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Since the equivalence interval can be anything, names for multi-period mosses are named as a smaller mos repeated (double, triple, quadruple, etc) some number of times. The prefix and abbreviation of the base mos is preceded by the number of duplications. For example, 2L 2s is double trivial, its prefix is 2triv-, and its abbreviation is 2trv.
Since the equivalence interval can be anything, names for multi-period mosses are named as a smaller mos repeated (double, triple, quadruple, etc) some number of times. The prefix and abbreviation of the base mos is preceded by the number of duplications. For example, 2L 2s is double trivial, its prefix is 2triv-, and its abbreviation is 2trv.


===Non-octave twins of diatonic===
===Non-octave twins of diatonic ===
{| class="wikitable"
{| class="wikitable"
|+
|+
Line 1,049: Line 1,049:
!Reasoning or ideas
!Reasoning or ideas
|-
|-
|1L 1s <6/5, 7/6, 20/17*, 19/8*><ref name=":1">Partial detemperament of diminished temperament</ref>
|1L 1s <32/27, 6/5, 7/6, etc.><ref name=":1">Partial detemperament of diminished temperament</ref>
|
|dorianic[2], aeolianic[2], phrygianic[2], locrianic[2]
|
|dor-, aeol-, phryg-, locri-,
|
|dor, aeol, phryg, locri
|
|
|-
|-
Line 1,063: Line 1,063:
!Reasoning or ideas
!Reasoning or ideas
|-
|-
|1L 2s <5/4, 9/7 (21/16), 14/11~33/26*, 13/10*>*
|1L 2s <81/64, 5/4, 9/7 (21/16), etc.>*
|Second magitonic or mystic antrial
|Second magitonic or mystic antrial
| colspan="2" rowspan="2" |use compound
| colspan="2" rowspan="2" |use compound
| rowspan="2" |Linear combination of undivided major third and equal multiples of whole tone, by analogy with magic temperament having a major third generator  
| rowspan="2" |Linear combination of undivided major third and equal multiples of whole tone, by analogy with magic temperament having a major third generator  
|-
|-
|2L 1s <5/4, 9/7 (21/16), 14/11~33/26*, 13/10*>*
|2L 1s <81/64, 5/4, 9/7 (21/16), etc.>*
|Second magitonic or mystic trial
|Second magitonic or mystic trial
|-
|-
Line 1,085: Line 1,085:
!Reasoning or ideas
!Reasoning or ideas
|-
|-
|1L 3s<7/5, 10/7, 11/8*, 3/2><ref>Partial detemperament of subaric temperament</ref>*
|1L 3s<729/512, 1024/729, 25/18 (45/32), 36/25 (64/45), 7/5 (49/36), 10/7 (72/49), 3/2, etc.><ref>Partial detemperament of subaric temperament</ref>*
|(hard) lydianic antetric
|(hard) lydianic antetric
| colspan="2" |use compound
| colspan="2" |use compound
|Linear combination of Lydian tetrachord and undivided tritone, analogous to 3:1 step ratio of hard mosses
|Linear combination of Lydian tetrachord and undivided tritone, analogous to 3:1 step ratio of hard mosses
|-
|-
|2L 2s <7/5, 10/7, 11/8*, 4/3><ref name=":1" />
|2L 2s <729/512, 1024/729, 25/18 (45/32), 64/45, 7/5, 10/7 (72/49), 4/3, etc.><ref name=":1" />
|locrianic  
|locrianic  
|locri-
|locri-
Line 1,096: Line 1,096:
|Locrian tritone is a diminished fifth
|Locrian tritone is a diminished fifth
|-
|-
|3L 1s<7/5, 10/7, 11/8*><ref>Partial detemperament of hedgehog temperament</ref>*
