Table of zeta-stretched edos - Revision history

Contribution: /* See also */

2025-08-28T17:20:04Z

Contribution: /* See also */

2025-08-28T17:19:44Z

Sintel: use high level heading, move calculation down

2025-08-15T23:57:39Z

use high level heading, move calculation down

← Older revision		Revision as of 23:57, 15 August 2025
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	All of the tunings listed on this page are [[zeta peak index]] tunings, e.g. 1zpi, 2zpi, 3zpi... However, not all zeta peak index tunings are listed here - only those with intervals close to the octave. For a more complete table see: [[zeta peak index]].		All of the tunings listed on this page are [[zeta peak index]] tunings, e.g. 1zpi, 2zpi, 3zpi... However, not all zeta peak index tunings are listed here - only those with intervals close to the octave. For a more complete table see: [[zeta peak index]].

	~~=== Calculation instructions ===~~		== Table ==
	~~How to calculate the third column using the free version of Wolfram Cloud:~~
	~~# Copy-paste <code><nowiki>Plot[Abs[RiemannSiegelZ[9.06472028x]], {x, 11.9, 12.1}]</nowiki></code> into a cell.~~
	~~# Change "'''11.9'''" and "'''12.1'''" to whatever values you want, e.g. to view the curve around 15edo you might use the values "'''14.9'''" and "'''15.1'''".~~
	~~# Ensure that cell is still selected~~
	~~# In the menu select Evaluation > Evaluate Cells~~

	=== Table ===
	This is a list of zeta peak-based octave tunings, which includes all EDOs up to 100 and certain noteworthy ones above 100.		This is a list of zeta peak-based octave tunings, which includes all EDOs up to 100 and certain noteworthy ones above 100.
	{\| class="wikitable sortable"		{\| class="wikitable sortable"
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	\|}		\|}

	=== Record zeta peaks ===		== Calculation instructions ==
			The third column of the above table can be calculated using the free version of Wolfram Cloud:
			# Copy-paste <code><nowiki>Plot[Abs[RiemannSiegelZ[9.06472028x]], {x, 11.9, 12.1}]</nowiki></code> into a cell.
			# Change "'''11.9'''" and "'''12.1'''" to whatever values you want, e.g. to view the curve around 15edo you might use the values "'''14.9'''" and "'''15.1'''".
			# Ensure that cell is still selected
			# In the menu select Evaluation > Evaluate Cells

			== Record zeta peaks ==
	<pre>		<pre>
	0.00000		0.00000

Lériendil: moved zeta records here

2025-04-09T19:24:11Z

moved zeta records here

@@ Line 229: / Line 229: @@
 | [[5818zpi]] || 684edo || 683.939 || 1.755 || 1200.107 || 5816
 |}
 == See also ==

ArrowHead294 at 14:16, 17 September 2024

2024-09-17T14:16:36Z

← Older revision		Revision as of 14:16, 17 September 2024
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	~~<noinclude>~~This table lists tuning instructions for [[EDO\|equal divisions of the octave]] which have been stretched or compressed using optimal octave stretch based on zeta peaks, as described here: [[the Riemann zeta function and tuning]].		This table lists tuning instructions for [[EDO\|equal divisions of the octave]] which have been stretched or compressed using optimal octave stretch based on zeta peaks, as described here: [[the Riemann zeta function and tuning]].

