User:Eufalesio/Holopyth and Hemipyth: Difference between revisions

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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

Revision as of 21:35, 14 February 2026

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:

  • Holopyth 2.3
  • Hemipyth √2.√3
  • Ouranpyth 2.√3
  • Demipyth √2.3

The nomenclature is called EPN and EHPN (Eufa's Pythagorean Nomenclature and Eufa's HemiPythagorean Nomenclature). It is based on some other musings I did.

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.

Category Name Mapping or Action Abbreviation Pitches (Revo) Pitches (Evo) Frequency (Hz)

Cents (c)

Prime 2 Prime 3
Pythagorean diatonic nominals unison 0 0 1 D4 293.3 Hz
fifth -1 1 5 A4 440 Hz
fourth 2 -1 4 G4 391.1 Hz
major second -3 2 M2 E4 330 Hz
minor seventh 4 -2 m2 C4 521.481 Hz
major sixth -4 3 M6 B4 495 Hz
minor third 5 -3 m3 F4 ~347.654 Hz
Pythagorean chromatic nominals major third -6 4 M3 P4 F#4 ~371.25 Hz
minor sixth 7 -4 m6 O4 Bb4 ~463.539 Hz
major seventh -7 5 M7 K4 C#4 556.875 Hz
minor second 8 -5 m2 L4 Eb4 ~309.026 Hz
tritone -9 6 TT T4 G#4 417.65625 Hz
Hemipythagorean interchromatic nominals mid third -0.5 0.5 N3 φ4 Ft4 ~359.258 Hz
mid sixth 1.5 -0.5 N6 θ4 Bd4 ~479.011 Hz
mid seventh -1.5 1.5 N7 η4 Ct4 ~538.888 Hz
mid second 2.5 -1.5 N2 λ4 Ed4 ~319.341 Hz
trinterfourth -3.5 2.5 4T γ4 Gt4 ~404.166 Hz
Hemipythagorean Interdiatonic nominals ouranic 0 0.5 67 ω4 Bf4 / Cp4 ~508.068 Hz
chthonic 1 -0.5 23 χ4 Ef4 / Fp4 ~338.712 Hz
naiadic -2 1.5 34 δ4 Gp4 ~381.051 Hz
cocytic 3 -1.5 45 κ4 Af4 ~451.616 Hz
tartaric -3 2.5 78 τ4 Dp5 ~571.577 Hz
barbaric 4 -2.5 12 β4 Df4 ~301.077 Hz
trinterfifth -5 3.5 5T α4 Ap4 ~428.683 Hz
Modifiers super- -19 12 S- DS4 +23.46c
sub- 19 -12 s- Ds4 -23.46c
hyper- -38 24 H- DH4 +46.92c
hypo- 38 -24 h- Dh4 -46.92c
semiper- -9.5 6 Z- DZ4 +11.73c
semisub- 9.5 -6 z- Dz4 -11.73
sesquiper- -28.5 18 Q- DQ4 +35.19c
sesquisub- 28.5 -18 q- Dq4 -35.19c
semimerc- -42 26.5 v- Dv4 ±1.8075c
merc- -84 53 w- Dw4 ±3.615c
semiqian- -242.5 153 σ- Dσ4 ±0.88487c
qian- -485 306 Σ- DΣ4 +1.7697c
co- 1 0 c- – 1200c
trans- see below r- Dr4 3.615c
alter- a- Da4 1.7697c
cis- explicit not trans- k- Dk4 0c
ipso- explicit not alter- i- Di4 0c
den- reverse direction n- –
Evo pitch accidentals -sharp -11 7 -# +113.685c
-flat 11 -7 -b -113.685c
-semisharp -5.5 3.5 -t +56.8425c
-semiflat 5.5 -3.5 -d -56.8425
-artosemisharp 4 -2.5 -f +45.1125c
-semipersemiflat -4 2.5 -p -45.1125c
Syntax interval: (den)(co)(alter)(trans)([semi]qian)([semi]merc)(super/sub/hyper/hypo/semiper/semisub/sesquiper/sesquisub)(nominal)
pitch: (alter)(trans)(pitch-class)([semi]qian)([semi]merc)(super/sub/hyper/hypo/semiper/semisub/sesquiper/sesquisub)(octave)
Extreme example dencoaltertransqianbimercsesquipertrinterfourth ncarΣwQ4T (-1795.53787428) <684 -432.5]

Etymologies of new nominals:

  • Barbaric: Greek-flavored interseptimals inspired by 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 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. Also called semiaugmented fourth by many.
