161/128 - Revision history

FloraC: Mean -> arithmetic mean

2023-03-02T16:46:13Z

Mean -> arithmetic mean

← Older revision		Revision as of 16:46, 2 March 2023
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	{{Infobox Interval		{{Infobox Interval
	\| Name = ~~just/Pythagorean~~ major third ~~meantone~~, octave-reduced 161th harmonic		\| Name = arithmetic mean major third, octave-reduced 161th harmonic
	\| Color name = 23oz4		\| Color name = 23oz4
	}}		}}

	In [[just intonation]], '''161/128''' is the frequency ratio between the 161th and the 128th harmonic.		In [[just intonation]], '''161/128''', the '''arithmetic mean major third''' is the frequency ratio between the 161th and the 128th harmonic. It is the [[arithmetic mean]] between the [[5/4\|just major third]] and the [[81/64\|Pythagorean major third]]: (5/4 + 81/64)/2 = 161/128.

	It is the mean between the [[5/4\|just major third]] and the [[81/64\|Pythagorean major third]]: (5/4 + 81/64)/2 = 161/128.

	It can also be calculated from the [[81/80\|syntonic comma]]: ((81/80 - 1)/2 + 1)⋅(5/4) = 161/128.		It can also be calculated from the [[81/80\|syntonic comma]]: ((81/80 - 1)/2 + 1)⋅(5/4) = 161/128.

Plumtree: Normalising usage of Infobox Interval

2022-10-25T14:16:03Z

Normalising usage of Infobox Interval

← Older revision		Revision as of 14:16, 25 October 2022
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	{{Infobox Interval		{{Infobox Interval
	~~\| Ratio = 161/128~~		\| Name = just/Pythagorean major third meantone, octave-reduced 161th harmonic
	~~\| Monzo = -7 0 0 1 0 0 0 0 1~~
	~~\| Cents = 397.10025~~
	\| Name = just/Pythagorean major third meantone, ~~<br>~~octave-reduced 161th harmonic
	~~\| FJS name = M3<sup>7,23</sup>~~
	\| Color name = 23oz4		\| Color name = 23oz4
	}}		}}
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	It can also be calculated from the [[81/80\|syntonic comma]]: ((81/80 - 1)/2 + 1)⋅(5/4) = 161/128.		It can also be calculated from the [[81/80\|syntonic comma]]: ((81/80 - 1)/2 + 1)⋅(5/4) = 161/128.

	~~[[Category:23-limit]]~~
	[[Category:Third]]		[[Category:Third]]
	[[Category:Major third]]		[[Category:Major third]]

FloraC: +categories

2022-10-21T11:50:34Z

+categories

← Older revision		Revision as of 11:50, 21 October 2022
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	\| Ratio = 161/128		\| Ratio = 161/128
	\| Monzo = -7 0 0 1 0 0 0 0 1		\| Monzo = -7 0 0 1 0 0 0 0 1
	\| Cents = 397.~~100253738~~		\| Cents = 397.10025
	\| Name = just/Pythagorean major third meantone, octave-reduced 161th harmonic		\| Name = just/Pythagorean major third meantone, <br>octave-reduced 161th harmonic
			\| FJS name = M3<sup>7,23</sup>
	\| Color name = 23oz4		\| Color name = 23oz4
	}}		}}

	In ~~Just Intonation~~, 161/128 is the frequency ratio between the 161th and the 128th harmonic.		In [[just intonation]], '''161/128''' is the frequency ratio between the 161th and the 128th harmonic.

	It is the mean between the [[5/4\|just major third]] and the [[81/64\|Pythagorean major third]]: (5/4 + 81/64)/2 = 161/128.		It is the mean between the [[5/4\|just major third]] and the [[81/64\|Pythagorean major third]]: (5/4 + 81/64)/2 = 161/128.
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	It can also be calculated from the [[81/80\|syntonic comma]]: ((81/80 - 1)/2 + 1)⋅(5/4) = 161/128.		It can also be calculated from the [[81/80\|syntonic comma]]: ((81/80 - 1)/2 + 1)⋅(5/4) = 161/128.