|3L 1s<1024/729, 25/18 (45/32), 36/25 (64/45), 7/5 (49/36), 10/7 (72/49), etc.><ref>Partial detemperament of hedgehog temperament</ref>*
|(hard) lydianic tetric
|(hard) lydianic tetric
| colspan="2" |use compound
| colspan="2" |use compound
Line 1,120: Line 1,120:
!Reasoning or ideas
!Reasoning or ideas
|-
|-
|1L 4s <8/5, 14/9 (32/21), 11/7~52/33*, 13/8*, 3/2>*
|1L 4s <augmented fifth>*
|indopedal, andorianic[5] minor
|indopedal
| rowspan="2" |use compound,
| colspan="2" |use compound
ador
|Linear combination of Hindu pentachord and undivided augmented fifth
| rowspan="2" |use compound,
 
ador-
| rowspan="2" |Linear combination of Hindu pentachord and undivided augmented fifth
Dorian hexachord of Mavila temperament
|-
|1L 4s <5/3, 12/7, 17/10*>*
|indopedal, andorianic[5] major
|-
|-
|2L 3s <4/3>*
|2L 3s <diminished sixth>*
|Micro-pentic
|Micro-pentic
| colspan="2" |use compound
| colspan="2" |use compound
|
|
|-
|-
|2L 3s <8/5, 14/9 (32/21), 11/7*, 13/8*>*
|3L 2s <128/81, 8/5, 14/9 (32/21), etc.>
|anaeolianic, anphrygianic[5] minor
|åeol-, aphryg-
|åeol, aphryg
|Aeolian (natural major) or Phrygian hexachord Mavila temperament
|-
|3L 2s <8/5, 14/9 (32/21), 11/7*, 13/8*>
|aeolianic, phrygianic[5]
|aeolianic, phrygianic[5]
|aeol-, phryg-
|aeol-, phryg-
Line 1,151: Line 1,137:
Phrygian hexachord is analogous to major scale
Phrygian hexachord is analogous to major scale
|-
|-
|4L 1s <8/5, 14/9, 11/7*, 13/8*, 3/2>*
|4L 1s <augmented fifth>*
|indomanual
|indomanual
| colspan="2" |use compound
| colspan="2" |use compound
|Linear combination of Hindu pentachord and undivided augmented fifth
|Linear combination of Hindu pentachord and undivided augmented fifth
|-
|-
|4L 1s <5/3, 12/7, 17/10*>
|4L 1s <27/16, 5/3, 12/7, etc.>
|dorianic[5]
|dorianic[5]
|dor-
|dor-
Line 1,170: Line 1,156:
!Reasoning or ideas
!Reasoning or ideas
|-
|-
|3L 3s <5/3, 12/7, 17/10*><ref name=":1" />
|3L 3s <diminished seventh><ref name=":1" />
|
|
|
|
Line 1,176: Line 1,162:
|
|
|-
|-
|1L 5s <15/8, 27/14, 9/5, 7/4, 5/3*, 12/7*, 17/10*>*
|1L 5s <15/8, 27/14 (63/32), 9/5, 7/4, 27/16, 5/3, 12/7, etc.>*
|Neapolitan-antimachinoid
|Neapolitan-antimachinoid
| colspan="2" |use compound
| colspan="2" |use compound
|Linear combination of Neapolitan hexachord and undivided augmented sixth
|Linear combination of Neapolitan hexachord and undivided augmented sixth
|-
|-
|4L 2s <9/5, 7/4><ref name=":0" />
|4L 2s <9/5, 7/4, etc.><ref name=":0" />
|mixolydianic, dorianic[6]
|mixolydianic, dorianic[6]
|mixo-, dor-
|mixo-, dor-
Line 1,188: Line 1,174:
Dorian heptachord is analogous to major scale
Dorian heptachord is analogous to major scale
|-
|-
|5L 1s <9/5, 7/4, 5/3*, 12/7*, 17/10*>*
|5L 1s <16/9, 9/5, 7/4, 27/16, 5/3, 12/7, etc.>*
|Neapolitan-machinoid
|Neapolitan-machinoid
| colspan="2" |use compound
| colspan="2" |use compound
|Linear combination of Neapolitan hexachord and undivided augmented sixth
|Linear combination of Neapolitan hexachord and undivided augmented sixth
|-
|-
|5L 1s <15/8, 27/14, 11/6*>
