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Brendan

Posts: 357
Joined: Oct. 30 2010
 

Music quite complicated, actually, s... 

Here the press release: https://www.cam.ac.uk/research/news/pythagoras-was-wrong-there-are-no-universal-musical-harmonies-study-finds

Link to the article in the text.

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  REPORT THIS POST AS INAPPROPRIATE |  Date Mar. 24 2024 10:19:18
 
Ricardo

Posts: 14912
Joined: Dec. 14 2004
From: Washington DC

RE: Music quite complicated, actuall... (in reply to Brendan

Oh gosh, here we go with that out of tune gong bong Javanese stuff again. Very misleading to imply they discovered Pythagoras was “wrong” about something mathematical. “Inharmonic”, great word as if those instruments DONT have basic scientifically driven law of overtones (news flash, that is IMPOSSIBLE). What they really mean is that those instruments are way the F out of tune and yet, some random idiots (4k out of … how many do we really have on this planet?), subjectively “like” it to some degree or other.

Next they seem to be “reinventing the wheel again” with the insinuation that non Western musics use DIFFERENT SCALES , and then finally qualify everything at the end with “in modern Pop music today…” and who really cares what the heck comes after that statement. I love how they deliberately fail to explain the great equalizer AUTOTUNE, that even grandparents know about today and can discern its usage, and how that might have been involved OR NOT in their “great study” which produces 250K of subjective “choices” by 4k tone deaf individuals (I mean were they TESTED first???)

My thought is instead of these types of studies, how about we teach the world to ween itself off of autotune? To recognize melody structure? To keep a freakin beat??

John McLaughlin - “we guitar players spend half of our lives tuning, and the other half playing OUT of tune”.

_____________________________

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  REPORT THIS POST AS INAPPROPRIATE |  Date Mar. 24 2024 14:37:27
 
Morante

 

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RE: Music quite complicated, actuall... (in reply to Brendan

  REPORT THIS POST AS INAPPROPRIATE |  Date Mar. 24 2024 16:33:13
 
Richard Jernigan

Posts: 3434
Joined: Jan. 20 2004
From: Austin, Texas USA

RE: Music quite complicated, actuall... (in reply to Ricardo

On my first trip to Bali in 1994 I was fortunate in my guide and driver, Nyoman Ratep. Not only is Nyoman fluent in English, knowledgeable and congenial, he is a musician in the main gamelan of Bangli.

When the Dutch showed up there were seven rajahs in Bali. Bangli was the capital of one of them. The city has retained its cultural sophistication and reverence for tradition. In Bali the only musician of a gamelan who is paid is the guru. The rest compete for membership and pay dues.

On my second trip to Bali I took a guitar. Nyoman asked me to play for him. After a few classical and flamenco pieces he invited me to a gamelan rehearsal at Bangli.

The guru was teaching the players a new piece in the gong kebyar style, in preparation for the annual island-wide gamelan competition at Denpasar. He played a xylophone-like instrument, the gender ugal, with bronze keys suspended over bamboo resonators. The keys are struck by a hammer made of horn. He played once a phrase of the part for a given section of the orchestra, who replied verbatim, then he moved on to the next orchestral section. Once each section had learned their part, the whole orchestra played the phrase together.

A typical competition composition, the piece was the length and complexity of an early Mozart symphony. Of course the tuned percussion instruments of the gamelan are incapable of modulation. Drama is supplied by changes of melody, decorative counterpoint and rhythm.

The tuning of the modern Balinese gamelan is pelog, demonstrated here.



It uses frequency ratios which do not appear in any Western scale.

Furthermore, the overtones of each note of the tuned metallophones do not follow the Western harmonic series. To experience this, mute your guitar strings with one hand and tap the bridge with the knuckles of the other. The resulting “thud” has no perceptible pitch because its frequency components are not harmonically related. The gamelan’s metallophones do produce identifiable pitches. The reason for this is not perfectly clear, since the mechanism of human pitch perception is the subject of a certain amount of controversy.

