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Natural Science Forum / Physics / Acoustics / October 2005music - 8 keys in an octave
Anyone on this newsgroup know theoretically why there are 8 keys in an octave in music? Is it a part of natural harmonic vibration that on the 8th key you have the same natural frequency but at a different wavelength or something like that? Essentially, why are there 8 keys in an octave and not, let's say 10 or 6. Do Re Mi Fa So La Ti Do Brian > Anyone on this newsgroup know theoretically why there are 8 keys in an > octave in music? Is it a part of natural harmonic vibration that on the 8th > key you have the same natural frequency but at a different wavelength or > something like that? Essentially, why are there 8 keys in an octave and > not, let's say 10 or 6. > Do Re Mi Fa So La Ti Do There was a very interesting post on this subject in comp.dsp a little while ago, but I'm afraid that I can't remember any details about the subject or the poster, for searching. My vague memory of the answer was something like this: What humans like to hear is sets of harmonics of a fundamental. Even tempered fundamental spacing doesn't give you that (other than at the octaves), BUT it happens that for sets of twelve geometrically spaced tones you can get sufficiently close to some pleasing ratios. (An octave is twelve semitones, not eight anything in particulars.) Apparently this also happens for a scale of (?15?, ?17?) tones, which is what is used in some "Eastern" music scales. Apparently it doesn't happen for any other reasonalbly small number of geometric steps: the geometric frequency and the harmonic interval frequencies differ by an amount unpleasant to the ear. Post might have been by Robert Bristow-Johnstone, perhaps? Worth chasing down. Cheers,  SignatureAndrew > Anyone on this newsgroup know theoretically why there are 8 keys in an > octave in music? Is it a part of natural harmonic vibration that on the [quoted text clipped - 5 lines] > > Brian I think you;re confusing keys with notes. A note is a specific frequency, a key is what a series of notes or chords belong to. There are twelve notes in an octave (you have to count the sharps and flats), and that is just one of many, many scales used in music around the world. Each octave is twice the frequency of the one below it. American music is usually based on the note middle "A" = 440 Hz, though that isn't always true. Therefore, in that particular tuning, the "A" notes in the audible spectrum would be: 27.5 Hz, 55 Hz, 110 Hz, 220 Hz, 440 Hz, 880 Hz, 1760 Hz, 3520 Hz, 7040 Hz, and 14080 Hz, the next "A", 28160 Hz, would be beyond audibility. There are many good articles in the Web, I suggest that you do a Google search for "musical notes", "music keys", and "music theory" for starters. >always true. Therefore, in that particular tuning, the "A" notes in the >audible spectrum would be: 27.5 Hz, 55 Hz, 110 Hz, 220 Hz, 440 Hz, 880 Hz, >1760 Hz, 3520 Hz, 7040 Hz, and 14080 Hz, the next "A", 28160 Hz, would be Not really. All our western instruments are "stretched" to such an amount, that singers have difficulties with octaves when trained on their home piano. For a deeper insight into music google for "just intonation". w. >>always true. Therefore, in that particular tuning, the "A" notes in the >>audible spectrum would be: 27.5 Hz, 55 Hz, 110 Hz, 220 Hz, 440 Hz, 880 Hz, [quoted text clipped - 9 lines] > > w. Wrong example, The octave is the only "just" interval on our "tempered" keybords. Western instrument is also wrong. Violonist play "just" when accompained with untempered instruments (most of strings exept guitars...) But will tend to temper when playing with tempered instrument like piano. >>>always true. Therefore, in that particular tuning, the "A" notes in the >>>audible spectrum would be: 27.5 Hz, 55 Hz, 110 Hz, 220 Hz, 440 Hz, 880 Hz, [quoted text clipped - 17 lines] >But will tend to temper when playing with tempered instrument >like piano. I said in the above posting, that is wrong, can't you read? Go to your piano and measure the octaves and do not spread your ignorance here. Pianos are stretched, harpsichords often are stretched today, historically not, church organs sometimes, depending on the tuner, historically they were not stretched. w. Ich schreibe korrektes TV Deutsch, so wie DIE auf Astra reden: Das Wetta von morchen: diesich, mäßich wolkich. >>>always true. Therefore, in that particular tuning, the "A" notes in the >>>audible spectrum would be: 27.5 Hz, 55 Hz, 110 Hz, 220 Hz, 440 Hz, 880 Hz, [quoted text clipped - 17 lines] >But will tend to temper when playing with tempered instrument >like piano. I said in the above posting, that is wrong, can't you read? Go to your piano and measure the octaves and do not spread your ignorance here. Pianos are ALWAYS stretched, harpsichords often are stretched today, historically not, church organs normally not because pipes have a different harmonics spectrum than strings, historically they were not stretched. w. Ich schreibe korrektes TV Deutsch, so wie DIE auf Astra reden: Das Wetta von morchen: diesich, mäßich wolkich. > Pianos are ALWAYS stretched, According to a paper in Scientific American (1980's something) they have to be in order to be perceived as properly tuned. There are also technically fascinating requirements for the tuning of each string of a note in order to obtain a proper, pure, sustain. Very worthwhile reading. Kind regards Peter Larsen Signature******************************************* * My site is at: http://www.muyiovatki.dk * ******************************************* >>>>always true. Therefore, in that particular tuning, the "A" notes in the >>>>audible spectrum would be: 27.5 Hz, 55 Hz, 110 Hz, 220 Hz, 440 Hz, 880 Hz, [quoted text clipped - 21 lines] > > Go to your piano and measure the octaves Done, Experimental device: Yamaha Clavinova CLP-950 Digital Piano Sound Card Sound Blaster Live Softare Raven 1.2 Demo. Each of the 8 A of the keybord is pressed strongly and maintainded pressed about 5 sec. The sample rate is 44100 Hz and the sample sized is increased to 12686 in orther to get a 3dB filter bandwidth of 5 Hz. The spectrum is computed on a sample avoiding the very beginning of the recording that widens the pics. A zoom is done on the first pic in the spectrum and the Cursor is placed on the pic. The frequency is shown in the GUI (unfortunately with integer). The frequencies mesured that way are: 28(27.5) 55 110 220 440 882(880) 1772(1760) 3589(3520) where (freq) are the theoretical value if not those observed. Though the twoo last are significantly corrupted, the last one also sounds wrong and is rather a defect in the piano, 4 of them are perfectly de double of the previous one and the first measure is compatible with expected value since no digit are available for representing 0.5 Hz. On this first spectrum, the 2nd and 3rd harmonics are 55 and 82(82.5). > and do not spread your ignorance here. > Pianos are ALWAYS stretched, harpsichords often are stretched today, > historically not, church organs normally not because pipes have a > different harmonics spectrum than strings, > historically they were not stretched. I probably misunderstood the term streched. What I just meaned is that octaves have a frequenty ratio of 2 confirmed by experiment. A tempered instrument is an instrument on which all half tones have the same frequency ratio, 2exp(1/12) for the 12 half tones leading to the correct factor 2 at 1 octave, whereas, for the quint?(C-G) for example , the frequency ratio should be 3/2 (1.5) and is 2exp(7/12)=1.498. If you want to have an exact keybord, it is only available in one tonality and modulation requires mechanical intervention. If organs are "stretched" and not violons, it is because it is more easy to modify slightly the finger positions than change the length of the pipes. > w. > Ich schreibe korrektes TV Deutsch, so wie DIE auf Astra reden: > Das Wetta von morchen: diesich, mäßich wolkich. > Done, > Experimental device: [quoted text clipped - 19 lines] > since no digit are available for representing 0.5 Hz. > On this first spectrum, the 2nd and 3rd harmonics are 55 and 82(82.5). An excellent example of the result of insufficient education. About like how our bureaucracies work. COMPLEX = BETTER ("no problem, someone else is paying for it".) There are 8 keys in an octave because that's how the western scale evolved. India has something else, ancient China yet another scale. You are better off studying number theory. Angelo Campanella > There are 8 keys in an octave because that's how the western scale evolved. > > India has something else, ancient China yet another scale. There's a bit more to it than that. I've found the post by robert bristow-johnson that I mentioned earlier. It's worth a read: http://groups.google.com/group/comp.dsp/msg/ff49352136292537?dmode=source&hl=en SignatureAndrew > > There are 8 keys in an octave because that's how the western scale evolved. > > [quoted text clipped - 10 lines] > -- > Andrew ...and the whole thing seems to fall apart as the SPL goes up and the scales stretch through some psycho-physical phenomenon that I don't fully understand. Then to further complicate matters there are the language factors. Human factors seem to really muck things up. Later... Ron Capik -- It's a long time since I've read it, but I'm pretty sure that the whole subject was very well covered by our friend Hermann von Helmholtz, in his 1863 book "On the Sensations of Tone as a Physiological Basis for the Theory of Music" For a more modern approach, it would be interesting to hear from experts on, for example, Indian (Asian) music. SignatureTony Woolf My e-mail address has no hyphen - but please don't use it, reply to the group. >>There's a bit more to it than that. >>I've found the post by robert bristow-johnson that I mentioned earlier. >>It's worth a read: >>http://groups.google.com/group/comp.dsp/msg/ff49352136292537?dmode=source&hl=en Just read it OK. That's wat i had in mind when I cited "number theory". Certaily late in the 19th century, math and acoustics had progressed sufficiently for some good reasoning in that branch of music theory. It is important to read and understand the results of those labors before we go ff in some 21st century specualtions and "new approaches". > ...and the whole thing seems to fall apart as the SPL goes up and the scales > stretch through some psycho-physical phenomenon that I don't fully understand. for one thing, at higher SPL's (over 75 dBA or so), nonlinear transmission through he middle ear generates harmonics, and to be sure a different timbre for any loud tone. > to further complicate matters there are the language factors. Human factors seem to > really muck things up. Agreed, the nonlinear effects above being among them. Angelo Campanella > < ...snip.. > > > ...and the whole thing seems to fall apart as the SPL goes up and the [quoted text clipped - 11 lines] > > Angelo Campanella I wasn't thinking harmonics but the apparent scale shift as suggested by Harvey Fletcher noted in F.Alton Everest's "The Master Handbook of Acoustics 