Skip to content

Locatelli, Mozart, Tunings, and Temperament

Locatelli

  • Op. 1 (1721) – 12 concerti grossi (in F, C minor, B flat, E minor, D, C minor, F, F minor, D, C, C minor, G minor)
  • Op. 2 (1732) – 12 flute sonatas (in G, D, B flat, G, D, G minor, A, F, E, G, D, G)
  • Op. 3 (1733) – L’ arte del violino 12 violin concertos (in D, C minor, F, E, C, G minor, B flat, E minor, G, F minor, A, D “Il laberinto armonico”)
  • Op. 4 (1735) – 6 Introduttione teatrale (in D, F, B flat, G, D, C) and 6 concerti grossi (in D, F, G, E, C minor, F)
  • Op. 5 (1736) – 6 trio sonatas (in G, E minor, E, C, D minor, G “Bizarria”)
  • Op. 6 (1737) – 12 violin sonatas (in F minor, F, E, A, G minor, D, C minor, C, B minor, A minor, E flat, D minor)
  • Op. 7 (1741) – 6 concerti a quatro (in D, B flat, G, F, G minor, E flat)
  • Op. 8 (1744) – 10 trio sonatas (in F, D, G minor, C, G, E flat, A, D, F minor, A)

Mozart:

https://en.wikipedia.org/wiki/Ludwig_Ritter_von_K%C3%B6chel

Ludwig Alois Ferdinand Ritter von Köchel (IPA: [ˈkœçəl]) (January 14, 1800 – June 3, 1877) was a musicologist, writer, composer, botanist and publisher. He is best known for cataloguing the works of Mozart and originating the ‘K-numbers’ by which they are known (K for Köchel).

Born in the town of Stein, Lower Austria, he studied law in Vienna, and for fifteen years was tutor to the four sons of Archduke Charles of Austria. Köchel was rewarded with a knighthood and a generous financial settlement, permitting him to spend the rest of his life as a private scholar. Contemporary scientists were greatly impressed by his botanical researches in North Africa, the Iberian Peninsula, the United Kingdom, the North Cape, and Russia. Additional to botany, he was interested in geology and mineralogy, but also loved music, and was a member of the Mozarteum Salzburg.

In 1862 he published the Köchel catalogue, a chronological and thematic register of the works of Mozart. This catalogue was the first on such a scale and with such a level of scholarship behind it; it has since undergone revisions. Mozart’s works are often referred to by their K-numbers (c.f. opus number); for example, the “Jupiter” symphony, Symphony No. 41 K. 551.

Moreover, Köchel arranged Mozart’s works into twenty-four categories, which were used by Breitkopf & Härtel when they published the first complete edition of Mozart’s works from 1877 to 1910, a venture partly funded by Köchel.

He also catalogued the works of Johann Fux.[1][2]

Ludwig Ritter von Köchel died at age 77 in Vienna.

https://docs.google.com/a/silentflame.com/Doc?id=dcrm3bt7_6f3tf8kjx

…In the decades after Mozart’s death there were several attempts to catalogue his compositions, but it was not until 1862 that Ludwig von Köchel succeeded. Köchel’s 551-page catalogue was titled Chronologisch – thematisches Verzeichnis sämtlicher Tonwerke Wolfgang Amadé Mozarts (Chronological – Thematic Catalogue of the Complete Musical Works of Wolfgang Amadé Mozart). The catalogue included the opening bars of each piece, a so-called incipit….

…Köchel attempted arranging the works in chronological order, but the compositions written before 1784 could only be estimated. Since Köchel’s work, many more pieces have been found, re-attributed, and re-dated, requiring three catalogue revisions. These revisions, especially the third edition by Alfred Einstein (1937), and the sixth edition by Franz Giegling, Gerd Sievers, and Alexander Weinmann (1964), incorporated many corrections…

https://en.wikipedia.org/wiki/K%C3%B6chel_Verzeichnis

The Köchel-Verzeichnis is a complete, chronological catalogue of compositions by Wolfgang Amadeus Mozart (born 1756) which was originally created by Ludwig von Köchel. It is abbreviated K or KV. For example, Mozart’s Requiem in D minor was, according to Köchel’s counting, the 626th piece Mozart composed. Thus, the piece is designated K. 626. Köchel catalog numbers not only attempt to establish chronology, but also give a helpful shorthand to refer to Mozart’s works.

Wo is Basel? …a friend arrives and helps the Moazarts find the wife’s hair ribbon before going for a drive. “…The first line, ‘Dearest Almond, where is my husband?’ indicates the level of nonsense present here…”

https://books.google.com/books?id=CChN90GGcQQC&pg=PA96&lpg=PA96&dq=Liebes+Mandel,+wo+is+Bandel%3F&source=web&ots=4f62VznQNm&sig=ttHP3RhxlRnZ_VcBblrT8KqNfUo&hl=en&sa=X&oi=book_result&resnum=2&ct=result

The link to Fuchs was suggestive. Italics mine. I’m thinking something about how Emma dragged them between branes.

https://docs.google.com/a/silentflame.com/Doc?id=dcrm3bt7_6f3tf8kjx

Info here:

The Gradus Ad Parnassum (Step or Ascent to Mount Parnassus) is a theoretical and pedagogical work written in Latin language, which Fux dedicated to Emperor Charles VI in 1725.

