Talk:Meantone temperament
| WikiProject Tunings, Temperaments, and Scales | |||||||||||
|---|---|---|---|---|---|---|---|---|---|---|---|
|
|||||||||||
This is what was in the article before I edited. I don't really understand it, and what I do understand doesn't seem strictly relevant to meantone, so I'm moving it here. I've replaced it with a stubby entry for now, but I'll be expanding it in time. --Camembert
Original article text follows
In a modern 12 note equal temperament the semitone is exactly half a tone logarithmically.
If the semitone is allowed to be more than half a tone, one can get a better approximation to just intonation.
If the semitone is a rational fraction of a tone logarithmically, one gets a finite number of notes in an octave.
Semitone/Tone Notes
1/2 12
4/7 43
3/5 31
5/8 50
2/3 19
One can make some intervals perfectly tuned. In Pythagorean tuning, 1:2 (the Octave) and 2:3 (the Fifth) are perfect and 9:10 is approximated by 8:9. This gives a semitone of 243:256, a tone of 8:9, and a major Third of 64:81 (1.265625). Quarter comma meantone tunes 1:2 and 4:5 (the major Third) perfectly, giving a tone ratio 2:sqrt(5), a semitone ratio 5^(5/4):8, and a Fifth of 5^(1/4) (1.495349).
Contents |
[edit] Notation and the wolf
The page as it stands has a nonstandard notation for accidentals (black notes). The usual is to notate all accidentals on the flatward side of the wolf as sharps, and vice versa. That is, if the wolf is between G# and Eb, you use F#, C#, G#, Eb, Bb. This is also easier to understand because A# is an unfamiliar note whereas Bb is very common. Then the flats and sharps form a mnemonic for which intervals are 'bad': the fifth G#-Eb is bad as are all thirds where the root is a sharp or where the third is a flat. --Tdent 21:53, 14 Apr 2005 (UTC)
[edit] Definition and history
The definition of meantone should not imply that the major 3rd is 'just', since in 1/5 comma, 1/6 comma, etc. etc. (all of which were historically referred to as mean-tone) it is not. The correct definition is that each perfect fifth is an equal interval apart from the wolf, with a corollary that the fifths are narrower than equal-tempered. (Otherwise Pythagorean tuning and equal temperament would also qualify.)
It would be useful to indicate the historical uses of (the various types of) mean-tone, which was widespread in the Renaissance, Baroque and early Classical eras. Even though keyboards began to be tuned to other types of temperament in the 18th century, vocal and wind/string instrument intonation was still taught according to a 1/6-comma meantone scheme in the time of Mozart. It appears likely that keyboard instruments were tuned to a slightly altered form of meantone through the 19th century, for example temperaments based on 1/8 comma meantone. --Tdent 22:24, 14 Apr 2005 (UTC)
[edit] Image copyright problem with Image:Tonraum30.11-14 1.jpg
The image Image:Tonraum30.11-14 1.jpg is used in this article under a claim of fair use, but it does not have an adequate explanation for why it meets the requirements for such images when used here. In particular, for each page the image is used on, it must have an explanation linking to that page which explains why it needs to be used on that page. Please check
-
- That there is a non-free use rationale on the image's description page for the use in this article.
- That this article is linked to from the image description page.
This is an automated notice by FairuseBot. For assistance on the image use policy, see Wikipedia:Media copyright questions. --15:42, 2 November 2008 (UTC)
[edit] 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 the spreadsheets which, kept permanently updated, are available for FREE. I also uploaded years ago a provisional "Update" to the book of 1978. The website lately gives information on the recently released new version of Unequal Temperaments 2008, which includes a detailed treatment of MEANTONE TEMPERAMENT. (Please note: the website does NOT sell the book)
I would find it useful to Wikipedia readers if my website was included among External Links:
Kind regards
Claudio
Dr. Claudio Di Veroli
Bray, Ireland
86.42.128.58 (talk) 17:19, 26 February 2009 (UTC)
[edit] Suggestion for improvement
As a musician with a strong math and physics background, I can still say that the introduction of the concepts of "5-limit musical", "7-limit musical", etc. early on without clarification makes the article difficult to understand at the outset. One would hope that at least some cursory explanation can be offered for these terms. Thanks KarlRKaiser (talk) 03:33, 21 September 2009 (UTC)
[edit] Clarification
What the hell does the shape of the keyboard have to do with anything? —Preceding unsigned comment added by 184.189.220.19 (talk) 00:28, 21 May 2011 (UTC)
[edit] Difficulties following argument; missing thummer.jpg
1> It seems that the .jpg of the "Thummer" keyboard is missing.
2a> As a physicist / singer / early music listener I find this article excellent, but have trouble following the para with Easley Lockwood's "R" and its relation to various mean tones. Accepting that the stated relationship is exact:
log2 [interval of fifth] = (3R+1)/(5R+2)
then it seems to me that R cannot be the ratio of (frequencies) for wholetone to semitone, but rather its logarithm (log2). Am I missing something?
- It's not even the logarithm of the ratio, but the ratio of the logarithms. —Tamfang (talk) 00:11, 23 October 2011 (UTC)
2b> The table "Meantone Tunings" is very useful. The relationship of column 1 to column 2 is clear (once I interpret R as a logarithm). But I have trouble relating (approximately) column 3 (the syntonic adjustment) to column 1 (R). I would be helpful to me to see explicit constructions from stacked tempered fifths of the wholetone and the diatonic semitone whose ratio defines "R". Is "R" the (log) ratio of pitch [F] to pitch [E] after [F]:[C], [C]:[D] and [D]:[E] have been constructed from stacked tempered fifths? And why is the relation of column 3 to column 1 only approximate -- are not the meantone fractions (1/4 or 1/6 or 1/11) also logarithmic?
68.239.154.181 (talk) 14:32, 19 September 2011 (UTC)
