Some frequency measurements of African scales http://www.anaphoria.com/SndofAfra.PDF and a discussion http://forum.emusictheory.com/read.php?5,7858,7909
Music can exist in a variety of forms. Take a look at the African frequencies I posted. What someone has grown up with might shape what they prefer. Theories about consonance, dissonance or whatever, should encompass all music known to man and not just cherry picked examples. Mathematical patterns exist in music but they are not the only determining factor of what music contains as it's basically been selected by the human ear/brain and not through Mathematical ratios or whatever. How does a Dolphin select the Sonar frequencies it uses? http://seaworld.org/en/animal-info/...nose-dolphins/communication-and-echolocation/ Not by knowing ratio patterns or any mathematics. DNA explains a fair bit of it.
The book is full of mathematics, hence my post above about mathematics. Look at his lattice (a graphlike configuration where each axis is devoted to tones generated by a specific prime number; a two-dimensional lattice) These lattices are all very good and so on, but they are really just another way to look at things in a rather mathematical way. Mathematics can't result in great musical outcomes on it's own, otherwise mathematicians would have been some of the greatest composers and I think Beethoven had trouble adding up his shopping bill. Writing a book and wrapping things up in nice formulas and all that is great for a book but does it cover the African note frequencies or Irving Berlin who knew no real theory but could write a better tune than the author. I'd tend to treat all theory and theories of theory with a grain of salt. Theory is useful up to a point. If mathematics is going to be a big factor driving composition, then the results will tend to be ... http://www.garygarrett.me/?p=204 Excerpts from Harmonic Experience by W.A.Mathieu Copyright © 1997 by W.A. Mathieu. All Rights Reserved. Definitions to highlighted words can be found in theses short glossary excerpts. (Excerpts from the glossary) comma: any very small interval between two tones near in pitch but disparate in harmonic generation. equal temperament: a system of tuning wherein the octave is divided into intervals of exactly equal size; twelve-tone equal temperament is the standard system of the Western world. harmony: refers primarily, in this book, to events that can be quantified by ratio, as opposed to events that can be measured by interval. interval: a quantifier of the melodic distance between two tones, usually without specification as to their harmonic interaction, as distinct from ratio (q.v.). just intonation: in some texts, the five-limit system of tuning; in this book, any system of tuning using low primes. lattice: a graphlike configuration where each axis is devoted to tones generated by a specific prime number; a two-dimensional lattice (i.e., on a page) is confined to a tuning system using two primes. A lattice of tones combines the graph principle with staff notation by skewing the direction of both axes. A lattice of twelve notes refers to the twelve most simply derived ratios; an extended lattice includes indefinitely more notes; a chord lattice abandons the staff notation and shows the major and minor triads by chord symbols only; in a key lattice, the symbols stand for keys. major: large; most narrowly, an adjective modifying a number, as in major sixth. meend: in Indian music, the sliding from resonance to resonance; the shaping of tones. melody: refers in this book to the up-and-down aspect of music, that which is quantifiable by intervallic measurement; as distinct from harmony (q.v.). modality: the quality of music within a mode. Most simply, the term refers to music that establishes clear choices of tones that relate to an unchanging music. pentamerous: harmony generated by the prime number five, that is, harmony characterized by the presence of 5:4 major thirds and their compounds and reciprocals. perfect: the quality assigned to 1:1 primes, 3:2 fifths, 4:3 fourths, and all octave expansions of these intervals. Pythagorean: generally, having to do with the thought (or supposed thought) of Pythagoras. In this book, Pythagorean refers to a three-limit system, that is, a system confined to 2:1 octaves and 3:2 fifths, and their compounds and reciprocals. resonance: the conventional definition is the reinforcement of tones by synchronous or near-related vibration; as used in this book, the term refers to sensible (that is, singable) combinations of tones related by low-prime ratios. sargam: in Indian music, the names of the degrees of the scale, specifically, sa, re, ga, ma, pa, dha, and ni, abbreviated s, r, g, m, p, d, and n. tonal harmony: generally refers to modulating harmony with identifiable tonics. A more narrow definition refers to the dominant-seventh-driven harmony of the common practice period.
