EMUSIC-L Digest Volume 27, Number 8 This issue's topics: Tonalities (15 messages) Your EMUSIC-D moderator is Joe McMahon. Please send articles to emusic-L@auvm.american.edu (or EMUSIC-L@AUVM.BITNET). Administrative mail should be directed to xrjdm@scfvm.nasa.gov. Digests will be distributed semi-monthly to monthly. For faster response to questions, subscribe to EMUSIC-L@AUVM.BITNET (or emusic-l@auvm.american.edu). The EMUSIC-L discussion group can alo be accessed via bit.listserv.emusic-l on Usenet. Subscribers to this list may send articles to EMUSIC-D@AUVM.BITNET (or emusic-d@auvm.american.edu); they will be reviewed and forwarded to EMUSIC-L. Back issues are available from xrjdm@scfvm.gsfc.nasa.gov. This is a manual operation, so requests for things like "all back issues" will take a long time. ------------------------------ Date: Mon, 18 Mar 91 22:20:34 EDT From: "allen h. lutins" Subject: Generating notes w/internal speaker I need help with what i expect is a simple, low-tech problem...i need to generate exact tones (no more than +/- 1 or 2 hz) through the internal speaker in my IBM compatible. Can i do this with some version of Basic? My GWBasic requires note names (vs. frequencies) to generate tones (using the command PLAY)...i need the "in-between" notes because i'm studying (on my own) the mathematics of notes, intervasls & scales, & i need to generate tones to hear the differences in, for example, tempered & just intonations... Unfortunately, i'm not yet MIDI-ized...neither do i have any other fancy stuff, like oscilliscopes or their modern equivalents...thus my need to use my computer to do the job... Thanks in advance for any replies to this query... -allen P.S. I may be getting ahead of my studies, & this postscript may generate more response than the body, but...why do we have 12 tones in our scale? ...and why are 12 tone scales so popular elsewhere in the world? I've reached the point where i understand what makes notes "consonant" (basically, a note whose frequency is based on a simple ratio to another note's frequency), but it seems that there are few notes (especially the 5th, 4th, major 3rd & minor 3rd, in that order) which fit the description, and they're not evenly spaced...so what is the basis for other notes, and again, why 12? (if this question requires an entire text book to answer, don't bother -- i'll learn eventually ;-} ... ------------------------------ Date: Tue, 19 Mar 91 10:41:00 EST From: TUTTEROW@UNCG.BITNET Subject: Why divide by 12 and not 15? Allen. This may not be appropriate for EMUSIC but then again it might for those that play with different tuning systems. These statements are taken from "A History of Western Music" by Donald J. Grout, which is the standard History book for most college music schools. The first written record of the ocatave being divided into twelve parts comes from the Greeks, possibly from Aristoxenus and Pythagoras. Pythagoras discovered concords from the simple ratios among the divisions of a sounding string. String lengths in the ratio of 2:1 produced an octave, 3:2 the fifth, and 4:3 the fourth. All other intervals were considered discords. For the Greeks, the concept of note and intervals were dependent on the a distinction between two kinds of movement of the human voice: the continuous, in which the voice changes pitch in a constant sliding up and down without fixing a pitch; and the diastematic, in which pitches are sustained with discreet intervals perceptible within the the pitches. Intervals such as tones (whole step), semitones (half step), and ditones (thirds) were combined into a system of scales. These systems of scales WERE bases on twelve even divisions of the 2:1 ratio. Different people divided Pythagoras' concords differently, but the division by twelve was the only one that lasted throughout the two thousand years of Western Musical development. All through history music has experimented with dividing the octave into different divisions of microtones, but none has stayed with us. (An argument for Darwinian survival of the fittest chord?) This equal division provided us with the perfect fourth, perfect fifth, and perfect octave, but all other intervals were dissonant, even more than now. This problem was not solved until the late seventeenth and early eight -teenth century when our modern tuning system came into being. The perfect fourth and perfect fifth were tuned slightly flat with the octave being left perfect. This in turn brought the other interval the major and minor third and major and minor sixth closer to