How was chant tuned?
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Equal temperament is a very recent development. 16th century Palestrina is credited with just intonation. But Gregorian chant is much older than this. What sort of tuning was used for the different modes of chant? Does Solesmes use an ancient tuning or equal temperament?
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Actually, 12-tone equal temperament (12-TET), also called 12 equal divisions of the octave (12-EDO) is quite ancient (as are other equal divisions of the octave, notably 7-EDO in Chinese tradition). Although the exact mathematics for 12-EDO (in terms of powers of 12th roots of 2) was not worked out (published) until the 1580s, the principles were understood at least as early as the 5th century BCE (possibly much earlier), and a set of 12-EDO bronze chime bells were found in the tomb of Marquis Yi of Zeng.
In Europe, 12-EDO was discussed as early as the 4th century BCE. Lute music for 12-EDO was composed as early as 1507 (by Francesco Spinacino), and it was not uncommon for lutes to have their frets set for playing in equal temperament.
Fretless stringed instruments and trombones (really sackbuts), as well as other instruments which could bend their tone could play in any temperament, but usually played in some form of just intonation, so as to be able to "tune" the various harmonies in music. Singers also sang polyphonic and other harmonised music in some form of just (or at least approximately just) intonation.
While we can't be absolutely certain as to how chant was sung, evidence strongly suggests that chant was also intoned in some form of just intonation. The further back one goes, though, the murkier the situation becomes, since it is possible that certain pitches (or scale degrees) may have been altered in ways that don't fit our western concepts of tonality (just or not).
Moreover, this begs the question as to what form of "just" (or unjust?) intonation should be used for chant today. I have some opinions on this but have already said enough for now.
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...but have already said enough for now.
It seemeth to me that thou hast only just begun.
Be pleased to carry on.
Fascinating this is.
(I do, though, think that just 'BC' will do for us non-PC Christian folk.) -
Yes, after I asked my question, I read in Barbour's Tuning and Temperament: A Historical Survey that "Aristoxenus was hailed by sixteenth century theorists as the inventor of equal temperament." (p. 2).Actually, 12-tone equal temperament (12-TET), also called 12 equal divisions of the octave (12-EDO) is quite ancient
If equal temperament is so old, why has it only recently become ubiquitous? Did the ancients have a reason not to prefer it over other systems? -
On p. 2-3 of Barbour:
Is this true? Was only Pythagorean tuning used in chant until circa 16th century? Are its "small semitones…excellent for melody" in "and its sharp major thirds" beneficial for chant?Just intonation, in either the Ptolemy or the Didymus version, was unknown throughout the Middle Ages. [The martyr] Boethius discussed [in De institutione musica] all three of the above-mentioned authorities [Pythagoras, Aristoxenus, Ptolemy] on tuning, but gave in mathematical detail only the system of Pythagoras. It was satisfactory for the unisonal Gregorian chant, for its small semitones are excellent for melody and its sharp major thirds are no drawback. Even when the first crude attempt at harmony resulted in the parallel fourths and fifths of organum, the Pythagorean tuning easily held its own.
He defines it on p. xi:Pythagorean Tuning — A system of tuning based on the octave (2:1) and the pure fifth (3:2). -
Why not BAD...?
Regarding the tuning, have any efforts been made to record chant in Pythagorean or other non-equal temperament tuning? (I realize that any excellent choir or ensemble naturally bends equal temperament for the sake of better intervals, but these are examples of bent ET, rather than Just or Pythagorean, right?Thanked by 1Geremia -
Pythagorean tuning/intonation, based on perfect fifths/fourths starting at some pitch, say E-flat, B-flat, F, C, G, D, A, E, B, G-sharp (which is quite distant from the enharmonic A-flat), is itself a form of just intonation, known as 3-just intonation (powers of 3 & 2 are permitted in frequency ratios). It is perhaps the first tuning (6th century BCE) given a solid mathematical basis ("just"-ification). While it gives narrow leading tones (256:243), its major thirds (81:64) have been variously held up as a flaw and a feature, flawed because (80:64=5:4) is much more consonant (less harsh), feature because of the leading tone.
