perfect interval tuning (yet again...sorry...)

[bloke]

Here is a REALLY good example of (nearly perfectly) tempered intonation.
Had they (somehow...but against their nature) sung in equal temperament, NOT ONLY would have the excitement been gone, but - well - it would have sounded quite bad.

Mathematically perfect (when not playing with keyboards or other fixed-pitch instruments) intonation is essential for exciting/inspiring performances, because things aren't just "technically accurate"; chords actually "ring". To clarify, equal temperament is completely/mathematically inaccurate (and most of the numbers involved with it probably don't even have final decimal points).

In the past, I've outlined how I train myself to "learn" BOTH equal temperament tuning (essential, when playing with a dominating fixed-pitch instrument...and not just popular music, but piano concerti and piano-dominant church gigs, etc.), but also to "learn" (though the ears guide a good listener) perfect tuning. (I do this using two cheap tuners, and nothing else.)

Clearly, very high overtones (not sung) are sympathetically ringing throughout this performance, and QUITE audibly.

I talk a LOT about "tuning"...I'm not the world's greatest at it, and I cannot hear the grass grow.
I do believe, though, that I pay attention to this (sure: a weakness of mine) a great deal more than do some,
and that my colleagues and patrons benefit from the time that I spend on it.

[Doc]

Here is a REALLY good example of (nearly perfectly) tempered intonation.
Had they (somehow...but against their nature) sung in equal temperament, NOT ONLY would have the excitement been gone, but - well - it would have sounded quite bad.

Mathematically perfect (when not playing with keyboards or other fixed-pitch instruments) intonation is essential for exciting/inspiring performances, because things aren't just "technically accurate"; chords actually "ring".

Clearly, very high overtones (not sung) are sympathetically ringing throughout this performance, and QUITE audibly.

Aside from being fun, easy, classic style, etc. ^^^THIS^^^ is the number one reason people love to sing and listen to barbershop. Ringing chords together. Hearing overtones. Expanded sound. Goose bumps. Tears of joy.

The only caveat is that the lead sings an even tempered melody, and everyone tunes correctly/naturally around him. That can become interesting when the lead is singing the 7th in a dominant chord (like a V7). Since the lead sings even temperament and doesn't flatten the 7th (like brass players would), whoever has the fifth in the chord, has to sing what seems abnormally high to be in tune and produce overtones. When the lead sings the third, whoever sings the 7th will have sing the lowest 7th in all of musicdom to ring the chord.

[iiipopes]

Here is a REALLY good example of (nearly perfectly) tempered intonation.
Had they (somehow...but against their nature) sung in equal temperament, NOT ONLY would have the excitement been gone, but - well - it would have sounded quite bad.

Mathematically perfect (when not playing with keyboards or other fixed-pitch instruments) intonation is essential for exciting/inspiring performances, because things aren't just "technically accurate"; chords actually "ring".

Clearly, very high overtones (not sung) are sympathetically ringing throughout this performance, and QUITE audibly.

Aside from being fun, easy, classic style, etc. ^^^THIS^^^ is the number one reason people love to sing and listen to barbershop. Ringing chords together. Hearing overtones. Expanded sound. Goose bumps. Tears of joy.

The only caveat is that the lead sings an even tempered melody, and everyone tunes correctly/naturally around him. That can become interesting when the lead is singing the 7th in a dominant chord (like a V7). Since the lead sings even temperament and doesn't flatten the 7th (like brass players would), whoever has the fifth in the chord, has to sing what seems abnormally high to be in tune and produce overtones. When the lead sings the third, whoever sings the 7th will have sing the lowest 7th in all of musicdom to ring the chord.

A couple of picky items: it is not the fifth of the chord that is abnormally high. A natural fifth only about two cents higher than an equally tempered fifth. The real irritation is the tempered third compared to the natural third: the natural third is about 14 cents lower in pitch than an equally tempered third, and the wobbling beats of the equally tempered third can be quite irritating on an electronic keyboard or fretted instrument. And yes, in just intonation, the dominant 7th in the bass is low, indeed.

[Doc]

Here is a REALLY good example of (nearly perfectly) tempered intonation.
Had they (somehow...but against their nature) sung in equal temperament, NOT ONLY would have the excitement been gone, but - well - it would have sounded quite bad.

Mathematically perfect (when not playing with keyboards or other fixed-pitch instruments) intonation is essential for exciting/inspiring performances, because things aren't just "technically accurate"; chords actually "ring".

Clearly, very high overtones (not sung) are sympathetically ringing throughout this performance, and QUITE audibly.

Aside from being fun, easy, classic style, etc. ^^^THIS^^^ is the number one reason people love to sing and listen to barbershop. Ringing chords together. Hearing overtones. Expanded sound. Goose bumps. Tears of joy.

The only caveat is that the lead sings an even tempered melody, and everyone tunes correctly/naturally around him. That can become interesting when the lead is singing the 7th in a dominant chord (like a V7). Since the lead sings even temperament and doesn't flatten the 7th (like brass players would), whoever has the fifth in the chord, has to sing what seems abnormally high to be in tune and produce overtones. When the lead sings the third, whoever sings the 7th will have sing the lowest 7th in all of musicdom to ring the chord.

