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Major changes because the trinterfifth was not truly a trinterfifth and many other things
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 12: Line 12:
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 19:
! 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" |Pythagorean diatonic nominals
|unison
|unison
|0
|0
Line 30: Line 31:
|1
|1
| colspan="2" |D4
| colspan="2" |D4
|293.<u>3</u>
|293.<u>3</u> Hz
|-
|-
|fifth
|fifth
Line 37: Line 38:
|5
|5
| colspan="2" |A4
| colspan="2" |A4
|440
|440 Hz
|-
|-
|fourth
|fourth
Line 44: Line 45:
|4
|4
| colspan="2" |G4
| colspan="2" |G4
|391.<u>1</u>
|391.<u>1</u> Hz
|-
|-
|major second
|major second
Line 51: Line 52:
|M2
|M2
| colspan="2" |E4
| colspan="2" |E4
|330
|330 Hz
|-
|-
|minor seventh
|minor seventh
Line 58: Line 59:
|m2
|m2
| colspan="2" |C4
| colspan="2" |C4
|521.<u>481</u>
|521.<u>481</u> Hz
|-
|-
|major sixth
|major sixth
Line 65: Line 66:
|M6
|M6
| colspan="2" |B4
| colspan="2" |B4
|495
|495 Hz
|-
|-
|minor third
|minor third
Line 72: Line 73:
|m3
|m3
| colspan="2" |F4
| colspan="2" |F4
|~347.654
|~347.654 Hz
|-
|-
! rowspan="5" |Pythagorean chromatic nominals
| rowspan="5" |Pythagorean chromatic nominals
|major third
|major third
|<nowiki>-6</nowiki>
|<nowiki>-6</nowiki>
Line 81: Line 82:
|P4  
|P4  
|F#4
|F#4
|~371.25
|~371.25 Hz
|-
|-
|minor sixth
|minor sixth
Line 89: Line 90:
|O4
|O4
|Bb4
|Bb4
|~463.539
|~463.539 Hz
|-
|-
|major seventh
|major seventh
Line 97: Line 98:
|K4
|K4
|C#4
|C#4
|556.875
|556.875 Hz
|-
|-
|minor second
|minor second
Line 105: Line 106:
|L4
|L4
|Eb4
|Eb4
|~309.026
|~309.026 Hz
|-
|-
|tritone
|tritone
Line 113: Line 114:
|T4
|T4
|G#4
|G#4
|417.65625
|417.65625 Hz
|-
|-
! rowspan="6" |Hemipythagorean interchromatic nominals
| rowspan="5" |Hemipythagorean interchromatic nominals
|mid third
|mid third
|<nowiki>-0.5</nowiki>
|<nowiki>-0.5</nowiki>
Line 122: Line 123:
|φ4
|φ4
|Ft4
|Ft4
|~359.258
|~359.258 Hz
|-
|-
|mid sixth
|mid sixth
Line 130: Line 131:
|θ4
|θ4
|Bd4
|Bd4
|~479.011
|~479.011 Hz
|-
|-
|mid seventh
|mid seventh
Line 138: Line 139:
|η4
|η4
|Ct4
|Ct4
|~538.888
|~538.888 Hz
|-
|-
|mid second
|mid second
Line 146: Line 147:
|λ4
|λ4
|Ed4
|Ed4
|~319.341
|~319.341 Hz
|-
|-
|trinterfourth
|trinterfourth
Line 154: Line 155:
|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" |Hemipythagorean Interdiatonic nominals
|ouranic
|ouranic
|0
|0
Line 170: Line 163:
|67
|67
|ω4
|ω4
|Bzt4 / CZd4
|Bf4 / Cp4
|~508.068
|~508.068 Hz
|-
|-
|chthonic
|chthonic
Line 178: Line 171:
|23
|23
|χ4
|χ4
|Ezt4 / FZd4
|Ef4 / Fp4
|~338.712
|~338.712 Hz
|-
|-
|naiadic
|naiadic
Line 186: Line 179:
|34
|34
|δ4
|δ4
|GZd4
|Gp4
|~381.051
|~381.051 Hz
|-
|-
|cocytic
|cocytic
Line 194: Line 187:
|45
|45
|κ4
|κ4
|Azt4
|Af4
|~451.616
|~451.616 Hz
|-
|-
|tartaric
|tartaric
Line 202: Line 195:
|78
|78
|τ4
|τ4
|DZd5
|Dp5
|~571.577
|~571.577 Hz
|-
|-
|barbaric
|barbaric
Line 210: Line 203:
|12
|12
|β4
|β4
|Dzt4
|Df4
|~301.077
|~301.077 Hz
|-
|-
! rowspan="18" |Modifiers
|trinterfifth
|<nowiki>-5</nowiki>
|3.5
|5T
|α4
|Ap4
|~428.683 Hz
|-
| rowspan="18" |Modifiers
|super-
|super-
|<nowiki>-19</nowiki>
|<nowiki>-19</nowiki>
