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User:Moremajorthanmajor/3L 1s (perfect fifth-equivalent): Difference between revisions

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}}'''3L 1s<3/2>''', is a fifth-repeating MOS scale. The notation "<3/2>" means the period of the MOS is 3/2, disambiguating it from octave-repeating [[3L 1s]]. The name of the period interval is called the '''sesquitave''' (by analogy to the [[tritave]]).  
}}'''3L 1s<3/2>''', is a fifth-repeating MOS scale. The notation "<3/2>" means the period of the MOS is 3/2, disambiguating it from octave-repeating [[3L 1s]]. The name of the period interval is called the '''sesquitave''' (by analogy to the [[tritave]]).  
   
   
 
The generator range is 171.4 to 240 cents, placing it near the [[9/8|diatonic major second]], usually representing a major second of some type. The dark (chroma-negative) generator is, however, its fifth complement (480 to 514.3 cents).  
The generator range is 171.4 to 240 cents, placing it near the [[9/8|diatonic major second]], usually representing a major second of some type. The dark (chroma-negative) generator is, however, its fifth complement (480 to 514.3 cents).  
 
 
Line 325: Line 325:
|Bbb
|Bbb
 
 
|3bb, 3cc
|3b, 3c
 
 
|10\15
|10\15
Line 357: Line 357:
|'''Bb'''
|'''Bb'''
 
 
|'''3b, 3c'''
|'''3'''
 
 
|'''11\15'''
|'''11\15'''
Line 393: Line 393:
|B
|B
 
 
|3
|3#
 
 
|12\15
|12\15
Line 429: Line 429:
|B#
|B#
 
 
|3#
|3x
 
 
|13\15
|13\15
Line 462: Line 462:
 
 
|Dob, Solb
|Dob, Solb
−
|Hb
|Hb
| 4b, 4c
−
|4b, 4c
−
|14\15
|14\15
   
   
−
646.153…
646.153…
−
|16\18
|16\18
   
   
−
619.354…
619.354…
−
|6\7
|6\7
   
   
−
600
600
−
|14\17
|14\17
   
   
−
579.310…
579.310…
−
|8\10
|8\10
   
   
−
564.705…
564.705…
−
|10\13
|10\13
 
 
Line 556: Line 535:
757.894…
757.894…
 
 
|20\18
| 20\18
 
 
774.193…
774.193…
 
 
| rowspan="2" |8\8
| rowspan="2" | 8\8
 
 
800
800
Line 572: Line 551:
847.058…
847.058…
 
 
|16\13
| 16\13
 
 
872.{{Overline|72}}
872.{{Overline|72}}
Line 592: Line 571:
821.052…
821.052…
 
 
|21\18
| 21\18
 
 
812.903…
812.903…
 
 
|19\17
| 19\17
 
 
786.206…
786.206…
 
 
|11\10
| 11\10
 
 
776.470…
776.470…
 
 
|14\13
| 14\13
 
 
763.{{Overline|63}}
763.{{Overline|63}}
Line 646: Line 625:
|-
|-
 
 
|Re#, La#
| Re#, La#
 
 
|C#
|C#
 
 
|5#
| 5#
 
 
|20\15
|20\15
Line 672: Line 651:
1034.482…
1034.482…
 
 
|15\10
| 15\10
 
 
1058.823…
1058.823…
Line 696: Line 675:
1010.526…
1010.526…
 
 
|26\18
| 26\18
 
 
1006.451…
1006.451…
Line 728: Line 707:
1073.684…
1073.684…
 
 
|28\18
| 28\18
 
 
1083.870…
1083.870…
Line 736: Line 715:
1100
1100
 
 
|27\17
| 27\17
 
 
1117.241…
1117.241…
 
 
|16\10
| 16\10
 
 
1129.411…
1129.411…
 
 
|21\9
| 21\9
 
 
1145.{{Overline|45}}
1145.{{Overline|45}}
Line 752: Line 731:
|Mi#, Si#
|Mi#, Si#
 
 
|D#
| D#
 
 
|6#
|6#
 
 
|24\15
| 24\15
 
 
1107.692…
1107.692…
 
 
| rowspan="2" |18\11
| rowspan="2" | 18\11
 
 
1136.842…
1136.842…
Line 768: Line 747:
1161.290…
1161.290…
 
 
|12\7
| 12\7
 
 
1200
1200
Line 790: Line 769:
|Ebb
|Ebb
 
 
|7bb, 7cc
|7b, 7c
 
 
|25\15
|25\15
Line 800: Line 779:
1122.580…
1122.580…
 
 
|11\7
| 11\7
 
 
1100
1100
Line 822: Line 801:
|'''Eb'''
|'''Eb'''
 
 
|'''7b, 7c'''
|'''7'''
 
 
|'''26\15'''
|'''26\15'''
Line 856: Line 835:
|Fa#, Do#
|Fa#, Do#
 
 
|E
| E
 
 
|7
|7#
 
 
|27\15
|27\15
Line 868: Line 847:
1263.157…
1263.157…
 
 
|33\18
| 33\18
 
 
1277.419…
1277.419…
Line 894: Line 873:
|E#
|E#
 
 
|7#
|7x
 
 
|28\15
|28\15
Line 908: Line 887:
1354.838…
1354.838…
 
 
|14\7
| 14\7
 
 
1400
1400
Line 952: Line 931:
1270.588…
1270.588…
 
 
|23\18
| 23\18
 
 
1254.{{Overline|54}}
1254.{{Overline|54}}
Line 962: Line 941:
!F
!F
 
 
!8, F
! 8, F
 
 
!30\15
! 30\15
 
 
1384.615…
1384.615…
 
 
!22\11
! 22\11
 
 
1389.473…
1389.473…
Line 980: Line 959:
1400
1400
 
 
!34\17
! 34\17
 
 
1406.896…
1406.896…
 
 
!20\10
! 20\10
 
 
1411.764…
1411.764…
Line 1,004: Line 983:
1430.769…
1430.769…
 
 
|23\11
| 23\11
 
 
1452.631…
1452.631…
Line 1,016: Line 995:
1500
1500
 
 
|37\17
| 37\17
 
 
1531.034…
1531.034…
 
 
|22\10
| 22\10
 
 
1552.941…
1552.941…
Line 1,030: Line 1,009:
|-
|-
 
 
|Reb, Lab
| Reb, Lab
 
 
|Gb
|Gb
Line 1,044: Line 1,023:
1515.789…
1515.789…
 
 
|39\18
| 39\18
 
 
1509.677…
1509.677…
Line 1,112: Line 1,091:
1642.105…
1642.105…
 
 
|43\18
| 43\18
 
 
1664.516…
1664.516…
 
 
| rowspan="2" |17\7
| rowspan="2" | 17\7
 
 
1700
1700
Line 1,204: Line 1,183:
|Mi#, Si#
|Mi#, Si#
 
 
|A#
| A#
 
 
|X#, A#
|X#, A#
Line 1,232: Line 1,211:
1976.470…
1976.470…
 
 
|37\13
| 37\13
 
 
2018.{{Overline|18}}
2018.{{Overline|18}}
Line 1,252: Line 1,231:
1819.354…
1819.354…
 
 
|18\7
| 18\7
 
 
1800
1800
Line 1,264: Line 1,243:
1764.705…
1764.705…
 
 
|32\13
| 32\13
 
 
1745.{{Overline|45}}
1745.{{Overline|45}}
Line 1,308: Line 1,287:
|Fa#, Do#
|Fa#, Do#
 
 
|B
| B
 
 
|E, C
|E, C
Line 1,320: Line 1,299:
1957.894…
1957.894…
 
 
|51\18
| 51\18
 
 
1974.193…
1974.193…
Line 1,446: Line 1,425:
|}
|}
   
   
−
{| class="wikitable"
{| class="wikitable"
−
|+Relative cents
|+Relative cents
! colspan="3" | Notation
−
! colspan="3" |Notation
−
!Supersoft
!Supersoft
−
!Soft
!Soft
−
!Semisoft
!Semisoft
−
!Basic
!Basic
−
!Semihard
!Semihard
−
!Hard
!Hard
−
!Superhard
!Superhard
−
|-
|-
! Diatonic
−
!Napoli
!Diatonic
! Bijou
!~15edf
−
!Napoli
−
!Bijou
−
!~15edf
−
!~11edf
!~11edf
−
!~18edf
!~18edf
−
!~7edf
!~7edf
−
!~17edf
!~17edf
−
!~10edf
!~10edf
−
!~13edf
!~13edf
−
|-
|-
−
|Do#, Sol#
|Do#, Sol#
−
|F#
|F#
−
|0#, D#
|0#, D#
−
|1\15
|1\15
   
