What is the significance of Pythagorean comma (as in why is there …
This difference, which ends up being about 21.5 cents, is called a Syntonic Comma (distinct from the Pythagorean Comma). Composers and theorists at the time were in love with thirds, so a popular tuning system used in the Renaissance and early Baroque was Quarter Comma Meantone. This system made all the fifths too flat by 1/4 of the Syntonic ...
How do you flatten a pure fifth by a fraction of the syntonic comma?
2016年1月16日 · A pythagorean fifth is the ratio 3/2. A fifth in 1/4 comma meantone is 5^1/4 (1.495). The syntonic comma is 81/80. When I try to calculate the size of the fifth I end up with 1.246875 instead of the expected 1.495. Here's how I'm getting there: subtracting (81/80 * 1/4) (a quarter of the syntonic comma) from a pure fifth (3/2). What am I doing ...
tuning - Music: Practice & Theory Stack Exchange
Solving the Pythagorean comma at a practical level was needed. The earliest solution that I know of was that of Pietro Aron in his book Toscanello in musica published in 1539: he proposed dividing the comma into four parts, and lowering the tuning of four consecutive fifths by that amount to create a perfect octave while retaining most of the ...
How can I improve my violin intonation for enharmonic notes?
2019年6月16日 · The violin is one such example and while a majority of music written for the violin still treats enharmonic notes as the same pitch, there is music where a distinction between E♯ and F exists (I believe that E♯ is slightly higher than F …
In Pythagorean tuning, what's the frequency of the tonic of each …
2014年6月6日 · That brings you to the "perfect Pythagorean B♭" (the frequencies given in dan04's answer). However, apart from being awkward to find, this is not really useful for playing music in B♭ major. The main problem: a double-stop between that B♭ and the open D string is a Pythagorean major third.
Do all tuning systems involving dividing the octave?
There are some commas computed by other than octave division. The Pythagorean comma is the difference between 12 fifths and 7 octaves; the syntonic comma is the difference between a Pythagorean major third and the just major third. All these commas can be rewritten as octave-based (though not necessarily the most natural way to look at them.)
history - Need help understanding the difference between …
In Pythagorean tuning, the diatonic semitone is 256:243 or 90.2¢ while the chromatic semitone is 2187:2048 or 113.7¢. The difference between those two is another instance of the Pythagorean comma. Share
Are there optimal intervals for major and minor 3rds?
2022年12月14日 · For a Pythagorean minor triad of 54:64:81, the implied fundamental is five octaves and a major sixth below the root, and the difference tones are 10, 17, and 27, or, in the C minor example, a rather flat G1, a somewhat sharp E♮2, and C3. Instead of a well tuned ♭VI, they define a poorly tuned major triad on the same root.
Please help me clarify this sentence about 'microtones' on Grove …
2022年5月23日 · The comma that quarter-comma meantone tuning cares about is the syntonic comma = 81:80 ≈ 21.51 cents (among others, this is the just intonation ratio difference between 4-perfect-fifths and 2-octaves-and-1-major-third - e.g. C4 to E6 - and between 1-octave-and-1-minor-third and 3-perfect-fourths - e.g. C4 to E♭5), and it flattens nearly all ...
Double Sharps in Just Intonation. The mathematics?
2015年6月23日 · One such Just system is the Pythagorean system, which only uses Just perfect fifths (a ratio of 3/2, or ~702 cents) and just octaves to generate all the notes of the scale. To find the mathematical ratio for any note, you just count how far it is from your reference note, along the line of fifths, and multiply by that power of (3/2).