Heptatonic notation - Revision history

ArrowHead294 at 18:02, 11 February 2025

2025-02-11T18:02:26Z

← Older revision		Revision as of 18:02, 11 February 2025
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	==Purpose and Principles==		== Purpose and Principles ==
	I{{who}} developed '''heptatonic notation''' in order to notate my microtonal music, which is written in a number of different [[EDO\|edos]]. Some principles were followed in the development this [[notation]] system:		I{{who}} developed '''heptatonic notation''' in order to notate my microtonal music, which is written in a number of different [[EDO\|edos]]. Some principles were followed in the development this [[notation]] system:

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	These periodic patterns occur because the sum of step sizes must equal the edo's order, and for any (L, s) MOS there is only one scale-step pattern.		These periodic patterns occur because the sum of step sizes must equal the edo's order, and for any (L, s) MOS there is only one scale-step pattern.

	==Accidentals==		== Accidentals ==
	For edos 7(n-1)+1 to 7n, the large step is n edo-intervals, so n-1 unique accidentals of each flat/sharp are required, plus a natural accidental. This ensures that the maximum or minimum accidentals always modify a nominal to a neighboring nominal, as in the double-flats and double-sharps of standard notation. I chose the following twenty-five accidentals to be usable with the [http://www.ekmelic-music.org/en/extra/ekmelily.htm Ekmelily] extension to [http://lilypond.org/ Lilypond], which I use to notate my music:		For edos 7(n-1)+1 to 7n, the large step is n edo-intervals, so n-1 unique accidentals of each flat/sharp are required, plus a natural accidental. This ensures that the maximum or minimum accidentals always modify a nominal to a neighboring nominal, as in the double-flats and double-sharps of standard notation. I chose the following twenty-five accidentals to be usable with the [http://www.ekmelic-music.org/en/extra/ekmelily.htm Ekmelily] extension to [http://lilypond.org/ Lilypond], which I use to notate my music:

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	[https://www.youtube.com/watch?v=jagxI__W-Mg Palinkalin Viharo (Flowers in the Mist)] by Jake Huryn ([https://drive.google.com/file/d/0BwJHTddN0-rdUFdwMEtfYnFJZ0E/view Score]): 22edo		[https://www.youtube.com/watch?v=jagxI__W-Mg Palinkalin Viharo (Flowers in the Mist)] by Jake Huryn ([https://drive.google.com/file/d/0BwJHTddN0-rdUFdwMEtfYnFJZ0E/view Score]): 22edo

			{{Navbox notation}}
	{{~~Notation navbox~~}}

	[[Category:notation]]		[[Category:notation]]

ArrowHead294: ArrowHead294 moved page Heptatonic Notation to Heptatonic notation: &lt;nowiki&gt;[[WP:NCCAPS]]&lt;/nowiki&gt;

2025-02-11T18:01:42Z

ArrowHead294 moved page Heptatonic Notation to Heptatonic notation: &lt;nowiki&gt;WP:NCCAPS&lt;/nowiki&gt;

← Older revision	Revision as of 18:01, 11 February 2025
(No difference)

BudjarnLambeth: Links

2024-12-24T06:28:51Z

Links

← Older revision		Revision as of 06:28, 24 December 2024
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	==Purpose and Principles==		==Purpose and Principles==
	I{{who}} developed '''heptatonic notation''' in order to notate my microtonal music, which is written in a number of different [[EDO\|edos]]. Some principles were followed in the development this notation system:		I{{who}} developed '''heptatonic notation''' in order to notate my microtonal music, which is written in a number of different [[EDO\|edos]]. Some principles were followed in the development this [[notation]] system:

	<ul><li>It should be nearly consistent with standard modern music notation.</li><li>It should be consistent between different edos.</li><li>It should be as non-arbitrary as possible.</li></ul>		<ul><li>It should be nearly consistent with standard modern music notation.</li><li>It should be consistent between different edos.</li><li>It should be as non-arbitrary as possible.</li></ul>

