BudjarnLambeth

I am a 23 year old man from regional New South Wales, Australia.

I have a casual interest in xenharmonic/microtonal music. My favourite artists are Brendan Byrnes, Sevish and Greystar.

Frontiers have always fascinated me: The unexplored depths of the Earth's ancient history, lost to deep time. The unexplored far reaches of the solar system, the galaxy and the universe. And, the unexplored depths of the infinite pitch spectrum, an infinite expanse, hiding in plain sight between the keys of the piano!

I am prone to making careless mistakes, especially when calculating things with numbers, so apologies in advance for any of those. Please correct them if you see them.

Music I've made

https://www.youtube.com/playlist?list=PLVHnByvMeRTohfmDPkc0EfOByWaX4xXAF

https://budjarnlambeth.bandcamp.com/

Contact information

https://www.facebook.com/budjarnlambeth/

Families of scales

This is a personal tool to help me navigate the wiki.

Just intonation scales

• Just intonation scales
  • Aliquot scales (modes of the subharmonic series) / EDLs
  • Chord cubes
  • Crystal balls
  • Highschool scales
  • Homothetic JI scales
  • Tritriadic scales
  • Tonality diamonds
    • Breed diamonds
    • Diaconv scales
  • Combination product sets
    • Dekanies
    • Eikosanies
    • Hexanies
    • Pentadekanies
    • Pentanies
  • Overtone scales (modes of the harmonic series) / AFDOs
    • Modes of the oddharmonic series
    • Modes of the prime harmonic series
    • Primodal scales
    • NEJI scales
    • Modes of the triangulharmonic series

Tempered scales

• Tempered scales
  • Clippers
  • Elves
  • Essentially tempered scales
  • Lesfip scales
  • Scales produced by well temperaments
    • Kartvelian scales
  • Dwarves
    • Especially tempered dwarves
    • Marvelous dwarves
  • Hobbits
    • Moment of symmetry scales
      • MOS cradles
  • Scales produced by regular temperaments
    • Scales produced by rank-4 temperaments
      • Scales produced by Keenanismic temperaments
      • Scales produced by Werckismic temperaments
      • Scales produced by Swetismic temperaments
      • Scales produced by Lehmerismic temperaments
      • Scales produced by Kalismic temperaments
    • Scales produced by rank-3 temperaments
      • Families defined by a 2.3.5 comma
        • see Tour of regular temperaments
      • Families defined by a 2.3.7 comma
        • see Tour of regular temperaments
      • Families defined by a 2.3.5.7 comma
        • see Tour of regular temperaments
      • Temperament groups defined by an 11-limit comma
        • see Tour of regular temperaments
    • Scales produced by rank-2 temperaments (map)
      • Scales produced by linear temperaments
      • Moment of symmetry scales
        • MOS cradles
      • Families defined by a 2.3 comma
        • see Tour of regular temperaments
      • Families defined by a 2.3.5 comma
        • see Tour of regular temperaments
      • Clans defined by a 2.3.7 comma
        • see Tour of regular temperaments
      • Clans defined by a 2.3.11 comma
        • see Tour of regular temperaments
      • Clans defined by a 2.3.13 comma
        • see Tour of regular temperaments
      • Clans defined by a 2.5.7 comma
        • see Tour of regular temperaments
      • Clans defined by a 3.5.7 comma
        • see Tour of regular temperaments
      • Temperament groups defined by a 2.3.5.7 comma
        • see Tour of regular temperaments
    • Scales produced by rank-1 temperaments / Equal-step tunings
      • Equal multiplications
        • Ambitonal sequences (AS) / Equal multiplications of a rational interval
        • Arithmetic pitch sequences (APS) / Equal multiplications of an irrational interval
      • Equal divisions
        • Equal divisions of the octave (EDOs or ED2s)
        • Zeta-stretched equal divisions
        • Edonois
          • Equal divisions of the third harmonic (EDTs or ED3s)
          • Equal divisions of the fourth harmonic (ED4s)
          • Equal divisions of the fifth harmonic (ED5s)
          • Equal divisions of the sixth harmonic (ED6s)
          • Equal divisions of the seventh harmonic (ED7s)
          • Equal divisions of the eighth harmonic (ED8s)
          • Equal divisions of the ninth harmonic (ED9s)
          • Equal divisions of the tenth harmonic (ED10s)
          • Equal divisions of the eleventh harmonic (ED11s)
          • ...
          • Equal divisions of the perfect fifth (EDFs or ED3/2s)
          • Equal divisions of the perfect fourth (ED4/3s)
          • Equal divisions of the major sixth (ED5/3s)
          • Equal divisions of the major third (ED5/4s)
          • ...
          • Equal divisions of 5/2 (EDXs or ED5/2s)
          • Equal divisions of 7/2 (ED7/2s)
          • ...
          • Equal divisions of 7/3 (ED7/3s)
          • Equal divisions of 8/3 (ED8/3s)
          • Equal divisions of 10/3 (ED10/3s)
          • ...
          • Equal divisions of 9/4 (EDIXs or ED9/4s)
          • Equal divisions of 11/5 (ED11/5s)
          • Equal divisions of Phi (Edφs)
          • n-cent equal tunings (n-cETs)