It is divided in two major parts. In the first part, Fux presents a summary of the theory on Musica Speculativa, or the analysis of intervals as proportions between numbers. This section is in a simple lecture style, and looks at music from a purely mathematical angle, in a theoretical tradition that goes back, through the works of Renaissance theoreticians, to the Ancient Greeks. The words of Mersenne, Cicero and Aristotle are among the references quoted by Fux in this section.

Easley Blackwood and Microtonality

Microtonal music may refer to all music which contains intervals smaller than the conventional contemporary Western semitone. The term implies music containing very small intervals. By this definition, the following systems are not microtonal: a diatonic scale in any meantone tuning; much Indonesian gamelan music; and Thai, Burmese, and African music which use 7 approximately equally spaced tones in each (approximate) octave.[citation needed] However, the term “microtonal” is also used to describe music using intervals not found in 12-tone equal temperament, so these musics, as well as musics using just intonation, meantone temperament, or other alternative tunings may be considered microtonal.

….

[edit]

Meantone tunings date from the early 1490s, as scholars such as Richard Taruskin and Patrizio Barbieri have pointed out.[citation needed] Since the time of Pietro Aron‘s treatise (Aron 1523), meantone tuning became extremely common and was considered to represent “correct” tuning throughout Europe until 1750 and in England and Spain until 1850.[citation needed]Such meantone tunings sound similar to, but more harmonious than, conventional Western tunings of 12 equal pitches per octave, when performed on an instrument limited to 12 pitches per octave, as long as the composer restricts him/herself to a narrow compass of musical keys close to the root note of the tuning (i.e., if the meantone tuning is tuned starting with C, the keys close to C major will sound like a more harmonious take on conventional Western music; distant keys, however, like Eb minor, will contain highly audibly exotic and sometimes discordant musical intervals.)[citation needed] Some early composers, however, deliberately wandered far afield from the root note of meantone tunings, producing highly microtonal effects in typical renditions of their music. One prominent example is “Ut, Re, Mi, Fa, Sol, La” by the British virginal composer John Bull (composed sometime between the 1580s and 1610, and included in the Fitzwilliam Virginal Book).[citation needed] Such extensive modulation in meantone tuning on a 12-note-per octave instrument sounds “wolf” fifths and other exotic musical intervals not found in contemporary Western music using 12 equal pitches per octave.[vague]

It was quite common in the heyday of meantone tuning to find keyboards with “split” keys or special organ stops, often allowing 13-16 pitches per octave of meantone tuning.[citation needed] In this way music by Handel and many other composers could be played in meantone tuning, maintaining smooth harmony and conventional-sounding melody even as the music modulated to distant keys. Teachers of string instruments, including Leopold Mozart, and of wind instruments, including Quantz, expected their students to distinguish all enharmonic pairs of pitches (like F# and Gb) in their playing, with the sharpened version of one diatonic tone being played lower than the flattened version of the next diatonic tone up.[citation needed] So composers in the meantone era who restricted their harmonic compass were doing so largely because they were writing for keyboard or an ensemble that included a keyboard.[citation needed]

In the decades after Mozart’s death there were several attempts to catalogue his compositions, but it was not until 1862 that Ludwig von Köchel succeeded. Köchel’s 551-page catalogue was titled Chronologisch – thematisches Verzeichnis sämtlicher Tonwerke Wolfgang Amadé Mozarts (Chronological – Thematic Catalogue of the Complete Musical Works of Wolfgang Amadé Mozart). The catalogue included the opening bars of each piece, a so-called incipit.


More on meantone tuning (from Kyle Gann’s website, “An Introduction to Historical Tunings”):

The generating principle behind meantone was that it was more important to preserve the consonance of the major thirds (C to E, F to A, G to B) than it was to preserve the purity of the perfect fifths (C to G, F to C, G to D). There are acoustical reasons for this, namely – though I wouldn’t want to go into the math involved – that the notes in a slightly out-of-tune third, being closer together than those in a fifth, create faster and more disturbing beats than those in a slightly out-of-tune fifth. (I can confirm this from experience with my own Steinway grand, which I keep tuned to an 18th-century tuning.) The aesthetic motivation for meantone was that composers had fallen in love with the sweetness of the major third, and were trying to get away from the medieval austerity of open perfect fifths.

There was no one invariable meantone tuning; before the 20th century, tuning was an art, not a science, and each tuner had his own method of tuning according to his own taste. The following is a chart of a meantone tuning defined in 1523 by Pietro Aaron.

Pitch: C C# D Eb E F F# G G# A A# B C
Cents: 0 76.0 193.2 310.3 386.3 503.4 579.5 696.8 772.6 889.7 1006.8 1082.9 1200

Because it determines what sounds good, tuning has a pervasive influence on compositional tendencies. Every piece of pitched music is the expression of a tuning. Meantone encouraged composers to use major and minor triads, to avoid open perfect fifths without thirds, and to not stray more than three or four steps in the circle of fifths away from a central key. Renaissance and early Baroque music played in meantone sounds seductively sweet and attractive. By playing it in modern equal temperament, we do violence to its essential nature. Perhaps that’s why this repertoire is no longer often heard. It’s been painted over with the ugly gray of equal temperament.

Leave a Reply

Your email address will not be published. Required fields are marked *

This site uses Akismet to reduce spam. Learn how your comment data is processed.