	From these principles I decided that it should be based on [[Nominal-Accidental_Chains\|nominal-accidental chains]], with seven nominals to an octave. In addition, accidentals should both be based on those of standard notation and give an approximation of their displacement size. From these principles is derived the fundamental rule behind this notation system:		From these principles I decided that it should be based on [[Nominal-Accidental_Chains\|nominal-accidental chains]], with seven nominals to an [[octave]]. In addition, accidentals should both be based on those of standard notation and give an approximation of their displacement size. From these principles is derived the fundamental rule behind this notation system:

	<ul><li>For each edo, nominals are assigned to the first mode of the [[Maximal_evenness\|maximally even]] heptatonic [[MOSScales\|MOS]].</li></ul>		<ul><li>For each edo, nominals are assigned to the first mode of the [[Maximal_evenness\|maximally even]] heptatonic [[MOSScales\|MOS]].</li></ul>

BudjarnLambeth: /* Scores and score-videos */

2024-12-03T03:28:37Z

Scores and score-videos

← Older revision		Revision as of 03:28, 3 December 2024
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	[[Category:notation]]		[[Category:notation]]
	~~[[Category:Pages with unattributed statements]]~~

BudjarnLambeth: /* Purpose and Principles */ replace manual stuff with proper who template

2024-12-03T03:25:11Z

Purpose and Principles: replace manual stuff with proper who template

← Older revision		Revision as of 03:25, 3 December 2024
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	==Purpose and Principles==		==Purpose and Principles==
	I~~<sup>~~{{~~lbrack}}[[Template:Who\|''~~who~~?'']]{{rbrack~~}}~~</sup>~~ developed '''heptatonic notation''' in order to notate my microtonal music, which is written in a number of different [[EDO\|edos]]. Some principles were followed in the development this notation system:		I{{who}} developed '''heptatonic notation''' in order to notate my microtonal music, which is written in a number of different [[EDO\|edos]]. Some principles were followed in the development this notation system:

	<ul><li>It should be nearly consistent with standard modern music notation.</li><li>It should be consistent between different edos.</li><li>It should be as non-arbitrary as possible.</li></ul>		<ul><li>It should be nearly consistent with standard modern music notation.</li><li>It should be consistent between different edos.</li><li>It should be as non-arbitrary as possible.</li></ul>

BudjarnLambeth at 23:49, 2 December 2024

2024-12-02T23:49:20Z

← Older revision		Revision as of 23:49, 2 December 2024
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	==Purpose and Principles==		==Purpose and Principles==
	I<sup>[[Template:Who\|who?]]</sup> developed '''heptatonic notation''' in order to notate my microtonal music, which is written in a number of different [[EDO\|edos]]. Some principles were followed in the development this notation system:		I<sup>{{lbrack}}[[Template:Who\|''who?'']]{{rbrack}}</sup> developed '''heptatonic notation''' in order to notate my microtonal music, which is written in a number of different [[EDO\|edos]]. Some principles were followed in the development this notation system:

	<ul><li>It should be nearly consistent with standard modern music notation.</li><li>It should be consistent between different edos.</li><li>It should be as non-arbitrary as possible.</li></ul>		<ul><li>It should be nearly consistent with standard modern music notation.</li><li>It should be consistent between different edos.</li><li>It should be as non-arbitrary as possible.</li></ul>

BudjarnLambeth: Add {{who}} and {{Notation navbox}}

2024-12-02T23:48:35Z

Add {{who}} and {{Notation navbox}}

← Older revision		Revision as of 23:48, 2 December 2024
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	=Purpose and Principles=		==Purpose and Principles==
	I developed heptatonic notation in order to notate my microtonal music, which is written in a number of different [[EDO\|edos]]. Some principles were followed in the development this notation system:		I<sup>[[Template:Who\|who?]]</sup> developed '''heptatonic notation''' in order to notate my microtonal music, which is written in a number of different [[EDO\|edos]]. Some principles were followed in the development this notation system:

	<ul><li>It should be nearly consistent with standard modern music notation.</li><li>It should be consistent between different edos.</li><li>It should be as non-arbitrary as possible.</li></ul>		<ul><li>It should be nearly consistent with standard modern music notation.</li><li>It should be consistent between different edos.</li><li>It should be as non-arbitrary as possible.</li></ul>
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	<ul><li>For each edo, nominals are assigned to the first mode of the [[Maximal_evenness\|maximally even]] heptatonic [[MOSScales\|MOS]].</li></ul>		<ul><li>For each edo, nominals are assigned to the first mode of the [[Maximal_evenness\|maximally even]] heptatonic [[MOSScales\|MOS]].</li></ul>

	=Nominals=		==Nominals==
	By finding these particular MOS scales in each edo, we can find that they, and thus that edo's nominals, follow a number of patterns:		By finding these particular MOS scales in each edo, we can find that they, and thus that edo's nominals, follow a number of patterns:

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	These periodic patterns occur because the sum of step sizes must equal the edo's order, and for any (L, s) MOS there is only one scale-step pattern.		These periodic patterns occur because the sum of step sizes must equal the edo's order, and for any (L, s) MOS there is only one scale-step pattern.

	=Accidentals=		==Accidentals==
	For edos 7(n-1)+1 to 7n, the large step is n edo-intervals, so n-1 unique accidentals of each flat/sharp are required, plus a natural accidental. This ensures that the maximum or minimum accidentals always modify a nominal to a neighboring nominal, as in the double-flats and double-sharps of standard notation. I chose the following twenty-five accidentals to be usable with the [http://www.ekmelic-music.org/en/extra/ekmelily.htm Ekmelily] extension to [http://lilypond.org/ Lilypond], which I use to notate my music:		For edos 7(n-1)+1 to 7n, the large step is n edo-intervals, so n-1 unique accidentals of each flat/sharp are required, plus a natural accidental. This ensures that the maximum or minimum accidentals always modify a nominal to a neighboring nominal, as in the double-flats and double-sharps of standard notation. I chose the following twenty-five accidentals to be usable with the [http://www.ekmelic-music.org/en/extra/ekmelily.htm Ekmelily] extension to [http://lilypond.org/ Lilypond], which I use to notate my music:

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	(To be continued. Feedback welcome, as I'm sure there are ways to make it better!)		(To be continued. Feedback welcome, as I'm sure there are ways to make it better!)

	=Scores and score-videos=		==Scores and score-videos==
	[https://www.youtube.com/watch?v=jagxI__W-Mg Palinkalin Viharo (Flowers in the Mist)] by Jake Huryn ([https://drive.google.com/file/d/0BwJHTddN0-rdUFdwMEtfYnFJZ0E/view Score]): 22edo		[https://www.youtube.com/watch?v=jagxI__W-Mg Palinkalin Viharo (Flowers in the Mist)] by Jake Huryn ([https://drive.google.com/file/d/0BwJHTddN0-rdUFdwMEtfYnFJZ0E/view Score]): 22edo


			{{Notation navbox}}

	[[Category:notation]]		[[Category:notation]]
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Wikispaces>FREEZE at 00:00, 17 July 2018

2018-07-17T00:00:00Z

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Wikispaces>jake.huryn: Imported revision 612807123 - Original comment:

2017-05-14T00:30:34Z

**Imported revision 612807123 - Original comment: **

Wikispaces>jake.huryn: Imported revision 612807115 - Original comment:

2017-05-14T00:30:04Z

**Imported revision 612807115 - Original comment: **

← Older revision		Revision as of 00:30, 14 May 2017
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	<h2>IMPORTED REVISION FROM WIKISPACES</h2>		<h2>IMPORTED REVISION FROM WIKISPACES</h2>
	This is an imported revision from Wikispaces. The revision metadata is included below for reference:<br>		This is an imported revision from Wikispaces. The revision metadata is included below for reference:<br>
	: This revision was by author [[User:jake.huryn\|jake.huryn]] and made on <tt>2017-05-14 00:30:04 UTC</tt>.<br>		: This revision was by author [[User:jake.huryn\|jake.huryn]] and made on <tt>2017-05-14 00:30:34 UTC</tt>.<br>
	: The original revision id was <tt>~~612807115~~</tt>.<br>		: The original revision id was <tt>612807123</tt>.<br>
	: The revision comment was: <tt></tt><br>		: The revision comment was: <tt></tt><br>
	The revision contents are below, presented both in the original Wikispaces Wikitext format, and in HTML exactly as Wikispaces rendered it.<br>		The revision contents are below, presented both in the original Wikispaces Wikitext format, and in HTML exactly as Wikispaces rendered it.<br>
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	* 6: bb dbv db^ b dv d^ n ‡v ‡^ # ‡#v ‡#^ x		* 6: bb dbv db^ b dv d^ n ‡v ‡^ # ‡#v ‡#^ x
	* 7: bb dbv db bv b^ d d^ n ‡v ‡ #v #^ ‡# ‡#^ x		* 7: bb dbv db bv b^ d d^ n ‡v ‡ #v #^ ‡# ‡#^ x
	* 8: bb dbv db bv b b^ d d^ n ‡v ‡ #v # #^ ‡# ‡#^ x (Because this results in values exactly in between twelfths, some discretion was used to determine these to be the most intuitive.)		* 8: bb dbv db bv b b^ d d^ n ‡v ‡ #v # #^ ‡# ‡#^ x (Because this results in values exactly in between twelfths, some discretion in was used in rounding to determine these to be the most intuitive.)
	* 9: bb bb^ db db^ bv b^ dv d nv n n^ ‡ ‡^ #v #^ ‡#v ‡# xv x		* 9: bb bb^ db db^ bv b^ dv d nv n n^ ‡ ‡^ #v #^ ‡#v ‡# xv x
	* 10: bb bb^ dbv db^ bv b b^ dv d^ nv n n^ ‡v ‡^ #v # #^ ‡#v ‡#^ xv x		* 10: bb bb^ dbv db^ bv b b^ dv d^ nv n n^ ‡v ‡^ #v # #^ ‡#v ‡#^ xv x
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	<br />		<br />
	where bb is a double flat, db is a three-half flat, b is a flat, d is a half-flat, n is a natural, ‡ is a half-sharp, # is a sharp, ‡# is a three-half sharp, and x is a double sharp. The v and ^ are arrows which are attached to the bottom and top of the accidentals, respectively. Because there are twelve flats and twelve sharps, these accidentals allow notation up to 84edo with full enharmonicity, as described above. In order to notate edos which use fewer accidentals, the accidentals used are chosen to best approximate the required modification value, assuming that the above accidentals are in increments of perfect twelfth-accidentals. For example, suppose we wish to notate 45edo; 45 = 76+3, so seven sharp and seven flat accidentals are required. To determine, say, the three-sevenths sharp we multiply that value by twelve: 123/7 = 5.14 ≈ 5, so we use the five-twelfths sharp, or #v. Doing this for all sets of fewer than or equal to twelve accidentals per sharp/flat class, we find