[HN Gopher] Werckmeister Temperment
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Werckmeister Temperment
Author : brudgers
Score : 17 points
Date : 2024-10-21 02:12 UTC (20 hours ago)
(HTM) web link (en.wikipedia.org)
(TXT) w3m dump (en.wikipedia.org)
| pyinstallwoes wrote:
| What's special about it?
| klodolph wrote:
| They're trying to solve various issues with harmony. You want
| to pick a set of notes that produce good harmonies with each
| other, but you don't want to pick too many notes. If you
| "fudge" some notes, which compromises the harmony, you can keep
| a small set of notes in the octave (like twelve!), and if
| you're careful about it, the music will still sound consonant /
| harmonious when it is supposed to sound that way.
|
| Historically, the older systems were some derivation of
| Pythagorean or just intonation, which are generated from small
| integer ratios like 3:2, 4:3, 5:4. If you continue building a
| tuning system out of these integer ratios, you get _weird_
| ratios like 81:80 (syntonic comma) or 531441:524288
| (Pythagorean comma); you can then choose to include these
| ratios in your tuning system (too complicated), stop before you
| reach them (too simple), or divide up the ratios and distribute
| them in other parts of your scale. This last approach is called
| "musical temperament".
|
| https://en.wikipedia.org/wiki/Musical_temperament
|
| Werkmeister devised a set of musical temperaments in the late
| 1600s. Alternative temperaments include mean-tone temperament
| (various flavors) and equal temperament. Mean-tone temperament
| divides the commas equally apart parts of the octave. Equal
| temperament divides the commas equally across the _entire_
| octave. Werkmeister temperaments divide the commas unequally.
| This results in some intervals which sound more consonant and
| some intervals which sound more dissonant, relative to equal
| temperament. Unlike equal temperament, different keys will have
| different character.
|
| Just to illustrate a more concrete problem: systems which
| improve the fifth often require sacrificing the third.
| Pythagorean has exactly perfect fifths but the thirds are not
| so good. Quarter-comma meantone goes the opposite direction and
| gives you exactly just thirds, but the fifths are not so good.
| Equal temperament is between the two, but much closer to
| Pythagorean.
|
| If you want to play with it immediately, and you have Logic Pro
| installed, you can go menu diving into the tuning settings for
| your project. Other DAWs too. Various synthesizers also have
| Werkmeister buried in the menus--some brands more than others
| (I know Yamaha has had them for ages).
| brudgers wrote:
| The manual for my Yamaha EW20 Windjamm'r is where I stumbled
| upon it. I find non-12TET temperaments anthropologically
| interesting in the context of European classical music
| culture...e.g. what does the exalted status of "perfect
| pitch" imply?
| klodolph wrote:
| "Perfect pitch" or "perfect interval"?
|
| Someone with perfect pitch can tell what note you are
| playing just by listening to that note in isolation. Most
| people can't do that. "Absolute pitch" is probably a better
| name, but it's usually called "perfect pitch".
|
| Perfect intervals are the intervals which don't have a
| smaller and larger version of an interval with the same
| name. It's nothing more than a naming convention for
| intervals. The 4th and 5th are perfect. So are the octave
| (8th) and unison (1). The other intervals (2nd, 3rd, 6th,
| and 7th), rather than being "perfect", come in minor and
| major versions.
|
| Basically, every interval either has minor/major, or
| perfect.
|
| It's a naming convention for intervals based on the western
| diatonic scale. Any interval which is smaller than
| minor/perfect is called "diminished", and an interval which
| is larger than major/perfect is "augmented". For example, C
| to Gb is a diminished fifth, and Ab to F# is an augmented
| sixth. Which number you use to name an interval is strictly
| based on the letter names of the note, ignoring sharps and
| flats.
| brudgers wrote:
| I used "perfect pitch" in the ordinary way ordinary
| people ordinarily use the phrase. Temperaments are
| interesting because the pitches (and intervals) in 12TET
| are different from the pitches (and intervals) in Mean
| Tone are different from the pitches (and intervals) in
| Werckmeister -- and within Werckmeister because
| Werkmeister made several temperaments.
|
| Never mind 31TET etc.
