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Line 1: Line 1:
[[Pythagorean tuning|Pythagorean]] and [[Hemipythagorean]] systematic nomenclature. Open to suggestions.
[[Pythagorean tuning|Pythagorean]] and [[Hemipythagorean]] systematic nomenclature proposal dispersion. Open to suggestions.


Pythagorean may be used to talk about both the non-hemi and yes-hemi structures but this is ambiguous, so Holopythagorean (Holopyth) 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 Holopythagorean (Holopyth) shall refer only to 2.3 NOT √2.√3 or √2.3 or 2.√3. Resumed:
Line 5: Line 5:
* 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]].  
Line 12: Line 13:
Important is to distinguish the '''interchromatic''' nominals and '''interdiatonic''' nominals (interseptimals). The key distinguishing feature is that interchromatics have √2 '''AND''' √3, Interdiatonics have √2 '''OR''' √3. No augmented/diminished in here, better dodecatonic or icositetratonic system, less difficult and also I don't like them. Included also new nominals to make all even more compact but not strict necessity.
Important is to distinguish the '''interchromatic''' nominals and '''interdiatonic''' nominals (interseptimals). The key distinguishing feature is that interchromatics have √2 '''AND''' √3, Interdiatonics have √2 '''OR''' √3. No augmented/diminished in here, better dodecatonic or icositetratonic system, less difficult and also I don't like them. Included also new nominals to make all even more compact but not strict necessity.
{| class="wikitable"
{| class="wikitable"
|+Bases for E(H)PN
! rowspan="2" |'''Category'''
! rowspan="2" |'''Category'''
! rowspan="2" |'''Name'''
! rowspan="2" |'''Name'''
Line 20: Line 20:
! rowspan="2" |'''Pitches (Evo)'''
! rowspan="2" |'''Pitches (Evo)'''
! rowspan="2" |'''Frequency (Hz)'''
! rowspan="2" |'''Frequency (Hz)'''
Cents (c)
|-
|-
!'''Prime 2'''
!'''Prime 2'''
!'''Prime 3'''
!'''Prime 3'''
|-
|-
! rowspan="7" |Pythagorean diatonic nominals
| rowspan="7" |Pyth-diatonic nominals
|unison
|unison
|0
|0
Line 30: Line 32:
|1
|1
| colspan="2" |D4
| colspan="2" |D4
|293.<u>3</u>
|293.<u>3</u> Hz
|-
|-
|fifth
|fifth
Line 37: Line 39:
|5
|5
| colspan="2" |A4
| colspan="2" |A4
|440
|440 Hz
|-
|-
|fourth
|fourth
Line 44: Line 46:
|4
|4
| colspan="2" |G4
| colspan="2" |G4
|391.<u>1</u>
|391.<u>1</u> Hz
|-
|-
|major second
|major second
Line 51: Line 53:
|M2
|M2
| colspan="2" |E4
| colspan="2" |E4
|330
|330 Hz
|-
|-
|minor seventh
|minor seventh
Line 58: Line 60:
|m2
|m2
| colspan="2" |C4
| colspan="2" |C4
|521.<u>481</u>
|521.<u>481</u> Hz
|-
|-
|major sixth
|major sixth
Line 65: Line 67:
|M6
|M6
| colspan="2" |B4
| colspan="2" |B4
|495
|495 Hz
|-
|-
|minor third
|minor third
Line 72: Line 74:
|m3
|m3
| colspan="2" |F4
| colspan="2" |F4
|~347.654
|~347.654 Hz
|-
|-
