User:Moremajorthanmajor/2L 1s (perfect fourth-equivalent): Difference between revisions

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[[Basic]] diatonic is in [[5ed4/3]], which is a very good fourth-based equal tuning similar to [[12edo]].
[[Basic]] diatonic is in [[5ed4/3]], which is a very good fourth-based equal tuning similar to [[12edo]].
==Notation==
==Notation==
There are 6 main ways to notate this scale. One method uses a simple fourth repeating notation consisting of 3 naturals (eg. Do Re Mi, Sol La Si). Given that 1-5/4-3/2 is fourth-equivalent to a tone cluster of 1-9/8-5/4, it may be more convenient to notate diatonic scales as repeating at the double, triple, quadruple, quintuple or sextuple fourth (minor seventh, tenth, thirteenth or sixteenth or diminished nineteenth), however it does make navigating the [[Generator|genchain]] harder. This way, 3/2 is its own pitch class, distinct from 9/8. Notating this way produces a minor tenth which is the Dorian mode of Middletown[6L 3s], also known as the Mahur scale in Persian/Arabic music, a minor thirteenth which is the Aeolian mode of Bijou[8L 4s]; the bastonic chromatic scale, a minor sixteenth which is the Phrygian mode of Hyperionic[10L 5s] or a diminished nineteenth which is the Locrian mode of Subsextal[12L 6s]. Since there are exactly 9 naturals in triple fourth notation, 12 in quadruple fourth, 15 in quintuple fourth and 18 in sextuple fourth notation, letters A-G plus J, Q or Q, S (GJABCQDEF or GABCQDSEF, flats written F molle) or dozenal, hex or duohex digits (0123456789XE0 or E1234567GABDE with flats written D molle or 123456789ABCDEF1 or 0123456789XɜABCDEF0 with flats written F molle) may be used.
There are 6 main ways to notate this scale. One method uses a simple fourth repeating notation consisting of 3 naturals (eg. Do Re Mi, Sol La Si). Given that 1-5/4-3/2 is fourth-equivalent to a tone cluster of 1-9/8-5/4 and a fourth has too few notes for a structure analogous to the major scale, it may be more convenient to notate diatonic scales as repeating at the double, triple, quadruple, quintuple or sextuple fourth (minor seventh, tenth, thirteenth or sixteenth or diminished nineteenth), however it does make navigating the [[Generator|genchain]] harder. This way, 3/2 is its own pitch class, distinct from 9/8. Notating this way produces a minor tenth which is the Dorian mode of Middletown[6L 3s], also known as the Mahur scale in Persian/Arabic music, a minor thirteenth which is the Aeolian mode of Bijou[8L 4s]; the bastonic chromatic scale, a minor sixteenth which is the Phrygian mode of Hyperionic[10L 5s] or a diminished nineteenth which is the Locrian mode of Subsextal[12L 6s]. Since there are exactly 9 naturals in triple fourth notation, 12 in quadruple fourth, 15 in quintuple fourth and 18 in sextuple fourth notation, letters A-G plus J, Q or Q, S (GJABCQDEF or GABCQDSEF, flats written F molle) or dozenal, hex or duohex digits (0123456789XE0 or E1234567GABDE with flats written D molle or 123456789ABCDEF1 or 0123456789XɜABCDEF0 with flats written F molle) may be used.
{| class="wikitable"
{| class="wikitable"
|+Cents
|+Cents
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|-
|-
|Do#, Sol#
|Do#, Sol#
د#,
ص#
|Sol#
|Sol#
ص#
|Re#
|Re#
ر#
|1\11, 46.154
|1\11, 46.154
|1\8, 63.158
|1\8, 63.158
Line 52: Line 57:
|-
|-
| Reb, Lab
| Reb, Lab
رb, لb
|Lab
|Lab
لb
|Mib
|Mib
م
|3\11, 138.462
|3\11, 138.462
|2\8, 126.316
|2\8, 126.316
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|-
|-
|'''Re, La'''
|'''Re, La'''
'''ر, ل'''
|'''La'''
|'''La'''
ل
|'''Mi'''
|'''Mi'''
م
|'''4\11,''' '''184.615'''
|'''4\11,''' '''184.615'''
|'''3\8,''' '''189.474'''
|'''3\8,''' '''189.474'''
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|-
|-
|Re#, La#
