30th-octave temperaments - Revision history

FloraC: Text replacement - "{{Technical data page}}

" to "{{Technical data page}}"

2025-04-13T13:41:58Z

Text replacement - "{{Technical data page}}<br><br>" to "{{Technical data page}}"

← Older revision		Revision as of 13:41, 13 April 2025
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	{{Technical data page}}~~<br><br>~~		{{Technical data page}}
	{{Infobox fractional-octave\|30}}		{{Infobox fractional-octave\|30}}
	30edo is by many metrics not a harmonically notable temperament, but some of its multiples are. Due to plenty of divisors of number 30, these temperaments are also difficult to catalog due to their belonging in multiple temperament families, and this page is designed to accommodate that.		30edo is by many metrics not a harmonically notable temperament, but some of its multiples are. Due to plenty of divisors of number 30, these temperaments are also difficult to catalog due to their belonging in multiple temperament families, and this page is designed to accommodate that.

BudjarnLambeth: {{Technical data page}}

+ "by many metrics"

2025-04-13T10:57:47Z

{{Technical data page}}<br><br> + "by many metrics"

← Older revision		Revision as of 10:57, 13 April 2025
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			{{Technical data page}}<br><br>
	{{Infobox fractional-octave\|30}}		{{Infobox fractional-octave\|30}}
	30edo is not a harmonically notable temperament, but some of its multiples are. Due to plenty of divisors of number 30, these temperaments are also difficult to catalog due to their belonging in multiple temperament families, and this page is designed to accommodate that.		30edo is by many metrics not a harmonically notable temperament, but some of its multiples are. Due to plenty of divisors of number 30, these temperaments are also difficult to catalog due to their belonging in multiple temperament families, and this page is designed to accommodate that.

	== Zinc ==		== Zinc ==

ArrowHead294 at 03:58, 14 February 2025

2025-02-14T03:58:59Z

← Older revision		Revision as of 03:58, 14 February 2025
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	{{~~Fractional~~-octave ~~navigation~~\|30}}		{{Infobox fractional-octave\|30}}
	30edo is not a harmonically notable temperament, but some of its multiples are. Due to plenty of divisors of number 30, these temperaments are also difficult to catalog due to their belonging in multiple temperament families, and this page is designed to accommodate that.		30edo is not a harmonically notable temperament, but some of its multiples are. Due to plenty of divisors of number 30, these temperaments are also difficult to catalog due to their belonging in multiple temperament families, and this page is designed to accommodate that.

	== Zinc ==		== Zinc ==
	: ''For technical data, see [[Landscape microtemperaments#Zinc]].''		: ''For technical data, see [[Landscape microtemperaments#Zinc]].''

BudjarnLambeth: navbox

2024-12-05T07:26:46Z

navbox

← Older revision		Revision as of 07:26, 5 December 2024
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	Within the reach of a standard 128-note MIDI keyboard, zinc has mos scales of size 60, 90, and 120. These scales are significantly distinct from either landscape rank-3 scales or the 10th-octave mos scales that produce neon or its descendant temperaments like [[deca]]. The 120-tone mos has [[65/64]] within reach.		Within the reach of a standard 128-note MIDI keyboard, zinc has mos scales of size 60, 90, and 120. These scales are significantly distinct from either landscape rank-3 scales or the 10th-octave mos scales that produce neon or its descendant temperaments like [[deca]]. The 120-tone mos has [[65/64]] within reach.

			{{Navbox fractional-octave}}

Eliora: /* Zinc */

2023-09-24T20:56:42Z

Zinc

← Older revision		Revision as of 20:56, 24 September 2023
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	''Zinc'' temperament is named after the 30th element and in the 7-limit it can be described by tempering out the [[landscape comma]] and the [[10th-octave temperaments#Neon\|neon comma]]. Tempering out the landscape comma divides the octave in 3, the neon comma in 10, and respectively zinc divides the octave into 3 x 10 = 30.		''Zinc'' temperament is named after the 30th element and in the 7-limit it can be described by tempering out the [[landscape comma]] and the [[10th-octave temperaments#Neon\|neon comma]]. Tempering out the landscape comma divides the octave in 3, the neon comma in 10, and respectively zinc divides the octave into 3 x 10 = 30.

	While the landscape comma is considered the "most important" comma of zinc, it can be played in ways that don't involve it. For example, it reaches the 11th harmonic in just 2 generators which can be found using the 90-tone mos. ~~Zinc~~ has mos scales of size 60 and 90. These scales are significantly distinct from either landscape rank-3 scales or the 10th-octave ~~MOS~~ scales that produce neon or its descendant temperaments like [[deca]].		While the landscape comma is considered the "most important" comma of zinc, it can be played in ways that don't involve it. For example, it reaches the 11th harmonic in just 2 generators which can be found using the 90-tone mos.

			Within the reach of a standard 128-note MIDI keyboard, zinc has mos scales of size 60, 90, and 120. These scales are significantly distinct from either landscape rank-3 scales or the 10th-octave mos scales that produce neon or its descendant temperaments like [[deca]]. The 120-tone mos has [[65/64]] within reach.

Eliora: /* Zinc */ compromise

2023-09-24T20:54:37Z

Zinc: compromise

← Older revision		Revision as of 20:54, 24 September 2023
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	30edo is not a harmonically notable temperament, but some of its multiples are. Due to plenty of divisors of number 30, these temperaments are also difficult to catalog due to their belonging in multiple temperament families, and this page is designed to accommodate that.		30edo is not a harmonically notable temperament, but some of its multiples are. Due to plenty of divisors of number 30, these temperaments are also difficult to catalog due to their belonging in multiple temperament families, and this page is designed to accommodate that.
	== Zinc ==		== Zinc ==
			: ''For technical data, see [[Landscape microtemperaments#Zinc]].''
	''Zinc'' temperament is named after the 30th element and in the 7-limit it can be described by tempering out the [[landscape comma]] and the [[10th-octave temperaments#Neon\|neon comma]]. Tempering out the landscape comma divides the octave in 3, the neon comma in 10, and respectively zinc divides the octave into 3 x 10 = 30.		''Zinc'' temperament is named after the 30th element and in the 7-limit it can be described by tempering out the [[landscape comma]] and the [[10th-octave temperaments#Neon\|neon comma]]. Tempering out the landscape comma divides the octave in 3, the neon comma in 10, and respectively zinc divides the octave into 3 x 10 = 30.

	While the landscape comma is considered the "most important" comma of zinc, it can be played in ways that don't involve it. For example, it reaches the 11th harmonic in just 2 generators which can be found using the 90-tone mos. Zinc has mos scales of size 60 and 90. These scales are significantly distinct from either landscape rank-3 scales or the 10th-octave MOS scales that produce neon or its descendant temperaments like [[deca]].		While the landscape comma is considered the "most important" comma of zinc, it can be played in ways that don't involve it. For example, it reaches the 11th harmonic in just 2 generators which can be found using the 90-tone mos. Zinc has mos scales of size 60 and 90. These scales are significantly distinct from either landscape rank-3 scales or the 10th-octave MOS scales that produce neon or its descendant temperaments like [[deca]].

Eliora: /* Zinc */

2023-09-24T20:54:01Z

Zinc

← Older revision		Revision as of 20:54, 24 September 2023
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	''Zinc'' temperament is named after the 30th element and in the 7-limit it can be described by tempering out the [[landscape comma]] and the [[10th-octave temperaments#Neon\|neon comma]]. Tempering out the landscape comma divides the octave in 3, the neon comma in 10, and respectively zinc divides the octave into 3 x 10 = 30.		''Zinc'' temperament is named after the 30th element and in the 7-limit it can be described by tempering out the [[landscape comma]] and the [[10th-octave temperaments#Neon\|neon comma]]. Tempering out the landscape comma divides the octave in 3, the neon comma in 10, and respectively zinc divides the octave into 3 x 10 = 30.