! rowspan="5" |Pythagorean chromatic nominals
| rowspan="5" |Pyth-chromatic nominals
|major third
|major third
|<nowiki>-6</nowiki>
|<nowiki>-6</nowiki>
Line 81: Line 83:
|P4  
|P4  
|F#4
|F#4
|~371.25
|~371.25 Hz
|-
|-
|minor sixth
|minor sixth
Line 89: Line 91:
|O4
|O4
|Bb4
|Bb4
|~463.539
|~463.539 Hz
|-
|-
|major seventh
|major seventh
Line 97: Line 99:
|K4
|K4
|C#4
|C#4
|556.875
|556.875 Hz
|-
|-
|minor second
|minor second
Line 105: Line 107:
|L4
|L4
|Eb4
|Eb4
|~309.026
|~309.026 Hz
|-
|-
|tritone
|tritone
Line 113: Line 115:
|T4
|T4
|G#4
|G#4
|417.65625
|417.65625 Hz
|-
|-
! rowspan="6" |Hemipythagorean interchromatic nominals
| rowspan="5" |Hemipyth interchromatic nominals
|mid third
|mid third
|<nowiki>-0.5</nowiki>
|<nowiki>-0.5</nowiki>
Line 122: Line 124:
|φ4
|φ4
|Ft4
|Ft4
|~359.258
|~359.258 Hz
|-
|-
|mid sixth
|mid sixth
Line 130: Line 132:
|θ4
|θ4
|Bd4
|Bd4
|~479.011
|~479.011 Hz
|-
|-
|mid seventh
|mid seventh
Line 138: Line 140:
|η4
|η4
|Ct4
|Ct4
|~538.888
|~538.888 Hz
|-
|-
|mid second
|mid second
Line 146: Line 148:
|λ4
|λ4
|Ed4
|Ed4
|~319.341
|~319.341 Hz
|-
|-
|trinterfourth
|trinterfourth
|<nowiki>-3.5</nowiki>
|<nowiki>-3.5</nowiki>
|2.5
|2.5
|4T
|4iT
|γ4
|γ4
|Gt4
|Gt4
|~404.166
|~404.166 Hz
|-
|trinterfifth
|4.5
|2.5
|5T
|α4
|Ad4
|~425.788
|-
|-
! rowspan="6" |Hemipythagorean Interdiatonic nominals
| rowspan="7" |Hemipyth-interdiatonic nominals
|ouranic
|ouranic
|0
|0
|0.5
|0.5
|67
|6i7
|ω4
|ω4
|Bzt4 / CZd4
|Bf4 / Cp4
|~508.068
|~508.068 Hz
|-
|-
|chthonic
|chthonic
|1
|1
|<nowiki>-0.5</nowiki>
|<nowiki>-0.5</nowiki>
|23
|2i3
|χ4
|χ4
|Ezt4 / FZd4
|Ef4 / Fp4
|~338.712
|~338.712 Hz
|-
|-
|naiadic
|naiadic
|<nowiki>-2</nowiki>
|<nowiki>-2</nowiki>
|1.5
|1.5
|34
|3i4
|δ4
|δ4
|GZd4
|Gp4
|~381.051
|~381.051 Hz
|-
|-
|cocytic
|cocytic
|3
|3
|<nowiki>-1.5</nowiki>
|<nowiki>-1.5</nowiki>
|45
|4i5
|κ4
|κ4
|Azt4
|Af4
|~451.616
|~451.616 Hz
|-
|-
|tartaric
|tartaric
|<nowiki>-3</nowiki>
|<nowiki>-3</nowiki>
|2.5
|2.5
|78
|7i8
|τ4
|τ4
|DZd5
|Dp5
|~571.577
|~571.577 Hz
|-
|-
|barbaric
|barbaric
|4
|4
|<nowiki>-2.5</nowiki>
|<nowiki>-2.5</nowiki>
|12
|1i2
|β4
|β4
|Dzt4
|Df4
|~301.077
|~301.077 Hz
|-
|-
! rowspan="18" |Modifiers
|trinterfifth
|<nowiki>-5</nowiki>
|3.5
|Ti5
|α4
|Ap4
|~428.683 Hz
|-
| rowspan="18" |Modifiers
|super-
|super-
|<nowiki>-19</nowiki>
|<nowiki>-19</nowiki>
Line 219: Line 221:
|S-
|S-
| colspan="2" |DS4
| colspan="2" |DS4
|
| +23.46c
|-
|-
|sub-
|sub-
Line 226: Line 228:
|s-
|s-
| colspan="2" |Ds4
| colspan="2" |Ds4
|
| -23.46c
|-
|-
|hyper-
|hyper-
Line 233: Line 235:
|H-
|H-
| colspan="2" |DH4
| colspan="2" |DH4
|
| +46.92c
|-
|-
|hypo-
|hypo-
Line 240: Line 242:
|h-
|h-
| colspan="2" |Dh4
| colspan="2" |Dh4
|
| -46.92c
|-
|-
|semiper-
|semiper-
Line 247: Line 249:
|Z-
|Z-
| colspan="2" |DZ4
| colspan="2" |DZ4
|
| +11.73c
|-
|-
|semisub-
|semisub-
Line 254: Line 256:
|z-
|z-
| colspan="2" |Dz4
| colspan="2" |Dz4
|
| -11.73
|-
|-
|sesquiper-
|sesquiper-
Line 261: Line 263:
|Q-
|Q-
| colspan="2" |DQ4
| colspan="2" |DQ4
|
| +35.19c
|-
|-
|sesquisub-
|sesquisub-
Line 268: Line 270:
|q-
|q-
| colspan="2" |Dq4
| colspan="2" |Dq4
|
| -35.19c
|-
|-
|semimerc-
|semimerc-
Line 275: Line 277:
|v-
|v-
| colspan="2" |Dv4
| colspan="2" |Dv4
|
|±1.8075c
|-
|-
|merc-
|merc-
Line 282: Line 284:
|w-
|w-
| colspan="2" |Dw4
| colspan="2" |Dw4
|
|±3.615c
|-
|-
|semiqian-
|semiqian-
Line 289: Line 291:
|σ-
|σ-
| colspan="2" |Dσ4
| colspan="2" |Dσ4
|
|±0.88487c
|-
|-
|qian-
|qian-
Line 296: Line 298:
|Σ-
|Σ-
| colspan="2" |DΣ4
| colspan="2" |DΣ4
|
| +1.7697c
|-
|-
|co-
|co-
Line 303: Line 305:
|c-
|c-
| colspan="2" |–
| colspan="2" |–
|
|1200c
|-
|-
|trans-
|trans-
| colspan="2" |± <-84 53];
| colspan="2" rowspan="2" |see below
 
fifthspan%53≥26:+
 
fifthspan%53≤26:-
|r-
|r-
| colspan="2" |Dr4
| colspan="2" |Dr4
|
|3.615c
|-
|-
|alter-
|alter-
| colspan="2" |± <-485 306];
fifthspan%53>153:+
fifthspan%53<153:-
|a-
|a-
| colspan="2" |Da4
| colspan="2" |Da4
|
|1.7697c
|-
|-
|cis-
|cis-
Line 329: Line 322:
|k-
|k-
| colspan="2" |Dk4
| colspan="2" |Dk4
|
|0c
|-
|-
|ipso-
|ipso-
| colspan="2" |explicit not alter-
| colspan="2" |explicit not alter-
|i-
|j-
| colspan="2" |Di4
| colspan="2" |Dj4
|
|0c
|-
|-
|den-
|den-
Line 341: Line 334:
|n-
|n-
| colspan="2" |
| colspan="2" |
|
|–
|-
|-
! rowspan="6" |Evo pitch accidentals
| rowspan="6" |Evo pitch accidentals
|<nowiki>-sharp</nowiki>
|<nowiki>-sharp</nowiki>
|<nowiki>-11</nowiki>
|<nowiki>-11</nowiki>
Line 349: Line 342:
|<nowiki>-#</nowiki>
|<nowiki>-#</nowiki>
| colspan="2" |
| colspan="2" |
|
| +113.685c
|-
|-
|<nowiki>-flat</nowiki>
|<nowiki>-flat</nowiki>
Line 356: Line 349:
|<nowiki>-b</nowiki>
|<nowiki>-b</nowiki>
| colspan="2" |
| colspan="2" |
|
| -113.685c
|-
|-
|<nowiki>-semisharp</nowiki>
|<nowiki>-semisharp</nowiki>
Line 363: Line 356:
|<nowiki>-t</nowiki>
|<nowiki>-t</nowiki>
| colspan="2" |
| colspan="2" |
|
| +56.8425c
|-
|-
|<nowiki>-semiflat</nowiki>
|<nowiki>-semiflat</nowiki>
Line 370: Line 363:
|<nowiki>-d</nowiki>
|<nowiki>-d</nowiki>
| colspan="2" |
| colspan="2" |
|
| -56.8425
|-
|-
|<nowiki>-semisubsharp</nowiki>
|<nowiki>-artosemisharp</nowiki>
|4
|4
|<nowiki>-2.5</nowiki>
|<nowiki>-2.5</nowiki>
|<nowiki>-zt</nowiki>
|<nowiki>-f</nowiki>
| colspan="2" |
| colspan="2" |
|
| +45.1125c
|-
|-
|<nowiki>-semiperflat</nowiki>
|<nowiki>-semipersemiflat</nowiki>
|<nowiki>-4</nowiki>
|<nowiki>-4</nowiki>
|2.5
|2.5
|<nowiki>-Zd</nowiki>
|<nowiki>-p</nowiki>
| colspan="2" |
| colspan="2" |
|
| -45.1125c
|-
|-
! rowspan="2" |Syntax
| rowspan="2" |Syntax
| colspan="7" |interval: (den)(co)(alter)(trans)([semi]qian)([semi]merc)(super/sub/hyper/hypo/semiper/semisub/sesquiper/sesquisub)nominal