A couple of picky items: it is not the fifth of the chord that is abnormally high. A natural fifth only about two cents higher than an equally tempered fifth. The real irritation is the tempered third compared to the natural third: the natural third is about 14 cents lower in pitch than an equally tempered third, and the wobbling beats of the equally tempered third can be quite irritating on an electronic keyboard or fretted instrument. And yes, in just intonation, the dominant 7th in the bass is low, indeed.

True, that 5th is not particularly high related to even temperament, but when that lead sings the 7th in even temperament (much higher than in natural tuning), that 5th does, by necessity, jump up enough to seem, at least for some, abnormally high. And, yes... it certainly isn't as much difference as that 7th in the other situation. That 7th is a lot lower than folks think! But when it's done correctly, it sure sounds great.

[bloke]

Those couple of hundreds of a semitone (5ths), though, are required to lock in to make a chord “ring“.

By tuning fifths nearly mathematically perfect, piano designers and piano tuners are able to get away with “stretch“ tuning - in addition to (aside from the stretch factor) equal temperament. The lowest pitches on the piano are actually a quarter tone flatter than the highest ones - via the “stretch” tuning system.

Piano chords never fully “ring” (other than the stretch-tuned fifths), but rely on large pieces of wood - for (seeming to “ring”) amplification.
yes…”Pounding” on low strings can cause strings - octaves higher - to “ring”, but that’s due to the phenomenon of strings vibrating sharp (at first), when struck very hard.

[iiipopes]

Those couple of hundreds of a semitone (5ths), though, are required to lock in to make a chord “ring“.

By tuning fifths nearly mathematically perfect, piano designers and piano tuners are able to get away with “stretch“ tuning - in addition to (aside from the stretch factor) equal temperament. The lowest pitches on the piano are actually a quarter tone flatter than the highest ones - via the “stretch” tuning system.

Piano chords never fully “ring” (other than the stretch-tuned fifths), but rely on large pieces of wood - for (seeming to “ring”) amplification.
yes…”Pounding” on low strings can cause strings - octaves higher - to “ring”, but that’s due to the phenomenon of strings vibrating sharp (at first), when struck very hard.

Indeed. I have discussed this personally with Dr. Kemp of St. Andrews University concerning bass strings and our respective experiments. He is mentioned in this article on the inharmonicity (overtones going sharp) of piano strings:
https://acta-acustica.edpsciences.org/a ... 00053.html
Now that I know, I use this phenomenon to my advantage when I tune my electric instruments: I watch for the flicker of the tuner on the sharp side for one flash before settling into the desired pitch, and know I am right on. Here is the link to the bass guitar applications:
https://news.st-andrews.ac.uk/archive/b ... igh-notes/
And here is the dialog from Dr. Kemp on my experiment to see if I could duplicate his findings:
https://www.talkbass.com/threads/physic ... 497/page-2

[djwpe]

I’ve been a little absent from the board lately, but this one grabbed me back in. The possibility of perfect interval tuning and ringing chords is why I live playing in a trombone section and trombone choir.

Don

[bloke]

another acoustic phenomenon:

When very high-pitched and loud trumpets are playing thirds (or sixths) the DIFFERENCE in the two frequencies often sounds (quite LOUDLY !!!) as some horribly out-of-tune "bass" note...

I don't believe those pitches are required to be mathematically in-tune (according to the overtone series in which they both occur) for this to happen.

[Doc]

another acoustic phenomenon:

When very high-pitched and loud trumpets are playing thirds (or sixths) the DIFFERENCE in the two frequencies often sounds (quite LOUDLY !!!) as some horribly out-of-tune "bass" note...

I don't believe those pitches are required to be mathematically in-tune (according to the overtone series in which they both occur) for this to happen.

Undertones are a very special and exciting phenomenon. I’ve experienced this a number of times when the voicing is right and the intonation is spot on. Huge bass note appears underneath what’s being sung/played.

[bloke]

Difference tones are real and have been programmed in 20th century flute pieces. Usually with a mediocre effect.

The issue with difference tones is that while low in frequency, the radiating beams are very narrow. That is, they are there, but the loudness of the difference tone varies greatly depending upon where the listener is.

For a difference tone to happen, all one needs is f1 and f2 to be appropriately spaced and played with enough amplitude. Mathematically those difference tones, abs(f1 - f2), are what one hears as undertones. Overtones are often the result from in-phase summation, f1 + f2, where the sum is the overtone heard.

This, of course, gets way more complicated when the instrument is emitting a Fourier series of tones.

Regarding “pure intonation” vocals, anyone listening to Top 40 radio in the 70s/80s/90s would’ve heard those (beautifully sung and produced) call station bumpers that exhibited fantastic intonation with resplendent overtones. Occasionally you’ll still hear them and they really are something to enjoy, even if for only a few seconds.

[bloke]

[excellent post]

When trumpets produce those tones in a quintet piece, it's extremely distracting (to me)...
...as if some novice is sitting next to me "messing around" with a trombone.
Usually, they are neither the pitch that I'm playing and nor are they pitches which are one of the standard 12 (neither equal temperament nor perfect-tuning).