Intro to Music Concepts

Under construction and Fix

Which Concept to Learn First? - step by step intro list of concepts

  1. Lesson 1: play Single Note - concept of Step (音级) and half step (semitone)
  2. Lesson 2: Play Two Notes - concept of Inverval (音程)

Music Note

  • note: each note is corresponding to a certain pitch/frequency. written with 7 letters from “ABCDEFG”, with additional number refering the octave range. like A4 = 440Hz, C4 = 261.6 Hz (Change of A4 frequency standards in history)
  • Semitone: the smallest distance measured in western music, the distance between any 2 nearby note/key in piano.
    • semitone notation for measure 2 notes:
      1. chromatic semitone: measure two notes using same letter, like C and C#
      2. diatonic semitone: measure two notes using different letter, like C and Db
  • Whole tone (Tone) = 2x Semitone
  • microtone: intervals smaller than a semitone, also called “microintervals”
  • solfeggio syllables: sing words corresponding to notes within the Scale's octave, with Do refering to “the start/first Note of the Scale”
    • so here is list of each Scale Degree's sing word
      • 1st note/degree of the scale = tonic (Do)
      • 2nd note/degree of the scale = supertonic (Re)
      • 3rd note/degree of the scale = Mediant (Mi)
      • 4th note/degree of the scale = Subdominant (Fa)
      • 5th note/degree of the scale = Dominant (Sol)
      • 6th note/degree of the scale = Submediant (La)
      • 7th note/degree of the scale = Leading tone/subtonic (Xi/Ti)
      • 8th note/degree of the scale = tonic/octave (Do)

Music Scale

  • scale definition: a set of notes at chosen frequency within range of a Octave (start at a frequency xHz, and ends at a frequency of 2xHz)
    1. scale step definition: step number is how many notes in the set of chosen scale, like in “major scale”, there are 7 steps in it.
      • Eg. Compare scale as a staircase, each note is a step in staircase and different between each step can vary as well like in real life design of staircase.
      1. interval definition: the frequency ratio difference between any step within the scale
        • Eg. Compare interval as each step height's ratio difference from sea level within the staircase, the interval between 2nd and 3rd step can be 2 times of the interval between 1st and 2nd step.
        1. intervals in diatonic scale definition: in diatonic scale there are 5 big steps (“whole step”, “whole-tone”) and 2 small steps (“half step”, “semi-tone”) within a Octave; secondly, the small steps are seperated by either 2 big steps or 3 big steps; thirdly, that big step is 2x height of that small step.
          • Eg. Compare to a staircase with 5 bigs steps and 2 small steps, after each small steps, there must be at least 2 or 3 big steps, that big step is like 20cm, that small step is like 10cm.
          1. so here comes “Major Scale” (Ionian in term of Mode) definition: one of diatonic scale variations, the sequence of its intervals are Big-Big-Small-Big-Big-Big-Small, one of its variation from note C well known as “C Major Scale” C=D=E-F=G=A=B-C (where = as big step, - as small step)
          2. and also comes “Minor Scale” (aka Natural minor scale, and Aeolian in term of Mode) definition: one of diatonic scale variations, the sequence of its intervals are Big-Small-Big-Big-Small-Big-Big, one of its variation from note A well known as “A Minor Scale” A=B-C=D=E-F=G=A (where = as big step, - as small step)
          3. thus comes concept called Relative Minor: A minor scale is relative minor of C Major scale because they are sharing same set of notes, more precisely, they are sharing the same Key signature
            • Key signature definition: a set of sharp or flat symbols placed together on the staff.
              • sharp (symbol #): a note played with a semi-tone (half step) higher frequency/pitch from original frequency/pitch; double sharp means whole tone higher (x); half sharp means half semitone higher (half #); triple sharp means 3 semitone higher (#x); or sometimes just means play a bit higher frequency/pitch.
              • flat (symbol b): a note played with a semi-tone (half step) lower frequency/pitch from original frequency/pitch; double flat means whole tone lower (bb); half flat means half semitone lower (slash b); triple flat means 3 semitone lower (bbb); or sometimes just means play a bit lower frequency/pitch.
              • staff: a set of 5 lines and 4 spaces, each represent a frequency/pitch, which is pre-defined by the chef symbol on its left side; once the reference point frequency note is set and the interval for each line and space is caculated based on diatonic scale
                1. G-clef: in example of treble clef with placing on 2nd line from bottom,indicating 2nd line from bottom is G4 note; something look like “&”
                2. C-clef: in example of alto clef with placing on 3rd line, indicating 3rd line (middle line) is C4 note; something look like “|3”
                3. F-clef: in example of bass clef with placing on 2nd line from top, indicating 2nd line from top is F3 note; something look like “9:”
                4. thus comes with situation like, 8& means octave higher than G4 note, &8 means octave lower than G4 note,
                5. other chef like “II” means percussion clef, each note indicate an instrument with no actual pitch.
                6. note: don't confuse Tab notation like guitar Tab with staff, as in Tab notation, each line represent a string, no space no use in that case.
          4. Since Major/minor scale can start from any note, as long as they follow the Scale Pattern (Big-Small-Big-Big-Small-Big-Big for Major scale, Big-Small-Big-Big-Small-Big-Big for minor scale), and shifting the notes by certain amount of semitones is called Transposition, thus those 12 Major scales can transposed into each other by shifting the notes together.
          5. Modes: same as Scale, arrangements of half and whole steps inside a octave, such some are variation change of Major scale or minor scale.
  • Based on Key signiture of 12 Major scales, and relative minor relation, circle of fifth table developed,
    • note: it is like a 12 number clock, because of 12 major scale and corresponding relative minor scale
    • each clock number is 7 semitone apart, (which in term of interval, called “Perfect Fifth”)