The production of gamelan instruments in Bali is pretty well concentrated in a single village. My Javanese friend, guide and translator Paul, and his driver Harry took me to visit. We entered a prosperous compound open to tourists. The members of a village gamelan were there, negotiating the purchase of a new set of instruments with the makers. The small children of the gamelan members played on the workshop floor, and were permitted unfettered access to the instruments. Harry, half-Balinese, translated highlights of the conversation, some of it in Indonesian, some in Balinese.

The instruments of a gamelan constitute a set, due to their intentional slight mutual mistuning. The degree of mistuning is negotiated between the makers and the players. Slight mistuning produces slow beats in the sound of the ensemble, heard as gentle and peaceful. A little greater degree of mistuning produces an ensemble sound with more rapid beats, heard as more brilliant and assertive. The shimmering beats are intentional and regarded as essential.

To summarize: Balinese scales (and Indonesian scales in general) use pitches which never appear in any version of Western scales. The overtones of gamelan instruments do not follow the harmonic series. Consequently the sensation of consonance differs from Western standards. Any mistuning among instruments is slight, intentional, and specified in the contract for a set of instruments.



RNJ

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  REPORT THIS POST AS INAPPROPRIATE |  Date Mar. 25 2024 1:44:45
 
Ricardo

Posts: 14912
Joined: Dec. 14 2004
From: Washington DC

RE: Music quite complicated, actuall... (in reply to Richard Jernigan

There is no “Western Harmonic series”. There is the nature one which is universal, and then there are various tuning systems that can exploit certain harmonics, eliminate them by canceling out of phase, or “stretching” which is off setting some higher harmonics that are usually barely perceptible anyways, etc., such as in equal temp electric pianos. There is nothing especially unique about chameleon gong bong vs other MODAL musics that exploit situations related to Pythagorean concept of overtones and the constructed scales. World music (modal, all of them pretty much) that don’t change keys, tend to apply more than 12 notes to the octave. In Asia some have 60, in Turkey we saw 53, in India 22 sruti, etc. From those, the fundamental view of ALL music systems appears to be some 7 note “scale” that has ballpark pitches with alternates that some guru that has taken years to distinguish teaches others. In some systems not all 7 are used in musical pieces or improvisations, it depends on the tradition and which notes are to be avoided (tritone type interval is one that leaves us with the happy Asian pentatonics and such).

https://en.wikipedia.org/wiki/Inharmonicity

I am glad you like the gong bong guys. They have been mentioned before and I am sure they will be in the future. But I can’t help but feel this type of “science” in this study that utilized their tradition as “exemplary” of their point (that Pythagoras was “wrong” about something musically speaking) of some random small study about perception, is yet another case of vilifying Western white people music for no good reason. Estebanana recently taught us how to “knock” on the bridge and get an F#…the “A” that I hear when doing so is apparently and illusion of the back vibrating (I am taking his word as a builder). In the end a guitar, western tuned, seems to have just as much “inharmonicity” going on as gong bong, or more perhaps. Also, Estebanana pointed me to the analysis of Bermudo’s vihuela tuning, which was essentially glueing the frets in (as close as humanly possible without a digital tuner) at 12-tone equal temperament. In otherwords, he was advocating autotune for all the Katy Perry’s and Taylor Swifts of 1555. I was surprised by the date, since they still argue whether Bach wanted Equal Temp, so I did a deeper dive on the subject, and turns out some guys were secretly traversing the circle of 5ths…secret out of fear of burning at the stake and all that. I get Western music had its dark side, however, reinventing the wheel is not good science IMO.

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  REPORT THIS POST AS INAPPROPRIATE |  Date Mar. 26 2024 11:01:00
 
Piwin

 

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  REPORT THIS POST AS INAPPROPRIATE |  Date Mar. 26 2024 17:56:14
 
Richard Jernigan

Posts: 3434
Joined: Jan. 20 2004
From: Austin, Texas USA

RE: Music quite complicated, actuall... (in reply to Ricardo

quote:

ORIGINAL: Ricardo

There is no “Western Harmonic series”. There is the nature one which is universal, and then there are various tuning systems that can exploit certain harmonics, eliminate them by canceling out of phase, or “stretching” which is off setting some higher harmonics that are usually barely perceptible anyways, etc., such as in equal temp electric pianos. There is nothing especially unique about chameleon gong bong vs other MODAL musics that exploit situations related to Pythagorean concept of overtones and the constructed scales.


