I'm working on quarter-tone scales, for my music. For present purposes, these would be scales that have at least one tone "in the cracks" between the piano keys, with a value ending in 50 cents. (i.e. 150, 250, 350, etc. cents.)
One approach is to modify familiar scales, by trial-and-error.
Another approach might be more formal -- to define a set of rules, and then generate all possible scales that conform to those rules.
If anyone wants to code this, or question the rules, let me know. If I don't get an answer here, I'll probably ask 69Dodge if he'll write a little Mac app that does this, or if he can generate a list of such scales some other way.
http://ift.tt/1jIlN8D
http://ift.tt/1kkr6ht
For my present purposes, it's not important that some Arabic music is probably tuned with more subtle intervals than 50-cent increments, or "quarter-tones". It's also not important to me that my rules describe the actual practice or theory of Arabic music. They reflect only my own taste.
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The rules:
1) Scales are *complete*: No other tones can be added without violating a rule. (There will be scales of as few as 6 pitches, I think. 8 or maybe 9 pitches will be the upper limit.)
2) Scales are *modular* (mod 24). (In musical terms, this is the same as saying that the scale repeats at the octave.)
3) There would be 24 possible pitches (numbered 0 to 23), but pitches 1, 23, 13, and 15 are not allowed, so there are 20 possible pitches. (This is the principle of avoiding pitches too close to the "root" and "fifth" of the scale.)
4) Pitch 0 is always the first pitch, and it is never omitted.
5) Any 3 pitches can occupy a region no smaller than 5. That is, the pitch sequences 0,2,3, or 0,2,4 or 3,4,5 or 3,5,7 etc. are not allowed. This is also a rule for the highest numbers where they combine with the lowest, because the system is modular. That is, 21 & 22 are not allowed together, nor are 20 & 22, nor is 22 & 2, because that would make the combination 21,22,0 or 22,0,2.
6) An interval of 13 or 15 (mod 24) is not allowed anywhere between any pitches. (Exclusion of "wolf" fifths, sort of.)
7) Scales must have at least 1 odd value (a "quarter-tone"). (Because of rule 6, there will probably always be at least 3 odd values.)
======================
One approach is to modify familiar scales, by trial-and-error.
Another approach might be more formal -- to define a set of rules, and then generate all possible scales that conform to those rules.
If anyone wants to code this, or question the rules, let me know. If I don't get an answer here, I'll probably ask 69Dodge if he'll write a little Mac app that does this, or if he can generate a list of such scales some other way.
http://ift.tt/1jIlN8D
http://ift.tt/1kkr6ht
For my present purposes, it's not important that some Arabic music is probably tuned with more subtle intervals than 50-cent increments, or "quarter-tones". It's also not important to me that my rules describe the actual practice or theory of Arabic music. They reflect only my own taste.
==================
The rules:
1) Scales are *complete*: No other tones can be added without violating a rule. (There will be scales of as few as 6 pitches, I think. 8 or maybe 9 pitches will be the upper limit.)
2) Scales are *modular* (mod 24). (In musical terms, this is the same as saying that the scale repeats at the octave.)
3) There would be 24 possible pitches (numbered 0 to 23), but pitches 1, 23, 13, and 15 are not allowed, so there are 20 possible pitches. (This is the principle of avoiding pitches too close to the "root" and "fifth" of the scale.)
4) Pitch 0 is always the first pitch, and it is never omitted.
5) Any 3 pitches can occupy a region no smaller than 5. That is, the pitch sequences 0,2,3, or 0,2,4 or 3,4,5 or 3,5,7 etc. are not allowed. This is also a rule for the highest numbers where they combine with the lowest, because the system is modular. That is, 21 & 22 are not allowed together, nor are 20 & 22, nor is 22 & 2, because that would make the combination 21,22,0 or 22,0,2.
6) An interval of 13 or 15 (mod 24) is not allowed anywhere between any pitches. (Exclusion of "wolf" fifths, sort of.)
7) Scales must have at least 1 odd value (a "quarter-tone"). (Because of rule 6, there will probably always be at least 3 odd values.)
======================
Quote:
SECOND BROTHER: And the Lord spake, saying, 'First shalt thou take out the Holy Pin. Then, shalt thou count to three. No more. No less. Three shalt be the number thou shalt count, and the number of the counting shall be three. Four shalt thou not count, nor either count thou two, excepting that thou then proceed to three. Five is right out. Once the number three, being the third number, be reached, then, lobbest thou thy Holy Hand Grenade of Antioch towards thy foe, who, being naughty in My sight, shall snuff it.' MAYNARD: Amen. KNIGHTS: Amen. |
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