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User:Eufalesio/Holopyth and Hemipyth: Difference between revisions

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* Holopyth 2.3
* Holopyth 2.3
* Hemipyth √2.√3
* Hemipyth √2.√3
* Ouranpyth 2.√3
* [[Ploidacot/Alpha-dicot|Alpha]]<nowiki/>[[Ploidacot/Alpha-dicot|-dicot]]<nowiki/>pyth 2.√3
* Demipyth √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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| rowspan="2" |superunison
| rowspan="2" |superunison
|-
|-
|pythcomma
|poma
|-
|-
|Mercator's comma
|Mercator's comma
| rowspan="2" |mercunison
| rowspan="2" |mercunison
|-
|-
|mercomma
|mercma
|-
|-
| 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
|-
|-
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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 ===
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.
* 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
* 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 wide
[[User:Eufalesio/Mappings of edos|See here for examples.]]
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