Line 219: Line 220:
|S-
|S-
| colspan="2" |DS4
| colspan="2" |DS4
|
| +23.46c
|-
|-
|sub-
|sub-
Line 226: Line 227:
|s-
|s-
| colspan="2" |Ds4
| colspan="2" |Ds4
|
| -23.46c
|-
|-
|hyper-
|hyper-
Line 233: Line 234:
|H-
|H-
| colspan="2" |DH4
| colspan="2" |DH4
|
| +46.92c
|-
|-
|hypo-
|hypo-
Line 240: Line 241:
|h-
|h-
| colspan="2" |Dh4
| colspan="2" |Dh4
|
| -46.92c
|-
|-
|semiper-
|semiper-
Line 247: Line 248:
|Z-
|Z-
| colspan="2" |DZ4
| colspan="2" |DZ4
|
| +11.73c
|-
|-
|semisub-
|semisub-
Line 254: Line 255:
|z-
|z-
| colspan="2" |Dz4
| colspan="2" |Dz4
|
| -11.73
|-
|-
|sesquiper-
|sesquiper-
Line 261: Line 262:
|Q-
|Q-
| colspan="2" |DQ4
| colspan="2" |DQ4
|
| +35.19c
|-
|-
|sesquisub-
|sesquisub-
Line 268: Line 269:
|q-
|q-
| colspan="2" |Dq4
| colspan="2" |Dq4
|
| -35.19c
|-
|-
|semimerc-
|semimerc-
Line 275: Line 276:
|v-
|v-
| colspan="2" |Dv4
| colspan="2" |Dv4
|
|±1.8075c
|-
|-
|merc-
|merc-
Line 282: Line 283:
|w-
|w-
| colspan="2" |Dw4
| colspan="2" |Dw4
|
|±3.615c
|-
|-
|semiqian-
|semiqian-
Line 289: Line 290:
|σ-
|σ-
| colspan="2" |Dσ4
| colspan="2" |Dσ4
|
|±0.88487c
|-
|-
|qian-
|qian-
Line 296: Line 297:
|Σ-
|Σ-
| colspan="2" |DΣ4
| colspan="2" |DΣ4
|
| +1.7697c
|-
|-
|co-
|co-
Line 303: Line 304:
|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 321:
|k-
|k-
| colspan="2" |Dk4
| colspan="2" |Dk4
|
|0c
|-
|-
|ipso-
|ipso-
Line 335: Line 327:
|i-
|i-
| colspan="2" |Di4
| colspan="2" |Di4
|
|0c
|-
|-
|den-
|den-
Line 341: Line 333:
|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 341:
|<nowiki>-#</nowiki>
|<nowiki>-#</nowiki>
| colspan="2" |
| colspan="2" |
|
| +113.685c
|-
|-
|<nowiki>-flat</nowiki>
|<nowiki>-flat</nowiki>
Line 356: Line 348:
|<nowiki>-b</nowiki>
|<nowiki>-b</nowiki>
| colspan="2" |
| colspan="2" |
|
| -113.685c
|-
|-
|<nowiki>-semisharp</nowiki>
|<nowiki>-semisharp</nowiki>
Line 363: Line 355:
|<nowiki>-t</nowiki>
|<nowiki>-t</nowiki>
| colspan="2" |
| colspan="2" |
|
| +56.8425c
|-
|-
|<nowiki>-semiflat</nowiki>
|<nowiki>-semiflat</nowiki>
Line 370: Line 362:
|<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 390:
* '''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 440: Line 438:
|major third
|major third
|-
|-
| rowspan="13" |Hemipythagorean nominals
| rowspan="12" |Hemipythagorean nominals
|hemitone
|hemitone
|semiperminor second
|semiperminor second
Line 474: Line 472:
|paramajor fourth
|paramajor fourth
|trinterfourth
|trinterfourth
|-
|paraminor fifth
|trinterfifth
|}
|}
{| class="wikitable mw-collapsible mw-collapsed"
{| class="wikitable mw-collapsible mw-collapsed"
Line 1,606: Line 1,601:
|551.2725
|551.2725
|transtrinterfourth
|transtrinterfourth
|rT4
|r4T
|1151.2725
|1151.2725
|transtartaric
|transtartaric
Line 1,624: Line 1,619:
|rZ12
|rZ12
|653.2275
|653.2275
|transsemipertrinterfifth
|transtrinterfifth
|rZ5T
|r5T
|-
|-
|<nowiki>-49</nowiki>
|<nowiki>-49</nowiki>
Line 1,717: Line 1,712:
|<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 1,793:
|574.7325
|574.7325
|transsupertrinterfourth
|transsupertrinterfourth
|rST4
|rS4T
|1174.7325
|1174.7325
|transsupertartaric
|transsupertartaric
Line 1,816: Line 1,811:
|rQ12
|rQ12
|676.6875
|676.6875
|transsesquipertrinterfifth
