5 ms·

It's a way of tuning so that all semitone intervals are an equal [2^(1/12)] frequency ratio. The vast majority of western music, today, uses equal temperament.

It's a way of tuning so that all semitone intervals are an equal [2^(1/12)] frequency ratio. The vast majority of western music, today, uses equal temperament. This includes most recorded performances of JS Bach's pieces. It wasn't particularly common in Bach's time, though, and the math to do it 'properly' wasn't even known outside of China. Today, though, it's everywhere. Modern Woodwinds are equal temperament due to the placement of the holes. To match that, the entire orchestra is in equal temperament, regardless of the requirements of the instrument. Guitars are in equal temperament due to the placement of their frets -- to do otherwise would require frets that bend between strings. In isolation, people will [attempt to] sing in equal temperament, because that's what 'all' accompaniment is like. Barbershop quartets, acapella groups, and to some extent string quartets have a tendency to shift harmony notes toward simple fractions of the root note of the chord, on the fly, even as the overall melody runs in equal temperament. This isn't a different 'tuning', per se, but it is a thing.

mrob 8y ago
Barbershop is notable for using the harmonic seventh, which doesn't exist in the standard 12 note scale. Its frequency is 7/4 times the frequency of the root, so a harmonic 7th above C is somewhere between A and B-flat. https://en.wikipedia.org/wiki/Harmonic_seventh_chord https://en.wikipedia.org/wiki/Harmonic_seventh_chord
- yesenadam 8y ago
  From that page: the harmonic seventh is '"sweeter in quality" than an "ordinary" minor seventh'. Well, as an ex- trumpet and trombone player,[0] what it sounds is out-of tune, and is generally avoided, although the out-of-tuneness can be compensated for by adjusting the trombone slide. It doesn't sound particularly bluesy to my ear. Sure, sliding around the flat 7 and flat 5 areas sound bluesy, but just that note as a melody note sounds very flat. [0] Playing brass instruments is a matter of using your lip to find the various harmonics, and using the valves to flatten them by various amounts.
  - mrob 8y ago
    I don't think there's anything inherently wrong with natural harmonics in a melody. The opening and ending of Britten's Serenade for Tenor, Horn and Strings, Op. 31 uses them, and it sound good to me. Because it's notated as equal temperament, the score is ambiguous, and there are two ways of playing it: https://www.youtube.com/watch?v=WxVnSkX4Fco https://www.youtube.com/watch?v=WxVnSkX4Fco (13th harmonic high note version) https://www.youtube.com/watch?v=mkLyK-oSQ7A https://www.youtube.com/watch?v=mkLyK-oSQ7A (14th harmonic high note version) I suspect that brass players are unusually sensitive to deviations from equal temperament because they have to work so hard to overcome them if they want to play with other instruments (including other brass instruments of different sizes).
    - yesenadam 8y ago
      >I don't think there's anything inherently wrong with natural harmonics in a melody. Not sure what you mean by 'natural harmonics', i.e. which ones you mean. I was just talking about how the Ab harmonic (on trombone/trumpet) sounds very flat. It's avoided because it sounds out of tune. I'm not sure what something being 'inherently wrong' would even mean. In music, if it sounds good, it is good. >I suspect that brass players are unusually sensitive to deviations from equal temperament because they have to work so hard to overcome them if they want to play with other instruments I don't know what you're referring to there - I've never had or even heard of that problem. And I hadn't noticed or heard, and don't believe, that 'brass players are unusually sensitive to deviations from equal temperament'.
      - mrob 8y ago
        By "natural harmonics" I mean notes at the resonant frequencies of the instrument. Several of them are obviously different from equal temperament, which means they will sound bad when played with other instruments. When brass players talk about "good intonation", they often mean adjusting these notes into equal temperament with valves/slides/embouchure/hand stopping. Because brass players actually have to pay attention to the tuning, I wouldn't be surprised if they were more sensitive to it than people who played fixed pitch instruments like piano. The Britten piece is notable for the parts where the horn player is instructed not to adjust the pitches to equal temperament, and because it's a solo it still sounds good.
jdietrich 8y ago
.Guitars are in equal temperament due to the placement of their frets -- to do otherwise would require frets that bend between strings. Interestingly enough, such a thing does exist. http://www.truetemperament.com/ http://www.truetemperament.com/
- boomlinde 8y ago
  True temperament is meant to address guitar intonation problems regardless of the temperament. It's basically impossible to get a guitar intoned correctly over the fret board using straight frets because of the different string gauges. So it's not specifically meant for just intonation.
natechols 8y ago
I would amend this to say that modern woodwinds are supposed to be equal temperament, but this is more aspirational than reality. Some instruments better than others, and in general they are all vastly improved over their 18th- and 19th-century ancestors, but a lot of the burden of making the pitches "equal" is left to the player. (Source: I play bassoon, probably the worst of the lot.)
posterboy 8y ago
> It's a way of tuning so that all semitone intervals are an equal [2^(1/12)] frequency ratio Or so I thought until I programmed an AVR. The F, I think it was, is terribly out of tune. I haven't found the wikipedia article again, that had the correct Frequencies noted in Hz, with F decidedly not in the scheme that you allege.
- systoll 8y ago
  If you shift F away from that ratio, you're not doing equal temperament anymore. Which is fine. There are many different tuning systems [ https://en.wikipedia.org/wiki/Musical_tuning#Systems_for_the_twelve-note_chromatic_scale https://en.wikipedia.org/wiki/Musical_tuning#Systems_for_the... ], and they all involve tradeoffs. Equal temperament's benefit is its flexibility, but that doesn't make it 'better'.

