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musicwiki:concepts [2021/05/27 16:42] – shining | musicwiki:concepts [2021/05/27 18:06] (current) – [Music Notation] ying | ||
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====== Music and Math ====== | ====== Music and Math ====== | ||
+ | * ref: | ||
+ | * interactive circle: https:// | ||
+ | * cn topic (音乐、音律与数学): | ||
+ | * cn topic (science in music): https:// | ||
+ | |||
+ | |||
+ | ===== A single Ratio Approach ===== | ||
* a single Note, such as C4, as frequency of a string (length unit as L=1), its 2x frequency C5 (1 octave higher note, length=1/ | * a single Note, such as C4, as frequency of a string (length unit as L=1), its 2x frequency C5 (1 octave higher note, length=1/ | ||
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^^ | ^^ | ||
^ combine | C | C# \\ Db | D | D# \\ Eb | E | F | F# \\ Gb | G | G# \\ Ab | A | A# \\ Bb | B | | ^ combine | C | C# \\ Db | D | D# \\ Eb | E | F | F# \\ Gb | G | G# \\ Ab | A | A# \\ Bb | B | | ||
+ | |||
+ | ===== A multi Ratio Approach ===== | ||
+ | |||
+ | * string length ratio can determine the frequency ratio, so simple ratio makes string simple to make. | ||
+ | * a perfect ratio like 1x,2x, 1/2 is simplest. | ||
+ | * other simple ratio ranking as: 1/2 > 2/3 > 3/4 > 4/5 | ||
+ | * compared to above definition, G4 is 2/3 from C4 | ||
+ | * compared to above definition, E4 (64/81) is mostly near 4/5 (x16 up/down = 64/80) | ||
+ | |||
+ | * **using 2/3 and 4/5 way of pushing** (Pure intonation) | ||
+ | * C4 is 1 | ||
+ | * E4 is 4/5 (48/60) | ||
+ | * G4 is 2/3 => B5 = 4/5 x 2/3 = 8/15 | ||
+ | * G4 is 2/3 => Eb4 = (2/3) / (4/5) = 10/12 (50/60) | ||
+ | * C5 is 1/2 => F4 = (1/2) / (2/3) = 3/4 | ||
+ | * F4 is 3/4 => A4 = 3/4 x 4/5 = 3/5 | ||
+ | * A4 is 3/5 => D4 = (3/5) / (2/3) = 9/10 (use 2/3 ratio from A4) | ||
+ | * G5 is 2/3 => D4 = (2/3) / (3/4) = 8/9 (use 3/4 ratio from G4) | ||
+ | * as you see, there is 2 way to get D4 ([[https:// | ||
+ | * the half step of each next note, like from E to Eb, are not the same, half step difference range from 104.1% to 108% | ||
+ | |||
+ | ===== Temperament Approach (no ratio) ===== | ||
+ | |||
+ | * **well temperament**: | ||
+ | * **equal temperament**: | ||
+ | |||
+ | ===== Conclusion on Music Note Tuning ===== | ||
+ | |||
+ | * different music to math definition means different music tuning system | ||
+ | * different time, different culture, different history, different instrument means their default sounding may be slightly different, based on their choice of taste of sound. | ||
+ | * modern equal temperament tuning is a balance of all for flexibility of sound adapting | ||
+ | |||
+ | ====== Music and Physics ====== | ||
+ | |||
+ | * string frequency: | ||
+ | * longer string, lower frequency | ||
+ | * shorter string, higher frequency | ||
+ | * more tense string tightens, higher frequency | ||
+ | * more loose string tightens, lower frequency | ||
+ | * heavier string, lower frequency | ||
+ | * lighter string, higher frequency | ||
+ | |||
+ | ====== Music Notation ====== | ||
+ | |||
+ | * ref: | ||
+ | * cn topic (五線譜): | ||
+ | |||
+ | ====== Music Theory ====== | ||
* ref: | * ref: | ||
- | * interactive circle: https://pianolit.com/tools/ | + | * cn topic (basics): https://www.youtube.com/watch? |
- | * cn topic (音乐、音律与数学): https:// | + | * cn topic (Circle |
+ | * cn topic (major scale, minor scale): https:// | ||