  • Trinterfifth: contraction of tritone-inter-fifth. NOT 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.

Table of synonyms
Alternate name Systematic name
Modifiers neutral- mid-
contra- trans-
Pythagorean comma superunison
pythcomma
Mercator's comma mercunison
mercomma
Holopythagorean nominals octave counison
tone major second
limma minor second
apotome superminor second
ditone major third
Hemipythagorean nominals hemitone semiperminor second
hemilimma barbaric
thalassic
hemifourth chthonic
hemififth mid third
hemisixth naiadic
hemioctave semisubtritone
hemitenth cocytic
hemitwelth ouranic
hemitritave
(hemipyth) meantone semisubmajor second
paramajor fourth trinterfourth
Table of Holopyth up to ±106 fifths
Fifthspan Cents Name Simplified
-106 1192.7699 bitransmercoctave rww1
-105 694.7249 transmercfifth rw5
-104 196.6799 transmercmajor second rwM2
-103 898.6349 transmercmajor sixth rwM6
-102 400.5899 transmercmajor third rwM3
-101 1102.5449 transmercmajor seventh rwM7
-100 604.4999 transmerctritone rwTT
-99 106.4549 transmercsuperminor second rwSm2
-98 808.4099 transmercsuperminor sixth rwSm6
-97 310.3649 transmercsuperminor third rwSm3
-96 1012.3199 transmercsuperminor seventh rwSm7
-95 514.2749 transmercsuperfourth rwS4
-94 16.2299 transmercsuperunison rwS1
-93 718.1849 transmercsuperfifth rwS5
-92 220.1399 transmercsupermajor second rwSM2
-91 922.0949 transmercsupermajor sixth rwSM6
-90 424.0499 transmercsupermajor third rwSM3
-89 1126.0049 transmercsupermajor seventh rwSM7
-88 627.9599 transmercsupertritone rwSTT
-87 129.9149 transmerchyperminor second rwHm2
-86 831.8699 transmerchyperminor sixth rwHm6
-85 333.8249 transmerchyperminor third rwHm3
-84 1035.7799 transmerchyperminor seventh rwHm7
-83 537.7349 transmerchyperfourth rwH4
-82 39.6899 transmerchyperunison rwH1
-81 741.6449 transmerchyperfifth rwH5
-80 243.5999 transmerchypermajor second rwHM2
-79 945.5549 merchypominor seventh whm7
-78 447.5099 merchypofourth wh4
-77 1149.4649 merchypoöctave wh1
-76 651.4199 merchypofifth wh5
-75 153.3749 merchypomajor second whM2
-74 855.3299 merchypomajor sixth whM6
-73 357.2849 merchypomajor third whM3
-72 1059.2399 merchypomajor seventh whM7
-71 561.1949 merchypotritone whTT
-70 63.1499 mercsubminor second wsm2
-69 765.1049 mercsubminor sixth wsm6
-68 267.0599 mercsubminor third wsm3
-67 969.0149 mercsubminor seventh wsm7
-66 470.9699 mercsubfourth ws4
-65 1172.9249 mercsuboctave ws1
-64 674.8799 mercsubfifth ws5
-63 176.8349 mercsubmajor second wsM2
-62 878.7899 mercsubmajor sixth wsM6
-61 380.7449 mercsubmajor third wsM3
-60 1082.6999 mercsubmajor seventh wsM7
-59 584.6549 mercsubtritone wsTT
-58 86.6099 mercminor second wm2
-57 788.5650 mercminor sixth wm6
-56 290.5200 mercminor third wm3
-55 992.4750 mercminor seventh wm7
-54 494.4300 mercfourth w4
-53 1196.3850 transmercoctave / transmercunison rw8 / rw1
-52 698.3400 transfifth r5
-51 200.2950 transmajor second rM2
-50 902.2500 transmajor sixth rM6
-49 404.2050 transmajor third rM3
-48 1106.1600 transmajor seventh rM7
-47 608.1150 transtritone rTT
-46 110.0700 transsuperminor second rSm2
-45 812.0250 transsuperminor sixth rSm6
-44 313.9800 transsuperminor third rSm3
-43 1015.9350 transsuperminor seventh rSm7
-42 517.8900 transsuperfourth rS4
-41 19.8450 transsuperunison rS1
-40 721.8000 transsuperfifth rS5
