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precise Precise rule(s) for calling a note sharp or flat in a given scale

Is there a precise rule (or set of rules) by which I can determine if a note should called sharp or flat?

Consider the two scales below. In the first C#/Db is C#, and in the second it's Db. By which rules would I be able to make this decision, given only a pitch class set like 0,1 1,2 2,4 4,5 5,6 6,7 7,9 9,10 10?

Scale 1783: "Youlan"

Youlan

Scale 1715: "Harmonic Minor Inverse"

harmonic minor inverseHarmonic minor inverse

precise rule(s) for calling a note sharp or flat in a given scale

Is there a precise rule (or set of rules) by which I can determine if a note should called sharp or flat?

Consider the two scales below. In the first C#/Db is C#, in the second it's Db. By which rules would I be able to make this decision, given only a pitch class set like 0,1,2,4,5,6,7,9,10?

Scale 1783: "Youlan"

Youlan

Scale 1715: "Harmonic Minor Inverse"

harmonic minor inverse

Precise rule(s) for calling a note sharp or flat in a given scale

Is there a precise rule (or set of rules) by which I can determine if a note should called sharp or flat?

Consider the two scales below. In the first C#/Db is C#, and in the second it's Db. By which rules would I be able to make this decision, given only a pitch class set like 0, 1, 2, 4, 5, 6, 7, 9, 10?

Scale 1783: "Youlan"

Youlan

Scale 1715: "Harmonic Minor Inverse"

Harmonic minor inverse

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precise rule(s) for calling a note sharp or flat in a given scale

Is there a precise rule (or set of rules) by which I can determine if a note should called sharp or flat?

Consider the two scales below. In the first C#/Db is C#, in the second it's Db. By which rules would I be able to make this decision, given only a pitch class set like 0,1,2,4,5,6,7,9,10?

Scale 1783: "Youlan"

Youlan

Scale 1715: "Harmonic Minor Inverse"

harmonic minor inverse