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Quasi-diatonic MOS notation: Difference between revisions

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== Note names ==
== Note names ==
The root is A (A4), fixed to 440Hz by default. Starting from B, the notes of the darkest mode of the MOS are labelled until A an equave up (thanks [[User:CompactStar]]!), where the nominals repeat. So nominals in order are always A, B, C, D, E, F, G, etc. with the darkest mode being on B. For example, in 5L3s, the darkest mode is sLsLLsLL, so the notes ABCDEFGH represent the scale LsLsLLsL on A. This is done to make it backwards-compatible with existing diatonic notation, which starts on B for its darkest mode, Locrian. I is skipped, as in Bohlen-Pierce, to avoid confusion, and V is skipped as well.
The root is A (A4), fixed to 440 Hz by default. Starting from B, the notes of the darkest mode of the MOS are labelled until A an equave up (thanks [[User:CompactStar]]!), where the nominals repeat. So nominals in order are always A, B, C, D, E, F, G, etc. with the darkest mode being on B. For example, in 5L 3s, the darkest mode is sLsLLsLL, so the notes ABCDEFGH represent the scale LsLsLLsL on A. This is done to make it backwards-compatible with existing diatonic notation, which starts on B for its darkest mode, Locrian. I is skipped, as in Bohlen-Pierce, to avoid confusion, and V is skipped as well.


Note that this is incompatible with conventional Bohlen-Pierce notation itself, as it refers to BP's note "C" as A.  
Note that this is incompatible with conventional Bohlen–Pierce notation itself, as it refers to BP's note "C" as A.  


Accidentals are # and b, which raise and lower by a chroma (the difference between a large and small step, L-s) respectively. Double sharp and double flat work as expected.
Accidentals are ♯ and ♭, which raise and lower by a chroma (the difference between a large and small step, {{nowrap|L − s}}) respectively. Double sharp and double flat work as expected.


So, in 13edo, the notes of 5L3s are:
So, in 13edo, the notes of 5L 3s are:


A, A#/Bb, B, C, C#/Db, D, E, E#/Fb, F, F#/Gb, G, H, H#/Ab, and A an octave higher.
A, A♯/B♭, B, C, C♯/D♭, D, E, E♯/F♭, F, F♯/G♭, G, H, H♯/A♭, and A an octave higher.


MODMOSes are notated using the MOS's base notation.
MODMOSes are notated using the MOS's base notation.
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Intervals are named analogously to diatonic: interval size classes are named with ordinal numbers starting from the scale step as the 2nd (i.e. they are 1-indexed). So a 2-step would be a third, a 3-step would be a fourth, etc. The exceptions are the 0-step (which is called the unison), and the equave (which is named after an Anglicized version of the Latin ordinal for the interval). A table of equave names will be available at the bottom of the page). (Note that these are not true Latin ordinals, unlike the corresponding Italian notation of ''ottava'' (see staff notation).)
Intervals are named analogously to diatonic: interval size classes are named with ordinal numbers starting from the scale step as the 2nd (i.e. they are 1-indexed). So a 2-step would be a third, a 3-step would be a fourth, etc. The exceptions are the 0-step (which is called the unison), and the equave (which is named after an Anglicized version of the Latin ordinal for the interval). A table of equave names will be available at the bottom of the page). (Note that these are not true Latin ordinals, unlike the corresponding Italian notation of ''ottava'' (see staff notation).)


Generators are perfect, other intervals are major and minor (where major refers to the larger of the two interval sizes, and minor refers to the smaller of the two). Augmented and diminished, for interval names, function as # and b do for note names respectively. So in 5L3s (and in fact, in any MOS with >3 notes and no consecutive small steps that is not an edo, due to the way the position of A in the scale is defined), A-C is a minor third, A-C# is a major third, and A-Cx is an augmented third. Augmented and diminished are also used to name the 1 imperfect generator interval of each class, depending on its size relative to the perfect generator. As such, in 5L3s, there are 7 perfect sixths and one augmented sixth.
Generators are perfect, other intervals are major and minor (where major refers to the larger of the two interval sizes, and minor refers to the smaller of the two). Augmented and diminished, for interval names, function as ♯ and ♭ do for note names respectively. So in 5L 3s (and in fact, in any MOS with > 3 notes and no consecutive small steps that is not an edo, due to the way the position of A in the scale is defined), A–C is a minor third, A–C♯ is a major third, and A–C𝄪 is an augmented third. Augmented and diminished are also used to name the 1 imperfect generator interval of each class, depending on its size relative to the perfect generator. As such, in 5L 3s, there are 7 perfect sixths and one augmented sixth.
 