-39 223.7550 transsupermajor second rSM2
-38 925.7100 transsupermajor sixth rSM6
-37 427.6650 transsupermajor third rSM3
-36 1129.6200 transsupermajor seventh rSM7
-35 631.5750 transsupertritone rSTT
-34 133.5300 transhyperminor second rHm2
-33 835.4850 transhyperminor sixth rHm6
-32 337.4400 transhyperminor third rHm3
-31 1039.3950 transhyperminor seventh rHm7
-30 541.3500 transhyperfourth rH4
-29 43.3050 transhyperunison / hypominor second rH1
-28 745.2600 transhyperfifth / hypominor sixth rH5
-27 247.2150 transhypermajor second / hypominor third rHM2
-26 949.1700 hypominor seventh hm7
-25 451.1250 hypofourth h4
-24 1153.0800 hypoöctave / hypounison h8 / h1
-23 655.0350 hypofifth h5
-22 156.9900 hypomajor second hM2
-21 858.9450 hypomajor sixth hM6
-20 360.9000 hypomajor third hM3
-19 1062.8550 hypomajor seventh hM7
-18 564.8100 hypotritone hTT
-17 66.7650 subminor second sm2
-16 768.7200 subminor sixth sm6
-15 270.6750 subminor third sm3
-14 972.6300 subminor seventh sm7
-13 474.5850 subfourth s4
-12 1176.5400 suboctave / subunison s8 / s1
-11 678.4950 subfifth s5
-10 180.4500 submajor second sM2
-9 882.4050 submajor sixth sM6
-8 384.3600 submajor third sM3
-7 1086.3150 submajor seventh sM7
-6 588.2700 subtritone sTT
-5 90.2250 minor second m2
-4 792.1800 minor sixth m6
-3 294.1350 minor third m3
-2 996.0900 minor seventh m7
-1 498.0450 fourth 4
0 0.0000 unison / octave 1 / 8
1 701.9550 fifth 5
2 203.9100 major second M2
3 905.8650 major sixth M6
4 407.8200 major third M3
5 1109.7750 major seventh M7
6 611.7300 tritone TT
7 113.6850 superminor second Sm2
8 815.6400 superminor sixth Sm6
9 317.5950 superminor third Sm3
10 1019.5500 superminor seventh Sm7
11 521.5050 superfourth S4
12 23.4600 superunison / superoctave S1 / S8
13 725.4150 superfifth S5
14 227.3700 supermajor second SM2
15 929.3250 supermajor sixth SM6
16 431.2800 supermajor third SM3
17 1133.2350 supermajor seventh SM7
18 635.1900 supertritone STT
19 137.1450 hyperminor second Hm2
20 839.1000 hyperminor sixth Hm6
21 341.0550 hyperminor third Hm3
22 1043.0100 hyperminor seventh Hm7
23 544.9650 hyperfourth H4
24 46.9200 hyperunison / hyperoctave H1 / H8
25 748.8750 hyperfifth H5
26 250.8300 hypermajor second HM2
27 952.7850 transhypominor seventh / hypermajor sixth rhm7
28 454.7400 transhypofourth / hypermajor third rh4
29 1156.6950 transhypoöctave / hypermajor third rh1
30 658.6500 transhypofifth / hypermajor third rh5
31 160.6050 transhypomajor second rhM2
32 862.5600 transhypomajor sixth rhM6
33 364.5150 transhypomajor third rhM3
34 1066.4700 transhypomajor seventh rhM7
35 568.4250 transhypotritone rhTT
36 70.3800 transsubminor second rsm2
37 772.3350 transsubminor sixth rsm6
38 274.2900 transsubminor third rsm3
39 976.2450 transsubminor seventh rsm7
40 478.2000 transsubfourth rs4
41 1180.1550 transsuboctave rs1
42 682.1100 transsubfifth rs5
43 184.0650 transsubmajor second rsM2
44 886.0200 transsubmajor sixth rsM6
45 387.9750 transsubmajor third rsM3
46 1089.9300 transsubmajor seventh rsM7
47 591.8850 transsubtritone rsTT
48 93.8400 transminor second rm2
49 795.7950 transminor sixth rm6
50 297.7500 transminor third rm3
51 999.7050 transminor seventh rm7
52 501.6600 transfourth r4
53 3.6150 mercunison / mercoctave w1 / w8
54 705.5700 mercfifth w5
55 207.5250 mercmajor second wM2
56 909.4800 mercmajor sixth wM6
