Secor wt17 - Revision history

Hkm at 16:54, 24 June 2025

2025-06-24T16:54:51Z

← Older revision		Revision as of 16:54, 24 June 2025
Line 39:		Line 39:
	[[Category:17-tone scales]]		[[Category:17-tone scales]]
	[[Category:Tempered scales]]		[[Category:Tempered scales]]
	~~[[Category:Pages with mostly numerical content]]~~
	[[Category:Well temperaments]]		[[Category:Well temperaments]]

Lériendil: Text replacement - "Category:Tempered scales" to "Category:Tempered scales Category:Pages with mostly numerical content"

2025-06-24T02:51:10Z

Text replacement - "Category:Tempered scales" to "Category:Tempered scales Category:Pages with mostly numerical content"

← Older revision		Revision as of 02:51, 24 June 2025
Line 39:		Line 39:
	[[Category:17-tone scales]]		[[Category:17-tone scales]]
	[[Category:Tempered scales]]		[[Category:Tempered scales]]
			[[Category:Pages with mostly numerical content]]
	[[Category:Well temperaments]]		[[Category:Well temperaments]]

FloraC: Style and categories

2023-01-23T17:21:47Z

Style and categories

← Older revision		Revision as of 17:21, 23 January 2023
Line 1:		Line 1:
	This is a 17-tone well tempered tuning by [[George Secor]], described in his article ''[http://anaphoria.com/Secor17puzzle.pdf The 17-tone Puzzle]'':		This is a 17-tone well tempered tuning by [[George Secor]], described in his article ''[http://anaphoria.com/Secor17puzzle.pdf The 17-tone Puzzle]'':

	''The requirements for a temperament having an irregular closed circle of fifths in ~~17...~~ are somewhat different from those for 12 in that many of the tempered intervals are used to represent two different just ratios. For example, ~~...6~~ system degrees of 17-ET (6º17) falls between 11:14 and 7:9. In a temperament with a circle of fifths of varying size, certain intervals will more closely approximate one of these ratios in one part of the circle and the other ratio in another part of the circle. The objective is to construct the temperament in such a way that the best approximations of these ratios will occur, in the desired keys, simultaneously in chords in which these intervals (or their inversions) are used in combination, e.g.~~, ...7~~:9:11 in 17.''		:''The requirements for a temperament having an irregular closed circle of fifths in 17… are somewhat different from those for 12 in that many of the tempered intervals are used to represent two different just ratios. For example, …6 system degrees of 17-ET (6º17) falls between 11:14 and 7:9. In a temperament with a circle of fifths of varying size, certain intervals will more closely approximate one of these ratios in one part of the circle and the other ratio in another part of the circle. The objective is to construct the temperament in such a way that the best approximations of these ratios will occur, in the desired keys, simultaneously in chords in which these intervals (or their inversions) are used in combination, e.g. …7:9:11 in 17.''

	''In my 17-WT, using primes 3, 7, 11, and 13, the best intonation occurs in five different keys (with B-flat, F, C, G, and D as fundamental tones)~~....~~ While the 6:7:9 (subminor) triad in 17-WT is not as good as in 22-ET, the best 6:7:9:11 tetrads in 17-WT are considerably better than those in 22-ET. Even though a significant improvement is made in the harmonic effect of 17-WT over 17-ET, the former retains the general melodic characteristics of the latter.''		:''In my 17-WT, using primes 3, 7, 11, and 13, the best intonation occurs in five different keys (with B-flat, F, C, G, and D as fundamental tones)… While the 6:7:9 (subminor) triad in 17-WT is not as good as in 22-ET, the best 6:7:9:11 tetrads in 17-WT are considerably better than those in 22-ET. Even though a significant improvement is made in the harmonic effect of 17-WT over 17-ET, the former retains the general melodic characteristics of the latter.''

	Secor advises using C = 264 Hz when playing alongside instruments tuned to [[17edo~~\|17EDO~~]], so that corresponding pitches of the scales would not deviate by more than 6.7 cents.		Secor advises using C = 264 Hz when playing alongside instruments tuned to [[17edo]], so that corresponding pitches of the scales would not deviate by more than 6.7 cents.

	Here's the beginning of a ~~17-WT~~ jazz piece by George Secor: [[:File:17WTjazz.mp3\|17WTjazz.mp3]]		Here's the beginning of a 17wt jazz piece by George Secor: [[:File:17WTjazz.mp3\|17WTjazz.mp3]]

	== Scala file ==		== Scala file ==
Line 37:		Line 37:

	[[Category:Pages with Scala files]]		[[Category:Pages with Scala files]]
	[[Category:Well ~~temperament~~]]		[[Category:17-tone scales]]
			[[Category:Tempered scales]]
			[[Category:Well temperaments]]

Xenwolf: +cat

2022-02-22T07:44:08Z

+cat

← Older revision		Revision as of 07:44, 22 February 2022
Line 35:		Line 35:
	1200.		1200.
	</pre>		</pre>

			[[Category:Pages with Scala files]]
			[[Category:Well temperament]]

Dave Keenan at 04:27, 22 February 2022

2022-02-22T04:27:52Z

← Older revision		Revision as of 04:27, 22 February 2022
Line 7:		Line 7:
	Secor advises using C = 264 Hz when playing alongside instruments tuned to [[17edo\|17EDO]], so that corresponding pitches of the scales would not deviate by more than 6.7 cents.		Secor advises using C = 264 Hz when playing alongside instruments tuned to [[17edo\|17EDO]], so that corresponding pitches of the scales would not deviate by more than 6.7 cents.