Just intonation usually refers to what is known as 5-just intonation (powers of 5, 3, and 2 are permitted in frequency rations). It makes for less harsh major thirds (5:4) and minor thirds (6:5). Its chief flaw, which we have learned to live with, is that it still leaves minor sevenths (think in a major key) rather impure. The ratio 7:4 would be ideal, but this necessitates going to 7-just intonation, and it was deemed rather unnecessary for early music which rarely, if ever, utilized a seventh chord in a major key.
Adam's point about singing above a drone (or utilising isons) in singing is the starting point for suspecting that some form of 5-just intonation was used in tempering the scales for chant (and becoming pervasive in Renaissance harmony).
More to come at a later time, perhaps.
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But BCE stands for Before Christian Era,
I've never heard this before, and I don't think that's the way the average person would interpret it. From:
When I was a kid, I was always taught to refer to years using BC (Before Christ) and AD (Anno Domini / year of our Lord). However, I somewhat regularly hear people referring to years as in the CE (Common Era) or BCE (Before the Common Era).
Why do people use the latter terminology? For one thing, I find it confusing. It doesn't help that BCE is similar to BC. But moreover, there is only one letter of difference between the two terms, whereas with BC and AD, the terms are clearly different and I find it easier to distinguish! Were BCE/CE established earlier than BC/AD?
BCE/CE usually refers to the Common Era (the years are the same as AD/BC). That is, BC is usually understood to mean "Before the Common Era" and CE to mean "Common Era," though it is possible to reinterpret the abbreviations as "Christian Era."
The simplest reason for using BCE/CE as opposed to AD/BC is to avoid reference to Christianity and, in particular, to avoid naming Christ as Lord (BC/AD: Before Christ/In the year of our Lord). Wikipedia, Anno Domini article:
For example, Cunningham and Starr (1998) write that "B.C.E./C.E. …do not presuppose faith in Christ and hence are more appropriate for interfaith dialog than the conventional B.C./A.D."
If there is a standardization or shift occurring, it's likely toward BCE/CE, at least in the United States. Common Era notation is used in many schools and academic settings.
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What sort of tuning was used for the different modes of chant?
The one that sounded the best.
Seriously, we don't know, and it probably varied with time, place and situation. If chanting with an organ in the Renaissance (either accompanying or alternatim in an organ Mass), chant probably drifted towards quarter-comma meantone. More usually, it probably approximated 5-limit just intonation. And there were probably cranks who held on to Pythagorean tuning because "All intervals derive from 3 just as all creation derives from the Holy Trinity" and berated the monks when their major thirds weren't wide enough.
When would we ask this question? If we're doing a concert or recording of a specific church repertoire, it might be appropriate. Paul McCreesh has done quite a bit of this, and if his solutions are at all accurate, we'd have to say that chant can take an immense amount of abuse. But we have in the US an authentic performance practice for chant in the liturgy : Solesmes-derived text and style, Roman Latin, 12tet-influenced tuning. To use a performance practice differing from that, while it might be interesting, would be inauthentic performance practice; we'd be trying to make a point different from the point of the liturgy.
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I can't tell the difference anyway. For many singers and listeners it all just disappears into the error term.
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☺there were probably cranks who held on to Pythagorean tuning because "All intervals derive from 3 just as all creation derives from the Holy Trinity" and berated the monks when their major thirds weren't wide enough. -
Barbour is an odd duck. It's difficult if not impossible to write a book on tuning without an axe to grind. Barbour's axe is equal temperament. I prefer Ross Duffin's axe in How Equal Temperament Ruined Harmony. Music will tell you which temperament it demands. One could hear Landini in Pythagorean, with dissonant major 3rds resolving to 5ths. but any music based on consonant 3rds (which stylistically defines the Renaissance in music) sounds like CRAP in it. So you're using "something else" for the 15th century. I think you're imposing a different definition of "Middle Ages" on Barbour. The ancient Greeks had a sophisticated tuning technology, which would have been rediscovered by that point.Keyboard instruments would have driven that forward, since in Pythagorean, you're going to have an obnoxiously narrow fifth somewhere ("circle of fifths" is a lie; it's a spiral)
If I were at work, I could probably dig up the first medieval theorist to discuss >3-limit tunings. I read Harry Partch in high school, Love the Ben Johnston quartets and Blackwood's microtonal etudes, and work at a music school where tuning theory is a big thing. But ultimately, it's a rabbit hole. -
My tuppence on the BC/BCE question
Since the reference point doesn't change, the only purpose is to dissociate the Christian calendar from Christ. Many other calendars exist and have existed in the past. They measure from other events, but don't usually measure backwards in time: in the Roman system, I've never seen anything dated "before the founding of the city of Rome". Even in an ancient Hebrew system ("In the year when King Uzziah died") no one measures backward from an event, to the best of my knowledge.