The news release linked by Brendan suffers from journalistic exaggeration. It claims the paper in Nature Communications shows that Pythagoras was wrong. The paper does no such thing. "Pythagoras" appears only once in the Nature paper. He is credited with a theory of consonance. Further theories are attributed to such famous names as Helmholz and Rameau, and to twenty-odd other researchers in the bibliography.

The paper addresses (at great length) the question whether the timbres of the individual tones in a chord influences the sensation of consonance.

The overtones of percussion instruments such as church bells and Indonesian metallophones do not follow the series of 2, 3, 4,...times the fundamental. A mathematical treatment of vibrating bodies via Fredholm integral equations is contained in the first three chapters of "Methods of Mathematical Physics" by Courant and Hilbert.

Over the centuries the design of English church bells has evolved to give clearer sensations of pitch and consonance. Saint Mary's church in Somerleyton, Suffolk, England has a full octave of bells, funded by the patrons of the church over a period of two centuries. It is one of the oldest full peals still existent in the country. The youngest bell is dated 1421. I first heard them, up close and rung for nearly an hour, by a crew of change ringers* on an Easter Sunday in the 1970s. I was struck by how different they sounded from more modern bells, and by the dissonant hum as they continued to vibrate in the intervals between "changes".

Here is a diagram of slendro and pegog tuning compared to the 12-tone equally tempered scale. 100 cents equals a half-step.

The 12-tone equally tempered scale only approximates the integral ratios of just temperament based on the harmonic series, but it's pretty close. For example a fifth in the equally tempered scale is 700 cents. in just temperament a fifth is 3/2 times the fundamental=701.9555 cents.

The closest note to 700 cents in either slendro or pegog is a lot further off than 2 cents.

RNJ



*"Change ringing" is the practice of ringing a set of bells in varying sequences. Often a set of changes begins and ends with the bells rung in ascending or descending pitch order. There are more the 40,000 possible sequences for ringing all the bells in an octave without repeating one, so the ringers must agree on a pattern for changing the sequence and practice it.

Change ringing crews are notoriously independent. They are one of the few English institutions fully resistant to the class system. A typical crew has members from a wide range of social backgounds. You can't hire them. All you can do for a special occasion is to announce that change ringers are wanted, and there will be food and a barrel of beer afterward.

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  REPORT THIS POST AS INAPPROPRIATE |  Date Mar. 26 2024 23:47:19
 
Ricardo

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Joined: Dec. 14 2004
From: Washington DC

RE: Music quite complicated, actuall... (in reply to Richard Jernigan

quote:

The paper does no such thing. "Pythagoras" appears only once in the Nature paper. He is credited with a theory of consonance. Further theories are attributed to such famous names as Helmholz and Rameau, and to twenty-odd other researchers in the bibliography.

The paper addresses (at great length) the question whether the timbres of the individual tones in a chord influences the sensation of consonance.


Ok, fair enough, regarding headline news fails again and that there is no insinuation that Pythagoras was wrong about harmony. But the issue I have is with “sensation of consonance”, vs “mathematic reality of consonance and dissonance”. By that I mean this: first of all Bells are not MUSIC. Sometimes they chime a short melody but the function is to alert humans to something in the vicinity that they can be heard within. Hence “Alarm” as a concept tied to sound. If dissonance is desired in a MUSICAL system, to the point that a specific rhythm beat expression between two intervals that are off is desired, and it takes a guru years to internalize that exact rhythm such that instruments can be designed and tuned consistently, well, that does not change the fact it is still DISSONANCE. The question becomes to what degree is dissonance giving a “pleasure” response versus a distaste for the sound. It is simply not fair to apply a test to average joe in this case. It removes what the guru function is and what art is truly about, in hopes to level the playing field of what basic math implies.

IN the book by Danilou, the guy teaches us a lot about modal musics of the globe, but is clearly biased as he puts down Western traditions such as not caring about sharp thirds or using exaggerated operatic vibrato. As if Western people don’t gravitate flat from EQ temp like every other human music on earth that has NO REFERENCE or training to avoid it. It all starts from the math of the one and only overtone series of nature.

