User:FloraC/Flora's 17-note well temperament - Revision history

Xenllium: Add categories

2024-01-02T12:30:01Z

Add categories

← Older revision		Revision as of 12:30, 2 January 2024
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	Similarly, the neutral third (diminished fourth) ranges mostly between [[11/9]] and [[16/13]], with the smallest interval of 340.737¢ at F#–Bb and the largest interval of 365.145¢ at Bb–C#.		Similarly, the neutral third (diminished fourth) ranges mostly between [[11/9]] and [[16/13]], with the smallest interval of 340.737¢ at F#–Bb and the largest interval of 365.145¢ at Bb–C#.

			[[Category:Pages with Scala files]]
			[[Category:17-tone scales]]
			[[Category:Tempered scales]]

FloraC: /* Definition */

2022-12-23T11:55:43Z

Definition

← Older revision		Revision as of 11:55, 23 December 2022
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	! canou2d.scl		! canou2d.scl
	!		!
	Canou II, Flora Canou's second well temperament, D = 0, single ~~chain~~ edition		Canou II, Flora Canou's second well temperament, D = 0, single circle edition
	17		17
	!		!

FloraC at 11:55, 23 December 2022

2022-12-23T11:55:18Z

← Older revision		Revision as of 11:55, 23 December 2022
Line 7:		Line 7:
	The commas in consideration are the [[17-comma]] ~ 66.7650¢, denoted ''p'', and the [[septimal comma]] ~ 27.2641¢, denoted ''c''.		The commas in consideration are the [[17-comma]] ~ 66.7650¢, denoted ''p'', and the [[septimal comma]] ~ 27.2641¢, denoted ''c''.

	The generator is a perfect fifth ~~tempered to~~ three sizes~~: ''G''<sub>~~1</~~sub>~~, ~~''G''<sub>2</sub>~~, and ~~''G''<sub>3</sub>. Their sizes and places are shown below~~.		The generator is a perfect fifth, which comes in three sizes, with eight 1/5-comma superpyth fifths, a 17edo fifth, and eight neogothic fifths. Specifically,

	* ''G''<sub>1</sub> = P5 + ''c''/5 ~ 707.4078¢		* ''g''<sub>1</sub> = P5 + ''c''/5 ~ 707.4078¢
	: at Bb–F, F–C, C–G, G–D, D–A, A–E, E–B, B–F#.		: at Bb–F, F–C, C–G, G–D, D–A, A–E, E–B, B–F#.

	* ''G''<sub>2</sub> = P5 + ''p''/17 ~ 705.8824¢ = 10\17		* ''g''<sub>2</sub> = P5 + ''p''/17 ~ 705.8824¢ = 10\17
	: at F#–C#.		: at F#–C#.

	* ''G''<sub>3</sub> = P5 + 2''p''/17 - ''c''/5 ~ 704.3569¢		* ''g''<sub>3</sub> = P5 + 2''p''/17 - ''c''/5 ~ 704.3569¢
	: at C#–G#, G#–D#, D#–A#, A#–Gb, Gb–Db, Db–Ab, Ab–Eb, Eb–Bb.		: at C#–G#, G#–D#, D#–A#, A#–Gb, Gb–Db, Db–Ab, Ab–Eb, Eb–Bb.

FloraC: This is no longer labeled as "XVII"

2022-12-23T11:40:24Z

This is no longer labeled as "XVII"

← Older revision		Revision as of 11:40, 23 December 2022
Line 1:		Line 1:
	The '''Canou ~~XVII~~''' is a seventeen-~~note~~ well temperament based on [[17edo\|~~17-et~~]]. In summary, it is 1/5-comma superpyth in the natural keys and close to Neo-Gothic tuning in the remote keys. The goal is the same as that of [[User:FloraC/Flora'~~s_12~~-~~note_well_temperament~~\|Canou ~~XII~~]], but this time superpyth instead of meantone.		The '''Canou II''' is a seventeen-tone well temperament based on [[17edo\|17et]]. In summary, it is 1/5-comma superpyth in the natural keys and close to Neo-Gothic tuning in the remote keys. The goal is the same as that of [[User:FloraC/Flora's 12-note well temperament\|Canou I]], but this time superpyth instead of meantone.

	The result is pretty close to [[George Secor]]'s well temperament, but my design ~~is with~~ [[9/7]] ~~in mind~~ instead of [[14/11]], basically the opposite of ~~his~~. The distribution of the ~~two tunings~~ is also quite different.		The result is pretty close to [[George Secor]]'s well temperament, but this design prioritizes targeting [[9/7]] instead of [[14/11]], basically the opposite of Secor's. The distribution of the generators is also quite different.

	== Definition ==		== Definition ==
Line 20:		Line 20:
	=== As Scala file ===		=== As Scala file ===
	<pre>		<pre>
	! ~~canou17d~~.scl		! canou2d.scl
	!		!
	Canou ~~XVII~~, Flora Canou's well temperament ~~based on 17-et~~, ~~starting with~~ D = 0		Canou II, Flora Canou's second well temperament, D = 0, single chain edition
	17		17
	!		!

