Logharmonic series - Revision history

ArrowHead294 at 13:29, 29 September 2025

2025-09-29T13:29:53Z

← Older revision		Revision as of 13:29, 29 September 2025
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	* [[Xenharmonic series]]		* [[Xenharmonic series]]
	* [[Logarithmic intonation]]		* [[Logarithmic intonation]]
	* ~~[https://en.wikipedia.org/wiki/Robert_Schneider~~#Non-~~Pythagorean_scale Robert_Schneider~~ - ~~Non-Pythagorean_scale~~ on Wikipedia]		* {{W\|Robert Schneider#Non-Pythagorean scale\|Robert Schneider's non-Pythagorean scale on Wikipedia}}

	[[Category:Otonality and utonality]]		[[Category:Otonality and utonality]]

ArrowHead294 at 13:29, 29 September 2025

2025-09-29T13:29:06Z

Show changes

Overthink: added "mathematical interest"

2025-09-29T06:27:44Z

added "mathematical interest"

← Older revision		Revision as of 06:27, 29 September 2025
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			{{Mathematical interest}}
	== Introduction ==		== Introduction ==

CompactStar at 10:23, 28 January 2024

2024-01-28T10:23:29Z

← Older revision		Revision as of 10:23, 28 January 2024
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	If a natural number is chosen as <span><math>b</math></span>, the resulting series will be a superset of the harmonic series, inserting extra pitches. For example, the 2-logharmonic series inserts an extra step in between the fundamental and the 2nd harmonic, so that it takes <span><math>2^1 = 2</math></span> steps to reach the 2nd harmonic instead of one. Then it inserts 3 extra steps in between the 2nd harmonic and 3rd harmonic so that it takes <span><math>2^2 = 4</math></span> steps instead of one. Then 7 extra steps before the 4th harmonic so it takes <span><math>2^3 = 8</math></span> steps instead of one.		If a natural number is chosen as <span><math>b</math></span>, the resulting series will be a superset of the harmonic series, inserting extra pitches. For example, the 2-logharmonic series inserts an extra step in between the fundamental and the 2nd harmonic, so that it takes <span><math>2^1 = 2</math></span> steps to reach the 2nd harmonic instead of one. Then it inserts 3 extra steps in between the 2nd harmonic and 3rd harmonic so that it takes <span><math>2^2 = 4</math></span> steps instead of one. Then 7 extra steps before the 4th harmonic so it takes <span><math>2^3 = 8</math></span> steps instead of one.

	[[Logarithmic intonation]] is an analogue of [[just intonation]] which uses the logharmonic series rather than the [[harmonic series]].		[[Logarithmic intonation]] is an analogue of [[just intonation]] which uses the base-e logharmonic series rather than the [[harmonic series]].

	== Frequencies ==		== Frequencies ==

CompactStar at 10:23, 28 January 2024

2024-01-28T10:23:07Z

← Older revision		Revision as of 10:23, 28 January 2024
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	If a natural number is chosen as <span><math>b</math></span>, the resulting series will be a superset of the harmonic series, inserting extra pitches. For example, the 2-logharmonic series inserts an extra step in between the fundamental and the 2nd harmonic, so that it takes <span><math>2^1 = 2</math></span> steps to reach the 2nd harmonic instead of one. Then it inserts 3 extra steps in between the 2nd harmonic and 3rd harmonic so that it takes <span><math>2^2 = 4</math></span> steps instead of one. Then 7 extra steps before the 4th harmonic so it takes <span><math>2^3 = 8</math></span> steps instead of one.		If a natural number is chosen as <span><math>b</math></span>, the resulting series will be a superset of the harmonic series, inserting extra pitches. For example, the 2-logharmonic series inserts an extra step in between the fundamental and the 2nd harmonic, so that it takes <span><math>2^1 = 2</math></span> steps to reach the 2nd harmonic instead of one. Then it inserts 3 extra steps in between the 2nd harmonic and 3rd harmonic so that it takes <span><math>2^2 = 4</math></span> steps instead of one. Then 7 extra steps before the 4th harmonic so it takes <span><math>2^3 = 8</math></span> steps instead of one.