Interval classes may be distinguished using TAMNAMS MOS prefixes. For example, the generator of armotonic might be called an armsixth to reduce ambiguity.
Interval classes may be distinguished using TAMNAMS MOS prefixes. For example, the generator of armotonic might be called an armsixth to reduce ambiguity.
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Additionally, if two of the same note on a staff line are equally close to A3, such as with an E clef in an octatonic scale, it refers to the note above A3.
Additionally, if two of the same note on a staff line are equally close to A3, such as with an E clef in an octatonic scale, it refers to the note above A3.
[[File:An example of VGQDMN that hopefully uses the right scale this time.png|thumb|An example of VGQDMN that hopefully uses the right scale this time]]
[[File:An example of VGQDMN that hopefully uses the right scale this time.png|thumb|An example of VGQDMN that hopefully uses the right scale this time]]
The MOS is always specified with text above the beginning of the score (for example, "oneirotonic", "5L3s", or "LLsLLsLs").  
The MOS is always specified with text above the beginning of the score (for example, "oneirotonic", "5L 3s", or "LLsLLsLs").  


8va markings work as normal, though the number is changed to match the number of steps in the equave, i.e. 9na for oneirotonic, or 10ma for gramitonic. It is read as the Italian ordinal for the given number, and the last two letters also come from that (with the ending changed to -a if necessary). (This follows from the use of 15ma in Western music.) It can be called an equava in general.
8va markings work as normal, though the number is changed to match the number of steps in the equave, i.e. 9na for oneirotonic, or 10ma for gramitonic. It is read as the Italian ordinal for the given number, and the last two letters also come from that (with the ending changed to -a if necessary). (This follows from the use of 15ma in Western music.) It can be called an equava in general.
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== Tables and other resources: ==
== Tables and other resources: ==
=== Equave names ===
=== Equave names ===
A table of what the equave is called based on how many steps it contains. This is distinct from the Greek numbers used to name harmonics, as the term "octave" comes from Latin. The -us ending is dropped from Latin numerals (as in second and quart) except where a final silent -e is kept to indicate a long vowel (as in octave), except where said -e would lead to confusion (as with non, where it would be confused with "none", also, the English pronunciation of the Latin non- root does not include a long vowel)
A table of what the equave is called based on how many steps it contains. This is distinct from the Greek numbers used to name harmonics, as the term "octave" comes from Latin. The -us ending is dropped from Latin numerals (as in second and quart) except where a final silent -e is kept to indicate a long vowel (as in octave), except where said -e would lead to confusion (as with non, where it would be confused with "none", also, the English pronunciation of the Latin non- root does not include a long vowel)
{| class="wikitable"
{| class="wikitable"
|+Equave names:
|+ style="font-size: 105%;" | Equave names:
!Steps (1-indexed)
|-
!Name
! Steps (1-indexed)
!Equava marking
! Name
! Equava marking
|-
|-
|[[1edo|2]]
| [[1edo|2]]
|Second
| Second
|2da "seconda"
| 2da "seconda"
|-
|-
|3
| 3
|Terce
| Terce
|3za "terza"
| 3za "terza"
|-
|-
|4
| 4
|Quart
| Quart
|4ta "quarta"
| 4ta "quarta"
|-
|-
|5
| 5
|Quint
| Quint
|5ta "quinta"
| 5ta "quinta"
|-
|-
|6
| 6
|Sext
| Sext
|6ta "sesta"
| 6ta "sesta"
|-
|-
|7
| 7
|Septim
| Septim
|7ma "settima"
| 7ma "settima"
|-
|-
|8
| 8
|Octave
| Octave
|8va "ottava"
| 8va "ottava"
|-
|-
|9
| 9
|Non
| Non
|9na "nona"
| 9na "nona"
|-
|-
|10
| 10
|Decim
| Decim
|10ma "decima"
| 10ma "decima"
|-
|-
|11
| 11
|Undecim
| Undecim
|11ma "undicesima"
| 11ma "undicesima"
|-
|-
|12
| 12
|Duodecim
| Duodecim
|12ma "dodicesima"
| 12ma "dodicesima"
|-
|-
|13
| 13
|Tertiodecim
| Tertiodecim
|13ma "tredicesima"
| 13ma "tredicesima"
|-
|-
|14
| 14
|Quartodecim
| Quartodecim
|14ma "quattordicesima"
| 14ma "quattordicesima"
|-
|-
|15
| 15
|Quintodecim
| Quintodecim
|15ma "quindicesima"
| 15ma "quindicesima"
|-
|-
|16
| 16
|Sextodecim
| Sextodecim
|16ma "sedicesima"
| 16ma "sedicesima"
|-
|-
|17
| 17
|Septimodecim
| Septimodecim
|17ma "diciassettesima"
| 17ma "diciassettesima"
|-
|-
|18
| 18
|Duodevicesim
| Duodevicesim
|18ma "diciottesima"
| 18ma "diciottesima"
|-
|-
|19
| 19
|Undevicesim
| Undevicesim
|19ma "diciannovesima"
| 19ma "diciannovesima"
|-
|-
|20
| 20
|Vicesim
| Vicesim
|20ma "ventesima"
| 20ma "ventesima"
|-
|-
|21
| 21
|Vicesimoprime
| Vicesimoprime
|21ma "ventunesima"
| 21ma "ventunesima"
|-
|-
|22
| 22
|Vicesimosecond
| Vicesimosecond
|22ma "ventiduesima"
| 22ma "ventiduesima"
|-
|-
|23
| 23
|Vicesimoterce
| Vicesimoterce
|23ma "ventitreesima"
| 23ma "ventitreesima"
|-
|-
|24
| 24
|Vicesimoquart
| Vicesimoquart
|24ma "ventiquattresima"
| 24ma "ventiquattresima"
|-
|-
|25
| 25
|Vicesimoquint
| Vicesimoquint
|25ma "venticinquesima"
| 25ma "venticinquesima"
|}
|}