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And there were probably cranks who held on to Pythagorean tuning because "All intervals derive from 3 just as all creation derives from the Holy Trinity" and berated the monks when their major thirds weren't wide enough.
Those cranks are still alive, well, and unfortunately with us. They are still carping about something all the time! LOL.Since the reference point doesn't change, the only purpose is to dissociate the Christian calendar from Christ.
Some scholars say Dennis the LIttle (Dionysius Exiguus) was wrong in his calendar calculations and had the birth of Christ off by perhaps 6 years or so. They say Christ was born near 5 or 6 B.C. So the basis for the calendar system is in error and it is more accurate to say "Common Era" than before Christ.
Others don't want the dating system tied in with Christ, period, and desire a secular dating system.
The east says 2016 is years 7524–7525 of the Byzantine calendar.The year started on 1 September and the year number used an Anno Mundi epoch derived from the Septuagint version of the Bible. It placed the date of creation at 5509 years before the Incarnation, and was characterized by a certain tendency which had already been a tradition among Jews and early Christians to number the years from the foundation of the world. (Latin: Annus Mundi or Ab Origine Mundi— "AM").[note 2] Its year one, the supposed date of creation, was September 1, 5509 BC to August 31, 5508 BC.
So speaketh St. Wiki the All Knowing and Wise. ;-)
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What the wiki doesn’t say is that trained singers vary (i.e. they err) in intonation, the fundamental frequency being placed on average between 8 and 30 cents off the mathematically correct pitch even when singing slow legato. So taking timbre, room acoustics, and group effects into account, what is the practical point of distinguishing vocal tuning systems that differ by such microscopic amounts? It's true that the invention of usable major thirds (an adjustment of 14 cents) does fall within this range of precision, but only barely.
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So the basis for the calendar system is in error and it is more accurate to say "Common Era" than before Christ.
There is no real evidence that the Calendar is wrong as to A.D. 1 / 1 B.C. being the Year Christ was born, they would like it to be wrong but that is only because theyhatedislike Christianity. As Christians we should not allow OUR calendar to be taken from us. I always point out the C in BCE / CE can only stand for Christian.
1. Christians chose the reference date that our calendar counts from.
2. Pope Gregory modified the calendar so it keeps up with Astrononmical time.
As for 'Common' our calendar is Not common to all, other cultures have their own. The only thing common to our calendar for the last 2000 years is Christianity.
If Pagans want a calendar they can do as the Romans did, count from an event... founding of a city etc, or even the birth of Darwin or Richard Dawkins! -
Calendar disputes are never ending. In the east even today, groups are condemning each other and pronouncing each other heretics and apostates over the Gregorian and Julian calendars.
The problem with all calendar systems is that origins such as the creation of the world and the birth of Christ have no verifiable documentation to prove their supposed dates. With the birth of Christ, for example, no one has any real proof as to when exactly it occurred. Using biblical info can get you into a range of years, but not exact dates and times. -
The problem with all calendar systems... [they] have no verifiable documentation...
Well, we know exactly when Thomas Tallis was born. Let's have a kalendar based on that.
Or (you'll love this!), how about AO and PO, for Ante-Ordinariatus and Post-Ordinariatus? Which would make this current year year IV PO. -
I don't spend any time worrying about calendars, but you wouldn't believe the discord and dissension calendars have caused. I have read over a month's worth of posts about the date of Easter and how the Julian calendar more closely follows Nicea. I made the point, which didn't make me very popular, that the bishops of Nicea were men of God, not men of science. Granted, the science was primitive at Nicea in comparison to today. I think I could safely say that dates such as Christmas and Easter are arbitrary dates selected by the Church. There has never been any evidence the events celebrated actually occurred on those dates.