You sir have ramblin' on the mind. And your example of what music would sound like was actually very nice. But that is just one persons slant on how it can be used. There are many. My whole reason for getting Harmonic Experience was so I could define much of what Steve Kimock was talking about, and he practices what he talks about. It's his sort of playing that compels me to move forward with HE definitions. Listen to Kimocks masterful use of these HE ideas. But as Steve has already said HE is not written around guitar, this is where Steve did his homework, bringing the ideas to an actual guitar and not just one string. Kudos to Steve for the brilliant work he has done, and then sharing some of it with us. Kimock and friends, Love For Japan - amazing intonation skills http://www.youtube.com/watch?v=xF-wKpwrc0s
dude? if i may, even though i'm truly no expert nor an authority, here: words & pure-math are not necessarily music, theory is not necessarily practise. mathieu's presentation of encouraging experience is not a call for you to subscribe to some kind of "religion", it's an offer which seems to encourage your own further experience of intonation, itself: experience cannot hurt you, if you have any discrimination-to-apply, whatsoever: there is nothing to defend against; nothing is really embedded within the offered experience that needs be reacted-to, all of the more purely social, a-social and/or anti-social judgments notwithstanding. it might be seen that, functionally, there is no inherent "kool-aid", here, unless & until we try to force that 'emotional' construct upon it; just, the experience of pitch relationships, which's absolutely fundamental to well-integrated music-making: a fact, there, i think; like it, or not. for a small slice of my own musical context...... [SOUNDCLOUD]https://soundcloud.com/jayapala/shumri-1[/SOUNDCLOUD] [SOUNDCLOUD]https://soundcloud.com/jayapala/helluva-ride_dt[/SOUNDCLOUD] [SOUNDCLOUD]https://soundcloud.com/jayapala/he-knew[/SOUNDCLOUD] [SOUNDCLOUD]https://soundcloud.com/jayapala/smashville-tenacity-dt[/SOUNDCLOUD] [SOUNDCLOUD]https://soundcloud.com/jayapala/unwry-respect-for-mssr-rc[/SOUNDCLOUD] [SOUNDCLOUD]https://soundcloud.com/jayapala/unravelled[/SOUNDCLOUD] [SOUNDCLOUD]https://soundcloud.com/jayapala/when-so-much-what[/SOUNDCLOUD]
Nailed it. I don't get why this book inspires the kind of reactions that it does. I got it from the library and found it to be pretty innocuous.
Right, so at some point in human evolution you would expect the entire planet to simultaneously develop musical systems that reflected low prime ratios, which would mean EVERYBODY would use octave equivalence and fifths up and down, or tonic, octave, fourth and fifth in their scales? Everybody does. Cherry pick your way around that. For some reason, and I really can't figure out where the disconnect is, folks like you continue to confuse "the overtone series" as we know it today, with the existence of overtones. The EXISTENCE of overtones drove that species wide parallel development, and it took 70,000 years to do it. The scientific, acoustical, mathematical, knowledge of what we currently refer to as the overtone series is just some icing on the cake in the last couple hundred years. Today we have a scientific explanation, because, today. . We figured it out. Previously we just had observation of the natural world with no explanation. Don't like the explanation? Well, you're stuck with "Aliens". .
Equal size in which space exactly? You could divide the interval like this fn{fb,fa} = (fb-fa)n/12 +fa,(n=0..11) And that's a way to divide the interval fb-fa into 12 equal parts of the exact same size. For the octave it would be fb=2fa. But that's not the 12ET tuning !(cents, hello?) I know the answer but it seems that most people is not aware of what the "equal" part is really all about. That's oxymoron and narrow. That also hints to a false dichotomy . According to that definition , there is harmony only for JI tunings LOL. Oxymoronic because A(c/b)=B which is the ratio . But A(c/b)-A = B-A which is the interval. The ratio in that interval is B/A=c/b . So, why the distinction ? A more useful definition of harmony would be the study of relationships between pitches with more focus in the frequency domain rather than the time domain (melody). Distances and ratio exists and coexists in both domains. Both domains exists and coexists . And that's it. Different cultures have different notions of what a pleasant harmony should be , but that's another issue not covered by that definition made up by the author. Sigh... Primes as prime numbers? like 1,2,3,5,7,9,11,13,17,19,23,29.... Why not? Well, in pythagorean tuning for instance, the minor third is the ratio 32/27, where nor the divisor nor the numerator are prime numbers . Maybe he is talking about some generator... You missed his point entirely.He is talking about a more general theory that shouldn't dismiss music made by some cultures . Not that all cultures should adapt to the "JI theory" of the author, where "ratios" is supposed to be some sort of elementary particle of music . Maybe that is a simple elementary school approach, but not the fundamental nature I want to hear dolphins playing the violin LOL. Mathematics can also be used to study the patterns of indeterministic systems . Music exhibits stochastic patterns . Mathematicians also found fractal patterns in a lot of compositions . Analogy: you can find some patterns in the weather , but you can't use that to decide how the weather should be , all you can do is some forecast using the most powerful computers in the world. But even then, "forecast" is different than "should" in a complex 'system' like music . Nowadays computers can trash out the greatest chess players of the world with easy, or you can even use some fractal algorithms to generate some interesting music . But those are just models and tools for something that already exists, like mimicking . Is not something that was predicted. You can't predict it! That's the real "elementary particle" of music, the unexpected result from the creativity of the musician based on what he or she already knows by the culture . So justifying a thesis of what music should be, the rules and why on the basis of simple ratios is laughable . But a different mathematical approach to study music is not inherently bad. In fact , math is so good that the standard and modern (western?) Music Theory is based on math . Math is just a great tool to study something (at least for non-mathematicians , the point of view of some mathematicians is something else )
Jeez, here we go with the troll "get the guy to repeat himself and then bail out" routine again. In the most general possible sense, if all the world's music were somehow "adapting itself" to the existence of overtones, and by extension, to low ratios, then the entire species at some point would have adopted 2:1, or octave equivalence. So, did we? Yeah, duh, everybody did. So 2:1's in. Let's just start there. Discredit or disprove octave equivalence and you're well on the way to making your point.