	Zinc has mos scales of size 60 and 90. These scales are significantly distinct from either landscape rank-3 scales or the 10th-octave MOS scales that produce neon or its descendant temperaments like [[deca]].		While the landscape comma is considered the "most important" comma of zinc, it can be played in ways that don't involve it. For example, it reaches the 11th harmonic in just 2 generators which can be found using the 90-tone mos. Zinc has mos scales of size 60 and 90. These scales are significantly distinct from either landscape rank-3 scales or the 10th-octave MOS scales that produce neon or its descendant temperaments like [[deca]].

	~~[[Subgroup]]: 2.3.5.7~~

	~~[[Comma list]]: 250047/250000, {{monzo\| -45 -24 14 18 }}~~

	~~{{Mapping\|legend=1\| 30 2 15 66 \| 0 5 6 2 }}~~

	~~[[Optimal tuning]] ([[CTE]]): ~53747712/52521875 = 1\30, ~216/175 = 364.389~~

	~~{{Optimal ET sequence\|legend=1\| 270, 1380, 1650, 1920, 2190, 4650 }}~~

	~~[[Badness]]: 0.0742~~

	~~=== 11-limit ===~~
	~~Subgroup: 2.3.5.7.11~~

	~~Comma list: 9801/9800, 250047/250000, 97869261875/97844723712~~

	~~Mapping: {{mapping\| 30 2 15 66 122 \| 0 5 6 2 -2 }}~~

	~~Optimal tuning (CTE): ~18865/18432 = 1\30, ~216/175 = 364.389~~

	~~{{Optimal ET sequence\|legend=1\| 270, 1110, 1380, 1650, 1920, 2190 }}~~

	~~Badness: 0.0220~~

	~~=== 13-limit ===~~
	~~Subgroup: 2.3.5.7.11~~

	~~Comma list: 9801/9800, 123201/123200, 250047/250000, 1990656/1990625~~

	~~Mapping: {{mapping\| 30 2 15 66 122 193 \| 0 5 6 2 -2 -9 }}~~

	~~Optimal tuning (CTE): ~351/343 = 1\30, ~216/175 = 364.389~~

	~~{{Optimal ET sequence\|legend=1\| 270, 1380, 1650, 1920, 2190, 4650, 6840e, 11490de }}~~

	~~Badness: 0.0150~~

Eliora at 17:24, 24 September 2023

2023-09-24T17:24:13Z

← Older revision		Revision as of 17:24, 24 September 2023
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	{{Fractional-octave navigation\|30}}		{{Fractional-octave navigation\|30}}
	30edo is not a harmonically notable temperament, but some of its multiples are.		30edo is not a harmonically notable temperament, but some of its multiples are. Due to plenty of divisors of number 30, these temperaments are also difficult to catalog due to their belonging in multiple temperament families, and this page is designed to accommodate that.
	== Zinc ==		== Zinc ==
	''Zinc'' temperament is named after the 30th element and in the 7-limit it can be described by tempering out the [[landscape comma]] and the [[10th-octave temperaments#Neon\|neon comma]]. Tempering out the landscape comma divides the octave in 3, the neon comma in 10, and respectively zinc divides the octave into 3 x 10 = 30.		''Zinc'' temperament is named after the 30th element and in the 7-limit it can be described by tempering out the [[landscape comma]] and the [[10th-octave temperaments#Neon\|neon comma]]. Tempering out the landscape comma divides the octave in 3, the neon comma in 10, and respectively zinc divides the octave into 3 x 10 = 30.

