Talk:Musical temperament

A Proposal

I think this article is the best place to add the details relating to the adjustment of pitch in western band and orchestra instruments from equal temperment to just temperment. Western college students are taught cents to make these adjustments. The article would help band and orchestra students learn when and why they need to adjust their pitch of individual notes upward or downward as a function of the key they are presently playing in.

I would like to add a section Just termperment and equal tempermant that would include a table of cents adjustments, and a tutorial for its use.

Alternatively, a separate article could be made, or it might be added as an application use in the cents article.

Mbbradford 21:25, 9 November 2006 (UTC)

2 is somewhat more special than 3 or 5 but not infinitely so

Are there any temperaments in use that adjust the octave, {instead of/as well as} the fifth or the third, to improve the worst of them? —Tamfang 05:53, 5 December 2006 (UTC)

Yes, but they're a bit more rare. Check out at the bottom of equal temperament. You should find the Bohlen-Pierce scale, and Wendy Carlos' alpha/beta scales as a couple of examples. - Rainwarrior 05:41, 6 December 2006 (UTC)

Unequal Temperaments book and website

Dear friends,

The Unequal Temperaments book of 1978 was described-in writing-as the definitive reference on the matter by authorities such as John Barnes, Hubert Bédard, Kenneth Gilbert, Igor Kipnis, Rudolf Rasch and others. In the 1990's I also developed the first professional-grade temperament spreadsheets.

Eventually I setup the "Unequal Temperaments" website, where I uploaded some updated information and then announced the new version of Unequal Temperaments 2008/2009. (Please note that the website does NOT sell the book). The book has received recently (Oct. 2009) a favourable review by the British Clavichord Society quarterly publication.

I find that for the benefit of Wikipedia readers my new book should be mentioned, or at least my website included among External Links:

• Unequal Temperaments website, with Preview of the new 2008 book by Claudio Di Veroli

Kind regards

Claudio

Dr. * [http://wiki.riteme.site/wiki/Claudio_Di_Veroli/ Claudio Di Veroli 86.42.128.58 (talk) 17:18, 26 February 2009 (UTC)

Post edit remarks

More detailed support for major edit and suggestions for possible further edits or revert+edits Specialists may find some technical error of which I am not aware, or, alternatively, the explanation in terms of wave form might more properly follow a paragraph elaborating on the musical utility of temperament. I propose that at some point a separate article develope with a title along the lines of Physics of Temperatment and that can be linked from the general article Musical temperament. This way, people who are inclined to understand this widely misunderstood topic from the perspective of wave forms etcetera will have a whole separate article. Also, I must be the first to confess that the explanation in those terms needs a graphic support and also there should be links in there to copyrighted explanations by professional textbook writers. One does what one can, and passes the torch to the next wikepedian...c'est la vie. Wikidgood (talk) 23:30, 4 December 2010 (UTC)

Have you seen Music and mathematics? —Tamfang (talk) 05:28, 5 December 2010 (UTC)

Kind of Heavily Relies on Jargon Without Clear Explanation for Non-specialists; Also to Express Support for Proposal

It would be nice to have hypertext to an article which explains some of the technical terminology, particularly in the first paragraph the terms:harmonic timbres, or tones with harmonic partials. This is a vast topic and although it is nice to have a succinct article it seems that quite a bit more can be said, agreed, please go forward with info on equal/just temperaments. Might eventually need to be split into a separate article. Is that topic the main priority, I wonder, for proceeding with this main article or is there a gap, a more pressing subtopic which warrants treatment? At any rate, looking forward to the contribution suggested by Mbbradford; I added a title to your post so now we have a table of contents, please feel free to modify the title if you so desire. Wikidgood (talk) 22:40, 4 December 2010 (UTC)

Personal Essay

The bulk of this article as it stands is unreferenced and written in a chatty personal style inapproprate to Wikipedia. Really it needs a very heavy trimming.Frank Zamjatin (talk) 14:10, 10 July 2011 (UTC)

Beating

The word "beating" is used several times in the Meantone and Well sections, but never described or defined. — Preceding unsigned comment added by JimHardy (talk • contribs) 07:41, 1 June 2018 (UTC)

Never mind, I found it. Jim Hardy (talk) 07:45, 1 June 2018 (UTC)

Digital Pianos

On some digital pianos from CASIO you can choose from the following temperaments: 00 Equal Temperament, 01 Pure Major, 02 Pure Minor, 03 Pythagorean, 04 Kirnberger 3, 05 Werckmeister, 06 Mean-Tone, 07 Rast, 08 Bayati, 09 Hijaz, 10 Saba, 11 Dashti, 12 Chahargah, 13 Segah, 14 Gurjari Todi, 15 Chandrakauns, 16 Charukashi. On som digital pianos from YAMAHA you can choose from the following temperaments: 1 Equal temperament, 2 Pure Major, 3 Pure Minor, 4 Pythagorean, 5 Meantone, 6 Werckmeister, 7 Kirnberger. From manuals from the two makers. — Preceding unsigned comment added by 83.223.9.100 (talk) 13:25, 10 October 2019 (UTC)

