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-Revision as of 00:01, 15 July 2022 (edit)
-Moremajorthanmajor (talk | contribs)
-(Undo revision 93402 by Moremajorthanmajor ([[User talk:Moremajorthanmajor|talk])
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-(Redirected page to Angel/Tuning specifications)
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 {{Infobox MOS
-+
-#REDIRECT [[Angel/Tuning specifications]]
+| Name = Diatonic/Angel
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-| Name = Diatonic
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 | Equave = 3/2
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 | nLargeSteps = 3
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 | nSmallSteps = 1
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 | Equalized = 2
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 | Paucitonic = 1
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 | Pattern = LLLs
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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]]).
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 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).
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 In the fifth-repeating version of the diatonic scale, each tone has a 3/2 perfect fifth above it. The scale has two major chords and two minor chords. P
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+[[Basic]] Angel is in [[7edf]], which is a very good fifth-based equal tuning similar to [[12edo]].
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-[[Basic]] diatonic is in [[7edf]], which is a very good fifth-based equal tuning similar to [[12edo]].
-−
 ==Notation==
 −
 There are 3 main ways to notate the diatonic scale. One method uses a simple sesquitave (fifth) repeating notation consisting of 4 naturals (eg. Do Re Mi Fa, Sol La Si Do). Given that 1-5/4-5/3 is fifth-equivalent to a tone cluster of 1-10/9-5/4, it may be more convenient to notate diatonic scales as repeating at the double or triple sesquitave (major ninth or thirteenth), however it does make navigating the [[Generator|genchain]] harder. This way, 5/3 is its own pitch class, distinct from 10/9. Notating this way produces a major ninth which is the Aeolian mode of Napoli[6L 2s] or a major thirteenth which is the Dorian mode of Bijou[9L 3s]. Since there are exactly 8 naturals in double sesquitave notation and 12 in triple sesquitave notation, letters A-H (FGABHCDEF) or dozenal digits (0123456789XE0 or D1234567FGACD with flats written C molle) may be used.
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 {| class="wikitable"
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 |+
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 Cents
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 ! colspan="3" |Notation
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 !Supersoft
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 !Soft
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 !Semisoft
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 !Basic
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 !Semihard
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 !Hard
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 !Superhard
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 |-
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 !Diatonic
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 !Napoli
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 !Bijou
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 !~15edf
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 !~11edf
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 !~18edf
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 !~7edf
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 !~17edf
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 !~10edf
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 !~13edf
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 |-
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 |Do#, Sol#
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 |F#
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 |0#, D#
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 |1\15
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 .153…
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 |1\11
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 .157…
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 |2\18
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 .419…
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 | rowspan="2" |1\7
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 |3\17
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 .137…
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 |2\10
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 .176…
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 |3\13
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 .{{Overline|63}}
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 |-
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 |Reb, Lab
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 |Gb
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 |1b, 1c
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 |3\15
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 .461…
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 |2\11
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 .315…
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 |3\18
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 .129…
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 |2\17
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 .758…
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 |1\10
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 .588…
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 |1\13
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 .{{Overline|54}}
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 |-
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 |'''Re, La'''
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 |'''G'''
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 |'''1'''
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 |'''4\15'''
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 '''184.615…'''
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 |'''3\11'''
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 '''189.473…'''
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 |'''5\18'''
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 '''193.548…'''
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 |'''2\7'''
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 '''200'''
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 |'''5\17'''
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 '''206.896…'''
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 |'''3\10'''
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 '''211.764…'''
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 |'''4\13'''
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 '''218.{{Overline|18}}'''
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 |-
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 |Re#, La#
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 |G#
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 |1#
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 |5\15
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 .769…
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 |4\11
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 .631…
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 |7\18
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 .967…
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 | rowspan="2" |3\7
-−
-−
 |8\17
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 .034…
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 |5\10
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 .941…
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 |7\13
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 .{{Overline|81}}
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 |-
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 |Mib, Sib
-−
 |Ab
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 |2b, 2c
-−
 |7\15
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 .076…
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 |5\11
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 .789…
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 |8\18
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 .677…
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 |7\17
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 .655…