| colspan="7" |interval: (den)(co)(alter)(trans)([semi]qian)([semi]merc)(super/sub/hyper/hypo/semiper/semisub/sesquiper/sesquisub)(nominal)
|-
|-
| colspan="7" |pitch: (alter)(trans)pitch-class([semi]qian)([semi]merc)(super/sub/hyper/hypo/semiper/semisub/sesquiper/sesquisub)(octave)
| colspan="7" |pitch: (alter)(trans)(pitch-class)([semi]qian)([semi]merc)(super/sub/hyper/hypo/semiper/semisub/sesquiper/sesquisub)(octave)
|-
|-
!Extreme example
|Extreme example
| colspan="7" |''dencoaltertransqianbimercsesquipertrinterfourth'' ncarΣwQ4T (-1795.53787428) <684 -432.5]
| colspan="7" |''dencoaltertransqianbimercsesquipertrinterfourth'' ncarΣwQ4T (-1795.53787428) <684 -432.5]
|}
|}
Line 398: Line 391:
* '''Barbaric''': Greek-flavored interseptimals inspired by [[Zhea Erose|Zhea]] for the unison-inter-second, based on barbarians because the interval sounds kinda harsh. Use ''thalassic'' if you don't like it but I think the name sounds kickass.
* '''Barbaric''': Greek-flavored interseptimals inspired by [[Zhea Erose|Zhea]] for the unison-inter-second, based on barbarians because the interval sounds kinda harsh. Use ''thalassic'' if you don't like it but I think the name sounds kickass.
* '''Tartaric''': Greek-flavored interseptimals inspired by [[Zhea Erose|Zhea]] for the seventh-inter-octave, based on the Tartarus, hell of eternal suffering because yes. Rhymes with barbaric, fitting because they are octave complements.
* '''Tartaric''': Greek-flavored interseptimals inspired by [[Zhea Erose|Zhea]] for the seventh-inter-octave, based on the Tartarus, hell of eternal suffering because yes. Rhymes with barbaric, fitting because they are octave complements.
* '''Trinterfourth''': contraction of tritone-inter-fourth.  
* '''Trinterfourth''': contraction of tritone-inter-fourth. Also called semiaugmented fourth by many.
* '''Trinterfifth''': contraction of tritone-inter-fifth. Technically misnomer because this is actually the octave complement of trinterfourth, the actual interval that's a true tritone-inter-fifth is sqrt(2187/1024) which here would be the semipertrinterfifth. Maybe not the best idea to keep this inconsistency.
* '''Trinterfifth''': contraction of tritone-inter-fifth. '''<u>NOT</u>''' a semidiminished fifth, Much like the trinterfourth, this is the geometric mean of the tritone and fifth, and since the tritone isn't 600c, this can't be the complement of the trinterfourth.
 
=== Trans and alter ===
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 (literally what ''trans'' means). They make the mercator and qian microalterations go in the opposite direction as the interval.
 
So you have the cisfourth -1 fifth, transfourth +52 fifths, cismercfourth is -54 fifths and transmercfourth +105 fifths. Same with alter.


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.
{| class="wikitable"
{| class="wikitable"
|+Table of synonyms
|+Table of synonyms
Line 417: Line 416:
| 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
Line 440: Line 439:
|major third
|major third
|-
|-
| rowspan="13" |Hemipythagorean nominals
|diabolus
|tritone
|-
|inversus
|subtritone
|-
| rowspan="12" |Hemipythagorean nominals
|hemitone
|hemitone
|semiperminor second
|semiperminor second
Line 464: Line 469:
|cocytic
|cocytic
|-
|-
|hemitwelth
|hemitwelfth
| rowspan="2" |ouranic
| rowspan="2" |ouranic
|-
|-
Line 474: Line 479:
|paramajor fourth
|paramajor fourth
|trinterfourth
|trinterfourth
|-
|paraminor fifth
|trinterfifth
|}
|}
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
!'''Fifthspan'''
!'''Fifthspan'''
!'''Cents'''
!'''Cents (just)'''
!'''Name'''
!'''Name'''
!'''Simplified'''
!'''Simplified'''
Line 1,558: Line 1,561:
! rowspan="2" |'''Simplified'''
! rowspan="2" |'''Simplified'''
|-
|-
!'''Cents'''
!'''Cents (just)'''
!'''Name'''
!'''Name'''
!'''Cents'''
!'''Cents'''
Line 1,606: Line 1,609:
|551.2725
|551.2725
|transtrinterfourth
|transtrinterfourth
|rT4
|r4T
|1151.2725
|1151.2725
|transtartaric
|transtartaric
Line 1,624: Line 1,627:
|rZ12
|rZ12
|653.2275
|653.2275
|transsemipertrinterfifth
|transtrinterfifth
|rZ5T
|r5T
|-
|-
|<nowiki>-49</nowiki>
|<nowiki>-49</nowiki>
Line 1,717: Line 1,720:
|<nowiki>-43.5</nowiki>
|<nowiki>-43.5</nowiki>
|664.9575
|664.9575
|transsupertrinterfifth
|transsemipertrinterfifth
|rST5
|rZ5T
|64.9575
|64.9575
|transsuperbarbaric
|transsuperbarbaric
Line 1,798: Line 1,801:
|574.7325
|574.7325
|transsupertrinterfourth
|transsupertrinterfourth
|rST4
|rS4T
|1174.7325
|1174.7325
|transsupertartaric
|transsupertartaric
Line 1,816: Line 1,819:
|rQ12
|rQ12
|676.6875
|676.6875
|transsesquipertrinterfifth
|transsupertrinterfifth
|rQ5T
|rS5T
|-
|-
|<nowiki>-37</nowiki>
|<nowiki>-37</nowiki>
Line 1,909: Line 1,912:
|<nowiki>-31.5</nowiki>
|<nowiki>-31.5</nowiki>
|688.4175
|688.4175
|transhypertrinterfifth
|transsesquipertrinterfifth
|rHT5
|rQ5T
|88.4175
|88.4175
|transhyperbarbaric
|transhyperbarbaric
Line 1,952: Line 1,955:
|rH1
|rH1
|643.3050
|643.3050
|transsesquipertritone / transsemimerctrinterfifth
|transsesquipertritone
|rQTT
|rQTT
|-
|-
Line 1,989: Line 1,992:
|<nowiki>-26.5</nowiki>
|<nowiki>-26.5</nowiki>
|598.1925
|598.1925
|hypotrinterfifth / transhypertrinterfourth
|transhypertrinterfourth
|hT5 / rHT4
|rH4T
|1198.1925
|1198.1925
|transsemimercoctave
|transsemimercoctave
Line 2,070: Line 2,073:
|507.9675
|507.9675
|hypotrinterfourth
|hypotrinterfourth
|hT4
|h4T
|1107.9675
|1107.9675
|hypotartaric
|hypotartaric
Line 2,088: Line 2,091:
|q12
|q12
|609.9225
|609.9225
|sesquisubtrinterfifth
|hypotrinterfifth
|q5T
|h5T
|-
|-
|<nowiki>-20</nowiki>
|<nowiki>-20</nowiki>
Line 2,181: Line 2,184:
|<nowiki>-14.5</nowiki>
|<nowiki>-14.5</nowiki>