57 411.4350 mercmajor third wM3
58 1113.3901 mercmajor seventh wM7
59 615.3451 merctritone wTT
60 117.3001 mercsuperminor second wSm2
61 819.2551 mercsuperminor sixth wSm6
62 321.2101 mercsuperminor third wSm3
63 1023.1651 mercsuperminor seventh wSm7
64 525.1201 mercsuperfourth wS4
65 27.0751 mercsuperunison wS1
66 729.0301 mercsuperfifth wS5
67 230.9851 mercsupermajor second wSM2
68 932.9401 mercsupermajor sixth wSM6
69 434.8951 mercsupermajor third wSM3
70 1136.8501 mercsupermajor seventh wSM7
71 638.8051 mercsupertritone wSTT
72 140.7601 merchyperminor second wHm2
73 842.7151 merchyperminor sixth wHm6
74 344.6701 merchyperminor third wHm3
75 1046.6251 merchyperminor seventh wHm7
76 548.5801 merchyperfourth wH4
77 50.5351 merchyperunison wH1
78 752.4901 merchyperfifth wH5
79 254.4451 merchypermajor second wHM2
80 956.4001 transmerchypominor seventh rwhm7
81 458.3551 transmerchypofourth rwh4
82 1160.3101 transmerchypoöctave rwh1
83 662.2651 transmerchypofifth rwh5
84 164.2201 transmerchypomajor second rwhM2
85 866.1751 transmerchypomajor sixth rwhM6
86 368.1301 transmerchypomajor third rwhM3
87 1070.0851 transmerchypomajor seventh rwhM7
88 572.0401 transmerchypotritone rwhTT
89 73.9951 transmercsubminor second rwsm2
90 775.9501 transmercsubminor sixth rwsm6
91 277.9051 transmercsubminor third rwsm3
92 979.8601 transmercsubminor seventh rwsm7
93 481.8151 transmercsubfourth rws4
94 1183.7701 transmercsuboctave rws1
95 685.7251 transmercsubfifth rws5
96 187.6801 transmercsubmajor second rwsM2
97 889.6351 transmercsubmajor sixth rwsM6
98 391.5901 transmercsubmajor third rwsM3
99 1093.5451 transmercsubmajor seventh rwsM7
100 595.5001 transmercsubtritone rwsTT
101 97.4551 transmercminor second rwm2
102 799.4101 transmercminor sixth rwm6
103 301.3651 transmercminor third rwm3
104 1003.3201 transmercminor seventh rwm7
105 505.2751 transmercfourth rw4
106 7.2301 bimercunison ww1
Table of Hemipyth up to ±53 fifths
Fifthspan Interchromatic-central Simplified Interdiatonic-central Simplified
Cents Name Cents Name
-53 1196.3850 transmercoctave / transmercunison rw8 / rw1 596.3850 transmercsemisubtritone rwzTT
-52.5 347.3625 transmid third rN3 947.3625 transouranic r67
-52 698.3400 transfifth r5 98.3400 transsemiperminor second rZm2
-51.5 1049.3175 transmid seventh rN7 449.3175 transnaiadic r34
-51 200.2950 transmajor second rM2 800.2950 transsemiperminor sixth rZm6
-50.5 551.2725 transtrinterfourth r4T 1151.2725 transtartaric r78
-50 902.2500 transmajor sixth rM6 302.2500 transsemiperminor third rZm3
-49.5 53.2275 transsemiperbarbaric rZ12 653.2275 transtrinterfifth r5T
-49 404.2050 transmajor third rM3 1004.2050 transsemiperminor seventh rZm7
-48.5 755.1825 transsemipercocytic rZ56 155.1825 transsemipermid second rZN2
-48 1106.1600 transmajor seventh rM7 506.1600 transsemiperfourth rZ4
-47.5 257.1375 transsemiperchthonic rZ23 857.1375 transsemipermid sixth rZN6
-47 608.1150 transtritone rTT 8.1150 transsemiperunison rZ1
-46.5 959.0925 transsemiperouranic rZ67 359.0925 transsemipermid third rZN3
-46 110.0700 transsuperminor second rSm2 710.0700 transsemiperfifth rZ5
-45.5 461.0475 transsemipernaiadic rZ34 1061.0475 transsemipermid seventh rZN7
-45 812.0250 transsuperminor sixth rSm6 212.0250 transsemipermajor second rZM2
-44.5 1163.0025 transsemipertartaric rZ78 563.0025 transsemipertrinterfourth rZ4T