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 |4\10
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 .352…
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 |5\13
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 .{{Overline|72}}
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 |-
-−
 |Mi, Si
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 |A
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 |2
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 |8\15
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 .230…
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 |6\11
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 .947…
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 |10\18
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 .096…
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 |4\7
-−
-−
 |10\17
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 .793…
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 |6\10
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 .529…
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 |8\13
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 .{{Overline|36}}
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 |-
-−
 |Mi#, Si#
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 |A#
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 |2#
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 |9\15
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 .384…
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 | rowspan="2" |7\11
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 .105…
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 |12\18
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 .516…
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 |5\7
-−
-−
 |13\17
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 .931…
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 |8\10
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 .705…
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 |11\13
-−
-−
 |-
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 |Fab, Dob
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 |Bbb
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 |3bb, 3cc
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 |10\15
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 .538…
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 |11\18
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 .806…
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 |4\7
-−
-−
 |9\17
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 .413…
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 |5\10
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 .941…
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 |6\13
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 .{{Overline|27}}
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 |-
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 |'''Fa, Do'''
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 |'''Bb'''
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 |'''3b, 3c'''
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 |'''11\15'''
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 '''507.692…'''
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 |'''8\11'''
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 '''505.263…'''
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 |'''13\18'''
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 '''503.225…'''
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 |'''5\7'''
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 '''500'''
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 |'''12\17'''
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 '''496.551…'''
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 |'''7\10'''
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 '''494.117…'''
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 |'''9\13'''
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 '''490.{{Overline|90}}'''
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 |-
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 |Fa#, Do#
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 |B
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 |3
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 |12\15
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 .846…
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 |9\11
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 .421…
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 |15\18
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 .645…
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 |6\7
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 |15\17
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 .689…
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 |9\10
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 .294…
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 |12\13
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 .{{Overline|54}}
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 |-
-−
 |Fax, Dox
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 |B#
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 |3#
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 |13\15
-−
-−
 | rowspan="2" |10\11
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 .578…
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 |17\18
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 .064…
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 |7\7
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 |18\17
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 .827…
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 |11\10
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 .470…
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 |15\13
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 .{{Overline|18}}
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 |-
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 |Dob, Solb
@@ Line 749: / Line 501: @@
 −
 |10\13
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 .{{Overline|45}}
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 |-
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 !Do, Sol
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 !H
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 !4
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 !'''15\15'''
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 '''692.307…'''
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 !'''11\11'''
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 '''694.736…'''
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 !'''18\18'''
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 '''696.774…'''
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 !'''7\7'''
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 '''700'''
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 !'''17\17'''
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 '''703.448…'''
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 !'''10\10'''
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 '''705.882…'''
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 !'''13\13'''
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 '''709.'''{{Overline|09}}
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 |-
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 |Do#, Sol#
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 |Η#
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 |4#
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 |16\15
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 .461…
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 |12\11
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 .894…
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 |20\18
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 .193…
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 | rowspan="2" |8\8
-−
-−
 |20\17
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 .586…
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 |12\10
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 .058…
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 |16\13
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 .{{Overline|72}}
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 |-
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 |Reb, Lab
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 |Cb
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 |5b, 5c
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 |18\15
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 .769…