|5L 1s <243/128, 15/8, 27/14 (63/32), etc.>
|ionianic[6], lydianic[6]
|ionianic[6], lydianic[6]
|ion-, lyd-
|ion-, lyd-
|ion, lyd
|ion, lyd
|Commonly invoked as Ionian (major) heptacbord
|Commonly invoked as Ionian (major) heptachord
|-
|-
! colspan="5" |8-note mosses
! colspan="5" |8-note mosses
Line 1,207: Line 1,193:
!Reasoning or ideas
!Reasoning or ideas
|-
|-
|4L 4s<7/4, 9/5, 15/8, 27/14, 21/11*, 15/7, 11/5*>*<ref name=":1" /><ref name=":0" />
|4L 4s<diminished ninth>*<ref name=":1" /><ref name=":0" />
|diminished
|diminished
|dimi-
|dimi-
Line 1,213: Line 1,199:
|coincidentally references scale closing at a diminished ninth
|coincidentally references scale closing at a diminished ninth
|-
|-
|5L 3s <15/7, 21/10, 11/5*>
|5L 3s <512/243, 32/15, 56/27, etc.>
|Neapolitan-oneirotonic
|Neapolitan-oneirotonic
| colspan="2" |use compound
| colspan="2" |use compound
|Neapolitan 6/9 scales appear just above oneirotonic proper
|Neapolitan 6/9 scales appear just above oneirotonic proper
|-
|-
|6L 2s <20/9, 16/7><ref name=":0">Major tempered variants</ref>
|6L 2s <20/9, 16/7, etc.><ref name=":0">Major tempered variants</ref>
|napolitonic
|napolitonic
|nap-
|nap-
Line 1,224: Line 1,210:
|Translates minor triad to Neapolitan sixth
|Translates minor triad to Neapolitan sixth
|-
|-
! colspan="5" |9-note mosses
! colspan="5" |9-note mosses (Dominant Seventh Scales)
|-
|-
!Mos
!Mos
Line 1,232: Line 1,218:
!Reasoning or ideas
!Reasoning or ideas
|-
|-
|6L 3s <12/5, 7/3, 40/17*, 19/8*><ref name=":0" />
|6L 3s <12/5, 7/3, etc.><ref name=":0" />
|mahuric
|mahuric
|mahu-
|mahu-
|mahu
|mahu
|Regularisation of Persian/Arabic Mahur scale
|Regularisation of Maqam Mahur scale
|-
|-
|7L 2s <5/2, 18/7 (21/8), 28/11~33/13*, 13/5*>
|7L 2s <81/16, 5/2, 18/7 (21/8), etc.>
|armodecadic
|armodecadic
|ardec-
|ardec-
Line 1,258: Line 1,244:
| rowspan="2" |More transparent of two given names, references how it puts triads in four parts
| rowspan="2" |More transparent of two given names, references how it puts triads in four parts
|-
|-
|8L 2s <14/5, 20/7, 11/4*, 3/1*><ref name=":0" />
|8L 2s <2048/729, 45/16, 72/25 (128/45), 14/5 (49/18), 20/7 (144/49), 3/1, etc.><ref name=":0" />
|choralic (Lydian)
|choralic (Lydian)*
|-
|-
! colspan="5" |11-note mosses
! colspan="5" |11-note mosses (Dominant Ninth Scales)
|-
|-
!Mos
!Mos
Line 1,269: Line 1,255:
!Reasoning or ideas
!Reasoning or ideas
|-
|-
|7L 4s <14/5, 20/7, 11/4*, 8/3*><ref name=":0" />
|7L 4s <729/256, 2048/729, 25/9 (45/16), 72/25 (128/45), 14/5 (49/18), 20/7 (144/49), 8/3, etc.,><ref name=":0" />
|Obikhodic (Locrian)*
|Obikhodic (Locrian)*
| rowspan="2" |obi-
| rowspan="2" |obi-
Line 1,286: Line 1,272:
!Reasoning or ideas
!Reasoning or ideas
|-
|-
|7L 5s <3/1, 14/5, 20/7, 11/4, 8/3, 16/5, 28/9 (64/21), 13/4*>*
|7L 5s <3/1, 729/256, 2048/729, 25/9 (45/16), 72/25 (128/45), 14/5 (49/18), 20/7 (144/49), 8/3, 16/5, 28/9 (64/21), etc.*>*
|
|
|
|
Line 1,292: Line 1,278:
|Canonical macrochromatic scale
|Canonical macrochromatic scale
|-
|-
|8L 4s <16/5, 28/9 (64/21), 22/7*~104/33*, 13/4*><ref name=":0" />
|8L 4s <256/81, 16/5, 28/9 (64/21), etc.><ref name=":0" />
|m-chromatic bastonic
|m-chromatic bastonic
|
|
Line 1,298: Line 1,284:
|bastonic is actually the macro-tetrawood temperament in a thirteenth (one of the '''four''' “Spanish” suits is '''wood'''en batons, or ''bastos'' in Spanish)
|bastonic is actually the macro-tetrawood temperament in a thirteenth (one of the '''four''' “Spanish” suits is '''wood'''en batons, or ''bastos'' in Spanish)
|-
|-
|9L 3s <10/3, 24/7, 17/5*><ref name=":0" />
|9L 3s <27/8, 10/3, 24/7, etc.><ref name=":0" />
|ivanimajiangic
|ivanimajiangic
|
|
Line 1,304: Line 1,290:
|majiangic is actually the macro-tcherepnin temperament in a thirteenth (mahjong tiles have 3 1-9 suits)
|majiangic is actually the macro-tcherepnin temperament in a thirteenth (mahjong tiles have 3 1-9 suits)
|-
|-
! colspan="5" |13-note mosses
! colspan="5" |13-note mosses (Dominant Eleventh Scales)
|-
|-
!Mos
!Mos
Line 1,312: Line 1,298:
!Reasoning or ideas
!Reasoning or ideas
|-
|-
|8L 5s <10/3, 24/7, 17/5*>
|8L 5s <diminished fourteenth>
|
|
|
|
Line 1,318: Line 1,304:
|
|
|-
|-
|9L 4s <18/5, 7/2>
|9L 4s <32/9, 18/5, 7/2, etc.>
|shōsūshoid
|shōsūshoid
|shō-
|shō-
Line 1,324: Line 1,310:
|References Japanese mahjong rules
|References Japanese mahjong rules
|-
|-
|10L 3s <15/4, 27/7, 11/3*>
|10L 3s <243/64, 15/4, 27/7 (63/16), etc.>
|
|
|
|
Line 1,330: Line 1,316:
|
|
|-
|-
! colspan="5" |15-note mosses
! colspan="5" |15-note mosses (Dominant Thirteenth Scales)
|-
|-
!Mos
!Mos
Line 1,338: Line 1,324:
!Reasoning or ideas
!Reasoning or ideas
|-
|-
|10L 5s <21/5, 30/7><ref name=":0" />
|10L 5s <1024/243, 64/15, 112/27, etc.><ref name=":0" />
|
|
|
|
Line 1,344: Line 1,330:
|
|
|-
|-
|11L 4s <9/2>
|11L 4s <9/2, 40/9, 32/7, etc.>
|
|
|
|
Line 1,358: Line 1,344:
!Reasoning or ideas
!Reasoning or ideas
|-
|-
|11L 5s <24/5, 14/3, 80/17*, 19/4*>
|11L 5s <128/27, 24/5, 14/3, etc.>
|
|
|
|
Line 1,364: Line 1,350:
|
|
|-
|-
|12L 4s <5/1, 36/7 (21/4), 56/11~66/13*, 26/5*><ref name=":0" />
|12L 4s <81/16, 5/1, 36/7 (21/4), etc.><ref name=":0" />
|quasiangelic
|quasiangelic
|qang-
|qang-
Line 1,384: Line 1,370:
|Canonical heptadecatonic macroenharmonic scale
|Canonical heptadecatonic macroenharmonic scale
|-
|-
|13L 4s <28/5, 40/7, 11/2*, 6/1*>
|13L 4s <729/128, 4096/729, 50/9 (45/8), 144/25 (256/45), 28/5 (49/9), 40/7 (288/49), 6/1, etc.>
|subsextal[17]
|subsextal[17]
|sub6-
|sub6-
Line 1,398: Line 1,384:
!Reasoning or ideas
!Reasoning or ideas
|-
|-
|12L 6s <28/5, 40/7, 11/2*, 16/3*><ref name=":0" />
|12L 6s <729/128, 4096/729, 50/9 (45/8), 256/45, 28/5, 40/7 (288/49), 16/3, etc.><ref name=":0" />
|subsextal[18]
|subsextal[18]
|sub6-
|sub6-
Line 1,418: Line 1,404:
!Reasoning or ideas
!Reasoning or ideas
|-
|-
|12L 7s <28/5, 40/7, 11/2*, 6/1, 16/3, 32/5, 56/9, 44/7~208/33*, 13/2*><ref name=":0" />
|12L 7s <diminished twentieth><ref name=":0" />
|
|
|
|
Line 1,424: Line 1,410:
|Canonical enneadecatonic macroenharmonic scale
|Canonical enneadecatonic macroenharmonic scale
|-
|-