I don’t need to know that some interval such as the 5th is off in either EQ Temp, or gong bong, I can hear the beats just as well as when I hear some “in between” Persian Santur note doesn’t seat on a guitar or piano. If you say that these two notes need to be “off” such that they pulse at 8th note = 120 bpm, fine. I get that it is deliberate. It is still OUT OF TUNE.

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  REPORT THIS POST AS INAPPROPRIATE |  Date Mar. 27 2024 11:02:08
 
Richard Jernigan

Posts: 3434
Joined: Jan. 20 2004
From: Austin, Texas USA

RE: Music quite complicated, actuall... (in reply to Ricardo

Why would the patrons of Saint Mary's (fathers, sons, grandsons, etc.) have gone to the rare trouble and expense of equipping the church with a full octave of bells, if the purpose was not significantly musical?

quote:

it takes a guru years to internalize that exact rhythm such that instruments can be designed and tuned consistently, well, that does not change the fact it is still DISSONANCE. The question becomes to what degree is dissonance giving a “pleasure” response versus a distaste for the sound. It is simply not fair to apply a test to average joe in this case.


During the 15 years or so that I travelled to Bali regularly the gong kebyar style of "classical" gamelan was wildly popular. Elements of it spilled over into Balinese/Javanese pop. The average Balinese Joe really dug it.

The harmonic series in nature:

For my fifteenth birthday my parents generously gave me a "Stradivarius" model trumpet by Vincent Bach of Mount Vernon, New York. It was pretty much the standard model in the USA for symphony orchestra players, and the one recommended by my teacher, the Principal Trumpet of the National Symphony of Washington, DC. It was expensive.

I was tickled to death. But after a few weeks of playing I became convinced that one of the "open" notes (no valves depressed) was a little flat. It was the second E above middle C. In theory the open tones of a brass instrument follow the harmonic series. Its frequency should have been 5 times that of the C below middle C, but it was just a little flat.

The open tones of the Getzen student model cornet I had played since I was nine years old were pretty accurately in tune. The E and its valved relatives on the Bach could be "lipped" in tune, but I was not used to it.

I mentioned it to my teacher. He tried out the horn and agreed. The U.S. Air Force Band was based on Bolling Air Force Base which Dad commanded, and they played Bach instruments. I asked the band's First Sergeant to bring up the issue with Bach, who said that the horn should be returned.

The horn came back in a week. It was the same one, since the serial number agreed, but now all the open tones were accurately in tune. I now regret failing to ask how the change was made, but I was just a 15-year old kid. The instrument was now a complete joy to play.

Now comes the question: Was the horn's overtone series "unnatural" in its original state? After all, it was a physcal object. You could hold it in your hands. It produced sounds. The sounds just didn't follow precisely the harmonic series. Did the horn become "natural" after Bach's artisan had modified it?

Few are more cautious about assigning a mathematical concept like the harmonic series to "Nature", than someone like me, trained in mathematics by experts.

Pythagorean Harmony:

My trumpet teacher taught his students to play in tune in two main ways. One was to play to a strobe tuner. The other was to play in ensembles.

I have particularly fond memories of the wind ensemble music of Giovanni Gabrieli, the organist and master of music at the Basilica San Marco in Venice at the beginning of the 17th century. Gabrieli's instruments lacked the brilliance and power of a modern brass ensemble, but his music is ideally suited to today's horns. With a good tuba to provide a solid foundation, there is physical feedback among all the players. When the tuba, trombones, French horns and trumpets all lock into a chord in frequency and phase, it makes the hair stand up on the back of your neck. It's as close as you can get to Pythagorean harmony. It's playing IN TUNE.

I had the privilege of playing Gabrieli in the National Cathedral on festive occasions. The music was written for antiphonal groups distributed in various parts of the Basilica San Marco. We played in the balconies above the crossing, where the transepts intersect the nave. The three brass choirs were led by Scimonelli, the Navy Band's cornet soloist; Luke Short, the Navy First Trumpet (who retired from the Navy and took the Principal chair at Boston); and my teacher, Lloyd Geisler (first president of the International Trumpeters' Guild). Scimonelli used to joke that when we started playing the congregation looked up startled, fearing Judgment Day had arrived.

