Major thirds: Just, Equal Temperament, Pythagorean

Hello - It's been great to be in touch with you, Jonathan and Elizabeth, and will be in touch with you, Brink and Joe before long. Unexpectedly, but very thankfully, I'm now home and expect to be at home for the foreseeable future. I believe this may be of interest to some on the tuning list.

Here are some thoughts I've had about harmony as I think they may still be underappreciated and "mentioning them to the music world" might do some good and some might say "Hmm - I hadn't thought of that before!"

I'm trying here to get down concrete observer evidence for some surprising "reverse parallels" between how replacing the 81/64 Pythagorean major third with the 5/4 just major third in the 1400s changed music over the course of that century and how the later replacing of the 5/4 just or mean tone major third with the 126/100 equal tempered major third towards 1900 with the near universal adoption of the 12 equal semitone steps per octave equal temperament scale changed music at the later time. The result of this last change was to bring about a faster paced and more "driving rhythm, far out" music than the more harmonious music of the period from the 1400s up to about 1900.

The change in the 1400s made music sound much more beautiful than it sounded before in the Ars Nova times. In the reverse direction, (at least many) people of the 20th century unfamiliar with the sound of the earlier mean tone music and who are used to the sound of equal tempered music find the mean tone music to sound strangely beautiful.

The just or nearly just 5/4 major third in chords seems to have the ability to tap into the brain's reward system.

In brief, I think I have at least a partial answer as to why just intervals and chords tap into our brains' reward systems: When fellow creatures are communicating - humans singing, dogs barking, or birds singing, etc., the sound production mechanism is a horn with partial frequencies - 1 2 3 4 5 6 7 8 9 ..... (integers in lock step). Non-living sounds in nature - blowing leaves, rolling rocks, babbling brooks - have sound component frequencies not related in such an integer step way. A tone with integer frequency partials cues one that a fellow living creature is making the sound - and communicating something that's likely important.

THREE LISTENER COMMENTS:

I Towards 1476 the music theorist Johannes Tinctoris wrote regarding the striking change in musical art brought about through the influence of English music which had taken place earlier in the century : "... At this time, consequently, the possibilities of our music have been so marvellously increased that there appears to be a new art, if I may so call it, whose fount and origin is held to be among the English, of whom Dunstable stood forth as chief. Contemporary with him in France were Dufay and Binchoys, to whom directly succeeded the moderns Ockeghem, Busnoys, Regis and Caron, who are the most excellent of all the composers I have ever heard..."

Again in the preface to a book published in 1477 Tinctoris wrote: "...although it seems beyond belief, there does not exist a single piece of music, not composed within the last forty years, that is regarded by the learned as worth hearing. Yet at this present time, not to mention innumerable singers of the most beautiful diction, there flourish, whether by the effect of some celestial influence or by the force of assiduous practice, countless composers, among them Jean Ockeghem, John Regis, Antoine Busnoys, .... who glory in having studied this divine art under John Dunstable, Gilles Binchoys, and Guillaume Dufay, recently deceased. Nearly all the works of these men exhale such sweetness that in my opinion they are to be considered most suitable, not only for men and heroes, but even for the immortal gods. Indeed I never hear them, I never examine them, without coming away happier and more enlightened."

II A music student auditioning at Florida State University in 1998, summing up her feelings regarding the difference between the sounds of same score passages of piano music played with the piano tuned in quarter comma mean tone temperament and with the piano tuned in equal temperament wrote at the end of her listening preference test:
"I appreciate the sound of mean tone tuning; it's just different enough to be almost exotic. I think it's just beautiful."

III A former university tutor in physiology with whom I shared a passion for music and with whom I'd kept up left me a phone message responding to a cassette tape I'd sent him in 1998 on which I'd recorded several familiar hymns played on my piano tuned to quarter comma mean tone temperament. This is his message (relevant parts):

"Hi Dave, Ed Redgate. I received your tape and just played it a few times. Indeed it does have a distinctive sound - a very rich harmony - I'd forgotten .... These harmonies, they're great! What have you done anyway? And then you're selecting numbers which push all my buttons. When my hair stands up on the back of my head and tears well up in my eyes I know you're pushing some emotional buttons. Yes it's a great tape .... and your technique is amazing - you hit all the keys exactly at the same time with exactly the same force to exert .... to elicit the harmonies. I'm actually quite surprised. If you're making a CD of these, I think it would be quite successful. I'll be in touch. I'm on my way to work. We had a great time in Baja. The weather was beautiful and we had a nice family reunion. .... "

What's in these comments is not "new" and yet they add up to underscore the fact that, as much or more than the 3/2 fifth, the 5/4 major third is psychologically important in music and it needs to be close to exactly 5/4 to have its full psychological effect. I feel that somehow, this fact is still underappreciated.