|Re#, La#
ر,# ل#
|La#
|La#
ل#
|Mi#
|Mi#
م#
|5\11, 230.769
|5\11, 230.769
|4\8, 252.632
|4\8, 252.632
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|-
|-
|'''Mib, Sib'''
|'''Mib, Sib'''
'''مb,تb'''
|'''Sib'''
|'''Sib'''
|'''Fa'''
تb
|'''F'''
'''ف'''
|'''7\11,''' '''323.077'''
|'''7\11,''' '''323.077'''
|'''5\8,''' '''315.789'''
|'''5\8,''' '''315.789'''
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|-
|-
|Mi, Si
|Mi, Si
م, ت
| Si
| Si
ت
|Fa#
|Fa#
ف#
|8\11, 369.231
|8\11, 369.231
|6\8, 378.947
|6\8, 378.947
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|-
|-
|Mi#, Si#
|Mi#, Si#
م,#ت#
|Si#
|Si#
ت#
|Fax
|Fax
فx
|9\11, 415.385
|9\11, 415.385
| rowspan="2" |7\8, 442.105
| rowspan="2" |7\8, 442.105
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|-
|-
|Dob, Solb
|Dob, Solb
دb,
صb
| Dob
| Dob
دb
|Solb
|Solb
صb
|10\11, 461.538
|10\11, 461.538
|11\13, 425.806
|11\13, 425.806
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|-
|-
!Do, Sol
!Do, Sol
د, ص
!Do
!Do
د
!Sol
!Sol
ص
!'''11\11,''' '''507.692'''
!'''11\11,''' '''507.692'''
!'''8\8,''' '''505.263'''
!'''8\8,''' '''505.263'''
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|-
|-
|Do#, Sol#
|Do#, Sol#
د#,
ص#
|Do#
|Do#
د#
|Sol#
|Sol#
ص#
|12\11, 553.846
|12\11, 553.846
|9\8, 568.421
|9\8, 568.421
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|-
|-
|Reb, Lab
|Reb, Lab
رb, لb
|Reb
|Reb
رb
|Lab
|Lab
لb
|14\11, 646.154
|14\11, 646.154
|10\8, 631.579
|10\8, 631.579
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|-
|-
|'''Re, La'''
|'''Re, La'''
'''ر, ل'''
|'''Re'''
|'''Re'''
ر
|'''La'''
|'''La'''
ل
|'''15\11,''' '''692.308'''
|'''15\11,''' '''692.308'''
|'''11\8'''  '''694.737'''
|'''11\8'''  '''694.737'''
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|-
|-
|Re#, La#
|Re#, La#
ر,# ل#
|Re#
|Re#
د#
|La#
|La#
ل#
|16\11, 738.462
|16\11, 738.462
|12\8, 757.895
|12\8, 757.895
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|-
|-
|'''Mib, Sib'''
|'''Mib, Sib'''
'''مb,تb'''
|'''Mib'''
|'''Mib'''
مb
|'''Sib'''
|'''Sib'''
تb
|'''18\11,''' '''830.769'''
|'''18\11,''' '''830.769'''
|'''13\8,''' '''821.053'''
|'''13\8,''' '''821.053'''
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|-
|-
|Mi, Si
|Mi, Si
م, ت
|Mi
|Mi
م
|Si
|Si
ت
|19\11, 876.923
|19\11, 876.923
|14\8, 884.211
|14\8, 884.211
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|-
|-
|Mi#, Si#
|Mi#, Si#
م,#ت#
| Mi#
| Mi#
م#
|Si#
|Si#
ت#
|20\11, 923.077
|20\11, 923.077
| rowspan="2" |15\8, 947.378
| rowspan="2" |15\8, 947.378
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|-
|-
|Dob, Solb
|Dob, Solb
دb,
صb
|Solb
|Solb
صb
|Reb
|Reb
رb
|21\11, 969.231
|21\11, 969.231
|24\13, 929.033
|24\13, 929.033
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|-
|-
!Do, Sol
!Do, Sol
د, ص
!Sol
!Sol
ص
!Re
!Re
ر
!22\11, 1015.385
!22\11, 1015.385
!16\8, 1010.526
!16\8, 1010.526
Line 1,155: Line 1,217:
|0
|0
|Do, Sol
|Do, Sol
د, ص
|perfect unison
|perfect unison
|0
|0
|Do, Sol
|Do, Sol
د, ص
|perfect fourth
|perfect fourth
|-
|-
| 1
| 1
|Mib, Sib
|Mib, Sib
صb, مb
|diminished third
|diminished third
| -1
| -1
|Re, La
|Re, La
ر, ل
|perfect second
|perfect second
|-
|-
|2
|2
|Reb, Lab
|Reb, Lab
رb, لb
|diminished second
|diminished second
| -2
| -2
|Mi, Si
|Mi, Si
ص, م
|perfect third
|perfect third
|-
|-
Line 1,177: Line 1,245:
|-
|-
|3
|3
|Dob, Solb
|Do, Sol
دb, صb
| diminished fourth
| diminished fourth
| -3
| -3
|Do#, Sol#
|Do#, Sol#
د, #ص#
|augmented unison (chroma)
|augmented unison (chroma)
|-
|-
|4
|4
|Mibb, Sibb
|Mibb, Sibb
مbb, صbb
|doubly diminished third
|doubly diminished third
| -4
| -4
|Re#, La#
|Re#, La#
ر ,# ل#
|augmented second
|augmented second
|}
|}
Line 1,213: Line 1,285:
|Mi#
|Mi#
Si#
Si#
|-
|مbb
تbb
|دb
صb
|رb
لb
|مb
تb
ص
ل
ت
|د#
ص#
|ر#
ل#
|م#
ت#
|-
|-
|dd3
|dd3