Here's Gabrieli's "Sonata Pian e Forte." The virtuosi on this recording consistently play in tune in the pian (quiet) parts. It's in the fortes (first one at 1:21) where the phase locking effect occurs. Imagine the soft parts wafting through the vastness of a cathedral, not especially obtrusive, then WHAMMO.



When players are trained in the European classical tradition they are shamed when told they are playing out of tune. "Out of tune" has both an objective meaning and a value judgment connotation. "In tune" is good, "out of tune" is bad.

But can anyone here say that Muddy Waters' and Little Walter's pitch bending in "Louisana Blues" is bad?



However I remember some of my youthful symphonic friends asking me how I could hang around with my jazz buddies, who "played out of tune." I would reply that in five seconds you could tell it was Miles Davis, Louis Armstrong, Dizzy Gillespie, Charlie Shavers or Clifford Brown, and they were each playing precisely the notes they wanted to.

I kind of get the idea that Ricardo doesn't much like Balinese gamelan. Maybe they sound bad to his classical and flamenco trained ear. "Gong bong" sounds a bit negative. That's OK with me--I don't mind. De gustibus...etc.

But I enjoy it. For me that validates its departure from the norms to which I was trained. And it makes me consider how much those norms have been culturally determined, compared to their basis in "Nature."

RNJ
  REPORT THIS POST AS INAPPROPRIATE |  Date Mar. 27 2024 21:51:40
 
Brendan

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Joined: Oct. 30 2010
 

RE: Music quite complicated, actuall... (in reply to Richard Jernigan

That went well. I don’t know anything about the indigenous music of Bali, but I do know a bit about academic publication. I can guarantee that the scientists who wrote the paper had nothing to do with the press release. Big Canonical Name Proved Wrong! Is a standard publicity trope. There are books out there called “Descartes’ Error” and “Galileo’s Error”. I duelled with a great dead intellect and won! Says Dr Hudat of Nope University. I thought the misdescription of the science in the press release was unusually hilarious in this case.

I advise against declaring that bell-ringing isn’t really music. Partly because ‘music’ is exactly the sort of word that resists definition, and partly because bell-ringers are well muscled and move in groups.

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  REPORT THIS POST AS INAPPROPRIATE |  Date Mar. 28 2024 9:57:49
 
Norman Paul Kliman

 

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Joined: Dec. 5 2023
 

RE: Music quite complicated, actuall... (in reply to Brendan

quote:

bell-ringers are well muscled and move in groups.


Yeah, mess with those guys and you’ll get your bell rung.

That version of Louisiana Blues has been a favorite of mine since the first time I heard it (along with Still a Fool). Works real well in G in standard tuning. I play it Chet-Atkins style as a medley with Spike Driver Blues by John Hurt and She's a Woman by The Beatles.
  REPORT THIS POST AS INAPPROPRIATE |  Date Mar. 28 2024 10:40:40
 
Ricardo

Posts: 14912
Joined: Dec. 14 2004
From: Washington DC

RE: Music quite complicated, actuall... (in reply to Brendan

One of the authors is referenced (Harrison) from older papers. But this vid gives a perfect background for the topic:



And he discusses Gamelan in detail, pay attention to 12:17, how off ET is from Harmonic series, his explanation at 14:00 that in Gamelan you in fact have to couple proper tuned harmonic instruments to ones that are as claimed in general HERE and in paper, as being “off” from the series, and his conclusion, essentially as I was saying all along, that Gamelan dissonance is fudged pretty much EXACTLY LIKE ET is fudged relative to Pythogoras.



So all that is “new” is the realization that some world music that is DIFFERENT than ET is “enjoyable”.

To be fair to the article posted, since I took time to check it out, the “Pythagoras is wrong” comes from this data set, which is splitting hairs at the intervals of “major 3rd” and “major 6th”, in other words, zoomed in, to see if JI is preferred, as it should be to ET, but they see small dips in the precise location where Overtones are present in both notes, vs Pure notes that smear across. The implication that there should be peaks right on the line of JI, instead of two peaks on either side (as per harmonicity model vs interference model).



