User:FloraC/Flora's 12-note well temperament - Revision history

Xenllium: Add categories

2024-01-02T12:26:24Z

Add categories

← Older revision		Revision as of 12:26, 2 January 2024
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	{\| class="wikitable center-all left-4"		{\| class="wikitable center-all left-4"
	\|+ Sizes and occurrences of ~~major~~ third		\|+ Sizes and occurrences of minor third
	! rowspan="2" \| Cents		! rowspan="2" \| Cents
	! colspan="2" \| Error		! colspan="2" \| Error
Line 126:		Line 126:
	\| Bb–Db, D#–F#		\| Bb–Db, D#–F#
	\|}		\|}

			[[Category:Pages with Scala files]]
			[[Category:12-tone scales]]
			[[Category:Tempered scales]]

FloraC at 11:48, 23 December 2022

2022-12-23T11:48:44Z

← Older revision		Revision as of 11:48, 23 December 2022
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	The commas in consideration are the [[Pythagorean comma]] ~ 23.4600¢, denoted ''p'', and the [[syntonic comma]] ~ 21.5063¢, denoted ''c''.		The commas in consideration are the [[Pythagorean comma]] ~ 23.4600¢, denoted ''p'', and the [[syntonic comma]] ~ 21.5063¢, 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 four 1/5-comma meantone fifths, four 12edo fifths, and four counterpyth fifths. Specifically,

	* ''G''<sub>1</sub> = P5 - ''c''/5 ~ 697.6537¢		* ''g''<sub>1</sub> = P5 - ''c''/5 ~ 697.6537¢
	: at C–G, G–D, D–A, A–E.		: at C–G, G–D, D–A, A–E.

	* ''G''<sub>2</sub> = P5 - ''p''/12 = 700¢ = 7\12		* ''g''<sub>2</sub> = P5 - ''p''/12 = 700¢ = 7\12
	: at Bb–F, F–C, E–B, B–F#.		: at Bb–F, F–C, E–B, B–F#.

	* ''G''<sub>3</sub> = P5 - ''p''/6 + ''c''/5 ~ 702.3463¢		* ''g''<sub>3</sub> = P5 - ''p''/6 + ''c''/5 ~ 702.3463¢
	: at F#–C#, C#–G#/Ab, G#/Ab–Eb, Eb–Bb.		: at F#–C#, C#–G#/Ab, G#/Ab–Eb, Eb–Bb.

FloraC: This is no longer labeled as "XII"

2022-12-23T11:37:37Z

This is no longer labeled as "XII"

← Older revision		Revision as of 11:37, 23 December 2022
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	The '''Canou ~~XII~~''' is a twelve-~~note~~ well temperament based on [[12edo\|~~12-et~~]]. In summary, it is [[1/~~5_syntonic_comma_meantone~~\|1/5-comma meantone]] in the natural keys and close to [[Pythagorean tuning]] in the remote keys. The goal of this temperament is to add a little bit spice to the equal [https://youtu.be/F9Zv6MGdh7Y shades of gray] without messing things up.		The '''Canou I''' is a twelve-tone well temperament based on [[12edo\|12et]]. In summary, it is [[1/5 syntonic comma meantone\|1/5-comma meantone]] in the natural keys and close to [[Pythagorean tuning]] in the remote keys. The goal of this temperament is to add a little bit spice to the equal [https://youtu.be/F9Zv6MGdh7Y shades of gray] without messing things up.

	== Definition ==		== Definition ==
Line 18:		Line 18:
	=== As Scala file ===		=== As Scala file ===
	<pre>		<pre>
	! ~~canou12d~~.scl		! canou1d.scl
	!		!
	Canou ~~XII~~, Flora Canou's well temperament ~~based on 12-et~~, ~~starting with~~ D = 0		Canou I, Flora Canou's first well temperament, D = 0, single circle edition
	12		12
	!		!

