Diamond-mos notation: Difference between revisions
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The mos pattern is marked on the score too. Just to the right of the diamonds, little boxes mark the steps of the mos. Hollow boxes represent small mossteps (s) and filled boxes represent large mossteps (L). To avoid clutter, only the small mossteps or the large mossteps are marked. The ones which get marked are the ones the mos has fewer of. (In the case of nL ns mosses, either is fine.) The boxes are another tool to make reading the score easier. | The mos pattern is marked on the score too. Just to the right of the diamonds, little boxes mark the steps of the mos. Hollow boxes represent small mossteps (s) and filled boxes represent large mossteps (L). To avoid clutter, only the small mossteps or the large mossteps are marked. The ones which get marked are the ones the mos has fewer of. (In the case of nL ns mosses, either is fine.) The boxes are another tool to make reading the score easier. | ||
[[File:Diamond-mos ledger lines.png|thumb|Notes with ledger lines on the diamond-mos staff using [[3L 4s]].]] | |||
The boxes on a barline show all of the mos steps the staff covers, including the steps immediately above the top line and below the bottom line. Diamond clefs cover more staff lines than other barlines, so they have more boxes. When notes on the staff use ledger lines, extra boxes may be needed to aid sightreading. If a note has more ledger lines than any other note in the same bar, extra boxes should be attached to the left side of the ledger lines. (You may add boxes to other notes if you feel it's necessary.) However, if the bar has a diamond clef on the left which already has all of the necessary boxes, boxes on ledger lines aren't needed. | |||
The staff can be extended up and down to have more than five lines when using non-diatonic mosses. You should use at least as many staff lines as is required to fit an octave in the staff, which for an n-tone mos is ceil(n/2 + 1). When more than five staff lines are used, at least one of the staff lines should be bolded. The bolded line doesn't represent anything in particular, but provides an extra visual reference for readability. | The staff can be extended up and down to have more than five lines when using non-diatonic mosses. You should use at least as many staff lines as is required to fit an octave in the staff, which for an n-tone mos is ceil(n/2 + 1). When more than five staff lines are used, at least one of the staff lines should be bolded. The bolded line doesn't represent anything in particular, but provides an extra visual reference for readability. | ||
==Accidentals== | |||
== Accidentals == | |||
[[File:Diamond-mos accidental names table.png|thumb|353x353px|A table of the accidentals in diamond-mos, their text representations, and their spoken names.]] | [[File:Diamond-mos accidental names table.png|thumb|353x353px|A table of the accidentals in diamond-mos, their text representations, and their spoken names.]] | ||
There are three types of accidentals in diamond-mos. There are diatonic accidentals (#, b, …), mos accidentals (&, @, …), and ups and downs (^, v, …). | There are three types of accidentals in diamond-mos. There are diatonic accidentals (#, b, …), mos accidentals (&, @, …), and ups and downs (^, v, …). | ||
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A subtle but important feature of the standard is that accidentals are separate from each other and do not stack. '''If a note has an accidental in front, that accidental fully overrides any preceding accidentals.''' For example, if a D with a # is followed by a D with only an ^, the second note is D^, not D^#. | A subtle but important feature of the standard is that accidentals are separate from each other and do not stack. '''If a note has an accidental in front, that accidental fully overrides any preceding accidentals.''' For example, if a D with a # is followed by a D with only an ^, the second note is D^, not D^#. | ||
== Note names == | ==Note names== | ||
When using a non-diatonic mos, the JKL… note names represent notes of the current mos. Only J has a fixed meaning (middle J = middle C); the remaining note names depend on both the mos pattern and the current mode of the mos (under our soft rule about what note names mean). For example, when you are writing in the LsLLsLsL mode of 5L3s, the “natural” note names JKLMNOPQ represent the scale LsLLsLsL on J. | When using a non-diatonic mos, the JKL… note names represent notes of the current mos. Only J has a fixed meaning (middle J = middle C); the remaining note names depend on both the mos pattern and the current mode of the mos (under our soft rule about what note names mean). For example, when you are writing in the LsLLsLsL mode of 5L3s, the “natural” note names JKLMNOPQ represent the scale LsLLsLsL on J. | ||