|13L 6s <32/5, 56/9 (128/21), 44/7~208/33*, 13/2*>
|13L 6s <512/81, 32/5, 56/9 (128/21), etc.>
|
|
|
|
Line 1,430: Line 1,416:
|
|
|-
|-
|14L 5s <20/3, 48/7, 34/5*>
|14L 5s <27/4, 20/3, 48/7, etc.>
|
|
|
|
Line 1,444: Line 1,430:
!Reasoning or ideas
!Reasoning or ideas
|-
|-
|13L 7s <20/3, 48/7, 34/5*>
|13L 7s <diminished twenty-first>
|Guidotonic (diminished)
|Guidotonic (diminished)
| rowspan="3" |guido-
| rowspan="3" |guido-
Line 1,450: Line 1,436:
| rowspan="3" |In reference to the Guidonian hand
| rowspan="3" |In reference to the Guidonian hand
|-
|-
|14L 6s <36/5, 7/1><ref name=":0" />
|14L 6s <36/5, 7/1, etc.><ref name=":0" />
|Guidotonic (dominant)
|Guidotonic (dominant)
|-
|-
|15L 5s <15/2, 54/7, 22/3*><ref name=":0" />
|15L 5s <243/32, 15/2, 54/7 (63/8), etc.><ref name=":0" />
|Guidotonic (major)
|Guidotonic (major)
|-
|-
Line 1,464: Line 1,450:
!Reasoning or ideas
!Reasoning or ideas
|-
|-
|15L 7s <42/5, 60/7>
|15L 7s <2048/243, 128/15, 224/27, etc.>
|
|
|
|
Line 1,470: Line 1,456:
|
|
|-
|-
|16L 6s <80/9, 64/7><ref name=":0" />
|16L 6s <80/9, 64/7, etc.><ref name=":0" />
|
|
|
|
Line 1,476: Line 1,462:
|
|
|-
|-
|17L 5s <48/5, 28/3, 9/1, 10/1, 72/7 (21/2)>*
|17L 5s <augmented twenty-third>*
|
|
|
|
Line 1,490: Line 1,476:
!Reasoning or ideas
!Reasoning or ideas
|-
|-
|16L 7s <48/5, 28/3, 160/17*, 19/2*>
|16L 7s <256/27, 48/5, 28/3, etc.>
|
|
|
|
Line 1,496: Line 1,482:
|
|
|-
|-
|17L 6s <10/1, 72/7 (21/2), 112/11~132/13*, 51/5*>
|17L 6s <81/8, 10/1, 72/7 (21/2), etc.>
|archangelic
|archangelic
|
|
Line 1,516: Line 1,502:
|In reference to Tressette scoring counting the whole deck as 10⅔ points  
|In reference to Tressette scoring counting the whole deck as 10⅔ points  
|-
|-
|18L 6s <56/5, 80/7, 11/1*, 12/1*><ref name=":0" />
|18L 6s <8192/729, 100/9 (45/4), 288/25 (512/45), 56/5 (98/9), 80/7 (576/49), 12/1, etc.><ref name=":0" />
|hendecoidal[24]
|hendecoidal[24]
|hendec-
|hendec-
Line 1,530: Line 1,516:
!Reasoning or ideas
!Reasoning or ideas
|-
|-
|19L 6s <56/5, 80/7, 11/1*, 32/3*>
|19L 6s <729/64, 8192/729, 100/9 (45/4), 288/25 (512/45), 56/5 (98/9), 80/7 (576/49), 32/3, etc.>
|hendecoidal[25]
|hendecoidal[25]
|hendec-
|hendec-
Line 1,550: Line 1,536:
!Reasoning or ideas
!Reasoning or ideas
|-
|-
|18L 8s <64/5, 112/9 (256/21), 88/7~416/33*, 13/1*><ref name=":0" />
|18L 8s <64/5, 112/9 (256/21), etc.><ref name=":0" />
|Petrushkatonic (minor)
|Petrushkatonic (minor)
| rowspan="2" |petrushka-
| rowspan="2" |petrushka-
Line 1,556: Line 1,542:
| rowspan="2" |In reference to the “27th chord” which appears in Stravinsky’s ''Petrushka''
| rowspan="2" |In reference to the “27th chord” which appears in Stravinsky’s ''Petrushka''
|-
|-
|19L 7s <40/3, 96/7, 52/5*, 68/5*>
|19L 7s <27/2, 40/3, 96/7, etc.>
|Petrushkatonic (major)
|Petrushkatonic (major)
|}
|}
Line 1,670: Line 1,656:
!''k''th descendant
!''k''th descendant
|-
|-
|From [[Diatonic, Chromatic, Enharmonic, Subchromatic]]
|From [[diatonic, chromatic, enharmonic, subchromatic]]
|n/a
|n/a
|n/a
|n/a
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