consonance, along with le lessoning the dissonance of the second and sixth. A good exercise for us in electronic music, especially if we are experimenting with different timbre qualities of patches would be to play with tuning our instruments differently in order to produce slightly different intervallic sounds. Then maybe experiment with different divisions of the octave and see what you can come up with. Write a tone poem based on a new scaling system and experiment. Twentieth century ears are not as attuned to consonance and dissonance as were earlier generations. Electronics can open up new ways of composition to take music into a brand new style having nothing to do with basic tonality as we know it. Experiment with tuning. What sounds bad today could be a hit ten years from now. I hope this wasn't to long and drawn out. Thanks. Kirk ------------------------------ Date: Wed, 20 Mar 91 11:29:00 EDT From: "William R(ay) Brohinsky" Subject: Re: Generating notes w/internal speaker WARNING: this is long. allen, Your posting and it's ps have hit exactly on some of the arguments (I wish they were just discussions) taking place on bix right now, and yours truely is one of the major combattants. I will answer you very much like I answered a similar question on bix, and we'll see if any Lucy Scale enthusiasts are on E-MUSIC... First, your question about PC speakers: The pc speaker is a very bad choice for tuning experiments. The primary reasons are poor reproduction quality, limited to a square/rectangle wave (only gives odd harmonics), and resolution of pitch ratios. The first two points are pretty much endemic to all beeper-speakers. What can you expect from a 2" speaker in the way of fidelity? The third comes from the following argument: Music theory is usually dealt with in one of two ways: the ratios between the frequencies of two notes are compared, either in terms of ratios (ascending fifth = 3/2) or cents (a pure fifth is somewhere close to 701.997 cents). A cent is one 1200th of an octave, expressed as the log base two. That means that 1200 cents is equal to the ratio of 2/1, and 100 cents is about 1.05946309436 (but who's counting) to one. 100 cents, however, is the ratio of the theoretically equal-tempered semitone. One cent is a good minimum value to use for adjusting notes, in theory, since it was chosen to be fairly beyond the hearing/dis- criminating level of most humans. (I tested out at about 2.5 cents, which I was told was fairly good.) However, since the pure interval for the fifth = 1.5, and the cents approximation of 702 cents is 1.500038989286, you'll get beats that shouldn't be there. This may seem like a small thing, but when you are studying tuning, and you set up an interval that wants to be beatless... To be comfortable that you're beatless intervals are fairly beatless, hundredths of cents is advisable. All of this requires getting the cents into an exponant of 2, thus: 2^(cents/1200) to get the ratio. This is time comsuming. Once you have the ratio, you have to apply it to one note to calculate the other. Since most reasonable timing algorithms deal in integers, an integer counter will get you to an resolution about three times bigger than you need for precise timing. (1.000015 vs 1.000005). That's if you use the full count for one of the notes, and some fraction of the count for the other, higher-pitched count. Needless to say, the time required for most computers to do a 65535-point count (empty loop w/decrement) is finite. If it is about 1 microsecond, the pitch of the lower note will be 1/.065535 Hz, or about 15 hertz. You can do some tests to determine how fast your computer can make one loop/decrement. That means, for full resolution with a 16-bit counter, you'll end up with one note about half as high in pitch as most ears can even detect... Once you convince yourself that you are willing to go through the problems of writing a program that will allow you to specify an interval in cents (good for temperaments, worthless for tunings) you face another difficulty with a pc speaker: it only makes one pitch at a time! You CAN get around this. Paul Lutus wrote a marvelous program for the Apple // that pulsed the speaker with a pulse-width modulated rectangle signal, which relied on the speaker's poor hi-freq response (and the ear's as well) to act as the low-pass filter. He'd calculate the two pitches to be played, and then control the rectangle signal like this: if both signals were high, use a long pulse. if one or the other is low, and the other is high, use a medium pulse if both