13ed8/3 - Revision history

BudjarnLambeth: /* Scales */

2025-10-05T09:23:24Z

Scales

← Older revision		Revision as of 09:23, 5 October 2025
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	== Scales ==		== Scales ==
	; Described by [[Budjarn Lambeth]]		; Described by [[Budjarn Lambeth]]
			''Tested by ear in [[Scale Workshop]] using the "jublag", "ugal", and "silver" aperiodic waveforms, and the "percussive (medium)" preset.''
	* 5-tone [[pelog]]-like scale: 1 1 3 1 3		* 5-tone [[pelog]]-like scale: 1 1 3 1 3
	* 7-tone [[pelog]]-like scale: 1 1 2 1 1 2 1		* 7-tone [[pelog]]-like scale: 1 1 2 1 1 2 1

2025-10-05T08:07:11Z

Properties

← Older revision		Revision as of 08:07, 5 October 2025
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	* The sharp [[perfect fourth]] of 522{{c}} is very dissonant in a triad with either fifth, but with the major 6th instead it makes a very pretty chord		* The sharp [[perfect fourth]] of 522{{c}} is very dissonant in a triad with either fifth, but with the major 6th instead it makes a very pretty chord

	13ed8/3 can be thought of as a 2.12.15.7.11.13.19 [[subgroup]] tuning. It has under 22% [[relative error]] (under 29{{c}} abs. error) on each of those [[harmonic]]s.		13ed8/3 can be thought of as a 2.12.15.7.11.13.19 [[subgroup]] tuning. It has under 22% [[relative error]] (under 29{{c}} abs. error) on each of those [[harmonic]]s, which is comparable to [[12edo]]'s approximation of the full [[7-limit]].

	== Harmonics ==		== Harmonics ==

2025-10-05T08:05:54Z

Properties

← Older revision		Revision as of 08:05, 5 October 2025
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	== Properties ==		== Properties ==
	~~13ed8/3 can be thought of as a 2.12.15.7.11.13.19 [[subgroup]] tuning.~~

	Gutierrez noted that:		Gutierrez noted that:
	* 13ed8/3 is like [[9edo]] with the octave compressed by 24 [[cents]]		* 13ed8/3 is like [[9edo]] with the octave compressed by 24 [[cents]]
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	* Its 1437{{c}} major 9th interval is about an octave above the [[8/7]] septimal whole tone (so it approximates [[16/7]])		* Its 1437{{c}} major 9th interval is about an octave above the [[8/7]] septimal whole tone (so it approximates [[16/7]])
	* The sharp [[perfect fourth]] of 522{{c}} is very dissonant in a triad with either fifth, but with the major 6th instead it makes a very pretty chord		* The sharp [[perfect fourth]] of 522{{c}} is very dissonant in a triad with either fifth, but with the major 6th instead it makes a very pretty chord

			13ed8/3 can be thought of as a 2.12.15.7.11.13.19 [[subgroup]] tuning. It has under 22% [[relative error]] (under 29{{c}} abs. error) on each of those [[harmonic]]s.

	== Harmonics ==		== Harmonics ==

2025-10-05T08:03:52Z

← Older revision		Revision as of 08:03, 5 October 2025
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	== Properties ==		== Properties ==
			13ed8/3 can be thought of as a 2.12.15.7.11.13.19 [[subgroup]] tuning.

	Gutierrez noted that:		Gutierrez noted that:
	* 13ed8/3 is like [[9edo]] with the octave compressed by 24 [[cents]]		* 13ed8/3 is like [[9edo]] with the octave compressed by 24 [[cents]]

2025-10-05T07:44:57Z

Related tunings

← Older revision		Revision as of 07:44, 5 October 2025
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	== Related tunings ==		== Related tunings ==
	13ed8/3 is a bit like [[9edo]] but with extreme [[octave shrinking]] (the octave is about 24 [[cents]] flat). As a [[23-limit]] equal [[temperament]] it could be considered a tuning for 9bdefhi (''see [[wart]]s'').		13ed8/3 is a bit like [[9edo]] but with extreme [[octave shrinking]] (the octave is about 24 [[cents]] flat). As a [[23-limit]] equal [[temperament]], 13ed8/3 could be considered a tuning for 9bdefhi (''see [[wart]]s'').