| klodolph wrote:
| > I used "perfect pitch" in the ordinary way ordinary
| people ordinarily use the phrase.
|
| I'm a little confused by what you are saying here,
| because most people who say "perfect pitch" mean that you
| can tell which note is being played in isolation. That's
| what "perfect pitch" means to ordinary people, as far as
| I can tell.
|
| It's something you have or don't have. Like, "I have
| perfect pitch" or "I don't have perfect pitch".
|
| If you mean something other than that definition, maybe
| you could find some alternative way to express it because
| I don't understand what meaning you are getting at. I'm
| not trying to be pedantic here, but "perfect pitch" is
| right there in the dictionary and it's most commonly used
| to mean that you can recognize pitch without a reference,
| i.e., absolute pitch recognition.
| brudgers wrote:
| It seemed as if you wanted to call it absolute pitch and
| talk about intervals.
|
| The "perfect" in "perfect pitch" glosses over the messy
| reality of temperaments. And "perfect" is a pretty strong
| word in a cannon of exaltent claims about Western
| classical music. That's what I find interesting.
|
| Or to explain further, providing a synopsis of tonal
| harmony in response to my comment is another of the sort
| of things I find anthropologically interesting.
| klodolph wrote:
| Ok, you're talking about perfect intervals, not perfect
| pitch. "Perfect pitch" doesn't make sense in context and
| so I was having a hard time figuring out what you were
| getting at. This is not pedantry. I'm not trying to make
| a point here, I just didn't understand what you meant.
|
| > The "perfect" in "perfect pitch" glosses over the messy
| reality of temperaments.
|
| Yeah. So do all the other terms like minor, major,
| diminished, augmented, second, third, fourth, fifth,
| sixth, seventh, consonant, dissonant, etc. All of those
| terms gloss over the messy reality of temperaments.
|
| The tuning system (including temperaments) are, in fact,
| what establish the possible relationships between these
| interval names and the actual pitch ratios. For example,
| a just major third is 5:4, a pythagorean major third is
| 81:64, and an equal temperament major third is [?]2:1.
|
| > Or to explain further, providing a synopsis of tonal
| harmony in response to my comment is another of the sort
| of things I find anthropologically interesting.
|
| I'm happy to answer questions but I don't like feeling
| like I'm being treated as an anthropological curiosity.
|
| If I'm providing more detail than you expect, then chalk
| it up to a property of Hacker News, which is full of
| pedants. Sometimes my comments here are damn _verbose_ ,
| just to get ahead of the pedants.
| recursive wrote:
| In the common usage "perfect pitch" is a property of a
| person, not of a sound.
| brudgers wrote:
| I don't disagree. However, its cultural claims about the
| nature of music gives me the blues.
| recursive wrote:
| Perfect pitch doesn't say anything about the cultural
| understanding of music. Except possibly that pitch is
| important within the context of music? Perfect pitch
| means that someone can identify pitches accurately.
| Nothing more. If you were a proponent of a style of music
| that didn't consider pitches to be significant, I can see
| why PP would be irrelevant. Beyond that, I don't
| understand what you're getting at.
| klodolph wrote:
| The commenter you're replying to is using the term
| "perfect pitch" incorrectly, that's all. They're talking
| about the word "perfect" when it's used to describe
| intervals, like perfect fifth or perfect fourth. I think.
| aithrowawaycomm wrote:
| It just means that melodies and harmonies are "supposed to
| be" sung and thus continuously pitched, where the ears of
| the musicians guide them to the proper harmonies. This is
| not feasible with keyboard or fretted instruments, so we
| have to make compromises if we want to play polytonal music
| on a single piano. 12-TET is a compromise that stood the
| test of time: ultimately a slightly "clangy" dominant
| seventh is preferable to the corrupt fifths and thirds you
| get with unequal temperaments.
|
| I really don't think there's much more to it than that,
| except composers with picky ears should just bite the
| bullet with 17-TET or something. (I am a guitarist and
| sometimes I wish I had flatter thirds and tritones without
| having to bend the strings.) As shown off-handedly in the
| Werckmeister Harmonies novel and film, composers who get
| too deep into the weeds of temperament systems often find
| themselves confusing form with function and waging
| ideological battles, forgetting that the point of the
| exercise is create interesting music.