are low, use a short pulse. This allowed him to get two notes from one line, both were square-wave approximations, and both worked pretty well. You can do this, but you'll find that it works best when the two pitches are integer multiples, and that the tuning between them is limiited in resolution. NOW, on to the other question: Why 12 tones in the scale? The reason is, that for the better part of 4 or 5 thousand years, we had no set limit on notes. Even while Pythagoras was making his theoretical scales, you'd start at what ever pitch felt right, and as you sang, the notes would pretty much go where it sounded good. In the case, specifically, of Pythagoras' scale, it was built out of pure fifths: 3/2 ratios. But if you do this 12 times, then divide by 2 seven times, you end up with different answers! the ratio of the original pitch to the derived one is 1:1.013643...this is clearly not identity! This method did allow generating a scale of twelve tones. The reason for not going beyond 12 tones is that the next tone generated after the first 12 (and before the first 24) will always be 1.013643... above one of the already generated notes. (this will actually continue even after 24 notes, but each new note will come out 1.013643 above one already-generated note, and 1.0274726 above another, and on, and on...) This scale, however, is present in nature. The pythagorean scale is common in solo music: where a voice or fretless instrument is played with no accompaniement. The third and seventh are quite high, but this sounds OK with no other notes simultaneously present to compare to. On the other hand, when adjustable-pitch instruments play in consort (the renaissance word), Just intonation is used. (intonation=tuning. temperament= detuning for a purpose). In this tuning system, each interval is tuned against others to produce beatless chords. Although some have claimed this to be dull, I think they are listening to sine-wave voices. Anything more complex than that will result in sum and differnce tones between the fundamental and partials of each voice, yeilding notes which are also beatless, but not being directly produced. This is because the partials of most natural instruments (excepting bells and the piano, the latter of which could be argued as to its naturalness :-) are in integer multiples of the fundamental, and are therefore beatless. The whole thing of ringing chords in barbershop is based on just intonation. Helmholz observed that when the best performances occurred, they were played in Just intonation by artists who adjusted their pitch to match each other. These kind of performances are usually characterized in descriptions by an emphasis on the sound, tone, and quality of the sound, rather than on just the music. The temperaments came about when fixed-pitch instruments were used in different keys. This is accompanied by a cataclysmic change in musical style, but NOT an elimination of Just intonation for group playing and Pythagorean for solo work! It is to be noted that even the most modern instrument, wind or string, is still actively adjustable when being played! Any time a person has his hands on the strings, slides, his lips on the reed, or his diaphragm at the bottom (or top) of the wind column, pitch can be controlled. It is the education of the player into this control that has been neglected in recent years, more's the pity. Keyboard instruments, however, lack this kind of control. Even Synths (which can be tuned by microtonal tables) still are fairly fixed-the mod wheel bends the pitch of the whole instrument. (ever tried to tie aftertouch to pitch control? Can it even be done???) The problem with Just intonation for truly fixed-pitched instruments is that the first two whole-tone intervals are not the same! The first is larger than the second. There is a `major' and `minor' semitone: one whole interval is made up of two major semis, the other from one major and one minor. That means that a keyboard tuned to play just in C will not play just in D. There are lots of other problems, not the least of which is, `where are you after four modulations by a fifth? After 12?' Each modulation brings with it a shift in some notes, so that by 12 modulations (remember Pythagoras?) you're completely off! I won't go into any of those, since the major-semi minor-semi problem is basically insurmountable in Just fixed-pitch instruments. What to do? Well, the theorists decided that, if they took the error interval between 12 fifths and seven octaves, and divided it by a quarter and applied it to the