   
−
''46.{{Overline|6}}''
''46.{{Overline|6}}''
−
|1\11
|1\11
   
   
−
''63.{{Overline|63}}''
''63.{{Overline|63}}''
−
|2\18
|2\18
   
   
−
''77.7̄''
''77.7̄''
−
| rowspan="2" |1\7
| rowspan="2" |1\7
   
   
−
''100''
''100''
| 3\17
   
   
−
|3\17
−
''123.529…''
''123.529…''
| 2\10
   
   
−
|2\10
−
''140''
''140''
−
|3\13
|3\13
   
   
−
''161.538…''
''161.538…''
−
|-
|-
−
|Reb, Lab
|Reb, Lab
| Gb
−
|Gb
−
|1b, 1c
|1b, 1c
−
|3\15
|3\15
   
   
−
''140''
''140''
−
|2\11
|2\11
   
   
−
''127.{{Overline|27}}''
''127.{{Overline|27}}''
−
|3\18
|3\18
   
   
−
''116.{{Overline|6}}''
''116.{{Overline|6}}''
| 2\17
   
   
−
|2\17
−
''82.352…''
''82.352…''
−
|1\10
|1\10
   
   
−
''70''
''70''
−
|1\13
|1\13
   
   
−
''53.846…''
''53.846…''
−
|-
|-
−
|'''Re, La'''
|'''Re, La'''
−
|'''G'''
|'''G'''
−
|'''1'''
|'''1'''
−
|'''4\15'''
|'''4\15'''
   
   
−
'''''186.{{Overline|6}}'''''
'''''186.{{Overline|6}}'''''
−
|'''3\11'''
|'''3\11'''
   
   
−
'''''190.{{Overline|90}}'''''
'''''190.{{Overline|90}}'''''
−
|'''5\18'''
|'''5\18'''
   
   
−
'''''194.{{Overline|4}}'''''
'''''194.{{Overline|4}}'''''
−
|'''2\7'''
|'''2\7'''
   
   
−
'''''200'''''
'''''200'''''
−
|'''5\17'''
|'''5\17'''
   
   
−
'''''205.882…'''''
'''''205.882…'''''
−
|'''3\10'''
|'''3\10'''
   
   
−
'''''210'''''
'''''210'''''
−
|'''4\13'''
|'''4\13'''
   
   
−
'''''215.384…'''''
'''''215.384…'''''
−
|-
|-
−
|Re#, La#
|Re#, La#
| G#
−
| 1#
|G#
−
|1#
−
|5\15
|5\15
   
   
−
''233.{{Overline|3}}''
''233.{{Overline|3}}''
−
|4\11
|4\11
   
   
−
''254.{{Overline|54}}''
''254.{{Overline|54}}''
−
|7\18
|7\18
   
   
−
''272.2̄''
''272.2̄''
−
| rowspan="2" |3\7
| rowspan="2" |3\7
   
   
−
''300''
''300''
−
|8\17
|8\17
   
   
−
''329.411…''
''329.411…''
−
|5\10
|5\10
   
   
−
''350''
''350''
−
|7\13
|7\13
   
   
−
''376.923…''
''376.923…''
−
|-
|-
−
|Mib, Sib
|Mib, Sib
−
|Ab
|Ab
−
|2b, 2c
|2b, 2c
−
|7\15
|7\15
   
   
−
''326.{{Overline|6}}''
''326.{{Overline|6}}''
−
|5\11
|5\11
   
   
−
''318.{{Overline|18}}''
''318.{{Overline|18}}''
| 8\18
   
   
−
|8\18
−
''311.{{Overline|1}}''
''311.{{Overline|1}}''
−
|7\17
|7\17
   
   
−
''288.235…''
''288.235…''
| 4\10
   
   
−
|4\10
−
''280''
''280''
−
|5\13
|5\13
   
   
−
''269.230…''
''269.230…''
−
|-
|-
−
|Mi, Si
|Mi, Si
−
|A
|A
| 2
−
|2
−
|8\15
|8\15
   
   
−
''373.{{Overline|3}}''
''373.{{Overline|3}}''
−
|6\11
|6\11
   
   
−
''381.{{Overline|81}}''
''381.{{Overline|81}}''
−
|10\18
|10\18
   
   
−
''388.{{Overline|8}}''
''388.{{Overline|8}}''
−
|4\7
|4\7
   
   
−
''400''
''400''
−
|10\17
|10\17
   
   
−
''411.764…''
''411.764…''
−
|6\10
|6\10
   
   
−
''420''
''420''
−
|8\13
|8\13
   
   
−
''430.769…''
''430.769…''
−
|-
|-
−
|Mi#, Si#
|Mi#, Si#
−
|A#
|A#
−
|2#
|2#
−
|9\15
|9\15
   
   
−
''420''
''420''
−
| rowspan="2" |7\11
| rowspan="2" |7\11
   
   
−
''445.{{Overline|45}}''
''445.{{Overline|45}}''
|12\18
   
   
−
|12\18
−
''466.{{Overline|6}}''
''466.{{Overline|6}}''
−
|5\7
|5\7
   
   
−
''500''
''500''
−
|13\17
|13\17
   
   
−
''535.294…''
''535.294…''
−
|8\10
|8\10
   
   
−
''560''
''560''
−
|11\13
|11\13
   
   
−
''592.307…''
''592.307…''
−
|-
|-
−
|Fab, Dob
|Fab, Dob
−
|Bbb
|Bbb
|3b, 3c
−
|3bb, 3cc
−
|10\15
|10\15
   
   
−
''466.{{Overline|6}}''
''466.{{Overline|6}}''
−
|11\18
|11\18
   
   
−
''427.{{Overline|7}}''
''427.{{Overline|7}}''
−
|4\7
|4\7
   
   
−
''400''
''400''
−
|9\17
|9\17
   
   
−
''370.588…''
''370.588…''
−
|5\10
|5\10
   
   
−
''350''
''350''
−
|6\13
|6\13
   
   
−
''323.076.…''
''323.076.…''
|-
−
|-
−
|'''Fa, Do'''
|'''Fa, Do'''
−
|'''Bb'''
|'''Bb'''
|'''3'''
−
|'''3b, 3c'''
−
|'''11\15'''
|'''11\15'''
   
   
−
'''''513.{{Overline|3}}'''''
'''''513.{{Overline|3}}'''''
−
|'''8\11'''
|'''8\11'''
   
   
−
'''''509.{{Overline|09}}'''''
'''''509.{{Overline|09}}'''''
−
|'''13\18'''
|'''13\18'''
   
   
−
'''''505.{{Overline|5}}'''''
'''''505.{{Overline|5}}'''''
−
|'''5\7'''
|'''5\7'''
   
   
−
'''''500'''''
'''''500'''''
−
|'''12\17'''
|'''12\17'''
   
   
−
'''''494.117…'''''
'''''494.117…'''''
−
|'''7\10'''
|'''7\10'''
   
   
−
'''''490'''''
'''''490'''''
−
|'''9\13'''
|'''9\13'''
   
   
−
'''''484.615…'''''
'''''484.615…'''''
−
|-
|-
−
|Fa#, Do#
|Fa#, Do#
| B
|3#
|12\15
   
   
−
''560''
|B
|9\11
   
   
−
''572.{{Overline|72}}''
|3
| 15\18
   
   
−
|12\15
−
''560''
−
|9\11
−
''572.{{Overline|72}}''
−
|15\18
−
''583.{{Overline|3}}''
''583.{{Overline|3}}''
−
|6\7
|6\7
   
   
−
''600''
''600''
−
|15\17
|15\17
   
   
−
''617.647…''
''617.647…''
−
|9\10
|9\10
   
   
−
''630''
''630''
−
|12\13
|12\13
   
   
−
''646.153…''
''646.153…''
−
|-
|-
| Fax, Dox
−
|Fax, Dox
−
|B#
|B#
|3x
−
|3#
−
|13\15
|13\15
   
   
−
''606. {{Overline|6}}''
''606. {{Overline|6}}''
−
| rowspan="2" |10\11
| rowspan="2" |10\11
   