Tallis, you say? He died in 1585 and may have been born around 1505. No one knows his date of birth. You would have to date the Tallis calendar from November 20 or 23, 1585 when he died. No one is sure which date.Thanked by 1M. Jackson Osborn -
What the wiki doesn’t say is that trained singers vary (i.e. they err) in intonation, the fundamental frequency being placed on average between 8 and 30 cents off the mathematically correct pitch even when singing slow legato.
Yep. Even with instruments there are variations. Who's to say the organs in one town tuned to Abelard's ear were even in tune with what Beowulf the Tracker Hacker was doing in another city. Standards and measurements were not as precise before devices were invented that could actually measure pitches. -
But a pair of organ pipes tuned in such a way should at least produce the same perfect fifth for the rest of the day, even if tuned by B the T H, surely.
My point is that two singers holding a perfect fifth will vary the interval by about 30 cents, or even more, while singing it. Physiology. Do organ pipes do that too? -
Do organ pipes do that too?
If the temperature changes enough. I remember having the organ tuned a week before Christmas one year. It sounded great. A day or two before Christmas Eve the temperature dropped by 45 degrees outside. The whole instrument was out of tune for Midnight Mass. Humidity, or lack of it, can make a difference, too.Thanked by 1M. Jackson Osborn -
...temperature dropped...
A good case for year-round temperature control.
Even then, 72 degrees by air-conditioning and the same temperature by heat makes a difference. -
Our temperature control is better than in the past, and the church is now not letting the temperature in the building go below 50 degrees in winter. However, it is an old building with two thermostats in a room 1/2 a city block long. The loft doesn't even have a thermostat and is always warmer than the main floor. We tune the organ at a room temperature of 74 degrees and it holds well for most of the year. A large enough weather event can still mess up tuning.
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Thanks for the book reference, Jeffrey Quick.I prefer Ross Duffin's axe in How Equal Temperament Ruined Harmony. Music will tell you which temperament it demands.
Speaking of Landini, this is a Vocaloid-synthesized version of his Ecco la primavera in Pythagorean tuning:Landini in Pythagorean, with dissonant major 3rds resolving to 5ths.
A Vocaloid-synthesized, Pythagorean-tuned rendition of a 3-part Guillaume de Machaut motet:
There's also a Vocaloid-synthesized version of Perotin's Alleluia Nativitas in Pythagorean tuning:
Thanked by 1Jes -
I reckon Just or Pythagorean are the way to go for chant and some polyphony.
Werkmeister II is good for chorales and hymn singing even some anachronistic modern hymns.
Anglican chants for ordinariate kinds will most likely use werkmeister a bit too.
Equal, ok for the classics onwards except with strings where I would say use just.
As for 70's hymns, I choose to play these a fourth sharp so that nobody requests those hymns again and says they are just too high to sing. -
"... As for 70's hymns, I choose to play these a fourth sharp so that nobody requests those hymns again and says they are just too high to sing. "
Made me laugh!!! -
They tuned by ear, of course.
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In fact, there are patents (e.g., this one) for keyboards or electric organs that automatically correct tuning errors.
I don't believe that the author of this patent has actually solved any of the real problems required for accomplishing something useful. Lots of rambling about intonation, and then the vague idea of a black box which magically solves the problem. How does he intend to re-tune organ pipes on the fly? What kind of real-time calculation is he employing to find the correct pitches to play use moment to moment?
The whole thing is speculative bullsh*t.
....aaaaand it was withdrawn in 1999.
siderant: LET ME EXPLAIN TO YOU WHY PATENTS ARE SO STUPID.....
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Charles
I will credit Michael Joncas for the fact that, when he penned OEW, he did not envision congregations singing the verses, but only the refrain. (As was common in those days, original octavos explained how the songs were intended to be sung.) Because he probably understood that beginning a song on the 7th would result in quite the cauliflower of sound if a congregation sang it.Thanked by 1CharlesW -
Liam, I had heard that account that he never meant it for congregational use. However, I also think he may have cried all the way to the bank over it.
I don't use OEW for any congregational use, only for funerals. It always seemed tasteless to argue over the body of a deceased loved one about music. I just hold my nose and play it. LOL.
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