Ptolemy's intense diatonic - Revision history

FloraC: Formatting & style

2025-12-20T09:47:51Z

Formatting & style

← Older revision		Revision as of 09:47, 20 December 2025
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	}}		}}
	{{Wikipedia\|Ptolemy's intense diatonic scale}}		{{Wikipedia\|Ptolemy's intense diatonic scale}}
	[[File:zarlino2.png\|~~500px~~\|thumb\|right\|The left and right handed variations of the just diatonic scale on the [[5-limit]] [[lattice]].]]		[[File:zarlino2.png\|400px\|thumb\|right\|The left and right handed variations of the just diatonic scale on the [[5-limit]] [[lattice]].]]
	'''Ptolemy's intense diatonic''' scale (also known as '''Zarlino''', or simply the '''just diatonic scale''') is a [[heptatonic]] [[5-limit]] [[JI]] [[scale]] with the [[nicetone]] step pattern.		'''Ptolemy's intense diatonic''' scale (also known as '''Zarlino''', or simply the '''just diatonic scale''') is a [[heptatonic]] [[5-limit]] [[JI]] [[scale]] with the [[nicetone]] step pattern. In [[Ben Johnston's notation]], the scale is the basic uninflected diatonic scale. It is a [[chiral scale]], meaning it comes in two variations, which are called right and left-handed. Both versions contain a [[40/27]] wolf fifth.
	In [[Ben Johnston's notation]], the scale is the basic uninflected diatonic scale.
	It is a [[chiral scale]], meaning it comes in two variations, which are called right and left-handed. Both versions contain a [[40/27]] wolf fifth.

	It can be constructed as a [[Fokker block]] in multiple ways, making it a [[wakalix]]. Another derivation is through a [[tetrachord]] consisting of [[16/15]], [[9/8]] and [[10/9]].		It can be constructed as a [[Fokker block]] in multiple ways, making it a [[wakalix]]. Another derivation is through a [[tetrachord]] consisting of [[16/15]], [[9/8]] and [[10/9]].

	It can also be derived from tuning the tonic, dominant and subdominant chords as 5-limit just major chords ([[4:5:6]]): {{dash\|FAC, CEG, GBD}}.		It can also be derived from tuning the tonic, dominant and subdominant chords as 5-limit just major chords ([[4:5:6]]): {{dash\|FAC, CEG, GBD}}.
			{{Clear}}
	<pre>		<pre>
	! zarlino-RH.scl		! zarlino-RH.scl
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	</pre>		</pre>

	The left-handed variation has 10/9 instead of 9/8 on the second degree.		The left-handed variation has 10/9 instead of 9/8 on the second degree. It can be obtained from the right-handed version by reversing its steps. It is most commonly encountered in the 6th mode (with 5/3 as the root) which gives the usual 5-limit minor diatonic: {{dash\|1/1, 9/8, 6/5, 4/3, 3/2, 8/5, 9/5, 2/1}}.
	It can be obtained from the right-handed version by reversing its steps.
	It is most commonly encountered in the 6th mode (with 5/3 as the root) which gives the usual 5-limit minor diatonic: {{dash\|1/1, 9/8, 6/5, 4/3, 3/2, 8/5, 9/5, 2/1}}.

	<pre>		<pre>

Sintel: add graphic

2025-12-19T17:11:13Z

add graphic

← Older revision		Revision as of 17:11, 19 December 2025
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	}}		}}
	{{Wikipedia\|Ptolemy's intense diatonic scale}}		{{Wikipedia\|Ptolemy's intense diatonic scale}}
			[[File:zarlino2.png\|500px\|thumb\|right\|The left and right handed variations of the just diatonic scale on the [[5-limit]] [[lattice]].]]
	'''Ptolemy's intense diatonic''' scale (also known as '''Zarlino''', or simply the '''just diatonic scale''') is a [[heptatonic]] [[5-limit]] [[JI]] [[scale]] with the [[nicetone]] step pattern.		'''Ptolemy's intense diatonic''' scale (also known as '''Zarlino''', or simply the '''just diatonic scale''') is a [[heptatonic]] [[5-limit]] [[JI]] [[scale]] with the [[nicetone]] step pattern.
	In [[Ben Johnston's notation]], the scale is the basic uninflected diatonic scale.		In [[Ben Johnston's notation]], the scale is the basic uninflected diatonic scale.

Hstraub at 21:55, 29 November 2025

2025-11-29T21:55:33Z

← Older revision		Revision as of 21:55, 29 November 2025
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			{{interwiki
			\| de = Durtonleiter
			\| en = Ptolemy's intense diatonic
			}}
	{{Wikipedia\|Ptolemy's intense diatonic scale}}		{{Wikipedia\|Ptolemy's intense diatonic scale}}
	'''Ptolemy's intense diatonic''' scale (also known as '''Zarlino''', or simply the '''just diatonic scale''') is a [[heptatonic]] [[5-limit]] [[JI]] [[scale]] with the [[nicetone]] step pattern.		'''Ptolemy's intense diatonic''' scale (also known as '''Zarlino''', or simply the '''just diatonic scale''') is a [[heptatonic]] [[5-limit]] [[JI]] [[scale]] with the [[nicetone]] step pattern.

