gentle region]]
* [[Gallery of just intervals]]

[[Category:Equable heptatonic]]
[[Category:Intervals]]
[[Category:Interval naming]]