   
−
''636.{{Overline|36}}''
''636.{{Overline|36}}''
−
|17\18
|17\18
   
   
−
''661.{{Overline|1}}''
''661.{{Overline|1}}''
−
|7\7
|7\7
   
   
−
''700''
''700''
−
|18\17
|18\17
   
   
−
''741.176…''
''741.176…''
−
|11\10
|11\10
   
   
−
''770''
''770''
−
|15\13
|15\13
   
   
−
''807.692…''
''807.692…''
−
|-
|-
−
|Dob, Solb
|Dob, Solb
−
|Hb
|Hb
−
|4b, 4c
|4b, 4c
−
|14\15
|14\15
   
   
−
''653.{{Overline|3}}''
''653.{{Overline|3}}''
−
|16\18
|16\18
   
   
−
''622.{{Overline|2}}''
''622.{{Overline|2}}''
−
|6\7
|6\7
   
   
−
''600''
''600''
| 14\17
   
   
−
|14\17
−
''576.470…''
''576.470…''
−
| 8\10
|8\10
   
   
−
''560''
''560''
−
|10\13
|10\13
   
   
−
''538.461…''
''538.461…''
−
|-
|-
−
!Do, Sol
!Do, Sol
−
!H
!H
−
!4
!4
−
! colspan="7" |''700''
! colspan="7" |''700''
−
|-
|-
−
|Do#, Sol#
|Do#, Sol#
−
|Η#
|Η#
−
|4#
|4#
−
|16\15
|16\15
   
   
−
''746.{{Overline|6}}''
''746.{{Overline|6}}''
−
|12\11
|12\11
   
   
−
''763.{{Overline|63}}''
''763.{{Overline|63}}''
−
|20\18
|20\18
   
   
−
''777.{{Overline|7}}''
''777.{{Overline|7}}''
−
| rowspan="2" |8\7
| rowspan="2" |8\7
   
   
−
''800''
''800''
−
|20\17
|20\17
   
   
−
''823.529…''
''823.529…''
−
|12\10
|12\10
   
   
−
''840''
''840''
−
|16\13
|16\13
   
   
−
''861.538…''
''861.538…''
−
|-
|-
−
|Reb, Lab
|Reb, Lab
−
|Cb
|Cb
−
|5b, 5c
|5b, 5c
−
|18\15
|18\15
   
   
−
''840''
''840''
−
|13\11
|13\11
   
   
−
''827.{{Overline|27}}''
''827.{{Overline|27}}''
−
|21\18
|21\18
   
   
−
''816.{{Overline|6}}''
''816.{{Overline|6}}''
| 19\17
   
   
−
|19\17
−
''782.352…''
''782.352…''
−
|11\10
|11\10
   
   
−
''770''
''770''
−
|14\13
|14\13
   
   
−
''753.846…''
''753.846…''
−
|-
|-
−
|'''Re, La'''
|'''Re, La'''
−
|'''C'''
|'''C'''
−
|'''5'''
|'''5'''
−
|'''19\15'''
|'''19\15'''
   
   
−
'''''886.{{Overline|6}}'''''
'''''886.{{Overline|6}}'''''
−
|'''14\11'''
|'''14\11'''
   
   
−
'''''890.{{Overline|90}}'''''
'''''890.{{Overline|90}}'''''
−
|'''23\18'''
|'''23\18'''
   
   
−
'''''894.{{Overline|4}}'''''
'''''894.{{Overline|4}}'''''
−
|'''9\7'''
|'''9\7'''
   
   
−
'''''900'''''
'''''900'''''
|'''22\17'''
   
   
−
|'''22\17'''
−
'''''905.882…'''''
'''''905.882…'''''
−
|'''13\10'''
|'''13\10'''
   
   
−
'''''910'''''
'''''910'''''
−
|'''17\13'''
|'''17\13'''
   
   
−
'''''915.384…'''''
'''''915.384…'''''
−
|-
|-
| Re#, La#
−
|Re#, La#
−
|C#
|C#
−
|5#
|5#
−
|20\15
|20\15
   
   
−
''933.{{Overline|3}}''
''933.{{Overline|3}}''
−
|15\11
|15\11
   
   
−
''954.{{Overline|54}}''
''954.{{Overline|54}}''
−
|25\18
|25\18
   
   
−
''972.{{Overline|2}}''
''972.{{Overline|2}}''
| rowspan="2" | 10\7
   
   
−
| rowspan="2" |10\7
−
''1000''
''1000''
−
|25\17
|25\17
   
   
−
''1029.411…''
''1029.411…''
−
|15\10
|15\10
   
   
−
''1050''
''1050''
−
|20\13
|20\13
   
   
−
''1076.923…''
''1076.923…''
−
|-
|-
−
|Mib, Sib
|Mib, Sib
−
|Db
|Db
−
|6b, 6c
|6b, 6c
−
|22\15
|22\15
   
   
−
''1026.{{Overline|6}}''
''1026.{{Overline|6}}''
−
|16\11
|16\11
   
   
−
''1018.{{Overline|18}}''
''1018.{{Overline|18}}''
−
|26\18
|26\18
   
   
−
''1011. {{Overline|1}}''
''1011. {{Overline|1}}''
−
|24\17
|24\17
   
   
−
''988.235…''
''988.235…''
−
|14\10
|14\10
   
   
−
''980''
''980''
−
|18\13
|18\13
   
   
−
''969.230…''
''969.230…''
−
|-
|-
−
|Mi, Si
|Mi, Si
−
|D
|D
−
|6
|6
| 23\15
   
   
−
|23\15
−
''1073.{{Overline|3}}''
''1073.{{Overline|3}}''
−
|17\11
|17\11
   
   
−
''1081.{{Overline|81}}''
''1081.{{Overline|81}}''
−
|28\18
|28\18
   
   
−
''1088.{{Overline|8}}''
''1088.{{Overline|8}}''
|11\7
   
   
−
|11\7
−
''1100''
''1100''
−
|27\17
|27\17
   
   
−
''1111.764…''
''1111.764…''
−
|16\10
|16\10
   
   
−
''1120''
''1120''
−
|21\13
|21\13
   
   
−
''1130.769…''
''1130.769…''
−
|-
|-
−
|Mi#, Si#
|Mi#, Si#
| D#
−
|D#
−
|6#
|6#
−
|24\15
|24\15
   
   
−
''1120''
''1120''
| rowspan="2" | 18\11
   
   
−
| rowspan="2" |18\11
−
''1145.{{Overline|45}}''
''1145.{{Overline|45}}''
−
|30\18
|30\18
   
   
−
''1166.{{Overline|6}}''
''1166.{{Overline|6}}''
−
|12\7
|12\7
   
   
−
''1200''
''1200''
| 30\17
   
   
−
|30\17
−
''1235.294…''
''1235.294…''
−
|18\10
|18\10
   
   
−
''1260''
''1260''
−
|24\13
|24\13
   
   
−
''1292.307…''
''1292.307…''
−
|-
|-
| Fab, Dob
−
| Ebb
|Fab, Dob
| 7b, 7c
−
|Ebb
−
|7bb, 7cc
−
|25\15
|25\15
   
   
−
''1166.{{Overline|6}}''
''1166.{{Overline|6}}''
−
|29\18
|29\18
   
   
−
''1127.{{Overline|7}}''
''1127.{{Overline|7}}''
−
|11\7
|11\7
   
   
−
''1100''
''1100''
−
|26\17
|26\17
   
   
−
''1070.588…''
''1070.588…''
−
|15\10
|15\10
   
   
−
''1050''
''1050''
−
|19\13
|19\13
   
   
−
''1023.076…''
''1023.076…''
−
|-
|-
−
|'''Fa, Do'''
|'''Fa, Do'''
−
|'''Eb'''
|'''Eb'''
|'''7'''
−
|'''7b, 7c'''
−
|'''26\15'''
|'''26\15'''
   
   
−
'''''1213.{{Overline|3}}'''''
'''''1213.{{Overline|3}}'''''
−
|'''19\11'''
|'''19\11'''
   
   
−
'''''1209.{{Overline|09}}'''''
'''''1209.{{Overline|09}}'''''
|'''31\18'''
   
   
−
|'''31\18'''
−
'''''1205.{{Overline|5}}'''''
'''''1205.{{Overline|5}}'''''
−
|'''12\7'''
|'''12\7'''
   
   
−
'''''1200'''''
'''''1200'''''
−
|'''29\17'''
|'''29\17'''
   
   
−
'''''1194.117…'''''
'''''1194.117…'''''
−
|'''17\10'''
|'''17\10'''
   
