Diamond-mos notation: Difference between revisions
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Diamond-mos notation is based in a specific tuning (such as an edo) at a given time, written at the top of the score. The naturals on the staff represent a specific mos. The mos pattern is written in large and small steps at the top of the score (if applicable, in edosteps), e.g. "LLsLLsLs" (or "33133131" in the [[hard]] tuning). The natural staff notes are the specific mode written, starting from middle J (which is always equivalent to middle C as discussed in [[#Staff]]). | Diamond-mos notation is based in a specific tuning (such as an edo) at a given time, written at the top of the score. The naturals on the staff represent a specific mos. The mos pattern is written in large and small steps at the top of the score (if applicable, in edosteps), e.g. "LLsLLsLs" (or "33133131" in the [[hard]] tuning). The natural staff notes are the specific mode written, starting from middle J (which is always equivalent to middle C as discussed in [[#Staff]]). | ||
Diamond-mos notation treats the diatonic mos ([[5L 2s]]) as special. If you are using 5L 2s, diamond-mos looks like standard music notation. It uses standard clefs, | Diamond-mos notation treats the diatonic mos ([[5L 2s]]) as special. If you are using 5L 2s, diamond-mos looks like standard music notation. It uses standard clefs, ♯/♭ accidentals, and ABCDEFG note names. If you're using 5L 2s, you don't need to write the mos pattern on the score, only the tuning. If you're using an edo that has 5L 2s, its notes can be used as an unchanging reference other mosses can be compared against. For example, you might say {{nowrap|"P@ {{=}} B♭"}} to provide a reference for which note P@ is. | ||
When using a non-diatonic mos, the mode you write for notation should be the mode you are writing in. This soft rule allows you to figure out the tonic just by looking at the key signature, as explained later. We call this a soft rule because there are situations where it makes less sense, such as if the tonic is ambiguous or shifting. If you break this rule, we would suggest making a note on the score when you do. | When using a non-diatonic mos, the mode you write for notation should be the mode you are writing in. This soft rule allows you to figure out the tonic just by looking at the key signature, as explained later. We call this a soft rule because there are situations where it makes less sense, such as if the tonic is ambiguous or shifting. If you break this rule, we would suggest making a note on the score when you do. | ||
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=== Transposed notation === | === Transposed notation === | ||
Some keys in are difficult to read and write, even in relatively small edos. For example, a piece in [[19edo]]'s diatonic key of G♯ major would require a key signature with six sharps and one double sharp. To solve this problem, it is possible to transpose the pitch of the entire score (or a section of a score) to improve readability. The transpose amount and direction is written at the top of the score. For example, writing "1\19 higher than written" would enable you to rewrite a 19edo | Some keys in are difficult to read and write, even in relatively small edos. For example, a piece in [[19edo]]'s diatonic key of G♯ major would require a key signature with six sharps and one double sharp. To solve this problem, it is possible to transpose the pitch of the entire score (or a section of a score) to improve readability. The transpose amount and direction is written at the top of the score. For example, writing "1\19 higher than written" would enable you to rewrite a 19edo G♯ major piece as G major. A transposition affects diatonic and non-diatonic notation equally, and J still always equals C. | ||
== Staff == | == Staff == | ||
[[File:Diamond-mos 4L3s staff boxes.png|thumb|The diamond-mos staff using the LsLLsLs mode of 4L 3s.]] | [[File:Diamond-mos 4L3s staff boxes.png|thumb|The diamond-mos staff using the LsLLsLs mode of 4L 3s.]] | ||
When using a mos different from 5L 2s, diamond-mos notation does not have traditional clefs. Instead, octaves on the staff are marked with diamonds on the left edge of the staff. The notes marked with diamonds are named J. The large diamond marks "middle J", which is enharmonic to middle C. The point of the diamonds is to provide a visual reference for where the octaves are. It would be difficult to sightread otherwise, especially when using non-heptatonic mosses. | When using a mos different from 5L 2s, diamond-mos notation does not have traditional clefs. Instead, octaves on the staff are marked with diamonds on the left edge of the staff. The notes marked with diamonds are named J. The large diamond marks "middle J", which is enharmonic to middle C. The point of the diamonds is to provide a visual reference for where the octaves are. It would be difficult to sightread otherwise, especially when using non-heptatonic mosses. | ||
The mos pattern is marked on the score too. On each barline (to the right of the diamonds if it's the leftmost line), 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 ''n''L ''n''s mosses, either is fine.) The boxes are another tool to make reading the score easier. | The mos pattern is marked on the score too. On each barline (to the right of the diamonds if it's the leftmost line), 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 ''n''L ''n''s 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]].]] | [[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 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. | ||