-44 313.9800 transsuperminor third rSm3 913.9800 transsemipermajor sixth rZM6
-43.5 664.9575 transsemipertrinterfifth rZ5T 64.9575 transsuperbarbaric rS12
-43 1015.9350 transsuperminor seventh rSm7 415.9350 transsemipermajor third rZM3
-42.5 166.9125 transsupermid second rSN2 766.9125 transsupercocytic rS56
-42 517.8900 transsuperfourth rS4 1117.8900 transsemipermajor seventh rZM7
-41.5 868.8675 transsupermid sixth rSN6 268.8675 transsuperchthonic rS23
-41 19.8450 transsuperunison rS1 619.8450 transsemipertritone rZTT
-40.5 370.8225 transsupermid third rSN3 970.8225 transsuperouranic rS67
-40 721.8000 transsuperfifth rS5 121.8000 transsesquiperminor second rQm2
-39.5 1072.7775 transsupermid third rSN7 472.7775 transsupernaiadic rS34
-39 223.7550 transsupermajor second rSM2 823.7550 transsesquiperminor sixth rQm6
-38.5 574.7325 transsupertrinterfourth rS4T 1174.7325 transsupertartaric rS78
-38 925.7100 transsupermajor sixth rSM6 325.7100 transsesquiperminor third rQm3
-37.5 76.6875 transsesquiperbarbaric rQ12 676.6875 transsupertrinterfifth rS5T
-37 427.6650 transsupermajor third rSM3 1027.6650 transsesquiperminor seventh rQm7
-36.5 778.6425 transsesquipercocytic rQ56 178.6425 transsesquipermid second rQN2
-36 1129.6200 transsupermajor seventh rSM7 529.6200 transsesquiperfourth rQ4
-35.5 280.5975 transsesquiperchthonic rQ23 880.5975 transsesquipermid sixth rQN6
-35 631.5750 transsupertritone rSTT 31.5750 transsesquiperunison rQ1
-34.5 982.5525 transsesquiperouranic rQ67 382.5525 transsesquipermid third rQN3
-34 133.5300 transhyperminor second rHm2 733.5300 transsesquiperfifth rQ5
-33.5 484.5075 transsesquipernaiadic rQ34 1084.5075 transsesquipermid seventh rQN7
-33 835.4850 transhyperminor sixth rHm6 235.4850 transsesquipermajor second rQM2
-32.5 1186.4625 transsesquipertartaric rQ78 586.4625 transsesquipertrinterfourth rQ4T
-32 337.4400 transhyperminor third rHm3 937.4400 transsesquipermajor sixth rQM6
-31.5 688.4175 transsesquipertrinterfifth rQ5T 88.4175 transhyperbarbaric rH12
-31 1039.3950 transhyperminor seventh rHm7 439.3950 transsesquipermajor third rQM3
-30.5 190.3725 transhypermid second rHN2 790.3725 transhypercocytic rH56
-30 541.3500 transhyperfourth rH4 1141.3500 transsesquipermajor seventh rQM7
-29.5 892.3275 transhypermid sixth rHN6 292.3275 transhyperchthonic rH23
-29 43.3050 transhyperunison rH1 643.3050 transsesquipertritone rQTT
-28.5 394.2825 transhypermid third rHN3 994.2825 transhyperouranic rH67
-28 745.2600 transhyperfifth rH5 145.2600 transsemimercmid second rvN3
-27.5 1096.2375 transhypermid third rHN7 496.2375 transhypernaiadic rH34
-27 247.2150 transhypermajor second rHM2 847.2150 transsemimercmid sixth rvN6
-26.5 598.1925 transhypertrinterfourth rH4T 1198.1925 transsemimercoctave rv8
-26 949.1700 hypominor seventh hm7 349.1700 semimercmid third vN3
-25.5 100.1475 hypomid second hN2 700.1475 hypococytic h56
-25 451.1250 hypofourth h4 1051.1250 semimercmid seventh vN7
-24.5 802.1025 hypomid sixth hN6 202.1025 hypochthonic h23
-24 1153.0800 hypoöctave / hypounison h8 / h1 553.0800 semimerctrinterfourth v4T
-23.5 304.0575 hypomid third hN3 904.0575 hypoouranic h67
-23 655.0350 hypofifth h5 55.0350 sesquisubminor second qm2
-22.5 1006.0125 hypomid seventh hN7 406.0125 hyponaiadic h34
-22 156.9900 hypomajor second hM2 756.9900 sesquisubminor sixth qm6