mrob 8y ago

Barbershop is notable for using the harmonic seventh, which doesn't exist in the standard 12 note scale. Its frequency is 7/4 times the frequency of the root, so a harmonic 7th above C is somewhere between A and B-flat. https://en.wikipedia.org/wiki/Harmonic_seventh_chord https://en.wikipedia.org/wiki/Harmonic_seventh_chord

yesenadam 8y ago
From that page: the harmonic seventh is '"sweeter in quality" than an "ordinary" minor seventh'. Well, as an ex- trumpet and trombone player,[0] what it sounds is out-of tune, and is generally avoided, although the out-of-tuneness can be compensated for by adjusting the trombone slide. It doesn't sound particularly bluesy to my ear. Sure, sliding around the flat 7 and flat 5 areas sound bluesy, but just that note as a melody note sounds very flat. [0] Playing brass instruments is a matter of using your lip to find the various harmonics, and using the valves to flatten them by various amounts.
- mrob 8y ago
  I don't think there's anything inherently wrong with natural harmonics in a melody. The opening and ending of Britten's Serenade for Tenor, Horn and Strings, Op. 31 uses them, and it sound good to me. Because it's notated as equal temperament, the score is ambiguous, and there are two ways of playing it: https://www.youtube.com/watch?v=WxVnSkX4Fco https://www.youtube.com/watch?v=WxVnSkX4Fco (13th harmonic high note version) https://www.youtube.com/watch?v=mkLyK-oSQ7A https://www.youtube.com/watch?v=mkLyK-oSQ7A (14th harmonic high note version) I suspect that brass players are unusually sensitive to deviations from equal temperament because they have to work so hard to overcome them if they want to play with other instruments (including other brass instruments of different sizes).
  - yesenadam 8y ago
    >I don't think there's anything inherently wrong with natural harmonics in a melody. Not sure what you mean by 'natural harmonics', i.e. which ones you mean. I was just talking about how the Ab harmonic (on trombone/trumpet) sounds very flat. It's avoided because it sounds out of tune. I'm not sure what something being 'inherently wrong' would even mean. In music, if it sounds good, it is good. >I suspect that brass players are unusually sensitive to deviations from equal temperament because they have to work so hard to overcome them if they want to play with other instruments I don't know what you're referring to there - I've never had or even heard of that problem. And I hadn't noticed or heard, and don't believe, that 'brass players are unusually sensitive to deviations from equal temperament'.
    - mrob 8y ago
      By "natural harmonics" I mean notes at the resonant frequencies of the instrument. Several of them are obviously different from equal temperament, which means they will sound bad when played with other instruments. When brass players talk about "good intonation", they often mean adjusting these notes into equal temperament with valves/slides/embouchure/hand stopping. Because brass players actually have to pay attention to the tuning, I wouldn't be surprised if they were more sensitive to it than people who played fixed pitch instruments like piano. The Britten piece is notable for the parts where the horn player is instructed not to adjust the pitches to equal temperament, and because it's a solo it still sounds good.

jdietrich 8y ago

.Guitars are in equal temperament due to the placement of their frets -- to do otherwise would require frets that bend between strings. Interestingly enough, such a thing does exist. http://www.truetemperament.com/ http://www.truetemperament.com/

boomlinde 8y ago
True temperament is meant to address guitar intonation problems regardless of the temperament. It's basically impossible to get a guitar intoned correctly over the fret board using straight frets because of the different string gauges. So it's not specifically meant for just intonation.

natechols 8y ago

I would amend this to say that modern woodwinds are supposed to be equal temperament, but this is more aspirational than reality. Some instruments better than others, and in general they are all vastly improved over their 18th- and 19th-century ancestors, but a lot of the burden of making the pitches "equal" is left to the player. (Source: I play bassoon, probably the worst of the lot.)

posterboy 8y ago

> It's a way of tuning so that all semitone intervals are an equal [2^(1/12)] frequency ratio Or so I thought until I programmed an AVR. The F, I think it was, is terribly out of tune. I haven't found the wikipedia article again, that had the correct Frequencies noted in Hz, with F decidedly not in the scheme that you allege.

systoll 8y ago
If you shift F away from that ratio, you're not doing equal temperament anymore. Which is fine. There are many different tuning systems [ https://en.wikipedia.org/wiki/Musical_tuning#Systems_for_the_twelve-note_chromatic_scale https://en.wikipedia.org/wiki/Musical_tuning#Systems_for_the... ], and they all involve tradeoffs. Equal temperament's benefit is its flexibility, but that doesn't make it 'better'.