== Key signatures == | ==Key signatures== | ||
[[File:5L3s LsLLsLsL key signature.png|thumb|298x298px|The 5L 3s key signature mentioned in this section.]] | [[File:5L3s LsLLsLsL key signature.png|thumb|298x298px|The 5L 3s key signature mentioned in this section.]] | ||
Transposing the score's notation, as mentioned in the Staff section, can do much of the job of key signatures. For non-diatonic scores which do not change key, we recommend to transpose the score so that the tonic is written as J. This is an especially useful option if the key signature would be very complicated otherwise. For scores which do modulate, however, key signatures are important for showing the relationship between the keys, especially since modulations often mix tones from the two keys as the change happens. Note that transposing the whole score is still an option for scores which modulate. For example, when modulating from the key of J^ to L^, transposing so that the keys are written as J natural and L natural improves readability. | Transposing the score's notation, as mentioned in the Staff section, can do much of the job of key signatures. For non-diatonic scores which do not change key, we recommend to transpose the score so that the tonic is written as J. This is an especially useful option if the key signature would be very complicated otherwise. For scores which do modulate, however, key signatures are important for showing the relationship between the keys, especially since modulations often mix tones from the two keys as the change happens. Note that transposing the whole score is still an option for scores which modulate. For example, when modulating from the key of J^ to L^, transposing so that the keys are written as J natural and L natural improves readability. | ||
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For example, if you want to notate the key of D in the 42442424 mode of [[5L 3s]] in [[26edo]]: | For example, if you want to notate the key of D in the 42442424 mode of [[5L 3s]] in [[26edo]]: | ||
* The chroma-positive generator of [[5L 3s]] is the subfourth, 461.5¢. | *The chroma-positive generator of [[5L 3s]] is the subfourth, 461.5¢. | ||
* D is reached by going 3 subfourth generators up from C. | *D is reached by going 3 subfourth generators up from C. | ||
* This means that the key signature should have three &’s, notated on the appropriate notes to represent the 42442424 scale on D. | *This means that the key signature should have three &’s, notated on the appropriate notes to represent the 42442424 scale on D. | ||
The new tonic (D) is spelled K in this mode, and the notes will be K L& M N O& P Q& J K. So the key signature will have an & on L, O and Q. | The new tonic (D) is spelled K in this mode, and the notes will be K L& M N O& P Q& J K. So the key signature will have an & on L, O and Q. | ||
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The order of the accidentals of the key signature from left to right should follow the generator chain, just like how 12edo key signatures follow the circle of fifths. | The order of the accidentals of the key signature from left to right should follow the generator chain, just like how 12edo key signatures follow the circle of fifths. | ||
=== Altered mosses === | ===Altered mosses=== | ||
[[File:D Ionian v3 v6 v7 (v2).png|alt=|thumb|A key signature representing the altered mos D Ionian v3 v6 v7, e.g. in [[34edo]]. The unmodified D major key signature (two sharps) is readable on the left side of the dotted line, making the tonic apparent.]] | [[File:D Ionian v3 v6 v7 (v2).png|alt=|thumb|A key signature representing the altered mos D Ionian v3 v6 v7, e.g. in [[34edo]]. The unmodified D major key signature (two sharps) is readable on the left side of the dotted line, making the tonic apparent.]] | ||
The mos mode written on the score, and represented by the boxes, must be a pure mos with no alterations. However, there is a way to make altered mos key signatures to avoid cluttering the score with accidentals. First, we write the key signature corresponding to the tonic as if the mos is not altered. This is so that you can still find the tonic just by counting the accidentals. Next, we add the alterations as extra accidentals to the right of the existing ones. There is a dotted line between the pure mos accidentals and the alteration accidentals to improve clarity. The dotted line has the word "ALT" attached below to reinforce its meaning. (If the pure key signature is blank, the dotted line is to the left of the alteration accidentals, with nothing to the left of the dotted line.) As discussed before, all accidentals in diamond-mos completely override any preceding accidentals. This