9-odd-limit - Revision history

Overthink: /* Table of 9-odd-limit intervals */ description

2026-06-21T18:11:55Z

Table of 9-odd-limit intervals: description

← Older revision		Revision as of 18:11, 21 June 2026
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	==Table of 9-odd-limit intervals==		==Table of 9-odd-limit intervals==
			Reduced to an octave, the intervals of the 9-odd-limit are:

	{\| class="wikitable"		{\| class="wikitable"

Overthink: /* Intervals */ header

2026-06-21T18:11:18Z

Intervals: header

← Older revision		Revision as of 18:11, 21 June 2026
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	The first edo to be consistent to the 9-odd-limit is [[5edo]], giving a rough outline for harmony with its relatively accurate 3/2 and 7/4 of 720 and 960 cents respectively, while very sharply mapping 5/4 to 480 cents. The first edo to be distinctly consistent in this limit is [[41edo]].		The first edo to be consistent to the 9-odd-limit is [[5edo]], giving a rough outline for harmony with its relatively accurate 3/2 and 7/4 of 720 and 960 cents respectively, while very sharply mapping 5/4 to 480 cents. The first edo to be distinctly consistent in this limit is [[41edo]].

	== Intervals ==		== Intervals of the 9-odd-limit ==
	Here are the intervals in the 9-odd-limit which are not part of any lower odd-limit. Note that the intervals of the 9-odd-limit are all contained within the [[7-limit\|7-prime-limit]], as 9 factors as 3 × 3.		Here are the intervals in the 9-odd-limit which are not part of any lower odd-limit. Note that the intervals of the 9-odd-limit are all contained within the [[7-limit\|7-prime-limit]], as 9 factors as 3 × 3.

Overthink: start intervals section

2026-06-21T18:10:58Z

start intervals section

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 |}
-==Approximation by edos==
+== Approximation by edos ==
-The first edo to be consistent to the 9-odd-limit is [[5edo]], giving a rough outline for harmony with its relatively accurate 3/2 and 7/4 of 720 and 960 cents respectively, while very sharply mapping 5/4 to 480 cents. The first edo to be distinctly consistent in this limit is [[41edo]].
+In terms of [[chthonic harmony]], it can be considered a subminor latus, as the fourth complement of [[6/5]].

Hotcrystal0: Edo approximation and stuff

2026-06-01T21:20:05Z

Edo approximation and stuff

← Older revision		Revision as of 21:20, 1 June 2026
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	{{Odd-limit navigation}}		{{Odd-limit navigation}}
	The '''9-[[odd-limit]]''' consists of all intervals where the largest allowable odd factor in the numerator and denominator is 9. Reduced to an octave, these are:		The '''9-[[odd-limit]]''' consists of all intervals where the largest allowable odd factor in the numerator and denominator is 9. Reduced to an octave, these are:

			==Table of 9-odd-limit intervals==

	{\| class="wikitable"		{\| class="wikitable"
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	\| Octave		\| Octave
	\|}		\|}

			==Approximation by edos==

			The first edo to be consistent to the 9-odd-limit is [[5edo]], giving a rough outline for harmony with its relatively accurate 3/2 and 7/4 of 720 and 960 cents respectively, while very sharply mapping 5/4 to 480 cents. The first edo to be distinctly consistent in this limit is [[41edo]].

Overthink: add navigation

2026-04-11T03:33:41Z

add navigation

← Older revision		Revision as of 03:33, 11 April 2026
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	{{WIP}}		{{WIP}}
			{{Odd-limit navigation}}
	The '''9-[[odd-limit]]''' consists of all intervals where the largest allowable odd factor in the numerator and denominator is 9. Reduced to an octave, these are:		The '''9-[[odd-limit]]''' consists of all intervals where the largest allowable odd factor in the numerator and denominator is 9. Reduced to an octave, these are:

Overthink: start page

2026-04-11T03:03:44Z

start page

New page

{{WIP}}
The '''9-[[odd-limit]]''' consists of all intervals where the largest allowable odd factor in the numerator and denominator is 9. Reduced to an octave, these are:

{| class="wikitable"
! Interval
! Cents
! Name
|-
| 1/1
| 0.0
| Unison
|-
| '''10/9'''
| '''182.4'''
| '''Minor whole tone,<br>Ptolemaic major 2nd'''
|-
| '''9/8'''
| '''203.9'''
| '''Major whole tone,<br>Pythagorean major 2nd'''
|-
| 8/7
| 231.2
| Septimal major 2nd
|-
| 7/6
| 266.9
| Septimal minor 3rd
|-
| 6/5
| 315.6
| Classical minor 3rd
|-
| 5/4
| 386.4
| Classical major 3rd
|-
| '''9/7'''
| '''435.1'''
| '''Septimal major 3rd'''
|-
| 4/3
| 498.0
| Perfect 4th
|-
| 7/5
| 582.5
| Lesser septimal tritone
|-
| 10/7
| 617.5
| Greater septimal tritone
|-
| 3/2
| 702.0
| Perfect 5th
|-
| '''14/9'''
| '''764.9'''
| '''Septimal minor 6th'''
|-
| 8/5
| 813.6
| Classical minor 6th
|-
| 5/3
| 884.4
| Classical major 6th
|-
| 12/7
| 933.1
| Septimal major 6th
|-
| 7/4
| 968.8
| Septimal minor 7th
|-
| '''16/9'''
| '''996.1'''
| '''Pythagoran minor 7th'''
|-
| '''9/5'''
| '''1017.6'''
| '''Classical minor 7th'''
|-
| 2/1
| 1200.0
| Octave
|}