Fokker blocks

• Fokker blocks
  • Moment of symmetry scales
    • MOS cradles
  • Superwakalixes
  • Wakalixes
    • r-wakalixes
      • Triple wakalixes
      • Quadruple wakalixes
      • Pentuple wakalixes
      • ...

Metascales

• Metascales
  • Compound scales
  • Scale products and scale powers
  • MOS cradles
  • MOS muddles
  • Polysystemic scales / Polymicrotonal scales

Periodic scales

• Periodic scales
  • Generator-offset scales
  • Maximal harmony epimorphic scales
  • Step-nested scales
    • Moment of symmetry scales
      • MOS cradles
  • Harmonotonic / step-monotonic tunings
    • Xenharmonic series
      • Ambitonal sequences (AS) / Equal multiplications of a rational interval
      • Aliquot scales (modes of the subharmonic series) / EDLs
      • Arithmetic pitch sequences (APS) / Equal multiplications of an irrational interval
      • Powharmonic series
      • Modes of the prime harmonic series
      • Logharmonic series
      • Modes of the metallic harmonic series
      • Modes of the oddharmonic series
      • Subpowharmonic series
      • Sublogharmonic series
      • Modes of the triangulharmonic series
    • Non-arithmetic harmonotonic tunings
      • Powharmonic series
      • Logharmonic series
      • Subpowharmonic series
      • Sublogharmonic series
    • Arithmetic tunings
      • Equal length step tunings
        • Aliquot scales (modes of the subharmonic series) / EDLs
      • Equal frequency step tunings
        • Overtone scales (modes of the harmonic series) / AFDOs
          • Modes of the oddharmonic series
          • Modes of the prime harmonic series
          • Primodal scales
          • NEJI scales
          • Modes of the triangulharmonic series
      • Equal pitch step tunings
        • Rank-1 temperaments / Equal-step tunings
          • Equal multiplications
            • Ambitonal sequences (AS) / Equal multiplications of a rational interval
            • Arithmetic pitch sequences (APS) / Equal multiplications of an irrational interval
          • Equal divisions
            • Equal divisions of the octave (EDOs or ED2s)
            • Zeta-stretched equal divisions
            • Edonois
              • Equal divisions of the third harmonic (EDTs or ED3s)
              • Equal divisions of the fourth harmonic (ED4s)
              • Equal divisions of the fifth harmonic (ED5s)
              • Equal divisions of the sixth harmonic (ED6s)
              • Equal divisions of the seventh harmonic (ED7s)
              • Equal divisions of the eighth harmonic (ED8s)
              • Equal divisions of the ninth harmonic (ED9s)
              • Equal divisions of the tenth harmonic (ED10s)
              • Equal divisions of the eleventh harmonic (ED11s)
              • ...
              • Equal divisions of the perfect fifth (EDFs or ED3/2s)
              • Equal divisions of the perfect fourth (ED4/3s)
              • Equal divisions of the major sixth (ED5/3s)
              • Equal divisions of the major third (ED5/4s)
              • ...
              • Equal divisions of 5/2 (EDXs or ED5/2s)
              • Equal divisions of 7/2 (ED7/2s)
              • ...
              • Equal divisions of 7/3 (ED7/3s)
              • Equal divisions of 8/3 (ED8/3s)
              • Equal divisions of 10/3 (ED10/3s)
              • ...
              • Equal divisions of 9/4 (EDIXs or ED9/4s)
              • Equal divisions of 11/5 (ED11/5s)
              • Equal divisions of Phi (Edφs)
              • n-cent equal tunings (n-cETs)

