Talk:Musical tuning

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One article[edit]

Since a) most of the articles on tuning schemes are stubs and b) there seems to be contention over which name means which scheme, I suggest we keep all the descriptions of musical tuning schemes on this page, each one under its own header (for now at least). That way we can see at a glance the differences, compare them, and resolve ambiguities on this single talk page -- Tarquin 10:16 Aug 4, 2002 (PDT)

I think that's a very good idea as an interim measure - this is a massive subject, and it does seem a bit odd that we have individual pages on meantone and just and so on without having a really good explanation of why there are 12 tones (notes, pitches, whatever :) to the octave in the west at all. --Camembert 10:37 Aug 4, 2002 (PDT)

Tomorrow, I will combine all of these entries into one page and attempt to tackle this topic in a real and thorough way. Any objections, let me know. JFQ

Someone anonymous has just split the types of tuning back into articles. Has the issue of the names been resolved? Even if it has, I am starting to think that they would be better off in a single article permanently, so the reader can easily compare their differences. -- Tarquin 23:36 Oct 18, 2002 (UTC)

I was just starting to think about how to work this. I think them being in different articles is not such a bad thing really, although they all need a lot of work as they stand. Having them all in one article is probably impractical in the long-term, because the number of different tunings used around the world at various times is almost endless. Having them all in one article didn't seem to provoke the frenzied editing it might have done, so maybe them being split up again is not such a bad thing.
I think the issue of names was more or less limited to "perfect fifth tuning", which I'd never heard of and assumed was referring to pythagorean tuning. I don't think that any more - I was just misunderstanding the concept. Honestly, I am going to work on these articles soon, really I am... --Camembert

Everything gets done on Wikipedia eventually. I started an article today I'd been meaning to write for weeks. -- Tarquin


On the single / many pages issue, I bow to your expertise :-) I think the list of links on this page would benefit from a bit of padding out if a brief summary of each type is possible. -- Tarquin


Would someone please put some sounds on some of these pages to give those of us who are tone-deaf at least one clue? -- isis 10:57 Oct 19, 2002 (UTC)

Yes, it might be a good idea to have a little sound sample of the same passage of music tuned in different ways to go alongside the brief summary of each system that Tarquin suggests. I'll put it on my to-do list. --Camembert

I was thinking you might play scales for the different systems, but a passage of music should work, either. I'd sure appreciate it, because nobody's ever been able to figure out, much less explain to me, what it is I don't hear about music that they do, but I might be able to hear a difference between the systems, and then I'd understand more about music. I think. I hope, anyhow. -- isis 11:46 Oct 19, 2002 (UTC)

It's a pity that PC soundcards don't seem to be able to play in different tunings. The Korg M1 synthesizer has several tuning settings. I think I found a sample somewhere once of major triads in diffferent tunings, but it was to emphasises how f# major can sound evry different in different C tunings. A scale might be best. -- Tarquin

It's possible to make a PC play in different tunings if you're talking about MIDI - you have to use the pitch-bend function. There are a few very handy programs that will take a normally tuned file and set all the pitch bends to fit any tuning you ask for. I think it's also possible to get programs that will do this retuning on the fly as you play a keyboard plugged into the PC live, though I've never tried that myself. Some old soundcards don't support pitch-bend, but my last computer had a very cheap soundcard bought in 1996, and that worked fine.
I was musing on this earlier today, and I think there are basically three ways to demonstrate different tunings in sound: you can have a simple scale; you can have a simple chord progression (something like a dominant seventh to tonic is not bad); or you can have a proper bit of music. All have advantages and disadvantages, but to pick on scales specifically: the problem is that the differences between the chromatic tunings are really quite subtle, and very difficult to detect if you just have a scale to go on - it's much easier to hear the differences when different notes are sounded at once (at least that's how I find it). Unless there's a reason not to, I'd like to try making examples of all three (scales, chords, and music) for each tuning. --Camembert