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 |13\11
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 .052…
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 |21\18
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 .903…
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 |19\17
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 .206…
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 |11\10
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 .470…
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 |14\13
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 .{{Overline|63}}
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 |-
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 |'''Re, La'''
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 |'''C'''
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 |'''5'''
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 |'''19\18'''
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 '''876.923…'''
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 |'''14\11'''
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 '''884.210…'''
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 |'''23\18'''
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 '''890.322…'''
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 |'''9\5'''
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 '''900'''
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 |'''22\17'''
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 '''910.344…'''
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 |'''13\10'''
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 '''917.647…'''
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 |'''17\13'''
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 '''927.{{Overline|27}}'''
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 |-
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 |Re#, La#
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 |C#
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 |5#
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 |20\15
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 .076…
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 |15\11
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 .368…
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 |25\18
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 .741…
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 | rowspan="2" |10\7
-−
-−
 |25\17
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 .482…
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 |15\10
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 .823…
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 |20\13
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 .{{Overline|90}}
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 |-
-−
 |Mib, Sib
-−
 |Db
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 |6b, 6c
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 |22\15
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 .384…
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 |16\11
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 .526…
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 |26\18
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 .451…
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 |24\17
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 .103…
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 |14\10
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 .235…
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 |18\13
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 .{{Overline|81}}
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 |-
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 |Mi, Si
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 |D
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 |6
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 |23\15
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 .538…
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 |17\11
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 .684…
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 |28\18
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 .870…
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 |11\7
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-−
 |27\17
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 .241…
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 |16\10
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 .411…
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 |21\9
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 .{{Overline|45}}
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 |-
-−
 |Mi#, Si#
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 |D#
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 |6#
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 |24\15
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 .692…
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 | rowspan="2" |18\11
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 .842…
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 |30\18
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 .290…
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 |12\7
-−
-−
 |30\17
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 .379…
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 |18\10
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 .588…
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 |24\13
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 .{{Overline|09}}
-−
 |-
-−
 |Fab, Dob
-−
 |Ebb
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 |7bb, 7cc
-−
 |25\15
-−
 .846…
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 |29\18
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 .580…
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 |11\7
-−
-−
 |26\17
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 .862…
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 |15\10
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 .823…
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 |19\13
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 .{{Overline|36}}
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 |-
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 |'''Fa, Do'''
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 |'''Eb'''
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 |'''7b, 7c'''
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 |'''26\15'''
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 '''1200'''
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 |'''19\11'''
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 '''1200'''
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 |'''31\18'''
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 '''1200'''
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 |'''12\7'''
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 '''1200'''
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 |'''29\17'''
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 '''1200'''
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 |'''17\10'''
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 '''1200'''
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 |'''22\13'''
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 '''1200'''
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 |-
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 |Fa#, Do#
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 |E
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 |7
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 |27\15
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 .153…
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 |20\11
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 .157…
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 |33\18
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 .419…
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 |13\7
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-−
 |32\17
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 .137…
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 |19\10
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 .176…
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 |25\13
-−
 .{{Overline|63}}
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 |-
-−
 |Fax, Dox
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 |E#
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 |7#
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 |28\15
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 .307…