3rd Edition" [Re: pg 50 ; An Experiment ] And of the language factors where perception of the circle of fifths is different for British vs American listeners. [Scientific American article some time in the 1980s] I believe Bernstein did some talks on the subject of language and musical perception. I believe both of these are psychoacoustic phenomenon rather than nonlinear harmonic generation effects. Later... Ron Capik -- As I keep reading these posts, I note that no one has followed up on my referral to The Leonard Bernstein lectures in "The Unanswered Question." In his first lecture he goes into detail on why only eight notes. He indicates that even as you go into Chinese scales and the like, you still get only eight notes. You use only eight notes of the 12 notes (13 including the octave interval) chromatic scale to get a good approximation to the in-tune scale. The different scales correspond, IIRC to the various modes. Thus, the same notes can be used for a minor scale as for a major scale. The only difference is where you start. Again, IIRC, C-major and a-minor use exactly the same keys on a piano. Bill > As I keep reading these posts, I note that no one has followed up on my > referral to The Leonard Bernstein lectures in "The Unanswered Question." In [quoted text clipped - 3 lines] > > Bill I haven't had a chance to follow up on the Bernstein series but wonder if the 8 notes to a scale holds up for the 13 tone scale experiments of Harry Partch, John Pierce and Max Mathews. [Kind of wish I had a better education in music theory.] About a dozen years ago Max stopped by Bell Labs with a talk and mini concert in the 13 tone scale. Sadly, I didn't understand very much of the music theory he presented. He also emonstrated his MIDI "pizza box" a very cool 3D Theremin type device with all kinds of axis options from tempo to timbre. {Don't know if this music theory stuff quite fits in alt.sci.physics.acoustics.} Later... Ron Capik -- >> There are 8 keys in an octave because that's how the western scale evolved. >> [quoted text clipped - 5 lines] > > It's worth a read: http://groups.google.com/group/comp.dsp/msg/ff49352136292537?dmode=source&hl =e> n hey, Andrew, sometimes you need to slap me on the side of the head. i didn't know you were looking for anything. i think i was gone to AES in NYC and missed this whole thing. a better Google link for the post is http://groups.google.com/group/comp.dsp/msg/ff49352136292537?fwc=1 because it forces it into a mono-spaced font. i'm glad you thought it was worth a read. Signaturer b-j rbj@audioimagination.com "Imagination is more important than knowledge." I understand there being 12 half step notes in an octave and how that produces ratios that are pleasant to the ear. However, why is there always 8 notes in a given key? I guess I don't fully understand what a key or a scale is. Who decides what 8 to pick for a given Scale? And, like I said, why 8 always? Brian > > Anyone on this newsgroup know theoretically why there are 8 keys in an > > octave in music? Is it a part of natural harmonic vibration that on the [quoted text clipped - 18 lines] > There are many good articles in the Web, I suggest that you do a Google > search for "musical notes", "music keys", and "music theory" for starters. For instance, if an octave has 12 half steps, why not 12 (or 13 as some would put it) notes in a given key? > I understand there being 12 half step notes in an octave and how that > produces ratios that are pleasant to the ear. However, why is there always [quoted text clipped - 26 lines] > > There are many good articles in the Web, I suggest that you do a Google > > search for "musical notes", "music keys", and "music theory" for starters. >For instance, if an octave has 12 half steps, why not 12 (or 13 as some >would put it) notes in a given key? The 8 notes and the 12 steps are arbitrary and traditional. On 10/13/05 7:08 PM, in article UqE3f.38913$q81.28684@trnddc06, "Brian" <bmkwhite@verizon.net.NO_SPAM> wrote: > Anyone on this newsgroup know theoretically why there are 8 keys in an > octave in music? Is it a part of natural harmonic vibration that on the 8th [quoted text clipped - 4 lines] > > Brian 20 years or so ago, PBS presented a series of four lectures by Leonard Bernstein that started out with a comparison of music and speech. He answered this question directly and indicated how the even tempered scale was a decent approximation to the diatonic scale. Video for that is probably still available if you could locate it. In essence, pleasant sounding combinations occur if notes that integer ratios of frequency are sounded. When you do that, you get 7 tones plus an eigth that is the second harmonic of the first. Bill > Anyone on this newsgroup know theoretically why there are 8 keys in an > octave in music? Is it a part of natural harmonic vibration that on the 8th [quoted text clipped - 4 lines] > > Brian This answers nicely but unfortunately in french. http://etiop.free.fr/gammes.htm On 10/13/05 7:08 PM, in article UqE3f.38913$q81.28684@trnddc06, "Brian" <bmkwhite@verizon.net.NO_SPAM> wrote: > Anyone on this newsgroup know theoretically why there are 8 keys in an > octave in music? Is it a part of natural harmonic vibration that on the 8th [quoted text clipped - 4 lines] > > Brian Because I am interested in the Bernstein lectures that answer your question, I found out that it is called "The Unanswered Question." The title arises from a piece by Charles Ives that Bernstein uses as an example. Bill |
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