No reason why we can't have all three. I hadn't thought of pitch bend. Maybe there are midi files out there that demonstrate it that we can play & record into OGG. What I wonder is: I have perfect pitch (on and off): I can name a note I hear. But which tuning do I hear in? -- Tarquin

There are quite a few MIDIs around the place demonstrating different tunings, but I thought I'd try to make some .oggs from scratch - I've done complete pieces like this before, so we should be OK. I might do the chord progressions using simple sawtooth waves rather than a MIDI instrument - that way you can hear the upper harmonics buzzing against each other quite clearly. As for perfect pitch... hopefully all will be revealed in time... --Camembert

Wow, I've been away a lot longer than I thought I had. Things are looking much better around here now, and I'm jazzed up to start tackling things again. What are the places that aren't on your to do lists that need some work? I'm a little out of the loop. JFQ


.oggs[edit]

Well, I've done .oggs for equal temperament and Pythagorean tuning. I decided to do them as harmonized C major scales to try and kill several birds with one stone. I've thrown a couple of squiffy chords in there (a supertonic major seventh and a diminished seventh) so we have a variety of intervals. The differences are quite subtle, but audible - the third in the pythagorean scale is clearly sharper than the equally tempered version, and the whole thing is not quite so "busy" to my ears. I'll do the other tunings some other time. I will probably also do different versions of these files with an instrument with a simpler timbre. And I still like the idea of retuning a snippet of a "proper" piece of music, something by Chopin or somebody, as alternative examples.

I'm not entriely happy with the quality of the files - they're 100 times bigger than the MIDIs, and don't sound so good. Can we upload midi files? Is there any reason to avoid them? Any comments? --Camembert


I don't see why we can't have MIDI alongside the OGGs. Those are about 30Kb each, which is tiny (and I'm on a modem, so I appreciate these things!). These are great, by the way. The wolf fifth really howls, it's painful! -- Tarquin 20:32 Nov 1, 2002 (UTC)
We actually can't upload Midi's right now. See: Wikipedia talk:Sound. Hyacinth 19:16, 28 Oct 2004 (UTC)

Removed[edit]

"Ray Van De Walker, a wikipedian and amateur musician, has cut wind-chime bells in both pythagorean and equal-tempered tunings. He reports, "The pythagorean bells were cut on simple-fractional ratios. They were arguably in tune, because there were no beats to the pythagorean bells when they rang together. However, to my modern ear, and even my unsophisticated relatives, they sounded dramatically out of tune, like primitive non-western music." However, wind-chimes do not produce harmonic tones, and thus may be a poor example of music in just intonation."

I removed this paragraph because of the following reasons:
  • The length of two otherwise identical windchimes one of which has a length double the other, unlike strings, does not create a pitch twice as high. This leads me to question the accuracy of Ray's tuning.
  • Relatedly, the spectra of wind chimes is not harmonic, thus the overtones of each justly tuned windchime, unlike strings, do not coincide, thus they will arguable not sound tune. This leads me to question Ray's tuning as he states that the chimes did not create interference beats when played together.
  • I also question the validity of information on wikipedia being referenced to the personal experience of wikipedians.
The last sentence is my original attempt at handling my objections.Hyacinth

Proposed reorg[edit]

Here's a proposal for re-organizing the presentation the topic of intonation and tuning of notated Western music:

An intonation is an assignment of a frequency to each note in the piece (as in, the C#4 in the first measure has frequency X). Just intonation is a system for assigning such frequencies.

A tuning is an assignment of a frequency to a note independent of the piece (as in, C#4 has frequency X). Thus tunings are a subset of intonations.

One of the principle challenges of tunings is to trade off the desires for closeness to perfection between 5ths and 3rds. At the extremes are Pythagorean and 1/4 comma meantone tunings.

A 12-tuning, or a tuning of a traditional keyboard instrument, has the additional challenge of using only 12 frequencies per octave. One of the principle challenges of 12-tunings is to trade off the desires for closeness to perfection in individual 3rds and 5ths, as in, "which intervals should we penalize to make which other intervals close to perfect?". At the extremes are 12-meantones with 11 quite good 3rds and 5ths but a bad set of wolf intervals, on the one hand, and equal temperament on the other.