|transsupertrinterfifth
|rQ5T
|rS5T
|-
|-
|<nowiki>-37</nowiki>
|<nowiki>-37</nowiki>
Line 1,909: Line 1,904:
|<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 1,947:
|rH1
|rH1
|643.3050
|643.3050
|transsesquipertritone / transsemimerctrinterfifth
|transsesquipertritone
|rQTT
|rQTT
|-
|-
Line 1,989: Line 1,984:
|<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 2,065:
|507.9675
|507.9675
|hypotrinterfourth
|hypotrinterfourth
|hT4
|h4T
|1107.9675
|1107.9675
|hypotartaric
|hypotartaric
Line 2,088: Line 2,083:
|q12
|q12
|609.9225
|609.9225
|sesquisubtrinterfifth
|hypotrinterfifth
|q5T
|h5T
|-
|-
|<nowiki>-20</nowiki>
|<nowiki>-20</nowiki>
Line 2,181: Line 2,176:
|<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 2,257:
|531.4275
|531.4275
|subtrinterfourth
|subtrinterfourth
|sT4
|s4T
|1131.4275
|1131.4275
|subtartaric
|subtartaric
Line 2,280: Line 2,275:
|z12
|z12
|633.3825
|633.3825
|semisubtrinterfifth
|subtrinterfifth
|z5T
|s5T
|-
|-
|<nowiki>-8</nowiki>
|<nowiki>-8</nowiki>
Line 2,373: Line 2,368:
|<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 2,449:
|554.8875
|554.8875
|'''trinterfourth'''
|'''trinterfourth'''
|T4
|4T
|1154.8875
|1154.8875
|'''tartaric'''
|'''tartaric'''
Line 2,472: Line 2,467:
|Z12
|Z12
|656.8425
|656.8425
|semipertrinterfifth
|'''trinterfifth'''
|Z5T
|5T
|-
|-
|4
|4
Line 2,565: Line 2,560:
|9.5
|9.5
|668.5725
|668.5725
|supertrinterfifth
|semipertrinterfifth
|ST5
|Z5T
|68.5725
|68.5725
|superbarbaric
|superbarbaric
Line 2,646: Line 2,641:
|578.3475
|578.3475
|supertrinterfourth
|supertrinterfourth
|ST4
|S4T
|1178.3475
|1178.3475
|supertartaric
|supertartaric
Line 2,664: Line 2,659:
|Q12
|Q12
|680.3025
|680.3025
|sesquipertrinterfifth
|supertrinterfifth
|Q5T
|S5T
|-
|-
|16
|16
Line 2,757: Line 2,752:
|21.5
|21.5
|692.0325
|692.0325
|hypertrinterfifth
|sesquipertrinterfifth
|HT5
|Q5T
|92.0325
|92.0325
|hyperbarbaric
|hyperbarbaric
Line 2,800: Line 2,795:
|H1
|H1
|646.9200
|646.9200
|sesquipertritone / semimerctrinterfifth
|sesquipertritone
|QTT
|QTT
|-
|-
Line 2,837: Line 2,832:
|26.5
|26.5
|601.8075
|601.8075
|hypertrinterfourth / transhypotrinterfifth
|hypertrinterfourth
|HT4 / rhT5
|H4T
|1.8075
|1.8075
|semimercunison
|semimercunison
Line 2,918: Line 2,913:
|511.5825
|511.5825
|transhypotrinterfourth
|transhypotrinterfourth
|rhT4
|rh4T
|1111.5825
|1111.5825
|transhypotartaric
|transhypotartaric
Line 2,936: Line 2,931:
|rq12
|rq12
|613.5375
|613.5375
|transsesquisubtrinterfifth
|transhypotrinterfifth
|rq5T
|rh5T
|-
|-
|33
|33
Line 3,029: Line 3,024:
|38.5
|38.5
|625.2675
|625.2675
|transsubtrinterfifth
|transsesquitrinterfifth
|rsT5
|rq5T
|25.2675
|25.2675
|transsubbarbaric
|transsubbarbaric
Line 3,110: Line 3,105:
|535.0425
|535.0425
|transsubtrinterfourth
|transsubtrinterfourth
|rsT4
|rs4T
|1135.0425
|1135.0425
|transsubtartaric
|transsubtartaric
Line 3,128: Line 3,123:
|rz12
|rz12
|636.9975
|636.9975
|transsemisubtrinterfifth
|transsubtrinterfifth
|rz5T
|rs5T
|-
|-
|45
|45
Line 3,221: Line 3,216:
|50.5
|50.5
|648.7275
|648.7275
|transtrinterfifth
|transsemisubtrinterfifth
|rT5
|rz5T
|48.7275
|48.7275
|transbarbaric
|transbarbaric
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