-21.5 507.9675 hypotrinterfourth h4T 1107.9675 hypotartaric h78
-21 858.9450 hypomajor sixth hM6 258.9450 sesquisubminor third qm3
-20.5 9.9225 sesquisubbarbaric q12 609.9225 hypotrinterfifth h5T
-20 360.9000 hypomajor third hM3 960.9000 sesquisubminor seventh qm7
-19.5 711.8775 sesquisubcocytic q56 111.8775 sesquisubmid second qN2
-19 1062.8550 hypomajor seventh hM7 462.8550 sesquisubfourth q4
-18.5 213.8325 sesquisubchthonic q23 813.8325 sesquisubmid sixth qN6
-18 564.8100 hypotritone hTT 1164.8100 sesquisuboctave q8
-17.5 915.7875 sesquisubouranic q67 315.7875 sesquisubmid third qN3
-17 66.7650 subminor second sm2 666.7650 sesquisubfifth q5
-16.5 417.7425 sesquisubnaiadic q34 1017.7425 sesquisubmid seventh qN7
-16 768.7200 subminor sixth sm6 168.7200 sesquisubmajor second qM2
-15.5 1119.6975 sesquisubtartaric q78 519.6975 sesquisubtrinterfourth q4T
-15 270.6750 subminor third sm3 870.6750 sesquisubmajor sixth qM6
-14.5 621.6525 sesquisubtrinterfifth q5T 21.6525 subbarbaric s12
-14 972.6300 subminor seventh sm7 372.6300 sesquisubmajor third qM3
-13.5 123.6075 submid second sN2 723.6075 subcocytic s56
-13 474.5850 subfourth s4 1074.5850 sesquisubmajor seventh qM7
-12.5 825.5625 submid sixth sN6 225.5625 subchthonic s23
-12 1176.5400 suboctave / subunison s8 / s1 576.5400 sesquisubtritone qTT
-11.5 327.5175 submid third sN3 927.5175 subouranic s67
-11 678.4950 subfifth s5 78.4950 semisubminor second zm2
-10.5 1029.4725 submid seventh sN7 429.4725 subnaiadic s34
-10 180.4500 submajor second sM2 780.4500 semisubminor sixth zm6
-9.5 531.4275 subtrinterfourth s4T 1131.4275 subtartaric s78
-9 882.4050 submajor sixth sM6 282.4050 semisubminor third zm3
-8.5 33.3825 semisubbarbaric z12 633.3825 subtrinterfifth s5T
-8 384.3600 submajor third sM3 984.3600 semisubminor seventh zm7
-7.5 735.3375 semisubcocytic z56 135.3375 semisubmid second zN2
-7 1086.3150 submajor seventh sM7 486.3150 semisubfourth z4
-6.5 237.2925 semisubchthonic z23 837.2925 semisubmid sixth zN6
-6 588.2700 subtritone sTT 1188.2700 semisuboctave z8
-5.5 939.2475 semisubouranic z67 339.2475 semisubmid third zN3
-5 90.2250 minor second m2 690.2250 semisubfifth z5
-4.5 441.2025 semisubnaiadic z34 1041.2025 semisubmid seventh zN7
-4 792.1800 minor sixth m6 192.1800 semisubmajor second zM2
-3.5 1143.1575 semisubtartaric z78 543.1575 semisubtrinterfourth z4T
-3 294.1350 minor third m3 894.1350 semisubmajor sixth zM6
-2.5 645.1125 semisubtrinterfifth z5T 45.1125 barbaric 12
-2 996.0900 minor seventh m7 396.0900 semisubmajor third zM3
-1.5 147.0675 mid second N2 747.0675 cocytic 56
-1 498.0450 fourth 4 1098.0450 semisubmajor seventh zM7
-0.5 849.0225 mid sixth N6 249.0225 chthonic 23
0 0.0000 unison / octave 1 600.0000 semisubtritone zTT
0.5 350.9775 mid third N3 950.9775 ouranic 67
1 701.9550 fifth 5 101.9550 semiperminor second Zm2
1.5 1052.9325 mid seventh N7 452.9325 naiadic 34
2 203.9100 major second M2 803.9100 semiperminor sixth Zm6
2.5 554.8875 trinterfourth 4T 1154.8875 tartaric 78
3 905.8650 major sixth M6 305.8650 semiperminor third Zm3
3.5 56.8425 semiperbarbaric Z12 656.8425 trinterfifth 5T
4 407.8200 major third M3 1007.8200 semiperminor seventh Zm7
4.5 758.7975 semipercocytic Z56 158.7975 semipermid second ZN2
5 1109.7750 major seventh M7 509.7750 semiperfourth Z4
5.5 260.7525 semiperchthonic Z23 860.7525 semipermid sixth ZN6
