Maybe this chart will help:

Modes: Ion D Phy Lyd Mix Aeo LocIon D Phy Lyd Mix Aeo Loc STEPS: W W H W W W H W W H W W W H Step Formula: 2 2 1 2 2 2 1 2 2 1 2 2 2 1 Scale degrees: |1 |2 |3|4 |5 |6 |7|1 |2 |3|4 |5 |6 |7|1 C major notes: C . D . E F . G . A . B C . D . E F . G . A . B C Chords I ii iii IV V vi vii I maj = C(maj7) C . . . E . . G . . .(B) ii min = Dm(7) D . . F . . . A . .(C) iii min = Em(7) E . . G . . . B . .(D) IV maj = F(maj7) F . . . A . . C . . .(E) V maj = G(7) G . . . B . . D . .(F) vi min = Am(7) A . . C . . . E . .(G) vii dim = Bdim (Bm7b5) B . . D . . F . . .(A)

Intervals are basically the distance between notes in semitones. Where 2 semitones = Whole-step and 1 semitone = Half-step.
C_D = 2 semitones = Wholestep = Major 2nd = M2
D_E = 2 semitones = Wholestep = Major 2nd = M2
E_F = 1 semitone = Halfstep = minor 2nd = m2

C Major               (TRIADS) Major Triad____Intervals (named from Root) Scale Degrees Distance between Notes Semitones Semitone Formula	C_______E_________G R_______M3_______P5 1________3_________5 < --M3----- >< ---m3----- > < ----4-------><-----3-------> 0________ 4________7
Dm Minor Triad____Intervals (named fromRoot) Scale Degrees Distance between Notes Semitones Semitone Formula	D________F________A R________m3______P5 1________b3________5 < ---m3----- >< ---M3----- > < -----3------>< ----4--------> 0________3_________7
C+ Augmented Triad____Intervals (named from Root) Scale Degrees Distance between Notes Semitones Semitone Formula	C_______E_________G# R_______M3_______A5 1________3________#5 < --M3----- >< ---M3----- > < -----4----- >< -----4-------> 0________4_________8
Bdim Diminished Triad____Intervals (named from Root) Scale Degrees Distance between Notes Semitones Semitone Formula	B________D________F R________m3______D5 1________b3_______b5 < ---m3----- >< ---m3------> < -----3-----  >< -----3------> 0________ 3________ 6
Cmaj7               (4-Note Chords) Major 7____Intervals (named from Root) Scale Degrees Distance between Notes Semitones Semitone Formula	C________E________G________B R_______M3_______P5_______M7 1________3_________5________7 < --M3---- >< -----m3---- >< ---M3---- > < ----4----- >< -------3---- >< -----4----- > 0_______ 4_________ 7_______ 11
G7 Dominant 7____Intervals (named from Root) Scale Degrees Distance between Notes Semitones Semitone Formula	G_______B_________D_______F R_______M3_______P5_______m7 1________3_________5_______b7 < --M3----->< ----m3----- >< ----m3---- > < ----4----- >< ------3----- >< -------3---- > 0_______ 4_________7________10
Dm7 Minor 7____Intervals (named from Root) Scale Degrees Distance between Notes Semitones Semitone Formula	D________F________A_______C R_______m3_______P5_______m7 1________b3_______ 5_______ b7 < ----m3---- >< ----M3-- >< ----m3---- > < ------3---- >< ------ 4--- >< ------3---- > 0________3________ 7________10
Bm7b5 Half-Diminished____Intervals (named fromRoot) Scale Degrees Distance between Notes Semitones Semitone Formula	B_______D________F_________A R_______m3_______D5_______m7 1_______b3________b5_______b7 < ---m3----><------m3---  >< ---M3---- > < -----3---- >< -------3 --- >< ------4---- > 0_______ 3_________6________10
Cdim7 Fully-Diminished____Intervals (named from Root) Scale Degrees Distance between Notes Semitones Semitone Formula	C_______Eb_______Gb_______A R_______m3_______D5_______m7 1_______b3________b5______bb7 < --- m3---->< ---m3----- >< ----m3---- > < ------3---->< -----3------>< ------3---- > 0________3________6________ 9

Thanks Adriano...a little overwhelming, but thanks! I think where I am running into problems is keeping up with the number of semi-tones in between intervals depending upon where I am starting from in the scale. Your charts did help in that aspect.