includes alteration accidentals in the key signature. | The mos mode written on the score, and represented by the boxes, must be a pure mos with no alterations. However, there is a way to make altered mos key signatures to avoid cluttering the score with accidentals. First, we write the key signature corresponding to the tonic as if the mos is not altered. This is so that you can still find the tonic just by counting the accidentals. Next, we add the alterations as extra accidentals to the right of the existing ones. There is a dotted line between the pure mos accidentals and the alteration accidentals to improve clarity. The dotted line has the word "ALT" attached below to reinforce its meaning. (If the pure key signature is blank, the dotted line is to the left of the alteration accidentals, with nothing to the left of the dotted line.) As discussed before, all accidentals in diamond-mos completely override any preceding accidentals. This includes alteration accidentals in the key signature. | ||
== Edo superset notation == | ==Edo superset notation== | ||
It’s often a good idea to notate small edos as subsets of larger edos. For example, notating 13edo as a subset of 26edo allows you to use ABC notation. To do this for a diamond-mos score, write “13edo, superset 26edo” at the top of the score. For the purposes of notation, the superset edo is the edo the score is in. However, you can’t stray outside the subset edo, because that wouldn’t make sense. | It’s often a good idea to notate small edos as subsets of larger edos. For example, notating 13edo as a subset of 26edo allows you to use ABC notation. To do this for a diamond-mos score, write “13edo, superset 26edo” at the top of the score. For the purposes of notation, the superset edo is the edo the score is in. However, you can’t stray outside the subset edo, because that wouldn’t make sense. | ||
Recommended supersets for nondiatonic edos (that are also not multiples of 5 or 7): | Recommended supersets for nondiatonic edos (that are also not multiples of 5 or 7): | ||
* [[8edo]]: [[24edo]] | *[[8edo]]: [[24edo]] | ||
* [[9edo]] and [[18edo]]: [[36edo]] | *[[9edo]] and [[18edo]]: [[36edo]] | ||
* [[11edo]]: [[22edo]] | *[[11edo]]: [[22edo]] | ||
* [[13edo]]: [[26edo]] | *[[13edo]]: [[26edo]] | ||
* [[16edo]]: [[48edo]] | *[[16edo]]: [[48edo]] | ||
* [[23edo]]: [[46edo]] | *[[23edo]]: [[46edo]] | ||
== Using edo notation to represent non-edo tunings == | ==Using edo notation to represent non-edo tunings== | ||
Diamond-mos notation is based on an edo, but that doesn’t mean it can only represent music in edos. The tones of an edo in diamond-mos can be retuned to any scale of the same size. After the edo, write “Retune [scale]” at the top of the score, with the scale’s tones written out explicitly. | Diamond-mos notation is based on an edo, but that doesn’t mean it can only represent music in edos. The tones of an edo in diamond-mos can be retuned to any scale of the same size. After the edo, write “Retune [scale]” at the top of the score, with the scale’s tones written out explicitly. | ||
If you don’t use a tone of the edo at all in the score, you can write “X” in your scale, e.g. “7edo, retune 24:26:X:32:36:39:43:48”. | If you don’t use a tone of the edo at all in the score, you can write “X” in your scale, e.g. “7edo, retune 24:26:X:32:36:39:43:48”. | ||
== Sightreading == | == Sightreading== | ||
[[File:Diamond-mos sightreading.png|thumb|An example of sightreading in diamond-mos. This 3-mosstep interval contains two hollow boxes (s). Other 3-mosstep intervals contain only one hollow box, so this interval would be minor if the notes were natural. However, since the upper note is natural and the lower note has @, the interval is one moschroma wider than that. Thus, this interval is a major 3-mosstep.]] | [[File:Diamond-mos sightreading.png|thumb|An example of sightreading in diamond-mos. This 3-mosstep interval contains two hollow boxes (s). Other 3-mosstep intervals contain only one hollow box, so this interval would be minor if the notes were natural. However, since the upper note is natural and the lower note has @, the interval is one moschroma wider than that. Thus, this interval is a major 3-mosstep.]] | ||
