Chord notation conventions simply not theoretically correct. It is a shorthand notation what notes should be played (with some rules for omissions). It evolved over time and since jazz musicians often have a very loose connection to music theory (enharmonics are not the same note nor do they have the same function), notation evolving from that state of mind cannot be expected to be theoretically correct.
It is not only the #9 vs. b10, but as well the #5 vs. b13 (a raised fifth means no pure fifth, otherwise it would not be raised) and sometimes even the b5 vs. the #11.
Even handwritten big band bass parts in rather basic keys have wrong enharmonics notated which makes unnecessarily difficult to understand the underlying chords by following the written notes. And this was not to avoid double accidentals nor to notate a simpler readable note.
Personally I try to write theoretically correct note names because it would be easier to improvise if you know the correct place in the scale and understand the function better but often get criticized for this.
If things get complicated, I use “simplifications” in big band parts that do not have to improvise but the correct ones throughout the whole part for the improvisers. Can be a bit mixing by up in the score and for the band leader, but it is a compromise that makes sense to me (and getting a bit less complaints).
@dreamadream99 remark (2) is correct for 7-note scales.
8-note scales, the „symmetrical“ ones (that are in no mathematical sense are symmetrical but have repetitive substructures) need one basic note name doubled, but they are rather artificial constructions.
Scales with two consecutive halftone steps have them only around the root or fifth of the tonic as they are leading notes to them. So (in general) modes of these scales don’t work as leading notes to the root and fifth of the tonic.
More than two consecutive halftone steps are simply an enrichment of possibilities, in almost any case a mixture from several scales where only one scale at a time is used (but fast switching between them is possible but generates disorientation).
Key signatures evolved rather early from medieval church scales (including Ionian aka major and aeolian aka natural minor). Accidentals followed some rules then and seldom were written out, so the key signatures evolved from that.
But more modern classical composers do use non-standard key signatures to avoid a lot of repeated accidentals, just not very often and only if it makes sense over a longer part of music.
It is not only the #9 vs. b10, but as well the #5 vs. b13 (a raised fifth means no pure fifth, otherwise it would not be raised) and sometimes even the b5 vs. the #11.
Even handwritten big band bass parts in rather basic keys have wrong enharmonics notated which makes unnecessarily difficult to understand the underlying chords by following the written notes. And this was not to avoid double accidentals nor to notate a simpler readable note.
Personally I try to write theoretically correct note names because it would be easier to improvise if you know the correct place in the scale and understand the function better but often get criticized for this.
If things get complicated, I use “simplifications” in big band parts that do not have to improvise but the correct ones throughout the whole part for the improvisers. Can be a bit mixing by up in the score and for the band leader, but it is a compromise that makes sense to me (and getting a bit less complaints).
@dreamadream99 remark (2) is correct for 7-note scales.
8-note scales, the „symmetrical“ ones (that are in no mathematical sense are symmetrical but have repetitive substructures) need one basic note name doubled, but they are rather artificial constructions.
Scales with two consecutive halftone steps have them only around the root or fifth of the tonic as they are leading notes to them. So (in general) modes of these scales don’t work as leading notes to the root and fifth of the tonic.
More than two consecutive halftone steps are simply an enrichment of possibilities, in almost any case a mixture from several scales where only one scale at a time is used (but fast switching between them is possible but generates disorientation).
Key signatures evolved rather early from medieval church scales (including Ionian aka major and aeolian aka natural minor). Accidentals followed some rules then and seldom were written out, so the key signatures evolved from that.
But more modern classical composers do use non-standard key signatures to avoid a lot of repeated accidentals, just not very often and only if it makes sense over a longer part of music.
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