We can be okay with that, or we can not be okay with it, but we can't deny that it's the case. Anyone actually notating music has to know whether a 3rd of some color is an alteration of a major 3rd or a minor 3rd. If some default intervals for the colors are based on a minor Pythagorean interval, while others are based on a major one, we're implicitly retaining the major/minor dichotomy even if we omit it from the names for those intervals. Trying to convince trained musicians to stop calling C-Eb or bIII "minor" is a non-starter.īut if we want to divorce higher-limit intervals from that dichotomy, it's hard to do that while keeping the Pythagorean backbone intact. Never ever, because they will always at minimum exist among the Pythagorean intervals. I mean, as long as we have a Pythagorean backbone, rather than a 7edo one, we're never getting away from major and minor. Presumably if all the color intervals are various commatic alterations of the default (major or perfect) Pythagorean intervals, the answers to your questions would be:ġ1/9 from C would be an E lowered by 729/704 (the difference between 81/64 and 11/9)Ħ/5 from D would be an F#, because it's an 81/64 lowered by 135/128ġ1/9 from D would be an F# lowered by 729/704 I'm not proposing anything, just pointing out what I see as being entailed by various principles and various choices that could be made. That would make a gEb from C an 81/64 that is lowered by 135/128 AND the apotome, for example. We could do that, and instead of referring to major and minor intervals in Pythagorean, do what we do with Roman numerals - add b and sharp to denote alterations of the naturals (or the notes of whatever key signature we're in). The only way we can really use colors to replace major/minor consistently is if we do what I said?always lower by a comma, always from the same default wa set. Sure, the language works as a shorthand that makes major and minor seem unnecessary, but it doesn't jive with the notation. We still have major and minor implied in the Pythagorean notation, we're just using Large and small instead. If we're notating a gu 3rd from C as gEb, but a yo 3rd from C as yE, we haven't escaped treating the gu 3rd as "minor" and the yo 3rd as "major", we're just obscuring that fact. This question triggered a whole thought process for me that I was writing out but ultimately deleted, because it really made something snap into place for me, which I will now struggle to articulate.īasically, if we are really, truly, trying to use colors to fully replace major and minor, then we should be notating all of the default intervals of every color as modifications *of the same natural nominals*.
That has the same effect as raising by 81/80 and then lowering by an apotome, though.ĭoes it help matters at all if, instead of treating the cancelling color-pairs as "raising and lowering by the same comma", we treat them as "always lowering by a comma, but by different commas that, when combined, cancel to lowering by an apotome"? That would lead to 6/5 being notated as C-gE.hmm. Or, it IS a modification of Ionian, but with the modified degrees being lowered by a different comma.
Thinking about this a little bit further, I think this has somewhat to do with the fact that, for example, the green/gu scale isn't a modification of the Ionian scale, it's a modification of the Aeolian. Unfortunately, if every interval in the white Ionian is raised or lowered by the comma of any other color to generate the default set of that color, we end up leaving out some tonality-diamond intervals, and including some intervals that are excessively complex.
SAMPLETANK 3 B3 VS FULL
I think the bigger issue is, we want the default sets for the colors of at least the 7-limit to encompass all the intervals of the 7-odd-limit tonality diamond, but we also want the color accidentals to unambiguously mean raising or lowering of a Pythagorean interval by the color's comma-AND, in order to retain full backwards compatibility for relative chord/interval notation, it's desirable to retain the Ionian-based default interval set for Pythagorean/white. Since # and b unambiguously mean "raise by an apotome" and "lower by an apotome", regardless of what color/prime limit we're dealing with, they don't have the issues associated with major and minor. One benefit to Ionian-centered notation is that a # *always* means augmented, and b *always* means minor (when minor is applicable, and diminished when it is not).
But the problem currently is that with the Dorian-centric notation, L and s serve a semi-useful function of signaling that things are different, whereas if we use # and b to replace L and s, everyone has to re-learn that III=m3, VII=m7, #III=M3, #VII=M7.
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