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1412Re: [clairseach] Re:: Who uses sister strings (na comhluighe) in tuning their harp and...

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  • Andy Hirt
    Feb 6, 2015
    Hello Cindy,

    These arguments are all rather confusing, especially with regard to the natural scale.

    The natural scale is the harmonic/overtone series. When you pluck a string, you not only hear the sound of the length of the string pushing the air, but two waves, three waves, etc. pushing the air. So you are actually hearing a series of pitches. The more the multiple waves on the string push the air (and since it is a regular pulsing, we hear different frequencies) the greater the sonic density or timbre. The overtones on harps are rather dull compared to wind instruments. When three bugles (natural trumpets, horns) are tuned to the same pitch and play different pitches, they are not actually playing different pitches; they are making one of the overtones louder than another. They are all producing the same series of notes. So when one plays what we could call a root and third and fifth, they are al exactly in tune with one another. 

    A harp is not like this. Harp strings are tuned to one another using a combination of the very lowest, principal waves and overtones, not the upper ones since they are barely heard. People developed a way of tuning strings based upon creating a cycle of fifths (ratio of 3:2) with octaves  (2:1) since these simply, low overtones were heard. When you do this, you create a diatonic scale. The number of notes are the same per octave. this is an exponential system with respect to frequency. The ratio of 5:4 does not fit into this system, so thirds are not in tune. Tuning to perfect fifths and octaves (with one or two faintly heard fourths) is what is called Pythagorean tuning. Bunting's tunings that he described (Sharp Key [G major; having one sharp] and the high bass/flatt key [C major; having no flats or sharps]) are types of Pythagorean tuning. It is not a tempered scale.

    Instruments playing the natural scale (harmonic series) are playing a scale that is linear and not exponential. harmonies played on natural instruments tuned to one another are exactly in tune. If you want to make a diatonic instrument play triads in tune, you need to adjust the principal notes of the strings to match the intonation of the natural scale. However, when you play any two strings that have been tuned a perfect fifth or fourth apart, their upper overtones will not match. This is no real problem for the harp since the upper overtones are very dull (you can't really hear them). If you adjust a harp so as to match the natural scale, it is called tempering. You alter the major thirds down by 22 cents so that one triad is perfect. This makes every other combination of triads off. So, depending upon what chords you want to play, you fudge with the tuning to make it bearable. Composers wrote music that used the intonation system that existed. They did not write new music and then create a new tuning system to make it work. So if you hear Chopin played on an instrument tuned in the manner that he had, it sounds quite different than the same piece played in equal temperament. Don't forget, you need to have a way of measuring the different frequencies in order to get fine changes in intonation. You didn't have good equal temperament until watches had second hands where you could count the number of beats between two strings/notes per second. They could only make the tuning system as complex as the technology allowed at the time.

    There has been a somewhat steady increase in pitch over time, what's called the Vienna Effect ("A" used by the Vienna Symphony is about 453 Hz.). Generally, older music is set to A=415 Hz and 440 otherwise, but it varies by orchestra. Bagpipes seem to have missed this inflation until the 1960s. So if you look at the article by Brown on the Ian Dal chanter (Barnaby Brown, “The Iain Dall Chanter: Material Evidence for Intonation and Pitch in Gaelic Scotland, 1650 – 1800,” in The Highland Bagpipe: Music, History, Tradition, ed. Joshua Dickson (Burlington: Ashgate Publishing Company, 2009), 35), you can get an inclination for older actual pitches used.

    Bunting's tunings are not tempered. There are various studies that show the actual frequencies of extant tuning forks. They also have old trumpets and some woodwind instruments that, when played today, will sound the same pitches as they did when they were constructed(allowing for intonational shifts between instrumentalists). There are also many different organs all over Europe that used different starting points of frequencies for its ranks. You should not base your starting frequency based upon the tuning of one organ, but should study the entire field of pitch variation over the ages and make a practical decision.

    Bunting's tuning systems are complete and intrinsically perfect unto themselves. You start with one string, which according to Bunting is always G. Decide the frequency that you'd like for that note (the material of the string, thickness and strength will vary according to this; the string's composition will be such that when stretched to almost its breaking point it will produce the frequency that you want at a set length). Then tune the other strings to this note. There is no tempering in this system. The distances between each note per octave will al be different. There are no true half and whole steps because that only occurs in exact equal temperament (concert pianos are still tuned today using the method of 1918). So if you tune your harp to the sharp key (G major) and then tune the F# down to F-natural, the two keys will have completely different "colours." So when you begin playing a scale in G major and play G, A, then that distance (frequency) is different than between the first two notes in C major, between C, D. This is of course adjusting for the exponential differences (the frequency differences will, of course, not be the same). 

    So as technology allowed, they were able to temper the diatonic scale more and more. This changed the different colours of the keys since the tuners were messing with the differences between set strings. When you changed keys, the distance would shift between the steps of the scale between two difference keys. So the difference between the first and second pitches (and second and third and third and fourth, etc.) of a major scale would vary depending upon which string you started the major scale.

