# Ponds Original Notes on the Scale of Infinite Ninths

Pond's Original Notes on the Scale of Infinite Ninths
2002, 08/31

I've been playing around with that interval chart this morning. I "discovered" it only addresses counting by steps. This works pretty well but does not address frequency, etc. When frequency is applied it does not work as expected but totally unexpected. So there is something of importance to be discovered here, I presume. My thoughts are running to things concerning the very most basic premises of what intervals are or supposed to represent. The issues are so convoluted they are appearing as a paradox and the solving of paradoxes always leads to new revelations. The problem is in the definition of "step". Each step throughout the octave has a different size - and we know we can't add apples and oranges. Steps are a generalization and not arithmetical certainties.

For instance if two Minor Seconds (16:15) are added together AS STEPS they equal a Major Second (9:8). Very neat.

But if we add 16:15 + 16:15 we get 32:15 which is a Minor Ninth!!!

The error is apparently the result of a misinterpretation of what 16:15 is. The reality is a Mn2 is NOT 16:15 (in this case). It is 1/15 plus the whole of 1:1 or 15:15 (Unison) which equals 16:15. So 1/15 + 15:15 = 16:15.

Since a Mj2 is 9:8 we must find the common denominator which is 120. 1/15 * 120 = 8. A Mn2 is 8 larger than Unison (120/120)+8/1 = 128/120. So each Mn2 step = 8. Which suggests a Mj2 is 8 larger than a Mn2 which works out to 136/120 where a Mn2 is 128/120. However error begins to creep in due to nonequivalence of fractional parts. In this case the error is 1/120. Because 16:15*120=128/120 and 9:8*120=135/120.

The bottom line is a Mn2 = 1/15 (8/120) over and above Unison a Mj2 = 1/8 (15/120) over and above Unison a Mn2 step (from Unison) = 8/120 a Mj2 step (from Unison) = 15/120 The Mj2 which we consider as 2 X Mn2 is actually smaller than this by 1/120 of the octave.

The two intervals are not octave harmonically equivalent or proportional by 1/120th of the octave.

It is presumed similar differences exist throughout the interval chart. This may not seem important and may even seem a waste of time. But I submit neither premise is correct. Musicians count by steps because that is the way we've been taught - and it works for practical music purposes. The fact is, steps are unequal and disproporational arithmetically and therefore when we think they create Harmony they are actually creating discord. In such suppositions we are operating from a place of illusion and nonreality and therefore we find ourselves fumbling around in the dark and not getting what we want or expect.

Keep in mind this scale is not a "music scale". It is a scale of vibration or oscillation as found in nature - and not in man's sensorial audio pleasures known as music.

Harmonic / Enharmonic Scale

All difference tones are base 23 and will not create discords.

 Octave C" 240/120 Minor 8th Cb 232/120 Major 7th B 224/120 Minor 7th Bb 216/120 Dim. 7th A# 208/120 Major 6th A 200/120 Minor 6th G# 192/120 Major 5th G 184/120 Minor 5th Gb 176/120 Major 4th F# 168/120 Minor 4th F 160/120 Major 3rd E 152/120 Minor 3rd D# 144/120 Major 2nd D 136/120 Minor 2nd C# 128/120 Unison C 120/120

2002, 09/01 Below is a "new" scale (subject to modification) that accounts for Harmony in such a way that all notes are equivalent and proportional. Any note and its immediate harmonics will form Harmony with all other notes and their immediate harmonics. No unresolved beats will occur - unresolved beats are a source of dissonance. A beat will resolve when it forms Harmony with the notes around it. All beats generated with this scale are multiples of two as are all the notes as also immediate harmonics. So any beats will resolve (form harmony) between themselves and the surrounding notes. If we use conventional music intervals beats occur which are unresolveable which means they may have a base of 1, 2, 3, 5 or 7. These odd numbers do not form Harmony or unison with anything other than themselves. Theoretically resolved beats will "disappear" to the ear as they merge with neighboring sounds. I don't know this for a practical thing but arithmetically and vibratorily this appears to be the case. The proof will come in the actually playing and hearing of it.

PS: As far as I know my idea of resolved and unresolved beats is new and unique. I've not read of it in any music theory I've come across.

The Dale Scale
 Interval Note cps/120 Octave C""" 2048 Minor 8th Cb 1920 Major 7th B 1856 Minor 7th Bb 1792 Dim. 7th A# 1728 Major 6th A 1664 Minor 6th G# 1600 Major 5th G 1536 Minor 5th Gb 1472 Major 4th F# 1408 Minor 4th F 1344 Major 3rd E 1280 Minor 3rd D# 1216 Major 2nd D 1152 Minor 2nd C# 1088 Octave C""' 1024 Minor 8th Cb 960 Major 7th B 928 Minor 7th Bb 896 Dim. 7th A# 864 Major 6th A 832 Minor 6th G# 800 Major 5th G 768 Minor 5th Gb 736 Major 4th F# 704 Minor 4th F 672 Major 3rd E 640 Minor 3rd D# 608 Major 2nd D 576 Minor 2nd C# 544 Octave C"" 512 Minor 8th Cb 480 Major 7th B 464 Minor 7th Bb 448 Dim. 7th A# 432 Major 6th A 416 Minor 6th G# 400 Major 5th G 384 Minor 5th Gb 368 Major 4th F# 352 Minor 4th F 336 Major 3rd E 320 Minor 3rd D# 304 Major 2nd D 288 Minor 2nd C# 272 Octave C' 256 Minor 8th Cb 240 Major 7th B 232 Minor 7th Bb 224 Dim. 7th A# 216 Major 6th A 208 Minor 6th G# 200 Major 5th G 192 Minor 5th Gb 184 Major 4th F# 176 Minor 4th F 168 Major 3rd E 160 Minor 3rd D# 152 Major 2nd D 144 Minor 2nd C# 136 Octave C 128 Minor 8th Cb 120 Major 7th B 116 Minor 7th Bb 112 Dim. 7th A# 108 Major 6th A 104 Minor 6th G# 100 Major 5th G 96 Minor 5th Gb 92 Major 4th F# 88 Minor 4th F 84 Major 3rd E 80 Minor 3rd D# 76 Major 2nd D 72 Minor 2nd C# 68 Octave C' 64 Minor 8th Cb 60 Major 7th B 58 Minor 7th Bb 56 Dim. 7th A# 54 Major 6th A 52 Minor 6th G# 50 Major 5th G 48 Minor 5th Gb 46 Major 4th F# 44 Minor 4th F 42 Major 3rd E 40 Minor 3rd D# 38 Major 2nd D 36 Minor 2nd C# 34 Unison C 32

2005, 01/04: This scale was initially called "The Dale Scale" at that time for lack of a better name. That name was changed to "Scale of Infinite Ninths" some time in 2003.