Miscellaneous scale structures

• Cartesian scales
• Euler-Fokker genera
• Omniconsonant scales
• Yantras

My favourite scales

Overtone scales

Dozenal Cliffedge

14/12

16/12

18/12

23/12

24/12

Dozenal Dungeon

15/12

16/12

18/12

19/12

24/12

Dozenal Freeway

14/12

16/12

18/12

20/12

22/12

24/12

Dozenal Geode

14/12

16/12

18/12

22/12

24/12

Spectral Mechanical

19/16

20/16

24/16

28/16

32/16

Spectral Mirage

18/16

21/16

24/16

25/16

30/16

32/16

Spectral Moonbeam

18/16

19/16

24/16

30/16

32/16

Spectral Springwater

18/16

20/16

24/16

28/16

32/16

Spectral Volcanic

17/16

20/16

24/16

28/16

32/16

Subharm Starship

42/40

42/34

42/32

42/28

42/24

42/21

15edo

Atoll

79.716

398.578

478.294

717.441

956.588

1195.735

Augmented

318.863

398.578

717.441

797.157

1116.020

1195.735

Equipentatonic

239.147

478.294

717.441

956.5881

1195.735

Firedance

239.147

558.010

717.441

956.588

1195.735

Monsoon

239.147

478.294

717.441

1036.304

1195.735

Rainbow

398.578

558.010

717.441

876.872

1036.304

1195.735

Rockpool

398.578

478.294

717.441

956.588

1195.735

21edo

Pelog Lima

114.28571428571429

285.7142857142857

685.7142857142858

800.

1200.

22edo

Manohari

272.72727272727275

490.90909090909093

709.0909090909091

927.2727272727273

981.8181818181819

1200.

Shailaja

272.72727272727275

709.0909090909091

763.6363636363636

981.8181818181819

1200.

Subminor Hexatonic

218.1818181818182

272.72727272727275

490.90909090909093

709.0909090909091

981.8181818181819

1200.

Subminor Pentatonic

272.72727272727275

490.90909090909093

709.0909090909091

981.8181818181819

1200.

43edo

Blues Aeolian Hexatonic

306.9767441860465

502.3255813953488

613.953488372093

697.6744186046511

809.3023255813954

1200.

Blues Aeolian Pentatonic I

306.9767441860465

502.3255813953488

697.6744186046511

809.3023255813954

1200.

Blues Aeolian Pentatonic II

306.9767441860465

697.6744186046511

809.3023255813954

1004.6511627906976

1200.

Blues Bright Double Harmonic

111.62790697674419

390.69767441860466

502.3255813953488

697.6744186046511

809.3023255813954

1004.6511627906976

1088.3720930232557

1200.

Blues Dark Double Harmonic

195.34883720930233

306.9767441860465

502.3255813953488

613.953488372093

697.6744186046511

809.3023255813954

1088.3720930232557

1200.

Blues Dorian Hexatonic

306.9767441860465

502.3255813953488

697.6744186046511

893.0232558139535

1004.6511627906976

1200.

Blues Dorian Pentatonic

306.9767441860465

697.6744186046511

893.0232558139535

1004.6511627906976

1200.

Blues Dorian Septatonic

306.9767441860465

502.3255813953488

613.953488372093

697.6744186046511

893.0232558139535

1004.6511627906976

1200.

Blues Harmonic Hexatonic

195.34883720930233

306.9767441860465

502.3255813953488

697.6744186046511

1088.3720930232557

1200.

Blues Harmonic Septatonic

306.9767441860465

502.3255813953488

613.953488372093

697.6744186046511

809.3023255813954

1088.3720930232557

1200.

Blues Leading

306.9767441860465

502.3255813953488

613.953488372093

697.6744186046511

1004.6511627906976

1088.3720930232557

1200.

Blues Minor

306.9767441860465

502.3255813953488

613.953488372093

697.6744186046511

1004.6511627906976

1200.

Blues Minor Maj7

306.9767441860465

502.3255813953488

613.953488372093

697.6744186046511

1088.3720930232557

1200.

Blues Pentachordal

195.34883720930233

306.9767441860465

502.3255813953488

613.953488372093

697.6744186046511

1200.

Dominant Pentatonic

195.34883720930233

390.69767441860466

697.6744186046511

1004.6511627906976

1200.

Dorian

195.34883720930233

306.9767441860465

502.3255813953488

697.6744186046511

893.0232558139535

1004.6511627906976

1200.

Double Harmonic

111.62790697674419

390.69767441860466

502.3255813953488

697.6744186046511

809.3023255813954

1088.3720930232557

1200.

Hirajoshi

195.34883720930233

306.9767441860465

697.6744186046511

809.3023255813954

1200.

Ionian Pentatonic

390.69767441860466

502.3255813953488

697.6744186046511

1088.3720930232557

1200.

Javanese Pentachordal

111.62790697674419

306.9767441860465

613.953488372093

697.6744186046511

1200.

Kokin-Joshi

195.34883720930233

306.9767441860465

697.6744186046511

893.0232558139535

1200.

Locrian

111.62790697674419

306.9767441860465

502.3255813953488

613.953488372093

809.3023255813954

1004.6511627906976

1200.

Lydian

195.34883720930233

390.69767441860466

613.953488372093

697.6744186046511

893.0232558139535

1088.3720930232557

1200.

Major

195.34883720930233

390.69767441860466

502.3255813953488

697.6744186046511

893.0232558139535

1088.3720930232557

1200.

Major Pentatonic

195.34883720930233

390.69767441860466

697.6744186046511

893.0232558139535

1200.

Minor

195.34883720930233

306.9767441860465

502.3255813953488

697.6744186046511

809.3023255813954

1004.6511627906976

1200.

Minor Harmonic

195.34883720930233

306.9767441860465

502.3255813953488

697.6744186046511

809.3023255813954

1088.3720930232557

1200.

Minor Harmonic Pentatonic

195.34883720930233

306.9767441860465

697.6744186046511

1088.3720930232557

1200.

Minor Hexatonic

195.34883720930233

306.9767441860465

502.3255813953488

697.6744186046511

1004.6511627906976

1200.

Minor Melodic

195.34883720930233

306.9767441860465

502.3255813953488

697.6744186046511

893.0232558139535

1088.3720930232557

1200.

Minor Pentatonic

306.9767441860465

502.3255813953488

697.6744186046511

1004.6511627906976

1200.

Mixolydian

195.34883720930233

390.69767441860466

502.3255813953488

697.6744186046511

893.0232558139535

1004.6511627906976

1200.

Mixolydian Harmonic

390.69767441860466

502.3255813953488

697.6744186046511

809.3023255813954

1004.6511627906976

1200.

Mixolydian Pentatonic

390.69767441860466

502.3255813953488

697.6744186046511

1004.6511627906976

1200.

Phrygian

111.62790697674419

306.9767441860465

502.3255813953488

697.6744186046511

809.3023255813954

1004.6511627906976

1200.

Phrygian Dominant

111.62790697674419

390.69767441860466

502.3255813953488

697.6744186046511

809.3023255813954

1004.6511627906976

1200.

Phrygian Dominant Hexatonic

111.62790697674419

390.69767441860466

502.3255813953488

697.6744186046511

1004.6511627906976

1200.

Phrygian Dominant Pentatonic

390.69767441860466

502.3255813953488

697.6744186046511

809.3023255813954

1200.

Phrygian Pentatonic

111.62790697674419

306.9767441860465

697.6744186046511

809.3023255813954

1200.

Picardy Hexatonic

195.34883720930233

390.69767441860466

502.3255813953488

697.6744186046511

809.3023255813954

1200.

Picardy Pentatonic

195.34883720930233

390.69767441860466

697.6744186046511

809.3023255813954

1200.

53edo

Dozenal Blues

271.6981132075472

498.1132075471698

611.3207547169811

701.8867924528302

1200.

Dozenal Cliffedge

271.6981132075472

498.1132075471698

701.8867924528302

1132.0754716981132

1200.

Dozenal Dungeon

384.90566037735846

498.1132075471698

701.8867924528302

792.4528301886792

1200.

Dozenal Geode

271.6981132075472

498.1132075471698

701.8867924528302

1041.509433962264

1200.

Spectral Arcade

384.90566037735846

475.47169811320754

701.8867924528302

973.5849056603773

1200.

Spectral Mechanical

294.33962264150944

384.90566037735846

701.8867924528302

973.5849056603773

1200.

Spectral Moonbeam

203.77358490566036

294.33962264150944

701.8867924528302

1086.7924528301887

1200.

Spectral Springwater

203.77358490566036

384.90566037735846

701.8867924528302

973.5849056603773

1200.

Spectral Starship

90.56603773584905

384.90566037735846

475.47169811320754

701.8867924528302

973.5849056603773

1200.

Spectral Volcanic

113.2075471698113

384.90566037735846

701.8867924528302

973.5849056603773

1200.