fifth, shortening it, they could end up with a pure third and a pure octave. (the third is hit after four iterations, so the quarter adjustment brought that note down to what was needed for a pure third). This is called 1/4-comma Meantone, the mean being the note between the tonic and the fifth. It was in use for many years, and is still the tuning of choice for some music. The reason was because the scale produced by iterated fifths which are reduced by the fourth of the comma (that discrepancy between 12 fifths and 7 octaves) are not always right, and two of them are quite bad for using in some keys. These keys were called `wolf keys', for their howling! However, the great composers were aware of this (how could they not be?) and used chords on those notes as tension heighteners: how much more alive and meaningful is their music when played in 1/4-comma mean tone, than when played on equally tempered instruments! Equal temperament sacrifices the third, in order to make the fifth more pleasant. This is the `emotional' argument. Mathematically, it takes the comma and divides it into 12 parts, subtracting the 12-th comma from each fifth in the iteration. This way, the octave remains constant, the third ends up high, but not as bad as with Pythagorean, and the fifth is just a bit flat. Since this does divide the octave by equal ratios, hence the name equal temperament, you can now play in any key, and have it sound just as good, or just as bad, as any other. Grout's comments on the life and livelyhood of temperaments other than equal is some decades old. That, in my opinion, answers for his naivity in re: the survival of Just and Pythagorean, and the revival of other temperaments. There ARE other temperaments than ET12. ET32 approximates 1/4-comma mean- tone, and another one (helmholz called it Mercatorial, after Mercator. I don't know if this is the same Mercator whose map projection was the accepted norm until just recently) which divides the octave into 53 parts. This one allows playing in very-near-Just intonation in all keys, but tends to be dificult to put on a keyboard 8^) A recent scale development, which has been hullaballooed with all to many claims of `increasing universal harmony, mapping all chaotic systems, making it possible for a musician to play in any scale of any culture, and making it possible to communicate with whales and dolphins' is the Lucy scale. Lucy has decided that our two-dimensional representation of scales by frequency ratios is naive. He postulates a scale built on PI. His results are (amoung other claimed scales) a 22-note scale that makes it possible to play out-of-tune equally in all 12 of our normal scales, but is supposed to be extendible to other levels of harmony. I list this here out of general wish to be fair, but with the admonishment that I haven't heard the results of music played with or written for this scale, nor have I seen a justification of the 3-D view of sound. I am reserving judgement for that time. I hope this hasn't burned your mind out completely. I recommend getting your hands on Helmholz (On the Sensation of Tone), in the latest Dover reprint. The text is interesting, but the appendices, especially those from 20 on, are a fascinating historical, theoretical, and even practical tretise on tuning. raybro ------------------------------ Date: Wed, 20 Mar 91 12:25:13 EST From: ronin Subject: Re: Generating notes w/internal speaker just a note on this... i don't mean at all to criticize the discussion at hand, i think it's wonderful... if memory serves, bit banging the speaker from assembly is actually pretty easy, and provides a fairly high degree of accuracy for frequency, as well as pulse-width, control. one counts system clock pulses for timing. in fact, i seem to remember there being a single command that sets or clears the speaker bit for a given number of clocks... you don't actually have to do the countdown yourself. of course, you have to do the hex math beforehand, to get the values in a lookup table. --------------------------< Eschew Obfuscation >------------------------- Eric Harnden (Ronin) The American University Physics Dept. Washington, D.C ------------------------------ Date: Wed, 20 Mar 91 12:55:20 EST From: "D. Yuen" Subject: Re: Generating notes w/internal speaker Ray, That was a great posting on tunings. A lot of it still goes over my head but I'm getting there slowly... Dan Yuen ------------------------------ Date: Wed, 20 Mar 91 15:29:28 -0500 From: Brian Adamson Subject: Re: Generating notes w/internal speaker You mention that: *************** A long time ago, when I very first got to play with a computer; My high school got an Apple II. I copied an assembly language program from some magazine which let you (via the tape interface) sample audio signals for playback through the Apple II's bit banger speaker. At the time I didn't really appreciate this technique, and now with a little more experience I see this as a pretty neat trick. I suspect the trick worked by using a fairly high sample rate just to capture the zero crossings of the waveform. You could use this one-bit A/D data for playback through the bit banger speaker. The program worked fine, as I remember, and I actually plugged in a tape player and sampled segments of music. Of course, the playback quality was horrible, but understandable, even speech was recognizable to some degree. I am curious if anyone else has tried low-end tricks like this, or is this forgotten lore? Brian Adamson ------------------------------ Date: Thu, 21 Mar 91 09:30:35 EST From: Joe McMahon Subject: Re: Generating notes w/internal speaker Yes, I still have the old "FOUR-VOICE MUSIC" program on my old Apple //e, written in Integer Basic. I actually went so far as to disassemble the music file, figure out the coding scheme, and write another couple of "arrangements" for it. My favorite one, though, was the one that I got by forgetting to resave the binary file after entering another piece; the program stumbled randomly through the unassigned memory and created some truly bizarre sounds. --- Joe M. ------------------------------ Date: Thu, 21 Mar 91 10:48:23 EDT From: "allen h. lutins" Subject: Re: Generating notes w/internal speaker Thanks to all who took the time to respond (sometimes in appreciable depth) to my initial inquiry -- i'm learning a lot very quickly... ...but one more (quick, easy & painless) question -- since i've been convinced that my IBM internal speaker is *not* the tool for pitch experiments: Will MIDI (once i get it) give me the capability to generate tones of (relatively) exact frequencies? -allen ------------------------------ Date: Thu, 21 Mar 91 13:06:00 EDT From: "William R(ay) Brohinsky" Subject: Re: Generating notes w/internal speaker MIDI will give you the ability to control a synthesizer. THe IBM midi board is essentially an FB01, with about a .8-cent variability. Since the pure fifth requires three decimals of variability to do well, that means that you will not get well tuned pure intervals. It does ET12 real well :-) The DX7II-MK-something or other is supposed to do microtuning tables. I don't know the exact variability, but you can tune it from the Front panel. So if you go that way, you could skip the IBM board and go for a simple MIDI interface. I'm sure someone else can say more about that. raybro . ------------------------------ Date: Thu, 21 Mar 91 13:17:00 EST From: TUTTEROW@UNCG.BITNET Subject: The mathematics of music. Raybro, Thanks for your lecture on tunings. You said it was long, but it was much shorter and more concise than any information that I have been able to get from my music professors. Maybe music teachers here don't understand why what they perform and hear works the way it does. Next question: The Univ. of North Carolina at Greensboro where I attend has a reputation of being one of the finest Schools of Music in the country concerning traditional music. But we have only one faculty member that knows a lot about electronic music and he teaches bassoon. We have no electronic music classes. Does anyone know of any universities that have good electronic music programs in their music department. This information may help me decide where to go for graduate school. Thanks. Kirk Tutterow ------------------------------ Date: Thu, 21 Mar 91 14:53:05 EST From: Pam Subject: tonalities >RAY, >THAT WAS A GREAT POSTING ON TUNINGS. A LOT OF IT STILL GOES OVER MY >HEAD BUT I'M GETTING THERE SLOWLY... > >DAN YUEN I HEARTILY agree! Thanks for taking the time to write so much!. As a newcomer to emusic and this kind of theory history I got really excited about the complexity of what you described. Especially I would be interested in an elaboration of this comment: >HOWEVER, THE GREAT COMPOSERS WERE AWARE OF THIS (HOW COULD THEY NOT >BE?) AND USED CHORDS ON THOSE NOTES AS TENSION HEIGHTENERS: HOW MUCH >MORE ALIVE AND MEANINGFUL IS THEIR MUSIC WHEN PLAYED IN 1/4-COMMA >MEAN TONE, THAN WHEN PLAYED ON EQUALLY TEMPERED INSTRUMENTS! Is this difference you are referring to, the difference between an orchestra playing vs a piano ? What is an example (instrumentation) of