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The third type of accidentals are ups and downs. '''^''' raises by one edostep and '''v''' lowers by one edostep. There are double and triple versions, '''^^'''/'''vv''' and '''^^^'''/'''vvv''', which represent movements of two and three edosteps respectively. Ups and downs can be combined with the other two types to create compound accidentals, such as '''^♯''' and '''vv@'''. Note: The ups and downs in diamond-mos do not necessarily follow the same rules as in Kite's original [[ups and downs notation|ups and downs standard]]. | The third type of accidentals are ups and downs. '''^''' raises by one edostep and '''v''' lowers by one edostep. There are double and triple versions, '''^^'''/'''vv''' and '''^^^'''/'''vvv''', which represent movements of two and three edosteps respectively. Ups and downs can be combined with the other two types to create compound accidentals, such as '''^♯''' and '''vv@'''. Note: The ups and downs in diamond-mos do not necessarily follow the same rules as in Kite's original [[ups and downs notation|ups and downs standard]]. | ||
The meaning of &/@ accidentals is dependent on the specific mos being used. &/@ have no meaning on the diatonic staff, so are not allowed in that case. Ups and downs can always be used. If the edo has 5L 2s, the meaning of ♯/♭ accidentals is fixed, not dependent on any context. However, in a non-diatonic mos context, ♯/♭ have no theoretical significance and could potentially be confusing. We heavily discourage ♯/♭ in a non-diatonic mos context for that reason. However, using them could be useful in very large edos where you need all the accidental options you can get. | The meaning of &/@ accidentals is dependent on the specific mos being used. &/@ have no meaning on the diatonic staff, so are not allowed in that case. Ups and downs can always be used. If the edo has 5L 2s, the meaning of ♯/♭ accidentals is fixed, not dependent on any context. However, in a non-diatonic mos context, ♯/♭ have no theoretical significance and could potentially be confusing. We heavily discourage ♯/♭ in a non-diatonic mos context for that reason. However, using them could be useful in very large edos where you need all the accidental options you can get. | ||
When using 5L 2s in an edo where t/d are one edostep, we encourage using {{demisharp2}}/{{demiflat2}} instead of ^/v. This is to increase consistency with existing microtonal notation, such as notation for 17edo, 24edo, and 31edo. The same rule does not apply to e/a semi-moschroma accidentals. | When using 5L 2s in an edo where t/d are one edostep, we encourage using {{demisharp2}}/{{demiflat2}} instead of ^/v. This is to increase consistency with existing microtonal notation, such as notation for 17edo, 24edo, and 31edo. The same rule does not apply to e/a semi-moschroma accidentals. | ||
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 ({{nowrap|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. | ||
With that out of the way, this is how to make non-diatonic key signatures. To change the tonic, we use the key signature of mos accidentals to indicate how many chroma-positive mos generators the tonic is above middle J = middle C. (A generator of a mos is called chroma-positive if the ''larger'' intervals in each generic interval class of the mos result from stacking the generator ''upwards''. For example, the chroma-positive generator of [[5L 2s]] is the fifth, because the major third is 4 fifths up and the minor third is 3 fifths down.) | With that out of the way, this is how to make non-diatonic key signatures. To change the tonic, we use the key signature of mos accidentals to indicate how many chroma-positive mos generators the tonic is above {{nowrap|middle J {{=}} middle C}}. (A generator of a mos is called chroma-positive if the ''larger'' intervals in each generic interval class of the mos result from stacking the generator ''upwards''. For example, the chroma-positive generator of [[5L 2s]] is the fifth, because the major third is 4 fifths up and the minor third is 3 fifths down.) | ||
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. | ||
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Similarly if your key is reached by stacking chroma-positive generators down, the number of generators taken to do so is the number of @'s in the key signature. | Similarly if your key is reached by stacking chroma-positive generators down, the number of generators taken to do so is the number of @'s in the key signature. | ||
What notes you put the accidentals on in the key signature will depend on the mode, but the number of accidentals only depends on the number of generators up from J = C. This rule allows you to figure out the tonic just by counting the accidentals in the key signature. | What notes you put the accidentals on in the key signature will depend on the mode, but the number of accidentals only depends on the number of generators up from {{nowrap|J {{=}} C}}. This rule allows you to figure out the tonic just by counting the accidentals in the key signature. | ||
If your key is not reachable from C by stacking a given generator in the edo (i.e. if the mos generator is contained in an edo subset), the key signature will indicate the number of generators (indicated by &'s or @'s) + the number of edo steps (indicated by shifting every accidental on the key signature by that fixed number of ^/v) the tonic is above C. For example, writing the key of F in 42442424 in 26edo will require one & on Q (to change the tonic from C to F♭), plus an ^ on every note in J…Q (to shift the tonic from F♭ to F). Thus the key signature will be: ^& on Q, ^ on every other note. | If your key is not reachable from C by stacking a given generator in the edo (i.e. if the mos generator is contained in an edo subset), the key signature will indicate the number of generators (indicated by &'s or @'s) + the number of edo steps (indicated by shifting every accidental on the key signature by that fixed number of ^/v) the tonic is above C. For example, writing the key of F in 42442424 in 26edo will require one & on Q (to change the tonic from C to F♭), plus an ^ on every note in J…Q (to shift the tonic from F♭ to F). Thus the key signature will be: ^& on Q, ^ on every other note. | ||
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== 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 do not span too many generators. For example, in 12edo diatonic, | 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 do not span too many generators. For example, in 12edo diatonic, "B♭ D♭ F" spans four fifths (D♭ A♭ E♭ B♭ F), while "B♭ C♯ F" spans nine fifths. | ||
== Exceptions == | == Exceptions == | ||
* There is 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 ♯/♭/{{demisharp2}}/{{demiflat2}} if using 5L 2s). Since non-edo notation does not use a fixed, finite set of pitches, retuning to an arbitrary scale is disallowed. | * There is 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 ♯/♭/{{demisharp2}}/{{demiflat2}} if using 5L 2s). Since non-edo notation does not use a fixed, finite set of pitches, retuning to an arbitrary scale is disallowed. | ||
* 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, ♯/♭ technically alter notes by zero edosteps, so they are disallowed. [[TAMNAMS #Step ratio spectrum|Equalized]] and [[TAMNAMS #Step ratio spectrum|collapsed]] 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, ♯/♭ technically alter notes by zero edosteps, so they are disallowed. [[TAMNAMS #Step ratio spectrum|Equalized]] and [[TAMNAMS #Step ratio spectrum|collapsed]] 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 == | ||
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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. | ||
However, you can paste raster images into MuseScore to use it for visual-only diamond-mos scores. | However, you can paste raster images into MuseScore to use it for visual-only diamond-mos scores. [[User:SupahstarSaga|SupahstarSaga]] has made a MuseScore score file from which you can copy diamond-mos symbols and paste them onto your own scores. The file can be downloaded [[:File:Diamond-mos palette.zip|here]]. Making scores this way is tedious but viable. | ||
If you use key signatures in your score, fiddling with the individual accidental images every time you use the key signature would be very tedious. A solution is to combine the diamond clef and the key signature accidentals into a single image and pasting that onto the score. You can make these images by editing from the PNG sheet linked above. | If you use key signatures in your score, fiddling with the individual accidental images every time you use the key signature would be very tedious. A solution is to combine the diamond clef and the key signature accidentals into a single image and pasting that onto the score. You can make these images by editing from the PNG sheet linked above. | ||
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== Scores == | == Scores == | ||
* [https://www.youtube.com/watch?v=uOsrbFEC6bQ HEHEHE I AM A SUPAHSTAR SAGA - Apartment in the Sky (10edo 3L 4s)] ([[:File:Apartment in the Sky diamond-mos.pdf|PDF]]) | * [https://www.youtube.com/watch?v=uOsrbFEC6bQ HEHEHE I AM A SUPAHSTAR SAGA - Apartment in the Sky (10edo 3L 4s)] ([[:File:Apartment in the Sky diamond-mos.pdf|PDF]]) | ||
* [https://www.youtube.com/watch?v=5r7UctUfAJ8&t=579s HEHEHE I AM A SUPAHSTAR SAGA - Moon (13edo 5L 3s)] ([https://drive.google.com/file/d/1TI8-Df_tYx2OI6bahqZtJCe8DFa44P8f PDF])<!-- | * [https://www.youtube.com/watch?v=5r7UctUfAJ8&t=579s HEHEHE I AM A SUPAHSTAR SAGA - Moon (13edo 5L 3s)] ([https://drive.google.com/file/d/1TI8-Df_tYx2OI6bahqZtJCe8DFa44P8f PDF])<!-- | ||
* [[:File:WT13C Prelude XII chip.mp3|Inthar - Well-Tempered 13edo Clavier: Prelude XII in F# (13edo 5L 3s)]] ([[:File:WT13C Prelude XII.pdf|PDF]]) | * [[:File:WT13C Prelude XII chip.mp3|Inthar - Well-Tempered 13edo Clavier: Prelude XII in F# (13edo 5L 3s)]] ([[:File:WT13C Prelude XII.pdf|PDF]]) | ||
* [[:File:WT13C Fugue XII chip.mp3|Inthar - Well-Tempered 13edo Clavier: Fugue XII in F# (13edo 5L 3s)]] ([[:File:WT13C Fugue XII.pdf|PDF]])--> | * [[:File:WT13C Fugue XII chip.mp3|Inthar - Well-Tempered 13edo Clavier: Fugue XII in F# (13edo 5L 3s)]] ([[:File:WT13C Fugue XII.pdf|PDF]])--> | ||
* [https://www.youtube.com/watch?v=mkSlVrpC7HI&t=221s HEHEHE I AM A SUPAHSTAR SAGA - Aquatic Ambience 18edo cover (18edo 5L 3s)] ([https://drive.google.com/file/d/12GwaxfIyxxCOyvYRqN4b3Ra894xL8MmC PDF]) | * [https://www.youtube.com/watch?v=mkSlVrpC7HI&t=221s HEHEHE I AM A SUPAHSTAR SAGA - Aquatic Ambience 18edo cover (18edo 5L 3s)] ([https://drive.google.com/file/d/12GwaxfIyxxCOyvYRqN4b3Ra894xL8MmC PDF]) | ||
{{Navbox notation}} | {{Navbox notation}} | ||