Scales - Ascending and descending. - Types of tuning systems

Rather than considering a scale as having an ascending pattern and a descending pattern; maybe it would be more rational to state that two different scales are used:

One to ascend and another to descend.

e.g. various Japanese pentatonics

See:

http://www.lucytune.com/new_to_lt/lucytuning_scales.html

for more details and examples.

Also see:

http://www.lucytune.com/new_to_lt/pitch_05.html

This system of ScaleCoding was the result of a late night discussion in the late 80's/early 90's between Jonathan Glasier, John Gibbon and myself.

Obviously the principle can be applied to any meantone (spiral) or edo (circular) system, any of which may be uniquely described by the size of the fifth and the octave ratio.

[Or Large and small interval sizes, (if you insist)]

It seems that for precise JI (integer frequency ratios) which contain inconsistent interval sizes, and other systems which use more than two (L&s) interval sizes,
you may have to extend the concept or come up with a "better" design.

Charles Lucy - lucy@harmonics.com
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Dear Charles,

Would you use two ladders, one for climbing up and another one for getting down? A scale should best be perceived as a static bi-directional stair-case, or a collection of connected staircases in the same vicinity, without any implication of movement. Let the gamut be the man taking the stairs. So a man may climb A-B-C-D-E-F#-G#-A staircase and return from A-G-F-E-D-C-B-A staircase to the same chamber. The two staircases together form the melodic minor scale, and the movement of the man would be the gamut in this case. The pattern forms not through the static scale, but through the motion of this gamut.

I should clarify that an ascending-descending order does not imply motion, but only an array independent of time-frame. The gamut is the motion that you are searching for I believe.

Another thing is that, the melodic minor could be said to consist of two diatonical scales (staircases in the example above), or a 9-note scale. But I prefer the prior personally.

Also, if I nominate a particular pitch of a scale to be the tonic, I would be defining a gamut, and if dominant and sub-dominant come into play along with modulation and transposition, a key.

Cordially,
Ozan

From: Charles Lucy
To: tuning@yahoogroups.com
Sent: 23 Mayıs 2005 Pazartesi 17:14
Subject: [tuning] Scales - Ascending and descending. - Types of tuning systems

Rather than considering a scale as having an ascending pattern and a
descending pattern; maybe it would be more rational to state that two
different scales are used:

One to ascend and another to descend.

e.g. various Japanese pentatonics

See:

http://www.lucytune.com/new_to_lt/lucytuning_scales.html

for more details and examples.

Also see:

http://www.lucytune.com/new_to_lt/pitch_05.html

This system of ScaleCoding was the result of a late night discussion
in the late 80's/early 90's between Jonathan Glasier, John Gibbon and
myself.

Obviously the principle can be applied to any meantone (spiral) or
edo (circular) system, any of which may be uniquely described by the
size of the fifth and the octave ratio.

[Or Large and small interval sizes, (if you insist)]

It seems that for precise JI (integer frequency ratios) which contain
inconsistent interval sizes, and other systems which use more than
two (L&s) interval sizes,
you may have to extend the concept or come up with a "better" design.

Hi again Paul,

It's harder now then ever keeping track of things, but don't think that I
have forgotten you. I forward my response to you to the tuning list.

As to `scales versus gamuts`, you should know that we trainees in piano
learn to play the `C major gamme` as 7 pitches of the C major scale in an
ascending-descending sequence of notes, each sounded right one after the
other, and the `C minor melodic gamme` as two minor diatonic scales
superimposed, one sounded in an ascending sequence, the other, in a
descending sequence of notes.

I understand Gamut to mean:

1. The note G on the first line of the bass stave (historical music),
2. Guido of Arezzo's scale of six overlapping hexachords, reaching from that
note up to E in the fourth space of the treble (historical music),
3. Any recognized scale or range of notes,
4. The whole compass of a voice or instrument; the full range or compass of
anything, eg the emotions.

[From gamma, the Greek letter G, adopted when it was required to name a note
added below the A with which the old scale began, and ut the Aretinian (qv)
syllable]

(c) Larousse plc. All rights reserved

However, it is evident from my example that there are different schools in
Europe which approach the matter otherwise. Whereas Wikipedia and Larousses
considers gamut to be synonymous with scale, pianists like myself consider
gamut or gamme to be an ascending-descending sequence of notes from a scale.

Furthermor, the scale has no qualities other than a tonic, or beginning,
hence C major, or C minor (any or all of the three minors). If the tonic
shifts in the same scale, you get modes:

Liturgical Modern Pitches in ascending order (* Ney)

I - Authentic modes (tones in medieval paralance)

Dorian Dorian |D| E F G (A) B C D Bolahenk
Phrygian Phrygian |E| F G A B (C) D E Davud
Lydian Lydian |F| G A B (C) D E F Shah
Mixolydian Mixolydian |G| A B C (D) E F G Mansur

II - Plagal modes (derived tones)

Hypodorian Aeolian A B C |D| E (F) G A Kiz
Hypophrygian Locrian B C D |E| F G (A) B Mustahzen
Hypolydian Ionian C D E |F| G (A) B C Sipurde
Hypomixolydian Dorian D E F |G| A B (C) D B. Nisfiye

[Grout 1973]

*My addition where the tonic of the mode gives the Rast diapason of the Ney

Where `enclosed pitch |X| is the 'finalis' of the mode, what we might today
call the tonic note; (and) the pitch enclosed (X) is the 'cofinalis' or what
we would call a dominant.`
http://graham.main.nc.us/~bhammel/MUSIC/Cmodes.html

Note, however, that the Plagal modes have their finalis on the fourth
degree, rather than the first as with Greek modes.

Key, on the other hand, implies that certain degrees of the scale have been
ascribed such roles as the dominant, sub-dominant, leading-tone, etc... so
as to allow modulations and transpositions within the sphere of what this
certain scale may permit.

Hence, scales do not ascend or descend, one ascends through them, or
descends through them. A scale is merely an assortment of pitches from low
to high with a beginning, and an end.

Do you think a ladder climbs? No, one climbs a ladder, the ladder is static,
its rungs unmoving. It is the person who climbs the ladder, or takes the
stairs.

I am not knowledged much in music, let alone English as compared to you,
but I think my point is well-made this time.

Cordially,
Ozan

----- Original Message -----
From: "wallyesterpaulrus" <wallyesterpaulrus@yahoo.com>
To: "Ozan Yarman" <ozanyarman@superonline.com>
Sent: 26 May�s 2005 Per�embe 2:20
Subject: Re: Scales - Ascending and descending. - Types of tuning systems

Hi Ozan,

I am working on an e-mail response for you about 34-equal; I'm also
awaiting some responses from you.

In the meantime, I'd like to say that though I've heard of ascending
vs. descending scales, I've never heard of ascending vs. descending
gamuts. 'Gamut' has meant the fixed, non-directional, non-ordered,
multiple-octave set of pitches (often with a lowest and highest
possible pitch specified) in every instance that I've seen it. Do you
have any references to the contrary?

Also, you wrote:

>Also, if I nominate a particular pitch of a scale to be the tonic, I
>would be defining a gamut

I definitely disagree with this as well. The gamut, wherever I've
seen it, is always given without reference to a tonic. A scale with a
particular tonic chosen is what I'd consider a *mode*.

Best,
Paul