By "12-meantone" I mean an idealized meantone tuning truncated to have only 12 notes per octave. This is frequently what people refer to when they use "meantone" but I think this distinction is useful. For example the flat 5ths of 1/4-comma meantone come from the 5th/3rd tradeoff, whereas the wolf fifth does not exist in the idealized meantone, it only exists as part of the tradeoffs needed to fit 12 frequencies per octave.

--Ben Denckla

You bring up at least one good subject, fifths and thirds (!), but not all, and possibly not most, tunings systems are "intonation systems" in the sense that they assign specific frequencies to specific notes, nor do any of them have to be. Tuning is based on relative pitch, not absolute pitch, most especially just intonation.Hyacinth
I think a good way to deal with the relative vs. absolute issue is to say that there are relative and absolute tunings and relative and absolute intonations. Usually we only care to discuss relative tunings and intonations, but my definitions above use "tuning" and "intonation" as synonyms for "absolute tuning" and "absolute intonation." The definitions could be amended to refer to "frequency ratio (to an undefined reference frequency)" instead of "frequency" and then they would be definitions for relative tuning and relative intonation. --Ben Denckla

Name of page[edit]

I found "Musical tuning systems" on the "List of encyclopedia topics" (which is a list of articles that an encyclopedia probably should have, but which are missing on Wikipedia). Therefore, I made a redirect from Musical Tuning Systems to Musical tuning. However, I think that "Musical tuning systems" would be a better name for this page. Then we could avoid the disambiguity with the actual process of tuning instruments vs. the tuning systems. Any comments? --Tbackstr 09:49, Oct 28, 2004 (UTC)

Introduction[edit]

I visited this page about a year ago (2004?) hoping to find out some information about the why of tuning systems. I felt at that stage (and until today) this page was missing the high level information that I was desperately after. The article mentioned concepts like "nice" and "perfect" without any real grounding of what this really meant.

I've since learnt a lot about this, particularly from the referenced Mathieu text (which is great!). To fix the articles short comings, I have added to the introduction of the article with the hope that it will give the reader a deeper understanding of what is going on in tuning systems, before they are hit with the details of individual tuning systems. I tried to keep this separate in content to the "Comparisons and controversies" section, while providing the prior-knowledge necessary to really understand it.

I have also removed the "nice" adjective and used the term "natural", since niceness isn't always the goal of musicians - seeing as harmony is often built on tension and dissonance. I tried to convey that there are various ways to find "natural" tunings, only two of which I mentioned. Anyway, hope this helps. Something like this sure would have helped me when I first came here :)

History of tuning (and links removed)[edit]

I removed the links to history since they did not exist and I found no evidence of them on the website. In general, I think a history of different tunings would be useful. My father used to be quite obsessed with various tunings. He built his own harpsichord, in part so that he could play it in different tuning modes. - Open2universe 00:26, 15 November 2005 (UTC)

The adoption (or indeed superimposition) of modality by your father's Dolmetch generation was something of a fad attempting to force vernacular music into a classical corset. Certainly, the tuning scale of the Highland Great Pipe is not merely scordatura, but positively irregular, as is that of a number of other bagpipes - the Northumbrian pipes, for example, have music written as if in the key of C but actually played in D, such is the drift in pitch since the instrument was first made. Part of this is because the HGP cannot play a direct scale because of conflicting inharmonics, and is therefore forced to pass through intermediate notes on the way, the roots of gracing. Equally, some attention should be paid to the harmonic identites between this and Arabic music, also in the use of pentatonic scales.
For further reference, the work of Erycius Puteanus and Vincenzo Galileo on the work of Hucbald (c880) about 1600 is an incontrovertible waypoint in the subject, completed by Athanasius Kircher some years later. I think you may find this is about the point at which pythagorean theory is understood and reintroduced into tuning, although I could be wrong - see Vincenzo Galileo's 1584 24 Dances as an example. It was this that drove Bach into his Wohl-temperierte Clavier studies, as his thesis is that a particular tuning not only sounds equally in tune in all keys, but also in modulation between them - the problem is nobody seems to know what that tuning is. Pythagorean equal temperament it most certainly is not, nor any musical temperament, as any violinist will tell you. Perhaps the great Johann Sebastian had spent too much time with his head buried in organ harmonics to realise he was seeking the impossible. The Concert pitch page contains much detail for later periods.