However, they don’t split hairs between the two groups of trained vs un trained musical ears, where I personally see important divergence between the two groups (red lines) at the exact same intervals, such that they generalize that the difference is trivial (highlighted parts).



The fact that trained vs untrained ears can discern “something” in this area is important when zooming in on the issue of JI vs ET with a GENERAL group. For example some ears are locked into that dip and know the thing intuitively, others used to a sharp Major 3rd prefer a bit sharp of harmonic JI (remember they are not using a fundamental with Harm series then pure tone at the Mj3, rather, both notes have harmonics hence complexity. Some ears therefore can notice and provide the data for the little dip right at JI because their ear can ignore the higher partial clash in favore of the upper note’s fundamental being importantly aligned with the LOWER note’s partial). The explanation for peak BELOW JI for me is that people with no conception of minor third vs major third might be hearing a consonant sharpened MINOR THIRD/MINOR 6TH. To explain the wacky situation of the Octave, again the interference situation described in the first video I posted here has examples.

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  REPORT THIS POST AS INAPPROPRIATE |  Date Mar. 29 2024 19:38:43
 
Richard Jernigan

Posts: 3434
Joined: Jan. 20 2004
From: Austin, Texas USA

RE: Music quite complicated, actuall... (in reply to Ricardo

Thanks a lot for the two videos. They summarize the facts succinctly and present some attractive theories.

I am amused by the video presenters' assertion that the harmonic series is present in "nature" and "universal," whereupon he fires up his electronic piano to give examples.

I am not saying that the electronic piano is not a natural object, though it only arrived in the 20th century. Just pointing out that the harmonic series developed and persisted as a mathematical theory, during a very long period when musical instruments only approximated the harmonic spectrum.

It's well known that the the higher the overtone of a physical string, the sharper it is relative to the harmonic series. This is due to the string's resistance to bending. The mathematical theory of the "ideal" string assumes no bending resistance. Furthermore the spectra of actual wind instruments only approximate the harmonic series.

I don't know how accurately the pipes of the more neutral sounding late medieval organ stops may reproduce the harmonic spectrum. As far as I know they may be a practical exception to the rule that only modern electronic instruments can accurately produce the harmonic spectrum.

And of course, bells, gongs, metallophones, Central American marimbas, and the like are strongly inharmonic, but can produce identifiable pitches and consonant chords. Musical theory researchers are no doubt grateful for their existence.

RNJ
  REPORT THIS POST AS INAPPROPRIATE |  Date Mar. 30 2024 23:15:27
 
Ricardo

Posts: 14912
Joined: Dec. 14 2004
From: Washington DC

RE: Music quite complicated, actuall... (in reply to Richard Jernigan

quote:

I am not saying that the electronic piano is not a natural object, though it only arrived in the 20th century. Just pointing out that the harmonic series developed and persisted as a mathematical theory, during a very long period when musical instruments only approximated the harmonic spectrum.


Well, I feel you might be conflating TUNING SYSTEM with natural overtone harmonics (Semantics?). That means, any SINGLE tone generated has the overtone series present (unless that tone is mixing with some other sound not meant to have been played, or if certain partials are deliberately shifted or cancelled which is “inharmonicity”, but mainly would refer to an INSTRUMENT, not a single Fundamental tone), and when an instrument is constructed, it will have more than ONE fundamental tone (as many notes as can be played), and therefore as many harmonic series groups making a complex dissonance.

The idea is you first ask “WHAT is THE MAIN Fundamental tone?” such that you can say what the other pitches will be RELATIVE TO THAT. Will they be more or less in line with the NATURAL partials that occur above THE MAIN fundamental? (Mainly the first 5 as they ring louder and variations will be noticed). By variations I mean then a new pitch is generated RELATIVE TO THE FUNDAMENTAL, it will contain its OWN fundamental and partials. Regardless whether the fundamental of the new pitch is DEAD ON to the main fundamental’s partial OR NOT, you have now created a “tuning system”. And therefore must stop talking about “harmonic series” being inherent to the instrument design. A piano or flute or any fixed instrument is not based on any “harmonic series”. It has as many harmonic series groups as it has NOTES that can be produced. And perhaps more if it also has resonance based on its physical material which deviates from the played notes.

