Those of you interested in such things (admittedly, probably not many of you!) might like to know that this topic was covered in an item forming part of BBC Radio 4's "More or Less" programme, which was transmitted today (7th August 2009).
Here is the link to listen to it via the internet:
Thanks for the link, Mix - quite interesting, but took quite a long time to tell us what we already know-
Equal Temperament <=> Perfectly and equally out of tune in every key.
Of related interest to guitarists, banjo, mandolin and "zouk" players is the fact that fretted instruments can only approximate to equal tempered tuning; this could be of advantage when playing music in a relatively small number of related keys.
In particular, how do you like your C natural? I understand that they used to be typically higher than "equal tempered" when played on the pipes, and often whistles. But it seems that now people's ears are used to the equal-tempered C. As are many instruments.
I was at the Carolan Harp Festival in Keadue a few days ago.
In the Senior Finals of the competition (1st prize €600) one of the competitors tuned using an electronic tuner (the others tuned by ear). The electronically tuned harp was noticeably out of tune compared with the rest. The adjudicator commented on the use of the tuner and also that the harp wasn't properly in tune. I imagine marks were docked (that competitor, needless to say, wasn't the winner).
Ah, equal temperament- I struggle with that every day, most often with tinny spinets that still sound out of tune no matter how much time I spend on them
If anyone wants to go into the detailed maths of intonation, one of the best sources is probably Helmholtz's "On the Sensations of Tone".
The text is available online at http://www.archive.org/stream/onsensationsofto00helmrich/onsensationsofto00helmrich_djvu.txt
and the book can also be purchased from Amazon (which may be more convenient for study, and it's not too expensive).
The renaissance pavane I referred to above was sung at a session in Keadue last week by a French-speaking Belgium couple (in Ireland for the set dancing) who sang it as a duet for soprano and bass. They sing in a madrigal consort, so their intonation was extremely good, even under session conditions. Their singing brought the house down.
Mathemetics, Music and Tempered Keyboards
Mathemetics, Music and Tempered Keyboards
Those of you interested in such things (admittedly, probably not many of you!) might like to know that this topic was covered in an item forming part of BBC Radio 4's "More or Less" programme, which was transmitted today (7th August 2009).
Here is the link to listen to it via the internet:
http://news.bbc.co.uk/1/hi/programmes/more_or_less
The item concerned begins 13 minutes into the programme.
# Posted on August 7th 2009 by Mix O'Lydian
Re: Mathemetics, Music and Tempered Keyboards
Thanks, I don't pretend to understand it but I am interested!
# Posted on August 7th 2009 by Rob
Re: Mathemetics, Music and Tempered Keyboards
Thanks for the link, Mix - quite interesting, but took quite a long time to tell us what we already know-
Equal Temperament <=> Perfectly and equally out of tune in every key.
Of related interest to guitarists, banjo, mandolin and "zouk"
players is the fact that fretted instruments can only approximate to equal tempered tuning; this could be of advantage when playing music in a relatively small number of related keys.
# Posted on August 7th 2009 by Rick Payman
So, what is the best tuning for trad music?
In particular, how do you like your C natural? I understand that they used to be typically higher than "equal tempered" when played on the pipes, and often whistles. But it seems that now people's ears are used to the equal-tempered C. As are many instruments.
# Posted on August 8th 2009 by sixholes
Re: Mathemetics, Music and Tempered Keyboards
I was at the Carolan Harp Festival in Keadue a few days ago.
In the Senior Finals of the competition (1st prize €600) one of the competitors tuned using an electronic tuner (the others tuned by ear). The electronically tuned harp was noticeably out of tune compared with the rest. The adjudicator commented on the use of the tuner and also that the harp wasn't properly in tune. I imagine marks were docked (that competitor, needless to say, wasn't the winner).
Now listen to the intonation of a midi source playing a 4-part renaissance pavane on
http://homepages.luc.edu/~avande1/belle-qui/belle-qui-tiens-ma-vie.htm
and compare that intonation with the intonation of a 4-part choir singing the same piece live on http://www.youtube.com/watch?v=YdwuJxZwyuw&feature=related
# Posted on August 8th 2009 by lazyhound
Re: Mathemetics, Music and Tempered Keyboards
Ah, equal temperament- I struggle with that every day, most often with tinny spinets that still sound out of tune no matter how much time I spend on them
# Posted on August 8th 2009 by Greg the Piano Tuner
Re: Mathematics, Music and Tempered Keyboards
If anyone wants to go into the detailed maths of intonation, one of the best sources is probably Helmholtz's "On the Sensations of Tone".
The text is available online at
http://www.archive.org/stream/onsensationsofto00helmrich/onsensationsofto00helmrich_djvu.txt
and the book can also be purchased from Amazon (which may be more convenient for study, and it's not too expensive).
# Posted on August 8th 2009 by lazyhound
Re: Mathemetics, Music and Tempered Keyboards
That's not really a text file, has some markup in it. My browser went off in a sulk to chew through the 2.5Mb of it.
But I found the facsimile nearby
http://www.archive.org/stream/onsensationsofto00helmrich#page/4/mode/2up which is abit more browser frendly.
Thanks lazyhound
# Posted on August 8th 2009 by david_h
Re: Mathemetics, Music and Tempered Keyboards
The renaissance pavane I referred to above was sung at a session in Keadue last week by a French-speaking Belgium couple (in Ireland for the set dancing) who sang it as a duet for soprano and bass. They sing in a madrigal consort, so their intonation was extremely good, even under session conditions. Their singing brought the house down.
# Posted on August 8th 2009 by lazyhound