User:BudjarnLambeth/74zpi - Revision history

BudjarnLambeth: BudjarnLambeth moved page 74zpi to User:BudjarnLambeth/74zpi

2025-11-17T09:04:14Z

BudjarnLambeth moved page 74zpi to User:BudjarnLambeth/74zpi

← Older revision	Revision as of 09:04, 17 November 2025
(No difference)

BudjarnLambeth at 09:02, 17 November 2025

2025-11-17T09:02:53Z

← Older revision		Revision as of 09:02, 17 November 2025
Line 88:		Line 88:
	* 1212.271		* 1212.271

	[[Category:Zeta peak indexes]][[Category:Pages with Scala files]][[Category:Tempered scales]][[Category:14-tone scales]]		[[Category:Zeta peak indexes]][[Category:Pages with Scala files]][[Category:Tempered scales]][[Category:21-tone scales]][[Category:21edo]]

BudjarnLambeth: /* Scala file */

2025-11-17T09:01:47Z

Scala file

← Older revision		Revision as of 09:01, 17 November 2025
Line 32:		Line 32:
	173.182		173.182
	230.909		230.909
	288.~~6360~~		288.636
	346.363		346.363
	404.09		404.090
	461.818		461.818
	519.545		519.545

BudjarnLambeth: /* Scala file */

2025-11-17T09:01:39Z

Scala file

← Older revision		Revision as of 09:01, 17 November 2025
Line 32:		Line 32:
	173.182		173.182
	230.909		230.909
	288.~~636~~		288.6360
	346.363		346.363
	404.09		404.09
Line 45:		Line 45:
	923.635		923.635
	981.362		981.362
	1039.09		1039.090
	1096.817		1096.817
	1154.544		1154.544

BudjarnLambeth: /* Scala file */

2025-11-17T09:01:28Z

Scala file

← Older revision		Revision as of 09:01, 17 November 2025
Line 28:		Line 28:
	21		21
	!		!
	86.~~329~~		57.727
	~~172~~.~~659~~		115.454
	~~258~~.~~988~~		173.182
	~~345~~.~~317~~		230.909
	~~431~~.~~647~~		288.636
	~~517~~.~~976~~		346.363
	~~604~~.~~306~~		404.09
	~~690~~.~~635~~		461.818
	~~776~~.~~964~~		519.545
	~~863~~.~~294~~		577.272
	~~949~~.~~623~~		634.999
	~~1035~~.~~952~~		692.726
	~~1122~~.~~282~~		750.454
	~~1208~~.~~611~~		808.181
			865.908
			923.635
			981.362
			1039.09
			1096.817
			1154.544
			1212.271
	</pre>		</pre>

BudjarnLambeth at 09:00, 17 November 2025

2025-11-17T09:00:51Z

← Older revision		Revision as of 09:00, 17 November 2025
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	{{Harmonics in cet\|57.7271958810858\|columns=15\|title=Approximation of harmonics in 74zpi}}		{{Harmonics in cet\|57.7271958810858\|columns=15\|title=Approximation of harmonics in 74zpi}}
	{{Harmonics in cet\|57.7271958810858\|columns=16\|start=16\|title=Approximation of harmonics in 74zpi}}		{{Harmonics in cet\|57.7271958810858\|columns=16\|start=16\|title=Approximation of harmonics in 74zpi}}


	{{Harmonics in cet\|57.1429\|columns=15\|title=21edo for comparison\|collapsed=1}}		{{Harmonics in cet\|57.1429\|columns=15\|title=21edo for comparison\|collapsed=1}}

BudjarnLambeth at 09:00, 17 November 2025

2025-11-17T09:00:41Z

@@ Line 1: / Line 1: @@
 {{Editable user page}}
 '''74 zeta peak index''' (abbreviated '''74zpi'''), is the [[Equal-step tuning|equal-step]] [[tuning system]] obtained from the 74th [[Zeta peak index|peak]] of the [[The Riemann zeta function and tuning|Riemann zeta function]].
 == Theory ==

BudjarnLambeth: Created page with "{{Editable user page}} '''74 zeta peak index''' (abbreviated '''74zpi'''), is the equal-step tuning system obtained from the 74th peak of the Riemann zeta function. {{ZPI | zpi = 42 | steps = 13.9002525327005 | step size = 86.3293668353859 | height = 4.592177 | integral = 0.984037 | gap = 14.097244 | edo = 14edo | octave = 1208.61113569540 | consistent = 7 | distinct = 5 }} == Theory..."

2025-11-17T09:00:28Z

Created page with "{{Editable user page}} '''74 zeta peak index''' (abbreviated '''74zpi'''), is the equal-step tuning system obtained from the 74th peak of the Riemann zeta function. {{ZPI | zpi = 42 | steps = 13.9002525327005 | step size = 86.3293668353859 | height = 4.592177 | integral = 0.984037 | gap = 14.097244 | edo = 14edo | octave = 1208.61113569540 | consistent = 7 | distinct = 5 }} == Theory..."

New page

{{Editable user page}}
'''74 zeta peak index''' (abbreviated '''74zpi'''), is the [[Equal-step tuning|equal-step]] [[tuning system]] obtained from the 74th [[Zeta peak index|peak]] of the [[The Riemann zeta function and tuning|Riemann zeta function]].

{{ZPI
| zpi = 42
| steps = 13.9002525327005
| step size = 86.3293668353859
| height = 4.592177
| integral = 0.984037
| gap = 14.097244
| edo = 14edo
| octave = 1208.61113569540
| consistent = 7
| distinct = 5
}}

== Theory ==
74zpi is like [[21edo]] but [[octave stretch]]ed by about 12 [[cents]].

It sounds best with aperiodic or metallophone [[timbre]]s (similar to [[gamelan]] instruments).

Compared to 21edo:
* It improves upon [[prime]]s 3, 5, 7, 19 and 23
* It worsens primes 2, 11, 13 and 17

=== Harmonic series ===
{{Harmonics in cet|57.7271958810858|columns=15|title=Approximation of harmonics in 74zpi}}
{{Harmonics in cet|57.7271958810858|columns=16|start=16|title=Approximation of harmonics in 74zpi}}

{{Harmonics in cet|57.1429|columns=15|title=21edo for comparison|collapsed=1}}
{{Harmonics in cet|57.1429|columns=16|start=16|title=21edo for comparison|collapsed=1}}

== Scala file ==
<pre>
! 74zpi.scl
! Created using Scale Workshop 3.1.0
!
! https://scaleworkshop.plainsound.org/scale/wbuk2CLvA
!
74th zeta peak index
21
!
86.329
172.659
258.988
345.317
431.647
517.976
604.306
690.635
776.964
863.294
949.623
1035.952
1122.282
1208.611
</pre>

== Scales ==
''See also: [[21edo#Scales]]''

Values given in [[cents]].

; Pseudo-[[equiheptatonic]]
* 173.182
* 346.363
* 519.545
* 692.726
* 865.908
* 1039.09
* 1212.271

; Pseudo-[[equipentatonic]]
* 230.909
* 519.545
* 692.726
* 981.362
* 1212.271

; 5-tone pseudo-[[pelog]]
* 115.454
* 288.636
* 692.726
* 808.181
* 1212.271

; 7-tone pseudo-pelog
* 115.454
* 288.636
* 519.545
* 692.726
* 808.181
* 1039.09
* 1212.271

[[Category:Zeta peak indexes]][[Category:Pages with Scala files]][[Category:Tempered scales]][[Category:14-tone scales]]