By looking at the boxes on the staff, you can quickly figure out what the interval between two notes is. What interval class ([[TAMNAMS|2-mosstep]], 3-mosstep, etc) the interval is is easy to see; just count the distance between the notes. From there, look at the boxes on the left of the score contained by the interval. This will tell you what the interval would be if the notes were natural. If the interval contains one more filled box than it could in another position, or one fewer hollow box, it’s major. If the interval contains one more hollow box than it could in another position, or one fewer filled box, it’s minor. (Generators are called perfect/augmented/diminished, not major and minor, but it’s the same idea. Every interval class has at most two sizes.) Finally, look at the accidentals on the notes, including ones implied by the key signature. If the bottom note is natural and the top note has &, for example, the interval is one moschroma wider than the boxes suggest. Remember that a moschroma is the difference between any major interval and its corresponding minor interval. | By looking at the boxes on the staff, you can quickly figure out what the interval between two notes is. What interval class ([[TAMNAMS|2-mosstep]], 3-mosstep, etc) the interval is is easy to see; just count the distance between the notes. From there, look at the boxes on the left of the score contained by the interval. This will tell you what the interval would be if the notes were natural. If the interval contains one more filled box than it could in another position, or one fewer hollow box, it’s major. If the interval contains one more hollow box than it could in another position, or one fewer filled box, it’s minor. (Generators are called perfect/augmented/diminished, not major and minor, but it’s the same idea. Every interval class has at most two sizes.) Finally, look at the accidentals on the notes, including ones implied by the key signature. If the bottom note is natural and the top note has &, for example, the interval is one moschroma wider than the boxes suggest. Remember that a moschroma is the difference between any major interval and its corresponding minor interval. | ||
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This method allows you to figure out the size of the interval just from the visual aids on the score. You still have to remember how many edosteps each mos interval is, but that’s much less work than memorizing all the interval sizes on every scale degree. | This method allows you to figure out the size of the interval just from the visual aids on the score. You still have to remember how many edosteps each mos interval is, but that’s much less work than memorizing all the interval sizes on every scale degree. | ||
== How to choose between enharmonics == | ==How to choose between enharmonics== | ||
Especially when working in small edos, there will be cases where there is more than one way to write a note. For example, J& and K@ may be enharmonic to each other. The way to choose which to write is similar to how you would make the choice in a 12edo score. The spelling you choose should reflect the mos structure of the piece. More practically speaking, you should choose spellings which lead to arrangements of notes which don’t span too many generators. For example, in 12edo diatonic, “Bb Db F” spans four fifths (Db Ab Eb Bb F), while “Bb C# F” spans nine fifths. | Especially when working in small edos, there will be cases where there is more than one way to write a note. For example, J& and K@ may be enharmonic to each other. The way to choose which to write is similar to how you would make the choice in a 12edo score. The spelling you choose should reflect the mos structure of the piece. More practically speaking, you should choose spellings which lead to arrangements of notes which don’t span too many generators. For example, in 12edo diatonic, “Bb Db F” spans four fifths (Db Ab Eb Bb F), while “Bb C# F” spans nine fifths. | ||
== Exceptions == | ==Exceptions== | ||
* There’s an exception to the rule that diamond-mos notation is always based on an edo. There is also the option of specifying a mos tuning which does not come from an edo. At the top of the score, write “Non-edo mos tuning” and specify the exact size of the generator. Instead of writing the mos mode in edosteps, use generic mos pattern notation, e.g. “LLsLsLs”. When using non-edo notation, ^/v have no meaning and are disallowed. The only available accidentals are the mos-based &/@/e/a accidentals (or #/b/t/d if using 5L 2s). Since non-edo notation doesn’t use a fixed, finite set of pitches, retuning to an arbitrary scale is disallowed. | * There’s an exception to the rule that diamond-mos notation is always based on an edo. There is also the option of specifying a mos tuning which does not come from an edo. At the top of the score, write “Non-edo mos tuning” and specify the exact size of the generator. Instead of writing the mos mode in edosteps, use generic mos pattern notation, e.g. “LLsLsLs”. When using non-edo notation, ^/v have no meaning and are disallowed. The only available accidentals are the mos-based &/@/e/a accidentals (or #/b/t/d if using 5L 2s). Since non-edo notation doesn’t use a fixed, finite set of pitches, retuning to an arbitrary scale is disallowed. | ||