	Here's the beginning of 17-WT jazz piece by George Secor: [[:File:17WTjazz.mp3\|17WTjazz.mp3]]		Here's the beginning of a 17-WT jazz piece by George Secor: [[:File:17WTjazz.mp3\|17WTjazz.mp3]]

	== Scala file ==		== Scala file ==

Dave Keenan: Added link to George Secor's 17-WT jazz piece

2022-02-22T04:27:28Z

Added link to George Secor's 17-WT jazz piece

← Older revision		Revision as of 04:27, 22 February 2022
Line 6:		Line 6:

	Secor advises using C = 264 Hz when playing alongside instruments tuned to [[17edo\|17EDO]], so that corresponding pitches of the scales would not deviate by more than 6.7 cents.		Secor advises using C = 264 Hz when playing alongside instruments tuned to [[17edo\|17EDO]], so that corresponding pitches of the scales would not deviate by more than 6.7 cents.

			Here's the beginning of 17-WT jazz piece by George Secor: [[:File:17WTjazz.mp3\|17WTjazz.mp3]]

	== Scala file ==		== Scala file ==

CritDeathX: Reverted it; found out there's a temperament section for 17EDO

2020-09-27T22:07:19Z

Reverted it; found out there's a temperament section for 17EDO

← Older revision		Revision as of 22:07, 27 September 2020
Line 6:		Line 6:

	Secor advises using C = 264 Hz when playing alongside instruments tuned to [[17edo\|17EDO]], so that corresponding pitches of the scales would not deviate by more than 6.7 cents.		Secor advises using C = 264 Hz when playing alongside instruments tuned to [[17edo\|17EDO]], so that corresponding pitches of the scales would not deviate by more than 6.7 cents.

	~~''See Also:'' [[User:CritDeathX/Sam's 17-note Well Temperament\|''Sam's 17-note Well Temperament'']]~~

	== Scala file ==		== Scala file ==

CritDeathX: Also added my 17-WT cause free promo

2020-09-27T22:04:59Z

Also added my 17-WT cause free promo

← Older revision		Revision as of 22:04, 27 September 2020
Line 6:		Line 6:

	Secor advises using C = 264 Hz when playing alongside instruments tuned to [[17edo\|17EDO]], so that corresponding pitches of the scales would not deviate by more than 6.7 cents.		Secor advises using C = 264 Hz when playing alongside instruments tuned to [[17edo\|17EDO]], so that corresponding pitches of the scales would not deviate by more than 6.7 cents.

			''See Also:'' [[User:CritDeathX/Sam's 17-note Well Temperament\|''Sam's 17-note Well Temperament'']]

	== Scala file ==		== Scala file ==

CritDeathX: Added reasoning for 17-WT

2020-09-27T22:02:04Z

Added reasoning for 17-WT

← Older revision		Revision as of 22:02, 27 September 2020
Line 1:		Line 1:
	This is a 17-tone well tempered tuning by [[George Secor]], described in his article ''[http://anaphoria.com/Secor17puzzle.pdf The 17-tone Puzzle]''~~. (The reasoning behind this temperament is also stated in there, but maybe we should copy it here?)~~		This is a 17-tone well tempered tuning by [[George Secor]], described in his article ''[http://anaphoria.com/Secor17puzzle.pdf The 17-tone Puzzle]'':

	Secor advises using C = 264 Hz when playing alongside instruments tuned to [[17edo]], so that corresponding pitches of the scales would not deviate by more than 6.7 cents.		''The requirements for a temperament having an irregular closed circle of fifths in 17... are somewhat different from those for 12 in that many of the tempered intervals are used to represent two different just ratios. For example, ...6 system degrees of 17-ET (6º17) falls between 11:14 and 7:9. In a temperament with a circle of fifths of varying size, certain intervals will more closely approximate one of these ratios in one part of the circle and the other ratio in another part of the circle. The objective is to construct the temperament in such a way that the best approximations of these ratios will occur, in the desired keys, simultaneously in chords in which these intervals (or their inversions) are used in combination, e.g., ...7:9:11 in 17.''

			''In my 17-WT, using primes 3, 7, 11, and 13, the best intonation occurs in five different keys (with B-flat, F, C, G, and D as fundamental tones).... While the 6:7:9 (subminor) triad in 17-WT is not as good as in 22-ET, the best 6:7:9:11 tetrads in 17-WT are considerably better than those in 22-ET. Even though a significant improvement is made in the harmonic effect of 17-WT over 17-ET, the former retains the general melodic characteristics of the latter.''

			Secor advises using C = 264 Hz when playing alongside instruments tuned to [[17edo\|17EDO]], so that corresponding pitches of the scales would not deviate by more than 6.7 cents.

	== Scala file ==		== Scala file ==

Arseniiv: Stub? I don't know what categories are appropriate. Didn’t find one for well temperaments

2020-09-27T20:25:08Z

Stub? I don't know what categories are appropriate. Didn’t find one for well temperaments

New page

This is a 17-tone well tempered tuning by [[George Secor]], described in his article ''[http://anaphoria.com/Secor17puzzle.pdf The 17-tone Puzzle]''. (The reasoning behind this temperament is also stated in there, but maybe we should copy it here?)

Secor advises using C = 264 Hz when playing alongside instruments tuned to [[17edo]], so that corresponding pitches of the scales would not deviate by more than 6.7 cents.

== Scala file ==

<pre>
! secor_wt17.scl
!
George Secor's 17-tone well temperament
17
!
66.741
144.856
214.441
278.339
353.610
428.882
492.780
562.364
640.479
707.220
771.118
849.233
921.661
985.559
1057.987
1136.102
1200.
</pre>