Silver third - Revision history

Overthink: add an interesting property

2026-02-27T05:20:41Z

add an interesting property

← Older revision		Revision as of 05:20, 27 February 2026
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	The '''silver third''' is the octave-reduced second [[Metallic_harmonic_series\|metallic mean]], and is either a wide minor third or a narrow supraminor one. It differs from the first metallic mean ([[acoustic phi]]) by an interval that can act as a [[flattone]] fifth.		The '''silver third''' is the octave-reduced second [[Metallic_harmonic_series\|metallic mean]], and is either a wide minor third or a narrow supraminor one. It differs from the first metallic mean ([[acoustic phi]]) by an interval that can act as a [[flattone]] fifth. This is not to be confused with [[argent tuning]], which uses the ''logarithmic'' silver ratio.

			An interesting property of this interval is that a tetrad can be formed with the root, the silver third, the [[3/2\|perfect fifth]], and a supermajor sixth 600{{C}} above the silver third (925.864{{C}}), such that the frequency difference between the sixth and the fifth is the same as that between the root. This means this tetrad has a [[DR]] signature of +1 +? +1, a property shared with tetrads like [[4:5:6:7]] (sometimes called the ''major tetrad'') and [[6:7:9:10]] (sometimes called the ''subminor tetrad''). This tetrad has this DR property, while also allowing tritone substitution due to the third and sixth being separated by 600{{C}}.

			== Temperaments ==
	It can be used as a generator for many temperaments using a sharpened [[6/5]], such as [[keemic]], [[orgone]] or [[doublewide]], and is closely approximated by [[11edo\|3\11]].		It can be used as a generator for many temperaments using a sharpened [[6/5]], such as [[keemic]], [[orgone]] or [[doublewide]], and is closely approximated by [[11edo\|3\11]].

	~~This is not to be confused with [[argent tuning]], which uses the ''logarithmic'' silver ratio.~~

Jerdle at 08:55, 15 October 2025

2025-10-15T08:55:14Z

← Older revision		Revision as of 08:55, 15 October 2025
Line 6:		Line 6:
	}}		}}

	The '''silver third''' is the octave-reduced second [[Metallic_harmonic_series\|metallic mean]], and is either a wide minor third or a narrow supraminor one. It differs from the first metallic mean ([[acoustic phi]]) by an interval that can act as a [[~~meantone~~]] fifth.		The '''silver third''' is the octave-reduced second [[Metallic_harmonic_series\|metallic mean]], and is either a wide minor third or a narrow supraminor one. It differs from the first metallic mean ([[acoustic phi]]) by an interval that can act as a [[flattone]] fifth.

	It can be used as a generator for many temperaments using a sharpened [[6/5]], such as [[keemic]], [[orgone]] or [[doublewide]], and is closely approximated by [[11edo\|3\11]].		It can be used as a generator for many temperaments using a sharpened [[6/5]], such as [[keemic]], [[orgone]] or [[doublewide]], and is closely approximated by [[11edo\|3\11]].

	This is not to be confused with [[argent tuning]], which uses the ''logarithmic'' silver ratio.		This is not to be confused with [[argent tuning]], which uses the ''logarithmic'' silver ratio.

Jerdle at 08:53, 15 October 2025

2025-10-15T08:53:41Z

← Older revision		Revision as of 08:53, 15 October 2025
Line 8:		Line 8:
	The '''silver third''' is the octave-reduced second [[Metallic_harmonic_series\|metallic mean]], and is either a wide minor third or a narrow supraminor one. It differs from the first metallic mean ([[acoustic phi]]) by an interval that can act as a [[meantone]] fifth.		The '''silver third''' is the octave-reduced second [[Metallic_harmonic_series\|metallic mean]], and is either a wide minor third or a narrow supraminor one. It differs from the first metallic mean ([[acoustic phi]]) by an interval that can act as a [[meantone]] fifth.

	It can be used as a generator for many temperaments using a sharpened [[6/5]], such as [[keemic]] or [[doublewide]], and is closely approximated by [[11edo\|3\11]].		It can be used as a generator for many temperaments using a sharpened [[6/5]], such as [[keemic]], [[orgone]] or [[doublewide]], and is closely approximated by [[11edo\|3\11]].

	This is not to be confused with [[argent tuning]], which uses the ''logarithmic'' silver ratio.		This is not to be confused with [[argent tuning]], which uses the ''logarithmic'' silver ratio.

Jerdle: Created page

2025-10-14T21:31:09Z

Created page

New page

{{Mathematical interest}}
{{Infobox Interval
| Ratio = \sigma = \frac{ 1 + \sqrt{2} }{2}
| Cents = 325.8639637963343
| Name = silver third
}}

The '''silver third''' is the octave-reduced second [[Metallic_harmonic_series|metallic mean]], and is either a wide minor third or a narrow supraminor one. It differs from the first metallic mean ([[acoustic phi]]) by an interval that can act as a [[meantone]] fifth.

It can be used as a generator for many temperaments using a sharpened [[6/5]], such as [[keemic]] or [[doublewide]], and is closely approximated by [[11edo|3\11]].

This is not to be confused with [[argent tuning]], which uses the ''logarithmic'' silver ratio.