To add to article

To add to this article: mention of the Rameau temperament. 173.88.246.138 (talk) 20:24, 19 December 2021 (UTC)

Broken SVG

The SVG appears broken at least for me on Microsoft Edge on macOS: Theone256 (talk) 10:59, 22 April 2024 (UTC)

And in Firefox on MacOS. —Tamfang (talk) 20:03, 22 April 2024 (UTC)

Incorrect definition for temperament and poor explanation of beating and interval purity

For the definition of temperament, I am referring to this excerpt of the article:

"Temperament refers to the various tuning systems for the subdivision of the octave," the four principal tuning systems being Pythagorean tuning, just intonation, mean-tone temperament, and equal temperament."

I would highly recommend reviewing the credibility of the source this is referencing. There are several issues with this definition:

1) Temperaments do not necessarily use the octave as a basis for division. This is a common misconception: While *most* temperaments do, it is false to include subdivision of the octave as part of the definition. As an example, see this article on "Carlos Alpha," a nonoctave equal temperament created by composer Wendy Carlos: [1]https://en.xen.wiki/w/Carlos_Alpha

2) The quote is phrased in an ambiguous way that risks misrepresenting Just Intonation as being included within the category of temperament. It seems as though the implication is: "Temperament refers to the various tuning systems for the subdivision of the octave, the four principal tuning systems [of said various systems] being Pythagorean tuning, just intonation, mean-tone temperament, and equal temperament." The fact that the other three listed tunings are indeed categories of temperament makes the incorrect implication even stronger. The subsequent paragraph clarifies that temperament is a deviation from JI, but I believe that this excerpt should be rephrased anyhow.

The subsequent paragraph is also vague and reflects several gaps in understanding:

"In just intonation, every interval between two pitches corresponds to a whole number ratio between their frequencies, allowing intervals varying from the highest consonance to highly dissonant. For instance, 660 Hz / 440 Hz (a ratio of 3:2) constitutes a fifth, and 880 Hz / 440 Hz (2:1) an octave. Such intervals (termed "just") have a stability, or purity to their sound, when played simultaneously (assuming they are played using timbres with harmonic partials) because pure intervals do not waver or beat regularly.^{[citation needed]}; the proportions of their frequencies can be expressed as whole numbers."

Here, it seems as though the two ways the author defines a "just" or "pure" interval are either

-An interval whose ratio can be expressed through whole numbers

-An interval which does not "beat"

These definitions are both misleading at best and incorrect at worst.

1) The proportion of *any* two rational frequencies can (and should always) be expressed as whole numbers. That is how ratios work: there will always be a common denominator. "Purity" of musical intervals is a relative concept relating to how simple the ratio between two frequencies is. The 3:2 ratio of a just fifth is usually considered "pure," but it is less pure than the 2:1 octave and more pure than the 5:4 major third. The harmonic series (which the author should reference specifically as the physics phenomenon being discussed, instead of vaguely referring to "just intonation",) extends infinitely and will eventually contain every possible rational interval, so defining purity by the presence or absence of an interval in the harmonic series also does not make sense.

2) "Beating" occurs due to interference between two frequencies. Beating as an auditory experience is different from beating as a mathematical phenomenon: Mathematically, the number of beats per second is equal to the difference in frequency between the two pitches. The only interval that literally does not beat is a pure unison, where the difference in frequency would be 0. Additionally, because frequency is exponential and not linear, the same interval will beat faster the higher it is played, making it a misleading way to measure "purity".

The auditory experience of beating is complicated: the human ear only perceives audible "beating" at about 7 beats or less per second (meaning when the difference between the two frequencies is 7 Hz or less). This is called the critical band. When an interval beats at more than 20 beats per second, we begin to perceive the beating as a third frequency which we call a difference tone. For example, if we play the 4th and 5th partial of a harmonic series (the 5:4 major third), it will beat at such a frequency that we "hear" the fundamental of that series as an imagined third "pitch". All this to say, using beating as a measure of interval purity is even more complicated than simply stating that "more beating=less pure." We perceive intervals as more pure when the frequency of the beating (the difference tone) forms a more simple ratio with the two original frequencies. This is why we do not perceive the beating of an octave, even though it still exists: Say we play A 440Hz and A 880Hz together. The interval will beat 440 times per second, giving the illusion of another 440 Hz frequency in unison with the bottom A.

I am very concerned about the quality and credibility of this article as a whole. On top of being factually misleading/incorrect and lacking many sources, it is also poorly written with a number of grammar, syntax, and punctuation errors. As someone who is very passionate about this area of music theory, I am concerned that this article reflects poorly on not only this individual author, but on the quality and credibility of research in this field as a whole. I would like to recommend that this article be taken down until it has been corrected, appropriately cited, and edited to an adequate standard of academic writing. Greenemily (talk) 23:57, 29 August 2024 (UTC)