	13ed8/3 is quite close to [[23zpi]] (''see [[ZPI]]'') but 13ed8/3 has a much better [[2/1]] than 23zpi, at the expense of most other [[prime]]s being a little worse than 23zpi.		13ed8/3 is quite close to [[23zpi]] (''see [[ZPI]]'') but 13ed8/3 has a much better [[2/1]] than 23zpi, at the expense of most other [[prime]]s being a little worse than 23zpi.

2025-10-05T07:44:32Z

Related tunings

← Older revision		Revision as of 07:44, 5 October 2025
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	== Related tunings ==		== Related tunings ==
	13ed8/3 is a bit like [[9edo]] but with extreme [[octave shrinking]] (the octave is about 24 [[cents]] flat). As a [[23-limit]] equal [[temperament]] it could be considered a tuning for 9bdefhi (see [[wart]]s).		13ed8/3 is a bit like [[9edo]] but with extreme [[octave shrinking]] (the octave is about 24 [[cents]] flat). As a [[23-limit]] equal [[temperament]] it could be considered a tuning for 9bdefhi (''see [[wart]]s'').

	13ed8/3 is quite close to [[~~zpi\|~~23zpi]] but 13ed8/3 has a much better [[2/1]] than 23zpi, at the expense of most other [[prime]]s being a little worse than 23zpi.		13ed8/3 is quite close to [[23zpi]] (''see [[ZPI]]'') but 13ed8/3 has a much better [[2/1]] than 23zpi, at the expense of most other [[prime]]s being a little worse than 23zpi.

			13ed8/3 is identical (octave less than 1{{c}} different) to ''every second step of'' [[62zpi]] (''see [[ZPI]]'').

	== Scales ==		== Scales ==

2025-10-05T07:42:33Z

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 == Intervals ==
 {{Interval table}}
 == Scales ==
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 * 5-tone [[pelog]]-like scale: 1 1 3 1 3
 * 7-tone [[pelog]]-like scale: 1 1 2 1 1 2 1

2025-10-05T07:37:09Z

← Older revision		Revision as of 07:37, 5 October 2025
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	== Related tunings ==		== Related tunings ==
	13ed8/3 is a bit like [[9edo]] but with extreme [[octave shrinking]] (the octave is about 24 [[cents]] flat). As an equal temperament it could be considered a tuning for 9bdefhi (see [[wart]]s).		13ed8/3 is a bit like [[9edo]] but with extreme [[octave shrinking]] (the octave is about 24 [[cents]] flat). As a [[23-limit]] equal [[temperament]] it could be considered a tuning for 9bdefhi (see [[wart]]s).

	13ed8/3 is quite close to [[zpi\|23zpi]] but 13ed8/3 has a much better [[2/1]] than 23zpi, at the expense of most other [[prime]]s being a little worse than 23zpi.		13ed8/3 is quite close to [[zpi\|23zpi]] but 13ed8/3 has a much better [[2/1]] than 23zpi, at the expense of most other [[prime]]s being a little worse than 23zpi.

2025-10-05T07:35:32Z

Related tunings

← Older revision		Revision as of 07:35, 5 October 2025
Line 38:		Line 38:

	== Related tunings ==		== Related tunings ==
	13ed8/3 is a bit like [[9edo]] but with extreme [[octave shrinking]] (the octave is about 24 [[cents]] flat).		13ed8/3 is a bit like [[9edo]] but with extreme [[octave shrinking]] (the octave is about 24 [[cents]] flat). As an equal temperament it could be considered a tuning for 9bdefhi (see [[wart]]s).

	13ed8/3 is quite close to [[zpi\|23zpi]] but 13ed8/3 has a much better [[2/1]] than 23zpi, at the expense of most other [[prime]]s being a little worse than 23zpi.		13ed8/3 is quite close to [[zpi\|23zpi]] but 13ed8/3 has a much better [[2/1]] than 23zpi, at the expense of most other [[prime]]s being a little worse than 23zpi.

2025-10-05T07:31:07Z

Related tunings

← Older revision		Revision as of 07:31, 5 October 2025
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	== Related tunings ==		== Related tunings ==
	13ed8/3 is like [[zpi\|23zpi]] but 13ed8/3 has a much better [[2/1]] than 23zpi, at the expense of most other [[prime]]s being a little worse than 23zpi.		13ed8/3 is a bit like [[9edo]] but with extreme [[octave shrinking]] (the octave is about 24 [[cents]] flat).

			13ed8/3 is quite close to [[zpi\|23zpi]] but 13ed8/3 has a much better [[2/1]] than 23zpi, at the expense of most other [[prime]]s being a little worse than 23zpi.