Extended meantone notation - Revision history

ArrowHead294 at 22:30, 4 May 2025

2025-05-04T22:30:45Z

← Older revision		Revision as of 22:30, 4 May 2025
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	Meantone can be notated with a [[chain of fifths]] consisting of the 7 natural notes along with sharps and flats:		[[Meantone]] can be notated with a [[chain of fifths]] consisting of the 7 natural notes along with sharps and flats:

	... {{dash\|F𝄫, C𝄫, G𝄫, D𝄫, A𝄫, E𝄫, B𝄫, F♭, C♭, G♭, D♭, A♭, E♭, B♭, F, C, G, D, A, E, B, F♯, C♯, G♯, D♯, A♯, E♯, B♯, F𝄪, C𝄪, G𝄪, D𝄪, A𝄪, E𝄪, B𝄪\|hair\|long}} ...		... {{dash\|F𝄫, C𝄫, G𝄫, D𝄫, A𝄫, E𝄫, B𝄫, F♭, C♭, G♭, D♭, A♭, E♭, B♭, F, C, G, D, A, E, B, F♯, C♯, G♯, D♯, A♯, E♯, B♯, F𝄪, C𝄪, G𝄪, D𝄪, A𝄪, E𝄪, B𝄪\|hair\|long}} ...

	The chain is theoretically infinite, and C♯ and D♭ are not equivalent. When meantone is extended beyond 12 notes, it may require double-sharps, double-flats and beyond. To avoid this, two new accidental pairs are introduced that raise/lower by the [[diesis]] and the [[kleisma]].		The chain is theoretically infinite, and C♯ and D♭ are not (in general) equivalent. When meantone is extended beyond 12 notes, it may require double-sharps, double-flats, and beyond. To avoid this, two new accidental pairs are introduced that raise/lower by the [[diesis]] and the [[kleisma]].

	{\| class="wikitable center-all"		{\| class="wikitable center-all"
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ArrowHead294 at 12:44, 1 May 2025

2025-05-01T12:44:57Z

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TallKite: major rewrite: keep it simple and get to the point!

2025-04-30T07:22:53Z

major rewrite: keep it simple and get to the point!

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ArrowHead294 at 19:56, 5 February 2025

2025-02-05T19:56:43Z

← Older revision		Revision as of 19:56, 5 February 2025
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	* D𝄫↓ and D♭♭♭− are equal to C		* D𝄫↓ and D♭♭♭− are equal to C

	[[~~9–odd–limit~~]] intervals and their notation relative to C:		[[9-odd-limit]] intervals and their notation relative to C:

	{\| class="wikitable center-all"		{\| class="wikitable center-all"

ArrowHead294 at 15:22, 10 December 2024

2024-12-10T15:22:05Z

← Older revision		Revision as of 15:22, 10 December 2024
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	Most musicians are familiar with the [[circle of fifths]]. This is a way of organizing and showing relationships between pitches as a sequence of [[3/2\|fifths]], and applies to any tuning system that can be generated by fifths and octaves. The generalized chain of fifths involves the 7 base note letters of the C major scale, along with sharps, double-sharps, flats, and double-flats (and beyond):		Most musicians are familiar with the [[circle of fifths]]. This is a way of organizing and showing relationships between pitches as a sequence of [[3/2\|fifths]], and applies to any tuning system that can be generated by fifths and octaves. The generalized chain of fifths involves the 7 base note letters of the C major scale, along with sharps, double-sharps, flats, and double-flats (and beyond):

	... {{dash\|F𝄫, C𝄫, G𝄫, D𝄫, A𝄫, E𝄫, B𝄫, F♭, C♭, G♭, D♭, A♭, E♭, B♭, F, C, G, D, A, E, B, F♯, C♯, G♯, D♯, A♯, E♯, B♯, F𝄪, C𝄪, G𝄪, D𝄪, A𝄪, E𝄪, B𝄪\|~~s=thin~~\|d=long}} ...		... {{dash\|F𝄫, C𝄫, G𝄫, D𝄫, A𝄫, E𝄫, B𝄫, F♭, C♭, G♭, D♭, A♭, E♭, B♭, F, C, G, D, A, E, B, F♯, C♯, G♯, D♯, A♯, E♯, B♯, F𝄪, C𝄪, G𝄪, D𝄪, A𝄪, E𝄪, B𝄪\|hair\|long}} ...

	In a general meantone tuning, a sharp is split into 2 different parts, the diesis and the kleisma.		In a general meantone tuning, a sharp is split into 2 different parts, the diesis and the kleisma.
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	For example, in 31 equal, the chromatic scale becomes:		For example, in 31 equal, the chromatic scale becomes:

	{{dash\|C, D𝄫, C♯, D♭, C𝄪, D, E𝄫, D♯, E♭, D𝄪, E, F♭, E♯, F, G𝄫, F♯, G♭, F𝄪, G, A𝄫, G♯, A♭, G𝄪, A, B𝄫, A♯, B♭, A𝄪, B, C♭, B♯, C\|~~s=thin~~\|d=long}}		{{dash\|C, D𝄫, C♯, D♭, C𝄪, D, E𝄫, D♯, E♭, D𝄪, E, F♭, E♯, F, G𝄫, F♯, G♭, F𝄪, G, A𝄫, G♯, A♭, G𝄪, A, B𝄫, A♯, B♭, A𝄪, B, C♭, B♯, C\|hair\|long}}

	Note that the base note letters alternate.		Note that the base note letters alternate.
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	Using semisharps and semiflats, this can be re-written as:		Using semisharps and semiflats, this can be re-written as:

	{{dash\|C, C{{demisharp2}}, C♯, D♭, D{{demiflat2}}, D, D{{demisharp2}}, D♯, E♭, E{{demiflat2}}, E, E{{demisharp2}}, F{{demiflat2}}, F, F{{demisharp2}}, F♯, G♭, G{{demiflat2}}, G, G{{demisharp2}}, G♯, A♭, A{{demiflat2}}, A, A{{demisharp2}}, A♯, B♭, B{{demiflat2}}, B, B{{demisharp2}}, C{{demiflat2}}, C\|~~s=thin~~\|d=long}}		{{dash\|C, C{{demisharp2}}, C♯, D♭, D{{demiflat2}}, D, D{{demisharp2}}, D♯, E♭, E{{demiflat2}}, E, E{{demisharp2}}, F{{demiflat2}}, F, F{{demisharp2}}, F♯, G♭, G{{demiflat2}}, G, G{{demisharp2}}, G♯, A♭, A{{demiflat2}}, A, A{{demisharp2}}, A♯, B♭, B{{demiflat2}}, B, B{{demisharp2}}, C{{demiflat2}}, C\|hair\|long}}
	<!--		<!--
	If true half-sharps and true half-flats are desired, which exactly bisect the chromatic semitone, the meantone fifth is split in half. This creates a new tuning system consisting of a two-dimensional lattice generated by a chain of neutral thirds, with meantone existing as every other note in the generator chain. This adds true half-sharps and half-flats, and creates a "neutral" version of each interval class.		If true half-sharps and true half-flats are desired, which exactly bisect the chromatic semitone, the meantone fifth is split in half. This creates a new tuning system consisting of a two-dimensional lattice generated by a chain of neutral thirds, with meantone existing as every other note in the generator chain. This adds true half-sharps and half-flats, and creates a "neutral" version of each interval class.

ArrowHead294 at 19:56, 9 December 2024

2024-12-09T19:56:10Z

← Older revision		Revision as of 19:56, 9 December 2024
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	\| 1		\| 1
	\| −1		\| −1
	\| Chromatic semitone is tempered out<ref group="note" name="chroma_note">In 7-tone equal temperament, the tempering out of the chromatic semitone means that sharps and flats are redundant (in the sense that they cannot alter the pitch).</ref>,<br>diesis is positive, and kleisma is negative<ref group="note" name="kleisma_note">A negative kleisma means that B♯ is lower in pitch than C♭ and E♯ is lower in pitch than F♭. Conversely, a positive kleisma means B♯ sits higher than C♭ and E♯ sits higher than F♭. In 19-tone equal temperament, the tempering out of the kleisma means that B♯ = C♭ and E♯ = F♭.</ref>		\| Chromatic semitone is tempered out<ref group="note" name="chroma_note">In 7-tone equal temperament, the tempering out of the chromatic semitone means that sharps and flats are redundant (in the sense that they cannot alter the pitch).</ref>,<br>diesis is positive, and kleisma is negative<ref group="note" name="kleisma_note">A negative kleisma means that B♯ is lower in pitch than C♭ and E♯ is lower in pitch than F♭. Conversely, a positive kleisma means B♯ sits higher than C♭ and E♯ sits higher than F♭. In 19-tone equal temperament, the tempering out of the kleisma means that {{nowrap\|B♯ {{=}} C♭}} and {{nowrap\|E♯ {{=}} F♭}}.</ref>
	\|-		\|-
	\| [[12edo\|12edo<br>(standard tuning)]]		\| [[12edo\|12edo<br>(standard tuning)]]

ArrowHead294 at 19:55, 9 December 2024

2024-12-09T19:55:16Z

← Older revision		Revision as of 19:55, 9 December 2024
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	== Notes ==		== Notes ==
	<references group="note" />		<references group="note" />


	{{Navbox notation}}		{{Navbox notation}}

ArrowHead294 at 19:55, 9 December 2024

2024-12-09T19:55:02Z

← Older revision		Revision as of 19:55, 9 December 2024
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	{\| class="wikitable center-all"		{\| class="wikitable center-all"
			\|-
	! colspan="2" \| Symbol		! colspan="2" \| Symbol
	! rowspan="2" \| Interval		! rowspan="2" \| Interval
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	{\| class="wikitable center-all"		{\| class="wikitable center-all"
			\|-
	! rowspan="2" \| Notes per octave		! rowspan="2" \| Notes per octave
	! rowspan="2" \| Approximate<br>[[81/80\|syntonic<br>comma]]<br>fraction		! rowspan="2" \| Approximate<br>[[81/80\|syntonic<br>comma]]<br>fraction
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	{\| class="wikitable center-all"		{\| class="wikitable center-all"
			\|-
	! Note		! Note
	\| C		\| C
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	{{~~Notation navbox~~}}		{{Navbox notation}}

	[[Category:Meantone]]		[[Category:Meantone]]
	[[Category:Notation]]		[[Category:Notation]]

BudjarnLambeth: {{Notation navbox}}

2024-12-02T23:21:03Z

← Older revision		Revision as of 23:21, 2 December 2024
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	== Notes ==		== Notes ==
	<references group="note" />		<references group="note" />


			{{Notation navbox}}

	[[Category:Meantone]]		[[Category:Meantone]]
	[[Category:Notation]]		[[Category:Notation]]

ArrowHead294 at 18:02, 21 May 2024

2024-05-21T18:02:28Z

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