TallKite: added the fact that it contains a 40/27 fifth

2025-10-30T01:47:18Z

added the fact that it contains a 40/27 fifth

← Older revision		Revision as of 01:47, 30 October 2025
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	'''Ptolemy's intense diatonic''' scale (also known as '''Zarlino''', or simply the '''just diatonic scale''') is a [[heptatonic]] [[5-limit]] [[JI]] [[scale]] with the [[nicetone]] step pattern.		'''Ptolemy's intense diatonic''' scale (also known as '''Zarlino''', or simply the '''just diatonic scale''') is a [[heptatonic]] [[5-limit]] [[JI]] [[scale]] with the [[nicetone]] step pattern.
	In [[Ben Johnston's notation]], the scale is the basic uninflected diatonic scale.		In [[Ben Johnston's notation]], the scale is the basic uninflected diatonic scale.
	It is a [[chiral scale]], meaning it comes in two variations, which are called right and left-handed.		It is a [[chiral scale]], meaning it comes in two variations, which are called right and left-handed. Both versions contain a [[40/27]] wolf fifth.

	It can be constructed as a [[Fokker block]] in multiple ways, making it a [[wakalix]]. Another derivation is through a [[tetrachord]] consisting of [[16/15]], [[9/8]] and [[10/9]].		It can be constructed as a [[Fokker block]] in multiple ways, making it a [[wakalix]]. Another derivation is through a [[tetrachord]] consisting of [[16/15]], [[9/8]] and [[10/9]].

Dummy index: /* See also */ +link

2025-10-15T15:27:24Z

Sintel: add info about chirality

2025-04-26T13:47:54Z

add info about chirality

← Older revision		Revision as of 13:47, 26 April 2025
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	{{Wikipedia\|Ptolemy's intense diatonic scale}}		{{Wikipedia\|Ptolemy's intense diatonic scale}}
	'''Ptolemy's intense diatonic''' scale (also known as '''Zarlino''', or simply the '''just diatonic scale''') is a [[heptatonic]] [[5-limit]] [[JI]] [[scale]] with the [[nicetone]] step pattern. ~~It is also the basis of~~ [[Ben Johnston's notation]].		'''Ptolemy's intense diatonic''' scale (also known as '''Zarlino''', or simply the '''just diatonic scale''') is a [[heptatonic]] [[5-limit]] [[JI]] [[scale]] with the [[nicetone]] step pattern.
			In [[Ben Johnston's notation]], the scale is the basic uninflected diatonic scale.
			It is a [[chiral scale]], meaning it comes in two variations, which are called right and left-handed.

	It can be constructed as a [[Fokker block]] in multiple ways, making it a [[wakalix]]. Another derivation is through a [[tetrachord]] consisting of [[16/15]], [[9/8]] and [[10/9]].		It can be constructed as a [[Fokker block]] in multiple ways, making it a [[wakalix]]. Another derivation is through a [[tetrachord]] consisting of [[16/15]], [[9/8]] and [[10/9]].
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	<pre>		<pre>
	! zarlino-RH~~.scl AKA dimeanmav1~~.scl		! zarlino-RH.scl
	Ptolemy's Intense Diatonic Systonon, also Zarlino's scale, mavchrome7, Dwarf(<7 11 16\|), or Dicot-meantone-mavila wakalix 1		Ptolemy's Intense Diatonic Systonon, also Zarlino's scale, mavchrome7, Dwarf(<7 11 16\|), or Dicot-meantone-mavila wakalix 1
	!		!
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	</pre>		</pre>

	The left-handed variation has 10/9 instead of 9/8 on the second degree. It is most commonly encountered in the 6th mode (with 5/3 as the root) which gives the usual 5-limit minor diatonic: {{dash\|1/1, 9/8, 6/5, 4/3, 3/2, 8/5, 9/5, 2/1}}.		The left-handed variation has 10/9 instead of 9/8 on the second degree.
			It can be obtained from the right-handed version by reversing its steps.
			It is most commonly encountered in the 6th mode (with 5/3 as the root) which gives the usual 5-limit minor diatonic: {{dash\|1/1, 9/8, 6/5, 4/3, 3/2, 8/5, 9/5, 2/1}}.

	<pre>		<pre>
	! zarlino-LH.scl		! zarlino-LH.scl
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	2/1		2/1
	</pre>		</pre>

			== Fokker blocks ==
			The scale can be found in three different [[Fokker block]]s, using the chromas [[25/24]], [[81/80]] and [[135/128]].