If the guy in the video wanted to use his warbling voice (a “natural” instrument) overdubbed as two tracks, to visualize harmonic series and then stretch the partials etc., understand that a warble has MULTIPLE HARMONIC SERIES SETS all clashing in a complex manner. Because the fundamental itself is moving slightly. So using a digitized sound is ideal. Keyboard didn’t matter, he could have used the keypad of the computer to generate the tone. The idea was the tone is fixed and we can see its partials, then a second tone can have its fundamental align with a partial or not.

This issue, of TUNING SYSTEM, we learned when we discussed Makkam, that “phrygian” was not actually going on with that one flamenco scale approximation, because the INSTRUMENT example that was given, was tuned based on ONE Makkam called RAST. Meaning, if we think C major is RAST, it had something closer to a JI tuned C major, that the E above could NOT in any way function as a PHRYGIAN TONIC, because it was TUNED relative to a pitch LOWER than it. And must have been sung or heard as “flat”, in other words, vs what we think of a modal Phrygian tonic. This is not trivial, but an extremely important distinction. It meant that the Phrygian approximation is not “strong” it is a weak “harmony” above a more fundamental strong tone, generated by the way the instrument itself might be designed, and the human voice must fall in line with that concept.

So when you say “harmonic series was being developed” what you most likely mean is WESTERN TUNING SYSTEM was being developed, that lead eventually to an electric keyboard, which has the luxury of not “approximating” anything, but manipulating digitally exact tuning systems globally, and much more when stripped into its partials, etc. Vs. “Harmonic series” which is a naturally occurring reality.

_____________________________

CD's and transcriptions available here:
www.ricardomarlow.com
  REPORT THIS POST AS INAPPROPRIATE |  Date Mar. 31 2024 17:15:52
 
Richard Jernigan

Posts: 3434
Joined: Jan. 20 2004
From: Austin, Texas USA

RE: Music quite complicated, actuall... (in reply to Ricardo

No.

I mean that for centuries, whenever you sounded a single note on a musical instrument, its overtones did not precisely follow the harmonic series.

This is still true today for non-electronic musical instruments.

For example, on the guitar, with a perfectly uniform string, the frequencies of the overtones ezceed those of the harmonic series, more and more for higher overtones. This is due to the string's resistance to bending. This is the same phenomenon that audibly stretches the spectrum of a piano's individual bass notes.It's called inharmonicity of individual notes.

(However, perfectly uniform guitar strings are not guaranteed. The D'Addario EJ-45s presently on my Abel Garcia classical yield a 12th fret first string "harmonic" that is at least 2 cents flat, according to a cheap headstock tuner. The string is not uniform. The same brand on the Romanillos gives a first string 12th fret harmonic that is equal to twice the fundamental, within less than one cent. I looked around and found my Seiko tuner that reads in cents with an analog needle. It agrees with the headstock tuner.)

Bending resistance is the reason that bass strings on a guitar are metal wire wound onto a core of multiple very thin strands of fiber. The tolerable limit of stiffness and the resulting inharmonicity is reached by the thick solid 3rd string. The construction of the bass strings is more flexible than a solid string would be, thus reducing inharmonicity to a tolerable level.

Savarez may still make string sets with second and third strings of nylon wound over a nylon core. These afford more mass, higher tension and greater loudness, without excessive inharmonicity. D'Addario makes greenish-brown third strings which are denser than nylon--and stiffer. These also afford higher tension and greater loudness, but I don't like their tone because of their inharmonicity.

The overtones of wind instruments are only approximately harmonic. On brass instruments you actually play the instrument's overtones. Watch a symphony trumpet player. On different notes he nods his head very slighly up or down. The horn deviates a little bit from the horizontal. The player is "lipping" the notes into the desired pitch.

When the trumpeter plays fortissimo the clashing overtones give the sound its characterisctic brilliance. When the whole brass section plays fortissimo chords the resulting brilliance is greater, even if the different players' fundamentals are locked into the harmonic series.

