Royal Society Introductory Lecture on the Structure of Music
Sept 19, 2017 17:13:31 GMT -6
King John, Ián B. Anglatzarâ, and 4 more like this
Post by Ián Tamorán S.H. on Sept 19, 2017 17:13:31 GMT -6
Does Music Count?
Outside of Talossa – and real life happens there too – I recently gave a talk on “Does Music Count?”
“Count” means a lot of different things in English – a degree of nobility, one of the primary processes of arithmetic, being of importance or relevance, a charge within a legal indictment, (+on) to rely upon, (+out) to exclude, and more. My personal training is that of mathematics, so my audience there expected figures and measurements – and perhaps you do too. But what I am doing in this essay is to go through some of the technical meaning of “count” to get to the real, base meaning – the important meaning.
Albert Einstein was a musician – a violinist – who loved particularly Mozart and Bach. You can find files on the internet which claim to be recordings of Einstein playing the violin – alas, they are fakes – there are no real recordings of Einstein’s playing. Now there was a man who lived a lot of his life around mathematics, but mathematics was not at the core of his music appreciation. He was once asked how an audience should approach a performance of a work by Bach, and his answer was “Just listen, just listen.”
Organ pipes of different lengths produce different notes. There is a non-simple relationship between the note sounded and the length of the pipe – and don’t believe those who say that relationship is simple! Yes, in the simplified theoretical world it’s a simple ratio between the length and the pitch – twice the length of pipe lowers the pitch by an octave – but in the real physical world there are many other things that affect the pitch – pipe diameter in relation to length, pipe cross section, wind pressure, and so on. It’s a complicated relationship, with much mathematics covering many details.
Strings of different lengths produce different notes: we all know about the low notes of the double base, and the high notes of the violin. We also known about “stopping” the strings – using fingers to make shorter that part of the string which is sounding. There there are two bits of mathematics – a simple bit (phew!) which covers the sounding of harmonics (ask any violinist what I mean by that – see the examples); and a complicated one (didn’t you just know it!) that describes the relationship of pitch to the length of the stopped string. Oh, and have I forgotten to mention the temperature, and the substances of which the strings are made, and the regularity of mass per unit length down the string, and the geometry of the string’s contact with the bridge (the string ends)? See en.wikipedia.org/wiki/String_instrument for an overview of the simple mathematics linking string length to pitch. For the complex mathematics, see for example reference en.wikipedia.org/wiki/Bridge_(instrument) which points out that the bridge at the end of a string flexes during the string’s vibration: the degree of flexing will be related not only to the energy coming from the string, but to the variable stiffness of the bridge itself – stiffness is related to pitch, so that a string of half the length does not necessarily produce a pitch exactly one octave higher. The Britannica reference www.britannica.com/art/stringed-instrument makes it even more clear that string length is not quite it appears to be at first sight).
So there’s lots of mathematics there – lots of counting – but is that what the musician or the listener thinks about?
There are many, many ways of making musical sounds: singing, whistling, stamping, using instruments (or many sorts), Konnakkol (“Indian Scat singing”), clapping... an almost countless number of ways. Is enumerating these part of what attracts the composer or the listener?
There are rhythms. I have pointed out, in a previous presentation, some of the complexities of rhythm that are used round the world. Both simple and complex rhythmic patterns exist in music everywhere. I can give you pointers (see later) to music that you may perhaps already know, that has complex patterns – again, see the list of references later.
But are the mathematical complexities of rhythm at the core of the composer’s thinking or the listener’s appreciation?
Notes can be chosen mathematically. I do not mean just in music from the twentieth and twenty-first centuries that relies upon the digits of π (pi) or the pattern of prime numbers, or the Fibonacci sequence (though I have one example of that!). No, I mean the patterns such as you find in J.S.Bach, or the inter-note relationships in fugues and canons or madrigals (Carlo Gesualdo is a good example – now there was a musician with an interesting life!).
But are those mathematical patterns what first attracts and entices the listener?
There are computers. Music has been written using computers as an aid, performed by computers, performed with help from computers, and even written by computers – I have examples of all of those here. The influence of computers upon the production of music is growing rapidly, and much of that influence is clearly visible – for example, there is computer-written music used in the film series of “Pirates of the Caribbean”, and in “Dr. Who”. We have heard music put together from “found sounds” - music built up from sounds discovered in the real world (Philip Glass is an example) and modified sounds (see en.wikipedia.org/wiki/Noise_music). The music written by Eric Whitacre is often performed with computer assistance (for example, Sleep and Lux Arumque).
Lengths of pipes, length of strings, types of sound, patterns of rhythm, choice of notes, compositional computation – do any of these really count?
No, they do not.
What really counts is the music itself, using voice and dance and instruments and melody; Music using computers and recordings and technology; Music with tune and rhythm; Music in joy and in sorrow, alone and with others. Melody, rhythm, voice, dance, instruments, music made, music found and – above all – music heard.
The inspiration of Music is held in how it captures your attention, how it makes you feel, how it brings delight in both joy and sorrow, how it uplifts the spirits, how it can fill the whole world with harmony. How it is a joyful noise.