	No such table could possibly be complete (as there are so many possible edos), so please add tunings of interest as you see fit.		No such table could possibly be complete (as there are so many possible edos), so please add tunings of interest as you see fit.
Line 7:		Line 7:
	=== Calculation instructions ===		=== Calculation instructions ===
	How to calculate the third column using the free version of Wolfram Cloud:		How to calculate the third column using the free version of Wolfram Cloud:
	# Copy-paste <code>Plot~~{{!(}}~~Abs~~{{!(}}~~RiemannSiegelZ~~{{!(}}~~9.06472028x~~{{))!}}~~, {~~{(}}~~x, 11.9, 12.1~~{{)}}{{)!}~~}</code> into a cell.		# Copy-paste <code><nowiki>Plot[Abs[RiemannSiegelZ[9.06472028x]], {x, 11.9, 12.1}]</nowiki></code> into a cell.
	# Change "'''11.9'''" and "'''12.1'''" to whatever values you want, e.g. to view the curve around 15edo you might use the values "'''14.9'''" and "'''15.1'''".		# Change "'''11.9'''" and "'''12.1'''" to whatever values you want, e.g. to view the curve around 15edo you might use the values "'''14.9'''" and "'''15.1'''".
	# Ensure that cell is still selected		# Ensure that cell is still selected
Line 14:		Line 14:
	=== Table ===		=== Table ===
	This is a list of zeta peak-based octave tunings, which includes all EDOs up to 100 and certain noteworthy ones above 100.		This is a list of zeta peak-based octave tunings, which includes all EDOs up to 100 and certain noteworthy ones above 100.
	~~</noinclude>~~{\| class="wikitable sortable"		{\| class="wikitable sortable"
	\|+ style="font-size: 105%;" \| Zeta-optimal tunings for selected EDOs		\|+ style="font-size: 105%;" \| Zeta-optimal tunings for selected EDOs
			\|-
	! Tuning !! Associated edo !! No. of steps per 1200 cents !! Step size (cents) !! Tuning of 2/1 (cents) !! Gram point index		! Tuning !! Associated edo !! No. of steps per 1200 cents !! Step size (cents) !! Tuning of 2/1 (cents) !! Gram point index
	\|-		\|-
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	\|-		\|-
	\| [[5818zpi]] \|\| 684edo \|\| 683.939 \|\| 1.755 \|\| 1200.107 \|\| 5816		\| [[5818zpi]] \|\| 684edo \|\| 683.939 \|\| 1.755 \|\| 1200.107 \|\| 5816
	\|}~~<noinclude>~~		\|}

	== See also ==		== See also ==
Line 235:		Line 236:
	[[Category:Lists of scales]]		[[Category:Lists of scales]]
	[[Category:Zeta peak indexes]]		[[Category:Zeta peak indexes]]
	~~</noinclude>~~

BudjarnLambeth: /* Table */

2024-09-16T21:33:12Z

Table

← Older revision		Revision as of 21:33, 16 September 2024
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	=== Table ===		=== Table ===
	This is a list of ~~all~~ zeta peak-based octave tunings, which includes all EDOs up to 100 and certain noteworthy ones above 100.		This is a list of zeta peak-based octave tunings, which includes all EDOs up to 100 and certain noteworthy ones above 100.
	</noinclude>{\| class="wikitable sortable"		</noinclude>{\| class="wikitable sortable"
	\|+ style="font-size: 105%;" \| Zeta-optimal tunings for selected EDOs		\|+ style="font-size: 105%;" \| Zeta-optimal tunings for selected EDOs

BudjarnLambeth: /* Table */ Removed the word complete. The list cannot be complete because there are infinite possible edos (or at least an impractically large number).

2024-09-16T21:32:59Z

Table: Removed the word complete. The list cannot be complete because there are infinite possible edos (or at least an impractically large number).

← Older revision		Revision as of 21:32, 16 September 2024
Line 13:		Line 13:

	=== Table ===		=== Table ===
	This is a ~~complete~~ list of all zeta peak-based octave tunings, which includes all EDOs up to 100 and certain noteworthy ones above 100.		This is a list of all zeta peak-based octave tunings, which includes all EDOs up to 100 and certain noteworthy ones above 100.
	</noinclude>{\| class="wikitable sortable"		</noinclude>{\| class="wikitable sortable"
	\|+ style="font-size: 105%;" \| Zeta-optimal tunings for selected EDOs		\|+ style="font-size: 105%;" \| Zeta-optimal tunings for selected EDOs

ArrowHead294 at 17:10, 13 September 2024

2024-09-13T17:10:09Z

← Older revision		Revision as of 17:10, 13 September 2024
Line 1:		Line 1:
	This table lists tuning instructions for [[EDO\|equal divisions of the octave]] which have been stretched or compressed using optimal octave stretch based on zeta peaks, as described here: [[the Riemann zeta function and tuning]].		<noinclude>This table lists tuning instructions for [[EDO\|equal divisions of the octave]] which have been stretched or compressed using optimal octave stretch based on zeta peaks, as described here: [[the Riemann zeta function and tuning]].

	No such table could possibly be complete (as there are so many possible edos), so please add tunings of interest as you see fit.		No such table could possibly be complete (as there are so many possible edos), so please add tunings of interest as you see fit.
Line 14:		Line 14:
	=== Table ===		=== Table ===
	This is a complete list of all zeta peak-based octave tunings, which includes all EDOs up to 100 and certain noteworthy ones above 100.		This is a complete list of all zeta peak-based octave tunings, which includes all EDOs up to 100 and certain noteworthy ones above 100.
	{\| class="wikitable sortable"		</noinclude>{\| class="wikitable sortable"
	\|+ style="font-size: 105%;" \| Zeta-optimal tunings for selected EDOs		\|+ style="font-size: 105%;" \| Zeta-optimal tunings for selected EDOs
	! Tuning !! Associated edo !! No. of steps per 1200 cents !! Step size (cents) !! Tuning of 2/1 (cents) !! Gram point index		! Tuning !! Associated edo !! No. of steps per 1200 cents !! Step size (cents) !! Tuning of 2/1 (cents) !! Gram point index
Line 227:		Line 227:
	\|-		\|-
	\| [[5818zpi]] \|\| 684edo \|\| 683.939 \|\| 1.755 \|\| 1200.107 \|\| 5816		\| [[5818zpi]] \|\| 684edo \|\| 683.939 \|\| 1.755 \|\| 1200.107 \|\| 5816
	\|}		\|}<noinclude>

	== See also ==		== See also ==
Line 235:		Line 235:
	[[Category:Lists of scales]]		[[Category:Lists of scales]]
	[[Category:Zeta peak indexes]]		[[Category:Zeta peak indexes]]
			</noinclude>

ArrowHead294 at 18:26, 9 September 2024

2024-09-09T18:26:45Z

← Older revision		Revision as of 18:26, 9 September 2024
Line 7:		Line 7:
	=== Calculation instructions ===		=== Calculation instructions ===
	How to calculate the third column using the free version of Wolfram Cloud:		How to calculate the third column using the free version of Wolfram Cloud:
	# Copy-paste <code>Plot[Abs[RiemannSiegelZ[9.06472028x]], {x, 11.9, 12.1}]</code> into a cell.		# Copy-paste <code>Plot{{!(}}Abs{{!(}}RiemannSiegelZ{{!(}}9.06472028x{{))!}}, {{(}}x, 11.9, 12.1{{)}}{{)!}}</code> into a cell.
	# Change "'''11.9'''" and "'''12.1'''" to whatever values you want, e.g. to view the curve around 15edo you might use the values "'''14.9'''" and "'''15.1'''".		# Change "'''11.9'''" and "'''12.1'''" to whatever values you want, e.g. to view the curve around 15edo you might use the values "'''14.9'''" and "'''15.1'''".
	# Ensure that cell is still selected		# Ensure that cell is still selected

FloraC: Recategorize

2024-08-10T07:53:45Z

Recategorize

← Older revision		Revision as of 07:53, 10 August 2024
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	* [[The Riemann zeta function and tuning]]		* [[The Riemann zeta function and tuning]]

	[[Category:~~Tables~~]]		[[Category:Lists of scales]]
	[[Category:Zeta peak indexes]]		[[Category:Zeta peak indexes]]
	~~[[Category:Non-integer edos]]~~

← Older revision		Revision as of 17:20, 28 August 2025
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	== See also ==		== See also ==
	* [[Zeta peak index]]		* [[Zeta peak index]]
			* [[User:Contribution/Gallery of Zeta Peak Indexes at sigma = 1\|Zeta Peak Indexes at sigma = 1]]
	* [[The Riemann zeta function and tuning]]		* [[The Riemann zeta function and tuning]]
	* [[User:Contribution/Gallery of Zeta Peak Indexes at sigma = 1\|Gallery of Zeta Peak Indexes at sigma = 1]]

	[[Category:Lists of scales]]		[[Category:Lists of scales]]
	[[Category:Zeta peak indexes]]		[[Category:Zeta peak indexes]]

← Older revision		Revision as of 17:19, 28 August 2025
Line 298:		Line 298:
	* [[Zeta peak index]]		* [[Zeta peak index]]
	* [[The Riemann zeta function and tuning]]		* [[The Riemann zeta function and tuning]]
			* [[User:Contribution/Gallery of Zeta Peak Indexes at sigma = 1\|Gallery of Zeta Peak Indexes at sigma = 1]]

	[[Category:Lists of scales]]		[[Category:Lists of scales]]
	[[Category:Zeta peak indexes]]		[[Category:Zeta peak indexes]]