Dalmatian scale

Equipentatonic

116/101

133/101

153/101

176/101

202/101

Blues Aeolian Hexatonic

120/101

135/101

143/101

151/101

160/101

202/101

Blues Aeolian Pentatonic I

120/101

135/101

151/101

160/101

202/101

Blues Aeolian Pentatonic II

120/101

151/101

160/101

180/101

202/101

Blues Bright Double Harmonic

107/101

127/101

135/101

151/101

160/101

180/101

191/101

202/101

Blues Dark Double Harmonic

113/101

120/101

135/101

143/101

151/101

160/101

191/101

202/101

Blues Dorian Hexatonic

120/101

135/101

151/101

170/101

180/101

202/101

Blues Dorian Pentatonic

120/101

151/101

170/101

180/101

202/101

Blues Dorian Septatonic

120/101

135/101

143/101

151/101

170/101

180/101

202/101

Blues Harmonic Hexatonic

113/101

120/101

135/101

151/101

191/101

202/101

Blues Harmonic Septatonic

120/101

135/101

143/101

151/101

160/101

191/101

202/101

Blues Leading

120/101

135/101

143/101

151/101

180/101

191/101

202/101

Blues Minor

120/101

135/101

143/101

151/101

180/101

202/101

Blues Minor Maj7

120/101

135/101

143/101

151/101

191/101

202/101

Blues Pentachordal

113/101

120/101

135/101

143/101

151/101

202/101

Dominant Pentatonic

113/101

127/101

151/101

180/101

202/101

Dorian

113/101

120/101

135/101

151/101

170/101

180/101

202/101

Double Harmonic

107/101

127/101

135/101

151/101

160/101

191/101

202/101

Hirajoshi

113/101

120/101

151/101

160/101

202/101

Ionian Pentatonic

127/101

135/101

151/101

191/101

202/101

Javanese Pentachordal

107/101

120/101

143/101

151/101

202/101

Kokin-Joshi

113/101

120/101

151/101

170/101

202/101

Locrian

107/101

120/101

135/101

143/101

160/101

180/101

202/101

Lydian

113/101

127/101

143/101

151/101

170/101

191/101

202/101

Major

113/101

127/101

135/101

151/101

170/101

191/101

202/101

Major Pentatonic

113/101

127/101

151/101

170/101

202/101

Minor

113/101

120/101

135/101

151/101

160/101

180/101

202/101

Minor Harmonic

113/101

120/101

135/101

151/101

160/101

191/101

202/101

Minor Harmonic Pentatonic

113/101

120/101

151/101

191/101

202/101

Minor Hexatonic

113/101

120/101

135/101

151/101

180/101

202/101

Minor Melodic

113/101

120/101

135/101

151/101

170/101

191/101

202/101

Minor Pentatonic

120/101

135/101

151/101

180/101

202/101

Mixolydian

113/101

127/101

135/101

151/101

170/101

180/101

202/101

Mixolydian Harmonic

127/101

135/101

151/101

160/101

180/101

202/101

Mixolydian Pentatonic

127/101

135/101

151/101

180/101

202/101

Phrygian

107/101

120/101

135/101

151/101

160/101

180/101

202/101

Phrygian Dominant

107/101

127/101

135/101

151/101

160/101

180/101

202/101

Phrygian Dominant Hexatonic

107/101

127/101

135/101

151/101

180/101

202/101

Phrygian Dominant Pentatonic

127/101

135/101

151/101

160/101

202/101

Phrygian Pentatonic

107/101

120/101

151/101

160/101

202/101

Picardy Hexatonic

113/101

127/101

135/101

151/101

160/101

202/101

Picardy Pentatonic

113/101

127/101

151/101

160/101

202/101

Dozenal Dungeon

126/101

135/101

152/101

160/101

202/101

Dozenal Freeway

118/101

135/101

152/101

168/101

185/101

202/101

Dozenal Geode

118/101

135/101

152/101

185/101

202/101

Hand-tuned Cliffedge

118/101

135/101

152/101

190/101

202/101

Hand-tuned Springwater

113/101

126/101

151/101

178/101

202/101

Pelog lima

108/101

119/101

150/101

160/101

202/101

Spectral Mechanical

120/101

126/101

152/101

177/101

202/101

Spectral Moonbeam

114/101

120/101

152/101

189/101

202/101

Spectral Volcanic

107/101

126/101

152/101

177/101

202/101