—Preceding unsigned comment added by 109.129.84.66 (talk) 21:46, 7 June 2010 (UTC)

Check out the French version[edit]

Whoa. Anyone want to translate some of that and bring it in here? It's fantastic.

Proposed merge[edit]

I'd like to see Tuning merged with this page and replaced with a disambiguation page, on the grouds that they are both "Musical tuning", and the lack of a distinctively different name is confusing. Please comment on this over at Talk:Tuning. Here is a proposed draft for the new page to appear here: User:Rainwarrior/TuningMerge. Rainwarrior 20:22, 5 February 2006 (UTC)

Sound[edit]

I've created a Category:Tuning examples on wikicommons (see http://commons.wikimedia.org/wiki/Category:Tuning_examples). Have a look and feel free to use some of it! --84.151.133.24 00:02, 26 March 2006 (UTC)

Piano Technicians Guild[edit]

Ummm, can someone tell me why my adding of a link to the Piano Technicians Guild article was reverted? Thanks. --TrustTruth 15:13, 2 May 2006 (UTC)

My guess is that you put it in the links for Tuning Systems, and it belongs to Tuning Practice (which doesn't yet have a links section). Even still, I don't think it's directly related to tuning, so probably doesn't deserve a link anyway. (This is my guess as to why Hyacinth reverted your edit.) - Rainwarrior 18:59, 2 May 2006 (UTC)
It belongs at piano tuning, where it is prominently featured. Hyacinth 19:06, 2 May 2006 (UTC)

Sound examples of musical tunings[edit]

I have recently uploaded Bach's Prelude #1, played in different musical tunings, see

,

,

,

,

,

. --Pete

They are pretty good. I suggest using them within the article in order to illustrate each tuning's section.--Isacdaavid (talk) 01:23, 19 May 2012 (UTC)

Tuning to a telephone[edit]

Does this really have a place on this page? It seems quite trivial to me. Why give a detailed description of how to do something that can no longer be done? It's interesting that people would have ever practiced this, but I don't think there's an appropriate place on this page for trivia. Perhaps if we had a detailed history of tuning practice at some point? - Rainwarrior 16:18, 7 June 2006 (UTC)

Other scale systems[edit]

The reasons for my cleanup of this section are the following:

  1. Removing the technical terms "hemitonic" and "anhemitonic" which are obscure and relevant only to pentatonic scales.
  2. If Pelog is a fusion of three pentatonic modes (is there a source for this?), that information belongs at the Pelog page. (Again, it's technical detail which doesn't really belong in a links section.)
  3. Removing the "Longitude" nickname, this just seems silly.

I also have a question about the following: this system was first promoted by al-Farabi using a 25 tone scale. What is a 25 tone scale, and in what way does it use quarter tones? Should this not be 24 tones? (Was the octave counted by mistake?) - Rainwarrior 18:00, 7 June 2006 (UTC)


I'm not that technical, but my PC-Tuner allows me to choose for 1/4 meantone, Kirnberger, Werckmeister and Kellner temperament. However, these are not mentioned in the section of the article. Don't ask me why they should, ask AP Tuner. Ciao --Selach 00:28, 22 February 2007 (UTC)

Tuning theory merge[edit]

I'm suggesting we merge Tuning theory to this page. It currently has little content, but its purpose is not significantly distinct from "Tuning systems" outlined on this page. - Rainwarrior 23:19, 28 June 2006 (UTC)

