IDM Mailing Archive

quoted 30 lines From: "ian" <ian@webice.net>

>From: "ian" <ian@webice.net> >Reply-To: <ian@webice.net> >To: <idm@hyperreal.org> >Subject: Re: [idm] music 101 >Date: Sat, 19 Aug 2000 11:34:01 -0500 > ><font color="black" face="verdana, helvetica, arial" size="2">---------- >Original Message ---------------------------------- >From: Ed Hall <edhall@screech.weirdnoise.com> >Date: Fri, 18 Aug 2000 19:03:19 -0700 > > >Not all music uses equal-tempered scales. In fact, even AE has used > >alternative tunings in some of their tracks (e.g. arch carrier on LP5). > >To someone immersed in equal temperament as most of us are, such scales > >sound vaguely out-of-tune, yet there can be an odd sense of harmonious- > >ness missing from equal-tempered tunings (at least in keys compatible > >with the tuning). > >wait wait hold on. alternate tunings? are you saying AE used quarter steps >or something? > > >Equal temperament is the ONLY tuning system where enharmonic keys are > >equivalent. It facilitates, but isn't necessary for, chromaticism. > >(Check a good music dictionary for definitions of the latter word, and > >other such terms.) > >I understand chromaticism, what the hell is equal temperament? > > >#@!$% ian

Equal Temperament is how instruments are tuned today in the Western world. It means that every note is equidistant from the on before and the one after it. Basically, the octave is divided up into 12 equal half steps, thus making the perfect 5th a bit flat and the Major 3rd a bit sharp from their natural values. This differs from how instruments were tuned during, say , the baroque era, when they were tuned in Just Intonation, in which the perfect 5th is made slightly flat but the "pure 3rd" between the 4th and 5th partial of the overtone series is preserved. This tuning was used because most music during that time was based on harmony of thirds. So, back in the day of JS Bach, some keys actually did sound "sadder" or "happier" to a certain extent, whereas there are no real differnces between one minor key and another minor key in Equal Temperament. Even older is the Pythagorean method of tuning, which is tuning based on "Perfect" 5ths, which facilitates music based on harmonies of 5ths but leaves 3rds badly out of tune. Equal Temperament equally allows 5ths and 3rds to be used harmonically, at least to our young western ears. Geez, I hope this clarifies things. take care, have fun with tuning!! Joshua \telefon tel aviv \benelli design labs sorry John last time ________________________________________________________________________ Get Your Private, Free E-mail from MSN Hotmail at http://www.hotmail.com --------------------------------------------------------------------- To unsubscribe, e-mail: idm-unsubscribe@hyperreal.org For additional commands, e-mail: idm-help@hyperreal.org

Actually, Josh is nearly right: In the equal temperament system, it's done by frequency... Each note has a particular frequency associated with it, for example the note A below middle C has a frequency of 440Hz. To get the note that's one octave above (A above middle C), you multiply the frequency by 2, so that becomes 880Hz. Now, each octave has twelve semitone steps in it, so it would seem sensible to mathematically divide each octave into twelve equal steps. So the frequency of the B below middle C, should be 513.333Hz. This is not how it works. If you think about it, go up another octave (to 1760Hz) the number of Hertz between the bottom note and the top note of the octave is now bigger than before. Instead of *adding* on a constant number of Hertz to the frequency, we *multiply* it by a constant factor, this being the 12th root of 2 (1.059463). So, in fact the frequency of B below middle C is 466.164Hz. Of course, when tuning a piano or whatever, the guy usually uses a 440Hz tuning fork to fix the A, and does the rest of the piano by ear. Watch someone doing it, it's pretty interesting. Hope this is useful. G-love. www.gram.org.uk

quoted 38 lines Equal Temperament is how instruments are tuned today in the

> Equal Temperament is how instruments are tuned today in the > Western world. > It means that every note is equidistant from the on before and > the one after > it. Basically, the octave is divided up into 12 equal half steps, thus > making the perfect 5th a bit flat and the Major 3rd a bit sharp > from their > natural values. This differs from how instruments were tuned > during, say , > the baroque era, when they were tuned in Just Intonation, in which the > perfect 5th is made slightly flat but the "pure 3rd" between the > 4th and 5th > partial of the overtone series is preserved. This tuning was > used because > most music during that time was based on harmony of thirds. So, > back in the > day of JS Bach, some keys actually did sound "sadder" or "happier" to a > certain extent, whereas there are no real differnces between one > minor key > and another minor key in Equal Temperament. Even older is the > Pythagorean > method of tuning, which is tuning based on "Perfect" 5ths, which > facilitates > music based on harmonies of 5ths but leaves 3rds badly out of > tune. Equal > Temperament equally allows 5ths and 3rds to be used harmonically, > at least > to our young western ears. > > Geez, I hope this clarifies things. > > take care, have fun with tuning!! > > Joshua > \telefon tel aviv > \benelli design labs > > sorry John last time