   
−
'''''1190'''''
'''''1190'''''
−
|'''22\13'''
|'''22\13'''
   
   
−
'''''1184.615…'''''
'''''1184.615…'''''
−
|-
|-
−
|Fa#, Do#
|Fa#, Do#
−
|E
|E
|7#
−
|7
−
|27\15
|27\15
   
   
−
''1260''
''1260''
−
|20\11
|20\11
   
   
−
''1272.{{Overline|72}}''
''1272.{{Overline|72}}''
| 33\18
   
   
−
|33\18
−
''1283.{{Overline|3}}''
''1283.{{Overline|3}}''
−
|13\7
|13\7
   
   
−
''1300''
''1300''
−
|32\17
|32\17
   
   
−
''1317.647…''
''1317.647…''
−
|19\10
|19\10
   
   
−
''1330''
''1330''
| 25\13
   
   
−
|25\13
−
''1346.153…''
''1346.153…''
−
|-
|-
−
|Fax, Dox
|Fax, Dox
−
|E#
|E#
|7x
−
|7#
−
|28\15
|28\15
   
   
−
''1306.{{Overline|6}}''
''1306.{{Overline|6}}''
−
| rowspan="2" |21\11
| rowspan="2" |21\11
   
   
−
''1336.{{Overline|36}}''
''1336.{{Overline|36}}''
−
|35\18
|35\18
   
   
−
''1361.{{Overline|1}}''
''1361.{{Overline|1}}''
−
|14\7
|14\7
   
   
−
''1400''
''1400''
−
|35\17
|35\17
   
   
−
''1441.176…''
''1441.176…''
−
|21\10
|21\10
   
   
−
''1470''
''1470''
−
|28\13
|28\13
   
   
−
''1507.692…''
''1507.692…''
−
|-
|-
−
|Dob, Solb
|Dob, Solb
−
|Fb
|Fb
|8b, Fc
|29\15
   
   
−
|8b, Fc
−
|29\15
−
''1333.{{Overline|3}}''
''1333.{{Overline|3}}''
−
|34\18
|34\18
   
   
−
''1322.{{Overline|2}}''
''1322.{{Overline|2}}''
−
|13\7
|13\7
   
   
−
''1300''
''1300''
−
|31\17
|31\17
   
   
−
''1276.470…''
''1276.470…''
−
|18\10
|18\10
   
   
−
''1260''
''1260''
−
|23\13
|23\13
   
   
−
''1238.461…''
''1238.461…''
−
|-
|-
−
!Do, Sol
!Do, Sol
−
!F
!F
−
!8, F
!8, F
−
! colspan="7" |''1400''
! colspan="7" |''1400''
−
|-
|-
−
|Do#, Sol#
|Do#, Sol#
−
|F#
|F#
−
|8#, F#
|8#, F#
−
|31\15
|31\15
   
   
−
''1446.{{Overline|6}}''
''1446.{{Overline|6}}''
−
|23\11
|23\11
   
   
−
''1463.{{Overline|63}}''
''1463.{{Overline|63}}''
−
|38\18
|38\18
   
   
−
''1477.7̄''
''1477.7̄''
−
| rowspan="2" |15\7
| rowspan="2" |15\7
   
   
−
''1500''
''1500''
−
|37\17
|37\17
   
   
−
''1523.529…''
''1523.529…''
−
|22\10
|22\10
   
   
−
''1540''
''1540''
| 29\13
   
   
−
|29\13
−
''1561.538…''
''1561.538…''
−
|-
|-
−
|Reb, Lab
|Reb, Lab
−
|Gb
|Gb
| 9b, Gc
−
|9b, Gc
−
|33\15
|33\15
   
   
−
''1540''
''1540''
−
|24\11
|24\11
   
   
−
''1527.{{Overline|27}}''
''1527.{{Overline|27}}''
−
|39\18
|39\18
   
   
−
''1516.{{Overline|6}}''
''1516.{{Overline|6}}''
| 36\17
   
   
−
|36\17
−
''1482.352…''
''1482.352…''
−
|21\10
|21\10
   
   
−
''1470''
''1470''
−
|27\13
|27\13
   
   
−
''1453.846…''
''1453.846…''
−
|-
|-
−
|'''Re, La'''
|'''Re, La'''
−
|'''G'''
|'''G'''
−
|'''9, G'''
|'''9, G'''
−
|'''34\15'''
|'''34\15'''
   
   
−
'''''1586.{{Overline|6}}'''''
'''''1586.{{Overline|6}}'''''
−
|'''25\11'''
|'''25\11'''
   
   
−
'''''1590.{{Overline|90}}'''''
'''''1590.{{Overline|90}}'''''
−
|'''41\18'''
|'''41\18'''
   
   
−
'''''1594.{{Overline|4}}'''''
'''''1594.{{Overline|4}}'''''
−
|'''16\7'''
|'''16\7'''
   
   
−
'''''1600'''''
'''''1600'''''
−
|'''39\17'''
|'''39\17'''
   
   
−
'''''1605.882…'''''
'''''1605.882…'''''
−
|'''23\10'''
|'''23\10'''
   
   
−
'''''1610'''''
'''''1610'''''
−
|'''30\13'''
|'''30\13'''
   
   
−
'''''1615.384…'''''
'''''1615.384…'''''
−
|-
|-
−
|Re#, La#
|Re#, La#
−
|G#
|G#
−
|9#, G#
|9#, G#
−
|35\15
|35\15
   
   
−
''1633.{{Overline|3}}''
''1633.{{Overline|3}}''
−
|26\11
|26\11
   
   
−
''1654.{{Overline|54}}''
''1654.{{Overline|54}}''
−
|43\18
|43\18
   
   
−
''1672.{{Overline|2}}''
''1672.{{Overline|2}}''
−
| rowspan="2" |17\7
| rowspan="2" |17\7
   
   
−
''1700''
''1700''
−
|42\17
|42\17
   
   
−
''1729.411…''
''1729.411…''
−
|25\10
|25\10
   
   
−
''1750''
''1750''
−
|33\13
|33\13
   
   
−
''1776.923…''
''1776.923…''
−
|-
|-
−
|Mib, Sib
|Mib, Sib
| Ab
−
|Ab
−
|Xb, Ac
|Xb, Ac
−
|37\15
|37\15
   
   
−
''1726.{{Overline|6}}''
''1726.{{Overline|6}}''
| 27\11
   
   
−
|27\11
−
''1718.{{Overline|18}}''
''1718.{{Overline|18}}''
−
|44\18
|44\18
   
   
−
''1711.{{Overline|1}}''
''1711.{{Overline|1}}''
−
|41\17
|41\17
   
   
−
''1688.235…''
''1688.235…''
| 24\10
   
   
−
''1680''
|24\10
−
''1680''
−
|31\13
|31\13
   
   
−
''1669.230…''
''1669.230…''
−
|-
|-
−
|Mi, Si
|Mi, Si
−
|A
|A
−
|X, A
|X, A
−
|38\15
|38\15
   
   
−
''1773.{{Overline|3}}''
''1773.{{Overline|3}}''
−
|28\11
|28\11
   
   
−
''1781.{{Overline|81}}''
''1781.{{Overline|81}}''
−
|46\18
|46\18
   
   
−
''1788.{{Overline|8}}''
''1788.{{Overline|8}}''
−
|18\7
|18\7
   
   
−
''1800''
''1800''
| 44\17
   
   
−
|44\17
−
''1811.764…''
''1811.764…''
−
|26\10
|26\10
   
   
−
''1820''
''1820''
−
|34\13
|34\13
   
   
−
''1830.769…''
''1830.769…''
−
|-
|-
−
|Mi#, Si#
|Mi#, Si#
−
|A#
|A#
−
|X#, A#
|X#, A#
−
|39\15
|39\15
   
   
−
''1820''
''1820''
−
| rowspan="2" |29\11
| rowspan="2" |29\11
   
   
−
''1845.{{Overline|45}}''
''1845.{{Overline|45}}''
−
|48\18
|48\18
   
   
−
''1866.{{Overline|6}}''
''1866.{{Overline|6}}''
−
|19\7
|19\7
   
   
−
''1900''
''1900''
−
|47\17
|47\17
   
   
−
''1935.294…''
''1935.294…''
−
|28\10
|28\10
   
   
−
''1960''
''1960''
| 37\13
   
   
−
|37\13
−
''1992.307…''
''1992.307…''
−
|-
|-
−
|Fab, Dob
|Fab, Dob
−
|Bbb
|Bbb
−
|Ebb, Ccc
|Ebb, Ccc
−
|40\15
|40\15
   