6 611.7300 tritone TT 11.7300 semiperunison Z1
6.5 962.7075 semiperouranic Z67 362.7075 semipermid third ZN3
7 113.6850 superminor second Sm2 713.6850 semiperfifth Z5
7.5 464.6625 semipernaiadic Z34 1064.6625 semipermid seventh ZN7
8 815.6400 superminor sixth Sm6 215.6400 semipermajor second ZM2
8.5 1166.6175 semipertartaric Z78 566.6175 semipertrinterfourth Z4T
9 317.5950 superminor third Sm3 917.5950 semipermajor sixth ZM6
9.5 668.5725 semipertrinterfifth Z5T 68.5725 superbarbaric S12
10 1019.5500 superminor seventh Sm7 419.5500 semipermajor third ZM3
10.5 170.5275 supermid second SN2 770.5275 supercocytic S56
11 521.5050 superfourth S4 1121.5050 semipermajor seventh ZM7
11.5 872.4825 supermid sixth SN6 272.4825 superchthonic S23
12 23.4600 superunison / superoctave S1 / S8 623.4600 semipertritone ZTT
12.5 374.4375 supermid third SN3 974.4375 superouranic S67
13 725.4150 superfifth S5 125.4150 sesquiperminor second Qm2
13.5 1076.3925 supermid third SN7 476.3925 supernaiadic S34
14 227.3700 supermajor second SM2 827.3700 sesquiperminor sixth Qm6
14.5 578.3475 supertrinterfourth S4T 1178.3475 supertartaric S78
15 929.3250 supermajor sixth SM6 329.3250 sesquiperminor third Qm3
15.5 80.3025 sesquiperbarbaric Q12 680.3025 supertrinterfifth S5T
16 431.2800 supermajor third SM3 1031.2800 sesquiperminor seventh Qm7
16.5 782.2575 sesquipercocytic Q56 182.2575 sesquipermid second QN2
17 1133.2350 supermajor seventh SM7 533.2350 sesquiperfourth Q4
17.5 284.2125 sesquiperchthonic Q23 884.2125 sesquipermid sixth QN6
18 635.1900 supertritone STT 35.1900 sesquiperunison Q1
18.5 986.1675 sesquiperouranic Q67 386.1675 sesquipermid third QN3
19 137.1450 hyperminor second Hm2 737.1450 sesquiperfifth Q5
19.5 488.1225 sesquipernaiadic Q34 1088.1225 sesquipermid seventh QN7
20 839.1000 hyperminor sixth Hm6 239.1000 sesquipermajor second QM2
20.5 1190.0775 sesquipertartaric Q78 590.0775 sesquipertrinterfourth Q4T
21 341.0550 hyperminor third Hm3 941.0550 sesquipermajor sixth QM6
21.5 692.0325 sesquipertrinterfifth Q5T 92.0325 hyperbarbaric H12
22 1043.0100 hyperminor seventh Hm7 443.0100 sesquipermajor third QM3
22.5 193.9875 hypermid second HN2 793.9875 hypercocytic H56
23 544.9650 hyperfourth H4 1144.9650 sesquipermajor seventh QM7
23.5 895.9425 hypermid sixth HN6 295.9425 hyperchthonic H23
24 46.9200 hyperunison / hyperoctave H1 646.9200 sesquipertritone QTT
24.5 397.8975 hypermid third HN3 997.8975 hyperouranic H67
25 748.8750 hyperfifth H5 148.8750 semimercmid second vN3
25.5 1099.8525 hypermid third HN7 499.8525 hypernaiadic H34
26 250.8300 hypermajor second HM2 850.8300 semimercmid sixth vN6
26.5 601.8075 hypertrinterfourth H4T 1.8075 semimercunison v1
27 952.7850 transhypominor seventh rhm7 352.7850 transsemimercmid third rvN3
27.5 103.7625 transhypomid second rhN2 703.7625 transhypococytic rh56
28 454.7400 transhypofourth rh4 1054.7400 transsemimercmid seventh rvN7
28.5 805.7175 transhypomid sixth rhN6 205.7175 transhypochthonic rh23
29 1156.6950 transhypoöctave / transhypounison rh8 / rh1 556.6950 transsemimerctrinterfourth rv4T
29.5 307.6725 transhypomid third rhN3 907.6725 transhypoouranic rh67
30 658.6500 transhypofifth rh5 58.6500 transsesquisubminor second rqm2
30.5 1009.6275 transhypomid seventh rhN7 409.6275 transhyponaiadic rh34
