C# major versus Db major

[1001gear]

 

Great idea Leo. Viva la revolution! In all seriousness do you think this system would have advantages over the one currently used? Its academic of course. Here I am, a total music theory noob trying to change western music notation. The gall! I am at the beginning of a long journey and my questions are based on issues I only vaguely sense through gut instinct. I don't yet have my head completely around the equal temperament issues but I feel they are the key to many of these doors I am blundering into. Back to the major scales and the Fretboard Warrior ! This is better than Tetris.

 

 

Careful. Noobs can sustain mind corruption from too many details.

[VengefulTikiGod]

Sweet, how about Logarithmic Pitch Notation? Pitches are expressed as the binary logarithm of their fundamental frequency, with C's represented as powers of two, middle-C being 8 (256 Hz). An octave below that is 7 (128 Hz) and an octave above it is 9 (512 Hz). Duodecimal numeration allows us to easily express equally-tempered semitones as fractions of an octave... 8'0 C (2^8'0 Hz) "middle-C" 8'1 (2^8'1 Hz) 8'2 D (2^8'2 Hz) 8'3 8'4 E 8'5 F 8'6 8'7 G 8'8 8'9 A 8'X 8'E B 9'0 C 9'1 9'2 D 9'3 9'4 E ... As you can see, all notes of the same letter name would end in the same number.

 

Duodecimal notation. Hardcore. You must get all the female theoretical physicists. In all seriousness, a one-number-for-one-note system seems pretty logical, doesn't it? Though I suppose the nice thing about the current system is that you at least know every key has one of each letter in it--that system would require memorizing 12 sets of numbers. Fun.

[Leo Plumtree]

In all seriousness, a one-number-for-one-note system seems pretty logical, doesn't it?

 

Well, that's what I think.

[enuenu]

Thanks for the input. One symbol/number to represent one frequency seemed logical to me. That issue aside, I am now delving deeper into music theory and I must say the whole system really is quite ingenious. Hats off to the developers of this language/system. The circle of fifths is like an elegant mathematical equation or computer program. Then I see there are more intricacies to the whole structure awaiting me (triads, chord construction and progressions etc etc) beyond the circle of fifths. I recall Bjork once saying that people who are good at maths are often good at music. At the time I heard this I thought that her statement seemed counterintuitive. I always thought it was all about "soul", man. Of course musical inspiration and genius can come to the most musically uneducated. However just as maths can be almost be an art at times, I am finding the art/science crossover within music theory is intriguing. I think I am going to get a lot out of this. Fascinating.

[Leo Plumtree]

The circle of fifths is made possible by twelve-tone equal temperament, which ties right into the "LPN." The circle of fifths can be described as the "circle of sevenths," ascending in seven twelfths of a doubled frequency (octave) and descending in five twelfths of a double (presently known as the circle of fourths).

 

In twelfths of an octave (a "double")

 

'0 '7 '2 '9 '4 'E '6 '1 '8 '3 'X '5

 

...and from '5 back to '0.

 

 

 

 

You just tell me to shut up any time ya feel like it!

[enuenu]

No, keep going, I love it! As you have realized I am new to this, however when I heard talk of intervals being contracted to sound better and that Db & C# are not necessarily equal, my logical brain immediately said "something is amiss here". I think you are onto something, even if it may just be for our amusement. These ideas of yours at least make me realize that the inconsistencies, vagaries and theoretical problems I thought I was seeing when I started reading music theory do actually exist. Bring on the fretless guitar (oh no, please, I didn't mean that).

[Leo Plumtree]

I think you are onto something, even if it may just be for our amusement. These ideas of yours at least make me realize that the inconsistencies, vagaries and theoretical problems I thought I was seeing when I started reading music theory do actually exist.

 

Yeah, since we're combining notes into the same frequency, I figure we might as well eliminate accidentals. One frequency gets only one numeric representation. Simple.

 

 

Bring on the fretless guitar (oh no, please, I didn't mean that).