FloraC: Improve table

2020-09-05T05:40:06Z

Improve table

← Older revision		Revision as of 05:40, 5 September 2020
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	{\| class="wikitable center-all left-4"		{\| class="wikitable center-all left-4"
	\|+ Sizes and occurrences of major third		\|+ Sizes and occurrences of major third
			! rowspan="2" \| Cents
			! colspan="2" \| Error
			! rowspan="2" \| Occurrences
	\|-		\|-
	! ~~Cents~~		! from 5/4
	~~! Error~~ from 5/4		! from 81/64
	! ~~Error~~ from 81/64
	~~! Occurrences~~
	\|-		\|-
	\| 390.615		\| 390.615
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	{\| class="wikitable center-all left-4"		{\| class="wikitable center-all left-4"
	\|+ Sizes and occurrences of major third		\|+ Sizes and occurrences of major third
			! rowspan="2" \| Cents
			! colspan="2" \| Error
			! rowspan="2" \| Occurrences
	\|-		\|-
	! ~~Cents~~		! from 6/5
	~~! Error~~ from 6/5		! from 32/27
	! ~~Error~~ from 32/27
	~~! Occurrences~~
	\|-		\|-
	\| 307.039		\| 307.039

FloraC: Created page with "The '''Canou XII''' is a twelve-note well temperament based on 12-et. In summary, it is 1/5-comma meantone in the natural keys and cl..."

2020-09-05T05:37:30Z

Created page with "The '''Canou XII''' is a twelve-note well temperament based on 12-et. In summary, it is 1/5-comma meantone in the natural keys and cl..."

New page

The '''Canou XII''' is a twelve-note well temperament based on [[12edo|12-et]]. In summary, it is [[1/5_syntonic_comma_meantone|1/5-comma meantone]] in the natural keys and close to [[Pythagorean tuning]] in the remote keys. The goal of this temperament is to add a little bit spice to the equal [https://youtu.be/F9Zv6MGdh7Y shades of gray] without messing things up.

== Definition ==

The commas in consideration are the [[Pythagorean comma]] ~ 23.4600¢, denoted ''p'', and the [[syntonic comma]] ~ 21.5063¢, 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 ~ 697.6537¢
: at C–G, G–D, D–A, A–E.

* ''G''2 = P5 - ''p''/12 = 700¢ = 7\12
: at Bb–F, F–C, E–B, B–F#.

* ''G''3 = P5 - ''p''/6 + ''c''/5 ~ 702.3463¢
: at F#–C#, C#–G#/Ab, G#/Ab–Eb, Eb–Bb.

=== As Scala file ===
<pre>
! canou12d.scl
!
Canou XII, Flora Canou's well temperament based on 12-et, starting with D = 0
12
!
102.346257054
195.307485892
304.692514108
395.307485892
502.346257054
600.
697.653742946
804.692514108
895.307485892
1004.692514108
1097.653742956
1200.
</pre>

== Intervals ==
The major third gradually shifts between [[5/4]] in the natural keys and [[81/64]] in the remote keys.

{| class="wikitable center-all left-4"
|+ Sizes and occurrences of major third
|-
! Cents
! Error from 5/4
! Error from 81/64
! Occurrences
|-
| 390.615
| +4.301
| -17.205
| C–E
|-
| 392.961
| +6.648
| -14.859
| F–A, G–B
|-
| 395.307
| +8.994
| -12.513
| Bb–D, D–F#
|-
| 400.000
| +13.686
| -7.820
| Eb–G, A–C#
|-
| 404.693
| +18.379
| -3.127
| Ab–C, E–G#
|-
| 407.039
| +20.725
| -0.781
| Db–F, B–D#
|-
| 409.385
| +23.071
| +1.565
| F#/Gb–A#/Bb
|}

The minor third gradually shifts between [[6/5]] in the natural keys and [[32/27]] in the remote keys.

{| class="wikitable center-all left-4"
|+ Sizes and occurrences of major third
|-
! Cents
! Error from 6/5
! Error from 32/27
! Occurrences
|-
| 307.039
| -8.603
| +12.904
| A–C, E–G
|-
| 304.693
| -10.949
| +10.558
| D–F, B–D
|-
| 302.346
| -13.295
| +8.211
| G–Bb, F#–A
|-
| 297.654
| -17.988
| +3.519
| C–Eb, C#–E
|-
| 295.307
| -20.334
| +1.172
| F–Ab, G#–B
|-
| 292.961
| -22.680
| -1.174
| Bb–Db, D#–F#
|}