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{| class="wikitable"
{| class="wikitable"
|+
!Scale size
!Staff lines
!Treble clef
!Bass clef
|-
|-
|3
! Scale size
|3
! Staff lines
|A (quarta up) on 2nd line
! Treble clef
|B on 2nd line
! Bass clef
|-
| 3
| 3
| A (quarta up) on 2nd line
| B on 2nd line
|-
|-
|4
| 4
|3
| 3
|A (quinta up) on 1st line
| A (quinta up) on 1st line
|A on 3rd line
| A on 3rd line
|-
|-
|5
| 5
|4
| 4
|E on 1st line
| E on 1st line
|D on 3rd line
| D on 3rd line
|-
|-
|6
| 6
|4
| 4
|A (settima up) on 2nd line
| A (settima up) on 2nd line
|E on 3rd line
| E on 3rd line
|-
|-
|7
| 7
|5
| 5
|G on 2nd line
| G on 2nd line
|F on 4th line
| F on 4th line
|-
|-
|8
| 8
|5
| 5
|E on 1st line
| E on 1st line
|G on 4th line
| G on 4th line
|-
|-
|9
| 9
|6
| 6
|G on 2nd line
| G on 2nd line
|H on 5th line
| H on 5th line
|-
|-
|10
| 10
|6
| 6
|E on 1st line
| E on 1st line
|J on 5th line
| J on 5th line
|-
|-
|11
| 11
|7
| 7
| rowspan="10" |G on 2nd line
| rowspan="10" | G on 2nd line
|K on 6th line
| K on 6th line
|-
|-
|12
| 12
|7
| 7
|L on 6th line
| L on 6th line
|-
|-
|13
| 13
|8
| 8
|M on 7th line
| M on 7th line
|-
|-
|14
| 14
|8
| 8
|N on 7th line
| N on 7th line
|-
|-
|15
| 15
|9
| 9
|O on 8th line
| O on 8th line
|-
|-
|16
| 16
|9
| 9
|P on 8th line
| P on 8th line
|-
|-
|17
| 17
|10
| 10
|Q on 9th line
| Q on 9th line
|-
|-
|18
| 18
|10
| 10
|R on 9th line
| R on 9th line
|-
|-
|19
| 19
|11
| 11
|S on 10th line
| S on 10th line
|-
|-
|20
| 20
|11
| 11
|T on 10th line
| T on 10th line
|}
|}