 

The endless flexibility of infinite tones to an octave would be nice. LPN can represent tones to any needed degree of precision, as well. For instance, 0'001 is twelfth of a twelfth of a twelfth of a double/octave (in decimal terms, 1/144 of a semitone and 1/1728 of an octave). These could replace decimal cents (0.01 semitone).

 

With that, you could represent any temperament or intonation to well within the threshold of what we can distinguish.

 

 

If you don't want to 'go fretless,' the next best option might be 19-tone equal temperament. The thirds are sweeter than those of 12-tone ET (a practically perfect minor third and a major third about half as far from the just ratio), but the fifths are a teeny bit flatter and it doesn't allow for symmetric scales (other than chromatic).

 

Another kewl thing about 19-tone ET is that any interval makes a circle. In 12-tone ET, the only intervals that cycle through the chromatic scale other than the minor second are the perfect fourth and fifth (which are inversions of one-another) because a fourth is 5 semitones which isn't a factor of twelve. In 19-tone ET, a progressive series of any interval cycles through the chromatic scale as 19 is prime.

 

And 19-tone ET would give you a separate C# and Db! The only ones that would be the same are E#/Fb and B#/Cb. If you still wanted to describe music diatonically (which I don't), that is.

[Jasco]

Leo,

 

I'd be interested to hear what kind of songs you write.

 

And, by the way, I've listened to some 19 tone music before, and, although the guitarist performing it was technically gifted, it sounded horribly warped out of tune to my 12 tone ears. (Almost as bad as when I play my fretless strat, LOL.)

 

Not saying that your music would sound the same, just stating my only experiences with 19 tone tunes.

 

- Jasco

[1001gear]

Yeah, since we're combining notes into the same frequency, I figure we might as well eliminate accidentals. One frequency gets only one numeric representation. Simple. The endless flexibility of infinite tones to an octave would be nice. LPN can represent tones to any needed degree of precision, as well. For instance, 0'001 is twelfth of a twelfth of a twelfth of a double/octave (in decimal terms, 1/144 of a semitone and 1/1728 of an octave). These could replace decimal cents (0.01 semitone). With that, you could represent any temperament or intonation to well within the threshold of what we can distinguish. If you don't want to 'go fretless,' the next best option might be 19-tone equal temperament. The thirds are sweeter than those of 12-tone ET (a practically perfect minor third and a major third about half as far from the just ratio), but the fifths are a teeny bit flatter and it doesn't allow for symmetric scales (other than chromatic). Another kewl thing about 19-tone ET is that any interval makes a circle. In 12-tone ET, the only intervals that cycle through the chromatic scale other than the minor second are the perfect fourth and fifth (which are inversions of one-another) because a fourth is 5 semitones which isn't a factor of twelve. In 19-tone ET, a progressive series of any interval cycles through the chromatic scale as 19 is prime. And 19-tone ET would give you a separate C# and Db! The only ones that would be the same are E#/Fb and B#/Cb. If you still wanted to describe music diatonically (which I don't), that is.

This seems very well suited to an artificial musician program.

[Leo Plumtree]

@Jasco;

 

I've never actually composed in 19-tone ET, I was just suggesting it. I have heard some music played in it, and while some of it can be "out there," I don't think it really has to be like that, as 19-tone ET provides good (better in some cases) approximations of the same intervals as does 12-tone ET.

 

12-tone ET isn't bad, though. In fact, some say it's ideal; that the slightly "impure" intervals actually have more flavor to our ears than do pure, yet "dull"(?), just intonation ratios. Cultural conditioning? Perhaps.

 

Though I'd like to experiment with 19-tone ET, I do feel a dozen tones to an octave is pretty ideal. That's why I chose duodecimal numbering for the system briefly described above.

 

 

 

This seems very well suited to an artificial musician program.

 

Yeah. If for nothing else, it could excel in that sort of application. Sure, it's doubtful it'll ever catch on in any capacity, but I can throw it out there anyway.

[1001gear]

Seriously. 19 tones might be enough res that with a little interpolation you could get a credible standard chromatic electric guitar or any other solo instrument.