Music counts. Not in maths, not in physics, not in knowledge of obscure things, but in lots of real ways: in beauty, in fellowship, in delight, outreach, history, art, rhythms, communication, melody, thought, contemplation – and much more. We make music because it really counts – it is of importance in what it brings and what it allows us to express.
Music counts.
Some external references:
Einstein: Albert Einstein Plays Violin - Mozart Sonata in B-flat KV378;
Organ pipes:
The Mighty Wurlitzer theatre organ pipes, Nethercutt Collection:
Organ_pipe_types
Lengths of strings:
See en.wikipedia.org/wiki/String_instrument for an overview of the simple mathematics linking string length to pitch.
For more complex mathematics, see for example reference en.wikipedia.org/wiki/Bridge_(instrument) which points out that the bridge at the end of a string flexes during the string’s vibration: the degree of flexing will be related not only to the energy coming from the string, but to the variable stiffness of the bridge itself – stiffness is related to pitch, so that a string of half the length does not necessarily produce a pitch exactly one octave higher. The Britannica reference www.britannica.com/art/stringed-instrument makes it even more clear that string length is not quite it appears to be at first sight).
Harmonics:
Violin harmonics:
Guitar harmonics:
Used in performance of real music:
… the hilarious
(Paganini would be both laughing and crying!). This particular piece is performed very largely using the harmonic series on the violin, and fewer stopped notes.
Sources of Sound:
Clapping:
Clapping Music for 5 Performers (by Santi Carcasona):
Epic Patty Cake Songs:
and
Longer list at www.youtube.com/playlist?list=PLpH5E8UDofiPZPKae4OinC5EwqipojAnF
Steve Reich - Clapping Music (Nonesuch staff performance):
This is a seminal composition, from which the 12-beat pattern is taken for many other clapping pieces (in, for example, the Santi Carcasona).
Konnakkol:
V Shivapriya BR Somashekar Jois Konnakol Duet MadRasana Unplugged Season 03 Episode 01
Shivapriya is a wonderfully talented performer, and I for one shall be following her artistic development
Fibonacci Konnakol (Konnakol from the Fibonacci series of numbers – the skill and speed is astounding):
Other instruments:
Percussion with chopped onions y trechas:
Throat Singing:
Female Mongolian Throat Singer:
This singer goes on to produce two notes simultaneously, which is a technique instructively and wonderfully demonstrated at
,
and carried on in the series from www.youtube.com/results?search_query=two+notes+same+time
Rhythms:
5 beat: Tchaikovsky Symphony No. 6 Pathetique Ⅱ- Allegro con grazia
Holst Mars
Maurice Ravel 'Daphnis et Chloe' (complete version) in HD (from 51:18 onwards)
7 beat: Nick Drake Riverman
Pink Floyd Money
11 beat: 11 beats etc Frank Zappa - Keep it Greasy (live) (Not very good quality)
A jam to a 19/16 part of that piece:
The Grateful Dead - The Eleven 82368
Pictures at an Exhibition, Promenade (part 1)
13 beat: 13 beat Tala - Indian Rhythms
For 15, 17, 19 beats (and others) you can look at music from Bulgaria, Romania, Serbia and other countries in that region.
Mathematical choice:
Gesualdo: Carlo Gesualdo - Madrigals, Book 6:
J.S.Bach: Bach - Choral Prelude ''Wachet auf, ruft uns die Stimme'' BWV 645:
Computers and technology:
Using:
Eurorack modular phonogene jam 15
Opanska; (mp3 www.kingdomoftalossa.net/tamoran/10_Opanska_US.mp3 and pdf www.kingdomoftalossa.net/tamoran/10_Opanska_US.mp3)
Leonard Rosenman - Fantastic Voyage (Main Title - Sound Effects Suite)
Performed by:
Tricia (mp3 www.kingdomoftalossa.net/tamoran/03_Tricia_US.mp3 and pdf www.kingdomoftalossa.net/tamoran/03_Tricia_US.pdf)
Polegna (this is also in 11 beat time) (mp3 www.kingdomoftalossa.net/tamoran/15_Polegna_e_Todoara_US.mp3 and pdf www.kingdomoftalossa.net/tamoran/15_Polegna_e_Todoara_US.pdf)
(For more music by Ian Kelly/Iàn Tamoràn see benkellyarts.com/blog/?page_id=234)
Performed using:
Didn’t My Lord Deliver Daniel - 11 singers from 8 countries - A Cappella choir
Eric Whitacre - Eric Whitacre's Virtual Choir 2.0, 'Sleep'
Eric Whitacre's Virtual Choir - 'Lux Aurumque'
This is a carol, or a Christmas meditation, with words in Latin:
Lux Aurumque
Lux calida, gravisque
Pura velat aurum et
canunt angeli molliter
modo natum
Light and gold
Light, warm and heavy
as pure gold, and the
angels sing softly to the
new-born baby.
Written by:
AIVA - 'Genesis' Symphonic Fantasy in A minor, Op. 21
Computer-Generated Jazz Improvisation: