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 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, #/b 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 "P@ = B♭" to provide a reference for which note P@ is.

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.

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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 {{nowrap|~~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 {{nowrap|&lceil;{{frac|''n''|2}} + 1$rceil;}}. 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 ==

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== 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 ==

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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]]:

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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.

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.

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* [[: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])

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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 treats the diatonic mos ([[5L&nbsp;2s]]) as special. If you are using 5L&nbsp;2s, diamond-mos looks like standard music notation. It uses standard clefs, #/b accidentals, and ABCDEFG note names. If you're using 5L&nbsp;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&nbsp;2s, its notes can be used as an unchanging reference other mosses can be compared against. For example, you might say "P@ = B♭" to provide a reference for which note P@ is.
+Diamond-mos notation treats the diatonic mos ([[5L&nbsp;2s]]) as special. If you are using 5L&nbsp;2s, diamond-mos looks like standard music notation. It uses standard clefs, ♯/♭ accidentals, and ABCDEFG note names. If you're using 5L&nbsp;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&nbsp;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.
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 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 {{nowrap|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 {{nowrap|&lceil;{{frac|''n''|2}} + 1$rceil;}}. 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 ==
@@ Line 53: / Line 53: @@
 == 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 ==
@@ Line 59: / Line 59: @@
 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&nbsp;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&nbsp;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&nbsp;3s]] in [[26edo]]:
@@ Line 70: / Line 70: @@
 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.
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 * [[:File:WT13C Fugue XII chip.mp3|Inthar - Well-Tempered 13edo Clavier: Fugue XII in F# (13edo 5L&nbsp;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&nbsp;3s)] ([https://drive.google.com/file/d/12GwaxfIyxxCOyvYRqN4b3Ra894xL8MmC PDF])
 {{Navbox notation}}