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[[Pythagorean tuning|Pythagorean]] and [[Hemipythagorean]] systematic nomenclature proposal dispersion. Open to suggestions.
A notation capable of notating all pythagorean, hemipyth, and then some.


Pythagorean may be used to talk about both the non-hemi and yes-hemi structures but this is ambiguous, so 3-limit or Monocotpyth shall refer only to 2.3 NOT √2.√3 or √2.3 or 2.√3. Resumed:
Pythagorean may be used to talk about both the non-hemi and yes-hemi structures but this is ambiguous, so 3-limit or Monocotpyth shall refer only to 2.3 NOT √2.√3 or √2.3 or 2.√3. Resumed:
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|1.7697c
|1.7697c
|-
|-
|den-
|ne-
| colspan="2" |negative interval
| colspan="2" |negative interval
|"-"
|"-"
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|-
|-
|Extreme example
|Extreme example
| colspan="7" |''dencorevolalterqianbimercsesquipotrinterfourth'' -crRΣJQ4T (-1795.53787428) <684 -432.5]
| colspan="7" |''necorevolalterqianbimercsesquipotrinterfourth'' -crRΣJQ4T (-1795.53787428c just) <684 -432.5]
|}
|}
Etymologies of new nominals:
Etymologies of new nominals:
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=== Alter and revol ===
=== Alter and revol ===
These prefixes are used to described intervals beyond ±26 fifths and beyond ±153 fifths, as to think a similar interval, but from the other side (thus ''alter-''). They make the mercator and qian microalterations go in the opposite direction as the interval.  
These prefixes are used to described intervals beyond ±26 fifths and beyond ±153 fifths, as to think a similar interval, but from the other side (thus ''alter-''). They make the mercator and qian microalterations go in the opposite direction the interval suggests, which eliminates the need of knowing which direction you need to alter by. ''Alter'' is more than enough for the overwhelming majority of cases.  


So you have the fourth -1 fifth, alterfourth +52 fifths, mercfourth is -54 fifths and altermercfourth +105 fifths. Same with revol.
So you have the fourth -1 fifth, alterfourth +52 fifths, mercfourth is -54 fifths and altermercfourth +105 fifths. Same with revol and qian.


See the tables for better understanding because it all makes sense in my head but probably not yours. I don't know how convoluted this feels so I invite you to shit on me in the discussion page if this is dumb.
See the tables for better understanding because it all makes sense in my head but probably not yours. I don't know how convoluted this feels so I invite you to shit on me in the discussion page if this is dumb.
=== Up and down, etc... ===
Use another set of accidentals for mapping rank-3 temperaments (such as [[septischismic]]) or complex rank-2 temperaments more simply (such as [[newt]]). An example of usage is here with [[User:Eufalesio/Ultimate#Nomenclature and notation]] for more info.
{| class="wikitable" data-darkreader-inline-color=""
{| class="wikitable" data-darkreader-inline-color=""
|+Table of synonyms
|+Table of synonyms
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|trinterfourth
|trinterfourth
|}
|}
Nominals in italics are either negative or bigger than than an octave.
All the hemis- can be semis- too. Nominals in italics are either negative or bigger than than an octave.  
{| class="wikitable mw-collapsible mw-collapsed" data-darkreader-inline-color=""
{| class="wikitable mw-collapsible mw-collapsed" data-darkreader-inline-color=""
|+Table of Monocot up to ±106 fifths
|+Table of Monocot up to ±106 fifths
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|J!TT
|J!TT
|}
|}
== How to use for temps in/and higher limits ==
EPN can handle tons of temperaments that are based on the chain of fifths, obviously the rank-2 monocots, dicots, alpha-dicots, and hemipyth ones; but also rank-3 ones with a free generator for other primes. However, there is a special case when the septischisma is tempered out due to the prevalence of the super/sub usage for septimal.


=== General case ===
=== General case ===
Not used necessarily with just fifths, can use ideally with fifths between 24\41 and 38\65 inclusive.
Can be used not 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
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* 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 qu/po prefixes, the meantone diesis
* Fifths flatter than 7\12 now use d2 to refer to qu/po prefixes, the meantone diesis
* Fifths flatter than 11\19 have to use aug/dim fractions because the mapped meantone diesis is far too wide
* Fifths flatter than 11\19 have to use aug/dim fractions because the mapped meantone diesis is far too wide.
 
=== Septischismic ===
Use the rightward names and symbols if the septischisma is tempered out since the poma is closer to 64/63 (the septischismic column). In there, the pomas and merccommas become are equated and often sound much closer to rumas and [[buzzardsma]]<nowiki/>s. If not, keep po and super distinct. There is no equivalent for septimal comma qian, on purpose. Assume ^/v are always [[aberschisma]]<nowiki/>s. This gives you a solid 13-limit basis that can be extended to [[olympic]].
 
* P1 — M2 — ^sM3 — HP4 — P5 — vHm6 — sm7 — ^sM7 — P8: [[8afdo]] in [[User:Eufalesio/Ultimate#Nomenclature and notation|Ultimate]] (see here for specifics of notation)


[[User:Eufalesio/Mappings of edos|See here for examples.]]
{| class="wikitable"
! colspan="2" |Pyth or distinct
! colspan="2" |64/63 or septischismic
! colspan="2" |Aberschismas
! colspan="3" |Septi(schismas)
|-
|po
|p
|(su)per
|S
|up
|^
| rowspan="4" |Schisma
|/
|bi
|-
|qu
|q
|sub
|s
|down
|v
|\
|bo
|-
|popo
|P
|hyper
|H
|dup
|^^
|//
|bibi
|-
|ququ
|Q
|hypo
|h
|dud
|w
|\\
|bobo
|-
|semipo
|¡
|semiper
|Z
|trup
|3^
| rowspan="4" |Septischis
|^\
|gi
|-
|semiqu
|!
|semisub
|z
|trud
|3v
|v/
|go
|-
|sesquipo
|p¡
|sesquiper
|SZ
|quup
|4^
|^^\\
|gi
|-
|sesquiqu
|q!
|sesquisub
|sz
|quud
|4v
|w//
|go
|-
|alter
|R
|trans
|L
|quip
|5^
| colspan="3" rowspan="2" |
|-
|merc
|J
|buzz
|Γ
|quid
|5v
|}
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