And to think I am doing this for "fun"! LOL!

Peace Always!
Todd

Here's the penultimate Table: I'm doing it for fun too.

Modes:                Ion  D  Phy  Lyd   Mix   Aeo Loc  Ion  D  Phy  Lyd   Mix   Aeo Loc

STEPS:                W    W  H    W    W    W  H    W    W  H    W    W    W   H

Step Formula:         2    2  1    2    2    2  1    2    2  1    2    2    2   1

From Root:        R   M2   M3 P4   P5   M6   M7 P8   M9   M10P11  P12  M13  M14 P15

Semi.From Root:   0    2    4  5    7    9   11 12   14    16 17   19   21   23 24

                    m2   m3      A4D5 m6   m7      m9   m10           m13

Semi.From Root:   0 1    3        6   8   10      13    15            20

                   Db    Eb     F#Gb  Ab   Bb      Db    Eb    F#Gb    Ab   Bb

Scale degrees:   |1   |2   |3 |4   |5   |6   |7 |8   |9   |10|11  |12  |13  |14|15                 

C major notes:    C .  D .  E  F .  G .  A .  B  C .  D .  E  F .  G .  A .  B  C

  Chords          I   ii  iii IV    V   vi   vii 

  I maj = C(maj7) C . . . . E . . . G . . . .(B) 

 ii min = Dm(7)        D . . . F . . . . A . . .(C)

iii min = Em(7)             E . . . G . . . . B . . .(D)

 IV maj = F(maj7)              F . . . . A . . . C . . . .(E)

  V maj = G(7)                      G . . . . B . . . D . . .(F)

 vi min = Am(7)                          A . . . C . . . . E . . .(G)

vii dim = Bdim (Bm7b5)                        B . . . D . . . F . . . .(A)

I have this book, so if there's a specific point you're not understanding let me know.

Personally I do think it makes it a little more complicated than it needs to be, talking about the "major scale of the lower note" (p.22).
You don't need to refer to a scale to understand intervals - except you do need to know the natural notes (C major scale) and that there's half-steps between B-C and E-F.

Here's a list of intervals within an octave, showing all the examples of each type in the C major scale (all ascending intervals):

NAME         NOTES APART  SEMITONES APART      EXAMPLES



Unison          1               0               C-C

Minor 2nd       2               1               B-C, E-F 

Major 2nd       2               2               A-B, C-D, D-E, F-G, G-A 

Minor 3rd       3               3               A-C, B-D, D-F, E-G 

Major 3rd       3               4               C-E, F-A, G-B

Perfect 4th     4               5               A-D, B-E, C-F, D-G, E-A, G-C 

Augmented 4th   4               6               F-B

Diminished 5th  5               6               B-F

Perfect 5th     5               7               A-E, C-G, D-A, E-B, F-C, G-D 

Minor 6th       6               8               A-F, B-G, E-C 

Major 6th       6               9               C-A, D-B, F-D, G-E

Minor 7th       7               10              A-G, B-F, D-C, E-D, G-F 

Major 7th       7               11              C-B, F-E

Octave          8               12              C-C

By the way, the book has one mistake in the answers (at least, my edition does).
Page 20, exercise 6: the 4th note shown on the first line is a Cb. The enharmonic equivalent of this is B natural, not B# (as the answers say)!

Awesome, Jon & Adrianno...I always enjoy a refresher myself.

But Jon made an important point; scales not being needed to be referred to in order to understand intervals. It is purely mathematic, and simple math at that, lucky for me.

Those will be handy charts for someone! very cool.

Craig

Jon,
You have mail!

Thanks,

Todd

somebody messed up their HTML!