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* It is acceptable to treat equal scales (sub-edos of the edo used for notation) as mosses for notation in diamond-mos, for example 9edo in 18edo. In that case, &/@ have no meaning and are disallowed. There are also no boxes on the staff. The only non-altered key signatures allowed are all-up (^) key signatures or similar. | * It is acceptable to treat equal scales (sub-edos of the edo used for notation) as mosses for notation in diamond-mos, for example 9edo in 18edo. In that case, &/@ have no meaning and are disallowed. There are also no boxes on the staff. The only non-altered key signatures allowed are all-up (^) key signatures or similar. | ||
* It is acceptable to use 5L 2s-based notation even for edos where the best fifth is 4\7 or 3\5. This is for consistency with existing microtonal notation that allows this. In the case of 4\7, #/b technically alter notes by zero edosteps, so they’re disallowed. [[TAMNAMS#Step ratio spectrum|Equalized]] and [[TAMNAMS#Step ratio spectrum|paucitonic]] tunings are only allowed for 5L 2s, not other mosses. | *It is acceptable to use 5L 2s-based notation even for edos where the best fifth is 4\7 or 3\5. This is for consistency with existing microtonal notation that allows this. In the case of 4\7, #/b technically alter notes by zero edosteps, so they’re disallowed. [[TAMNAMS#Step ratio spectrum|Equalized]] and [[TAMNAMS#Step ratio spectrum|paucitonic]] tunings are only allowed for 5L 2s, not other mosses. | ||
* It is possible to use non-octave equal tunings and non-octave mosses with diamond-mos. In this case, the diamonds mark the structural [[equave]] (the period or occasionally a multiple of the period). JKL note names repeat at this same equave. Explicitly write out what this equave is along with the tuning and mos pattern. | *It is possible to use non-octave equal tunings and non-octave mosses with diamond-mos. In this case, the diamonds mark the structural [[equave]] (the period or occasionally a multiple of the period). JKL note names repeat at this same equave. Explicitly write out what this equave is along with the tuning and mos pattern. | ||
* So far, we have assumed that the choice of perfect fifth for the diatonic mos is unambiguous. However, larger edos can have more than one size of interval capable of generating 5L 2s. If you're using such an edo, the default fifth used for diatonic notation is the fifth closest to 3/2. If you want to use a different fifth for diatonic notation, write it at the top of the score, e.g. "54edo, diatonic fifth = 31\54". | *So far, we have assumed that the choice of perfect fifth for the diatonic mos is unambiguous. However, larger edos can have more than one size of interval capable of generating 5L 2s. If you're using such an edo, the default fifth used for diatonic notation is the fifth closest to 3/2. If you want to use a different fifth for diatonic notation, write it at the top of the score, e.g. "54edo, diatonic fifth = 31\54". | ||
== Use in software == | ==Use in software == | ||
[[File:Diamond-mos raster full sheet.png|thumb|The transparent png sheet of all the diamond-mos accidentals. The purple pixels are to help you align them to the staff lines. Corresponds to musescore with Leland font at 800% zoom.]] | [[File:Diamond-mos raster full sheet.png|thumb|The transparent png sheet of all the diamond-mos accidentals. The purple pixels are to help you align them to the staff lines. Corresponds to musescore with Leland font at 800% zoom.]] | ||
Creating a plugin to make diamond-mos scores play back correctly in MuseScore could be very difficult, and there are currently no plans to make one. MuseScore also doesn't support custom accidentals or even importing new musical fonts. | Creating a plugin to make diamond-mos scores play back correctly in MuseScore could be very difficult, and there are currently no plans to make one. MuseScore also doesn't support custom accidentals or even importing new musical fonts. | ||
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The raster images of diamond-mos accidentals have been designed and created, so you can draw up diamond-mos notation in image editing software. You can also paste raster images into MuseScore to use it for visual-only diamond-mos scores. [TODO: Make a "palette" mscz file with diamond-mos images included to make this easier.] | The raster images of diamond-mos accidentals have been designed and created, so you can draw up diamond-mos notation in image editing software. You can also paste raster images into MuseScore to use it for visual-only diamond-mos scores. [TODO: Make a "palette" mscz file with diamond-mos images included to make this easier.] | ||
[[Category:Notation]][[Category:MOS]] | [[Category:Notation]] | ||
[[Category:MOS]] | |||