the following:<br />		where bb is a double flat, db is a three-half flat, b is a flat, d is a half-flat, n is a natural, ‡ is a half-sharp, # is a sharp, ‡# is a three-half sharp, and x is a double sharp. The v and ^ are arrows which are attached to the bottom and top of the accidentals, respectively. Because there are twelve flats and twelve sharps, these accidentals allow notation up to 84edo with full enharmonicity, as described above. In order to notate edos which use fewer accidentals, the accidentals used are chosen to best approximate the required modification value, assuming that the above accidentals are in increments of perfect twelfth-accidentals. For example, suppose we wish to notate 45edo; 45 = 76+3, so seven sharp and seven flat accidentals are required. To determine, say, the three-sevenths sharp we multiply that value by twelve: 123/7 = 5.14 ≈ 5, so we use the five-twelfths sharp, or #v. Doing this for all sets of fewer than or equal to twelve accidentals per sharp/flat class, we find the following:<br />
	<ul><li>For two accidentals: bb b n # x</li><li>3: bb db^ dv n ‡^ ‡#v x</li><li>4: bb db b d n ‡ # ‡# x</li><li>5: bb dbv bv b^ d^ n ‡v #v #^ ‡#^ x</li><li>6: bb dbv db^ b dv d^ n ‡v ‡^ # ‡#v ‡#^ x</li><li>7: bb dbv db bv b^ d d^ n ‡v ‡ #v #^ ‡# ‡#^ x</li><li>8: bb dbv db bv b b^ d d^ n ‡v ‡ #v # #^ ‡# ‡#^ x (Because this results in values exactly in between twelfths, some discretion was used to determine these to be the most intuitive.)</li><li>9: bb bb^ db db^ bv b^ dv d nv n n^ ‡ ‡^ #v #^ ‡#v ‡# xv x</li><li>10: bb bb^ dbv db^ bv b b^ dv d^ nv n n^ ‡v ‡^ #v # #^ ‡#v ‡#^ xv x</li><li>11: bb bb^ dbv db db^ bv b b^ dv d d^ nv n^ ‡v ‡ ‡^ #v # #^ ‡#v ‡# ‡#^ xv x</li><li>12: bb bb^ dbv db db^ bv b b^ dv d d^ nv n n^ ‡v ‡ ‡^ #v # #^ ‡#v ‡# ‡#^ xv x</li></ul><br />		<ul><li>For two accidentals: bb b n # x</li><li>3: bb db^ dv n ‡^ ‡#v x</li><li>4: bb db b d n ‡ # ‡# x</li><li>5: bb dbv bv b^ d^ n ‡v #v #^ ‡#^ x</li><li>6: bb dbv db^ b dv d^ n ‡v ‡^ # ‡#v ‡#^ x</li><li>7: bb dbv db bv b^ d d^ n ‡v ‡ #v #^ ‡# ‡#^ x</li><li>8: bb dbv db bv b b^ d d^ n ‡v ‡ #v # #^ ‡# ‡#^ x (Because this results in values exactly in between twelfths, some discretion in was used in rounding to determine these to be the most intuitive.)</li><li>9: bb bb^ db db^ bv b^ dv d nv n n^ ‡ ‡^ #v #^ ‡#v ‡# xv x</li><li>10: bb bb^ dbv db^ bv b b^ dv d^ nv n n^ ‡v ‡^ #v # #^ ‡#v ‡#^ xv x</li><li>11: bb bb^ dbv db db^ bv b b^ dv d d^ nv n^ ‡v ‡ ‡^ #v # #^ ‡#v ‡# ‡#^ xv x</li><li>12: bb bb^ dbv db db^ bv b b^ dv d d^ nv n n^ ‡v ‡ ‡^ #v # #^ ‡#v ‡# ‡#^ xv x</li></ul><br />
	This would clearly require a significant amount of memorization to be at all efficient. However, two &quot;shorthand&quot; systems can be made, for three and five accidentals per class:<br />		This would clearly require a significant amount of memorization to be at all efficient. However, two &quot;shorthand&quot; systems can be made, for three and five accidentals per class:<br />
	<ul><li>3: bb db d n ‡ ‡# x</li><li>5: bb db bv b^ d n ‡ #v #^ ‡# x</li></ul><br />		<ul><li>3: bb db d n ‡ ‡# x</li><li>5: bb db bv b^ d n ‡ #v #^ ‡# x</li></ul><br />