Went out of town to snowboard for a few days and clear my head a bit. Worked out well! I fear there is a bit of trolling going on in this thread, but seems like it's being handled. I'm going to spend the next day or so reading through the article Kimock posted. So far, pretty good stuff IMO. Also, thanks for the posts Splatt! Always an enjoyable read when you post, so for that, I thank you! I just spent the last hour with my guitar and a looper. I just got a drone going on A and added a few harmonics for the 2nd, 3rd, 4th and 5th partials. I noodled with it for a bit trying to hear and feel the natural octaves, thirds and fifths. Once I had it in my ears I started to add some fretted stuff to see what I could do with it. I was able to play all of these notes (octaves, unisons, thirds and fifths) fretted to some degree without beating but I found almost every fifth and third that I grabbed (without manipulation of some sort) was initially beating against the drone. I was able to manipulate them to a steady pitch that would eventually fade into the drone. I found it best to raise a fretted fifth just slightly. Which seems right because an ET P5 is about 2 cents flat, yes? But, should I be able to hear 2 cents?? Either way, the fifths sound better to my ears (in this context) when bent up the slightest bit. The thirds were a bit more tricky. The only way I could get them not to beat was to come from a fret below and bend up, which was an inconsistent situation, but once I found the pitch, it was all good. With a slide, I was able to get pretty close cold. After a bit I added the 3rd partial of E with a harmonic on the 7th fret of the low E string to see how that worked over all of this. Overall, pretty neat sound and it felt to me like it belonged there. I found in this case though that the M2/9 was well sharp (fretted) of the harmonic. The beating over the drone with that harmonic and the fretted B (4th fret G string) was actually a very cool effect! As with the thirds I was able to match this pitch by bending up from a fret below. I'm not sure how this is all helping me at the moment, with the exception of the fact that playing over that drone was rather meditative. I do kind of feel like my ear is getting better because of it and with that, I am starting to be able to hear how I want to manipulate some of these notes. Thanks for all of the encouragement and help!!
Yes, two times one equals two. I can't disprove that. You have a very strong case. That makes it a rule, not just a pattern.
I understand these topics aren't for everyone. Post #3 of the thread, and you asked a question. Post #4 it was answered. You have now repeatedly stated your opinions. I ask that you now let them either stand on their own merit, or start another thread of your own. Please leave this one to the people who want to discuss working through this particular book. I see no productivity from repeating your arguments as to the merits of the theories and concepts presented in HE. This thread is not about proving any type of validity. It was stated in the OP that this thread is to discuss working through the book. If you feel it is your duty to "warn" people of the folly of working through HE, then great. You have done so. People reading what you've already posted will read your thoughts and decide for themselves whether to heed your words, or not. That part is beyond your or my control. So, please stop contributing to this thread. Doing something productive will benefit us all much more. No disrespect meant here. Just trying to maintain ONE thread on this forum that doesn't become either derailed or bogged down with useless distractions. Cheers to everyone for sharing their thoughts and experiences. PLEASE focus on the OP. That's all I'm saying.
Ok, I asked about the 9:8 and 10:9 M2 earlier. I assume that the answer to my question lies somewhere in here (from the article): "For example, if 9:8 or 10:9 represented the second scale degree of a scale being tested (these two intervals are within 22 cents of each other), the algorithm would use 9:8 rather than 10:9 to form an interval with a perfect fifth (3:2) because this choice produces the interval (4:3 versus 27:20) with the higher percentage similarity. Conversely, the algorithm would use 10:9 rather than 9:8 to form an interval with a major sixth (5:3) because this choice produces the interval (3:2 versus 40:27) with the higher percentage similarity." @Kimock, can you help me get my head around that? I'm just not sure where the P5 and M6 come into play according to this example. Thanks!
"Thus both the five-note and seven-note scales preferred in much music worldwide comprise intervals that conform optimally to a harmonic series." I feel like this statement justifies my curiosity in reading through this book!
Last thing before I head out for work tonight. I just reread the section (still in the beginning) about the M3. He says to tune your low E down to C and get the M3 from the harmonic. Easy enough. With my looper I got these sounds playing a drone. I added the octave and P5 harmonic as well and then tried to find M3 and P5 around the neck. What I found was really quite beautiful. When I hit these notes right, they disappear. It's one sound, but it's just huge. It almost didn't matter what volume I played them at, as long as I nailed the pitch. Getting TO that pitch was an adventure, but that sound just rings when you get it. That's what I was looking for. Now I can move on! Haha, I know, this is all probably quite simple and means very little to some of you, but being able to make that sound is really exciting for me. That's the part of music that I'm trying to connect with. Now I just have to be able to find these sounds on the fly! I'm sure that'll be easy!! Sorry for the rambling today. Pretty insightful stuff coming at me though so I figured I'd share, and for those of us who are still crawling through this text, if you haven't done this little exercise yet, I suggest you check it out.