Line 246: Line 246:


== Examples ==
== Examples ==
=== Pentic ===
=== Pentic ===
{| class="wikitable"
{| class="wikitable"
|+
!Interval
!Steps subtended
!Note name (from A = unison)
!Soft tuning
|-
|-
|perfect unison
! Interval
| -
! Steps subtended
|A
! Note name (from {{nowrap|A {{=}} unison}})
|0c
! Soft tuning
|-
| perfect unison
| —
| A
| 0{{c}}
|-
|-
|minor second
| minor second
|s
| s
|Bb
| Bb
|200c
| 200{{c}}
|-
|-
|major second
| major second
|L
| L
|B
| B
|300c
| 300{{c}}
|-
|-
|diminished third
| diminished third
|2s
| 2s
|Cb
| Cb
|400c
| 400{{c}}
|-
|-
|perfect third
| perfect third
|L+s
| {{nowrap|L + s}}
|C
| C
|500c
| 500{{c}}
|-
|-
|perfect fourth
| perfect fourth
|L+2s
| {{nowrap|L + 2s}}
|D
| D
|700c
| 700{{c}}
|-
|-
|augmented fourth
| augmented fourth
|2L+s
| {{nowrap|2L + s}}
|D#
| D#
|800c
| 800{{c}}
|-
|-
|minor fifth
| minor fifth
|1L+3s
| {{nowrap|1L + 3s}}
|Eb
| Eb
|900c
| 900{{c}}
|-
|-
|major fifth
| major fifth
|2L+2s
| {{nowrap|2L + 2s}}
|E
| E
|1000c
| 1000{{c}}
|-
|-
|perfect sext
| perfect sext
|2L+3s
| {{nowrap|2L + 3s}}
|A
| A
|1200c
| 1200{{c}}
|}
|}


=== Oneirotonic ===
=== Oneirotonic ===
{| class="wikitable"
{| class="wikitable"
!Interval
!Steps subtended
!Note name (from A = unison)
!Soft tuning
|-
|-
|perfect unison
! Interval
| -
! Steps subtended
|A
! Note name (from A = unison)
|0c
! Soft tuning
|-
|-
|minor second
| perfect unison
|s
| —
|Bb
| A
|114.29c
| 0{{c}}
|-
|-
|major second
| minor second
|L
| s
|B
| Bb
|171.43c
| 114.29{{c}}
|-
|-
|minor third
| major second
|L+s
| L
|C
| B
|285.71c
| 171.43{{c}}
|-
|-
|major third
| minor third
|2L
| {{nowrap|L + s}}
|C#
| C
|342.86c
| 285.71{{c}}
|-
| major third
| 2L
| C#
| 342.86{{c}}
|-
|-
|diminished fourth
| diminished fourth
|L+2s
| {{nowrap|L + 2s}}
|Db
| Db
|400.00c
| 400.00{{c}}
|-
|-
|perfect fourth
| perfect fourth
|2L+s
| {{nowrap|2L + s}}
|D
| D
|457.14c
| 457.14{{c}}
|-
|-
|minor fifth
| minor fifth
|2L+2s
| {{nowrap|2L + 2s}}
|E
| E
|571.43c
| 571.43{{c}}
|-
|-
|major fifth
| major fifth
|3L+s
| {{nowrap|3L + s}}
|E#
| E#
|628.57c
| 628.57{{c}}
|-
|-
|perfect sixth
| perfect sixth
|3L+2s
| {{nowrap|3L + 2s}}
|F
| F
|742.86c
| 742.86{{c}}
|-
|-
|augmented sixth
| augmented sixth
|4L+s
| {{nowrap|4L + s}}
|F#
| F#
|800.00c
| 800.00{{c}}
|-
|-
|minor seventh
| minor seventh
|3L+3s
| {{nowrap|3L + 3s}}
|Gb
| Gb
|857.14c
| 857.14{{c}}
|-
|-
|major seventh
| major seventh
|4L+2s
| {{nowrap|4L + 2s}}
|G
| G
|914.29c
| 914.29{{c}}
|-
|-
|minor eighth
| minor eighth
|4L+3s
| {{nowrap|4L + 3s}}
|H
| H
|1028.57c
| 1028.57{{c}}
|-
|-
|major eighth
| major eighth
|5L+2s
| {{nowrap|5L + 2s}}
|H#
| H#
|1085.71c
| 1085.71{{c}}
|-
|-
|perfect non
| perfect non
|5L+3s
| {{nowrap|5L + 3s}}
|A
| A
|1200c
| 1200{{c}}
|}
|}


== Compatibility with German and fixed-do systems ==
== Compatibility with German and fixed-do systems ==
=== German H system ===
=== German H system ===
As each interval in a MOS has one of two values, the note in the expected place of B is labelled H; the note that is the other size of second above A is labelled B. This note should usually be English B flat, as the last interval of the darkest mode of any MOS is always an L step. For notating edos as degenerate MOSes, the note name B is preferred over H, but H is still skipped after G. For scales with more than two sizes of second, the note a second above A that is furthest from H is labelled B. This means the German H system is only compatible with 23 notes, as opposed to the English system's 24.
As each interval in a MOS has one of two values, the note in the expected place of B is labelled H; the note that is the other size of second above A is labelled B. This note should usually be English B flat, as the last interval of the darkest mode of any MOS is always an L step. For notating edos as degenerate MOSes, the note name B is preferred over H, but H is still skipped after G. For scales with more than two sizes of second, the note a second above A that is furthest from H is labelled B. This means the German H system is only compatible with 23 notes, as opposed to the English system's 24.
Line 404: Line 403:
The vowels are the five-vowel system, the pronunciation of each consonant is as follows:
The vowels are the five-vowel system, the pronunciation of each consonant is as follows:
{| class="wikitable"
{| class="wikitable"
!Consonant
!IPA value
!English example
|-
|-
|d
! Consonant
! IPA value
! English example
|-
| d
| /d/
| /d/
|'''d'''oor
| '''d'''oor
|-
|-
|r
| r
|/r/
| /r/
|wa'''t'''er<ref group="cnote">This is actually the "whatever rhotic", the English example is just the closest English sound to the most common rhotic, /r/. </ref>
| wa'''t'''er<ref group="cnote">This is actually the "whatever rhotic", the English example is just the closest English sound to the most common rhotic, /r/. </ref>
|-
|-
|m
| m
|/m/
| /m/
|'''m'''an
| '''m'''an
|-
|-
|f
| f
|/f/
| /f/
|'''f'''ine
| '''f'''ine
|-
|-
|k
| k
|/k/
| /k/
|'''c'''ar
| '''c'''ar
|-
|-
|b
| b
|/b/
| /b/
|'''b'''est
| '''b'''est
|-
|-
|n
| n
|/n/
| /n/
|'''n'''orth
| '''n'''orth
|-
|-
|g
| g
|/g/
| /g/
|'''g'''ate
| '''g'''ate
|-
|-
|t
| t
|/t/
| /t/
|'''t'''ell
| '''t'''ell
|-
|-
|s
| s
|/s/
| /s/
|'''s'''ee
| '''s'''ee
|-
|-
|l
| l
|/l/
| /l/
|'''l'''aw<ref group="cnote">Can be pronounced the same as r, as no note ''*ra'' exists that would cause an ambiguity with ''la''.</ref>
| '''l'''aw<ref group="cnote">Can be pronounced the same as r, as no note ''*ra'' exists that would cause an ambiguity with ''la''.</ref>
|}
|}
<references group="cnote" />
<references group="cnote" />
{| class="wikitable"
{| class="wikitable"
!Alphabetic
!German H
!Solfege consonant
!Solfege vowel
!Full solfege
|-
|-
|C
! Alphabetic
! German H
! Solfege consonant
! Solfege vowel
! Full solfege
|-
| C
| C
| C
|'''d'''
| '''d'''
|'''o'''
| '''o'''
|do
| do
|-
|-
|D
| D
|D
| D
|r
| r
|e
| e
|re
| re
|-
|-
|E
| E
|E
| E
|m
| m
|i
| i
|mi
| mi
|-
|-
|F
| F
|F
| F
|f
| f
|a
| a
|fa
| fa
|-
|-
|G
| G
|G
| G
|k
| k
|u
| u
|ku
| ku
|-
|-
|H
| H
|J
| J
|b
| b
|'''o'''
| '''o'''
|bo
| bo
|-
|-
|J
| J
|K
| K
|n
| n
|e
| e
|ne
| ne
|-
|-
|K
| K
|L
| L
|g
| g
|i
| i
|gi
| gi
|-
|-
|L
| L
|M
| M
|t
| t
|a
| a
|ta
| ta
|-
|-
|M
| M
|N
| N
|'''d'''
| '''d'''
|u
| u
|du
| du
|-
|-
|N
| N
|O
| O
|r
| r
|'''o'''
| '''o'''
|ro
| ro
|-
|-
|O
| O
|P
| P
|m
| m
|e
| e
|me
| me
|-
|-
|P
| P
|Q
| Q
|f
| f
|i
| i
|fi
| fi
|-
|-
|Q
| Q
|R
| R
|k
| k
|a
| a
|ka
| ka
|-
|-
|R
| R
|S
| S
|b
| b
|u
| u
|bu
| bu
|-
|-
|S
| S
|T
| T
|n
| n
|'''o'''
| '''o'''
|no
| no
|-
|-
|T
| T
|U
| U
|g
| g
|e
| e
|ge
| ge
|-
|-
|U
| U
|W
| W
|t
| t
|i
| i
|te<ref group="tnote">''te'' replaces ''*ti'' to avoid confusion with the note ''si''</ref>
| te<ref group="tnote">''te'' replaces ''*ti'' to avoid confusion with the note ''si''</ref>
|-
|-
|W
| W
|X
| X
|'''d'''
| '''d'''
|a
| a
|da
| da
|-
|-
|X
| X
|Y
| Y
|r
| r
|u
| u
|ru
| ru
|-
|-
|Y
| Y
|Z
| Z
|m
| m
|'''o'''
| '''o'''
|mo
| mo
|-
|-
|'''''(Last note)'''''
| '''''(Last note)'''''
|'''''(Last note)'''''
| '''''(Last note)'''''
|'''''-'''''
| '''''-'''''
|'''''-'''''
| '''''-'''''
|'''''sol'''''
| '''''sol'''''
|-
|-
|'''''A'''''
| '''''A'''''
|'''''A'''''
| '''''A'''''
|'''''-'''''
| '''''-'''''
|'''''-'''''
| '''''-'''''
|'''''la'''''
| '''''la'''''
|-
|-
|'''''B flat'''''
| '''''B flat'''''
|'''''B'''''
| '''''B'''''
|'''''-'''''
| '''''-'''''
|'''''-'''''
| '''''-'''''
|'''''si bemol'''''
| '''''si bemol'''''
|-
|-
|'''''B'''''
| '''''B'''''
|'''''H'''''
| '''''H'''''
|'''''-'''''
| '''''-'''''
|'''''-'''''
| '''''-'''''
|'''''si'''''
| '''''si'''''
|}
|}
<references group="tnote" />
<references group="tnote" />
Line 614: Line 616:
{{Navbox notation}}
{{Navbox notation}}


[[Category:Notation]][[Category:MOS scale]]
[[Category:Notation]]
[[Category:MOS scale]]
Retrieved from "https://en.xen.wiki/w/Quasi-diatonic_MOS_notation"