| klodolph wrote:
| Note that the technical term for this is "just".
| analog31 wrote:
| Has anybody made a guitar with double frets? I once saw a
| viola da gamba performance, and the VdG had some double
| frets, so I asked about it. Their purpose is to allow for
| some options when playing those thirds and tritones.
| Since the frets are tied on, you can have as many as you
| want, and they're also movable, so you can play around
| with temperaments if you want.
| klodolph wrote:
| Does that work for just major thirds? They're only 14
| cents away from equal temperament, and I would think that
| the frets would be too close together, if you moved them
| into place for just major thirds.
| TheOtherHobbes wrote:
| It's a different take on trying to set up the pitches on a
| piano/organ/synth keyboard so you can shift between keys and
| everything still sounds tuneful.
|
| Ideally you want exact numeric ratios between the various note
| combinations. (E.g. the frequency of a G should be 1.5 times
| the frequency of a C.)
|
| If you start with a C and set up perfect ratios, you get a
| smooth sound as long as you play in the key of C.
|
| But if you change key and move pitch patterns up and down the
| keyboard - transposition - the pitches will be off. Sometimes
| by a lot.
|
| So you have these different systems that try to approximate a
| solution in different ways.
|
| Modern Western music uses Equal Temperament, where the
| frequency ratio between notes is the same all the way up the
| keyboard (exactly the 12th root of 2.)
|
| This is super-simple and gives close-enough ratios that aren't
| quite exact but are very usable.
|
| The cost is a hint of sourness in some note combinations, but
| mostly we just hear those as movement within the sound.
|
| The older alternatives to Equal (mean tone, Werckmeister,
| Kirnberger, and others) smooth out the ratios more selectively.
| So some note combinations are less sour, others are more sour.
|
| They sound quite spicy if you're not used to them - somewhat
| out of tune (ironic...) but most people are so used to Equal
| Temperament anything else sounds exotic.
|
| So something like this is of historic interest. These tunings
| are sometimes used for authentic performances of very old
| ('early') music, and some old church organs were built with
| them.
|
| It's very rare to find them being used for effect in modern
| songs. (Does happen, but very unusual.)
|
| The best solution is dynamic tuning which takes into account
| the surrounding notes and shifts pitches a little up and down
| for the smoothest effect. Choirs and orchestras tend to do this
| anyway, but making it happen in software is a much harder
| problem.
| thih9 wrote:
| About software implementations of dynamic tuning - Logic Pro
| supports this, under the name "Hermode Tuning"
|
| https://support.apple.com/en-
| gb/guide/logicpro/lgcpa88a63e7/...
|
| > Hermode Tuning automatically controls the tuning of
| electronic keyboard instruments (...). It retains the pitch
| relationship between keys and notes, while correcting the
| individual notes of electronic instruments, ensuring a high
| degree of tonal purity. This process makes up to 50 finely
| graded frequencies available per note, while retaining
| compatibility with the fixed tuning system of 12 notes per
| octave.
|
| Other DAWs have similar options, e.g. Cubase:
| https://www.steinberg.help/r/cubase-
| pro/13.0/en/cubase_nuend...
| andrei_says_ wrote:
| Bela Tar's film Werkmeister Harmonies is a masterpiece and this
| article makes me think its title would be more precisely
| translated as Werkmeister Temperments.
| squidsoup wrote:
| I'm not sure, I think the well tempered clavier is known as "A
| jol hangolt zongora" in Hungarian (literally "the well-tuned
| piano"), so the choice of "harmoniak" was probably deliberate.
| Any native hungarian speakers please correct me if I'm wrong.
| Given the change in temperament is a metaphor in the film for
| human progress deviating from the natural order and introducing
| disharmony, perhaps "harmonies" is more fitting.
|
| I absolutely agree with you about the film - more people should
| experience his work.
| tsm wrote:
| If you find this remotely intriguing, I highly recommend Ross
| Duffin's book _How Equal Temperament Ruined Harmony (And Why You
| Should Care)_
|
| https://search.worldcat.org/title/How-equal-temperament-ruin...
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