With no objections after several weeks, I have done this merge. - Rainwarrior 05:46, 26 July 2006 (UTC)

Stopper Tuning[edit]

Should Bernhard Stopper's tuning system be listed here? I don't know much about it, but he sells products based on this special tuning. Is he and/or his tuning system well-respected? Dallasvaughan (talk) 21:46, 6 October 2008 (UTC)

Impossibility of perfect tuning[edit]

The article states: "It is impossible to tune the twelve-note chromatic scale so that all intervals are "perfect" - I'd be very grateful if anyone knows enough about the subject to explain why it is impossible? Or if such an explanation exists elsewhere? Joeflintham (talk) 11:47, 29 October 2008 (UTC)

The simple answer is that 2^(7/12) is not exactly equal to 3/2, but instead is 1.4983... Yet BOTH of these are the "correct" definition of a perfect 5th.

Yes, BUT: if one were to say "because my dog doesn't like the sound", such an explanation would be unsatisfying -- though technically correct -- if the definition of "perfect" were to involve whether my dog found the sound pleasing... What seems to be missing from the simple answer above is an explanation for why 2^(7/12) and 3/2 are relevant to the issue and why "BOTH of these" make any sense for being a "correct definition". It would be much appreciated by many of us if some sort of explanation could be given in sufficient depth so as to be understandable as making sense... — Preceding unsigned comment added by 98.125.235.136 (talk) 18:14, 26 June 2013 (UTC)


On the one hand, we have the harmonic series (nodes on a single string) with frequencies f,2f,3f,4f,5f...corresponding to C,C,G,C,E,G,C... Thus quite clearly a perfect 5th is a factor of 3f/2f i.e. 1.5. We also have the octave as a factor of 2. Now, by using the "cycle of 5ths", going repeatedly up a 5th and down an octave, we can get all the notes for a chromatic scale.

Unfortunately, such a chromatic scale isn't self-consistent. The size of a semitone varies depending on the key (so we can't modulate), and if you keep on with the cycle of 5ths for long enough, you *don't* get back where you started! --RichardNeill (talk) 07:18, 22 April 2009 (UTC)

That's true, but the tempered fifth is quite close to a pure 3/2. So, depending on the timbre and musical context, it might not be that noticeable, just a slow beating sound. A better example, because more extreme is to look at pure major thirds. In the twelve tone system three major thirds stack up to make the octave 2/1. But if you use the fifth harmonic just intonation 5/4, then three of them stack up to make 125/64 which at 1158.9411 cents is a long way away from an octave, nearly a quarter tone away from it. So there is no way to have the octave and the major third even close to just intonation in the twelve tone system. I'll put this into the article, it would be good to have something to explain that comment which won't be easy for a newbie to understand. Robert Walker (talk) 19:56, 28 August 2012 (UTC)
Just made that edit. Also ended up rewriting the just intonation summary as well. It's a little longer than the other sections now, but I think perhaps it is worth doing it like that as the issues involved in just intonation help to make the motivation for the other tunings clearer. Robert Walker (talk) 20:45, 28 August 2012 (UTC)

Some audible examples[edit]

Sox (in Linux) makes it very easy to synthesise some chords in the different tunings.

5ths (first in equal-temperament, then in just-intonation). They sound quite similar.

 play -n -c1 synth sin 440 sin 659.255 fade q 0.1 3 0.1
 play -n -c1 synth sin 440 sin 660 fade q 0.1 3 0.1

3rds (first in equal-temperament, then in just-intonation). These sound VERY different.

 play -n -c1 synth sin 440 sin 544.599 fade q 0.1 3 0.1
 play -n -c1 synth sin 440 sin 550 fade q 0.1 3 0.1

--RichardNeill (talk) 07:18, 22 April 2009 (UTC)