FloraC: Created page with "The '''Canou XVII''' is a seventeen-note well temperament based on 17-et. In summary, it is 1/5-comma superpyth in the natural keys and close to Neo-Gothic tuning in..."

2020-09-05T05:51:11Z

Created page with "The '''Canou XVII''' is a seventeen-note well temperament based on 17-et. In summary, it is 1/5-comma superpyth in the natural keys and close to Neo-Gothic tuning in..."

New page

The '''Canou XVII''' is a seventeen-note well temperament based on [[17edo|17-et]]. In summary, it is 1/5-comma superpyth in the natural keys and close to Neo-Gothic tuning in the remote keys. The goal is the same as that of [[User:FloraC/Flora's_12-note_well_temperament|Canou XII]], but this time superpyth instead of meantone.

The result is pretty close to [[George Secor]]'s well temperament, but my design is with [[9/7]] in mind instead of [[14/11]], basically the opposite of his. The distribution of the two tunings is also quite different.

== Definition ==

The commas in consideration are the [[17-comma]] ~ 66.7650¢, denoted ''p'', and the [[septimal comma]] ~ 27.2641¢, denoted ''c''.

The generator is a perfect fifth tempered to three sizes: ''G''1, ''G''2, and ''G''3. Their sizes and places are shown below.

* ''G''1 = P5 + ''c''/5 ~ 707.4078¢
: at Bb–F, F–C, C–G, G–D, D–A, A–E, E–B, B–F#.

* ''G''2 = P5 + ''p''/17 ~ 705.8824¢ = 10\17
: at F#–C#.

* ''G''3 = P5 + 2''p''/17 - ''c''/5 ~ 704.3569¢
: at C#–G#, G#–D#, D#–A#, A#–Gb, Gb–Db, Db–Ab, Ab–Eb, Eb–Bb.

=== As Scala file ===
<pre>
! canou17d.scl
!
Canou XVII, Flora Canou's well temperament based on 17-et, starting with D = 0
17
!
66.0118364414
144.227403157
214.815638451
277.776542324
352.941176471
429.631276902
492.592180775
561.654949784
639.870516500
707.407819225
770.368723098
848.584289814
922.223457676
985.184361549
1057.29806313
1135.51362984
1200.
</pre>

== Intervals ==
The major third gradually shifts between 9/7 in the natural keys and 14/11 in the remote keys.

{| class="wikitable center-all left-4"
|+ Sizes and occurrences of major third
! rowspan="2" | Cents
! colspan="2" | Error
! rowspan="2" | Occurrences
|-
! from 9/7
! from 14/11
|-
| 429.631
| -5.453
| +12.123
| Bb–D, F–A, C–E, G–B, D–F#
|-
| 428.106
| -6.978
| +10.598
| A–C#
|-
| 426.580
| -8.504
| +9.072
| Eb–G
|-
| 425.055
| -10.029
| +7.547
| E–G#
|-
| 423.529
| -11.555
| +6.021
| Ab–C
|-
| 422.004
| -13.080
| +4.496
| B–D#
|-
| 420.478
| -14.606
| +2.971
| Db–F
|-
| 418.953
| -16.131
| +1.445
| F#–A#
|-
| 417.428
| -17.657
| -0.080
| C#–E#, G#–B#, Fb–Ab, Cb–Eb, Gb–Bb
|}

The minor third gradually shifts between 7/6 in the natural keys and 13/11 in the remote keys.

{| class="wikitable center-all left-4"
|+ Sizes and occurrences of minor third
! rowspan="2" | Cents
! colspan="2" | Error
! rowspan="2" | Occurrences
|-
! from 7/6
! from 13/11
|-
| 277.777
| +10.906
| -11.433
| G–Bb, D–F, A–C, E–G, B–D, F#–A
|-
| 279.302
| +12.431
| -9.908
| C#–E
|-
| 280.827
| +13.957
| -8.382
| C–Eb
|-
| 282.353
| +15.482
| -6.857
| G#–B
|-
| 283.878
| +17.008
| -5.331
| F–Ab
|-
| 285.404
| +18.533
| -3.806
| D#–F#
|-
| 286.929
| +20.058
| -2.280
| A#–C#, E#–G#, B#/Db–D#/Fb, Ab–Cb, Eb–Gb, Bb–Db
|}

In addition, the neutral second (augmented unison) ranges between [[12/11]], [[13/12]] and [[14/13]], with the largest interval of 151.855¢ at F–F# and Bb–B, and the smallest interval of 130.498¢ at G#–Bb and C#–Eb.

Similarly, the neutral third (diminished fourth) ranges mostly between [[11/9]] and [[16/13]], with the smallest interval of 340.737¢ at F#–Bb and the largest interval of 365.145¢ at Bb–C#.