User:Eufalesio/Holopyth and Hemipyth - Revision history

Eufalesio at 08:17, 26 May 2026

2026-05-26T08:17:28Z

← Older revision		Revision as of 08:17, 26 May 2026
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	* Holopyth 2.3		* Holopyth 2.3
	* Hemipyth √2.√3		* Hemipyth √2.√3
	* [[Ploidacot/~~Dicot~~\|~~Dicot~~]]<nowiki/>pyth 2.√3		* [[Ploidacot/Alpha-dicot\|Alpha]]<nowiki/>[[Ploidacot/Alpha-dicot\|-dicot]]<nowiki/>pyth 2.√3
	* [[Ploidacot/Diploid monocot\|Diploid]]<nowiki/>pyth √2.3		* [[Ploidacot/Diploid monocot\|Diploid]]<nowiki/>pyth √2.3
			Hemipyth implies (P8/2, P5/2) pergen; Alpha-dicotpyth implies (P8, P4/2), (P8, P5/2) is a subset of hemipyth.

	The nomenclature is called EPN and EHPN (Eufa's Pythagorean Nomenclature and Eufa's HemiPythagorean Nomenclature). It is based on [[User:Eufalesio/PLIN\|some other musings I did]].		The nomenclature is called EPN and EHPN (Eufa's Pythagorean Nomenclature and Eufa's HemiPythagorean Nomenclature). It is based on [[User:Eufalesio/PLIN\|some other musings I did]].
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	!'''Prime 3'''		!'''Prime 3'''
	\|-		\|-
	\| rowspan="7" \|~~Pythagorean~~ diatonic nominals		\| rowspan="7" \|Pyth-diatonic nominals
	\|unison		\|unison
	\|0		\|0
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	\|~347.654 Hz		\|~347.654 Hz
	\|-		\|-
	\| rowspan="5" \|~~Pythagorean~~ chromatic nominals		\| rowspan="5" \|Pyth-chromatic nominals
	\|major third		\|major third
	\|<nowiki>-6</nowiki>		\|<nowiki>-6</nowiki>
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	\|417.65625 Hz		\|417.65625 Hz
	\|-		\|-
	\| rowspan="5" \|~~Hemipythagorean~~ interchromatic nominals		\| rowspan="5" \|Hemipyth interchromatic nominals
	\|mid third		\|mid third
	\|<nowiki>-0.5</nowiki>		\|<nowiki>-0.5</nowiki>
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	\|<nowiki>-3.5</nowiki>		\|<nowiki>-3.5</nowiki>
	\|2.5		\|2.5
	\|4T		\|4iT
	\|γ4		\|γ4
	\|Gt4		\|Gt4
	\|~404.166 Hz		\|~404.166 Hz
	\|-		\|-
	\| rowspan="7" \|~~Hemipythagorean Interdiatonic~~ nominals		\| rowspan="7" \|Hemipyth-interdiatonic nominals
	\|ouranic		\|ouranic
	\|0		\|0
	\|0.5		\|0.5
	\|67		\|6i7
	\|ω4		\|ω4
	\|Bf4 / Cp4		\|Bf4 / Cp4
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	\|1		\|1
	\|<nowiki>-0.5</nowiki>		\|<nowiki>-0.5</nowiki>
	\|23		\|2i3
	\|χ4		\|χ4
	\|Ef4 / Fp4		\|Ef4 / Fp4
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	\|<nowiki>-2</nowiki>		\|<nowiki>-2</nowiki>
	\|1.5		\|1.5
	\|34		\|3i4
	\|δ4		\|δ4
	\|Gp4		\|Gp4
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	\|3		\|3
	\|<nowiki>-1.5</nowiki>		\|<nowiki>-1.5</nowiki>
	\|45		\|4i5
	\|κ4		\|κ4
	\|Af4		\|Af4
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	\|<nowiki>-3</nowiki>		\|<nowiki>-3</nowiki>
	\|2.5		\|2.5
	\|78		\|7i8
	\|τ4		\|τ4
	\|Dp5		\|Dp5
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	\|4		\|4
	\|<nowiki>-2.5</nowiki>		\|<nowiki>-2.5</nowiki>
	\|12		\|1i2
	\|β4		\|β4
	\|Df4		\|Df4
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	\|<nowiki>-5</nowiki>		\|<nowiki>-5</nowiki>
	\|3.5		\|3.5
	\|5T		\|Ti5
	\|α4		\|α4
	\|Ap4		\|Ap4
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	\|ipso-		\|ipso-
	\| colspan="2" \|explicit not alter-		\| colspan="2" \|explicit not alter-
	\|i-		\|j-
	\| colspan="2" \|~~Di4~~		\| colspan="2" \|Dj4
	\|0c		\|0c
	\|-		\|-
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	=== General case ===		=== General case ===
	Not used necessarily with just fifths, ideally with fifths between 24\41 and 38\65 inclusive.		Not used necessarily with just fifths, can use ideally with fifths between 24\41 and 38\65 inclusive.

	* Use normally for any tunings with fifths inside that range.		* Use normally for any tunings with fifths inside that range.