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 | rowspan="2" |21\11
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 .315…
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 |35\18
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 .838…
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 |14\7
-−
-−
 |35\17
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 .275…
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 |21\10
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 .352…
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 |28\13
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 .{{Overline|27}}
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 |-
-−
 |Dob, Solb
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 |Fb
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 |8b, Fc
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 |29\15
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 .461…
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 |34\18
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 .129…
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 |13\7
-−
-−
 |31\17
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 .758…
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 |18\10
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 .588…
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 |23\18
-−
 .{{Overline|54}}
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 |-
-−
 !Do, Sol
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 !F
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 !8, F
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 !30\15
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 .615…
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 !22\11
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 .473…
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 !36\18
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 .548…
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 !14\7
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-−
 !34\17
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 .896…
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 !20\10
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 .764…
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+!26\13
-!26\9
-−
 .{{Overline|18}}
-−
 |-
-−
 |Do#, Sol#
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 |F#
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 |8#, F#
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 |31\15
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 .769…
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 |23\11
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 .631…
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 |38\18
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 .967…
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 | rowspan="2" |15\7
-−
-−
 |37\17
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 .034…
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 |22\10
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 .941…
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 |29\13
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 .{{Overline|81}}
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 |-
-−
 |Reb, Lab
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 |Gb
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 |9b, Gc
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 |33\15
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 .076…
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 |24\11
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 .789…
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 |39\18
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 .677…
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 |36\17
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 .655…
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 |21\10
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 .352…
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 |27\13
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 .{{Overline|72}}
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 |-
-−
 |'''Re, La'''
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 |'''G'''
-−
 |'''9, G'''
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 |'''34\15'''
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 '''1569.230…'''
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 |'''25\11'''
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 '''1578.947…'''
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 |'''41\18'''
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 '''1587.096…'''
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 |'''16\7'''
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 '''1600'''
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 |'''39\17'''
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 '''1613.793…'''
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 |'''23\10'''
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 '''1623.529…'''
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 |'''30\13'''
-−
 '''1636.{{Overline|36}}'''
-−
 |-
-−
 |Re#, La#
-−
 |G#
-−
 |9#, G#
-−
 |35\15
-−
 .384…
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 |26\11
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 .105…
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 |43\18
-−
 .516…
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 | rowspan="2" |17\7
-−
-−
 |42\17
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 .931…
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 |25\10
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 .705…
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 |33\13
-−
-−
 |-
-−
 |Mib, Sib
-−
 |Ab
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 |Xb, Ac
-−
 |37\15
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 .692…
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 |27\11
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 .263…
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 |44\18
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 .225…
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 |41\17
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 .551…
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 |24\10
-−
 .117…
-−
 |31\13
-−
 .{{Overline|90}}
-−
 |-
-−
 |Mi, Si
-−
 |A
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 |X, A
-−
 |38\15
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 .846…
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 |28\11
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 .421…
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 |46\18
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 .645…
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 |18\7
-−
-−
 |44\17
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 .689…
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 |26\10
-−
 .294…
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 |34\13
-−
 .{{Overline|54}}
-−
 |-
-−
 |Mi#, Si#
-−
 |A#
-−
 |X#, A#
-−
 |39\15
-−
-−
 | rowspan="2" |29\11
-−
 .578…
-−
 |48\18
-−
 .064…
-−
 |19\7
-−
-−
 |47\17
-−
 .827…
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 |28\10
-−
 .470…
-−
 |37\13
-−
 .{{Overline|18}}
-−
 |-
-−
 |Fab, Dob
-−
 |Bbb
-−
 |Ebb, Ccc
-−
 |40\15
-−
 .153…
-−
 |47\18
-−
 .354…
-−
 |18\7
-−
-−
 |43\17
-−
 .310…
-−
 |25\10
-−
 .705…
-−
 |32\13
-−
 .{{Overline|45}}
-−
 |-
-−
 |'''Fa, Do'''
-−
 |'''Bb'''
-−
 |Eb, Cc
-−
 |'''41\15'''
-−
 '''1892.307…'''
-−
 |'''30\11'''
-−
 '''1894.736…'''
-−
 |'''49\18'''
-−
 '''1896.774…'''
-−
 |'''19\7'''
-−
 '''1900'''
-−
 |'''46\17'''
-−
 '''1903.448…'''
-−
 |'''27\10'''
-−
 '''1905.882…'''
-−
 |'''35\13'''
-−
 '''1909.{{Overline|09}}'''
-−
 |-
-−
 |Fa#, Do#
-−
 |B
-−
 |E, C
-−
 |42\15
-−
 .461…
-−
 |31\11
-−
 .894…
-−
 |51\18
-−
 .193…
-−
 |20\7
-−
-−
 |49\17
-−
 .586…
-−
 |29\10
-−
 .470…
-−
 |38\13
-−
 .{{Overline|72}}
-−
 |-
-−
 |Fax, Dox
-−
 |B#
-−
 |Ex, Cx
-−
 |43\15
-−
 .615…
-−
 | rowspan="2" |32\11
-−
 .052…
-−
 |53\18
-−
 .612…
-−
 |21\7
-−
-−
 |52\17
-−
 .724…
-−
 |31\10
-−
 .235…
-−
 |41\13
-−
 .{{Overline|36}}
-−
 |-
-−
 |Dob, Solb
-−
 |Hb
-−
 |0b, Dc
-−
 |44\15
-−
 .769…
-−
 |52\18
-−
 .903…
-−
 |20\7
-−
-−
 |48\17
-−
 .206…
-−
 |28\10
-−
 .470…
-−
 |36\13
-−
 .{{Overline|63}}
-−
 |-
-−
 !Do, Sol
-−
 !H
-−
 !0, D
-−
 !45\15
-−
 .923…
-−
 !33\11
-−
 .210…
-−
 !54\18
-−
 .322…
-−
 !21\7
-−
-−
 !51\17
-−
 .344…
-−
 !30\10
-−
 .647…
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 !39\13
-−
 .{{Overline|27}}
-−
 |}

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