User:BudjarnLambeth: Difference between revisions
| Line 15: | Line 15: | ||
https://www.facebook.com/budjarnlambeth/ | https://www.facebook.com/budjarnlambeth/ | ||
=== Families of scales | === Families of scales === | ||
This is a personal tool to help me navigate the wiki. | This is a personal tool to help me navigate the wiki. | ||
| Line 43: | Line 43: | ||
==== Tempered scales ==== | ==== Tempered scales ==== | ||
*[[Temperament| | *[[Temperament|Tempered scales]] | ||
**[[Clippers]] | **[[Clippers]] | ||
**[[Elves]] | **[[Elves]] | ||
**[[List of essentially tempered scales|Essentially tempered scales]] | **[[List of essentially tempered scales|Essentially tempered scales]] | ||
**[[Lesfip scales]] | **[[Lesfip scales]] | ||
**[[Well temperament| | **Scales produced by [[Well temperament|well temperaments]] | ||
***[[Kartvelian scales]] | ***[[Kartvelian scales]] | ||
**[[Dwarves]] | **[[Dwarves]] | ||
| Line 56: | Line 56: | ||
***[[MOS scale|Moment of symmetry scales]] | ***[[MOS scale|Moment of symmetry scales]] | ||
****[[MOS Cradle|MOS cradles]] | ****[[MOS Cradle|MOS cradles]] | ||
**[[Regular temperament| | **Scales produced by [[Regular temperament|regular temperaments]] | ||
***[[Rank-4 temperament| | ***Scales produced by [[Rank-4 temperament|rank-4 temperaments]] | ||
****[[Keenanismic temperaments]] | ****Scales produced by [[Keenanismic temperaments]] | ||
****[[Werckismic temperaments]] | ****Scales produced by [[Werckismic temperaments]] | ||
****[[Swetismic temperaments]] | ****Scales produced by [[Swetismic temperaments]] | ||
****[[Lehmerismic temperaments]] | ****Scales produced by [[Lehmerismic temperaments]] | ||
****[[Kalismic temperaments]] | ****Scales produced by [[Kalismic temperaments]] | ||
*** [[Rank-3 temperament| | *** Scales produced by [[Rank-3 temperament|rank-3 temperaments]] | ||
**** Families defined by a 2.3.5 comma | **** Families defined by a 2.3.5 comma | ||
*****''see [[Tour of regular temperaments]]'' | *****''see [[Tour of regular temperaments]]'' | ||
| Line 72: | Line 72: | ||
**** Temperament groups defined by an 11-limit comma | **** Temperament groups defined by an 11-limit comma | ||
*****''see [[Tour of regular temperaments]]'' | *****''see [[Tour of regular temperaments]]'' | ||
*** [[Rank-2 temperament| | *** Scales produced by [[Rank-2 temperament|rank-2 temperaments]] ([[Map of rank-2 temperaments|map]]) | ||
****[[Map of linear temperaments| | ****Scales produced by [[Map of linear temperaments|linear temperaments]] | ||
****[[Linear temperament|Moment of symmetry scales]] | ****[[Linear temperament|Moment of symmetry scales]] | ||
*****[[MOS Cradle|MOS cradles]] | *****[[MOS Cradle|MOS cradles]] | ||
| Line 92: | Line 92: | ||
****Temperament groups defined by a 2.3.5.7 comma | ****Temperament groups defined by a 2.3.5.7 comma | ||
*****''see [[Tour of regular temperaments]]'' | *****''see [[Tour of regular temperaments]]'' | ||
*** [[Equal-step tuning| | *** Scales produced by [[Equal-step tuning|rank-1 temperaments / Equal-step tunings]] | ||
****Equal multiplications | ****Equal multiplications | ||
*****[[Ambitonal sequence|Ambitonal sequences (AS) / Equal multiplications of a rational interval]] | *****[[Ambitonal sequence|Ambitonal sequences (AS) / Equal multiplications of a rational interval]] | ||
Revision as of 09:56, 16 April 2023
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. I am nervous, timid, and care a lot about what other people think of me, but I want to be as helpful as I can be.
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
- Combination product sets
- 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
- Dwarves
- Hobbits
- 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
- Families defined by a 2.3.7 comma
- Families defined by a 2.3.5.7 comma
- Temperament groups defined by an 11-limit comma
- Scales produced by rank-2 temperaments (map)
- Scales produced by linear temperaments
- Moment of symmetry scales
- Families defined by a 2.3 comma
- Families defined by a 2.3.5 comma
- Clans defined by a 2.3.7 comma
- Clans defined by a 2.3.11 comma
- Clans defined by a 2.3.13 comma
- Clans defined by a 2.5.7 comma
- Clans defined by a 3.5.7 comma
- Temperament groups defined by a 2.3.5.7 comma
- Scales produced by rank-1 temperaments / Equal-step tunings
- Equal multiplications
- 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)
- Scales produced by rank-4 temperaments
Fokker blocks
- Fokker blocks
- Moment of symmetry scales
- Superwakalixes
- Wakalixes
- r-wakalixes
- Triple wakalixes
- Quadruple wakalixes
- Pentuple wakalixes
- ...
- r-wakalixes
Metascales
Periodic scales
- Periodic scales
- Generator-offset scales
- Maximal harmony epimorphic scales
- Step-nested scales
- 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
- Arithmetic tunings
- Equal length step tunings
- 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
- Overtone scales (modes of the harmonic series) / AFDOs
- Equal pitch step tunings
- Rank-1 temperaments / Equal-step tunings
- Equal multiplications
- 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)
- Rank-1 temperaments / Equal-step tunings
- Xenharmonic series
Miscellaneous scale structures
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
Manohari
118/101
134/101
152/101
173/101
178/101
202/101
Shailaja
118/101
152/101
157/101
178/101
202/101
Subminor Hexatonic
115/101
118/101
134/101
152/101
178/101
202/101
Subminor Pentatonic
118/101
134/101
152/101
178/101
202/101
Pelog lima
108/101
119/101
150/101
160/101
202/101