			[[Logarithmic intonation]] is an analogue of [[just intonation]] which uses the logharmonic series rather than the [[harmonic series]].

	== Frequencies ==		== Frequencies ==

CompactStar at 03:54, 3 November 2023

2023-11-03T03:54:40Z

← Older revision		Revision as of 03:54, 3 November 2023
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	[[Powharmonic series]]: another type of non-arithmetic harmonotonic tuning.		[[Powharmonic series]]: another type of non-arithmetic harmonotonic tuning.

	[[~~Xenharmonic_series~~]]		[[Xenharmonic series]]

			[[Logarithmic intonation]]

	[https://en.wikipedia.org/wiki/Robert_Schneider#Non-Pythagorean_scale Robert_Schneider - Non-Pythagorean_scale on Wikipedia]		[https://en.wikipedia.org/wiki/Robert_Schneider#Non-Pythagorean_scale Robert_Schneider - Non-Pythagorean_scale on Wikipedia]

BudjarnLambeth: Added to category "xenharmonic series"

2023-04-26T05:17:22Z

Added to category "xenharmonic series"

← Older revision		Revision as of 05:17, 26 April 2023
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	[[Category:Subharmonic]]		[[Category:Subharmonic]]
	[[Category:Subharmonic series‏‎]]		[[Category:Subharmonic series‏‎]]
			[[Category:Xenharmonic series]]

Fredg999: Categories

2021-08-30T04:01:35Z

Fredg999: /* Frequencies */ Fixed typo

2021-08-29T03:21:40Z

Frequencies: Fixed typo

← Older revision		Revision as of 03:21, 29 August 2021
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	\| colspan="6" rowspan="7" \|		\| colspan="6" rowspan="7" \|
	\|-		\|-
	\|1		\|10
	\|log<sub>2</sub>10		\|log<sub>2</sub>10
	\|3.321928095		\|3.321928095

Cmloegcmluin: sublogharmonic series note

2021-03-25T23:13:57Z

sublogharmonic series note

← Older revision		Revision as of 23:13, 25 March 2021
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	\|}		\|}
	An analogous [https://en.xen.wiki/w/Powharmonic_series#Emulatory_edharmonic_series emulatory edharmonic series] exists.		An analogous [https://en.xen.wiki/w/Powharmonic_series#Emulatory_edharmonic_series emulatory edharmonic series] exists.

			== Sublogharmonic series ==

			Just like the subharmonic series can be found by using one over the frequency of any step of the harmonic series, an equivalent sublogharmonic series may be found by using one over the frequency of any step of a logharmonic series.

	== Sound of the logharmonic series as a timbre ==		== Sound of the logharmonic series as a timbre ==

← Older revision		Revision as of 04:01, 30 August 2021
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	[https://en.wikipedia.org/wiki/Robert_Schneider#Non-Pythagorean_scale Robert_Schneider - Non-Pythagorean_scale on Wikipedia]		[https://en.wikipedia.org/wiki/Robert_Schneider#Non-Pythagorean_scale Robert_Schneider - Non-Pythagorean_scale on Wikipedia]

	[[Category:~~Overtone]]~~		[[Category:Otonality and utonality]]
	~~[[Category:Overtone‏‎ series~~]]
	[[Category:Otonality]]		[[Category:Otonality]]
	[[Category:Harmonic]]		[[Category:Harmonic]]
	[[Category:Harmonic series‏‎]]		[[Category:Harmonic series‏‎]]

	~~[[Category:Undertone]]~~
	~~[[Category:Undertone series]]~~
	[[Category:Utonality]]		[[Category:Utonality]]
	[[Category:Subharmonic]]		[[Category:Subharmonic]]
	[[Category:Subharmonic series‏‎]]		[[Category:Subharmonic series‏‎]]

	~~[[Category:Otonality and utonality]]~~