what you are saying and for what music? Thanks! ------------------------------ Date: Thu, 21 Mar 91 15:29:02 EST From: Joe McMahon Subject: Re: tonalities raybro's posting reminds me of a J. S. Bach story. It seems that Bach was a proponent of equal temperment over meantone and had a longstanding argument about this with an organ maker in the area. The organmaker had just completed a new organ (tuned meantone) and asked Bach to demonstrate it for the new owners. Bach said, "Why, certainly", and sat down and proceeded to play something in F# major, guaranteeing that he would hot all of the wolf tones. The organmaker got so angry he ran up and tore the wig off Bach's head. --- Joe M. ------------------------------ Date: Thu, 21 Mar 91 14:10:00 EDT From: "William R(ay) Brohinsky" Subject: Re: The mathematics of music. UNC/Greensboro's only E-music literate faculty member is a bassoon prof? That's funny, I was a bassoon major! Odd coincidences aside, I can't recommend any of the U's or colleges in Connecticut, although I'm not that familiar with Wesleyan. They are very much into ethnic music, so they might just have an E-music studio hidden away there, somewhere. I don't think I did a very good job on that listing, actually. I'm still in flux in my feelings about scale evolution---it seems to me that prior to the renaissance, scales were largely 8-toned in the West, with the building blocks of whole and half tones being the prime mover. At least, all the ancient Greek scales that were noticed by renaissance theorists and used (well, the names were used on the wrong modes, but what the hey?) were eight-toned. The name diatonic, though , infers that the two-toned ness was what differentiated these scales from the chromatic (which name refers to the `coloration' possible in a 12-toned scale). After the temperaments started being used (and 1800 years before, when Pythagoras had at his theories) the scales were 12-toned, and based on successions of fourths and/or fifths. The effort of all the tempering theorists (and the practicioner[sp]s like Werkemeister) was towards getting a 12 note scale that was homogeneously transposable on a fixed- pitch instrument, and the efforts of such instrument designers as Bohm and Sax were toward making flexible-pitch instruments into fixed pitch ones. All of this deserves more thought on my part before taking a mental dump on all of you. However, the last posting had the benifit of being shorter than helmholz... raybro . ^too much time on bix... ------------------------------ Date: Thu, 21 Mar 91 16:20:00 EDT From: "William R(ay) Brohinsky" Subject: Re: tonalities >>>>>>>>>>>>>>>original posting contains:<<<<<<<<<<<<<<<<<<<<<<<<< Subject: Re: Generating notes w/internal speaker >RAY, >THAT WAS A GREAT POSTING ON TUNINGS. A LOT OF IT STILL GOES OVER MY >HEAD BUT I'M GETTING THERE SLOWLY... > >DAN YUEN I HEARTILY agree! Thanks for taking the time to write so much!. As a newcomer to emusic and this kind of theory history I got really excited about the complexity of what you described. Especially I would be interested in an elaboration of this comment: >HOWEVER, THE GREAT COMPOSERS WERE AWARE OF THIS (HOW COULD THEY NOT >BE?) AND USED CHORDS ON THOSE NOTES AS TENSION HEIGHTENERS: HOW MUCH >MORE ALIVE AND MEANINGFUL IS THEIR MUSIC WHEN PLAYED IN 1/4-COMMA >MEAN TONE, THAN WHEN PLAYED ON EQUALLY TEMPERED INSTRUMENTS! Is this difference you are referring to, the difference between an orchestra playing vs a piano ? What is an example (instrumentation) of what you are saying and for what music? Thanks! >>>>>>>>>>>>>>>>>>end of post, start of reply<<<<<<<<<<<<<<<<<<<<<<<<< warning: I am not sure how long this will go on... Well, As far as instrumentation goes... 1/4-comma mean tone was used for a very long time in europe. It was fairly late in Bach's life when he finely found and fell in love with the Well-Temperament. Prior to that, from the middle-late 1500's, keyboards were being tuned in mean-tone temperaments. I'm not exactly sure when before that they were tuned in mean-tone (lapse in memory, or something) but prior to mean-tone they were pretty much tuned to just or maybe Pythagorean (which resulted in much theoretical writing on just how un-useful those tunings were for fixed-pitch instruments!) In actual fact, any instrument that can be tuned can be played in mean-tone. The differentiating characteristeric is the composer's music. A digression: When Carleen Hutchens was developing her [now famous] violin family, she tried a few experiments. One such was to take a viola, and