2005-03-01 [Simuir]: I hope it's OK for me to burst in like this. If not, please flame me and I'll go hide under a rock. Now that that's out of the way, let me take it from the beginning and provide you with a few definitions: In music, you generally combine "notes" sequentially (and quite often simultaneously, this is what makes a "chord") to create songs. Each "note" has a specific base frequency; all instances of that note share this approximate base frequency (overtones are not relevant to this definition, but they *are* relevant to music production). A "scale" is the full set of notes that are utilized to produce some part of a song. "Pitch" corresponds vaguely to frequency (higher pitch, higher frequency).

2005-03-01 [Simuir]: Most scales are arranged from lowest pitch to highest pitch. Now, let's give each note an index; for, say, five neighbouring notes you could give them the indices 1, 2, 3, 4 and 5. A scale normally extends infinitely both ways, so you're bound to get negative indices at the lower pitches. Let's arrange this in a graphical curve, with the index as the horizontal axis and the frequency as the vertical axis. For the "traditional" full scale which is used in pretty much every music production system and most modern instruments the curve is an approximate exponential one, where for each 12 notes the frequency has doubled. Thus, to calculate the frequency of any note, you can use a formula:

2005-03-01 [Simuir]: Lets put origo at the middle A (that's a note), so it has the index 0. It also has the precise frequency 440.0Hz (by definition). The formula is then 2^(index/12)*440.0Hz

2005-03-01 [Simuir]: The standard notation for the notes in a full octave (12 notes) is: A, A# (or Bb), B, C, C# (or Db), D, D# (or Eb), E, F, F# (or Gb), G, G# (or Ab). The letters stem from a simpler scale that has eight notes per octave (thus "octave") but was later completed with the addition of sharp notes (#) and flat notes (b) which are the notes in between. I hope I'm not being too longwinded by the way... there's more to come.

2005-03-01 [Simuir]: Two notes sound "well" together when their waveforms overlap nicely. When the waveforms create a chaotic pattern, it tends to sound horrible. For example, if I play the notes C (index 3) and G (index 10) together, the frequencies I play will be 2^(3/12)*440.0Hz = approx. 523.25Hz and 2^(10/12)*440.0Hz = approx. 784Hz. Imagine two sine curves at these frequencies, where time is on the horizontal axis. Because 784Hz / 523.25Hz is approx. 1.5, they will almost be in synch. Subsequentially, they blend together in a way that "fills" the sound rather than "breaks" it. Harmonics seem to depend a lot on this principle. If we move the G somewhat to 523.25Hz*1.5 = 784.875Hz, they blend even better.

2005-03-01 [Simuir]: If I were to play, say, A and A# together, I would get the frequencies 440.0Hz (obviously) and 2^(1/12)*440.Hz. These waveforms do not stay in synch for very long, and this brings a disturbing sound. The shower scene in the movie "psycho" is a fine example of this type of combination. Another "terrible" sounding interval is at exactly half an octave, that's 6 "halfnotes" apart (they are called halfnotes because of the old letter-based scale). I recall vaguely from one of my music or history lessons that one of these was at some time named the "devil's interval", and that you could get severely punished for playing it.

2005-03-01 [Simuir]: Interestingly enough, music tends to get boring unless you "break" the harmony a bit by adding inharmonious intervals. Both the 1-halfnote and 6-halfnote intervals are used quite a lot in modern music.. A good example is the chord D7, where the notes D, F#, A and C are involved. Consider the relations between all notes here; the relation between C and F# is a 6-halfnote interval. Now, the real question is, does phi have anything to do with this? The thought never occurred to me before I saw this discussion.

2005-03-01 [Simuir]: There is a lot more to the subject, but I think this is enough for the time being, or I'll be flooding the chat.. :D

2005-03-01 [Amtharnis]: We are getting closer to the answer. Are you familiar with the fibonacci series, Simuir? I am just thinking with your knowledge of musical theory, if you look at the fibonacci series, you might be able to relate it to the sound frequencies that make up the notes in the scales. I read somewhere that Chord construction follows the fibonacci rule, so I suspect it would repeatedly show up in music in other ways.

2005-03-01 [Simuir]: I already knew about the Golden Section, but I was taught at a photo class that it was exactly 2/3. :D Anyway, I read the page at the link you posted, so now I know what the true meaning of phi is, and now I know a little about the fibonacci series. I still don't see how harmonious frequencies and phi might relate, but there is another dimension to music, and that is rhythm, which is based on time. Rhythm tends to sound more lively when it "swings", and I think phi may very easily be applied there. The question is whether or not it sounds better... I'll try it out.

2005-03-02 [Simuir]: Maybe I should've put all that stuff in a wiki rather than in this chat? .. oh well, done is done, isn't it? :D

2005-03-17 [(eeob)]: Say, have you ever read, "The Ancient Secret Of The Flower Of Life"? And hello.

2005-03-17 [wwwwwwwww]: No, I haven't. Why?

2005-03-17 [wwwwwwwww]: " still don't see how harmonious frequencies and phi might relate, but there is another dimension to music, and that is rhythm, which is based on time. Rhythm tends to sound more lively when it "swings", and I think phi may very easily be applied there. The question is whether or not it sounds better... I'll try it out. " That's possible, but I think rhythm is just a component of music, like notes are. Alone, it is nothing special.. there is a complex relationship between rhythm and notes that creates music (beautiful or otherwise)

2005-03-17 [wwwwwwwww]: Perhaps it is this relationship which is in truth "music"

2005-03-18 [Simuir]: Not all rhythm requires actual *notes* and it can still be quite interesting as a piece of music, samba rhythms are a good example of this :D ..but in most cases I'd agree with you.

2005-03-18 [Simuir]: I still haven't tried applying phi as a swing ratio, because none of my music software supports it. I've been intending for a while to write a proglet that generates a .wav file with an arbitrary swing ratio, just to try it out. Haven't gotten around to it yet though.

2005-05-04 [Lost in Illusions]: ~wanders into the wiki and looks around, waving shyly~ Hello... I was invited here, I think, based on the merit provided by my nonconformity rant and the essay contained on my house. Anyway, Id just like to say that I love philosophy and will talk about pretty much any issue or ideal and welcome all comments my way.

2005-05-11 [x0x0x0x0x0]: just head on to the questions and answers page and either take up an argument or start your own

2005-05-11 [Lost in Illusions]: hmmmm... that I can do... It may take a few days... Im still recovering from my Philosophy class.

2006-11-08 [Dil*]: wow...that convo up there sounds pretty intense.