--- Outgoing mail is certified Virus Free. Checked by AVG anti-virus system (http://www.grisoft.com). Version: 6.0.176 / Virus Database: 85 - Release Date: 26/07/00 __________________________________________________ Do You Yahoo!? Talk to your friends online with Yahoo! Messenger. http://im.yahoo.com --------------------------------------------------------------------- To unsubscribe, e-mail: idm-unsubscribe@hyperreal.org For additional commands, e-mail: idm-help@hyperreal.org

quoted 72 lines From: "Medium Graham" <medium_graham@yahoo.co.uk>

>From: "Medium Graham" <medium_graham@yahoo.co.uk> >To: <ian@webice.net>, "Investigative Data Mining" <idm@hyperreal.org> >Subject: RE: [idm] music 101/tunings >Date: Sun, 20 Aug 2000 12:59:21 +0100 > >Actually, Josh is nearly right: In the equal temperament system, it's done >by frequency... > >Each note has a particular frequency associated with it, for example the >note A below middle C has a frequency of 440Hz. To get the note that's one >octave above (A above middle C), you multiply the frequency by 2, so that >becomes 880Hz. Now, each octave has twelve semitone steps in it, so it >would >seem sensible to mathematically divide each octave into twelve equal steps. >So the frequency of the B below middle C, should be 513.333Hz. This is not >how it works. > >If you think about it, go up another octave (to 1760Hz) the number of Hertz >between the bottom note and the top note of the octave is now bigger than >before. Instead of *adding* on a constant number of Hertz to the frequency, >we *multiply* it by a constant factor, this being the 12th root of 2 >(1.059463). So, in fact the frequency of B below middle C is 466.164Hz. > >Of course, when tuning a piano or whatever, the guy usually uses a 440Hz >tuning fork to fix the A, and does the rest of the piano by ear. Watch >someone doing it, it's pretty interesting. > >Hope this is useful. > > >G-love. > >www.gram.org.uk > > > > Equal Temperament is how instruments are tuned today in the > > Western world. > > It means that every note is equidistant from the on before and > > the one after > > it. Basically, the octave is divided up into 12 equal half steps, thus > > making the perfect 5th a bit flat and the Major 3rd a bit sharp > > from their > > natural values. This differs from how instruments were tuned > > during, say , > > the baroque era, when they were tuned in Just Intonation, in which the > > perfect 5th is made slightly flat but the "pure 3rd" between the > > 4th and 5th > > partial of the overtone series is preserved. This tuning was > > used because > > most music during that time was based on harmony of thirds. So, > > back in the > > day of JS Bach, some keys actually did sound "sadder" or "happier" to a > > certain extent, whereas there are no real differnces between one > > minor key > > and another minor key in Equal Temperament. Even older is the > > Pythagorean > > method of tuning, which is tuning based on "Perfect" 5ths, which > > facilitates > > music based on harmonies of 5ths but leaves 3rds badly out of > > tune. Equal > > Temperament equally allows 5ths and 3rds to be used harmonically, > > at least > > to our young western ears. > > > > Geez, I hope this clarifies things. > > > > take care, have fun with tuning!! > > > > Joshua > > \telefon tel aviv > > \benelli design labs > >

I probably should have been more specific in my explanation. Each note in an Equally Tempered scale is equidistant in PITCH from the one before and the one after it, NOT in frequency. Before the days of frequency measuring devices, pitches were tuned by ear to be equidistant from one another on the basis of preserving the perfect octave, or what G is referring to by means of mathematics as the 2:1 ratio of say, C4 and C5. This is of course achievable only by taking the frequency of one note and multiplying that number by G's number 1.059463 (wow, that's tight, I just do it by ear!) to get the pitch of the next note. It is in this case that the real distinction between *pitch* and *frequency* seems to be drawn. What to our ears represents an octave divided into 12 equal PITCH INTERVALS of a minor 2nd is a frequency that is multiplied by an EQUAL or same amount (1.059463 pretty much), that when multiplied with an exponent of 12, preserves the 2:1 aspect ratio of the perfect octave. Oh-I think that 466.164 is Bb above middle C, but don't quote me on that. B below middle C should be around 247 hz, I think. respect to G for the l33t math skills. Thanks for the clarification. peace _J_ ________________________________________________________________________ Get Your Private, Free E-mail from MSN Hotmail at http://www.hotmail.com --------------------------------------------------------------------- To unsubscribe, e-mail: idm-unsubscribe@hyperreal.org For additional commands, e-mail: idm-help@hyperreal.org