isbell@marvin.DEC (Chris Isbell ) (03/07/84)
<Mystical line> Quote from seismo!tiberio: >Is there any need for a discussion on the virtues of untempered scales >(as played by woodwinds, they go flatter in the higher octaves) verses >tempered scales (played by ugg pianos, they go sharper). > >learn to play a flute! The classic work on this subject is by Hermann Helmholtz, On the Sensation of Tone. There is a translation published by Dover in paperback. It is heavy going, but worth it if you are interested in the subject. In general modern woodwind instruments are tuned to the equal tempered scale, the same at modern keyboard instruments. Early woodwind instruments (recorders, capped reeds etc.) give the player much greater control of the pitch. I can vary the pitch of a note by about a semitone each side of normal on most of my capped reed instruments. In general flutes (fipple and transverse) tend to be sharp in the higher registers when played by unskilled players (just listen to a class of school children playing recorders!). If you wish to go flat in the upper registers, take up a reed instrument or a member of the violin family. The greater variation in pitch of early woodwind instruments has two effects. Firstly, an inexperienced early music consort is usually out of tune. Secondly, a good consort will play in non-equal temperament - usually just intonation. This means that the pitch of some notes of the scale change in pitch as the music changes key. The reason for having different temperaments is complex, but briefly, I is a result of the fact that roots of two are irrational numbers. The octave, which is the most basic musical interval is a frequency ratio of 2:1. Any attempt to divide the octave into a finite number of equal frequency ratios will result in intervals which are based on roots of two. If the octave is not divided into equal ratios, than certain keys will be out of tune. However, the musical intervals which are pleasing to the ear are simple frequency ratios such as 2:3 (fifth), 3:4 (fourth), 4:5 (major third) etc. Any deviation from simple ratios will cause interference between the two sound sources which, if the deviation is small, results in a beating sensation. The modern equal tempered scale has a frequency ratio between semitones of the twelfth root of two. This means that certain intervals are out of tune. In particular, the major third is too wide. My subjective feeling is that this produces a harsh edge to the music which I find unpleasant. Chris Isbell. (...decwrl!rhea!marvin!isbell)
ken@ihuxq.UUCP (ken perlow) (03/07/84)
-- >>> ...Any deviation from simple ratios will cause >>> interference between the two sound sources which, if the deviation is >>> small, results in a beating sensation. The modern equal tempered scale >>> has a frequency ratio between semitones of the twelfth root of two. This >>> means that certain intervals are out of tune. In particular, the major >>> third is too wide. My subjective feeling is that this produces a harsh >>> edge to the music which I find unpleasant. >>> Chris Isbell. >>> (...decwrl!rhea!marvin!isbell) So do I. After an evening with my viol consort I can't go home and listen to Mozart. Actually, my beef with recordings of Mozart's symphonic music is that it sounds demented when played by a 102 piece orchestra and those damned modern instruments. The worst offender is modern violin construction and technique: The piercing screech and wide vibrato totally mask the beautiful interplay of, for example, the last movement of the Jupiter. If you haven't heard music of the Baroque and Classical periods performed on Baroque instruments, you have not heard it at all. -- *** *** JE MAINTIENDRAI ***** ***** ****** ****** 07 Mar 84 [17 Ventose An CXCII] ken perlow ***** ***** (312)979-7261 ** ** ** ** ..ihnp4!ihuxq!ken *** ***
ark@rabbit.UUCP (Andrew Koenig) (03/07/84)
Pianos are generally tuned with "stretched octaves." In other words, the high notes on the keyboard are slightly higher than one would expect and the low notes are slightly lower. Perhaps one reason for this is that the upper partials of an individual piano string are also stretched: the second harmonic (say) is very slightly more than twice the frequency of the fundamental. It would therefore make sense to tune the upper notes to match the actual harmonics of the lower notes. The out-of-tune harmonics are one of the things that makes a piano sound like a piano.
peters@cubsvax.UUCP (03/08/84)
Just a followup to the subject of temperment. It is easy (technically)
for vocalists and players of unfretted string instruments to play
in just temperment (the natural harmonic scale). I used to sing
(many years ago) in the Renaissance Chorus of N. Y. (anyone out
there remember it?), and our director used to spend great amounts
of time trying to make us sing natural harmonic intervals. When
you "lock in" to a perfect unison, octave, fourth, or fifth, there's
a resonance effect -- a diminution of the effort to sing the note --
that's almost euphoric. Problem is, most people with musical training
have grown up with the piano and the well-tempered scale. Those
people had a lot more trouble singing true intervals, and doing it
without vibrato, so that the director found it easier to work with
people with only minimal prior training.