Hi Dave,

Those Tinctoris quotes are great! Where did you find them?

-Carl

--- In tuning@yahoogroups.com, Ralph Hill <ASCEND11@...> wrote:
>
> Hello - It's been great to be in touch with you, Jonathan and
> Elizabeth, and will be in touch with you, Brink and Joe before
> long.
//
> Towards 1476 the music theorist Johannes Tinctoris
> wrote regarding the striking change in musical art brought
> about through the influence of English music which had taken
> place earlier in the century : "... At this time, consequently,
> the possibilities of our music have been so marvellously
> increased that there appears to be a new art, if I may so
> call it, whose fount and origin is held to be among the
> English, of whom Dunstable stood forth as chief. Contemporary
> with him in France were Dufay and Binchoys, to whom directly
> succeeded the moderns Ockeghem, Busnoys, Regis and Caron, who
> are the most excellent of all the composers I have ever heard..."
>
> Again in the preface to a book published in 1477 Tinctoris wrote:
> "...although it seems beyond belief, there does not exist a
> single piece of music, not composed within the last forty years,
> that is regarded by the learned as worth hearing. Yet at this
> present time, not to mention innumerable singers of the most
> beautiful diction, there flourish, whether by the effect of some
> celestial influence or by the force of assiduous practice,
> countless composers, among them Jean Ockeghem, John Regis,
> Antoine Busnoys, .... who glory in having studied this divine
> art under John Dunstable, Gilles Binchoys, and Guillaume Dufay,
> recently deceased. Nearly all the works of these men exhale
> such sweetness that in my opinion they are to be considered most
> suitable, not only for men and heroes, but even for the immortal
> gods. Indeed I never hear them, I never examine them, without
> coming away happier and more enlightened."

On Wed, Sep 26, 2012 at 1:57 AM, Ralph Hill <ASCEND11@...> wrote:
>
> I Towards 1476 the music theorist Johannes Tinctoris wrote regarding the
> striking change in musical art brought about through the influence of
> English music which had taken place earlier in the century : "... At this
> time, consequently, the possibilities of our music have been so marvellously
> increased that there appears to be a new art, if I may so call it, whose
> fount and origin is held to be among the English, of whom Dunstable stood
> forth as chief. Contemporary with him in France were Dufay and Binchoys, to
> whom directly succeeded the moderns Ockeghem, Busnoys, Regis and Caron, who
> are the most excellent of all the composers I have ever heard..."
>
> Again in the preface to a book published in 1477 Tinctoris wrote:
> "...although it seems beyond belief, there does not exist a single piece of
> music, not composed within the last forty years, that is regarded by the
> learned as worth hearing. Yet at this present time, not to mention
> innumerable singers of the most beautiful diction, there flourish, whether
> by the effect of some celestial influence or by the force of assiduous
> practice, countless composers, among them Jean Ockeghem, John Regis, Antoine
> Busnoys, .... who glory in having studied this divine art under John
> Dunstable, Gilles Binchoys, and Guillaume Dufay, recently deceased. Nearly
> all the works of these men exhale such sweetness that in my opinion they are
> to be considered most suitable, not only for men and heroes, but even for
> the immortal gods. Indeed I never hear them, I never examine them, without
> coming away happier and more enlightened."

Hi Ralph,

I echo Carl's sentiments on these comments. What is the source for
this? I'd -love- to hear more about what composers at the time thought
about the rise of triadic harmony.

-Mike

On 26 September 2012 15:57, Ralph Hill <ASCEND11@...> wrote:
>
> The just or nearly just 5/4 major third in chords seems to have the ability to tap into the brain's reward system.
>

Singing perfectly tuned triads with competent singers (especially
one-to-a-part) is one of my greatest thrills as a musician.

This week a quartet of us were having a sectional for a performance
with a pianist-composer for a couple of her pieces. I think our
well-tuned chords (unsullied at that stage by the other accompaniment
;-) ) really thrilled her...

Vaughan