Yahoo Tuning Groups Ultimate Backup mills-tuning-list 88CET Ear Training CDs, Part 10

Another Quick Break from Interval-Hearing:
- Nomenclatural quiz to identify the pitches that form off-octave
intervals. (First identifying these intervals upward then
downward.)
- Similarly for off-double-octaves (upward only).

Back to Interval-Hearing:
- A brief practice listening then singing major sixths, brief since
they're pretty close to traditional major sixths.
- A brief practice at 7:4 subminor sevenths, brief since we worked
with them earlier.
- A brief practice with major ninths, brief since they're pretty close
to traditional.
- Neutral sevenths (11:6) listening then singing.
- Neutral ninths (15:7) listening then singing.

Quoting Harmonic-Series-Fragment Chords:
- "Repeat after me the sequence of intervals in a harmonic-series-
fragment chord".
- Interval-sequence quiz.
- Quiz to quote them by pitch names.
- Harmonic chord sing-along (if possible - difficult because of wide
range).

Analogous Exercises for Subharmonic-Series-Fragment Chords.

Quiz: Distinguishing Harmonic- and Subharmonic-Series Block Chords.

Melodic Exercise - The Biggie: Note-Stream Identification:
Play a long series of notes, and I am to identify each note in the
sequence, one-by-one, knowing the pitch of the previous note, and
hearing the pitch-difference of the next note from the previous.

Third-Stack Chords:
- Listen to stacks of three, four, five, and six neutral thirds.
- Listen to stacks of three, four, and five supramajor thirds.

Chord-Type Distinction:
"Listen to the following block chords, and tell me if they are
harmonic-series-fragment, subharmonic-series-fragment, neutral-third-
stack, or supramajor-third stack chords.

🔗A440A <A440A@...>

Gary wrote:

<< The entire point of a comma is that there is a conceptual framework -
often 12-tone-per-octave scales - wherein we'd like two different pitches
to have turned out the same, but they didn't. >>

I agree that is one point of the comma, but not "entirely". (This
borders on dissing dissonance)
A different perspective is that the comma is source for dissonance, (or
something other than Just harmony). It is by tonal contrasts that so much
music makes its beauty, so the comma provides an essential ingredient.
Commas are not bad things to be computed out of musical composition, they
are a measurement of tonality!

Regards,
Ed Foote

🔗mr88cet@texas.net (Gary Morrison)

>As most theorists have done, he called this comma an "error"
>(I've also seen it called an "anomaly"). However, I don't think "error"
>is an appropriate name for this occurance, since it is a natural feature
>of the spiral of 5ths...

I can see Neil's concern here.

Calling a comma an "error" is, more or less, using the mathematical
usage of the word, which doesn't suggest anything like a mistake.

The entire point of a comma is that there is a conceptual framework -
often 12-tone-per-octave scales - wherein we'd like two different pitches
to have turned out the same, but they didn't. For example in the case of
the pythagorean comma, the 12-toned conceptual framework suggest that a
stack of 12 3:2 should be the same as 7 2:1s. And indeed they fail to
coincide because they DO obey the laws of nature (or mathematics at least),
and NOT our simplified conceptualizations.

So perhaps the concern here boils down to me, and others, failing to
make clear which of the two is "in error". To the degree that this usage
of "error" can be thought of as a mistake or inadequacy or such, the
12-toned conceputal framework is what's inadequate, not the meaningfulness
of 3:2 or 2:1.