31 160.6050 transhypomajor second rhM2 760.6050 transsesquisubminor sixth rqm6
31.5 511.5825 transhypotrinterfourth rh4T 1111.5825 transhypotartaric rh78
32 862.5600 transhypomajor sixth rhM6 262.5600 transsesquisubminor third rqm3
32.5 13.5375 transsesquisubbarbaric rq12 613.5375 transhypotrinterfifth rh5T
33 364.5150 transhypomajor third rhM3 964.5150 transsesquisubminor seventh rqm7
33.5 715.4925 transsesquisubcocytic rq56 115.4925 transsesquisubmid second rqN2
34 1066.4700 transhypomajor seventh rhM7 466.4700 transsesquisubfourth rq4
34.5 217.4475 transsesquisubchthonic rq23 817.4475 transsesquisubmid sixth rqN6
35 568.4250 transhypotritone rhTT 1168.4250 transsesquisuboctave rq8
35.5 919.4025 transsesquisubouranic rq67 319.4025 transsesquisubmid third rqN3
36 70.3800 transsubminor second rsm2 670.3800 transsesquisubfifth rq5
36.5 421.3575 transsesquisubnaiadic rq34 1021.3575 transsesquisubmid seventh rqN7
37 772.3350 transsubminor sixth rsm6 172.3350 transsesquisubmajor second rqM2
37.5 1123.3125 transsesquisubtartaric rq78 523.3125 transsesquisubtrinterfourth rq4T
38 274.2900 transsubminor third rsm3 874.2900 transsesquisubmajor sixth rqM6
38.5 625.2675 transsesquitrinterfifth rq5T 25.2675 transsubbarbaric rs12
39 976.2450 transsubminor seventh rsm7 376.2450 transsesquisubmajor third rqM3
39.5 127.2225 transsubmid second rsN2 727.2225 transsubcocytic rs56
40 478.2000 transsubfourth rs4 1078.2000 transsesquisubmajor seventh rqM7
40.5 829.1775 transsubmid sixth rsN6 229.1775 transsubchthonic rs23
41 1180.1550 transsuboctave rs1 580.1550 transsesquisubtritone rqTT
41.5 331.1325 transsubmid third rsN3 931.1325 transsubouranic rs67
42 682.1100 transsubfifth rs5 82.1100 transsemisubminor second rzm2
42.5 1033.0875 transsubmid seventh rsN7 433.0875 transsubnaiadic rs34
43 184.0650 transsubmajor second rsM2 784.0650 transsemisubminor sixth rzm6
43.5 535.0425 transsubtrinterfourth rs4T 1135.0425 transsubtartaric rs78
44 886.0200 transsubmajor sixth rsM6 286.0200 transsemisubminor third rzm3
44.5 36.9975 transsemisubbarbaric rz12 636.9975 transsubtrinterfifth rs5T
45 387.9750 transsubmajor third rsM3 987.9750 transsemisubminor seventh rzm7
45.5 738.9525 transsemisubcocytic rz56 138.9525 transsemisubmid second rzN2
46 1089.9300 transsubmajor seventh rsM7 489.9300 transsemisubfourth rz4
46.5 240.9075 transsemisubchthonic rz23 840.9075 transsemisubmid sixth rzN6
47 591.8850 transsubtritone rsTT 1191.8850 transsemisuboctave rz8
47.5 942.8625 transsemisubouranic rz67 342.8625 transsemisubmid third rzN3
48 93.8400 transminor second rm2 693.8400 transsemisubfifth rz5
48.5 444.8175 transsemisubnaiadic rz34 1044.8175 transsemisubmid seventh rzN7
49 795.7950 transminor sixth rm6 195.7950 transsemisubmajor second rzM2
49.5 1146.7725 transsemisubtartaric rz78 546.7725 transsemisubtrinterfourth rz4T
50 297.7500 transminor third rm3 897.7500 transsemisubmajor sixth rzM6
50.5 648.7275 transsemisubtrinterfifth rz5T 48.7275 transbarbaric r12
51 999.7050 transminor seventh rm7 399.7050 transsemisubmajor third rzM3
51.5 150.6825 transmid second rN2 750.6825 transcocytic r56
52 501.6600 transfourth r4 1101.6600 transsemisubmajor seventh rzM7
52.5 852.6375 transmid sixth rN6 252.6375 transchthonic r23
53 3.6150 mercunison / mercoctave w1 / w8 603.6150 mercsemisubtritone wzTT
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