Eliora: /* Zinc */

2023-09-24T17:03:54Z

Zinc

← Older revision		Revision as of 17:03, 24 September 2023
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	== Zinc ==		== Zinc ==
	''Zinc'' temperament is named after the 30th element and in the 7-limit it can be described by tempering out the [[landscape comma]] and the [[10th-octave temperaments#Neon\|neon comma]]. Tempering out the landscape comma divides the octave in 3, the neon comma in 10, and respectively zinc divides the octave into 3 x 10 = 30.		''Zinc'' temperament is named after the 30th element and in the 7-limit it can be described by tempering out the [[landscape comma]] and the [[10th-octave temperaments#Neon\|neon comma]]. Tempering out the landscape comma divides the octave in 3, the neon comma in 10, and respectively zinc divides the octave into 3 x 10 = 30.

			Zinc has mos scales of size 60 and 90. These scales are significantly distinct from either landscape rank-3 scales or the 10th-octave MOS scales that produce neon or its descendant temperaments like [[deca]].

	[[Subgroup]]: 2.3.5.7		[[Subgroup]]: 2.3.5.7

Eliora: zinc is better addressed here and so there's continuous navigation 28 - 29 - 30 - 31 - 32

2023-09-24T16:54:51Z

zinc is better addressed here and so there's continuous navigation 28 - 29 - 30 - 31 - 32

New page

{{Fractional-octave navigation|30}}
30edo is not a harmonically notable temperament, but some of its multiples are.
== Zinc ==
''Zinc'' temperament is named after the 30th element and in the 7-limit it can be described by tempering out the [[landscape comma]] and the [[10th-octave temperaments#Neon|neon comma]]. Tempering out the landscape comma divides the octave in 3, the neon comma in 10, and respectively zinc divides the octave into 3 x 10 = 30.

[[Subgroup]]: 2.3.5.7

[[Comma list]]: 250047/250000, {{monzo| -45 -24 14 18 }}

{{Mapping|legend=1| 30 2 15 66 | 0 5 6 2 }}

[[Optimal tuning]] ([[CTE]]): ~53747712/52521875 = 1\30, ~216/175 = 364.389

{{Optimal ET sequence|legend=1| 270, 1380, 1650, 1920, 2190, 4650 }}

[[Badness]]: 0.0742

=== 11-limit ===
Subgroup: 2.3.5.7.11

Comma list: 9801/9800, 250047/250000, 97869261875/97844723712

Mapping: {{mapping| 30 2 15 66 122 | 0 5 6 2 -2 }}

Optimal tuning (CTE): ~18865/18432 = 1\30, ~216/175 = 364.389

{{Optimal ET sequence|legend=1| 270, 1110, 1380, 1650, 1920, 2190 }}

Badness: 0.0220

=== 13-limit ===
Subgroup: 2.3.5.7.11

Comma list: 9801/9800, 123201/123200, 250047/250000, 1990656/1990625

Mapping: {{mapping| 30 2 15 66 122 193 | 0 5 6 2 -2 -9 }}

Optimal tuning (CTE): ~351/343 = 1\30, ~216/175 = 364.389

{{Optimal ET sequence|legend=1| 270, 1380, 1650, 1920, 2190, 4650, 6840e, 11490de }}

Badness: 0.0150

30th-octave temperaments - Revision history

FloraC: Text replacement - "{{Technical data page}}" to "{{Technical data page}}"

BudjarnLambeth: {{Technical data page}} + "by many metrics"

ArrowHead294 at 03:58, 14 February 2025

BudjarnLambeth: navbox

Eliora: /* Zinc */

Eliora: /* Zinc */ compromise

Eliora: /* Zinc */

Eliora at 17:24, 24 September 2023

Eliora: /* Zinc */

Eliora: zinc is better addressed here and so there's continuous navigation 28 - 29 - 30 - 31 - 32

FloraC: Text replacement - "{{Technical data page}}

" to "{{Technical data page}}"

BudjarnLambeth: {{Technical data page}}

+ "by many metrics"