   
−
''1866.{{Overline|6}}''
''1866.{{Overline|6}}''
−
|47\18
|47\18
   
   
−
''1827.{{Overline|7}}''
''1827.{{Overline|7}}''
−
|18\7
|18\7
   
   
−
''1800''
''1800''
−
|43\17
|43\17
   
   
−
''1770.588…''
''1770.588…''
−
|25\10
|25\10
   
   
−
''1750''
''1750''
−
|32\13
|32\13
   
   
−
''1723.076…''
''1723.076…''
−
|-
|-
−
|'''Fa, Do'''
|'''Fa, Do'''
−
|'''Bb'''
|'''Bb'''
−
|Eb, Cc
|Eb, Cc
−
|'''41\15'''
|'''41\15'''
   
   
−
'''''1913.{{Overline|3}}'''''
'''''1913.{{Overline|3}}'''''
−
|'''30\11'''
|'''30\11'''
   
   
−
'''''1909.{{Overline|09}}'''''
'''''1909.{{Overline|09}}'''''
−
|'''49\18'''
|'''49\18'''
   
   
−
'''''1905.{{Overline|5}}'''''
'''''1905.{{Overline|5}}'''''
−
|'''19\7'''
|'''19\7'''
   
   
−
'''''1900'''''
'''''1900'''''
−
|'''46\17'''
|'''46\17'''
   
   
−
'''''1894.117…'''''
'''''1894.117…'''''
−
|'''27\10'''
|'''27\10'''
   
   
−
'''''1890'''''
'''''1890'''''
−
|'''35\13'''
|'''35\13'''
   
   
−
'''''1884.615…'''''
'''''1884.615…'''''
−
|-
|-
−
|Fa#, Do#
|Fa#, Do#
−
|B
|B
−
|E, C
|E, C
| 42\15
   
   
−
|42\15
−
''1960''
''1960''
−
|31\11
|31\11
   
   
−
''1972.{{Overline|72}}''
''1972.{{Overline|72}}''
−
|51\18
|51\18
   
   
−
''1983.{{Overline|3}}''
''1983.{{Overline|3}}''
−
|20\7
|20\7
   
   
−
''2000''
''2000''
−
|49\17
|49\17
   
   
−
''2017.647…''
''2017.647…''
−
|29\10
|29\10
   
   
−
''2030''
''2030''
−
|38\13
|38\13
   
   
−
''2046.153…''
''2046.153…''
−
|-
|-
−
|Fax, Dox
|Fax, Dox
−
|B#
|B#
−
|Ex, Cx
|Ex, Cx
−
|43\15
|43\15
   
   
−
''2006.{{Overline|6}}''
''2006.{{Overline|6}}''
−
| rowspan="2" |32\11
| rowspan="2" |32\11
   
   
−
''2036.{{Overline|36}}''
''2036.{{Overline|36}}''
−
|53\18
|53\18
   
   
−
''2061. {{Overline|1}}''
''2061. {{Overline|1}}''
−
|21\7
|21\7
   
   
−
''2100''
''2100''
|52\17
   
   
−
|52\17
−
''2141.176…''
''2141.176…''
−
|31\10
|31\10
   
   
−
''2170''
''2170''
−
|41\13
|41\13
   
   
−
''2207.692…''
''2207.692…''
−
|-
|-
| Dob, Solb
−
|Dob, Solb
−
|Hb
|Hb
−
|0b, Dc
|0b, Dc
−
|44\15
|44\15
   
   
−
''2053.{{Overline|3}}''
''2053.{{Overline|3}}''
−
|52\18
|52\18
   
   
−
''2022.{{Overline|2}}''
''2022.{{Overline|2}}''
−
|20\7
|20\7
   
   
−
''2000''
''2000''
−
|48\17
|48\17
   
   
−
''1976.470…''
''1976.470…''
−
|28\10
|28\10
   
   
−
''1960''
''1960''
| 36\13
   
   
−
|36\13
−
1938.615…
1938.615…
−
|-
|-
−
!Do, Sol
!Do, Sol
!H
−
!H
−
!0, D
!0, D
−
! colspan="7" |2100
! colspan="7" |2100
−
|}
|}
   
   
−
−
==Intervals==
==Intervals==
−
{| class="wikitable"
{| class="wikitable"
−
!Generators
!Generators
! Sesquitave notation
−
!Sesquitave notation
−
!Interval category name
!Interval category name
−
!Generators
!Generators
−
!Notation of 3/2 inverse
!Notation of 3/2 inverse
−
!Interval category name
!Interval category name
−
|-
|-
−
| colspan="6" |The 4-note MOS has the following intervals (from some root):
| colspan="6" |The 4-note MOS has the following intervals (from some root):
−
|-
|-
−
|0
|0
−
|Do, Sol
|Do, Sol
−
|perfect unison
|perfect unison
−
|0
|0
−
|Do, Sol
|Do, Sol
−
|sesquitave (just fifth)
|sesquitave (just fifth)
−
|-
|-
−
|1
|1
−
|Fa, Do
|Fa, Do
−
|perfect fourth
|perfect fourth
−
| -1
| -1
−
|Re, La
|Re, La
−
|perfect second
|perfect second
−
|-
|-
−
|2
|2
−
|Mib, Sib
|Mib, Sib
−
|minor third
|minor third
−
| -2
| -2
−
|Mi, Si
|Mi, Si
−
|major third
|major third
−
|-
|-
−
|3
|3
−
|Reb, Lab
|Reb, Lab
−
|diminished second
|diminished second
−
| -3
| -3
−
|Fa#, Do#
|Fa#, Do#
|augmented fourth
−
|augmented fourth
−
|-
|-
−
| colspan="6" |The chromatic 7-note MOS also has the following intervals (from some root):
| colspan="6" |The chromatic 7-note MOS also has the following intervals (from some root):
−
|-
|-
−
|4
|4
−
|Dob, Solb
|Dob, Solb
−
|diminished sesquitave
|diminished sesquitave
| -4
−
| Do#, Sol#
| -4
−
|Do#, Sol#
−
|augmented unison (chroma)
|augmented unison (chroma)
−
|-
|-
−
|5
|5
−
|Fab, Dob
|Fab, Dob
−
|diminished fourth
|diminished fourth
−
| -5
| -5
−
|Re#, La#
|Re#, La#
−
|augmented second
|augmented second
−
|-
|-
−
|6
|6
| Mibb, Sibb
−
|diminished third
|Mibb, Sibb
| -6
−
|diminished third
−
| -6
−
|Mi#, Si#
|Mi#, Si#
−
|augmented third
|augmented third
|}  
−
|}
−
==Genchain==
==Genchain==
   
   
−
The generator chain for this scale is as follows:
The generator chain for this scale is as follows:
−
{| class="wikitable"
{| class="wikitable"
−
|Mibb
|Mibb
   
   
−
Sibb
Sibb
−
|Fab
|Fab
   
   
−
Dob
Dob
−
|Dob
|Dob
   
   
−
Solb
Solb
−
|Reb
|Reb
   
   
−
Lab
Lab
−
|Mib
|Mib
   
   
−
Sib
Sib
−
|Fa
|Fa
   
   
−
Do
Do
−
|Do
|Do
   
   
−
Sol
Sol
−
|Re
|Re
   
   
−
La
La
−
|Mi
|Mi
   
   
−
Si
Si
−
|Fa#
|Fa#
   
   
−
Do#
Do#
−
|Do#
|Do#
   
   
−
Sol#
Sol#
−
|Re#
|Re#
   
   
−
La#
La#
−
|Mi#
|Mi#
   
   
−
Si#
Si#
−
|-
|-
−
|d3
|d3
−
|d4
|d4
|d5
−
|d6
−
|d2
|d2
| m3
−
|m3
−
|P4
|P4
−
|P1
|P1
−
|P2
|P2
−
|M3
|M3
−
|A4
|A4
| A1
|A2
|A3
|}
==Modes==
   