    The reason why you need to start tuning to the two Gs (by the bye, na comhluighe means the couplers/lovers not the sisters, a term that the prudish Edwardians et al. decided upon) I tried to hypothesis in the published paper (attached – jump to the very end of the article). Simply put, harpers shifted the intonation of F-F# and C-C# so as to play with bagpipes, trumpets, different ranges of voices (soprano/tenor vs alto/baritone), and the diatonic (art music) and natural (folk) scales.

    Organ tuning is a very complicated subject. The organ builders generally decided upon the tuning themselves. Once it was installed, the musician in charge would tell the builders to make adjustments (often). Of course, it's easier to cut off material than put it back on. Where I live, the cathedral organ has its pitch so sharp that competition bagpipes play in A and match the organ's Bb (A mixolydian bagpipes are now at a sharp Bb). Pitch was flexible. Everyone was expected to adjust. 


    From: "Joe Ennis bigjoe@... [clairseach]" <clairseach@...>
    To: clairseach@...
    Sent: Thursday, February 5, 2015 5:57 PM
    Subject: [clairseach] Re:: Who uses sister strings (na comhluighe) in tuning their harp and...

    Good morning Cindy

    Yes to the Organ at St. Ann;s Church being tuned like other organs of its time, but things have changed all over, with space and time.

    Musicians usually do not consider that the pitch of music changes or that there has been more than one musical scale.  But it does.  The people that make music instruments are more sensitive to these changes.  If I make an instrument that does not reflect these changes, the musician just brings it back for refund and says: "it does not sound right".  

    The time that Bunting and Burney were writing was the time of the big change in musical scales.  It was also the time of J. S. Bach.  The Just scale was getting dis-credited, because it could not do the harmony that was in fashion at that time.  In the Just scale there are not sharps and flats, in the Just scale the pitch between each note is irregular, but the Just scale is also called the Pure or True scale, best for singing and sweetest.  The problem with the Just scale is that the pitch of its notes do not quite line up with their harmonics.  

    So to fix the Just scale, some Music Philosophers divided the scale into more than 8 and others into more than 12 steps ... there was one Dude, Patch, that divided what we know as an Octave (Latin for 8) into 43 steps (called the Patch 43 :-)  Then there were two other major schools of Music Philosophers one branch was the Mean Scale and the other branch was the Well Scale.    So the Music Philosophers spent over 100 years working (fighting and being rude to each other) out different scales and none of them were a very good fix to the Just scale.  Finally Neiper wrote his thesis on logarithms and finally the Music Philosophers had the math that they needed to make the Equal scale.  However, only in the Equal scale is a sharp the same pitch as its enhormonic  flat!  In the Mean and Well scale, one needs twice as many "black" keys on the keyboard :-)

    Now as late as the early twentieth century, the Music Philosophers could NOT agree on which pitch (frequency) to assign to each note.  We have the International Pitch for A as 440 and the Concert Pitch for the same A as 432.  This results in the pitch of every note in a scale being different between the two scales.  So if you tune your Harp to your Piano at Home that is tuned to the International A and then go to the concert to play and there the Piano is tuned to Concert Pitch, your Harp will sound a little sharp.

    So what I disagree with you on your prior post is: "Why would there be any doubt, then, that na comhluighe would be tuned to the Gs below middle C? Taking into account, of course, that our modern G strings might be tuned to a slightly different frequency than that common at Bunting's time? I really can't believe that the organ at St. Ann's would have been tuned to pitches radically different than other organs of its time: why would it be? Singers/choirs still had to produce the notes as written while singing with the organ. The physiognomy of the human vocal apparatus, and the resulting limitations in the tones it can produce, has not changed substantially in the past 200 years. 

    But let's say you're right and we can't make any assumptions about what specific frequency Bunting thought of as "G." What suggestions do you have about how a modern player should go about deciding what strings on his/her own harp to designate as na comhluighe? "

    My suggestion is: "that it really doesn't matter, so do not worry".  

    However; I had a tuning fork made to G = 196.0 Hertz and I use this tuning fork as my authoritarian source for tuning my  na comhluighe,   We can recover the scale and frequency of the Organ in St. Ann's Church when Bunting was the organist, others have already looked into this problem.  Also know that there was big arguments in Europe during this period as to what pitch (frequency) a certain note should be. And why should everyone not agree?  Religious differences! they just had the 30 year war, they could not even agree on what year it was. Further know that they did not have any way to measure frequency of sound during this period in time.  All the Music Philosophers could do was compare one note to another. The closest they had to frequency measuring test equipment involved revolving mirrors. They did know that sound was a vibration phenomenon and was waves, the Ancient Greeks knew this much. 

    Know that J. S. Bach was alive during this period and had some opinions on the Mean, Well and Equal music scales.  Bach did not like the Equal, he thought it un-necessary.  Bach even went to the trouble to write on front of his manuscript for the Well Tempered Clavier .. "DO NOT PLAY THIS IN EQUAL TEMPERAMENT";   well it does sound rather poor when played in Equal.


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