I think it depends on how demanding and permissive you are in and of your ear, as it opens the question to what extent perfect pitch exists. It tends to be an instrumentalist's psychosis, as they become increasingly sensitive to pitch beat over years of tuning - particularly with fixed-interval instruments like woodwind, who can only change their root tuning by adjusting the length between the mouthpiece and key-holes. For example, I tune my harp that way - which can generate the kind of circular recursion you talk about above working on half-length harmonics to generate fifths above and below, iteratively to cover the entire scale. At least that way the beast is internally consistent, until some joker plays an A-440 which is about A-440.85673 or whatever and expects you to retune fifty-odd strings in musical in twenty seconds - the answer is to slip the oboist a pint beforehand! Some very popular bands are quite wild (for no particular reason André Réus springs to mind, probably quite unfairly) because they can get away with it by their stage presence. The key is keeping the customer satisfied, not yourself, as if you pursue that route you can get into some almost Gouldesque introversions. —Preceding unsigned comment added by 109.129.84.66 (talk) 22:06, 7 June 2010 (UTC)

Why A?[edit]

I came here to find information about a simple question, but couldn't. Why is the most frequently use reference for tuning (and for instance the one used to define the international standard concert pitch) the "A above the middle C", which is also the pitch of the vast majority (at least in my experience) of tuning forks. Of course the answer could be that one needs to choose some note, and this one is no worse than any other. Maybe it has to do with the way violins are usually tuned; this would at least explain why it is not the middle C, which in other respects seems to be a more common reference point. (But then D seems a good candidate as well.) I think if some reliable information on this is known, this article would be a good place... Marc van Leeuwen (talk) 09:33, 29 April 2011 (UTC)

Stringed instruments must tune open strings. Violins (and double basses) could therefore settle for G, D, A, or E, but have no C string. Violas and cellos have C G D and A, but no E string. Of the three notes they have in common, the A is the highest (for the violin, viola, and cello) and therefore in a slightly more favourable range than G or D for the ear to discriminate pitch. All this is purely Original Research, of course. Perhaps a source can be found to confirm this, and it could then be added to the article.—Jerome Kohl (talk) 22:15, 29 April 2011 (UTC)

Tabla: pitched or unpitched?[edit]

Are South Asian drums such as the tabla or mridangam considered pitched or unpitched? I'd like to mention them in the subsection on percussion instruments. These drums are "tuned" with an added mass, the syahi, in the middle of the head. __ Just plain Bill (talk) 15:00, 31 March 2012 (UTC)

According to Randel, Don Michael (2003). The Harvard Dictionary of Music, p.864. ISBN 9780674011632: "The conical right-hand drum (tablā or dāhinā)...is tuned to a definite pitch. The kettle-shaped left-hand drum (bāyā)...is tuned to a lower but indefinite pitch." The right hand drum appears to be tuned to Sa. Hyacinth (talk) 23:27, 31 March 2012 (UTC)
Looking further, it seems that the black spot is more about timbre, and is applied when the drum is made. __ Just plain Bill (talk) 04:20, 1 April 2012 (UTC)
The black spot is about timbre but is also connected to pitch, in that it suppresses the inharmonic overtones, making it possible (and important) to tune the drum to a degree of the scale. See vibrations of a drum head. Andrewa (talk) 06:49, 10 April 2012 (UTC)

Link to Spanish wiki is wrong[edit]

The page in the Spanish Wikipedia this article points to is about absolute tuning and corresponds to concert pitch, as opposed to the tuning systems used to define intervals.

I couldn't find a similar article page covering musical tuning systems in Spanish, so the link should be removed. I'm posting this as a warning before I delete it, just in case that someone comes up with a better idea. --Isacdaavid (talk) 01:18, 19 May 2012 (UTC)

Are you going to add it to Concert pitch? Hyacinth (talk) 03:05, 19 May 2012 (UTC)

Wrong alias[edit]

Tone system and musical tunings are two different things!

I changed the alias link. An entry "tone system" should also refer to the Ancient Greek and various other tone systems used since Byzantium until today. It is a completely different subject, because its structure is not a direct subject of intervals (only in a very eurocentric concept of music theory). Any objections? Platonykiss (talk) 13:29, 3 September 2013 (UTC)