   
−
|A1
−
|A2
−
|A3
−
|}
−
==Modes==
−
The mode names are based on the species of fifth:
The mode names are based on the species of fifth:
−
{| class="wikitable"
{| class="wikitable"
−
!Mode
!Mode
−
!Scale
!Scale
−
![[Modal UDP Notation|UDP]]
![[Modal UDP Notation|UDP]]
−
! colspan="3" |Interval type
! colspan="3" |Interval type
−
|-
|-
−
!name
!name
−
!pattern
!pattern
−
!notation
!notation
−
!2nd
!2nd
−
!3rd
!3rd
−
!4th
!4th
−
|-
|-
−
|Lydian
|Lydian
|LLLs
−
|LLLs
−
|<nowiki>3|0</nowiki>
|<nowiki>3|0</nowiki>
−
|P
|P
−
|M
|M
| A
−
|A
−
|-
|-
−
|Major
|Major
−
|LLsL
|LLsL
−
|<nowiki>2|1</nowiki>
|<nowiki>2|1</nowiki>
−
|P
|P
−
|M
|M
−
|P
|P
−
|-
|-
| Minor
−
|Minor
−
|LLsL
|LLsL
−
|<nowiki>1|2</nowiki>
|<nowiki>1|2</nowiki>
| P
−
|P
−
|m
|m
−
|P
|P
−
|-
|-
−
|Phrygian
|Phrygian
−
|sLLL
|sLLL
−
|<nowiki>0|3</nowiki>
|<nowiki>0|3</nowiki>
−
|d
|d
−
|m
|m
| P
−
|}  
|P
−
|}
−
==Temperaments==
==Temperaments==
   
   
−
The most basic rank-2 temperament interpretation of diatonic is '''Napoli'''. The name "Napoli" comes from the “Neapolitan” sixth triad spelled <code>root-(p-2g)-(2p-3g)</code> (p = 3/2, g = the whole tone) which serves as its minor triad approximating 5:6:8 in pental interpretations or 18:21:28 in septimal ones. Basic ~7edf fits both interpretations.
The most basic rank-2 temperament interpretation of diatonic is '''Napoli'''. The name "Napoli" comes from the “Neapolitan” sixth triad spelled <code>root-(p-2g)-(2p-3g)</code> (p = 3/2, g = the whole tone) which serves as its minor triad approximating 5:6:8 in pental interpretations or 18:21:28 in septimal ones. Basic ~7edf fits both interpretations.
−
==='''Napoli-Meantone'''===
==='''Napoli-Meantone'''===
   
   
−
[[Subgroup]]: 3/2.6/5.8/5
[[Subgroup]]: 3/2.6/5.8/5
   
   
−
[[Comma]] list: [[81/80]]
 
[[POL2]] generator: ~9/8 = [[Tel:192.6406|192.6406]]
 
[[Mapping]]: [{{val|1 1 2}}, {{val|0 -2 -3}}]
 
[[Vals]]: {{val list|~(7edf, 11edf, 18edf)}}
==='''Napoli-Superpyth'''===
   
   
[[Subgroup]]: 3/2.7/6.14/9
   
   
−
[[Comma]] list: [[64/63]]
[[Comma]] list: [[81/80]]
 
[[POL2]] generator: ~8/7 = [[Tel:218.6371|218.6371]]
 
[[Mapping]]: [{{val|1 1 2}}, {{val|0 -2 -3}}]
 
[[Vals]]: {{val list|~(7edf, 10edf, 13edf, 16edf)}}
====Scale tree====
   
   
−
The spectrum looks like this:
{| class="wikitable"
! colspan="3" rowspan="2" |Generator
   
