11–20 of 65 posts
I never realized until now that in the the two different circles pictured (the Chromatic Circle and the Circle of Fifths) the pairs of notes opposite each other are the same in each circle. For example in both circles B is opposite from F. And if you move around the Chromatic Circle, swapping every second pair of notes with its opposite on the other side of the circle, you have the Circle of Fifths.
The diagrams look nice, but in the end of the day, they are merely nice visualizations of what's fundamentally algebra. There is not much geometry going on besides a quite simple group structure of order 12.
Besides geometry there is not a lot of music either, in the sense that even this simple symmetry is kinda fake, effectively a forced resolution of an essentially unsolvable "problem": hammering the intervals into place to inject some "logic" into the task of dividing the octave in heptatonic scales. Despite the unrepentant Pythogereans across all ages, our musical brain is not mathematical except in a very loose way.…
that's not task. The octave has already been divided into twelve tones here.
The task is to pick sets of those twelve tones to serve some aesthetic purpose. The sets may be of various sizes, though 7 is common in a lot of european music.
If the task was to generate heptatonic scales from within the octave, there are a huge number of possibilities not described here, and most of them are rarely used (though many more than the ones based on a 12TET system are).
The diagrams look nice, but in the end of the day, they are merely nice visualizations of what's fundamentally algebra. There is not much geometry going on besides a quite simple group structure of order 12.
The diagrams look nice, but in the end of the day, they are merely nice visualizations of what's fundamentally algebra. There is not much geometry going on besides a quite simple group structure of order 12.
I love this. Here's another interesting thing I encountered. It's a way of organizing chromatic subsets by brightness https://www.reddit.com/r/musictheory/comments/1etydas/i_made...
That is cool and different. Glancing at the bottom several rows I tend to agree with the classification, as a trained musician. I wonder though, what is (the mathematical principle) behind it that is causing the brightness/ darkness in the sound of these chords? Don't say "dissonance" (or explain what dissonance is)- that much is obvious, looking for something a bit more detailed, e.g. why 1-2-5 sounds brighter than…
I love this. Here's another interesting thing I encountered. It's a way of organizing chromatic subsets by brightness https://www.reddit.com/r/musictheory/comments/1etydas/i_made...
That is cool and different. Glancing at the bottom several rows I tend to agree with the classification, as a trained musician. I wonder though, what is (the mathematical principle) behind it that is causing the brightness/ darkness in the sound of these chords? Don't say "dissonance" (or explain what dissonance is)- that much is obvious, looking for something a bit more detailed, e.g. why 1-2-5 sounds brighter than…
Earlier quoted context omitted.
That is cool and different. Glancing at the bottom several rows I tend to agree with the classification, as a trained musician. I wonder though, what is (the mathematical principle) behind it that is causing the brightness/ darkness in the sound of these chords? Don't say "dissonance" (or explain what dissonance is)- that much is obvious, looking for something a bit more detailed, e.g. why 1-2-5 sounds brighter than…
It is going to be the relative amplitudes of the overtones. Pure tone (like flute) is bright, many overtones present with the appropriate mix can sound dark (french horn). Next, you are going to ask me for the coefficients, but I don’t know that. Break into the nearest church with a proper pipe organ and start pulling and pushing stops to see what happens. (Or ask your friend the organist to take you so that you don’…
I never realized until now that in the the two different circles pictured (the Chromatic Circle and the Circle of Fifths) the pairs of notes opposite each other are the same in each circle. For example in both circles B is opposite from F. And if you move around the Chromatic Circle, swapping every second pair of notes with its opposite on the other side of the circle, you have the Circle of Fifths.
Although there have been some claims in these comments to the contrary, harmony is particularly mathematical. Symmetry and the breaking of within the integers mod 12 form the foundational principles of harmony.
Earlier quoted context omitted.
Besides geometry there is not a lot of music either, in the sense that even this simple symmetry is kinda fake, effectively a forced resolution of an essentially unsolvable "problem": hammering the intervals into place to inject some "logic" into the task of dividing the octave in heptatonic scales. Despite the unrepentant Pythogereans across all ages, our musical brain is not mathematical except in a very loose way.…
> the task of dividing the octave in heptatonic scales. that's not task. The octave has already been divided into twelve tones here. The task is to pick sets of those twelve tones to serve some aesthetic purpose. The sets may be of various sizes, though 7 is common in a lot of european music. If the task was to generate heptatonic scales from within the octave, there are a huge number of possibilities not described h…
Aesthetic in the musical or visual sense? The visual aspect is based on the Z12 symmetry and it is pleasant - like all symmetries.
The question is what does the visual experience have to do with the music experience?
The first disconnect with the musical experience is that the 12TET itself is not what people would, e.g., choose to sing in [1].
The second disconnect is that the Greek modes of the major scale are not remotely covering all the scales people enjoy, even adopting a Eurocentric point [2].
[1] https://music.stackexchange.com/questions/41383/do-capable-h...