table showing accidentals count and the staff notations

Music Interval

  • interval table
    • note: the interval name counts in term of the Staff's line and space letters, thus, there is only 7 numbers (letters) within a octave instead of 12 numbers (letters+flat/sharp version) in the interval names
    • note: interval quality name: P = Perfect, M = major, m = minor, d = diminished, A = augmented
    • note: those major interval and minor intervals are fit like piano white and black keys within a octave, except m5
      1. note: Perfect and Major interval are like White keys
      2. note: minor interval are made based on Major interval - 1 semitone (like flatten-ed white key)
      3. note: augmented intervals are maded based on Major/Pefect interval + 1 semitone (like sharp-ed white key)
      4. note: diminished interval are maded based on minor/Pefect interval - 1 semitone (like flatten-ed black key)
  • interval inverted:
    • 2-7 ⇒ 7-2
    • Major ⇔ minor
    • Augmented ⇔ diminished
    • Perfect stays
interval names by quality
0 P1 d2
1 m2 A1
2 M2 d3
3 m3 A2
4 M3 d4
5 P4 A3
6 A4 d5
7 P5 d6
8 m6 A5
9 M6 d7
10 m7 A6
11 M7 d8
12 P8 A7
  • Interval in term of frequency ratio:
    • when intervals are measured in term of frequency ratios instead of semitone difference, it is easy to tell “Why some intervals are called Perfect?”
      • P8 (Perfect 8th): is a octave higher (12 semitones higher), that also is 2:1 frequency ratio difference.
      • P1 unision: is 1:1 frequency ratio difference.
      • if we say 1st note frequency is 1x, 13th note frequency is 2x, and inbetween, n-th note is 2^[(n-1)/12]x; for n=1, value = 1x, for n=13, a octave higher, value=2x; thus for P4, that is 6th note, value = 2^(5/12) = 1.334x, roughly 4/3
      • for P5, that is 8th note, value = 2^(7/12) = 1.498x, roughly 3/2
      • for comparision,
        • M3, that is 5th note, value = 2^(4/12) = 1.259, roughly 5/4;
        • M7, value= 2^(11/12) = 1.88x, roughly 47/25, which make even more no sense.
      • therefore, P4 is roughly 4/3, P5 is rougly 3/2, fitting the sequency like P8 2:1, P1 1:1
      • while, M3 should be as well good, since it is roughly 5/4.
        • thus, another name called “just intervals/pure intervals” are created for M3 like, intervals with small-integer ratios, and people call their sound Consonant - pleasant and well-tuned.
  • thus, from above, you will realized, Scientifically Mathamatically right equal frequency ratio (interval) is 2^(1/12), and that results P4 and P5 such is approximately closing to Ideal Consonant or just/pure interval, and that Mathamatically-right-equal-intrument tuning is called 12-tone equal temperament
    • common method of tuning for modern fix pitch instrument (e.g. piano)
  • and alternative, tuning instrument based on perfect frequency ratio (just/pure interval), thus with unequal semitones along octave, are called Just intonation tuning system
    • common method for ancient times and string length based instrument, due to easy physical meansurements of small integer ratio
    • one example is Five-limit tuning:
      1. A twelve tone scale can also be created by compounding harmonics up to the fifth.
      2. C 1:1
      3. C/3 ⇒ F 4:3 ⇒ (/3) Bb 16/9
      4. C*3 ⇒ G 3:2 ⇒ (*3) D 9/8
      5. C*5 ⇒ E 5:4
        1. E/3 ⇒ A 5:3 ⇒ (/3) D 10/9
        2. E*3 ⇒ B 15:8 ⇒ (*3) F# 45/32
      6. C/5 ⇒ Ab 8:5
        1. Ab/3 ⇒ Db 16:15 ⇒ (/3) Gb 64:45
        2. Ab*3 ⇒ Eb 6:5 ⇒ (*3) Bb 9:5

Music Chord

  • Chord: a concept based Interval, is combination of intervals starting from a common note - the Root of the Chord
chord interval number
Major chord 0 4 7 1 3 5

Music Chord Progression

  • Chord Progression: to do

More Concetps Extened

So Now You What is “Scale”, it bring out tons of concepts. Let us go deep into some of the important concepts based on it.

  • categorization of music scale
    • most popular scale:
      1. major scale: 1 2 3 4 5 6 7
  • Pentatonic Scale: a scale with 5 notes per octave
  • Hexatonic Scale: a scale with 6 notes per octave
  • Heptatonic Scale: a scale with 7 notes per octave
  • Octatonic Scale: a scale with 8 notes per octave
  • Japanese scale
    • 1-b2-4-5-b6
    • others
      • 1-b2-4-5-7: Kokin Joshi in key of D, D-G-A-C - D-D#-G-A-C - D-D#-G-A (string 1,5 in unison, so 2,7)
      • 1-b2-4-b5-7: Kumoi Joshi in key of D: D-G-G#-C - D-D#-G-G#-C - D-D#-G-A
      • 1-2-4-5-7: Gaku Joshi in key of D, D-G-A-C - D-E-G-A-C - D-E-G-A (string 1,5 in unison)

Music Dicationary

  • Baritone voice range: (A2–A4) with reference to middle C (C4).
    so it covers D3 (+5) G3 (+4) B3 (+5) E4
  • Ukelele standard tuning: G3 (+5) C4 (+4) E4 (+5) A4
    and comparing to guitar D3 (+5) G3 (+4) B3 (+5) E4, it is like D3 → (+5) → G3, extact 5 semi-tone (half-step, half-tone) higher

Tuning Apps

  • Online flash string tuning reference app:

Reference Reading