   
(bright)
−
! colspan="2" |Cents
[[POL2]] generator: ~9/8 = 192.6406
! rowspan="2" |L
! rowspan="2" |s
−
! rowspan="2" |L/s
! rowspan="2" | Comments
|-
−
!<u>Normalised</u>
[[Mapping]]: [{{val|1 1 2}}, {{val|0 -2 -3}}]
!''ed7\12''
|-
−
| 1\4
|
|
−
|<u>171.428…</u>
[[Vals]]: {{val list|~(7edf, 11edf, 18edf)}}
|''175''
|1
−
|1
==='''Napoli-Superpyth'''===
|1.000
|Equalised
−
|-
[[Subgroup]]: 3/2.7/6.14/9
|6\23
|
−
|
|<u>180</u>
|''182.608…''
−
|6
[[Comma]] list: [[64/63]]
|5
|1.200
−
|
|-
|
−
| 11\42
[[POL2]] generator: ~8/7 = 218.6371
|
|<u>180.821…</u>
−
|''183.{{Overline|3}}''
|11
|9
−
|1.222
[[Mapping]]: [{{val|1 1 2}}, {{val|0 -2 -3}}]
|
|-
−
|5\19
|
|
−
|<u>181.{{Overline|81}}</u>
[[Vals]]: {{val list|~(7edf, 10edf, 13edf, 16edf)}}
|''184.210…''
|5
−
|4
====Scale tree====
|1.250
|
−
|-
The spectrum looks like this:
|
|14\53
−
|
{| class="wikitable"
|<u>182.608…</u>
|''184.905…''
−
|14
! colspan="3" rowspan="2" |Generator
|11
|1.273
−
|
(bright)
|-
|
−
|9\34
! colspan="2" |Cents
|
|<u>183.050…</u>
−
|''185.294…''
! rowspan="2" |L
| 9
|7
−
|1.286
! rowspan="2" |s
|
−
! rowspan="2" |L/s
−
! rowspan="2" |Comments
−
|-
|-
|4\15
−
|
!<u>Normalised</u>  
|
|<u>184.615…</u>
−
|''186.{{Overline|6}}''
!''ed7\12''
|4
|3
−
|1.333
|
|-
|-
|
−
|11\41
|1\4
|
|<u>185.915…</u>
−
|''187.804…''
|
−
|
−
|<u>171.428…</u>
−
|''175''
−
|1
−
|1
−
|1.000
−
|Equalised
−
|-
−
|6\23
−
|
−
|
−
|<u>180</u>
−
|''182.608…''
−
|6
−
|5
−
|1.200
−
|
−
|-
−
|
−
|11\42
−
|
−
|<u>180.821…</u>
−
|''183.{{Overline|3}}''
−
|11
−
|9
−
|1.222
−
|
−
|-
−
|5\19
−
|
−
|
−
|<u>181.{{Overline|81}}</u>
−
|''184.210…''
−
|5
−
|4
−
|1.250
−
|
−
|-
−
|
−
|14\53
−
|
−
|<u>182.608…</u>
−
|''184.905…''
−
|14
−
|11
−
|1.273
−
|
−
|-
−
|
−
|9\34
−
|
−
|<u>183.050…</u>
−
|''185.294…''
−
|9
−
|7
−
|1.286
−
|
−
|-
−
|4\15
−
|
−
|
−
|<u>184.615…</u>
−
|''186.{{Overline|6}}''
−
|4
−
|3
−
|1.333
−
|
−
|-
−
|
−
|11\41
−
|
−
|<u>185.915…</u>
−
|''187.804…''
−
|11
|11
| 8
−
|8
−
|1.375
|1.375
|
−
|
−
|-
|-
|
−
|
−
|7\26
|7\26
|
−
|
−
|<u>186.{{Overline|6}}</u>
|<u>186.{{Overline|6}}</u>
−
|''188.461…''
|''188.461…''
−
|7
|7
−
|5
|5
−
|1.400
|1.400
|
−
|
−
|-
|-
|
−
|
−
|10\37
|10\37
|
−
|
−
|<u>187.5</u>
|<u>187.5</u>
−
|''189.{{Overline|189}}''
|''189.{{Overline|189}}''
−
|10
|10
| 7
−
| 1.429
|7
|
−
|1.429
−
|
−
|-
|-
|
−
|
−
|13\48
|13\48
−
|
|
−
|<u>187.951…</u>
|<u>187.951…</u>
−
|''189.58{{Overline|3}}''
|''189.58{{Overline|3}}''
−
|13
|13
−
|9
|9
−
|1.444
|1.444
−
|
|
|-
−
|
|-
|16\59
|
−
|<u>188.235…</u>
|
|''189.830…''  
−
|16\59
−
|
−
|<u>188.235…</u>
−
|''189.830…''
−
|16
|16
−
|11
|11
−
|1.4545
|1.4545
−
|
|
−
|-
|-
| 3\11
−
|
|3\11
−
|
|
−
|
−
|<u>189.473…</u>
|<u>189.473…</u>
−
|''190.{{Overline|90}}''
|''190.{{Overline|90}}''
| 3
−
|3
−
|2
|2
−
|1.500
|1.500
−
|Napoli-Meantone starts here
|Napoli-Meantone starts here
−
|-
|-
−
|
−
|17\62
−
|
|
−
|<u>190.654…</u>
−
|''191.935…''
−
|17
−
|11
−
|1.5455
−
|
−
|-
−
|
−
|14\51
|14\51
|
−
|
−
|<u>190.{{Overline|90}}</u>
|<u>190.{{Overline|90}}</u>
−
|''192.156…''
|''192.156…''
−
|14
|14
| 9
−
| 1.556
|9
|
−
|1.556
−
|
−
|-
|-
−
|
|
−
|11\40
|11\40
|
−
|
−
|<u>191.304…</u>
|<u>191.304…</u>
−
|''192.5''
|''192.5''
−
|11
|11
| 7
−
| 1.571
|7
−
|1.571
−
|
|
−
|-
|-
|
−
|
−
|8\29
|8\29
|
−
|
−
|<u>192</u>
|<u>192</u>
−
|''193.103…''
|''193.103…''
| 8
−
| 5
|8
−
|5
−
|1.600
|1.600
−
|
|
−
|-
|-
|
−
|
−
|5\18
|5\18
|  
−
|
−
|<u>193.548…</u>
|<u>193.548…</u>
−
|''194.{{Overline|4}}''
|''194.{{Overline|4}}''
−
|5
|5
−
|3
|3
−
|1.667
|1.667
−
|
|
−
|-
|-
−
|
|
−
|
|
−
|12\43
|12\43
−
|<u>194.{{Overline|594}}</u>
|<u>194.{{Overline|594}}</u>
−
|''195.348…''
|''195.348…''
| 12
−
| 7
|12
−
|7
−
|1.714
|1.714
−
|
|
−
|-
|-
|
−
|
−
|7\25
|7\25
|
−
|
−
|<u>195.348…</u>
|<u>195.348…</u>
−
|''196''
|''196''
−
|7
|7
−
|4
|4
−
|1.750
|1.750
|  
−
|
−
|-
|-
|  
−
|
−
|9\32
|9\32
|
−
|
−
|<u>196.{{Overline|36}}</u>
|<u>196.{{Overline|36}}</u>
−
|''196.875''
|''196.875''
−
|9
|9
−
|5
|5
−
|1.800
|1.800
−
|
|
−
|-
|-
−
|
|
−
|11\39
|11\39
−
|
|
−
|<u>197.014…</u>
|<u>197.014…</u>
−
|''197.435…''
|''197.435…''
−
|11
|11
| 6
−
|6
−
|1.833
|1.833
−
|
|
−
|-
|-
|  
−
|
−
|13\46
|13\46
−
|
|
−
|<u>197.468…</u>
|<u>197.468…</u>
−
|''197.826…''
|''197.826…''
| 13
−
| 7
|13
| 1.857
−
|7
−
|1.857
−
|
|
−
|-
|-
|
−
|
−
|15\53
|15\53
−
|
|
−
|<u>197.802…</u>
|<u>197.802…</u>
−
|''198.113…''
|''198.113…''
−
|15
|15
−
|8
|8
−
|1.875
|1.875
−
|
|
−
|-
|-
−
|
−
|17\60
−
|
|
| 17\60
−
|
|<u>198.058…</u>
|<u>198.058…</u>
−
|''198.{{Overline|3}}''
|''198.{{Overline|3}}''
−
|17
|17
| 9
−
| 1.889
|9
−
|1.889
−
|
|
−
|-
|-
|
−
|
−
|19\67
|19\67
|  
−
|
−
|<u>198.260…</u>
|<u>198.260…</u>
−
|''198.507…''
|''198.507…''
−
|19
|19
| 10
−
|10
−
|1.900
|1.900
−
|
|
−
|-
|-
−
|
|
−
|21\74
|21\74
−
|
|
−
|<u>198.425…</u>
|<u>198.425…</u>
| ''198.{{Overline |''198.''{{Overline|648}}
−
|''198.{{Overline|648}”''
−
|21
|21
| 11
−
|11
−
|1.909
|1.909
|  
−
|
−
|-
|-
−
|
|
−
|23\81
|23\81
−
|
|
−
|<u>198.561…</u>
|<u>198.561…</u>
−
|''198.765…''
|''198.765…''
−
|23
|23
−
|12
|12
| 1.917
−
|1.917
−
|
|
−
|-
|-
−
|
−
|25\88
−
|
|
| 25\88
−
|
|<u>198.675…</u>
|<u>198.675…</u>
−
|''198.8{{Overline|63}}''
|''198.8{{Overline|63}}''
−
|25
|25
| 13
−
|13
−
|1.923
|1.923
−
|
|
−
|-
|-
−
|
|
−
|27\95
|27\95
|  
−
|
−
|<u>198.773…</u>
|<u>198.773…</u>
−
|''198.947…''
|''198.947…''
−
|27
|27
−
|14
|14
−
|1.929
|1.929
−
|
|
−
|-
|-
−
|
|
−
|29\102
|29\102
−
|
|
−
|<u>198.857…</u>
|<u>198.857…</u>
−
|''199.019…''
|''199.019…''
−
|29
|29
−
|15
|15
−
|1.933
|1.933
−
|
|
−
|-
|-
|  
−
| 31\109
|
|
−
|31\109
−
|
−
|<u>198.930…</u>
|<u>198.930…</u>
−
|''199.082…''
|''199.082…''
−
|31
|31
−
|16
|16
−
|1.9375
|1.9375
−
|
|
−
|-
|-
−
|
|
−
|33\116
|33\116
−
|
|
−
|<u>198.994…</u>
|<u>198.994…</u>
−
|''199.137…''
|''199.137…''
−
|33
|33
−
|17
|17
−
|1.941
|1.941
−
|
|
−
|-
|-
|
−
|
−
|35\123
|35\123
−
|
|
−
|<u>199.052…</u>
|<u>199.052…</u>
−
|''199.186…''
|''199.186…''
−
