User:BudjarnLambeth/42zpi - Revision history

BudjarnLambeth: remove stub since it's a user page (not priority)

2025-11-17T09:03:17Z

remove stub since it's a user page (not priority)

← Older revision		Revision as of 09:03, 17 November 2025
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	~~{{Stub}}~~

	[[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:14-tone scales]]

BudjarnLambeth: BudjarnLambeth moved page 42zpi to User:BudjarnLambeth/42zpi: Not complete enough for main space yet

2025-05-27T08:43:48Z

BudjarnLambeth moved page 42zpi to User:BudjarnLambeth/42zpi: Not complete enough for main space yet

← Older revision	Revision as of 08:43, 27 May 2025
(No difference)

BudjarnLambeth at 08:43, 27 May 2025

2025-05-27T08:43:37Z

← Older revision		Revision as of 08:43, 27 May 2025
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			{{Editable user page}}
	'''42 zeta peak index''' (abbreviated '''42zpi'''), is the [[Equal-step tuning\|equal-step]] [[tuning system]] obtained from the 42nd [[Zeta peak index\|peak]] of the [[The Riemann zeta function and tuning\|Riemann zeta function]].		'''42 zeta peak index''' (abbreviated '''42zpi'''), is the [[Equal-step tuning\|equal-step]] [[tuning system]] obtained from the 42nd [[Zeta peak index\|peak]] of the [[The Riemann zeta function and tuning\|Riemann zeta function]].

BudjarnLambeth: Created page with "'''42 zeta peak index''' (abbreviated '''42zpi'''), is the equal-step tuning system obtained from the 42nd 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 == 42zpi is the closes..."

2025-05-27T08:42:36Z

Created page with "'''42 zeta peak index''' (abbreviated '''42zpi'''), is the equal-step tuning system obtained from the 42nd 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 == 42zpi is the closes..."

New page

'''42 zeta peak index''' (abbreviated '''42zpi'''), is the [[Equal-step tuning|equal-step]] [[tuning system]] obtained from the 42nd [[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 ==
42zpi is the closest [[zeta peak index]] to [[14edo]]. It is effectively a [[octave stretch|stretched]] version of 14edo which improves on its tuning of most [[primes]].

=== Harmonic series ===
{{Harmonics in cet|86.3293668353859|columns=15|title=Approximation of harmonics in 42zpi}}
{{Harmonics in cet|86.3293668353859|columns=16|start=16|title=Approximation of harmonics in 42zpi}}

== Scala file ==
<pre>
! 42zpi.scl
! Created using Scale Workshop 3.1.0
!
! https://scaleworkshop.plainsound.org/scale/g8qoINpGf
!
42nd zeta peak index
14
!
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>

{{Stub}}

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