Eufalesio: /* General case */

2026-05-08T09:34:48Z

General case

← Older revision		Revision as of 09:34, 8 May 2026
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	\| rowspan="2" \|superunison		\| rowspan="2" \|superunison
	\|-		\|-
	\|~~pythcomma~~		\|poma
	\|-		\|-
	\|Mercator's comma		\|Mercator's comma
	\| rowspan="2" \|mercunison		\| rowspan="2" \|mercunison
	\|-		\|-
	\|~~mercomma~~		\|mercma
	\|-		\|-
	\| rowspan="7" \|Holopythagorean nominals		\| rowspan="7" \|Holopythagorean nominals
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	=== General case ===		=== General case ===
	~~For mapping purposes alone:~~		Not used necessarily with just fifths, ideally with fifths between 24\41 and 38\65 inclusive.

	* Fifths wider than 10\17 have to use m2 fractions as the mapped ~~pythagorean comma~~ is far too big		* Use normally for any tunings with fifths inside that range.
			* Fifths wider than 10\17 have to use m2 fractions as the mapped poma is far too big
	* Compton has to use aug/dim fractions		* Compton has to use aug/dim fractions
	* Fifths flatter than 7\12 now use d2 to refer to sub/super prefixes, the meantone diesis		* Fifths flatter than 7\12 now use d2 to refer to sub/super prefixes, the meantone diesis
	* Fifths flatter than 11\19 have to use aug/dim fractions because the mapped meantone diesis is far too ~~big~~		* Fifths flatter than 11\19 have to use aug/dim fractions because the mapped meantone diesis is far too wide

	[[User:Eufalesio/Mappings of edos\|See here for examples.]]		[[User:Eufalesio/Mappings of edos\|See here for examples.]]

Eufalesio at 20:09, 30 April 2026

2026-04-30T20:09:53Z

← Older revision		Revision as of 20:09, 30 April 2026
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	* Holopyth 2.3		* Holopyth 2.3
	* Hemipyth √2.√3		* Hemipyth √2.√3
	* ~~Ouranpyth~~ 2.√3		* [[Ploidacot/Dicot\|Dicot]]<nowiki/>pyth 2.√3
	* ~~Demipyth~~ √2.3		* [[Ploidacot/Diploid monocot\|Diploid]]<nowiki/>pyth √2.3

	The nomenclature is called EPN and EHPN (Eufa's Pythagorean Nomenclature and Eufa's HemiPythagorean Nomenclature). It is based on [[User:Eufalesio/PLIN\|some other musings I did]].		The nomenclature is called EPN and EHPN (Eufa's Pythagorean Nomenclature and Eufa's HemiPythagorean Nomenclature). It is based on [[User:Eufalesio/PLIN\|some other musings I did]].

Eufalesio: Examples

2026-02-20T13:38:00Z

Examples

← Older revision		Revision as of 13:38, 20 February 2026
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	\|+Table of Holopyth up to ±106 fifths		\|+Table of Holopyth up to ±106 fifths
	!'''Fifthspan'''		!'''Fifthspan'''
	!'''Cents'''		!'''Cents (just)'''
	!'''Name'''		!'''Name'''
	!'''Simplified'''		!'''Simplified'''
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	! rowspan="2" \|'''Simplified'''		! rowspan="2" \|'''Simplified'''
	\|-		\|-
	!'''Cents'''		!'''Cents (just)'''
	!'''Name'''		!'''Name'''
	!'''Cents'''		!'''Cents'''
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	\|wzTT		\|wzTT
	\|}		\|}

			=== General case ===
			For mapping purposes alone:

			* Fifths wider than 10\17 have to use m2 fractions as the mapped pythagorean comma is far too big
			* Compton has to use aug/dim fractions
			* Fifths flatter than 7\12 now use d2 to refer to sub/super prefixes, the meantone diesis
			* Fifths flatter than 11\19 have to use aug/dim fractions because the mapped meantone diesis is far too big

			[[User:Eufalesio/Mappings of edos\|See here for examples.]]

Eufalesio: more synonyms

2026-02-15T15:17:01Z

more synonyms

← Older revision		Revision as of 15:17, 15 February 2026
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	\|mercomma		\|mercomma
	\|-		\|-
	\| rowspan="5" \|Holopythagorean nominals		\| rowspan="7" \|Holopythagorean nominals
	\|octave		\|octave
	\|counison		\|counison
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	\|ditone		\|ditone
	\|major third		\|major third
			\|-
			\|diabolus
			\|tritone
			\|-
			\|inversus
			\|subtritone
	\|-		\|-
	\| rowspan="12" \|Hemipythagorean nominals		\| rowspan="12" \|Hemipythagorean nominals
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	\|cocytic		\|cocytic
	\|-		\|-
	\|~~hemitwelth~~		\|hemitwelfth
	\| rowspan="2" \|ouranic		\| rowspan="2" \|ouranic
	\|-		\|-

Eufalesio at 21:39, 14 February 2026

2026-02-14T21:39:41Z

← Older revision		Revision as of 21:39, 14 February 2026
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	\|trinterfourth		\|trinterfourth
	\|}		\|}
			Nominals in italics are either negative or bigger than than an octave.
	{\| class="wikitable mw-collapsible mw-collapsed"		{\| class="wikitable mw-collapsible mw-collapsed"
	\|+Table of Holopyth up to ±106 fifths		\|+Table of Holopyth up to ±106 fifths

Eufalesio: Major changes because the trinterfifth was not truly a trinterfifth and many other things

2026-02-14T21:35:34Z

Major changes because the trinterfifth was not truly a trinterfifth and many other things

Show changes

Eufalesio: Birth

2026-02-14T17:45:32Z

Birth

Show changes