|35
|35
−
|18
|18
−
|1.944
|1.944
−
|
|
−
|-
|-
−
|2\7
|2\7
−
|
|
−
|
|
−
|<u>200</u>
|<u>200</u>
−
|''200''
|''200''
−
|2
|2
−
|1
|1
−
|2.000
|2.000
| Napoli-Meantone ends, Napoli-Pythagorean begins
−
|Napoli-Meantone ends, Napoli-Pythagorean begins
−
|-
|-
−
|
|
−
|19\66
−
|
−
|<u>201.769…</u>
−
|''201.{{Overline|51}}''
−
|19
−
|9
−
|2.111
−
|
−
|-
−
|
−
|17\59
|17\59
−
|
|
−
|<u>201.980…</u>
|<u>201.980…</u>
−
|''201.694…''
|''201.694…''
−
|17
|17
−
|8
|8
−
|2.125
|2.125
|  
−
|
−
|-
|-
−
|
|
| 15\52
−
|  
|15\52
−
|
−
|<u>202.247…</u>
|<u>202.247…</u>
−
|''201.923…''
|''201.923…''
−
|15
|15
−
|7
|7
−
|2.143
|2.143
−
|
|
−
|-
|-
−
|
|
−
|13\45
|13\45
−
|
|
−
|<u>202.597…</u>
|<u>202.597…</u>
−
|''202.{{Overline|2}}''
|''202.{{Overline|2}}''
−
|13
|13
−
|6
|6
−
|2.167
|2.167
−
|
|
−
|-
|-
−
|
|
−
|11\38
|11\38
−
|
|
−
|<u>203.076…</u>
|<u>203.076…</u>
−
|''202.631…''
|''202.631…''
−
|11
|11
−
|5
|5
−
|2.200
|2.200
−
|
|
−
|-
|-
−
|
|
−
|9\31
|9\31
−
|
|
−
|<u>203.773…</u>
|<u>203.773…</u>
−
|''203.225…''
|''203.225…''
−
|9
|9
−
|4
|4
| 2.250
−
|
|2.250
−
|
−
|-
|-
−
|
|
−
|7\24
|7\24
−
|
|
−
|<u>204.878…</u>
|<u>204.878…</u>
−
|''204.1{{Overline|6}}''
|''204.1{{Overline|6}}''
| 7
−
|7
−
|3
|3
−
|2.333
|2.333
−
|
|
−
|-
|-
−
|
−
|
|
|
−
|12\41
|12\41
−
|<u>205.714…</u>
|<u>205.714…</u>
−
|''204.878…''
|''204.878…''
−
|12
|12
−
|5
|5
−
|2.400
|2.400
−
|
|
−
|-
|-
−
|
|
−
|5\17
|5\17
|
−
|
−
|<u>206.896…</u>
|<u>206.896…</u>
−
|''205.882…''
|''205.882…''
−
|5
|5
−
|2
|2
−
|2.500
|2.500
−
|Napoli-Neogothic heartland is from here…
|Napoli-Neogothic heartland is from here…
−
|-
|-
−
|
−
|
|
|
−
|18\61
|18\61
−
|<u>207.692…</u>
|<u>207.692…</u>
−
|''206.557…''
|''206.557…''
−
|18
|18
−
|7
|7
| 2.571
−
|
|2.571
−
|
−
|-
|-
−
|
|
|
−
|
−
|13\44
|13\44
−
|<u>208</u>
|<u>208</u>
|''206.{{Overline|81}}''
−
|''206.8̄1̄''
−
|13
|13
| 5
−
| 2.600
|5
−
|2.600
−
|
|
−
|-
|-
−
|
|
−
|8\27
|8\27
−
|
|
−
|<u>208.695…</u>
|<u>208.695…</u>
|''207.{{Overline|407}}''
−
| 8
|''207.4̄0̄7̄''
−
|8
−
|3
|3
−
|2.667
|2.667
−
|…to here
|…to here
−
|-
|-
|
−
|
−
|11\37
|11\37
−
|
|
−
|<u>209.523…</u>
|<u>209.523…</u>
|''208.{{Overline|108}}''
−
|''208.1̄0̄8̄''
−
|11
|11
−
|4
|4
| 2.750
−
|2.750
−
|
|
−
|-
|-
−
|
|
−
|14\47
|14\47
−
|
|
−
|<u>210</u>
|<u>210</u>
−
|''208.510…''
|''208.510…''
| 14
−
| 5
|14
−
|5
−
|2.800
|2.800
−
|
|
−
|-
|-
|
−
|
−
|17\57
|17\57
−
|
|
−
|<u>210.309…</u>
|<u>210.309…</u>
−
|''208.771…''
|''208.771…''
−
|17
|17
−
|6
|6
−
|2.833
|2.833
|  
−
|
−
|-
|-
−
|
|
| 20\67
−
|20\67
−
|
|
−
|<u>210.526…</u>
|<u>210.526…</u>
−
|''208.955…''
|''208.955…''
| 20
−
|20
−
|7
|7
−
|2.857
|2.857
−
|
|
−
|-
|-
−
|
|
| 23\77
−
|23\77
−
|
|
−
|<u>210.687…</u>
|<u>210.687…</u>
−
|''209.{{Overline|09}}''
|''209.{{Overline|09}}''
−
|23
|23
−
|8
|8
−
|2.875
|2.875
−
|
|
−
|-
|-
−
|3\10
|3\10
|
−
|
−
|
|
−
|<u>211.764…</u>
|<u>211.764…</u>
−
|''210''
|''210''
−
|3
|3
| 1
−
|1
−
|3.000
|3.000
−
|Napoli-Pythagorean ends, Napoli-Superpyth begins
|Napoli-Pythagorean ends, Napoli-Superpyth begins
−
|-
|-
|
−
|
−
|22\73
|22\73
|  
−
|
−
|<u>212.903…</u>
|<u>212.903…</u>
−
|''210.958…''
|''210.958…''
−
|22
|22
−
|7
|7
−
|3.143
|3.143
|  
−
|
−
|-
|-
−
|
|
−
|19\63
|19\63
|  
−
|
−
|<u>213.084…</u>
|<u>213.084…</u>
−
|''211.{{Overline|1}}''
|''211.{{Overline|1}}''
−
|19
|19
−
|6
|6
−
|3.167
|3.167
−
|
|
−
|-
|-
−
|
|
−
|16\53
|16\53
−
|
|
−
|<u>213.{{Overline|3}}</u>
|<u>213.{{Overline|3}}</u>
−
|''211.320…''
|''211.320…''
−
|16
|16
−
|5
|5
−
|3.200
|3.200
−
|
|
−
|-
|-
|
−
|
−
|13\43
|13\43
−
|
|
−
|<u>213.698…</u>
|<u>213.698…</u>
−
|''211.627…''
|''211.627…''
−
|13
|13
−
|4
|4
−
|3.250
|3.250
−
|
|
−
|-
|-
−
|
|
| 10\33
−
|10\33
−
|
|
−
|<u>214.285…</u>
|<u>214.285…</u>
−
|''212.{{Overline|12}}''
|''212.{{Overline|12}}''
−
|10
|10
−
|3
|3
−
|3.333
|3.333
−
|
|
−
|-
|-
−
|
|
−
|7\23
|7\23
−
|
|
−
|<u>215.384…</u>
|<u>215.384…</u>
−
|''213.043…''
|''213.043…''
−
|7
|7
−
|2
|2
−
|3.500
|3.500
−
|
|
−
|-
|-
−
|
|
−
|11\36
|11\36
−
|
|
−
|<u>216.393…</u>
|<u>216.393…</u>
−
|''213.{{Overline|3}}''
|''213.{{Overline|3}}''
| 11
−
|11
−
|3
|3
−
|3.667
|3.667
|
−
|
−
|-
|-
−
|
|
−
|15\49
|15\49
−
|
|
−
|<u>216.867…</u>
|<u>216.867…</u>
−
|''214.285…''
|''214.285…''
−
|15
|15
−
|4
|4
−
|3.750
|3.750
−
|
|
−
|-
|-
−
|4\13
|4\13
−
|
|
−
|
|
−
|<u>218.{{Overline|18}}</u>
|<u>218.{{Overline|18}}</u>
−
|''215.385…''
|''215.385…''
−
|4
|4
−
|1
|1
−
|4.000
|4.000
−
|
|
−
|-
|-
−
|
|
−
|13\42
|13\42
−
|
|
−
|<u>219.718…</u>
|<u>219.718…</u>
−
|''216.{{Overline|6}}''
|''216.{{Overline|6}}''
−
|13
|13
−
|3
|3
−
|4.333
|4.333
−
|
|
−
|-
|-
−
|
|
−
|9\29
|9\29
−
|
|
−
|<u>220.408…</u>
|<u>220.408…</u>
−
|''217.241…''
|''217.241…''
−
|9
|9
−
|2
|2
−
|4.500
|4.500
|  
−
|
−
|-
|-
−
|
|
−
|14\45
|14\45
−
|
|
−
|<u>221.052…</u>
|<u>221.052…</u>
−
|''217.{{Overline|7}}''
|''217.{{Overline|7}}''
−
|14
|14
| 3
−
| 4.667
|3
−
|4.667
−
|
|
−
|-
|-
−
|5\16
|5\16
−
|
|
−
|
|
−
|<u>222.{{Overline|2}}</u>
|<u>222.{{Overline|2}}</u>
−
|''218.75''
|''218.75''
−
|5
|5
| 1
−
|1
−
|5.000
|5.000
−
|Napoli-Superpyth ends
|Napoli-Superpyth ends
−
|-
|-
−
|
|
−
|16\51
|16\51
−
|
|
−
|<u>223.255…</u>
|<u>223.255…</u>
−
|''219.607…''
|''219.607…''
−
|16
|16
−
|3
|3
−
|5.333
|5.333
−
|
|
−
|-
|-
−
|
|
−
|11\35
|11\35
−
|
|
−
|<u>223.728…</u>
|<u>223.728…</u>
−
|''220''
|''220''
−
|11
|11
−
|2
|2
−
|5.500
|5.500
−
|
|
−
|-
|-
−
|
|
−
|17\54
|17\54
−
|
|
−
|<u>224.175…</u>
|<u>224.175…</u>
−
|''220.{{Overline|370}}''
|''220.{{Overline|370}}''
| 17
−
| 3
|17
−
|3
−
|5.667
|5.667
−
|
|
−
|-
|-
−
|6\19
|6\19
|
−
|  
|
−
|
−
|<u>225</u>
|<u>225</u>
−
|''221.052…''
|''221.052…''
−
|6
|6
−
|1
|1
−
|6.000
|6.000
|
−
|
−
|-
|-
−
|1\3
|1\3
|
−
|
|
−
|
−
|<u>240</u>
|<u>240</u>
−
|''233.{{Overline|3}}''
|''233.{{Overline|3}}''
−
|1
|1
−
|0
|0
−
|→ inf
|→ inf
−
|Paucitonic
|Paucitonic
−
|}
|}
Retrieved from "https://en.xen.wiki/w/User:Moremajorthanmajor/3L_1s_(perfect_fifth-equivalent)"