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Quasi-diatonic MOS notation: Difference between revisions

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== Interval names ==
== Interval names ==
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 takes the -ave suffix following a Latin number root indicating the scale step, to indicate that it is the equave - note that in a 2-note MOS, it is called the ''triave'', which is distinct from the ''tritave'' (a ratio of 3/1). A table of equave names will be available at the bottom of the page).
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 takes the -ave suffix following a Latin number root indicating the scale step, to indicate that it is the equave - note that in a 2-note MOS, it is called the ''triave'', which is distinct from the ''tritave'' (a ratio of 3/1). 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 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 b do for note names respectively. So in 5L3s (and in fact, in any MOS with >3 notes 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.
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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", "5L3s", or "LLsLLsLs").  
[[File:H and J clefs.png|thumb|H and J clefs from Bohlen-Pierce, by Kjell Hansen, recommended for the notes H and J in VGQDMN. ]]
[[File:H and J clefs.png|thumb|H and J clefs from Bohlen-Pierce, by Kjell Hansen, recommended for the notes H and J in VGQDMN. ]]
8va markings work as normal, though the number is changed to match the number of steps in the equave, i.e. 9va for oneirotonic, or 10va for gramitonic.
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.


Key signatures are notated as you would expect given the principle of generalizing from diatonic.
Key signatures are notated as you would expect given the principle of generalizing from diatonic.
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=== Equave names ===
=== Equave names ===
A table of what the equave is called based on how many steps it contains, using number prefixes analogous to the Latin numbers used to name -illions. This is distinct from the Greek numbers used to name harmonics, as the term "octave" comes from Latin:
A table of what the equave is called based on how many steps it contains, using number prefixes analogous to the Latin numbers used to name -illions. This is distinct from the Greek numbers used to name harmonics, as the term "octave" comes from Latin. Note that unlike the equava markings which use Italian ordinals like ottava, these do not use true Latin ordinals, but instead just the -ave suffix, for recognizability as an interval name:
{| class="wikitable"
{| class="wikitable"
|+Equave names:
|+Equave names:
!Steps (1-indexed)
!Steps (1-indexed)
!Name
!Name
!Equava marking
|-
|-
|[[1edo|2]]
|[[1edo|2]]
|Biave
|Biave
|2da "seconda"
|-
|-
|3
|3
|Triave
|Triave
|3za "terza"
|-
|-
|4
|4
|Quadrave
|Quadrave
|4ta "quarta"
|-
|-
|5
|5
|Quintave
|Quintave
|5ta "quinta"
|-
|-
|6
|6
|Sextave
|Sextave
|6ta "sesta"
|-
|-
|7
|7
|Septave
|Septave
|7ma "settima"
|-
|-
|8
|8
|Octave
|Octave
|8va "ottava"
|-
|-
|9
|9
|Nonave
|Nonave
|9na "nona"
|-
|-
|10
|10
|Decave
|Decave
|10ma "decima"
|-
|-
|11
|11
|Undecave
|Undecave
|11ma "undicesima"
|-
|-
|12
|12
|Duodecave
|Duodecave
|12ma "dodicesima"
|-
|-
|13
|13
|Tredecave
|Tredecave
|13ma "tredicesima"
|-
|-
|14
|14
|Quattuordecave
|Quattuordecave
|14ma "quattordicesima"
|-
|-
|15
|15
|Quindecave
|Quindecave
|15ma "quindicesima"
|-
|-
|16
|16
|Sexdecave
|Sexdecave
|16ma "sedicesima"
|-
|-
|17
|17
|Septendecave
|Septendecave
|17ma "diciassettesima"
|-
|-
|18
|18
|Octodecave
|Octodecave
|18ma "diciottesima"
|-
|-
|19
|19
|Novemdecave
|Novemdecave
|19ma "diciannovesima"
|-
|-
|20
|20
|Vigintave
|Vigintave
|20ma "ventesima"
|-
|-
|21
|21
|Unvigintave
|Unvigintave
|21ma "ventunesima"
|-
|-
|22
|22
|Duovigintave
|Duovigintave
|22ma "ventiduesima"
|-
|-
|23
|23
|Tresvigintave
|Tresvigintave
|23ma "ventitreesima"
|-
|-
|24
|24
|Quattuorvigintave
|Quattuorvigintave
|24ma "ventiquattresima"
|-
|-
|25
|25
|Quinvigintave
|Quinvigintave
|25ma "venticinquesima"
|}
|}


=== Optimal clefs ===
=== Optimal clefs ===
This is the table of optimal clef layouts to be analogous to the treble and bass clef for scales with different sizes. This assumes that A3 is the top line of the bass clef. Preferably, the second line from the bottom of the staff is used as the treble clef, and the second line from the top is used as the bass clef, except when that would cause a clef with an ottava which could be avoided by using a different line for the clef indicator.
This is the table of optimal clef layouts to be analogous to the treble and bass clef for scales with different sizes. This assumes that A3 is the top line of the bass clef. Preferably, the second line from the bottom of the staff is used as the treble clef, and the second line from the top is used as the bass clef, except when that would cause a clef with an equave up/down which could be avoided by using a different line for the clef indicator.
{| class="wikitable"
{| class="wikitable"
|+
|+
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|3
|3
|3
|3
|A (ottava up) on 2nd line
|A (quarta up) on 2nd line
|B on 2nd line
|B on 2nd line
|-
|-
|4
|4
|3
|3
|A (ottava up) on 1st line
|A (quinta up) on 1st line
|A on 3rd line
|A on 3rd line
|-
|-
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|6
|6
|4
|4
|A (ottava up) on 2nd line
|A (settima up) on 2nd line
|E on 3rd line
|E on 3rd line
|-
|-
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