|621.6525
|621.6525
|subtrinterfifth
|sesquisubtrinterfifth
|sT5
|q5T
|21.6525
|21.6525
|subbarbaric
|subbarbaric
Line 2,262: Line 2,265:
|531.4275
|531.4275
|subtrinterfourth
|subtrinterfourth
|sT4
|s4T
|1131.4275
|1131.4275
|subtartaric
|subtartaric
Line 2,280: Line 2,283:
|z12
|z12
|633.3825
|633.3825
|semisubtrinterfifth
|subtrinterfifth
|z5T
|s5T
|-
|-
|<nowiki>-8</nowiki>
|<nowiki>-8</nowiki>
Line 2,373: Line 2,376:
|<nowiki>-2.5</nowiki>
|<nowiki>-2.5</nowiki>
|645.1125
|645.1125
|'''trinterfifth'''
|semisubtrinterfifth
|T5
|z5T
|45.1125
|45.1125
|'''barbaric'''
|'''barbaric'''
Line 2,454: Line 2,457:
|554.8875
|554.8875
|'''trinterfourth'''
|'''trinterfourth'''
|T4
|4T
|1154.8875
|1154.8875
|'''tartaric'''
|'''tartaric'''
Line 2,472: Line 2,475:
|Z12
|Z12
|656.8425
|656.8425
|semipertrinterfifth
|'''trinterfifth'''
|Z5T
|5T
|-
|-
|4
|4
Line 2,565: Line 2,568:
|9.5
|9.5
|668.5725
|668.5725
|supertrinterfifth
|semipertrinterfifth
|ST5
|Z5T
|68.5725
|68.5725
|superbarbaric
|superbarbaric
Line 2,646: Line 2,649:
|578.3475
|578.3475
|supertrinterfourth
|supertrinterfourth
|ST4
|S4T
|1178.3475
|1178.3475
|supertartaric
|supertartaric
Line 2,664: Line 2,667:
|Q12
|Q12
|680.3025
|680.3025
|sesquipertrinterfifth
|supertrinterfifth
|Q5T
|S5T
|-
|-
|16
|16
Line 2,757: Line 2,760:
|21.5
|21.5
|692.0325
|692.0325
|hypertrinterfifth
|sesquipertrinterfifth
|HT5
|Q5T
|92.0325
|92.0325
|hyperbarbaric
|hyperbarbaric
Line 2,800: Line 2,803:
|H1
|H1
|646.9200
|646.9200
|sesquipertritone / semimerctrinterfifth
|sesquipertritone
|QTT
|QTT
|-
|-
Line 2,837: Line 2,840:
|26.5
|26.5
|601.8075
|601.8075
|hypertrinterfourth / transhypotrinterfifth
|hypertrinterfourth
|HT4 / rhT5
|H4T
|1.8075
|1.8075
|semimercunison
|semimercunison
Line 2,918: Line 2,921:
|511.5825
|511.5825
|transhypotrinterfourth
|transhypotrinterfourth
|rhT4
|rh4T
|1111.5825
|1111.5825
|transhypotartaric
|transhypotartaric
Line 2,936: Line 2,939:
|rq12
|rq12
|613.5375
|613.5375
|transsesquisubtrinterfifth
|transhypotrinterfifth
|rq5T
|rh5T
|-
|-
|33
|33
Line 3,029: Line 3,032:
|38.5
|38.5
|625.2675
|625.2675
|transsubtrinterfifth
|transsesquitrinterfifth
|rsT5
|rq5T
|25.2675
|25.2675
|transsubbarbaric
|transsubbarbaric
Line 3,110: Line 3,113:
|535.0425
|535.0425
|transsubtrinterfourth
|transsubtrinterfourth
|rsT4
|rs4T
|1135.0425
|1135.0425
|transsubtartaric
|transsubtartaric
Line 3,128: Line 3,131:
|rz12
|rz12
|636.9975
|636.9975
|transsemisubtrinterfifth
|transsubtrinterfifth
|rz5T
|rs5T
|-
|-
|45
|45
Line 3,221: Line 3,224:
|50.5
|50.5
|648.7275
|648.7275
|transtrinterfifth
|transsemisubtrinterfifth
|rT5
|rz5T
|48.7275
|48.7275
|transbarbaric
|transbarbaric
Line 3,267: Line 3,270:
|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.]]
Retrieved from "https://en.xen.wiki/w/User:Eufalesio/Holopyth_and_Hemipyth"