A good orchestra's strings play closer to just intonation than equal temperament, so the wind players have to compensate not only for their equally tempered tuning, but also for their inharmonicity.

Pitched percussion instruments are the most inharmonic. Throughout southern Mexico and Central America you hear marimbas of different sonorities, though with about the same pitches. Marimbas are built with resonators under the wooden keys. Different marimbas may have differently shaped resonators or other variations in construction.

The fundamental of a struck marimba key excites the resonator under it, providing overtones that are closer to the harmonic series, while the overtones of the struck key may be nowhere near harmonic. Some marimbas sound "sweeter'" than others, perhaps because the resonators may be louder.

RNJ
  REPORT THIS POST AS INAPPROPRIATE |  Date Mar. 31 2024 23:44:33
 
Ricardo

Posts: 14912
Joined: Dec. 14 2004
From: Washington DC

RE: Music quite complicated, actuall... (in reply to Richard Jernigan

No disagreement with anything you wrote. Except that you are describing “centuries” of “Western Tuning system” and its instruments. 470 years ago Bermudo wanted frets glued in a hair off of ET. Meanwhile in the Middle East a flute constructed TODAY (not centuries ago), that is tuned to RAST, can only play notes that align with derivative Makkams (meaning a small sub set of the 53 available pitches in the system). They have different flutes constructed for this reason (only one ‘key” can be used at a time). Perhaps deliberate bending or “lipping” can change some notes other than the fundamental, but a totally different purpose than blending orchestral instruments. In other words, they don’t use “ficta” notes or accidentals in the manner the WEST uses them to change key (modulate). Modulation was already occurring 470 years ago in the WEST, with or with out instruments (meaning the voice could wander around the yet undescribed circle of 5ths, however the thirds and such pull a capella groups FLAT of starting pitch, even today, if no reference is guiding the naked voices).

The only other issue is that as the guy in the video points out, the higher partials don’t matter as much as those first 5 or so, to human ears (not the superhuman ones that can tell a Blanca from a negra blind folded haha!). So any instrument that has overtones misaligned with the harmonic series is doing so as part of its inherent tuning system based on the tradition of music it will likely be used for. And physical strings, like the human voice “warbles” if and when struck hard, which is simply shifting those harmonics (partials) up and down as the fundamental itself settles into a ball park frequency of its own. Back to Gamelan, as I pointed out the guy names instruments that are tuned “harmonically”, including the human voice (we tune vowels and formants which resonate in the skull and affect what harmonics are emphasized in the series, not getting into vibrato), an inevitable fact of “nature”, which are juxtaposed against the deliberately “inharmonic” metalaphone INSTRUMENTS, as their tradition has developed on purpose. It is those lower partials that are “a problem” for musicians like me, and beating off by design. But I have the same “problem” with ET and lots of other tuning systems.

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  REPORT THIS POST AS INAPPROPRIATE |  Date Apr. 1 2024 17:31:15
 
Richard Jernigan

Posts: 3434
Joined: Jan. 20 2004
From: Austin, Texas USA

RE: Music quite complicated, actuall... (in reply to Ricardo

quote:

No disagreement with anything you wrote. Except that you are describing “centuries” of “Western Tuning system” and its instruments. 470 years ago Bermudo wanted frets glued in a hair off of ET.


Not entirely. Up through the 6th paragraph I was writing only of the overtones of a single note, regardless of the tuning system that selected its fundamental.

Then for examples of the resulting effects, I began to involve European scales.

RNJ
  REPORT THIS POST AS INAPPROPRIATE |  Date Apr. 1 2024 20:29:49
 
Piwin

Posts: 3565
Joined: Feb. 9 2016
 

RE: Music quite complicated, actuall... (in reply to Ricardo

quote:

beating off by design.


"Your honor, I admit that I was beating off in public, but I humbly submit to the court that it was accidental, not by design."

Sorry, couldn't resist.

_____________________________

"Anything you do can be fixed. What you cannot fix is the perfection of a blank page. What you cannot fix is that pristine, unsullied whiteness of a screen or a page with nothing on it—because there’s nothing there to fix."
  REPORT THIS POST AS INAPPROPRIATE |  Date Apr. 2 2024 5:39:04
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