{philabs,cmcl2!rocky2}!cubsvax!peters Peter S. Shenkin
Dept of Biol. Sci.; Columbia Univ.; New York, N. Y. 10027; 212-280-5517graham@parsec.UUCP (03/11/84)
#R:decwrl:-608200:parsec:39000002:000:1067 parsec!graham Mar 10 14:10:00 1984 .. > Just a followup to the subject of temperment. It is easy (technically) > for vocalists and players of unfretted string instruments to play > in just temperment (the natural harmonic scale). I used to sing > (many years ago) in the Renaissance Chorus of N. Y. (anyone out > there remember it?), and our director used to spend great amounts > of time trying to make us sing natural harmonic intervals. When > you "lock in" to a perfect unison, octave, fourth, or fifth, there's > a resonance effect -- a diminution of the effort to sing the note -- > that's almost euphoric. The sound judges of SPEBSQSA (Society for the Preservation and Encouragement of Barber Shop Quartet Singing in America) call that euphoria "expanded sound". SPEBSQSA quartets and choruses sing in the style you suggest, but matching the vowel sounds as well as tuning the intervals is required to maximize the euphoria. Try it, you'll like it. Marv Graham; ConVex Computer Corp. {allegra,ihnp4,uiucdcs,ctvax}!parsec!graham PS: look up your local SPEBSQSA chapter in the phone book
mcmillan@eosp1.UUCP (Tobias D. Robison) (03/11/84)
To put it more simply, when playing or hearing harmonic music, humans clearly prefer untempered intervals. A singer or string instrument can easily play untempered pitches, and can easily shift to other untempered scales when the music modulates. Wind players can do this only with great difficulty, and the piano (and similar instruments) can only be tuned for one untempered scale (and a very limited modulation capability) at one time. Therefore, musicians are trained to play temepered scales. However, untempered sounds can be much sweeter, and certainly occur in unaccompanied vocal music. One summer I tuned a harpsichord to an untempered scale, and played quite a bit of baroque music on it. I liked the sound very much, but I had to be very selective about the keys (and degree of modulation) of the music I played. - Toby Robison allegra!eosp1!robison decvax!ittvax!eosp1!robison princeton!eosp1!robison (NOTE! NOT McMillan; Robison.)
isbell@marvin.DEC (Chris Isbell ) (03/22/84)
[Mystics line] Quote from Jim Janney: >Any woodwind instrument, however well made, is the result of many >compromises between tuning conflicts and has many notes that sound out >of tune. The player must make adjustments to correct for these. In >general, the size of these adjustments far outweighs the differences >between the even-tempered scale and more natural scales. Wot I think: I agree fully with the first two points, but I am less certain if the compromises in the instrument outweigh the errors inherent in the equal tempered scale. According to my calculations, the equal tempered major third has a frequency ratio of 1.2599..., while the just third is exactly 1.25. This is an error of 0.8 percent. (An error of a whole semitone is 6 percent.) I have not taken any scientific measurement of the tuning errors in modern woodwind instruments, but my subjective experience is that this error *is* significant. I find it much easier to play in just intonation on a recorder compared to a modern flute. Also, my feeble attempts at playing other modern woodwind instruments are, in general, fairly in tune (equal tempered) which again suggests to me that the errors inherent in equal tempered scales are significant. Does anyone have any data on the actual tuning errors found in woodwind instruments? Asides: I have a number of the cheaper Moeck wooden recorders. On these, the whole instrument has been made slightly flat, and the A has been sharpened to bring it up to concert pitch. If you want to scare animals or make a fool of yourself, try playing a French Bombarde. Chris Isbell. (decwrl!rhea!marvin!isbell) ------- End of Returned Message
geoff@callan.UUCP (Geoff Kuenning) (03/25/84)
Chris Isbell says: > According to my calculations, the equal tempered major > third has a frequency ratio of 1.2599..., while the just third is > exactly 1.25. This is an error of 0.8 percent. (An error of a whole > semitone is 6 percent.) I have not taken any scientific measurement of > the tuning errors in modern woodwind instruments, but my subjective > experience is that this error *is* significant. Indeed, this should be significant. Piano tuners measure tuning errors as a percentage of a semitone, called 'cents'. My tuner tells me that the human ear can distingish half a 'cent' in tuning error (when comparing two notes); this works out to a 0.03 percent error using the units of the paragraph above. A 0.8 percent error works out to about 13 'cents'. My piano was recently 20 'cents' out of tune, and it was *GROSS* to my ear. Incidentally, I note that some of this apparently depends on ear training. As a modern listener, I find that most early instruments sound out-of-tune. I always attributed this to their being harder to play, but apparently this is actually because I have learned to prefer equally-tempered scales to "correctly-tuned scales". Geoff Kuenning ...!ihnp4!sdcrdcf!trwrb!wlbr!callan!geoff