re-make the bouts (the sides that hold the top to the back) to a height of 1/2", instead of the inch and three-quarters (or so) usually used. She figured that the body resonance (at Bb in the normal viola) might be sapping the strength of the viola at other pitches, and she thought this first experiment (making the air-cavity resonance very high and reducing the cavity volume) would make the viola very weak-sounding throughout the bottom range. Quite the contrary, if memory serves me right, the new viola sounded very even and loud throughtout it's range! This occasioned a few AB tests with a variety of listeners and players. All prefered the old viola. She claimed that she finally narrowed this unreasonable conclusion's cause to the fact that she'd used Mozart's viola concerto as the test piece. Her conjecture was that Mozart knew that the viola had a strong peak at Bb, and so he `played to [that] gallery' by putting the piece in Bb. He then contoured the music to use the strong tonic and weaker dominant as features of the instrument, rather than weaknesses. When played on the new viola, the resulting over-emphasis on the previously weaker parts of the scale resulted in a parody of viola-feeling. Although this is a very subjective sport (at the very least!), I feel she's hit the target on the bullseye. To return to my point: Because the wolf keys in mean-tone temperament are the odd ones (an instrument tuned mean-tone in C starts to get really bad on chords like E, which use the G#), those chords are used rarely in baroque music, and when they come, their effect is so tension-building that the arival at the tonic has a much heightened effect. This is true whether the music is played by an orchestra, a harpsichord, violin, bassoon, or voices. AS LONG AS THE TUNING IS ADHERED TO! It is not always possible to tell from concurrent musicological sources just what intonation or temperament was in use for a particular composer, but a sensitive observer can `read' the temperament from the chord useage. The scientist I work for has a few early-baroque pieces he's played recently that he remarked to me just this point: When played on modern instruments fixed at ET12, the pieces would sound stock, Bb arrangements, despite the quality of the players. When his little band (harpsichord, 2 baroque oboes, baroque bassoon) play them using 1/6th-comma mean-tone (which he just happens to like a bit more than 1/4-comma because the fifths are a bit purer) the music springs out at you. Baroque music is claimed by the theorists of the time to be a more emotional music. I've heard lots of performances of baroque music from the early 1960's which, although bombastic, were very un-differentiated and dull. Newer recordings of the same pieces with some attention paid to intonation/temperament result in wonderfully moving music, even for friends of mine who are relatively antithetical to baroque music. As for what music, English music from Byrd to Purcell (Holborne, Gibbons, Jenkins, North, Dowland), French and Italian music from the early to the high baroque (Vivaldi, Gabrielli, Costello, Lully, Couperin,etc.) Notice I mentioned Gabrielli: although his wind-band stuff was most likely played Just, his keyboard stuff is most likely intended for mean-tone. Early Bach, pre-dating the `Well Tempered Clavier' by a few years. OH, Yeah---There's an old Deutsche Grammophone recording of Ralph Kirkpatrick (from when he still had time to practice!) doing the Well-Tempered Clavier (Wolhe Tempierte Klavier-I think that's the German Spelling) on a clavichord tuned to Well-temperament. Find this at your local college library, and compare it to, say, Wanda Landowska (harpsichord) or any other 1950s harpsichord rendings ('scuse-renditions). Amazing difference. It's interesting to me as a transplanted-to-connecticutan, that UCONN's performance auditorium is named after Jorgensen. He was one of the first to give Temperament Concerts: he'd have two Grand Pianos and a harpsichord. One Grand would be modern ET12 (stretched, because of the non-harmonic overtones of steel strings under tension), one grand tuned in Well-Tempered, and the harpsichord in 1/4-comma Mean. He play pieces on both the modern ET12 and on which other temperament they were probably written for, contrasting the sound for audiences. He has left behind a book on tuning the temperaments, interesting reading even if you can't tell which end of a tuning hammer is used for driving the nails 8^) raybro ------------------------------ End of the EMUSIC-L Digest ******************************