			[[Category:23-limit]]
	~~Its factorization into primes is 2<sup>-7</sup>⋅7⋅23; its FJS name is M3<sup>7,23</sup>.~~		[[Category:Third]]
			[[Category:Major third]]

Contribution at 13:41, 12 June 2020

2020-06-12T13:41:39Z

← Older revision		Revision as of 13:41, 12 June 2020
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	\| Monzo = -7 0 0 1 0 0 0 0 1		\| Monzo = -7 0 0 1 0 0 0 0 1
	\| Cents = 397.100253738		\| Cents = 397.100253738
	\| Name = just/~~pythagorean~~ major third meantone, octave-reduced 161th harmonic		\| Name = just/Pythagorean major third meantone, octave-reduced 161th harmonic
	\| Color name = 23oz4		\| Color name = 23oz4
	}}		}}

Contribution at 13:32, 12 June 2020

2020-06-12T13:32:28Z

← Older revision		Revision as of 13:32, 12 June 2020
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	\| Monzo = -7 0 0 1 0 0 0 0 1		\| Monzo = -7 0 0 1 0 0 0 0 1
	\| Cents = 397.100253738		\| Cents = 397.100253738
	\| Name = ~~161th harmonic octave-reduced,~~ just/pythagorean major third meantone		\| Name = just/pythagorean major third meantone, octave-reduced 161th harmonic
	\| Color name = 23oz4		\| Color name = 23oz4
	}}		}}

Contribution at 10:19, 12 June 2020

2020-06-12T10:19:40Z

← Older revision		Revision as of 10:19, 12 June 2020
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	\| Monzo = -7 0 0 1 0 0 0 0 1		\| Monzo = -7 0 0 1 0 0 0 0 1
	\| Cents = 397.100253738		\| Cents = 397.100253738
	\| Name = 161th harmonic octave-reduced ; just/pythagorean major third meantone		\| Name = 161th harmonic octave-reduced, just/pythagorean major third meantone
	\| Color name = 23oz4		\| Color name = 23oz4
	}}		}}

Contribution at 10:19, 12 June 2020

2020-06-12T10:19:05Z

← Older revision		Revision as of 10:19, 12 June 2020
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	Its factorization into primes is 2<sup>-7</sup>⋅7⋅23 ; its FJS name is M3<sup>7,23</sup>.		Its factorization into primes is 2<sup>-7</sup>⋅7⋅23; its FJS name is M3<sup>7,23</sup>.

Contribution at 10:17, 12 June 2020

2020-06-12T10:17:00Z

← Older revision		Revision as of 10:17, 12 June 2020
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	In Just Intonation, 161/128 is the frequency ratio between the 161th and the 128th harmonic.		In Just Intonation, 161/128 is the frequency ratio between the 161th and the 128th harmonic.

	It is the mean between the [[5/4\|just major third]] and the [[81/64\|Pythagorean major third]] : (5/4 + 81/64)/2 = 161/128.		It is the mean between the [[5/4\|just major third]] and the [[81/64\|Pythagorean major third]]: (5/4 + 81/64)/2 = 161/128.

	It can also be calculated from the [[81/80\|syntonic comma]] : ((81/80 - 1)/2 + 1)⋅(5/4) = 161/128.		It can also be calculated from the [[81/80\|syntonic comma]]: ((81/80 - 1)/2 + 1)⋅(5/4) = 161/128.


	Its factorization into primes is 2<sup>-7</sup>⋅7⋅23 ; its FJS name is M3<sup>7,23</sup>.		Its factorization into primes is 2<sup>-7</sup>⋅7⋅23 ; its FJS name is M3<sup>7,23</sup>.

Contribution: Created page with "{{Infobox Interval | Ratio = 161/128 | Monzo = -7 0 0 1 0 0 0 0 1 | Cents = 397.100253738 | Name = 161th harmonic octave-reduced ; just/pythagorean major third meantone | Colo..."

2020-06-12T10:16:30Z

Created page with "{{Infobox Interval | Ratio = 161/128 | Monzo = -7 0 0 1 0 0 0 0 1 | Cents = 397.100253738 | Name = 161th harmonic octave-reduced ; just/pythagorean major third meantone | Colo..."

New page

{{Infobox Interval
| Ratio = 161/128
| Monzo = -7 0 0 1 0 0 0 0 1
| Cents = 397.100253738
| Name = 161th harmonic octave-reduced ; just/pythagorean major third meantone
| Color name = 23oz4
}}

In Just Intonation, 161/128 is the frequency ratio between the 161th and the 128th harmonic.

It is the mean between the [[5/4|just major third]] and the [[81/64|Pythagorean major third]] : (5/4 + 81/64)/2 = 161/128.

It can also be calculated from the [[81/80|syntonic comma]] : ((81/80 - 1)/2 + 1)⋅(5/4) = 161/128.

Its factorization into primes is 2<sup>-7</sup>⋅7⋅23 ; its FJS name is M3<sup>7,23</sup>.