	; Fokker block 1		; Fokker block 1

Sintel: fix the tetrachord ordering

2025-04-24T22:36:58Z

fix the tetrachord ordering

← Older revision		Revision as of 22:36, 24 April 2025
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	'''Ptolemy's intense diatonic''' scale (also known as '''Zarlino''', or simply the '''just diatonic scale''') is a [[heptatonic]] [[5-limit]] [[JI]] [[scale]] with the [[nicetone]] step pattern. It is also the basis of [[Ben Johnston's notation]].		'''Ptolemy's intense diatonic''' scale (also known as '''Zarlino''', or simply the '''just diatonic scale''') is a [[heptatonic]] [[5-limit]] [[JI]] [[scale]] with the [[nicetone]] step pattern. It is also the basis of [[Ben Johnston's notation]].

	It can be constructed as a [[Fokker block]] in multiple ways, making it a [[wakalix]]. Another derivation is through a [[tetrachord]] consisting of [[9/8]], [[10/9]] and [[16/15]].		It can be constructed as a [[Fokker block]] in multiple ways, making it a [[wakalix]]. Another derivation is through a [[tetrachord]] consisting of [[16/15]], [[9/8]] and [[10/9]].

	It can also be derived from tuning the tonic, dominant and subdominant chords as 5-limit just major chords ([[4:5:6]]): {{dash\|FAC, CEG, GBD}}.		It can also be derived from tuning the tonic, dominant and subdominant chords as 5-limit just major chords ([[4:5:6]]): {{dash\|FAC, CEG, GBD}}.

Sintel: LH minor scale

2025-04-03T18:31:21Z

LH minor scale

← Older revision		Revision as of 18:31, 3 April 2025
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	2/1		2/1
	</pre>		</pre>

			The left-handed variation has 10/9 instead of 9/8 on the second degree. It is most commonly encountered in the 6th mode (with 5/3 as the root) which gives the usual 5-limit minor diatonic: {{dash\|1/1, 9/8, 6/5, 4/3, 3/2, 8/5, 9/5, 2/1}}.
	<pre>		<pre>
	! zarlino-LH.scl		! zarlino-LH.scl

Sintel: remove polynomials

2025-04-03T18:25:17Z

remove polynomials

← Older revision		Revision as of 18:25, 3 April 2025
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	! zarlino-RH.scl AKA dimeanmav1.scl		! zarlino-RH.scl AKA dimeanmav1.scl
	Ptolemy's Intense Diatonic Systonon, also Zarlino's scale, mavchrome7, Dwarf(<7 11 16\|), or Dicot-meantone-mavila wakalix 1		Ptolemy's Intense Diatonic Systonon, also Zarlino's scale, mavchrome7, Dwarf(<7 11 16\|), or Dicot-meantone-mavila wakalix 1
	~~! x^7-11x^5-10x^4+21x^3+30x^2+9*x~~
	!		!
	! wakalix info:		! wakalix info:
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	!		!
	Ptolemy's Intense Diatonic Systonon, also Zarlino's scale, mavchrome7, Dwarf(<7 11 16\|)		Ptolemy's Intense Diatonic Systonon, also Zarlino's scale, mavchrome7, Dwarf(<7 11 16\|)
	~~! x^7-11x^5-10x^4+21x^3+30x^2+9*x~~
	7		7
	!		!

Sintel: constructions

2025-04-03T18:18:48Z

constructions

← Older revision		Revision as of 18:18, 3 April 2025
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	{{Wikipedia\|Ptolemy's intense diatonic scale}}		{{Wikipedia\|Ptolemy's intense diatonic scale}}
	'''Ptolemy's intense diatonic''' scale (also known as '''Zarlino''', or simply the '''just diatonic scale''') is a [[heptatonic]] [[5-limit]] [[JI]] [[scale]] with the [[nicetone]] step pattern. It is also the basis of [[Ben Johnston's notation]].		'''Ptolemy's intense diatonic''' scale (also known as '''Zarlino''', or simply the '''just diatonic scale''') is a [[heptatonic]] [[5-limit]] [[JI]] [[scale]] with the [[nicetone]] step pattern. It is also the basis of [[Ben Johnston's notation]].

			It can be constructed as a [[Fokker block]] in multiple ways, making it a [[wakalix]]. Another derivation is through a [[tetrachord]] consisting of [[9/8]], [[10/9]] and [[16/15]].

			It can also be derived from tuning the tonic, dominant and subdominant chords as 5-limit just major chords ([[4:5:6]]): {{dash\|FAC, CEG, GBD}}.

	<pre>		<pre>

← Older revision		Revision as of 15:27, 15 October 2025
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	* [[Nicetone]] – regular 3L 2m 2s scale		* [[Nicetone]] – regular 3L 2m 2s scale
	* [[Superzarlino]]		* [[Superzarlino]]
			* [[mavchrome6]], [[dimeanmav2]]

	[[Category:7-tone scales]]		[[Category:7-tone scales]]